Fig-4: Temperature distribution during filling process of molten metal at different time

다이캐스팅 시뮬레이션: 자동차 스티어링 쉘의 수축 결함 제거 및 최적화

이 기술 요약은 LI Jing, XU Teng-Gang, ZHU Jian-Jun이 저술하여 2017년 IJRET(International Journal of Research in Engineering and Technology)에 게재한 “SIMULATION ANALYSIS AND OPTIMIZATION OF DIE-CASTING FOR AUTOMOBILE STEERING SERVE SHELL” 논문을 기반으로 STI C&D 기술 전문가에 의해 분석 및 요약되었습니다.

키워드

  • Primary Keyword: 다이캐스팅 시뮬레이션
  • Secondary Keywords: 수축 다공성, 결함 최적화, 자동차 주조, 스티어링 서보 쉘, Anycasting, CAE 해석

Executive Summary

  • 도전 과제: 다이캐스팅으로 생산되는 알루미늄 자동차 스티어링 서보 쉘의 높은 수축 및 표면 다공성 결함으로 인해 제품 합격률이 저조했습니다.
  • 해결 방법: Anycasting 소프트웨어를 사용한 수치 시뮬레이션을 통해 기존 다이캐스팅 설계의 충전 및 응고 과정을 정밀하게 분석했습니다.
  • 핵심 돌파구: 시뮬레이션을 통해 두꺼운 부위에서 발생하는 고립된 용탕 영역이 수축의 근본 원인임을 확인했으며, 이 부위에 국소 냉각 시스템을 추가하여 결함을 획기적으로 감소시켰습니다.
  • 핵심 결론: CAE 기반의 최적화, 특히 냉각 채널 추가는 치명적인 수축 결함을 효과적으로 예측하고 제거하여 복잡한 다이캐스팅 부품의 수율을 극적으로 향상시킬 수 있습니다.

도전 과제: 이 연구가 CFD 전문가에게 중요한 이유

자동차 스티어링 서보 하우징은 터빈과 웜을 고정 및 보호하는 핵심 부품으로, 높은 강도와 내충격성이 요구됩니다. 그러나 실제 다이캐스팅 생산 과정에서 이 부품은 심각한 수축 및 표면 다공성 결함 문제에 직면했습니다. 이러한 결함은 제품의 기계적 특성을 저하시켜 최종 제품의 합격률을 낮추는 주된 원인이 되었습니다. 생산 수율을 높이고 제품 품질을 보장하기 위해서는 결함의 원인을 정확히 파악하고 이를 해결하기 위한 체계적인 공정 최적화가 시급한 상황이었습니다. 이는 금형 수정 횟수를 줄이고 개발 비용을 절감하는 데 필수적인 과제입니다.

접근 방식: 연구 방법론 분석

본 연구는 다이캐스팅 공정의 충전 및 응고 단계를 수치적으로 시뮬레이션하기 위해 Anycasting 소프트웨어를 활용했습니다. 연구의 신뢰성을 확보하기 위해 다음과 같은 구체적인 조건과 변수를 설정했습니다.

  • 소재: ADC12 알루미늄 합금 (액상선 온도: 580°C)
  • CAD 모델링: UG 소프트웨어를 사용하여 서보 쉘의 3D 모델을 설계하고 STL 파일 형식으로 변환했습니다.
  • 공정 파라미터:
    • 주조 환경 온도: 25°C
    • 금형 예열 온도: 200°C
    • 주입 온도: 680°C
    • 사출 속도: 300cm/s
  • 열전달 계수:
    • 주조-금형: 0.6 Cal/cm²S°C
    • 주조-표면: 0.05 Cal/cm²S°C
    • 금형-공기: 0.001 Cal/cm²S°C
  • 최적화 방안: 시뮬레이션 분석을 통해 결함 발생이 예측된 부위에 국소 냉각 장치(냉각수 채널)를 추가하여 금형의 냉각 효율을 개선했습니다.

돌파구: 주요 발견 및 데이터

결과 1: 기존 설계의 결함 – 시뮬레이션을 통해 밝혀진 수축 다공성의 근본 원인

초기 설계안에 대한 시뮬레이션 결과, 용탕 충전 과정 자체는 비교적 원활했으며 용탕 선단의 온도가 액상선 온도(580°C) 이상으로 유지되어 미충전이나 콜드셧과 같은 문제는 발생하지 않았습니다(Figure 4).

그러나 문제는 응고 과정에서 발생했습니다. Figure 5의 응고 과정 시뮬레이션에서 볼 수 있듯이, 주조품의 두꺼운 보강 부위는 다른 얇은 부위에 비해 냉각 속도가 느려 응고 마지막 단계(t=13.7411s)에서 두 개의 큰 고립된 용탕 영역(isolated liquid region)을 형성했습니다. 결정적으로, 이 고립된 용탕 영역이 완전히 응고되기 전에 게이트가 먼저 응고되어 버려 외부로부터의 용탕 보충(feeding)이 차단되었습니다. 이로 인해 최종 응고 시 부피 수축을 보상할 수 없게 되어 해당 부위에 심각한 수축 다공성 결함이 집중적으로 발생했습니다.

Fig-4: Temperature distribution during filling process of molten metal at different time
Fig-4: Temperature distribution during filling process of molten metal at different time
FLOW-3D CAST를 이용한 예시 알아보기

결과 2: 국소 냉각을 통한 해결 – 최적화된 설계로 결함 획기적 감소

시뮬레이션 분석을 바탕으로, 결함이 집중된 두꺼운 보강 부위의 금형에 냉각수 채널을 추가하는 최적화 방안을 적용했습니다. 최적화된 설계의 응고 시뮬레이션 결과(Figure 6), 게이트가 완전히 응고되었을 때 보강 부위에 남아있는 고립된 용탕 영역의 부피가 기존 설계에 비해 현저하게 감소한 것을 확인할 수 있었습니다. 이는 국소 냉각을 통해 해당 부위의 응고 속도를 높여 전체적인 응고 균형을 맞춘 결과입니다.

이러한 시뮬레이션 결과는 실제 생산을 통해 검증되었습니다. 개선된 설계를 적용하여 생산된 실제 주조품(Figure 7)은 표면에 눈에 띄는 결함이 없었습니다. 특히, 결함 부위의 단면을 광학 현미경으로 관찰한 결과(Figure 9), 기존 설계(b)에서 관찰된 큰 수축공 대신 개선된 설계(a)에서는 미세하고 분산된 수축만이 관찰되어, 수축 다공성 결함이 크게 개선되었음을 입증했습니다.

R&D 및 운영을 위한 실질적 시사점

  • 공정 엔지니어: 본 연구는 주조품의 두꺼운 부위에 국소 냉각 채널을 추가하여 냉각 속도를 높이고 합리적인 온도 구배를 형성하는 것이 수축 결함을 제거하거나 줄이는 데 매우 효과적임을 시사합니다.
  • 품질 관리팀: 논문의 Figure 9에 제시된 현미경 사진은 허용 가능한 수준의 미세 수축(개선안)과 불량으로 판정되는 큰 수축 다공성(기존안)을 명확히 비교하여 보여줍니다. 이는 유사 부품의 품질 검사 기준을 수립하는 데 유용한 시각적 근거를 제공할 수 있습니다.
  • 설계 엔지니어: 연구 결과는 부품의 두께 변화가 응고 과정에서 결함 형성에 얼마나 큰 영향을 미치는지를 명확히 보여줍니다. 따라서 설계 초기 단계부터 두꺼운 부위에 대한 금형 냉각 채널 설계를 고려하는 것이 응고 관련 결함을 예방하는 데 매우 중요한 요소임을 시사합니다.

논문 상세 정보

SIMULATION ANALYSIS AND OPTIMIZATION OF DIE-CASTING FOR AUTOMOBILE STEERING SERVE SHELL

1. 개요:

  • 제목: SIMULATION ANALYSIS AND OPTIMIZATION OF DIE-CASTING FOR AUTOMOBILE STEERING SERVE SHELL
  • 저자: LI Jing, XU Teng-Gang, ZHU Jian-Jun
  • 발행 연도: 2017
  • 게재 학술지/학회: IJRET: International Journal of Research in Engineering and Technology
  • 키워드: steering serve shell; die-casting; simulation analysis; defect optimization

2. 초록:

본 연구는 자동차 스티어링 밸브 쉘의 실제 주조 생산에서 발생하는 수축 및 표면 다공성 결함 문제에 초점을 맞추었다. 이러한 결함은 제품의 낮은 합격률을 야기할 수 있다. 다이캐스팅의 충전 및 응고 과정은 Anycasting 소프트웨어를 사용하여 수치적으로 시뮬레이션되었다. 시뮬레이션 결과를 바탕으로 문제의 원인을 분석하고 개선 방안을 제시하였다. 금형에 추가적인 냉각 시스템을 설치하는 방안을 통해 개선된 설계의 시뮬레이션을 수행한 결과, 볼록한 결합 부위의 기공이 사라지고 두꺼운 벽 영역의 고립 현상이 현저히 감소함을 확인했다. 개선된 공정은 실제 생산을 통해 검증되었으며, 시뮬레이션 결과는 생산 결과와 일치했고 제품의 수율은 명백히 증가했다.

3. 서론:

현대 과학 기술의 발전과 함께 다이캐스팅 기업들은 CAE를 활용하여 다이캐스팅 생산에 대한 시뮬레이션 분석 기술을 도입하기 시작했다. 이를 통해 주조품에 나타날 수 있는 결함의 위치를 예측하고, 결함 원인의 심층 분석 및 목표 최적화를 통해 주조 제품의 합격률을 높이고 시험 금형 수정 횟수를 줄일 수 있다. 본 논문은 Anycasting 소프트웨어를 사용하여 한 다이캐스팅 기업이 생산하는 자동차 스티어링 서보 쉘 주조품에 대한 시뮬레이션 분석을 수행하고, 발생 가능한 주조 결함 분포를 예측하며 그 원인을 분석하여 상응하는 개선 조치를 제안함으로써 CAE 다이캐스팅 생산 기업에 기술적 지원을 제공한다.

4. 연구 요약:

연구 주제의 배경:

자동차 스티어링 서보 하우징은 고정된 쉘 터빈과 웜을 보호하는 조립체의 중요 부품으로, 높은 강도와 내충격성이 요구된다. 이 부품의 다이캐스팅 생산 과정에서 수축 및 다공성 결함이 빈번하게 발생하여 제품 불량률이 높았다.

이전 연구 현황:

CAE 기술은 다이캐스팅 공정에서 결함을 예측하고 최적화하는 데 널리 사용되기 시작했다.

연구 목적:

Anycasting 시뮬레이션을 통해 자동차 스티어링 서보 쉘의 다이캐스팅 공정에서 발생하는 수축 결함의 원인을 분석하고, 금형 설계를 최적화하여 결함을 제거함으로써 제품의 수율을 향상시키는 것을 목표로 한다.

핵심 연구:

기존 다이캐스팅 공정의 충전 및 응고 과정을 시뮬레이션하여 결함 발생 위치와 원인을 파악했다. 이를 바탕으로 두꺼운 부위에 냉각수 채널을 추가하는 최적화 방안을 제안하고, 개선된 설계의 시뮬레이션 및 실제 생산 검증을 통해 그 효과를 입증했다.

5. 연구 방법론

연구 설계:

비교 연구 설계를 채택하여 기존 다이캐스팅 공정과 냉각 시스템을 추가한 최적화 공정의 시뮬레이션 결과를 비교 분석하고, 실제 생산품과 대조하여 검증했다.

데이터 수집 및 분석 방법:

  • 데이터 수집: UG 소프트웨어로 3D CAD 모델을 생성하고, Anycasting 소프트웨어를 통해 충전 및 응고 과정의 온도 분포, 응고 시간 등의 데이터를 수집했다. 실제 생산품의 결함 부위는 단면을 절단하여 광학 현미경으로 관찰했다.
  • 분석 방법: 시뮬레이션 결과를 통해 온도장과 응고 과정을 분석하여 고립된 용탕 영역의 형성을 확인하고, 이를 수축 결함의 원인으로 지목했다. 최적화 전후의 시뮬레이션 결과와 실제 제품의 현미경 사진을 비교하여 개선 효과를 정량적으로 평가했다.

연구 주제 및 범위:

본 연구는 ADC12 알루미늄 합금으로 제작되는 특정 자동차 스티어링 서보 쉘의 다이캐스팅 공정에 국한된다. 연구의 핵심은 수축 다공성 결함의 원인 분석과 냉각 시스템 추가를 통한 공정 최적화에 있다.

6. 주요 결과:

주요 결과:

  • 기존 공정의 시뮬레이션 결과, 충전 과정은 양호했으나 응고 과정에서 두꺼운 보강 부위에 고립된 용탕 영역이 형성되어 수축 다공성 결함이 발생하는 것으로 나타났다.
  • 금형의 두꺼운 부위에 냉각수 채널을 추가하는 최적화 방안을 적용한 결과, 시뮬레이션 상에서 고립된 용탕 영역의 부피가 현저히 감소했다.
  • 최적화된 공정을 실제 생산에 적용한 결과, 주조품의 수축 다공성 결함이 크게 개선되어 제품 수율이 눈에 띄게 증가했으며, 이는 시뮬레이션 결과와 일치했다.

Figure 목록:

  • Fig-1: 3D model of steering servo shell
  • Fig-2: Actual shrinkage and pores defects of steering servo shell
  • Fig-3: Finite element model of the original production plan
  • Fig-4: Temperature distribution during filling process of molten metal at different time
  • Fig-5: Solidification process of metal liquid at different time in the original scheme
  • Fig-6: solidification sequence of castings after optimization
  • Fig-7: Actual casting under the optimized scheme.
  • Fig-8 (a) Under the scheme
  • Fig.9 (b) Under the original scheme improved

7. 결론:

Anycasting 다이캐스팅 시뮬레이션 소프트웨어를 사용하여 스티어링 기어 케이스의 다이캐스팅 과정에서 발생하는 수축 및 다공성 결함의 원인을 분석하고, 냉각수 채널을 추가하여 금형 구조를 최적화했다. 다음과 같은 결론을 도출했다.

  1. 주조품의 두꺼운 벽 부위에 냉각수 채널을 추가하는 것은 주조품이 냉각 과정에서 합리적인 온도장을 얻는 데 도움이 되며, 고립된 액상 부피를 줄여 수축을 제거하거나 감소시킨다.
  2. 다이캐스팅 생산 디버깅 과정에서 CAE 기술은 주조 결함을 신속하고 효과적으로 예측하고 그 원인을 분석할 수 있어, 금형 구조를 수정하고 공정을 최적화하는 기초를 제공한다.
Fig-7: Actual casting under the optimized scheme.
Fig-7: Actual casting under the optimized scheme.

8. 참고 문헌:

  1. Huang Xiaofeng, XieRui, TianZaiyou, etal. Development status and Prospect of die casting technology [J]. New technology and new process, 2008 (7):50 – 55.
  2. Yang Liwei. Present situation and future development trend of casting CAE technology [J]. Emphasis on technology, 2015 (3): 62 – 66.
  3. Zhen Xiao Zhen, Li Zhi Li, Fu Hui, etal. Optimal design of ultrasonic cutter based on finite element model [J]. Piezoelectric and acoustooptic, 2015, 37 (6): 1083 – 1087.
  4. Chen Hongkai, Song Yunmei. Simulation of J finite element numerical form Chongqing Hechuan mill dangerous rock mass[J]. Journal of Chongqing Normal University (NATURAL SCIENCE EDITION), 2016 (1): 36 – 39.
  5. Niu Po, Yang Ling, Zhang Ting Ting, etal. Finite element analysis of rotary tiller used in micro tillage machines based on ANSYS Workbench. Journal of Southwestern University (NATURAL SCIENCE EDITION), 2015, 37 (12): 162 – 167.
  6. Li Dongze, GuoXiaonan, Yan Zhuo Cheng, etal. Abaqus based finite element analysis of PDMS [J]. Electronic components and materials, 2015 (11): 57 – 60.
  7. Siku, Chen Shenggui bell, Huanhuan. Finite element simulation of laser transmission welding of polycarbonate[J]. Numerical laser journal, 2015 (6): 104 – 107.
  8. Zhang Wenshan, Liu Shuqin. Design of drive motor of magnetic levitation artificial heart pump combined with magnetic circuit method and finite element method [J]. Electrical machinery and control applications, 2016, 43 (4): 71-76.
  9. Song Bo. Numerical simulation analysis of die casting of aluminum alloy wheel. [J]. Casting technology, 2014 (10): 2352-2354.
  10. Jiang Zheng, XueKemin. Numerical simulation analysis of aluminum alloy die casting technology [J]. Precision forming engineering, 2012 (2): 42 – 45.

전문가 Q&A: 주요 질문과 답변

Q1: Figure 4의 충전 시뮬레이션은 원활해 보이는데, 왜 공정 최적화가 필요했나요?

A1: 논문에 따르면 충전 과정 자체는 문제가 없었습니다. 용탕의 온도는 액상선 이상으로 유지되어 미충전과 같은 결함은 발생하지 않았습니다. 그러나 문제는 충전 이후의 ‘응고’ 단계에서 발생했습니다. Figure 5의 응고 해석에서 볼 수 있듯이, 결함은 충전이 완료된 후 냉각 과정에서 형성되었기 때문에 응고 과정에 대한 최적화가 필수적이었습니다.

Q2: 기존 설계에서 수축 결함을 유발한 구체적인 메커니즘은 무엇이었나요?

A2: Figure 5의 분석에 따르면, 두꺼운 보강 부위는 주변의 얇은 부위보다 냉각 속도가 느렸습니다. 이로 인해 응고 마지막 단계에서 큰 ‘고립된 용탕 영역’이 형성되었습니다. 이 영역이 응고되기 전에 용탕을 공급하는 게이트가 먼저 응고되어 버렸고, 결과적으로 부피 수축을 보상할 용탕 공급이 차단되어 내부 빈 공간, 즉 수축 다공성이 발생했습니다.

Q3: 냉각 시스템 추가가 구체적으로 어떻게 문제를 해결했나요?

A3: 추가된 냉각수 채널은 결함이 발생한 두꺼운 보강 부위의 냉각 속도를 의도적으로 높였습니다. 이로 인해 해당 부위의 응고가 빨라져 다른 부위와의 응고 시간 차이가 줄어들었습니다. 그 결과, Figure 6에서 보듯이 응고 마지막 단계에 형성되는 고립된 용탕 영역의 부피가 크게 감소하여 수축을 최소화할 수 있었습니다.

Q4: 시뮬레이션 결과가 실제 생산을 정확하게 반영한다고 얼마나 확신할 수 있나요?

A4: 본 연구는 시뮬레이션을 통해 도출된 최적화 설계를 실제 생산에 적용하여 그 결과를 검증했습니다. Figure 8과 9에서 볼 수 있듯이, 개선된 금형으로 생산된 실제 주조품은 기존 제품에 비해 수축 다공성 결함이 현저히 감소했습니다. 이처럼 “시뮬레이션 결과가 생산 결과와 일치했다”고 논문에서 명시하고 있어, 시뮬레이션의 신뢰성이 높다고 할 수 있습니다.

Q5: 이 연구에서 사용된 ADC12 알루미늄 합금 외에 다른 재료에도 이 최적화 방법이 유효할까요?

A5: 논문은 ADC12 합금에 초점을 맞추고 있지만, 결함 발생 메커니즘 자체는 재료의 고유 특성보다는 주조품의 기하학적 형상(두께 차이)과 열전달 조건에 기인합니다. 따라서 두꺼운 부위와 얇은 부위가 혼재된 다른 다이캐스팅 합금 부품에서도 국소 냉각을 통해 응고 과정을 제어하는 이 접근 방식은 수축 결함을 줄이는 데 유사하게 효과적일 가능성이 높습니다.

결론: 더 높은 품질과 생산성을 향한 길

자동차 부품의 복잡성이 증가함에 따라, 수축 다공성과 같은 다이캐스팅 결함은 생산 수율과 제품 신뢰성에 큰 걸림돌이 됩니다. 본 연구는 다이캐스팅 시뮬레이션이 어떻게 문제의 근본 원인을 정확히 진단하고, 데이터 기반의 해결책을 제시할 수 있는지를 명확하게 보여줍니다. 두꺼운 부위에 냉각 채널을 추가하는 간단한 최적화만으로도 치명적인 수축 결함을 효과적으로 제어하고, 이는 곧바로 생산성 향상으로 이어졌습니다.

STI C&D는 최신 산업 연구 결과를 적용하여 고객이 더 높은 생산성과 품질을 달성할 수 있도록 지원하는 데 전념하고 있습니다. 이 논문에서 논의된 과제가 귀사의 운영 목표와 일치한다면, 저희 엔지니어링 팀에 연락하여 이러한 원칙을 귀사의 부품에 어떻게 구현할 수 있는지 알아보십시오.

(주)에스티아이씨앤디에서는 고객이 수치해석을 직접 수행하고 싶지만 경험이 없거나, 시간이 없어서 용역을 통해 수치해석 결과를 얻고자 하는 경우 전문 엔지니어를 통해 CFD consulting services를 제공합니다. 귀하께서 당면하고 있는 연구프로젝트를 최소의 비용으로, 최적의 해결방안을 찾을 수 있도록 지원합니다.

  • 연락처 : 02-2026-0450
  • 이메일 : flow3d@stikorea.co.kr

저작권 정보

  • 이 콘텐츠는 “LI Jing” 외 저자의 논문 “SIMULATION ANALYSIS AND OPTIMIZATION OF DIE-CASTING FOR AUTOMOBILE STEERING SERVE SHELL”을 기반으로 한 요약 및 분석 자료입니다.
  • 출처: http://www.ijret.org

이 자료는 정보 제공 목적으로만 사용됩니다. 무단 상업적 사용을 금합니다. Copyright © 2025 STI C&D. All rights reserved.

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Fig.5 Simulated solute dissolution and homogenization in wheel spoke after solution treatment for t=900 s (a), t=4500 s (b), t=13500 s (c) and t=57600 s (d)

마그네슘 합금 주조의 기계적 물성 예측: 미세조직 시뮬레이션으로 품질과 생산성 극대화

이 기술 요약은 HAN Guomin, HAN Zhiqiang, HUO Liang, DUAN Junpeng, ZHU Xunming, LIU Baicheng이 저술하고 ACTA METALLURGICA SINICA (2012)에 게재된 학술 논문 “MICROSTRUCTURE SIMULATION AND MECHANICAL PROPERTY PREDICTION OF MAGNESIUM ALLOY CASTING CONSIDERING SOLID SOLUTION AND AGING PROCESS”를 기반으로 하며, STI C&D의 기술 전문가에 의해 분석 및 요약되었습니다.

키워드

  • Primary Keyword: 마그네슘 합금 주조
  • Secondary Keywords: 미세조직 시뮬레이션, 기계적 물성 예측, 자동차 휠, 고용화 처리, 시효 처리, 셀룰러 오토마타(CA) 모델

Executive Summary

  • 도전 과제: 마그네슘 합금 주조품의 최종 기계적 물성은 주조, 고용화, 시효 처리 과정에서 발생하는 복잡한 미세조직 변화에 크게 좌우되므로 이를 정확히 예측하기 어렵습니다.
  • 해결 방법: 연구팀은 미세조직 진화를 위한 수정된 셀룰러 오토마타(CA) 모델과 Mg-Al 합금의 기계적 물성 모델을 결합한 포괄적인 시뮬레이션 모델을 개발했습니다.
  • 핵심 돌파구: 개발된 모델은 마그네슘 합금 자동차 휠의 주조, 고용화 처리, 시효 처리 상태에서의 인장 강도와 항복 강도를 성공적으로 예측했으며, 이는 실제 측정값과 높은 일치도를 보였습니다.
  • 핵심 결론: 이 통합 시뮬레이션 접근법은 공정 변수에 기반하여 기계적 물성을 정확하게 예측할 수 있게 하여, 부품 성능 향상을 위한 주조 및 열처리 공정 최적화를 가능하게 합니다.

도전 과제: 이 연구가 CFD 전문가에게 중요한 이유

주조 공정에서 공정 변수는 주조품의 미세조직을 결정하고, 이는 최종 기계적 물성에 직접적인 영향을 미칩니다. 특히 자동차 휠과 같이 고성능이 요구되는 마그네슘 합금 부품의 경우, 주조 후 고용화 및 시효 처리와 같은 열처리를 통해 기계적 특성을 제어합니다.

기존에는 최적의 공정 조건을 찾기 위해 수많은 실험에 의존해야 했습니다. 이는 시간과 비용이 많이 소요될 뿐만 아니라, 공정-조직-물성 간의 관계를 경험적으로만 파악할 수 있다는 한계가 있었습니다. 따라서 주조부터 최종 열처리에 이르는 전 과정에서 미세조직의 변화를 시뮬레이션하고, 이를 바탕으로 기계적 물성을 정량적으로 예측할 수 있는 통합 모델의 개발은 업계의 오랜 과제였습니다. 이러한 모델은 제품 설계를 최적화하고 공정 개선을 지도하여 품질과 생산성을 동시에 향상시키는 데 필수적입니다.

Fig.3 Wheel casting temperature measurement points and detected positions
Fig.3 Wheel casting temperature measurement points and detected positions

접근 방식: 연구 방법론 분석

본 연구에서는 마그네슘 합금 주조품의 미세조직 진화와 기계적 물성을 예측하기 위해 통합된 모델링 접근법을 채택했습니다.

1. 미세조직 진화 모델: 연구팀은 기존의 셀룰러 오토마타(CA) 모델을 개선하여 주조, 고용화 처리, 시효 처리 전 과정에 걸친 미세조직 변화를 모사했습니다. – 주조(응고) 과정: 비평형 응고 조건을 고려하여, 액상의 용질 농도가 공정점에 도달하면 공정 조직이 형성되는 과정을 모델링했습니다. 이는 실제 주조 환경과 유사한 미세조직 예측을 가능하게 합니다. – 고용화 처리 과정: 주조 상태에서 형성된 공정 조직(β-Mg17Al12 상)이 고용체(α-Mg) 속으로 용해되고, 기지 내 용질 원소가 균일하게 확산되는 과정을 시뮬레이션했습니다. – 시효 처리 과정: 고용화 처리 후 과포화된 고용체에서 석출상(β’-Mg17Al12)이 핵 생성, 성장, 조대화되는 과정을 고전적인 석출 이론을 기반으로 한 해석적 모델을 통해 계산했습니다.

2. 기계적 물성 모델: 계산된 미세조직 특성(결정립 크기, 용질 농도, 석출물의 크기 및 분포 등)을 바탕으로 Mg-Al 합금의 기계적 물성을 예측하는 모델을 구축했습니다. 이 모델은 다음과 같은 다양한 강화 기구를 종합적으로 고려합니다. – 고유 격자 마찰력 – 고용 강화 (용질 원자에 의한 강화) – 결정립계 강화 (Hall-Petch 관계식) – 석출 강화 (Orowan 메커니즘)

이 두 모델을 연계하여 특정 공정 조건 하에서 마그네슘 합금 자동차 휠의 주요 부위별 미세조직과 최종 기계적 물성을 예측했습니다.

핵심 돌파구: 주요 발견 및 데이터

연구팀은 개발된 모델을 실제 마그네슘 합금 자동차 휠에 적용하여 시뮬레이션 예측 결과와 실험 측정값을 비교 검증했습니다.

발견 1: 미세조직 진화 과정의 정확한 모사

모델은 주조 및 고용화 처리 과정에서 나타나는 미세조직의 변화를 매우 정확하게 예측했습니다. – 주조 상태: 그림 4는 시뮬레이션으로 예측된 주조 미세조직(a)과 실제 금속 조직 사진(b)을 비교한 것입니다. 수지상정 사이의 공간에 공정 조직(붉은색 부분)이 형성된 모습이 실제와 매우 유사함을 확인할 수 있습니다. – 고용화 처리 상태: 그림 6은 고용화 처리 후의 결정립 조직을 보여줍니다. 시뮬레이션 결과(a)는 실제 조직(b)과 유사한 결정립 크기와 형태를 나타내어, 모델이 고용화 과정에서 일어나는 공정상의 용해 및 균일화 과정을 효과적으로 모사했음을 입증합니다.

발견 2: 신뢰성 있는 기계적 물성 예측

시뮬레이션을 통해 예측된 기계적 물성은 실제 부품에서 측정한 값과 높은 일치도를 보였습니다. – 인장 강도 및 항복 강도: 표 2와 그림 7은 자동차 휠의 림(Rim), 플랜지(Flange), 스포크(Spoke) 부위에서 측정한 인장 강도(σu)와 항복 강도(σy)를 예측값과 비교한 결과입니다. – 구체적 데이터: 예를 들어, 시효 처리(Aging treatment) 상태의 스포크 부위에서 예측된 인장 강도는 228 MPa로, 실제 측정된 평균값 231 MPa와 거의 일치했습니다. 주조(As-Cast) 및 고용화 처리(Solution treatment) 상태의 항복 강도 예측값 또한 측정값과 매우 근사한 결과를 보였습니다. 시효 처리 상태의 항복 강도는 다소 차이를 보였으나, 이는 석출물 강화 모델의 단순화에 기인한 것으로 분석되었습니다. 전반적으로, 인장 강도 예측은 모든 조건에서 매우 정확했습니다.

Fig.5 Simulated solute dissolution and homogenization in wheel spoke after solution treatment for t=900 s (a), t=4500 s (b), t=13500 s (c) and t=57600 s (d)
Fig.5 Simulated solute dissolution and homogenization in wheel spoke after solution treatment for t=900 s (a), t=4500 s (b), t=13500 s (c) and t=57600 s (d)

R&D 및 운영을 위한 실질적 시사점

본 연구 결과는 마그네슘 합금 부품의 개발 및 생산 현장에 다음과 같은 실질적인 가이드를 제공합니다.

  • 공정 엔지니어: 이 연구는 열처리 온도 및 시간과 같은 공정 변수가 미세조직(그림 5) 및 최종 기계적 물성에 미치는 영향을 정량적으로 예측할 수 있음을 보여줍니다. 이를 통해 수많은 시행착오 없이 최적의 열처리 사이클을 설계하여 생산 효율을 높이고 원하는 기계적 특성을 확보할 수 있습니다.
  • 품질 관리팀: 시뮬레이션 모델은 휠의 림, 플랜지, 스포크 등 복잡한 형상의 부위별 물성 편차(그림 7)를 예측할 수 있습니다. 이는 품질 관리팀이 취약 부위를 사전에 파악하고 물성 저하의 근본 원인을 분석하여 품질 검사 기준을 강화하는 데 활용될 수 있습니다.
  • 설계 엔지니어: 주조 및 후속 열처리 공정이 부품의 국부적인 기계적 물성에 미치는 영향을 이해함으로써, 설계 엔지니어는 초기 설계 단계에서부터 부품의 성능 변화를 고려한 최적 설계를 수행할 수 있습니다. 이는 제품의 신뢰성과 내구성을 향상시키는 데 기여합니다.

논문 상세 정보

考虑固溶及时效处理的镁合金铸件微观组织模拟及力学性能预测 (MICROSTRUCTURE SIMULATION AND MECHANICAL PROPERTY PREDICTION OF MAGNESIUM ALLOY CASTING CONSIDERING SOLID SOLUTION AND AGING PROCESS)

1. 개요:

  • 제목: 考虑固溶及时效处理的镁合金铸件微观组织模拟及力学性能预测 (MICROSTRUCTURE SIMULATION AND MECHANICAL PROPERTY PREDICTION OF MAGNESIUM ALLOY CASTING CONSIDERING SOLID SOLUTION AND AGING PROCESS)
  • 저자: HAN Guomin, HAN Zhiqiang, HUO Liang, DUAN Junpeng, ZHU Xunming, LIU Baicheng
  • 발행 연도: 2012
  • 학술지/학회: 金属学报 (ACTA METALLURGICA SINICA), Vol. 48, No. 3
  • 키워드: 镁合金 (magnesium alloy), 微观组织演化模型 (microstructure evolution model), 力学性能模型 (mechanical property model), 汽车轮毂 (automobile wheel casting)

2. 초록:

수정된 셀룰러 오토마타(CA) 모델을 기반으로 주조, 고용화 처리, 시효 처리 과정에서의 미세조직 진화를 시뮬레이션하는 마그네슘 합금 주조의 미세조직 모델을 수립했다. Mg-Al 합금의 2차상 석출 및 강화 메커니즘을 고려한 기계적 물성 모델을 개발했다. 수립된 모델을 마그네슘 합금 자동차 휠 주조품의 미세조직 진화 시뮬레이션 및 기계적 물성 예측에 적용했다. 결과적으로 예측된 인장 강도는 평균 측정값과 잘 일치했으며, 예측된 항복 강도는 주조 및 고용화 처리 상태에서 평균 측정값과 잘 일치했다.

3. 서론:

주조품 생산 과정의 공정 변수는 미세조직에 영향을 미치고, 이는 다시 기계적 물성에 큰 영향을 준다. 주조 공학 분야에서는 주조 공정-미세조직-물성 간의 정량적 관계를 수립하는 것이 중요한 연구 주제이다. 전통적인 방법은 대량의 실험을 통해 공정이 조직과 물성에 미치는 영향을 파악하는 것이나, 이는 경험적 묘사에 그치는 경우가 많다. 컴퓨터 시뮬레이션을 통해 공정 변수가 미세조직과 기계적 물성에 미치는 영향을 예측하고 제품 설계 및 공정을 최적화하는 것이 최근 주목받고 있다. 본 연구는 기존의 미세조직 시뮬레이션 연구를 확장하여, 주조뿐만 아니라 고용화 및 시효 처리 과정을 모두 고려한 통합 미세조직 진화 모델 및 기계적 물성 예측 모델을 개발하고, 이를 자동차 휠에 적용하여 유효성을 검증하고자 한다.

4. 연구 요약:

연구 주제의 배경:

마그네슘 합금은 경량화 소재로 주목받고 있으나, 그 기계적 물성은 주조 및 열처리 공정에 따라 크게 변한다. 따라서 공정 제어를 통해 원하는 물성을 확보하는 것이 중요하다.

이전 연구 현황:

이전 연구들은 주로 마그네슘 합금의 응고 과정 중 수지상정 형상 모사에 집중했으나, 계산량이 많고 고용화 및 시효 처리와 같은 후속 열처리 과정을 고려하지 않아 실제 주조품의 최종 물성을 예측하는 데 한계가 있었다.

연구 목적:

주조, 고용화 처리, 시효 처리를 포함하는 마그네슘 합금 주조품의 전체 생산 공정에 대한 미세조직 진화 모델과 기계적 물성 예측 모델을 개발하여, 공정 최적화 및 제품 설계에 기여하고자 한다.

핵심 연구:

  1. 수정된 셀룰러 오토마타(CA) 모델을 기반으로 주조-고용화-시효 전 과정의 미세조직 진화 모델 수립.
  2. Mg-Al 합금의 강화 기구(고용 강화, 결정립계 강화, 석출 강화 등)를 고려한 기계적 물성 모델 개발.
  3. 개발된 모델을 실제 마그네슘 합금 자동차 휠에 적용하여 주요 부위의 미세조직과 기계적 물성을 예측하고 실험 결과와 비교 검증.

5. 연구 방법론

연구 설계:

컴퓨터 시뮬레이션과 실험적 검증을 결합한 연구를 설계했다. 먼저, 이론적 모델을 구축하고 이를 수치 해석 프로그램으로 구현했다. 그 후, 실제 자동차 휠 주조품을 제작하여 특정 위치에서 시편을 채취하고, 금속 조직 관찰 및 기계적 물성 시험을 통해 시뮬레이션 결과를 검증했다.

데이터 수집 및 분석 방법:

  • 시뮬레이션: 주조 공정 중 온도 변화 데이터는 주형 내에 설치된 열전대를 통해 측정된 값을 입력 데이터로 사용했다. 미세조직 진화는 CA 모델로, 기계적 물성은 개발된 물성 모델로 계산했다.
  • 실험: 제작된 자동차 휠의 림, 플랜지, 스포크 부위에서 시편을 채취하여 광학 현미경으로 미세조직을 관찰하고, 만능시험기를 사용하여 인장 강도와 항복 강도를 측정했다.

연구 주제 및 범위:

본 연구는 Mg-Al 계열 AZ91 마그네슘 합금을 대상으로 하며, 중력 주조로 생산된 자동차 휠을 연구 사례로 한정했다. 주조, 고용화 처리, 시효 처리 상태에서의 미세조직과 기계적 물성(항복 강도, 인장 강도) 예측에 초점을 맞추었다.

6. 주요 결과:

주요 결과:

  • 개발된 미세조직 진화 모델은 주조, 고용화, 시효 처리 과정에서 나타나는 미세조직 변화를 성공적으로 예측했다.
  • 시뮬레이션을 통해 예측된 인장 강도 값은 자동차 휠의 모든 부위와 모든 처리 조건에서 실제 측정된 평균값과 매우 잘 일치했다.
  • 주조 및 고용화 처리 상태에서의 항복 강도 예측값은 실제 측정값과 잘 일치했으나, 시효 처리 상태에서는 약간의 오차를 보였다. 이는 석출 강화 모델의 단순화에 기인한 것으로 판단된다.
  • 본 연구에서 개발된 통합 모델은 마그네슘 합금 주조품의 기계적 물성을 공정 변수로부터 신뢰성 있게 예측할 수 있는 유용한 도구임을 입증했다.

그림 목록:

  • 图1 连续析出的 3′-Mg17A112 相几何模型示意图
  • 图2 镁合金汽车轮毂铸件几何模型
  • 图3 轮毂铸件测温点及检测位置示意图
  • 图4 模拟得到的轮毂铸件轮辐部位铸态微观组织同实际金相照片的对比
  • 图5 模拟得到的轮毂铸件轮辐部位固溶处理过程中共晶组织溶解及溶质的均匀化过程
  • 图6 镁合金轮毂铸件轮辐位置固溶处理后晶粒组织模拟结果与实际金相照片的对比
  • 图7 镁合金轮毂铸件轮辋、轮缘和轮辐部位不同状态下屈服强度和抗拉强度模拟预测结果和实际检测结果的对比

7. 결론:

  1. 공정 조직의 형성, 고용화 및 시효 처리 과정에서의 미세조직 변화를 고려하여 기존의 CA 모델을 확장한 마그네슘 합금 주조품 미세조직 진화 모델을 성공적으로 구축했다.
  2. Mg-Al 합금의 다양한 강화 기구를 바탕으로, 주조, 고용화, 시효 등 각기 다른 상태에서의 기계적 물성을 예측할 수 있는 모델을 개발했다.
  3. 개발된 모델을 자동차 휠에 적용한 결과, 주조 및 고용화 상태의 항복 강도와 모든 상태의 인장 강도 예측값이 실제 측정값과 잘 일치함을 확인했다. 이는 본 모델이 실제 산업 현장에서 마그네슘 합금 주조품의 물성을 예측하고 공정을 최적화하는 데 효과적으로 사용될 수 있음을 시사한다.

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전문가 Q&A: 주요 질문과 답변

Q1: 이 연구에서 복잡한 수지상정 형상 모델링 대신 단순화된 셀룰러 오토마타(CA) 모델을 사용한 이유는 무엇입니까?

A1: 본 연구의 목적은 실제 산업 현장에서 활용할 수 있는 효율적인 예측 모델을 개발하는 것이었습니다. 미세한 수지상정 형상을 정밀하게 모사하는 것은 계산량이 매우 커서, 자동차 휠과 같은 대형 주조품 전체에 적용하기 어렵습니다. 따라서 계산 효율을 높이고 공학적 적용 가능성을 확보하기 위해, 응고, 고용화, 시효 처리 전반에 걸친 거시적인 미세조직 변화(공정상 형성, 용해, 석출 등)에 초점을 맞춘 단순화된 CA 모델을 채택했습니다.

Q2: 논문에서 시효 처리 상태의 항복 강도 예측값과 측정값 사이에 약간의 차이가 발생했다고 언급했는데, 주된 원인은 무엇입니까?

A2: 그 차이는 주로 기계적 물성 모델, 특히 석출 강화 효과(Orowan 강화)를 계산하는 부분의 단순화 때문입니다. 실제 β’-Mg17Al12 석출상은 판상(plate-like) 형태를 가지지만, 계산 모델에서는 이를 등가 부피를 갖는 구형 입자로 가정하여 계산했습니다. 이러한 형태적 차이를 무시한 것이 Orowan 강화 효과를 실제보다 다소 다르게 예측하게 하여 항복 강도 예측에 오차를 유발한 것으로 분석됩니다.

Q3: 모델은 고용화 처리 중 공정 조직이 용해되는 현상을 어떻게 시뮬레이션합니까?

A3: 모델은 확산 기반 메커니즘을 통해 이 현상을 시뮬레이션합니다. 1.2절에 설명된 바와 같이, 고용화 처리 온도에서 공정 조직으로 정의된 셀(cell) 내부의 용질 원자가 주변의 α-Mg 기지로 확산됩니다. 이 확산 과정으로 인해 셀 내부의 용질 농도가 Mg 기지 내 최대 고용도 이하로 떨어지면, 해당 셀의 상태는 ‘공정상’에서 ‘초정상’으로 변경됩니다. 이 과정을 통해 거시적으로 공정 조직이 기지 속으로 용해되는 현상을 모사합니다.

Q4: 기계적 물성 모델에 포함된 주요 강화 기구에는 어떤 것들이 있습니까?

A4: 2.1절에 명시된 바와 같이, 모델은 Mg-Al 합금의 강도를 결정하는 여러 강화 기구를 종합적으로 고려합니다. 여기에는 (1)결정 격자의 고유 마찰력(σo), (2)Al 원자에 의한 고용 강화(σss), (3)결정립 미세화에 따른 결정립계 강화(σgs), (4)시효 처리 시 석출된 입자에 의한 석출 강화(Orowan 강화, σOr), (5)변형 불일치로 인한 강화(σp)가 포함됩니다. 각 상태(주조, 고용화, 시효)에 따라 활성화되는 강화 기구를 조합하여 최종 항복 강도를 계산합니다.

Q5: 결정립계 강화를 계산하는 Hall-Petch 관계식(식 12)에 사용된 파라미터(kgs)는 어떤 근거로 결정되었습니까?

A5: 논문에서는 해당 파라미터 값의 근거로 참고문헌 [25], [27], [30]을 인용하고 있습니다. 특히 Cáceres 등의 연구[27]와 Nussbaum 등의 연구[25]에서 Mg-Al 합금에 대한 광범위한 실험을 통해 결정립 크기와 강도 사이의 관계를 분석하여 Hall-Petch 관계식의 계수들을 실험적으로 결정했습니다. 본 연구에서는 이러한 선행 연구 결과를 바탕으로 신뢰성 있는 파라미터 값을 채택하여 모델의 정확도를 높였습니다.

결론: 더 높은 품질과 생산성을 향한 길

이 연구는 주조부터 최종 열처리에 이르는 복잡한 공정을 거치는 마그네슘 합금 주조 부품의 최종 기계적 물성을 신뢰성 있게 예측하는 통합 시뮬레이션 모델을 제시했다는 점에서 큰 의미가 있습니다. 미세조직의 진화 과정을 정밀하게 추적하고 이를 바탕으로 강도를 예측함으로써, 기업들은 더 이상 값비싼 시행착오에 의존하지 않고도 제조 공정을 최적화하고 제품 품질을 한 단계 끌어올릴 수 있습니다.

STI C&D는 최신 산업 연구 결과를 적용하여 고객이 더 높은 생산성과 품질을 달성할 수 있도록 지원하는 데 전념하고 있습니다. 이 백서에서 논의된 과제가 귀사의 운영 목표와 일치한다면, 저희 엔지니어링 팀에 연락하여 이러한 원칙을 귀사의 부품에 어떻게 구현할 수 있는지 논의해 보십시오.

(주)에스티아이씨앤디에서는 고객이 수치해석을 직접 수행하고 싶지만 경험이 없거나, 시간이 없어서 용역을 통해 수치해석 결과를 얻고자 하는 경우 전문 엔지니어를 통해 CFD consulting services를 제공합니다. 귀하께서 당면하고 있는 연구프로젝트를 최소의 비용으로, 최적의 해결방안을 찾을 수 있도록 지원합니다.

  • 연락처 : 02-2026-0450
  • 이메일 : flow3d@stikorea.co.kr

저작권 정보

  • 이 콘텐츠는 “HAN Guomin, HAN Zhiqiang, HUO Liang, DUAN Junpeng, ZHU Xunming, LIU Baicheng”이 저술한 논문 “MICROSTRUCTURE SIMULATION AND MECHANICAL PROPERTY PREDICTION OF MAGNESIUM ALLOY CASTING CONSIDERING SOLID SOLUTION AND AGING PROCESS”를 기반으로 한 요약 및 분석 자료입니다.
  • 출처: https://doi.org/10.3724/SP.J.1037.2011.00586

이 자료는 정보 제공 목적으로만 사용됩니다. 무단 상업적 사용을 금합니다. Copyright © 2025 STI C&D. All rights reserved.

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Fig.9 Control points of FFD set to T shape runner

실시간 CFD: GPU 가속 SPH와 형상 변형 기술로 다이캐스팅 런너 설계를 혁신하다

이 기술 요약은 精密工学会誌/Journal of the Japan Society for Precision Engineering에 발표된 徳永 仁史, 岡根 利光, 岡野 豊明의 논문 “高速な流れ解析手法を統合した流路設計のための設計インタフェース -湯流れ解析下におけるダイカスト湯道設計への適用一” (2016)을 기반으로, STI C&D의 기술 전문가에 의해 분석 및 요약되었습니다.

키워드

  • Primary Keyword: 다이캐스팅
  • Secondary Keywords: SPH (Smoothed Particle Hydrodynamics), GPU, CFD, 유동 해석, 런너 설계, 설계 인터페이스, 실시간 시뮬레이션

Executive Summary

  • The Challenge: 기존의 CFD 시뮬레이션은 계산 시간이 길어 반복적인 다이캐스팅 런너 설계에 비효율적이며, 이는 최적화되지 않은 설계와 품질 문제로 이어집니다.
  • The Method: 본 연구는 고속 GPU 가속 SPH(Smoothed Particle Hydrodynamics) 유동 해석 기법과 FFD(Free-Form Deformation) 형상 변형 기술을 통합했습니다.
  • The Key Breakthrough: 이 통합 기술을 통해 엔지니어는 시뮬레이션이 실행되는 동안 런너 형상을 실시간으로 수정하고 용탕 유동 거동에 미치는 영향을 즉시 확인할 수 있습니다.
  • The Bottom Line: 이 양방향 설계 접근법은 설계-평가 주기를 획기적으로 단축하여, 향상된 주조 품질을 위한 유로의 신속한 최적화를 가능하게 합니다.

The Challenge: Why This Research Matters for CFD Professionals

제품의 성능과 품질은 설계 단계의 결정에 크게 좌우됩니다. 이는 다이캐스팅과 같은 제조 공정의 설계(방안 검토)에서도 마찬가지입니다. 효율적인 설계 및 제조 사이클을 위해서는 프로토타입 제작과 같은 물리적 검증 이전에, 설계 단계에서 반복적으로 설계안을 검증하고 개선하는 과정이 필수적입니다.

이를 위해 다양한 공학 해석(CAE) 도구가 사용되어 왔지만, 기존의 유동 해석 기법 대부분은 계산 시간이 방대하여 설계안을 반복적으로 검증하고 개선하기에는 한계가 있었습니다. 특히 다이캐스팅 공정에서 런너와 게이트의 미세한 형상 변화가 제품 품질에 결정적인 영향을 미치지만, 긴 해석 시간 때문에 데이터 기반의 신속한 최적화보다는 설계자의 경험과 직관에 의존하는 경우가 많았습니다. 이러한 비효율성은 개발 기간을 지연시키고 잠재적인 품질 문제를 야기하는 핵심 원인이었습니다.

The Approach: Unpacking the Methodology

본 연구는 설계와 해석 프로세스를 통합하여 설계 효율을 극대화하는 새로운 인터페이스를 제안합니다. 이 방법론의 핵심은 고속 유동 해석 기술과 실시간 형상 변형 기술의 결합입니다.

  • 고속 유동 해석 (GPU-Accelerated SPH): 해석 기법으로는 입자 기반의 SPH(Smoothed Particle Hydrodynamics)를 채택했습니다. SPH는 자유 표면 유동 해석에 강점을 가지며, 형상이 변형될 때마다 복잡한 격자를 재생성할 필요가 없어 본 연구에 이상적입니다. 특히, 계산 과정을 GPU(Graphics Processing Unit)에서 병렬 처리하여 기존의 CPU(1코어) 계산 대비 120배 이상의 압도적인 속도 향상을 달성했습니다 (Table 1).
  • 실시간 형상 변형 (Free-Form Deformation, FFD): 설계자가 유로 형상을 직관적으로 수정할 수 있도록 FFD 기법을 도입했습니다. FFD는 수정하려는 형상 주위에 제어 격자점을 설정하고, 이 제어점들을 이동시켜 내부 형상을 부드럽게 변형시키는 방식입니다 (Fig. 3).
  • 통합 설계-해석 워크플로우: 본 연구의 핵심은 이 두 기술을 통합한 양방향 워크플로우입니다 (Fig. 2).
    1. 초기 런너 형상(STL 데이터)을 SPH 경계 입자로 변환합니다.
    2. 설계자는 FFD 제어점을 조작하여 런너 형상을 실시간으로 수정합니다.
    3. 시스템은 변경된 형상에 대해 즉시 고속 SPH 유동 해석을 수행합니다.
    4. 설계자는 용탕의 유동 변화를 시각적으로 확인하고, 만족스러운 결과를 얻을 때까지 형상 수정과 해석을 반복합니다.

이러한 접근법은 설계자의 아이디어가 즉각적으로 시뮬레이션에 반영되는 실시간 피드백 루프를 구축하여 설계 최적화 과정을 혁신적으로 단축시킵니다.

The Breakthrough: Key Findings & Data

본 연구는 제안된 기법을 다이캐스팅 런너 설계에 적용하여 그 유효성을 입증했습니다.

Finding 1: 복잡한 런너 유동 현상의 정확한 재현

새로운 해석 기법의 신뢰성을 검증하기 위해, 유동 특성이 잘 알려진 T형 런너와 V형 런너의 용탕 충전 거동을 시뮬레이션했습니다. 그 결과, 기존의 실험 및 상용 소프트웨어 해석 결과와 정성적으로 일치하는 결과를 얻었습니다. – T형 런너: 용탕이 런너를 완전히 채우기 전에 게이트에서 먼저 사출되고, 게이트를 통과한 용탕이 넓게 퍼지는 현상(사출각 β가 90°에 미치지 못함)이 정확하게 재현되었습니다 (Fig. 7). 이는 공기 혼입의 원인이 될 수 있습니다. – V형 런너: 용탕이 런너 형상을 따라 부드럽게 유동하며, 게이트에서 거의 90°에 가까운 안정적인 사출각(β)을 유지하는 모습이 확인되었습니다 (Fig. 8).

Finding 2: 실시간 설계 최적화 및 즉각적인 피드백

본 연구의 가장 핵심적인 성과는 실시간 형상 변경을 통한 설계 개선 가능성을 입증한 것입니다. 문제가 있는 T형 런너를 기반으로 시뮬레이션을 실행하는 도중에 FFD 제어점을 이용해 게이트의 위치를 상하로 이동시켰습니다.

  • 게이트 상향 이동: 게이트 위치를 6.36mm 위로 이동시키자, 사출각(β)이 기존 86.71°에서 90.00°로 개선되었습니다 (Table 2). 이는 용탕의 흐름을 안정시켜 T형 런너의 설계 결함을 실시간으로 해결했음을 의미합니다 (Fig. 10a).
  • 게이트 하향 이동: 반대로 게이트 위치를 5.45mm 아래로 이동시키자, 사출각(β)은 79.01°로 악화되어 유동이 더욱 불안정해지는 것을 즉각적으로 확인할 수 있었습니다 (Fig. 10b).

약 84만 개의 입자를 사용한 이 시뮬레이션은 NVIDIA GeForce GTX 980 GPU 환경에서 초당 약 85 프레임의 속도로 실행되어, 설계자가 지연 없이 상호작용하며 설계안을 탐색할 수 있음을 보여주었습니다.

Practical Implications for R&D and Operations

  • 공정 엔지니어: 이 연구는 런너 및 게이트 형상을 실시간으로 수정하며 공기 혼입을 최소화하고 금형 충전 패턴을 개선하는 등 공정 최적화를 신속하게 수행할 수 있는 가능성을 제시합니다.
  • 품질 관리팀: 논문의 [Table 2]와 [Figure 10] 데이터는 게이트 위치라는 특정 형상 변화가 사출각(β)이라는 핵심 품질 지표에 미치는 영향을 명확하게 보여주므로, 불량의 근본 원인을 파악하고 새로운 검사 기준을 수립하는 데 정보를 제공할 수 있습니다.
  • 설계 엔지니어: 이 결과는 설계자가 고가의 금형을 제작하기 전에 훨씬 더 넓은 설계 공간을 단시간에 탐색할 수 있음을 의미합니다. 단순한 T형이나 V형을 넘어, 유동에 최적화된 새로운 형태의 런너를 발견할 수 있는 강력한 도구가 될 수 있습니다.

Paper Details

高速な流れ解析手法を統合した流路設計のための設計インタフェース -湯流れ解析下におけるダイカスト湯道設計への適用一 (Design Interface for Flow Channel Design Integrated with Highly Efficient Fluid Flow Analysis Method – Application to Runner Design of Die-Casting during Casting Flow Simulation -)

1. Overview:

  • Title: 高速な流れ解析手法を統合した流路設計のための設計インタフェース -湯流れ解析下におけるダイカスト湯道設計への適用一
  • Author: 徳永 仁史 (Hitoshi TOKUNAGA), 岡根 利光 (Toshimitsu OKANE), 岡野 豊明 (Takaaki OKANO)
  • Year of publication: 2016
  • Journal/academic society of publication: 精密工学会誌/Journal of the Japan Society for Precision Engineering (Vol.82, No.1)
  • Keywords: flow channel design, fluid flow analysis, form deformation, smoothed particle hydrodynamics, GPGPU, die-casting, runner design, computer-aided design, computer-aided engineering

2. Abstract:

There are a number of useful fluid flow analysis methods that support designers to design flow channels of engineering products or to design flow channels used in manufacturing processes. It is important to derive better design by the iteration of evaluation and refinement of the design proposal so that the resulting product could achieve the required performance. However, most of the conventional methods are not so efficient that the evaluation and refinement cannot be executed enough. In order to make the evaluation part of the iteration process efficient, our previous paper presented a highly efficient fluid flow analysis method that adopted smoothed particle hydrodynamics (SPH) method, and that accelerated its calculation using graphics processing unit (GPU). Furthermore, in order to support designers more efficiently, this paper presents a new method for flow channel design based on form deformation techniques integrated with the analysis method, which enables the modeling of flow channel shape during simulating the flow behavior in it. In order to confirm the usefulness of the method, it is applied to an example of runner design of die-casting during casting flow simulation.

3. Introduction:

제품의 설계 단계에서의 결정은 최종 제품의 성능이나 품질에 큰 영향을 미친다. 제품의 제조 공정에서도 방안 검토라는 프로세스 설계 단계가 존재하며, 이는 제조의 성패와 제품의 품질을 결정한다. 효율적인 설계 및 제조 사이클을 실현하기 위해서는, 물리적 제조 이전에 설계 단계에서 반복적으로 설계안을 검증하고 개선하는 것이 중요하다. 이를 지원하기 위해 다양한 공학 해석 기법이 제안되었으나, 기존 기법 대부분은 계산 시간이 방대하여 반복적인 검증 및 개선을 지원하는 도구로는 부적합했다. 이러한 문제에 대해 저자들은 이전 연구에서 유로를 가진 제품 설계 및 주조/다이캐스팅 공정 방안 검토를 대상으로 고속의 간편한 유동 해석 기법을 제안했다. 이는 해석 프로세스를 고속화하여 효율화를 꾀하는 것이었다(Fig. 1b). 본 연구에서는 한 걸음 더 나아가 설계와 해석 프로세스의 통합을 통해(Fig. 1c) 추가적인 효율화를 실현하고자 한다. 구체적으로는, 저자들이 제안한 해석 기법에 해석 중 실행 가능한 형상 변형 기법을 도입하여 양방향 유로 설계 기법을 제안한다.

4. Summary of the study:

Background of the research topic:

제품 및 제조 공정의 설계 단계에서 반복적인 검증과 개선은 최종 품질을 위해 매우 중요하지만, 기존 공학 해석(CAE) 도구의 긴 계산 시간으로 인해 비효율적이다.

Status of previous research:

저자들은 이전 연구에서 SPH(Smoothed Particle Hydrodynamics) 입자법을 GPU를 이용해 고속화하는 유동 해석 기법을 제안하여, 설계-해석 반복 과정 중 해석 부분의 시간을 단축시키는 연구를 수행했다.

Purpose of the study:

본 연구의 목적은 이전 연구를 발전시켜, 고속 유동 해석 기법에 실시간 형상 변형 기법을 통합함으로써 설계와 해석 프로세스 자체를 통합하는 것이다. 이를 통해 설계자가 시뮬레이션 중에 직접 형상을 수정하며 유동 변화를 즉각적으로 확인할 수 있는 양방향(interactive) 설계 인터페이스를 제안하고, 그 유효성을 검증하고자 한다.

Core study:

제안된 양방향 설계 기법을 다이캐스팅 공정의 런너(탕도) 형상 설계 문제에 적용한다. T형 런너를 기반으로 시뮬레이션 중에 FFD(Free-Form Deformation)를 이용해 게이트 형상을 실시간으로 변형시키고, 이에 따른 용탕의 사출 거동(사출각 등) 변화를 분석하여 설계 개선 가능성을 평가한다.

5. Research Methodology

Research Design:

본 연구는 고속 유동 해석 기법과 형상 변형 기법을 통합한 새로운 설계 인터페이스를 개발하고, 이를 다이캐스팅 런너 설계라는 구체적인 사례에 적용하여 유효성을 검증하는 방식으로 설계되었다. 초기 형상(T형 런너)을 기준으로 실시간 변형을 가했을 때의 유동 거동 변화를 상용 해석 소프트웨어 결과와 비교하여 정성적 일치성을 확인한다.

Data Collection and Analysis Methods:

  • 유동 해석: 입자법의 일종인 SPH(Smoothed Particle Hydrodynamics)를 사용. 지배 방정식으로는 질량 보존, 운동량 보존, 열전도/열전달 방정식을 사용하며, 다이캐스팅 공정의 고압 환경을 고려한 상태 방정식과 반발력 모델을 적용.
  • 고속화: 모든 SPH 계산을 GPU(NVIDIA GeForce GTX 980) 상에서 CUDA 7.0을 이용해 병렬 처리.
  • 형상 변형: FFD(Free-Form Deformation) 기법을 사용하여 제어점 이동을 통해 경계 입자들의 위치와 법선 벡터를 실시간으로 재계산.
  • 사례 연구: 알루미늄 합금 ADC12를 용탕으로 사용하고, 직경 70mm의 슬리브 내에서 플런저를 1m/s 속도로 이동시켜 폭 20mm, 두께 2mm의 게이트를 통해 용탕을 사출하는 조건을 설정.

Research Topics and Scope:

연구의 범위는 GPU 가속 SPH 유동 시뮬레이션 환경 하에서 FFD를 이용한 실시간 형상 변형을 구현하고, 이를 다이캐스팅 런너 형상 설계에 적용하여 그 가능성을 탐색하는 데에 중점을 둔다. 공기 혼입이나 응고와 같은 복잡한 물리 현상은 고려하지 않으며, 정성적인 유동 경향을 신속하게 파악하는 것을 목표로 한다.

6. Key Results:

Key Results:

  • GPU를 이용한 SPH 계산은 CPU(1코어) 대비 120배 이상의 속도 향상을 보였다 (Table 1).
  • 제안된 기법은 T형 런너와 V형 런너의 특징적인 유동 거동(런너 내 충전 양상, 게이트 사출각 등)을 상용 소프트웨어 결과와 유사하게 재현했다 (Fig. 7, 8).
  • 시뮬레이션 중 T형 런너의 게이트 위치를 실시간으로 상향 이동(6.36mm)시키자, 사출각(β)이 86.71°에서 90.00°로 개선되는 것을 확인했다 (Table 2, Fig. 10).
  • 반대로 게이트 위치를 하향 이동(-5.45mm)시키자, 사출각(β)이 79.01°로 악화되는 것을 즉각적으로 확인했다 (Table 2, Fig. 10).
  • 약 84만 개 입자 모델에 대해 초당 약 85 프레임의 계산 및 렌더링 속도를 달성하여 원활한 양방향 조작이 가능함을 입증했다.
Fig.9 Control points of FFD set to T shape runner
Fig.9 Control points of FFD set to T shape runner

Figure List:

  • Fig.1 Basic idea of increase in efficiency of design/analysis iterative process
  • Fig.2 Outline of interactive design/analysis process proposed in this paper
  • Fig.3 Free-form deformation (FFD) applied to shape defined with particles
  • Fig.4 Die-casting process using die-casting machine
  • Fig.5 Evaluation of runner shape by injected molten metal behavior
  • Fig.6 Example design of runner and gates in a die-casting machine
  • Fig.7 Simulated behavior of molten metal injected through T shape runner
  • Fig.8 Simulated behavior of molten metal injected through V shape runner
  • Fig.9 Control points of FFD set to T shape runner
  • Fig.10 Simulated behavior in the process of form deformation by user

7. Conclusion:

본 연구에서는 그래픽스 디바이스(GPU)를 통해 고속화된 SPH법 유체 시뮬레이션 기법에 형상 변형 기법을 도입하고, 그 연계 기법을 제안함으로써 유동 해석 하에서의 양방향 유로 형상 변경에 기반한 유로 설계 기법을 제안했다. 이 기법을 다이캐스팅의 런너 형상 검토에 적용 가능함을 보임으로써, 본 기법의 유효성을 나타냈다. 향후, 해석 결과의 정량적 평가 기법, 더 큰 변형 조작에의 대응, 더 복잡한 문제에의 적용, 다른 제조 공정 설계 및 제품 설계에의 적용 등을 검토하고자 한다. 또한, 응고 등을 포함한 더 상세한 해석 기법과의 연계도 검토할 계획이다.

8. References:

  1. H. Tokunaga, T. Okane, and T. Okano: Application of GPU-Accelerated SPH Fluid Simulation to Casting Design, Proceedings of the 2012 Asian Conference on Design and Digital Engineering (ACDDE2012), 100042, (2012).
  2. 例えば、J. J. Monaghan: Simulating Free Surface Flows with SPH, Journal of Computational Physics, 110, (1994) 399.
  3. T. W. Sederberg and S. R. Parry: Free-Form Deformation of Solid Geometric Models, Proceedings of SIGGRAPH’86, 20, 4, (1986) 151.
  4. 三谷純:幾何制約を持つ形状のためのデザインインタフェース, 精密工学会誌, 79, 6, (2013) 477.
  5. 例えば、M. Müller, D. Charypar and M. Gross: Particle-Based Fluid Simulation for Interactive Applications, Proceedings of Eurographics/SIGGRAPH Symposium on Computer Animation, (2003).
  6. 三谷純,五十嵐健夫: 流体シ뮬レーションを統合した対話的な形状設計手法, 第16回インタラクティブシステムとソフトウェアに関するワークショップ (WISS2008), 日本ソフトウェア科学会研究会資料シリーズ, 58, (2008) 25.
  7. N. Umetani, K. Takayama, J. Mitani, T. Igarashi: A Responsive Finite Element Method to Aid Interactive Geometric Modeling, Computer Graphics and Applications, IEEE, 31, 5, (2010) 43.
  8. A. Ferrari, M. Dumbser, E. F. Toro, and A. Armanini: A New 3D Parallel SPH Scheme for Free Surface Flows, Computers & Fluids, 38, (2009) 1203.
  9. P. W. Cleary, J. Ha, M. Prakash, T. Nguyen: 3D SPH Flow Predictions and Validation for High Pressure Die Casting of Automotive Components, Applied Mathematical Modelling, 30, (2006) 1406.
  10. 西直美:誰でも分かる鋳物基礎講座,公益社団法人日本鋳造工学会関東支部, http://www.j-imono.com/column/daredemo/33.html 2015.4.7 アクセス.
  11. 神戸洋史,多胡博司,畠山武,鞘師守,中村孝夫: ダイカストにおけるゲートからの溶湯射出挙動の直接観察, 1998 日本ダイカスト会議論文集, JD98-33, (1998).
  12. 佐藤武志,砂川美穂、神戸洋史: ダイカストのゲートからの溶湯射出挙動の観察とシ뮬レーションとの比較、型技術, 30, 3, (2015) 38.
  13. AnyCasting, http://anycastsoftware.com/en/software/anycastingtm.php 2015.6.22 アクセス.

Expert Q&A: Your Top Questions Answered

Q1: 이 양방향 접근법을 위해 유한요소법(FEM)과 같은 전통적인 격자 기반 방식 대신 SPH를 선택한 이유는 무엇입니까?

A1: SPH는 격자(mesh)가 없는 입자 기반 방법론이기 때문입니다. FEM과 같은 격자 기반 방법은 형상이 변형될 때마다 복잡하고 시간이 많이 소요되는 격자 재생성(remeshing) 과정이 필요합니다. 이는 실시간 상호작용에 큰 걸림돌이 됩니다. SPH는 이러한 과정이 필요 없어 형상이 동적으로 변하는 환경에 매우 적합하며, 본 연구가 목표하는 양방향 설계 인터페이스 구현에 이상적인 선택이었습니다.

Q2: 논문에서 GPU를 사용하여 120배 이상의 속도 향상을 언급했는데, 이 성능은 입자 수에 따라 어떻게 변합니까?

A2: 논문의 [Table 1]에 따르면, 입자 수가 증가함에 따라 프레임당 계산 시간은 늘어나지만, CPU 대비 GPU의 속도 향상 비율(CPU/GPU)은 약 15만 개에서 79만 개의 입자 수 범위에서 120~130배 수준으로 일관되게 높게 유지됩니다. 이는 제안된 GPU 병렬화 기법이 다양한 문제 크기에 걸쳐 효과적으로 작동함을 시사합니다.

Q3: 다양한 형상 변형 기법 중 FFD(Free-Form Deformation)를 채택한 특별한 이유가 있습니까?

A3: 논문에 따르면, FFD는 형상 표면뿐만 아니라 그 주변 공간 전체의 변형을 다룰 수 있기 때문에 채택되었습니다. SPH에서는 경계면을 표현하는 입자들이 단순히 표면 위에만 있는 것이 아니라, 그 주변에 여러 층으로 배치될 수 있습니다. FFD는 이러한 공간적 변형을 자연스럽게 처리할 수 있는 가장 기본적인 기법 중 하나로, 입자 기반 모델링에 적합하다고 판단되었습니다.

Q4: 다이캐스팅의 고압 환경에서 입자들이 경계를 뚫고 나가는 문제없이 어떻게 안정적인 해석을 수행했습니까?

A4: 본 연구에서는 다이캐스팅의 고압 환경을 고려하여 수정된 상태 방정식(Eq. 7)과 반발력 모델(Eq. 8)을 사용했습니다. 이 식들은 최대 유속(Vmax)을 명시적으로 고려하여 압력과 반발력을 계산합니다. Vmax 값을 적절히 설정함으로써, 고압으로 인해 발생할 수 있는 계산 불안정성이나 입자의 경계 투과 현상을 효과적으로 방지할 수 있었습니다.

Q5: [Table 2]의 해석 결과를 보면, 제안된 기법과 기존 상용 소프트웨어의 사출각(β) 값에 차이가 있습니다. 사용자는 이 차이를 어떻게 해석해야 합니까?

A5: 논문의 고찰(Discussion) 부분에서 언급하듯이, 서로 다른 해석 기법들은 정량적인 결과에서 차이를 보이는 것이 일반적입니다. 본 연구 기법의 주된 목표는 유동 거동의 정성적 경향을 빠르고 정확하게 파악하는 것입니다. 결과적으로 게이트를 올리면 사출각이 개선되고 내리면 악화된다는 경향성은 두 방법에서 동일하게 나타났습니다. 따라서 이 도구는 설계 초기 단계에서 다양한 아이디어를 신속하게 탐색하고 경향을 파악하는 데 매우 유용하며, 최종적인 정량 검증은 실험이나 고정밀 시뮬레이션을 통해 보완할 수 있습니다.

Conclusion: Paving the Way for Higher Quality and Productivity

기존의 긴 해석 시간은 다이캐스팅 공정에서 최적의 런너 설계를 찾는 데 큰 장벽이었습니다. 본 연구는 GPU 가속 SPH 해석과 실시간 형상 변형 기술을 통합하여 이 문제를 해결하는 혁신적인 돌파구를 제시했습니다. 설계자가 시뮬레이션 중에 직접 형상을 수정하고 그 결과를 즉시 확인함으로써, 설계-평가 주기를 획기적으로 단축하고 데이터에 기반한 신속한 의사결정을 내릴 수 있게 되었습니다.

이러한 양방향 설계 환경은 다이캐스팅 부품의 품질을 향상시키고 개발 기간을 단축하는 데 기여할 강력한 잠재력을 가지고 있습니다.

“STI C&D에서는 고객이 더 높은 생산성과 품질을 달성할 수 있도록 최신 산업 연구를 적용하는 데 전념하고 있습니다. 이 논문에서 논의된 과제가 귀사의 운영 목표와 일치한다면, 저희 엔지니어링 팀에 연락하여 이러한 원칙을 귀사의 부품에 어떻게 구현할 수 있는지 논의해 보십시오.”

(주)에스티아이씨앤디에서는 고객이 수치해석을 직접 수행하고 싶지만 경험이 없거나, 시간이 없어서 용역을 통해 수치해석 결과를 얻고자 하는 경우 전문 엔지니어를 통해 CFD consulting services를 제공합니다. 귀하께서 당면하고 있는 연구프로젝트를 최소의 비용으로, 최적의 해결방안을 찾을 수 있도록 지원합니다.

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  • This content is a summary and analysis based on the paper “高速な流れ解析手法を統合した流路設計のための設計インタフェース -湯流れ解析下におけるダイカスト湯道設計への適用一” by “徳永 仁史, 岡根 利光, 岡野 豊明”.
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Fig. 1 Sample of aluminum alloy castings with residual resin defects.

소모성 패턴 주조(EPC) 공정의 숨은 결함: 용탕 유속이 알루미늄 주물 밀도에 미치는 영향 분석

이 기술 요약은 Sadatoshi Koroyasu가 작성하여 2022년 Materials Transactions에 게재한 논문 “Effect of Melt Velocity on Density of Aluminum Alloy Castings in Expendable Pattern Casting Process”를 기반으로 합니다. STI C&D의 기술 전문가들이 분석하고 요약했습니다.

키워드

  • Primary Keyword: 소모성 패턴 주조 공정 (Expendable Pattern Casting Process)
  • Secondary Keywords: 알루미늄 합금 주조, 주조 밀도, 용탕 유속, 잔류 수지 결함, 감압 주조, X-ray CT

Executive Summary

  • The Challenge: 소모성 패턴 주조(EPC) 공정에서 용탕 유속이 증가할수록 패턴 분해 과정에서 생성된 액상 수지가 용탕에 혼입되어, 최종 주물의 밀도를 저하시키고 기계적 특성에 악영향을 미치는 문제를 해결해야 합니다.
  • The Method: 알루미늄 합금(JIS AC2A)을 사용하여 평판 형상의 EPS 패턴을 상향 및 하향 주조 방식으로 주조했습니다. 용탕 유속, 주입 온도, 감압 조건을 변경하며 주물의 밀도를 측정하고 X-ray CT 촬영을 통해 내부 결함을 관찰했습니다.
  • The Key Breakthrough: 용탕 유속이 증가할수록 주물 밀도는 감소하는 경향을 보였으며, 이는 액상 수지의 혼입 증가 때문으로 분석됩니다. 특히 상향 주조 시 감압 조건을 적용하면 밀도가 향상되었으나, 고온·고속 조건에서는 ‘용탕 선행 유동’ 현상으로 인해 오히려 밀도가 감소하는 예외가 발견되었습니다.
  • The Bottom Line: EPC 공정에서 고품질의 알루미늄 주물을 생산하기 위해서는 용탕 유속, 주입 방식, 압력 조건을 정밀하게 제어하여 잔류 수지 결함을 최소화하는 것이 핵심이며, 이는 최종 제품의 신뢰성과 직결됩니다.

The Challenge: Why This Research Matters for CFD Professionals

소모성 패턴 주조(EPC) 공정은 복잡한 형상의 주물을 코어 없이 일체형으로 생산할 수 있어 자동차 엔진의 실린더 헤드와 같은 부품 제작에 널리 사용됩니다. 하지만 이 공정은 EPS(발포 폴리스티렌) 패턴이 용탕에 의해 열분해되면서 발생하는 가스와 액상 수지를 원활하게 배출해야 하는 기술적 과제를 안고 있습니다.

특히 알루미늄 합금과 같이 용융점이 낮은 금속의 경우, 패턴이 완전히 기화되지 않고 대부분 액화되어 용탕과 직접 접촉하며 충전이 이루어집니다. 이 과정에서 액상 수지가 용탕에 혼입되면 그림 1과 같은 잔류 수지 결함(residual resin defects)을 유발합니다. 이러한 결함은 주물의 기계적 특성과 기밀성에 치명적인 영향을 미치므로, 이를 정량적으로 평가하고 제어하는 기술이 매우 중요합니다. 기존에는 용탕 유속, 감압 조건, 주조 방안 등이 결함 발생에 영향을 미칠 것으로 예상되었으나, 이에 대한 체계적인 연구는 부족한 실정이었습니다. 본 연구는 이러한 산업 현장의 문제를 해결하기 위해 시작되었습니다.

Fig. 1 Sample of aluminum alloy castings with residual resin defects.
Fig. 1 Sample of aluminum alloy castings with residual resin defects.

The Approach: Unpacking the Methodology

본 연구에서는 EPC 공정의 핵심 변수들이 주물 밀도에 미치는 영향을 규명하기 위해 정밀하게 통제된 실험을 설계했습니다.

  • 주조 장치 및 패턴: 내경 200mm, 깊이 300mm의 강철 주형 플라스크를 사용했으며, 감압을 위한 흡입 포트를 갖추었습니다. 폭 70mm, 높이 200mm, 두께 10mm의 평판형 EPS 패턴을 사용하여 상향(bottom pouring) 및 하향(top pouring) 주조 클러스터를 조립했습니다(그림 2, 3 참조).
  • 용탕 유속 측정: 패턴 내부에 10, 55, 100, 145, 190mm 지점에 텅스텐 와이어로 제작된 접촉 센서를 삽입하여 용탕의 도달 시간을 측정하고, 이를 통해 평균 용탕 유속을 계산했습니다.
  • 핵심 변수:
    • 용탕 유속: 투과성이 다른 3종류의 상용 코팅제(A, B, C)와 코팅 두께(0.5mm ~ 2.5mm)를 조절하여 약 10mm/s에서 100mm/s 범위의 유속을 구현했습니다.
    • 주입 온도: 약 973K와 1073K 두 가지 조건으로 설정했습니다.
    • 압력 조건: 대기압(비감압) 조건과 13.3kPa의 감압 조건을 적용했습니다.
    • 주조 방식: 상향 주조와 하향 주조 방식을 비교했습니다.
  • 결함 평가: 주조된 알루미늄 합금(JIS AC2A) 전체의 밀도를 아르키메데스법으로 측정하여 결함을 정량적으로 평가했습니다. 일부 시편은 X-ray CT(Computed Tomography)를 사용하여 내부 결함의 형상과 분포를 직접 관찰했습니다.

The Breakthrough: Key Findings & Data

Finding 1: 용탕 유속 증가는 주물 밀도 저하의 직접적인 원인

실험 결과, 상향 및 하향 주조 방식 모두에서 용탕 유속이 증가할수록 주물의 밀도가 감소하는 뚜렷한 경향이 나타났습니다.

그림 5(상향 주조, 비감압)와 그림 6(하향 주조, 비감압)에서 볼 수 있듯이, 용탕 유속(u)이 10mm/s 근처에서 80mm/s 이상으로 증가함에 따라 주물 밀도(ρ)는 약 2.76 x 10³ kg/m³에서 2.72 x 10³ kg/m³ 이하로 점차 감소했습니다. 이는 용탕 유속이 빠를수록 코팅 벽면에 존재하는 액상 수지가 용탕 내부로 혼입될 가능성이 커지기 때문으로 해석됩니다. 즉, 빠른 유속은 수지가 코팅층을 통해 배출될 시간을 주지 않고 용탕 흐름에 휩쓸리게 만들어 내부 결함을 형성하는 것입니다.

Fig. 7 Discharge mechanism of liquid resin.
Fig. 7 Discharge mechanism of liquid resin.

Finding 2: 감압 및 주조 방식이 결함 저감에 미치는 영향과 그 한계

감압 조건과 주조 방식은 주물 밀도에 상당한 영향을 미쳤으며, 특정 조건에서는 예상과 다른 결과가 관찰되었습니다.

  • 감압 효과: 그림 10(973K, 상향 주조)에서 감압 조건(●)은 비감압 조건(○)보다 전반적으로 높은 주물 밀도를 보였습니다. 이는 감압으로 인해 코팅층 내외부의 압력 차이가 커져 액상 수지의 배출이 촉진되었기 때문입니다.
  • 주조 방식 효과: 그림 8과 9를 보면, 동일한 온도와 유속 조건에서 하향 주조(●)가 상향 주조(○)보다 높은 밀도를 나타냈습니다. 이는 상향 주조 시 액상 수지의 부력과 용탕의 흐름 방향이 일치하여 수지 혼입이 심화되는 반면, 하향 주조에서는 두 방향이 반대여서 혼입이 억제되기 때문으로 분석됩니다.
  • 고온·고속 조건의 예외 현상: 흥미롭게도, 1073K의 고온에서 상향 주조를 할 때, 고속 영역에서는 감압 조건(●)의 밀도가 비감압 조건(○)보다 오히려 낮아지는 현상이 관찰되었습니다(그림 12, High velocity region). 이는 ‘용탕 선행 유동(forward flow of molten metal)’ 현상 때문으로, 감압 상태에서 용탕이 EPS 패턴과 코팅의 계면으로 먼저 흘러 들어가면서 EPS 패턴을 붕괴시키고 용탕 내로 혼입시켜 밀도를 저하시키는 것으로 추정됩니다. 그림 14는 이 현상이 발생한 주물의 단면을 보여줍니다.

Practical Implications for R&D and Operations

  • For Process Engineers: 본 연구는 용탕 유속이 잔류 수지 결함의 핵심 제어 인자임을 시사합니다. 코팅제의 종류와 두께를 조절하여 최적의 유속을 설정하고, 감압 시스템을 도입하면 코팅층을 통한 수지 배출을 촉진하여 주물 품질을 향상시킬 수 있습니다. 단, 고온·고속 주조 시에는 ‘용탕 선행 유동’ 현상을 주의해야 합니다.
  • For Quality Control Teams: 주물 밀도 측정은 내부 잔류 수지 결함을 평가하는 효과적인 비파괴 검사 방법이 될 수 있습니다. 그림 17의 X-ray CT 데이터는 밀도 저하가 실제 내부 기공(void)의 크기 및 분포와 직접적인 관련이 있음을 보여주므로, 밀도 값을 새로운 품질 관리 기준으로 설정하는 것을 고려할 수 있습니다.
  • For Design Engineers: 주입 방안 설계가 결함 형성에 큰 영향을 미칩니다. 액상 수지의 부력과 용탕 흐름을 고려할 때, 수지 혼입을 최소화하기 위해 하향 주조 방식이 상향 주조 방식보다 유리할 수 있습니다. 초기 설계 단계에서 이러한 유동 특성을 고려하는 것이 중요합니다.

Paper Details

Effect of Melt Velocity on Density of Aluminum Alloy Castings in Expendable Pattern Casting Process

1. Overview:

  • Title: Effect of Melt Velocity on Density of Aluminum Alloy Castings in Expendable Pattern Casting Process
  • Author: Sadatoshi Koroyasu
  • Year of publication: 2022
  • Journal/academic society of publication: Materials Transactions, Vol. 63, No. 4 (2022) pp. 629 to 635, ©2022 Japan Foundry Engineering Society
  • Keywords: expendable pattern casting process, aluminum alloy, casting density, melt velocity, casting design, reduced pressure, X-ray CT

2. Abstract:

The casting defects inside the aluminum alloy castings in the expendable pattern casting (EPC) process were evaluated by measuring the density of castings. The effect of melt velocity on the density of plate aluminum alloy castings was investigated experimentally. There was the tendency for the casting density to decrease with increasing melt velocity. This result seemed to be due to the increased entrainment of pattern decomposed liquid resin into the molten metal. In the case of bottom pouring, the casting density with reduced pressure is larger than that with non-reduced pressure. The result seems to be due to the increase in the discharge of the liquid resin at the coat surface through the coat layer. However, when the pouring temperature was high, in the high melt velocity region, there was the tendency for the casting density to be lower than that with non-reduced pressure. This phenomenon seemed to be caused by the forward flow of molten metal. In the case of top pouring, the casting density was higher than that in bottom pouring, and the effect of the reduced pressure was not significant. From the result of observing the castings by an X-ray computed tomography (CT) imaging, it was predicted that the density decrease of the castings might be due to voids by the residual resin defects.

3. Introduction:

The expendable pattern casting (EPC) process is very attractive for complex-shaped castings as it allows for near-net-shape products without parting lines or cores. It has been applied to parts like aluminum alloy cylinder heads. In the EPC process, molten metal replaces an expendable polystyrene (EPS) pattern, and the resulting decomposition gas and liquid resin are discharged through a coat layer into dry sand. For aluminum alloys, which have a lower melt temperature, the pattern mostly liquefies rather than gasifies. This can lead to the entrainment of liquid resin into the molten metal, causing internal residual resin defects, as shown in Fig. 1. These defects significantly affect mechanical properties and airtightness. Therefore, it is important to quantitatively estimate these defects. This study investigates the effects of melt velocity, reduced pressure, and casting design on residual resin defects by measuring the casting density and using X-ray CT imaging.

4. Summary of the study:

Background of the research topic:

The EPC process is advantageous for complex aluminum alloy castings but is prone to internal residual resin defects due to the liquefaction of the EPS pattern. These defects degrade the casting’s mechanical properties and airtightness.

Status of previous research:

While the generation of residual resin defects is known to be influenced by melt velocity, reduced pressure, and casting design, few recent studies have quantitatively investigated these relationships. Existing mold-filling analysis systems for the EPC process also rarely simulate liquid resin entrainment.

Purpose of the study:

This study aims to experimentally examine the effects of melt velocity, reduced pressure, and casting design (bottom vs. top pouring) on the residual resin defects in aluminum alloy plate castings. Casting density measurement is used as the primary method for evaluating these defects, supplemented by X-ray CT imaging.

Core study:

The core of the study involves casting aluminum alloy plates under various conditions of melt velocity, pouring temperature, pressure (atmospheric vs. reduced), and pouring design (bottom vs. top). The density of the resulting castings is measured and analyzed as a function of these variables to quantify the extent of internal defects.

5. Research Methodology

Research Design:

An experimental study was designed to investigate the causal relationship between process parameters (melt velocity, pressure, pouring design, temperature) and the outcome (casting density). A cylindrical steel molding flask with a suction port for pressure reduction was used.

Data Collection and Analysis Methods:

  • Casting: JIS AC2A (A319 equivalent) aluminum alloy was melted and cast into plate-shaped EPS patterns.
  • Variable Control: Melt velocity was controlled by using three different commercial coats with varying permeabilities and by adjusting the coat thickness. Pressure was controlled at atmospheric and a reduced pressure of 13.3 kPa. Pouring temperatures were set to 973 K and 1073 K.
  • Data Collection: Melt arrival times were measured using touch sensors to calculate average melt velocity. The density of the whole casting was measured using the Archimedean method. Select castings were observed using X-ray CT imaging to visualize internal defects.
  • Analysis: The collected casting density data was plotted against melt velocity for different experimental conditions to identify trends and relationships.

Research Topics and Scope:

The research focuses on plate-shaped aluminum alloy castings produced by the EPC process. The scope is limited to the experimental conditions defined: two pouring temperatures, two pressure levels, two casting designs (bottom and top pouring), and a melt velocity range of approximately 10 to 100 mm·s⁻¹.

6. Key Results:

Key Results:

  • There was a tendency for casting density to decrease with increasing melt velocity for both bottom and top pouring.
  • In bottom pouring, applying reduced pressure resulted in a higher casting density compared to non-reduced pressure, except at high pouring temperatures and high melt velocities.
  • At high pouring temperature (1073 K) and high melt velocity, the casting density under reduced pressure was conversely lower than that under non-reduced pressure for bottom pouring, likely due to the “forward flow of molten metal”.
  • Top pouring resulted in higher casting density than bottom pouring, and the effect of reduced pressure was not significant in this case.
  • X-ray CT imaging confirmed that the decrease in casting density was caused by voids resulting from residual resin defects.
Fig. 14 Casting view of final melt flow section for bottom pouring, pouring temperature of 1073 K, and reduced pressure condition.
Fig. 14 Casting view of final melt flow section for bottom pouring, pouring temperature of 1073 K, and reduced pressure condition.

Figure List:

  • Fig. 1 Sample of aluminum alloy castings with residual resin defects.
  • Fig. 2 Schematic diagram of casting apparatus for bottom pouring.
  • Fig. 3 Schematic diagram of casting apparatus for top pouring.
  • Fig. 4 Schematic diagram of casting apparatus for top pouring.
  • Fig. 5 Effects of melt velocity and pouring temperature on casting density for bottom pouring and non-reduced pressure.
  • Fig. 6 Effects of melt velocity and pouring temperature on casting density for top pouring and non-reduced pressure.
  • Fig. 7 Discharge mechanism of liquid resin.
  • Fig. 8 Effects of melt velocity and casting design on casting density for pouring temperature of 973 K and non-reduced pressure.
  • Fig. 9 Effects of melt velocity and casting design on casting density for pouring temperature of 1073 K and non-reduced pressure.
  • Fig. 10 Effects of melt velocity and reduced pressure on casting density for bottom pouring at pouring temperature of 973 K.
  • Fig. 11 Effects of melt velocity and reduced pressure on casting density for top pouring at pouring temperature of 973 K.
  • Fig. 12 Effects of melt velocity and reduced pressure on casting density for bottom pouring at pouring temperature of 1073 K.
  • Fig. 13 Effects of melt velocity and reduced pressure on casting density for top pouring at pouring temperature of 1073 K.
  • Fig. 14 Casting view of final melt flow section for bottom pouring, pouring temperature of 1073 K, and reduced pressure condition.
  • Fig. 15 Effects of melt velocity and casting design on casting density for pouring temperature of 973 K and reduced pressure.
  • Fig. 16 Effects of melt velocity and casting design on casting density for pouring temperature of 1073 K and reduced pressure.
  • Fig. 17 Sectional views of castings in Fig. 5 by X-ray CT imaging.

7. Conclusion:

The study successfully evaluated residual resin defects in EPC aluminum alloy castings by measuring their density. The key conclusions are: 1. Casting density decreased with increasing melt velocity, attributed to increased entrainment of decomposed liquid resin. 2. For bottom pouring, reduced pressure generally increased casting density by enhancing resin discharge. However, at high temperature and high velocity, a “forward flow” phenomenon caused a density decrease. 3. Top pouring yielded higher density than bottom pouring, and the effect of reduced pressure was not significant. 4. X-ray CT images confirmed that the density decrease was due to voids from residual resin defects.

8. References:

  1. A.T. Speda: Mod. Cast. (2001) 29.
  2. General Motors Asia Pacific Japan: SOKEIΖΑΙ (1994) 5.
  3. S. Koroyasu: J. JFS 81 (2009) 377–383.
  4. M.R. Barone and D.A. Caulk: Int. J. Heat Mass Transfer 48 (2005) 4132–4149.
  5. J. Zhu, I. Ohnaka, T. Ohmichi, K. Mineshita and Y. Yoshioka: J. JFS 72 (2000) 715–719.
  6. F. Sonnenberg: LOST FOAM Casting Made Simple, (American Foundry Society, Schaumburg, Illinois, 2008).
  7. for example, F. Kinoshita: J. JFS 86 (2014) 927–930.
  8. S. Koroyasu: J. JFS 88 (2016) 192–197.
  9. T. Maruyama, K. Katsuki and T. Kobayashi: J. JFS 78 (2006) 53–58.
  10. T. Maruyama, N. Goto and T. Kobayashi: J. JFS 81 (2009) 117–122.
  11. S. Kashiwai, J.D. Zhu and I. Ohnaka: J. JFS 73 (2001) 592–597.
  12. EPC Process Technical Meeting: Characteristic and Standardization of Coat for EPC Process, (Kansai Branch of JFS, 1996) 18.
  13. H. Taniyama and K. Tomita: J. JILM 34 (1984) 278–282.
  14. S. Koroyasu and M. Matsuda: J. JFS 76 (2004) 679–686.
  15. S. Koroyasu and A. Ikenaga: Mater. Trans. 53 (2012) 224–228.
  16. S. Koroyasu: J. JFS 91 (2019) 737–742.
  17. K. Lee, G. Cho, K. Choe, H. Jo, A. Ikenaga and S. Koroyasu: Mater. Trans. 47 (2006) 2798–2803.
  18. S. Katashima, S. Tashima, R.S. Yan, T. Kondo and K. Tsukumo: ΙΜΟΝΟ 62 (1990) 112–116.
  19. I. Ohnaka: Computer Den-netsu Gyoukokaiseki Nyumon, (Maruzen, Tokyo, 1990) p. 327.
  20. C.E. Lapple and C.B. Shepherd: Ind. Eng. Chem. 32 (1940) 605–617.

Expert Q&A: Your Top Questions Answered

Q1: 연구에서 투과성이 다른 세 종류의 코팅제를 사용한 이유는 무엇인가요?

A1: 용탕 유속을 효과적으로 제어하기 위해서입니다. 코팅층은 EPS 패턴 분해 시 발생하는 가스와 액상 수지의 배출 통로 역할을 하며, 코팅의 투과성은 이 배출 속도에 영향을 주어 결과적으로 용탕의 충전 속도, 즉 유속을 결정합니다. 투과성이 낮은 코팅(Coat A)부터 높은 코팅(Coat C)까지 사용하여 광범위한 용탕 유속(약 10~100 mm/s)을 구현하고, 유속이 주물 밀도에 미치는 영향을 체계적으로 분석할 수 있었습니다.

Q2: 주입 온도가 973K일 때보다 1073K로 높을 때 전반적으로 주물 밀도가 더 높은 경향을 보이는 이유는 무엇인가요?

A2: 이는 용탕 내로 혼입된 액상 수지의 부상(buoyancy)과 관련이 있습니다. 주입 온도가 높으면(1073K) 용탕의 응고 완료까지 걸리는 시간이 길어집니다. 이 시간 동안, 용탕보다 가벼운 액상 수지 방울이 부력에 의해 용탕 표면으로 상승하여 제거될 기회가 더 많아집니다. 반면, 온도가 낮으면(973K) 용탕이 빠르게 응고되어 수지가 미처 떠오르지 못하고 주물 내부에 갇히게 되어 밀도를 저하시키는 것입니다.

Q3: 그림 12에서, 고온(1073K) 및 고속 조건의 상향 주조 시 감압을 적용했을 때 오히려 밀도가 더 낮아지는 이유는 무엇인가요?

A3: 이 현상은 “용탕 선행 유동(forward flow of molten metal)” 때문으로 설명됩니다. 일반적인 상황에서는 용탕이 패턴을 녹이며 전진하지만, 고온·고속·감압 조건에서는 용탕이 EPS 패턴과 코팅 사이의 미세한 틈으로 먼저 빠르게 스며들어갑니다. 이 선행 유동이 EPS 패턴을 불안정하게 붕괴시키고, 그 조각들을 용탕 흐름에 직접 혼입시켜 더 심각한 내부 결함을 유발하고 결과적으로 주물 밀도를 저하시키는 것입니다.

Q4: 상향 주조(bottom pouring)가 하향 주조(top pouring)보다 주물 밀도가 낮은 경향을 보이는 이유는 무엇인가요?

A4: 액상 수지의 부력과 용탕의 흐름 방향 사이의 상호작용 때문입니다. 상향 주조에서는 용탕이 아래에서 위로 흐르는데, 액상 수지 역시 가볍기 때문에 부력에 의해 위로 떠오르려는 힘을 받습니다. 두 힘의 방향이 일치하여 수지가 용탕 흐름에 쉽게 휩쓸리고 혼입이 촉진됩니다. 반면, 하향 주조에서는 용탕이 위에서 아래로 흐르지만 수지의 부력은 여전히 위를 향하므로, 두 힘이 상쇄되어 수지 혼입이 상대적으로 억제되는 효과가 있습니다.

Q5: X-ray CT 분석(그림 17)을 통해 밀도 감소의 근본 원인이 무엇이라고 결론 내릴 수 있나요?

A5: X-ray CT 이미지는 밀도 감소가 잔류 수지 결함으로 인해 생성된 내부 기공(voids) 때문임을 명확히 보여줍니다. 그림 17(a)와 (b)를 비교하면, 밀도가 상대적으로 낮은 시편(a)에서 더 크고 명확한 기공이 관찰됩니다. 이는 측정된 거시적 밀도 차이가 주물 내부에 존재하는 수 mm 크기의 미세 기공들의 총 부피 차이에서 비롯됨을 의미하며, 밀도 측정이 내부 결함을 평가하는 유효한 지표임을 입증합니다.

Conclusion: Paving the Way for Higher Quality and Productivity

본 연구는 소모성 패턴 주조 공정(Expendable Pattern Casting Process)에서 용탕 유속, 압력, 주조 방식과 같은 핵심 공정 변수들이 어떻게 내부 결함 형성과 주물 밀도에 영향을 미치는지 실험적으로 규명했습니다. 용탕 유속이 증가할수록 수지 혼입이 증가하여 밀도가 감소하며, 감압 조건과 하향 주조 방식이 결함 저감에 유리하다는 사실을 데이터로 입증했습니다. 특히 고온·고속 조건에서 발생하는 ‘용탕 선행 유동’이라는 예외 현상을 발견한 것은 공정 최적화에 중요한 시사점을 제공합니다.

STI C&D는 최신 산업 연구 결과를 적용하여 고객이 더 높은 생산성과 품질을 달성할 수 있도록 지원하는 데 전념하고 있습니다. 이 논문에서 논의된 과제가 귀사의 운영 목표와 일치한다면, 저희 엔지니어링 팀에 연락하여 이러한 원칙을 귀사의 부품에 어떻게 구현할 수 있는지 논의해 보십시오.

(주)에스티아이씨앤디에서는 고객이 수치해석을 직접 수행하고 싶지만 경험이 없거나, 시간이 없어서 용역을 통해 수치해석 결과를 얻고자 하는 경우 전문 엔지니어를 통해 CFD consulting services를 제공합니다. 귀하께서 당면하고 있는 연구프로젝트를 최소의 비용으로, 최적의 해결방안을 찾을 수 있도록 지원합니다.

  • 연락처 : 02-2026-0450
  • 이메일 : flow3d@stikorea.co.kr

Copyright Information

  • This content is a summary and analysis based on the paper “Effect of Melt Velocity on Density of Aluminum Alloy Castings in Expendable Pattern Casting Process” by “Sadatoshi Koroyasu”.
  • Source: https://doi.org/10.2320/matertrans.F-M2021857

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FIG. 3. Histograms of the atomic volumes at 0K for the HEA equilibrated at 400K (red) and 800K (blue). The dashed lines indicate the ground state atomic volume of the single-element FCC structures. Atomic volumes are obtained from Voronoi tesselation38{41 of 20 snapshots at 0 K.

고엔트로피 합금(High-Entropy Alloy)의 방사선 저항성: 국부 편석과 방사선 효과의 상호작용 분석

이 기술 요약은 Leonie Koch 외 저자가 J. Appl. Phys. (2017)에 게재한 논문 “Local segregation versus irradiation effects in high-entropy alloys: Steady-state conditions in a driven system”을 기반으로 하며, STI C&D 기술 전문가에 의해 분석 및 요약되었습니다.

Keywords

  • Primary Keyword: 고엔트로피 합금(High-Entropy Alloy)
  • Secondary Keywords: 방사선 손상, 분자 동역학 시뮬레이션, 결함 형성, 상 안정성, CuNiCoFe 합금, 재료 모델링

Executive Summary

  • The Challenge: 고엔트로피 합금(HEA)은 우수한 방사선 저항성으로 차세대 원자력 및 항공우주 재료로 주목받지만, 저온에서 발생하는 성분 원소의 분리(편석) 경향과 이온 조사(irradiation) 효과 사이의 복잡한 상호작용은 명확히 규명되지 않았습니다.
  • The Method: 본 연구에서는 하이브리드 몬테카를로/분자 동역학(MC/MD) 시뮬레이션 기법을 사용하여 모델 합금인 CuNiCoFe 고엔트로피 합금이 이온 조사 환경에서 겪는 질서 전이와 결함 형성 과정을 분석했습니다.
  • The Key Breakthrough: 이온 조사는 고엔트로피 합금의 초기 상태(원소 무작위 분포 또는 부분적 편석)와 무관하게 일정한 결함 농도와 화학적 단범위 규칙(short-range order)을 갖는 정상 상태(steady state)로 시스템을 유도함을 발견했습니다.
  • The Bottom Line: 고엔트로피 합금의 뛰어난 방사선 저항성은 방사선에 의해 생성된 격자 결함이 구리(Cu) 원소의 편석을 위한 싱크(sink) 역할을 하여 대규모 상분리를 억제하고, 결함 생성과 소멸이 균형을 이루는 안정적인 미세구조를 형성하기 때문입니다.

The Challenge: Why This Research Matters for CFD Professionals

고엔트로피 합금(HEA)은 네 가지 이상의 주원소를 거의 동등한 비율로 혼합하여 만든 신소재로, 높은 강도와 내마모성 등 뛰어난 기계적 특성으로 주목받고 있습니다. 특히, 원자력 발전소나 우주 환경과 같은 극한 방사선 환경에 사용될 재료로서의 잠재력이 크게 평가되고 있습니다. 이는 HEA의 화학적 무질서도가 결함의 이동을 방해하고 열 분산을 지연시켜 방사선으로 인한 손상 축적을 억제할 수 있기 때문입니다.

하지만 HEA 내부에서는 복잡한 열역학적 힘들이 경쟁합니다. 고온에서는 엔트로피 효과로 원소들이 무작위로 섞인 단상 고용체를 안정적으로 형성하지만, 온도가 낮아지면 특정 원소들(예: 구리)이 뭉치는 편석 현상이 발생하여 다상(multiphase) 구조로 변할 수 있습니다. 여기에 이온 조사라는 외부 에너지가 가해지면, 시스템은 평형 상태에서 멀어지면서 상분리가 촉진될 수도, 혹은 오히려 무질서한 상태로 되돌아갈 수도 있습니다. 이처럼 구성 엔트로피, 혼합/분리 경향성, 그리고 방사선 유도 효과 간의 미묘한 상호작용을 이해하는 것은 HEA의 신뢰성을 확보하고 성능을 예측하는 데 매우 중요합니다. 본 연구는 바로 이 문제를 해결하기 위해 시작되었습니다.

FIG. 1. Snapshots of the CuNiCoFe alloy, equilibrated in the VC-SGC ensemble at 800K (left) and 400K (right). The ar- row highlights a clustering of copper atoms, indicating that phase separation occurs at lower temperatures.
FIG. 1. Snapshots of the CuNiCoFe alloy, equilibrated in the VC-SGC ensemble at 800K (left) and 400K (right). The arrow highlights a clustering of copper atoms, indicating that phase separation occurs at lower temperatures.

The Approach: Unpacking the Methodology

연구팀은 실제 실험의 한계를 극복하고 원자 단위의 동적 거동을 정밀하게 관찰하기 위해 분자 동역학(MD) 시뮬레이션 기법을 활용했습니다.

  • 모델 시스템: 저온에서 구리(Cu) 편석 경향을 보이는 4성분계 CuNiCoFe 합금을 모델 HEA로 선택했습니다. 원자 간 상호작용은 내장 원자법(EAM) 포텐셜을 사용하여 기술했습니다.
  • 초기 구조 생성: 두 가지 초기 상태의 샘플을 준비했습니다. 하나는 고온(800K)에서 원소들이 무작위로 분포된 고엔트로피 상태이고, 다른 하나는 저온(400K)에서 Cu 원자들이 부분적으로 클러스터를 형성한 다상(multiphase) 상태입니다. 이 구조들은 몬테카를로(MC)와 분자 동역학(MD) 단계를 교대로 수행하는 하이브리드 시뮬레이션을 통해 열역학적 평형 상태로 제작되었습니다.
  • 방사선 조사 시뮬레이션: 준비된 두 종류의 HEA 샘플과 비교를 위한 순수 니켈(Ni) 샘플에 대해 일련의 이온 조사 시뮬레이션을 수행했습니다. PARCAS MD 코드를 사용하여 5 keV 에너지의 반동(recoil) 이벤트를 총 1,500회 발생시켜 재료 내부에 누적되는 손상을 모사했습니다. 이는 장시간 중성자나 고에너지 이온에 노출되는 실제 환경과 유사합니다.
  • 분석: 시뮬레이션 결과로 얻어진 원자 배열로부터 단범위 규칙(SRO) 파라미터, 결함 농도, 원자 부피 등을 계산하여 이온 조사가 재료의 화학적 질서와 구조적 결함에 미치는 영향을 정량적으로 분석했습니다.

The Breakthrough: Key Findings & Data

시뮬레이션 결과, 고엔트로피 합금은 순수 금속과 다른 독특한 방사선 손상 거동을 보이며, 이는 재료의 안정성과 직결됨을 확인했습니다.

Finding 1: 방사선 조사 하에서 결함 농도의 정상 상태 도달

고엔트로피 합금은 이온 조사 초기에 결함 농도가 빠르게 증가하지만, 특정 수준(약 4%)에서 더 이상 증가하지 않고 안정적인 정상 상태(steady state)에 도달했습니다. 반면, 순수 니켈(Ni)은 결함이 지속적으로 합쳐져 더 큰 결함 클러스터(예: 적층 결함 사면체, Frank 루프)를 형성하며 결함 농도가 느리지만 꾸준히 변화하는 경향을 보였습니다.

이는 HEA 내부의 복잡한 원자 환경이 점결함(point defect)의 이동성을 감소시켜 결함들이 서로 만나 소멸하거나 큰 클러스터로 성장하는 것을 억제하기 때문입니다. 결과적으로 HEA 내에서는 결함의 생성과 소멸이 동적 평형을 이루게 되어, 지속적인 방사선 환경에서도 구조적 안정성을 유지할 수 있습니다. Figure 4(d)는 이러한 차이를 명확하게 보여줍니다. HEA(파란색 선)는 약 0.1 dpa(손상량 단위) 이후 결함 농도가 포화되는 반면, Ni(노란색 선)는 다른 양상을 보입니다.

Finding 2: 방사선 유도 결함이 구리(Cu) 편석의 싱크(Sink)로 작용

연구팀은 방사선 조사를 마친 HEA 샘플을 다시 열역학적 평형 시뮬레이션(MC/MD)에 노출시켜 원소들의 재분배를 관찰했습니다. 그 결과, 방사선에 의해 생성된 격자 결함(공공, 전위 루프 등) 주변으로 Cu 원자들이 집중적으로 모여드는 현상을 발견했습니다.

Table I는 이 결과를 정량적으로 보여줍니다. 방사선 조사 직후 결함 내부의 Cu 농도는 26.9%였으나, 후속 평형화 과정 후에는 49.4%로 급증했습니다. 이는 결함 부위가 제공하는 추가적인 부피(excess volume)에 상대적으로 원자 크기가 큰 Cu가 자리 잡아 시스템의 전체 변형 에너지를 낮추기 때문입니다. 즉, 결함이 Cu 편석을 위한 ‘싱크’ 역할을 하여, 결함이 없는 완벽한 격자 내에서 대규모 상분리가 일어나는 것을 효과적으로 억제하는 것입니다. Figure 7은 결함 구조(회색) 주변에 Cu 원자(빨간색)가 집중되는 모습을 시각적으로 보여줍니다.

Practical Implications for R&D and Operations

  • For Process Engineers: 본 연구는 CuNiCoFe와 같은 HEA가 장시간의 방사선 노출 환경에서도 지속적인 성능 저하 대신 안정적인 미세구조를 유지할 수 있음을 시사합니다. 이는 차세대 원자로의 핵연료 피복관이나 구조 부품 설계 시 재료의 수명 예측과 신뢰성 향상에 기여할 수 있습니다.
  • For Quality Control Teams: Table I과 Figure 7의 데이터는 방사선 조사 후 HEA 부품의 미세구조 분석 시, 결함 주변의 성분 편석을 새로운 품질 검사 기준으로 고려할 수 있음을 보여줍니다. 결함과 특정 원소의 상호작용은 재료의 국부적인 기계적 특성에 영향을 미칠 수 있습니다.
  • For Design Engineers: HEA의 고유한 방사선 저항성과 자가 안정화 메커니즘은 극한 환경용 부품 설계에 새로운 가능성을 제시합니다. 특히, 방사선에 의해 생성된 결함이 오히려 재료의 상 안정성을 높이는 역설적인 현상은 다른 HEA 시스템에서도 합금 원소 설계를 통해 적극적으로 활용할 수 있는 중요한 설계 변수가 될 수 있습니다.

Paper Details

Local segregation versus irradiation effects in high-entropy alloys: Steady-state conditions in a driven system

1. Overview:

  • Title: Local segregation versus irradiation effects in high-entropy alloys: Steady-state conditions in a driven system
  • Author: Leonie Koch, Fredric Granberg, Tobias Brink, Daniel Utt, Karsten Albe, Flyura Djurabekova, and Kai Nordlund
  • Year of publication: 2017
  • Journal/academic society of publication: J. Appl. Phys. 122, 105106
  • Keywords: high-entropy alloys, irradiation effects, molecular dynamics, segregation, defect formation

2. Abstract:

우리는 분자 동역학 시뮬레이션을 통해 모델 고엔트로피 합금(CuNiCoFe)이 이온 조사 하에서 겪는 질서 전이와 결함 형성을 연구합니다. 하이브리드 몬테카를로/분자 동역학 기법을 사용하여, 고온에서는 구성 엔트로피에 의해 열역학적으로 안정하지만 저온에서는 구리 석출에 의해 부분적으로 분해되는 모델 합금을 생성합니다. 고엔트로피 상태와 다상 상태의 샘플을 각각 입자 조사 시뮬레이션에 적용합니다. 손상 축적을 분석하고 순수 니켈(Ni) 참조 시스템과 비교합니다. 결과는 고엔트로피 합금이 초기 구성과 무관하게 입자 조사 중에도 일정한 비율의 단범위 규칙을 형성함을 보여줍니다. 또한, 결과는 고엔트로피 합금에서 결함 축적이 감소한다는 증거를 제공합니다. 이는 점결함의 이동성 감소가 결함 생성과 소멸의 정상 상태로 이어지기 때문입니다. 방사선에 의해 생성된 격자 결함은 구리(Cu) 편석의 싱크 역할을 하는 것으로 나타났습니다.

3. Introduction:

고엔트로피 합금(HEA)은 고성능 재료 분야에서 최근 상당한 주목을 받고 있는 비교적 새로운 종류의 재료입니다. 이 합금은 최소 4~5개의 주원소가 동등하거나 거의 동등한 비율로 구성되어, 각 원소의 분율이 5% 미만으로 떨어지거나 35%를 초과하지 않습니다. HEA라는 이름은 깁스 자유 에너지에 대한 구성 엔트로피의 큰 기여에서 유래했으며, 이 엔트로피의 영향이 저온에서도 무작위 고용체를 안정화시킨다고 가정됩니다. 그러나 혼합 엔탈피와 구성 원소 간의 원자 크기 불일치가 저온에서의 상 선택 기준에 결정적으로 기여하며, 2차상의 형성을 완전히 피하기는 어려운 경우가 많습니다. HEA에 대한 관심은 주로 뛰어난 기계적 특성 때문에 발생하며, 특정 초합금이나 금속 유리의 대안으로 제시됩니다. HEA는 큰 구성 엔트로피뿐만 아니라, 원자 크기 차이로 인한 국부 격자 뒤틀림에서 발생하는 높은 원자 수준의 응력으로도 특징지어집니다. 구조적 및 화학적 무질서가 결함 동역학과 열 분산 모두에 영향을 미친다고 보고되었으며, 이는 방사선 저항성 재료의 맥락에서 특히 흥미롭습니다.

4. Summary of the study:

Background of the research topic:

고엔트로피 합금(HEA)은 방사선 저항성이 우수하여 원자력 및 항공우주 분야의 차세대 소재로 각광받고 있습니다. 그러나 HEA는 저온에서 특정 원소가 분리되어 석출물을 형성하려는 열역학적 경향과, 외부 방사선 조사가 유발하는 비평형 효과가 복잡하게 얽혀있어 그 거동을 예측하기 어렵습니다.

Status of previous research:

이전의 분자 동역학 연구들은 다성분계 합금이 순수 금속에 비해 방사선 조사 시 결함 농도가 현저히 감소할 수 있음을 보여주었습니다. 이러한 장점은 감소된 결함 이동성과 그에 따른 결함 클러스터의 느린 성장 속도에 기인하는 것으로 설명되었습니다. 또한, 화학적 무질서가 열전도도를 감소시켜 결함 소멸을 촉진함으로써 큰 결함 클러스터의 형성을 막는다고 가정되었습니다.

Purpose of the study:

본 연구의 목적은 모델 4성분계 CuNiCoFe 합금을 대상으로, 열역학적 평형 상태와 입자 조사 환경 하에서 화학적 질서와 구조적 결함이 어떻게 변화하는지를 규명하는 것입니다. 특히, 단상 HEA에서 다상 합금으로의 전이를 연구하고, 방사선 조사가 구리(Cu)의 분해(decomposition)를 촉진하는지, 아니면 억제하는지를 밝히고자 합니다.

Core study:

하이브리드 MC/MD 시뮬레이션을 사용하여 고온(800K)에서 안정적인 HEA와 저온(400K)에서 Cu 클러스터가 석출된 부분 분해된 샘플을 생성했습니다. 이 두 샘플을 5 keV 반동 이벤트를 이용한 이온 조사 시뮬레이션에 적용하여 손상 축적 과정을 순수 Ni과 비교 분석했습니다. 이를 통해 방사선 조사가 HEA의 단범위 규칙(SRO)과 결함 구조에 미치는 영향을 평가하고, 방사선 유도 결함과 Cu 편석 간의 상호작용을 규명했습니다.

5. Research Methodology

Research Design:

본 연구는 계산 시뮬레이션 기반의 연구 설계를 채택했습니다. 먼저, 하이브리드 MC/MD 기법을 사용하여 CuNiCoFe 합금의 두 가지 초기 상태(고온의 무작위 고용체, 저온의 부분 분해 구조)를 생성했습니다. 그 후, 이 구조들과 순수 Ni 참조 구조에 대해 동일한 조건의 이온 조사 시뮬레이션을 수행하여 결과를 비교 분석하는 방식으로 설계되었습니다.

Data Collection and Analysis Methods:

  • 시뮬레이션 코드: 평형 구조 생성에는 LAMMPS 코드를, 방사선 조사 시뮬레이션에는 PARCAS 코드를 사용했습니다.
  • 데이터 분석: 시뮬레이션 결과는 OVITO 소프트웨어를 사용하여 시각화하고 분석했습니다. 화학적 정렬도를 평가하기 위해 Warren-Cowley 단범위 규칙(SRO) 파라미터를 계산했습니다. 격자 결함은 공통 이웃 분석(CNA)과 전위 추출 알고리즘(DXA)을 통해 식별하고 정량화했습니다. 원자 부피는 보로노이 테셀레이션(Voronoi tesselation)을 통해 계산했습니다.

Research Topics and Scope:

  • 연구 주제: CuNiCoFe 고엔트로피 합금의 (1) 열역학적 평형 상태에서의 상 안정성 및 Cu 편석 경향, (2) 이온 조사 하에서의 결함 축적 메커니즘 및 순수 금속과의 비교, (3) 방사선 조사가 화학적 질서(SRO)에 미치는 영향, (4) 방사선 유도 결함과 Cu 편석 간의 상호작용.
  • 연구 범위: 시뮬레이션은 약 100,000개의 원자로 구성된 시스템에서 수행되었으며, 방사선 조사는 총 1,500회의 5 keV 반동 이벤트(총 손상량 0.57 dpa)에 해당하는 범위까지 진행되었습니다.

6. Key Results:

Key Results:

  • 고엔트로피 합금(HEA)은 저온(400K)에서 열역학적으로 구리(Cu)가 클러스터를 형성하며 부분적으로 분해되는 경향을 보입니다. 이는 구성 엔트로피보다 혼합 엔탈피의 영향이 더 우세하기 때문입니다.
  • 이온 조사 시, HEA는 순수 Ni보다 높은 결함 농도에서 빠르게 포화되어 안정적인 정상 상태(steady state)에 도달합니다. 이는 HEA 내에서 점결함의 이동성이 낮아 결함의 생성과 소멸이 균형을 이루기 때문입니다.
  • HEA는 초기 상태(무작위 또는 부분 분해)와 상관없이, 이온 조사를 통해 거의 동일한 최종 단범위 규칙(SRO) 값으로 수렴합니다. 이는 시스템이 동적으로 대부분 무작위적인 정상 상태로 구동됨을 의미합니다.
  • 방사선에 의해 생성된 격자 결함(공공, 전위 등)은 Cu 원자의 편석을 위한 ‘싱크(sink)’ 역할을 합니다. 결함 부위의 증가된 부피로 인해 원자 크기가 큰 Cu가 우선적으로 이동하여, 결함이 없는 격자 내에서의 대규모 상분리를 억제합니다.
FIG. 3. Histograms of the atomic volumes at 0K for the HEA equilibrated at 400K (red) and 800K (blue). The dashed lines indicate the ground state atomic volume of the single-element FCC structures. Atomic volumes are obtained from Voronoi tesselation38{41 of 20 snapshots at 0 K.
FIG. 3. Histograms of the atomic volumes at 0K for the HEA equilibrated at 400K (red) and 800K (blue). The dashed lines indicate the ground state atomic volume of the single-element FCC structures. Atomic volumes are obtained from Voronoi tesselation38{41 of 20 snapshots at 0 K.

Figure List:

  • FIG. 1. Snapshots of the CuNiCoFe alloy, equilibrated in the VC-SGC ensemble at 800K (left) and 400K (right).
  • FIG. 2. Warren-Cowley parameters α1 (a) and α2 (b) for the CuNiCoFe alloy system at 800 K and 400 K. (c) The change of α1Cu,Cu with temperature.
  • FIG. 3. Histograms of the atomic volumes at 0K for the HEA equilibrated at 400 K (red) and 800 K (blue).
  • FIG. 4. Analysis of the build-up of lattice defects during irradiation.
  • FIG. 5. Evolution of the SRO during irradiation.
  • FIG. 6. Final order parameters for the first (a) and second neighbor shell (b) after irradiation with a dose of 0.57 dpa.
  • FIG. 7. VC-SGC simulations of the HEA sample after irradiation.

7. Conclusion:

구리 편석 경향을 가진 모델 CuNiCoFe HEA를 사용하여, 시스템이 초기 구조와 무관하게 방사선 조사 하에서 결함 농도와 화학적 질서의 정상 상태에 도달함을 관찰했습니다. 순수 금속과 달리, 방사선 조사는 HEA에서 이동성이 낮은 점결함을 생성하며, 이는 재결합이나 군집화 대신 더 많은 수의 고립된 결함을 야기합니다. 예를 들어, Ni는 결함이 더 크고 안정한 구조로 군집화되면서 결함 농도가 계속 증가하는 반면, HEA는 결함 생성과 소멸의 정상 상태에 빠르게 도달합니다. 방사선 조사는 구리의 혼합 분리를 위한 열적 활성화를 제공하지만, 동시에 원소 분포를 재무작위화합니다. 결과적으로 화학적 질서의 정상 상태는 무작위 고용체에 가깝지만, 여전히 국부적인 석출의 흔적을 보입니다. 또한, 시뮬레이션은 다양한 격자 결함이 구리를 위한 싱크 역할을 함을 보여줍니다. 이는 구리 원자가 가장 큰 종이고 결함이 여분의 부피를 제공하기 때문일 가능성이 높습니다. 이러한 효과들이 종합적으로 HEA의 높은 방사선 저항성을 설명합니다.

FIG. 4. Analysis of the build-up of lattice defects during irradiation. (a) DXA analysis of the initially segregated HEA at di erent irradiation doses. (b) The same for a Ni sample. Empty space represents the perfect FCC lattice; the structures do not collapse during irradiation. Green lines indicate h112i partial dislocations, turquoise lines indicate a Frank loop, pur- ple lines belong to stacking fault tetrahedra, and red surfaces enclose defects that cannot be recognized by DXA. Videos of these simulations can be found in the supplementary material (CuNiCoFe-ordered-DXA-during-irradiation.avi and Ni-DXA-during-irradiation.avi). (c) A closer look at those red regions reveals that they represent vacancies and vacancy clusters. In (d), a plot of the concentration of defective atoms as identi ed by CNA is shown as a function of the irradiation dose. In agreement with the DXA results, we can see that the HEA quickly reaches a high defect concentration that saturates around 4 %. These defects consist mostly of vacancies and small dislocation networks. Pure Ni builds up the defect concentration more slowly. At rst|similar to the HEA|vacancies and small dislocation networks appear, then these start disappearing in favor of stacking-fault tetrahedra and a Frank loop.
FIG. 4. Analysis of the build-up of lattice defects during irradiation. (a) DXA analysis of the initially segregated HEA at different irradiation doses. (b) The same for a Ni sample. Empty space represents the perfect FCC lattice; the structures do not collapse during irradiation. Green lines indicate h112i partial dislocations, turquoise lines indicate a Frank loop, purple lines belong to stacking fault tetrahedra, and red surfaces enclose defects that cannot be recognized by DXA. Videos of these simulations can be found in the supplementary material (CuNiCoFe-ordered-DXA-during-irradiation.avi and Ni-DXA-during-irradiation.avi). (c) A closer look at those red regions reveals that they represent vacancies and vacancy
clusters. In (d), a plot of the concentration of defective atoms as identi ed by CNA is shown as a function of the irradiation dose. In agreement with the DXA results, we can see that the HEA quickly reaches a high defect concentration that saturates around 4 %. These defects consist mostly of vacancies and small dislocation networks. Pure Ni builds up the defect concentration more slowly. At rst|similar to the HEA|vacancies and small dislocation networks appear, then these start disappearing in favor
of stacking-fault tetrahedra and a Frank loop.

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PDF View

Fig. 6—(a) A typical entrainment defect in the commercial-purity Mg-alloy casting under the protection of 0.5 pct SF6/air, (b) EDS result of spectrum 1, (c) local magnified outside layer of film, and (d) EDS of spectrum 2.

Mg-Alloy 주조 품질의 열쇠: Entrainment Defect 소비 메커니즘 분석 및 기계적 물성 향상

이 기술 요약은 TIAN LI, J.M.T. DAVIES, DAN LUO가 Metallurgical and Materials Transactions B (2021)에 발표한 논문 “Consumption of Entrained Gases Within Bifilms During a Mg-Alloy Casting Process”를 기반으로 하며, STI C&D가 기술 전문가를 위해 분석 및 요약하였습니다.

키워드

  • Primary Keyword: Entrainment Defect
  • Secondary Keywords: Mg-Alloy Casting, Bifilm Defects, Double Oxide Film, Gas Consumption, Mechanical Properties, Cover Gas

Executive Summary

  • The Challenge: Mg-alloy 주조 시 발생하는 Entrainment Defect(이중 산화막 결함 또는 바이필름)는 제품의 기계적 물성과 신뢰성을 저하시키는 주요 원인입니다.
  • The Method: 상용 순수 Mg-alloy를 SF6/air 및 SF6/CO2 보호 가스 환경에서 주조 실험을 진행하고, 열역학적 계산을 결합하여 결함의 진화 과정을 연구했습니다.
  • The Key Breakthrough: Entrainment Defect 내부에 갇힌 가스는 주변 용탕과의 화학 반응을 통해 소모되어 고체 화합물로 변환될 수 있으며, 이는 결함의 빈 공간(void volume)을 줄여 결함의 유해성을 완화시킬 수 있음을 발견했습니다.
  • The Bottom Line: 공기(air)와 같이 반응성이 더 높은 캐리어 가스를 사용하면 Entrainment Defect 내부 가스 소모를 촉진하여, 최종 주조품의 기계적 특성(특히 연신율)을 향상시킬 수 있습니다.

The Challenge: Why This Research Matters for CFD Professionals

자동차 부품 등에서 Mg-alloy의 수요가 증가함에 따라, 주조품의 품질과 재현성을 확보하는 것이 중요해졌습니다. 그러나 주조 공정 중 용탕 표면의 산화막이 말려 들어가면서 국부적인 대기를 포집하여 형성되는 Entrainment Defect는 경량 합금 주조품의 기계적 물성과 재현성에 치명적인 영향을 미치는 주요 요인입니다. 특히 Mg-alloy는 반응성이 높아 결함 형성이 용이하지만, 이 결함이 용탕 내에서 어떻게 거동하고 진화하는지에 대한 연구는 제한적이었습니다. 기존 Al-alloy 연구에서는 포집된 질소 가스가 반응하기 어려워 결함 제거가 쉽지 않았지만, Mg-alloy는 질소와도 쉽게 반응하므로 결함의 거동이 다를 수 있다는 가능성이 제기되었습니다. 이 연구는 Mg-alloy 주조에서 Entrainment Defect 내부 가스의 소모 메커니즘을 규명하여 주조 품질을 향상시킬 수 있는 새로운 가능성을 제시합니다.

Fig. 1—Sketch of surface entrainment event in a light alloy casting (reprinted from Ref. 8).
Fig. 1—Sketch of surface entrainment event in a light alloy casting (reprinted from Ref. 8).

The Approach: Unpacking the Methodology

본 연구는 실제 주조 실험과 이론적 분석을 결합하여 Entrainment Defect의 거동을 심층적으로 분석했습니다.

  • 소재 및 용해: 상용 순수 Mg-alloy 3kg을 중주파 유도로에서 용해했으며, 0.5 pct SF6/air 또는 0.5 pct SF6/CO2를 보호 가스로 사용했습니다. 용탕은 700°C ± 5°C로 유지되었고, 아르곤 가스로 15분간 탈가스 처리를 진행했습니다.
  • 주조: 수지 결합 실리카 샌드 몰드를 사용하여 인장 시험용 시편을 주조했습니다. 주입 전, 몰드는 보호 가스로 20분간 퍼징(flushing)되었습니다.
  • 산화 셀(Oxidation Cell) 실험: Entrainment Defect 내부의 제한된 가스 환경을 모사하기 위해, 밀폐된 산화 셀을 설계했습니다. 이 셀 내에서 Mg-alloy를 다양한 시간(5~30분) 동안 유지하며 표면 산화막의 성장 과정을 관찰했습니다.
  • 기공 가스 분석(Pore Gas Analysis): 실시간 X-ray로 주조품 내부의 가스 기포를 확인한 후, 기공 가스 분석기를 사용하여 기포 내부의 가스 성분을 직접 분석했습니다. 질량 분석기는 분자량 100 미만의 화합물을 감지할 수 있었습니다.
  • 분석: 파단된 인장 시편의 파단면과 결함의 단면을 주사전자현미경(SEM)과 에너지 분산형 분광법(EDS)을 사용하여 구조와 성분을 분석했습니다.
Fig. 2—Dimensions of the sand mold used for casting test bars (unit: mm).
Fig. 2—Dimensions of the sand mold used for casting test bars (unit: mm).

The Breakthrough: Key Findings & Data

Finding 1: Entrainment Defect의 구조는 가스 소모에 따라 진화한다

주조품 내에서 발견된 Entrainment Defect는 단일 구조가 아니었습니다. 초기 단계의 결함은 MgO로 구성된 내부와 MgO 및 MgF2로 구성된 외부 층을 가진 구조를 보였습니다(Figure 6). 반면, 가스 소모가 더 진행된 결함에서는 내부의 다공성 MgO 층과 외부의 치밀한 MgF2 이중 층으로 구성된 ‘샌드위치’ 구조가 관찰되었으며, 두 산화막 층이 서로 성장하여 붙어있는 모습이 확인되었습니다(Figure 7). 이는 결함 내부에 갇힌 가스가 주변 용탕과 반응하며 소모되고, 그 결과로 산화막이 성장하여 결함의 빈 공간을 채워나감을 시사합니다.

Finding 2: 포집된 가스는 반응을 통해 고체 화합물로 변환된다

기공 가스 분석 결과, 결함 내부에서는 수소(H2)와 질소(N2)가 검출되었으나, 산소(O2)나 SF6 분해 생성물은 검출되지 않았습니다(Figure 12b). 이는 산소와 SF6 가스가 용탕과의 반응을 통해 완전히 소모되었음을 의미합니다. 또한, 일부 파단면에서는 질화물(nitride)이 포함된 결함이 발견되었습니다(Figure 10).

열역학적 계산(Figure 15)은 이 과정을 3단계로 설명합니다. – 1단계: SF6의 불소가 우선적으로 소모되어 MgF2를 형성합니다. – 2단계: 남은 산소와 황이 반응하여 MgSO4와 MgO를 형성합니다. – 3단계: 마지막으로, 잔류 가스 내 질소가 반응하여 MgS와 Mg3N2를 형성합니다. 이 모델은 실제 관찰된 다양한 구조의 결함들을 성공적으로 설명합니다.

Finding 3: 캐리어 가스 종류가 결함 소모 속도와 기계적 물성에 영향을 미친다

보호 가스의 캐리어 가스로 공기(air)와 CO2를 사용했을 때, 산화막 성장 속도에 뚜렷한 차이가 나타났습니다. 산화 셀 실험에서 SF6/air 환경의 산화막이 SF6/CO2 환경보다 훨씬 빠르게 성장했습니다(Figure 13). 이는 공기를 사용했을 때 포집된 가스의 소모 속도가 더 빠르다는 것을 의미합니다.

이러한 차이는 최종 주조품의 기계적 물성에도 영향을 미쳤습니다. 인장 시험 결과, SF6/air를 사용하여 제작된 주조품의 연신율 데이터 포인트 중 약 40%가 SF6/CO2로 제작된 주조품의 데이터 분포보다 통계적으로 유의미하게 높게 나타났습니다(Figure 14). 이는 빠른 가스 소모가 Entrainment Defect의 유해성을 효과적으로 감소시켜 기계적 물성을 향상시켰음을 보여주는 강력한 증거입니다.

Fig. 6—(a) A typical entrainment defect in the commercial-purity Mg-alloy casting under the protection of 0.5 pct SF6/air, (b) EDS result of spectrum 1, (c) local magnified outside layer of film, and (d) EDS of spectrum 2.
Fig. 6—(a) A typical entrainment defect in the commercial-purity Mg-alloy casting under the protection of 0.5 pct SF6/air, (b) EDS result of spectrum 1, (c) local magnified outside layer of film, and (d) EDS of spectrum 2.

Practical Implications for R&D and Operations

  • For Process Engineers: 이 연구는 보호 가스의 캐리어 가스로 CO2 대신 공기를 사용하는 것이 Entrainment Defect의 자가 치유(self-healing)를 촉진하여 주조 품질을 향상시킬 수 있음을 시사합니다. 이는 긴 용탕 유지 시간 없이도 결함의 부정적 효과를 줄일 수 있는 실용적인 방법이 될 수 있습니다.
  • For Quality Control Teams: 파단면에서 발견되는 결함의 화합물(예: MgF2, MgSO4, Mg3N2)을 분석하면, 해당 결함의 가스 소모가 어느 단계까지 진행되었는지 추정할 수 있습니다. 이는 결함의 유해성을 평가하는 새로운 품질 검사 기준으로 활용될 수 있습니다.
  • For Design Engineers: 주조 방안 설계 시, 난류 발생을 최소화하는 것이 여전히 중요하지만, 이 연구는 일부 Entrainment Defect가 형성되더라도 그 부정적 영향이 공정 조건에 따라 완화될 수 있음을 보여줍니다. 이는 주조 방안 설계에 있어 더 넓은 유연성을 제공할 수 있습니다.

Paper Details

Consumption of Entrained Gases Within Bifilms During a Mg-Alloy Casting Process

1. Overview:

  • Title: Consumption of Entrained Gases Within Bifilms During a Mg-Alloy Casting Process
  • Author: TIAN LI, J.M.T. DAVIES, and DAN LUO
  • Year of publication: 2021
  • Journal/academic society of publication: METALLURGICAL AND MATERIALS TRANSACTIONS B
  • Keywords: Entrainment defects, double oxide film defects, bifilms, Mg-alloy, casting, protective gases

2. Abstract:

이중 산화막 결함 또는 바이필름으로 알려진 Entrainment Defect의 형성을 상용 순수 Mg-alloy를 보호 가스 하에서 사용하여 실제 실험과 이론적 열역학 계산을 결합하여 조사했습니다. Entrainment Defect의 진화를 연구했으며, 이전에 보고된 Mg-alloy 용탕 표면 필름의 단일층 구조와 다른 이중층 구조의 산화막이 발견되었습니다. 기공 가스 분석기를 사용하여 결함 내에 갇힌 가스를 분석했으며, H2와 N2(공기로부터)가 검출되었습니다. 포집된 가스는 주변 액체 Mg-alloy와의 반응을 통해 고갈될 수 있으며, 이로 인해 산화막이 용탕 내에서 함께 성장하는 것으로 나타났습니다. 포집된 가스가 고체상 화합물로 변환되면 결함의 빈 공간 부피를 줄일 수 있으며, 이는 주조품 품질에 대한 Entrainment Defect의 부정적인 영향을 감소시킬 수 있습니다.

3. Introduction:

최근 Mg-alloy의 전 세계적 수요가 증가하면서 자동차 부품용 Mg-alloy 주조품 사용에 대한 관심이 높아지고 있습니다. 그러나 Mg-alloy 주조품의 기계적 특성과 재현성은 주조 공정 중 형성되는 결함에 의해 영향을 받습니다. 예를 들어, Entrainment Defect(이중 산화막 결함 또는 바이필름)는 경량 합금 주조품의 재현성과 최종 특성에 영향을 미치는 주요 요인으로, Mg-alloy 주조품에서도 발견되었습니다. 용탕으로 소량의 국부 대기가 유입되면 주조 공정 중 심각한 결함을 형성할 수 있으며, 이는 주조 특성의 가변성에 영향을 미치는 핵심 요소입니다. 포집된 가스는 주변 용탕과의 반응을 통해 소모될 수 있으며, 이는 Al-alloy 주조에서 처음 보고되었습니다. 그러나 Al-alloy의 경우 포집된 공기 중 질소(78%)가 반응하기 매우 어려워 결함 치유가 제한적이었습니다. Mg-alloy는 질소와 더 쉽게 반응하므로, Entrainment Defect 내의 빈 공간 부피가 상대적으로 쉽게 줄어들 수 있습니다. 이 연구는 SF6 보호 가스 하에서 상용 순수 Mg-alloy 주조 시 포집된 가스의 소모와 그 효과를 실험적 및 이론적 접근을 통해 조사했습니다.

4. Summary of the study:

Background of the research topic:

Mg-alloy 주조품의 기계적 물성은 주조 과정에서 발생하는 Entrainment Defect(바이필름)에 의해 크게 저하될 수 있습니다. 이 결함은 용탕 표면의 산화막이 접혀 들어가면서 내부에 가스를 포집하여 형성됩니다.

Status of previous research:

Al-alloy에서는 바이필름 내부의 가스(특히 질소)가 잘 소모되지 않아 결함이 지속되는 문제가 있었습니다. Mg-alloy는 질소와도 반응성이 높지만, 보호 가스(예: SF6)가 존재하는 환경에서 바이필름 내부 가스의 거동과 소모에 대한 연구는 부족했습니다.

Purpose of the study:

본 연구의 목적은 Mg-alloy 주조 공정 중 Entrainment Defect 내부에 포집된 가스가 어떻게 소모되는지, 그리고 이 소모 과정이 결함의 구조와 최종 주조품의 품질에 어떤 영향을 미치는지 규명하는 것입니다.

Core study:

상용 순수 Mg-alloy를 사용하여 SF6/air와 SF6/CO2 보호 가스 조건에서 주조 실험을 수행했습니다. 실제 주조품의 결함 분석, 제한된 가스 환경을 모사한 산화 셀 실험, 결함 내부 가스 직접 분석, 열역학적 시뮬레이션을 통해 포집된 가스의 소모 메커니즘과 그 효과를 종합적으로 분석했습니다.

5. Research Methodology

Research Design:

실험적 접근과 이론적 계산을 병행했습니다. 두 가지 다른 캐리어 가스(air, CO2)를 사용한 SF6 보호 가스 환경에서 주조 실험을 설계하여 캐리어 가스의 영향을 비교 분석했습니다.

Data Collection and Analysis Methods:

  • 주조 및 인장 시험: 샌드 몰드를 이용해 시편을 주조하고, 인장 시험기를 통해 기계적 물성(UTS, 연신율)을 측정했습니다.
  • 미세구조 분석: SEM 및 EDS를 사용하여 파단면과 결함 단면의 형상 및 화학 성분을 분석했습니다.
  • 산화막 성장 관찰: 특수 제작된 산화 셀을 이용하여 제한된 가스 환경에서 시간에 따른 표면 산화막의 두께와 구조 변화를 관찰했습니다.
  • 기공 가스 분석: 질량 분석기를 장착한 기공 가스 분석 장비를 사용하여 주조품 내 기공의 가스 성분을 정성적으로 분석했습니다.
  • 열역학 계산: HSC 시뮬레이션 소프트웨어를 사용하여 Mg 용탕과 포집된 가스 간의 반응을 시뮬레이션하고, 반응 생성물의 변화를 예측했습니다.

Research Topics and Scope:

연구는 상용 순수 Mg-alloy를 대상으로 하며, SF6 기반 보호 가스 환경에서의 Entrainment Defect 형성과 진화에 초점을 맞춥니다. 포집된 가스의 소모 과정, 그에 따른 결함 구조의 변화, 그리고 캐리어 가스 종류가 최종 기계적 물성에 미치는 영향을 다룹니다.

6. Key Results:

Key Results:

  • Mg-alloy 주조에서 발견된 Entrainment Defect는 이전에 보고된 표면 산화막과 다른 이중층(double-layered) 구조를 가졌습니다.
  • 결함 내부에 포집된 가스(SF6, O2 등)는 주변 Mg 용탕과 반응하여 소모되며, 이 과정에서 산화막이 성장하여 결함의 양쪽 막이 서로 붙는 ‘샌드위치’ 구조를 형성할 수 있습니다.
  • 기공 가스 분석 결과, 결함 내부에서 H2와 N2가 검출되어, 공기 유입 및 용탕 내 수소 확산이 동시에 일어남을 확인했습니다.
  • 열역학적 계산 결과, 가스 소모는 3단계(MgF2 형성 → MgSO4/MgO 형성 → MgS/Mg3N2 형성)로 진행되는 것으로 예측되었으며, 이는 실제 관찰된 다양한 결함 구조와 일치했습니다.
  • SF6/air 보호 가스는 SF6/CO2보다 포집된 가스를 더 빠르게 소모시켰으며(더 빠른 산화막 성장), 그 결과 최종 주조품의 연신율이 통계적으로 더 높게 나타났습니다.

Figure List:

  • Fig. 1-Sketch of surface entrainment event in a light alloy casting (reprinted from Ref. 8).
  • Fig. 2-Dimensions of the sand mold used for casting test bars (unit: mm).
  • Fig. 3-Schematic of the oxidation cell (reprinted from Ref. 19).
  • Fig. 4-Dimensions of the sand mold for pore gas analysis (unit: mm) (reprint from Ref. 28).
  • Fig. 5-Schematic of the pore gas analyser.
  • Fig. 6-(a) A typical entrainment defect in the commercial-purity Mg-alloy casting under the protection of 0.5 pct SF6/air, (b) EDS result of spectrum 1, (c) local magnified outside layer of film, and (d) EDS of spectrum 2.
  • Fig. 7-(a) Another entrainment defect found in the commercial-purity Mg alloy casting, (b) the inner section of the defect indicated that the oxide films had grown together, (c) EDS spectrum of the point denoted in (b), (d) a magnified observation edge of the defect, showing a compact single-layer oxide film, (e) through (h) element maps of the area shown in (d).
  • Fig. 8-(a) A entrainment defect on the fracture surfaces of a commercial-purity Mg alloy test bar; (b) a local magnified section of the boundary between the dark and bright regions, and (c) a further magnified observation to the surface of the dark region. The dimension of the fracture surface is 5 mm x 6 mm. The acceleration voltage was 15 kV.
  • Fig. 9-Schematic for an entrainment defect contained in the test bar (a) before facture and (b) after fracture.
  • Fig. 10-(a) An entrainment defect on the fracture surface of another commercial-purity Mg alloy test bar, (b) spectrum of the oxide film (the acceleration voltage was 5kV), indicating nitride contained in the oxide film, and (c) a magnified observation of the oxide film.
  • Fig. 11-Surface films on the liquid Mg alloy formed in the sealed oxidation cell that was held for different time in SF6/air and their EDS mapping: (a) 0 min; (b) 5 min, and (c) 30 min.
  • Fig. 12-(a) X-ray image of a trapped bubble contained in the casting under 0.5 pct SF6/air and (b) mass spectroscopy result of the pore gas analysis.
  • Fig. 13-Comparison of the oxide film growth rates in 0.5 pct SF6/air and 0.5 pct SF6/CO2.
  • Fig. 14-2-sigma diagram of the mechanical properties of the commercial-purity Mg-alloy castings produced in 0.5 pct SF6/air and 0.5 pct SF6/CO2.
  • Fig. 15-An equilibrium diagram for the reaction at 1 atm and 700 °C with 7e-7 kg gas of 0.5 pct SF6/air. The X-axis is the amount of Mg having reacted with the entrained gas, and the vertical Y-axis denotes the amounts of the reactants and products.
  • Fig. 16-Schematic of the double oxide film defects corresponding to the three reaction stages under different atmospheres shown in Figure 15: (a) stage 1, (b) stage 2, and (c) stage 3.

7. Conclusion:

(1) 주조 공정 중 발생하는 Entrainment Defect의 진화 과정이 SF6/air 보호 가스 하에서 실험적으로, 그리고 이론적 열역학 계산을 통해 조사되었습니다. 포집된 가스 내 불소는 우선적으로 소모되는 경향을 보였고, 황은 잔류 가스에 축적되었습니다. 산화막은 결함이 처한 반응 단계에 따라 다른 구조와 화합물 조합을 가졌습니다. 결함 내 포집된 보호 가스는 고갈되어 샌드위치 같은 구조를 형성할 수 있었습니다. 이러한 구조는 포집된 가스의 소모가 Entrainment Defect를 감소시키고 Mg 주조품의 품질을 향상시킬 잠재력을 가지고 있으므로 장려되어야 합니다.

(2) 포집된 SF6/air 가스는 포집된 SF6/CO2보다 더 빠르게 소모되었으며, 이는 더 빠르게 성장하는 산화막을 초래하여 Entrainment Defect의 크기와 빈 공간 부피를 줄일 더 큰 기회를 가졌습니다. 이는 0.5 pct SF6/air에서 생산된 상용 순수 Mg-alloy 주조품의 연신율 데이터 포인트 중 40%가 0.5 pct SF6/CO2 보호 가스로 생산된 거의 모든 것보다 상대적으로 높다는 인장 시험 결과에 의해 뒷받침됩니다.

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Expert Q&A: Your Top Questions Answered

Q1: 실제 주조품 분석 외에 별도의 산화 셀(oxidation cell)을 사용한 이유는 무엇입니까?

A1: 산화 셀은 실제 Entrainment Defect 내부와 유사한 ‘제한된 가스 공급’ 환경을 정밀하게 모사하기 위해 사용되었습니다. 실제 주조품에서는 결함의 크기와 형성 시점이 다양하여 시간에 따른 변화를 체계적으로 관찰하기 어렵습니다. 산화 셀을 통해 정해진 양의 보호 가스가 Mg 용탕과 반응하며 표면 산화막이 어떻게 성장하고 구조가 변하는지를 시간대별(0분, 5분, 30분)로 명확하게 관찰할 수 있었고(Figure 11), 이는 가스 소모 메커니즘을 이해하는 데 결정적인 데이터를 제공했습니다.

Q2: 기공 가스 분석에서 수소(H2)가 검출되었는데, 이는 어디서 온 것이며 어떤 의미를 가집니까?

A2: 논문에서는 이 수소가 용탕에 용해되어 있던 것이 Entrainment Defect 내부의 빈 공간으로 확산해 들어온 것으로 추정합니다. 이는 Campbell이 이전에 제기했던 ‘수소 확산 현상’ 가설을 직접적인 증거로 뒷받침합니다. 이는 수소 기공 문제와 Entrainment Defect가 서로 무관하지 않으며, 용탕 내 수소 함량이 결함의 거동에 영향을 줄 수 있음을 시사합니다.

Q3: 공기(air)는 CO2보다 보호 성능이 낮은데도 불구하고, 왜 SF6/air를 사용한 주조품의 연신율이 더 높게 나타났습니까?

A3: 공기는 산소를 포함하고 있어 CO2보다 반응성이 높습니다. 이 높은 반응성 때문에 Entrainment Defect 내부에 포집된 가스가 더 빠르게 소모되었습니다(Figure 13). 가스가 빠르게 소모되면서 결함의 빈 공간 부피가 효과적으로 줄어들고, 산화막이 서로 붙어 결함의 유해성이 감소했습니다. 결과적으로, 더 많은 산화물을 생성할 수 있다는 잠재적 단점보다, 결함을 ‘치유’하는 긍정적 효과가 기계적 물성(특히 연신율)에 더 크게 작용한 것입니다.

Q4: 논문에서 제안한 가스 소모의 3단계 반응을 구체적으로 설명해 주십시오.

A4: 열역학적 모델(Figure 15)에 따르면 가스 소모는 다음과 같은 3단계로 진행됩니다. 1단계(Stage 1): 반응성이 가장 높은 불소(F)가 먼저 Mg와 반응하여 MgF2를 형성합니다. 2단계(Stage 2): 불소가 고갈된 후, 남은 산소(O2)와 이산화황(SO2)이 Mg와 반응하여 MgSO4 및 MgO를 형성합니다. 3단계(Stage 3): 마지막으로 잔류 가스에 남은 질소(N2)가 Mg와 반응하여 MgS 및 Mg3N2(질화마그네슘)를 형성하며 모든 가스가 소모됩니다.

Q5: 파단면에서는 질화물(nitride)이 발견되었지만, 연마된 단면 시편에서는 발견되지 않은 이유는 무엇입니까?

A5: 저자들은 질화마그네슘(Mg3N2)이 물과 쉽게 반응하여 가수분해되기 때문일 것으로 추정합니다. 시편을 연마할 때 물을 사용하는데, 이 과정에서 Mg3N2가 분해되어 질소가 암모니아(NH3) 가스 형태로 빠져나가 버려 EDS 분석에서 검출되지 않았을 가능성이 높습니다. 반면, 인장 시험 후의 파단면은 물과 접촉하지 않았기 때문에 원래의 질화물 성분이 보존될 수 있었습니다.

Conclusion: Paving the Way for Higher Quality and Productivity

이 연구는 Mg-alloy 주조에서 발생하는 Entrainment Defect가 정적인 결함이 아니라, 주변 용탕과의 반응을 통해 적극적으로 변화하고 소모될 수 있는 동적인 존재임을 명확히 보여주었습니다. 핵심은 결함 내부에 갇힌 가스가 고체 화합물로 변환되면서 결함의 빈 공간이 줄어들고, 그 유해성이 크게 완화될 수 있다는 점입니다. 특히, 공기와 같이 반응성이 높은 캐리어 가스를 사용하면 이 ‘자가 치유’ 과정을 가속화하여 최종 제품의 연신율과 같은 핵심 기계적 물성을 향상시킬 수 있습니다.

STI C&D는 최신 산업 연구 결과를 적용하여 고객이 더 높은 생산성과 품질을 달성할 수 있도록 지원하는 데 전념하고 있습니다. 본 논문에서 논의된 과제가 귀사의 운영 목표와 일치한다면, 저희 엔지니어링 팀에 연락하여 이러한 원칙을 귀사의 부품에 어떻게 구현할 수 있는지 논의해 보십시오.

(주)에스티아이씨앤디에서는 고객이 수치해석을 직접 수행하고 싶지만 경험이 없거나, 시간이 없어서 용역을 통해 수치해석 결과를 얻고자 하는 경우 전문 엔지니어를 통해 CFD consulting services를 제공합니다. 귀하께서 당면하고 있는 연구프로젝트를 최소의 비용으로, 최적의 해결방안을 찾을 수 있도록 지원합니다.

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Copyright Information

  • This content is a summary and analysis based on the paper “Consumption of Entrained Gases Within Bifilms During a Mg-Alloy Casting Process” by “TIAN LI, J.M.T. DAVIES, and DAN LUO”.
  • Source: https://doi.org/10.1007/s11663-021-02237-z

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Figure 4.3.5: W distributions at the moment when the elongation of the gauge section reaches the experimental rupture elongation: Comparison of the three mesh sizes l e = 1.00mm, l e = 0.50mmand l e = 0.25mm.

결정론적 해석을 넘어서: 고압 다이캐스팅 신뢰성을 위한 확률론적 파괴 모델링 가이드

이 기술 요약은 Octavian Knoll이 2015년 노르웨이 과학기술대학교(NTNU) 및 카를스루에 공과대학교(KIT)에서 발표한 박사 학위 논문 “A Probabilistic Approach in Failure Modelling of Aluminium High Pressure Die-Castings”을 기반으로 하며, STI C&D의 기술 전문가에 의해 분석 및 요약되었습니다.

키워드

  • 주요 키워드: 확률론적 파괴 모델링
  • 보조 키워드: 고압 다이캐스팅(HPDC), 알루미늄 합금, 주조 결함, 바이불 분포, 충돌 시뮬레이션, FEA, 구조 신뢰성, FLOW-3D

Executive Summary

  • 도전 과제: 고압 다이캐스팅(HPDC) 알루미늄 부품의 주조 결함으로 인해 발생하는 재료 연성의 불규칙한 편차는 기존의 결정론적 해석 방법으로는 정확하게 예측하기 어렵습니다.
  • 연구 방법: 실제 HPDC 부품에서 채취한 시편으로 광범위한 인장 시험을 수행하여 연성 변화를 정량화하고, 이를 Cockcroft-Latham 파괴 기준과 바이불(Weibull)의 최약 링크(weakest-link) 모델에 기반한 확률론적 파괴 모델 개발에 활용했습니다.
  • 핵심 돌파구: 개발된 확률론적 모델은 단일 유한요소(FE) 시뮬레이션만으로도 고가의 몬테카를로 시뮬레이션과 동일한 수준의 파괴 확률을 예측할 수 있으며, 실제 부품 테스트에서 관찰된 파괴 거동의 편차를 성공적으로 재현했습니다.
  • 핵심 결론: 이 연구는 제조 공정에서 발생하는 불확실성을 설계 단계에 직접 통합하여, 특히 자동차 충돌 안전성과 같은 고신뢰성이 요구되는 분야에서 HPDC 부품의 구조적 신뢰성을 획기적으로 향상시킬 수 있는 검증된 방법론을 제시합니다.
Figure 2.0.1: Examples of casting products made of metal, concrete and plastic.
Figure 2.0.1: Examples of casting products made of metal, concrete and plastic.

도전 과제: CFD 전문가에게 이 연구가 중요한 이유

자동차 산업을 필두로 경량화와 구조적 강성이 동시에 요구되는 분야에서 알루미늄 고압 다이캐스팅(HPDC) 부품의 사용이 증가하고 있습니다. HPDC 공법은 복잡한 형상의 부품을 일체형으로 생산할 수 있는 장점이 있지만, 공정 중 발생하는 수축공, 가스 기공, 산화막과 같은 주조 결함은 피할 수 없는 문제입니다. 이러한 결함들은 부품 내에서 불균일하게 분포하며, 특히 재료의 연성(ductility)에 큰 편차를 유발합니다.

기존의 유한요소해석(FEA)에서 사용되는 결정론적 파괴 모델은 단일한 평균 물성치를 사용하기 때문에, 이러한 연성의 통계적 분포, 즉 ‘편차(scatter)’를 고려하지 못합니다. 이는 충돌 상황과 같이 극한 하중을 받는 안전 필수 부품의 파괴 시점과 거동을 예측하는 데 있어 심각한 불확실성을 야기합니다. 엔지니어들은 실제 테스트 결과와 시뮬레이션 예측 사이의 괴리로 인해 과도하게 보수적인 설계를 하거나, 값비싼 물리적 프로토타입 테스트를 반복해야 하는 문제에 직면합니다. 이 연구는 바로 이 지점, 즉 제조 공정의 불확실성을 어떻게 신뢰성 있는 수치 모델에 통합할 것인가라는 산업계의 오랜 난제를 해결하기 위해 시작되었습니다.

연구 접근법: 방법론 분석

본 연구는 주조 결함이 HPDC 부품의 파괴 거동에 미치는 영향을 실험적으로 규명하고, 이를 바탕으로 신뢰성 있는 수치 모델을 개발하기 위해 실험과 시뮬레이션을 병행하는 접근법을 채택했습니다.

1. 실험적 특성 분석: 연구진은 실제 자동차 후방 구조물에 사용되는 것과 유사한 U자형 HPDC 부품(Castasil-37 알루미늄 합금, F 조건)을 대상으로 광범위한 재료 특성 분석을 수행했습니다. 특히, 주조 시스템(게이트 측 vs. 진공 측)에 따른 전역적이고 체계적인 연성 변화와 공정 변동에 따른 국부적인 무작위 연성 변화를 모두 파악하기 위해, 여러 개의 동일한 부품에서, 그리고 각 부품의 서로 다른 위치(게이트 측, 중간 웹, 진공 측)에서 인장 시편을 채취했습니다. 이 시편들을 대상으로 단축 인장 시험을 수행하여 파괴 시까지의 응력-변형률 곡선을 확보하고, Cockcroft-Latham 파괴 기준의 임계값(Wc)을 측정하여 재료 연성의 통계적 분포를 정량화했습니다.

2. 확률론적 수치 모델 개발: 실험적으로 확인된 재료 연성의 무작위 편차를 모델링하기 위해, 연구진은 ‘최약 링크(weakest-link)’ 이론과 바이불(Weibull) 분포를 결합한 확률론적 파괴 모델을 개발했습니다. 이 모델은 재료 내에서 가장 취약한 결함이 전체 파괴를 유발한다는 개념에 기반합니다. 개발된 모델은 상용 유한요소 해석 소프트웨어인 LS-DYNA에 사용자 정의 재료 루틴(User-defined Material Routine, MR#1 ~ MR#4) 형태로 구현되었습니다.

  • MR#1: 단일 시뮬레이션 내에서 각 요소의 생존 확률을 곱하여 전체 구조물의 파괴 확률을 직접 계산하는 새로운 접근법입니다.
  • MR#2: 각 요소에 바이불 분포에 따라 무작위로 파괴 임계값을 할당하고, 다수의 반복 시뮬레이션(몬테카를로 시뮬레이션)을 통해 파괴 확률을 추정하는 전통적인 접근법입니다.
  • MR#3 & MR#4: 해석용 유한요소(FE) 메쉬와 재료 물성 분포용 가상 메쉬(MS Mesh)를 분리하는 ‘비연계 모델링(uncoupled modelling)’ 접근법으로, 메쉬 의존성 문제를 해결하기 위해 도입되었습니다.

핵심 돌파구: 주요 발견 및 데이터

발견 1: 실험적 편차를 정확히 재현하는 확률론적 모델의 검증

이 연구의 가장 중요한 성과는 개발된 확률론적 파괴 모델이 실제 부품 테스트에서 관찰된 파괴 거동의 편차를 매우 정확하게 예측했다는 점입니다. 연구진은 U자형 부품의 3점 굽힘 테스트 결과를 시뮬레이션과 비교했습니다.

결정론적 모델과 달리, 확률론적 모델(MR#2)을 사용한 몬테카를로 시뮬레이션은 실험 결과와 마찬가지로 파괴가 시작되는 변위가 시뮬레이션마다 다르게 나타났습니다. 더 놀라운 점은, 단 한 번의 시뮬레이션으로 파괴 확률을 직접 계산하는 새로운 접근법(MR#1)이 수십 번의 시뮬레이션이 필요한 몬테카를로 방법과 거의 동일한 파괴 확률 곡선을 예측했다는 것입니다(논문 Figure 10.2.5 참조). 이는 계산 비용을 획기적으로 줄이면서도 통계적 신뢰성을 확보할 수 있는 강력한 방법론임을 입증합니다.

발견 2: 메쉬 의존성 문제 해결을 위한 ‘비연계 모델링’ 접근법 제시

확률론적 모델링의 고질적인 문제 중 하나는 해석에 사용되는 유한요소 메쉬의 크기에 따라 결과가 달라지는 ‘메쉬 의존성’입니다. 메쉬가 미세해질수록 더 작은 체적을 가진 요소가 많아지고, 최약 링크 이론에 따라 극단적인(매우 낮은) 파괴 임계값을 가질 확률이 높아져 수렴된 결과를 얻기 어렵습니다.

본 연구에서는 이 문제를 해결하기 위해 재료 물성 분포를 정의하는 가상 메쉬(MS Mesh)와 구조 해석을 수행하는 유한요소 메쉬(FE Mesh)를 분리하는 ‘비연계 모델링’ 접근법(MR#3)을 제시했습니다. 이 방법을 사용하자, FE 메쉬 크기를 변경해도 일관된 파괴 개시 거동을 예측할 수 있었고, 성공적으로 메쉬 수렴성을 확보했습니다(논문 Figure 10.1.8 참조). 이는 확률론적 모델의 강건성과 신뢰성을 크게 향상시키는 중요한 진전입니다.

Figure 4.3.5: W distributions at the moment when the elongation of the gauge section reaches the experimental rupture elongation: Comparison of the three mesh sizes l e = 1.00mm, l e = 0.50mmand l e = 0.25mm.
Figure 4.3.5: W distributions at the moment when the elongation of the gauge section reaches the experimental rupture elongation: Comparison of the three mesh sizes l e = 1.00mm, l e = 0.50mmand l e = 0.25mm.

R&D 및 운영을 위한 실질적 시사점

  • 공정 엔지니어: 본 연구는 주조 시스템(게이트 및 진공 채널의 위치)이 부품의 연성 분포에 체계적인 영향을 미친다는 것을 명확히 보여줍니다. FLOW-3D와 같은 주조 시뮬레이션 결과를 활용하여 공기 혼입 시간(Air Contact Time)과 같은 지표를 분석하고, 이를 통해 재료 품질을 예측하여 게이팅 시스템을 최적화하는 데 중요한 단서를 제공합니다.
  • 품질 관리팀: 논문의 데이터는 특정 부위(예: 진공 측)에서 파괴 연성의 편차가 더 크게 나타날 수 있음을 시사합니다. 이는 해당 부위에 대한 품질 검사 기준을 강화하거나, 통계적 공정 관리(SPC) 기법을 도입하여 제조 공정의 안정성을 모니터링해야 할 필요성을 제기합니다.
  • 설계 엔지니어: 이 연구에서 검증된 확률론적 파괴 모델을 사용하면, 설계 초기 단계부터 제조 편차를 고려한 신뢰성 기반 설계를 수행할 수 있습니다. 특정 부위의 파괴 확률을 정량적으로 평가하고, 목표 신뢰도를 만족시키기 위해 리브 보강이나 두께 조절과 같은 설계 변경을 효과적으로 수행할 수 있습니다.

논문 상세 정보

A Probabilistic Approach in Failure Modelling of Aluminium High Pressure Die-Castings

1. 개요:

  • 제목: A Probabilistic Approach in Failure Modelling of Aluminium High Pressure Die-Castings (알루미늄 고압 다이캐스팅의 파괴 모델링에 대한 확률론적 접근)
  • 저자: Octavian Knoll
  • 발행 연도: 2015
  • 학술지/학회: PhD Thesis, Norwegian University of Science and Technology / Karlsruhe Institute of Technology
  • 키워드: Probabilistic failure modelling, High-pressure die-casting (HPDC), Aluminium alloys, Casting defects, Weibull distribution, Crash simulation, FEA, Structural reliability

2. 초록:

알루미늄 고압 다이캐스팅은 최근 몇 년간 현대 자동차 차체의 필수 요소가 되었습니다. 고압 다이캐스팅 방법은 복잡한 기하학적 구조의 얇은 벽 부품을 생산할 수 있게 해줍니다. 이 장점은 구조적 노드와 커넥터 요소를 일체형 부품으로 만드는 데 사용됩니다. 이러한 부품들은 충돌 상황과 같은 극한 하중을 받으며 차체의 구조적 무결성을 유지해야 합니다. 알루미늄 고압 다이캐스팅 부품의 구조적 거동을 분석하고 구조적 신뢰성을 보장하기 위해서는 수치 모델이 필요합니다.

알루미늄 고압 다이캐스팅 부품의 재료 연성은 주조 결함에 의해 크게 영향을 받습니다. 일반적인 주조 결함으로는 수축공, 가스 기공, 산화막 등이 있습니다. 이러한 주조 결함은 주조 시스템과 주조 과정 중의 변동으로 인해 발생합니다. 결과적으로 주조 결함은 부품 내에서 다양하게 나타납니다. 더 나아가, 이 변화는 주조 시스템에 따른 전역적 체계적 변화와 공정 변동으로 인한 국부적 유사-무작위 변화로 구분될 수 있습니다. 주조 결함은 국부적인 재료 연성을 감소시키는 초기 재료 손상으로 간주될 수 있습니다. 결과적으로 재료 연성은 전역적 체계적 변화와 국부적 유사-무작위 변화를 보입니다. 본 연구의 주요 목적은 이 두 가지 유형의 변화에 대한 실험적 및 수치적 분석입니다.

실험 연구의 주요 목적은 알루미늄 HPDC 합금의 재료 연성에서 전역적 체계적 변화와 국부적 유사-무작위 변화를 조사하는 것이었습니다. 여기서는 주조 상태의 AlSi9Mn 합금으로 만들어진 일반 고압 다이캐스팅 부품을 고려했습니다. 단축 인장 시험을 사용하여 광범위한 재료 특성 분석을 수행했습니다. 시편은 일반 주조 부품의 다른 추출 위치뿐만 아니라 복제된 추출 위치에서도 가공되었습니다. 이 샘플링 접근법을 통해 체계적 변화와 국부적 유사-무작위 변화를 분석할 수 있었습니다. 인장 시험 결과의 기계적 분석은 복제된 추출 위치에서 재현 가능한 변형 경화 거동을 보였지만, 파괴 변형률은 다른 추출 위치와 복제된 위치 내에서 다양했습니다. 인장 시험 결과에 대한 상세한 통계 분석이 수행되었고, 가설 검정을 적용하여 비슷한 재료 연성을 가진 추출 위치를 식별했습니다. 가설 검정에서 얻은 결과를 바탕으로, 일반 주조 부품을 비슷한 재료 연성을 가진 특징적인 부분으로 분리할 수 있다고 결론지었습니다. 또한, 재료 연성의 국부적 유사-무작위 변화는 최약 링크 바이불 분포로 설명될 수 있음을 보였습니다. 추가적으로, 선택된 시편의 파단면을 SEM 분석으로 검사했으며, 예상대로 각 파단면에서 주조 결함이 발견되었고 파괴의 지배적인 요인으로 확인되었습니다. 재료 시험 외에도, 일반 주조 부품에 대한 굽힘 시험과 축 방향 압축 시험이 수행되었습니다. 특히, 굽힘 시험에서 얻은 실험 결과는 강한 편차를 보였습니다.

결과적으로, 수치 연구에서는 파괴 모델링에 확률론적 접근법을 고려했습니다. 이를 통해 재료 연성의 국부적 유사-무작위 변화를 포착할 수 있었습니다. 확률론적 파괴 모델은 현상학적 Cockcroft-Latham 파괴 기준과 바이불의 최약 링크 모델을 기반으로 했습니다. 필요한 양인 응력 상태와 등가 소성 변형률은 등방성 저탄성-소성 구성 모델에 의해 제공되었습니다. 주조 부품의 파괴 확률에 대한 수치적 예측에 초점을 맞췄습니다. 일반적으로 파괴 확률은 유사-무작위로 분포된 임계 파괴 값을 사용하는 다양한 유한 요소 시뮬레이션에 기반한 몬테카를로 시뮬레이션에서 추정됩니다. 본 연구에서는 단일 유한 요소 시뮬레이션에서 파괴 확률을 예측하는 접근법을 제시했습니다. 두 접근법을 수치 분석에서 비교했으며, 두 접근법이 동일한 파괴 확률 예측으로 이어진다는 것을 보였습니다. 파괴 확률의 직접 계산에 기반한 접근법은 굽힘 시험과 일반 주조 부품의 축 방향 압축 시험의 유한 요소 시뮬레이션에 적용되었습니다. 재료 특성 분석에 따라, 일반 주조 부품의 FE 모델은 세 부분으로 분할되었습니다. 각 부분에 대해 구성 모델과 확률론적 파괴 모델의 매개변수는 해당 실험 결과에서 찾았습니다. 두 하중 사례 모두에서 수치적으로 예측된 파괴 확률과 실험적으로 추정된 파괴 확률이 매우 잘 상관관계가 있음이 입증되었습니다. 결과적으로, 적용된 확률론적 파괴 모델은 검증된 것으로 간주되었습니다. 또한, 임계 파괴 값의 유사-무작위 분포에 대한 새로운 접근법이 제시되었고 비연계 모델링 접근법의 개념이 도입되었습니다. 비연계 모델링 접근법 덕분에, 유사-무작위로 분포된 임계 파괴 값을 사용하는 유한 요소 모델에 대한 메쉬 수렴 연구를 수행할 수 있었습니다. 그러나 확률론적 파괴 모델은 재료 연성의 국부적 유사-무작위 변화만을 포착했습니다. 따라서, 주조 시뮬레이션 결과와 주조 품질 정의를 기반으로 한 сквозной(through-process) 모델링 접근법이 제시되었습니다. 이 접근법은 단지 수치적으로만 조사되었습니다.

3. 서론:

현대 자동차 차체의 경량 설계는 무게 감소와 구조적 강성 및 충돌 안전성 증가로 특징지어집니다. 이러한 요구 사항은 구조 부품에 고장력강, 알루미늄 합금, 섬유 강화 플라스틱을 사용하여 충족됩니다. 구조적 거동은 부품 형상과 적용된 재료에 의해 정의됩니다. 또한, 적용된 재료의 특성은 대부분 제조 공정에 의해 영향을 받습니다. 특히, 알루미늄 고압 다이캐스팅은 차체 설계의 필수 요소가 되었습니다. 고압 다이캐스팅 방법은 복잡한 형상의 얇은 벽 알루미늄 부품을 생산할 수 있게 해줍니다. 이 장점은 성능 최적화 및 다기능 부품을 설계하는 데 사용됩니다. 따라서 알루미늄 고압 다이캐스팅 부품은 주로 높은 힘이 국부적으로 도입되고 다양한 부품을 연결해야 하는 구조적 노드 및 커넥터 요소로 사용됩니다. 그러나 재료 연성은 고압 다이캐스팅 공정으로 인해 발생하는 주조 결함에 의해 지배됩니다. 주조 결함의 결과로, 재료 연성은 부품 내에서 심하게 변동합니다. 이 변화는 특히 충돌 설계에서 고려되어야 합니다. 여기서 충돌 설계를 분석하는 가장 일반적인 도구는 유한요소법입니다. 다양한 하중 시나리오에 노출된 구조물의 변형 및 파괴 거동은 유한요소법을 사용하여 수치적으로 예측할 수 있습니다. 알루미늄 고압 다이캐스팅 부품의 신뢰할 수 있는 수치 설계를 위해서는 주조 결함으로 인한 재료 연성의 변화를 고려해야 합니다. 이 요구 사항이 본 연구의 전반적인 목표입니다.

4. 연구 요약:

연구 주제의 배경:

알루미늄 고압 다이캐스팅(HPDC) 부품은 자동차 산업에서 경량화와 복잡한 형상 구현을 위해 필수적으로 사용되고 있습니다. 특히 충돌 안전성과 직결된 구조 부품으로 사용될 때, 이 부품들의 파괴 거동을 정확히 예측하는 것은 매우 중요합니다. 하지만 HPDC 공정의 특성상 발생하는 기공, 산화막 등의 내부 결함은 재료의 기계적 특성, 특히 연성에 큰 편차를 유발합니다. 이는 동일한 공정으로 생산된 부품이라도 위치에 따라, 혹은 부품마다 다른 파괴 거동을 보이는 원인이 됩니다.

이전 연구 현황:

기존의 연구들은 대부분 결정론적(deterministic) 관점에서 HPDC 부품의 파괴를 모델링했습니다. 즉, 여러 번의 실험에서 얻은 물성치의 평균값을 사용하여 단일한 파괴 기준을 정의했습니다. 이러한 접근법은 실험 결과에서 나타나는 상당한 편차(scatter)를 설명하지 못하며, 구조물의 신뢰성을 평가하는 데 한계가 있었습니다. 일부 연구에서 확률론적 접근법이 시도되었지만, 실험 데이터에 기반한 체계적인 검증이나, 전역적/국부적 변동성을 분리하여 분석하고 이를 수치 모델에 통합하려는 시도는 부족했습니다.

연구 목적:

본 연구의 핵심 목적은 HPDC 알루미늄 합금의 파괴 거동에 내재된 불확실성을 정량적으로 분석하고, 이를 예측할 수 있는 신뢰성 있는 확률론적 파괴 모델을 개발 및 검증하는 것입니다. 구체적으로 다음 두 가지 변동성을 규명하고 모델링하고자 했습니다. 1. 전역적 체계적 변동성(Global Systematic Variation): 주조 방안(게이팅 시스템, 진공 시스템 등)에 따라 부품의 위치별로 체계적으로 나타나는 연성 차이. 2. 국부적 유사-무작위 변동성(Local Pseudo-random Variation): 동일한 위치에서도 공정의 미세한 변동으로 인해 무작위적으로 발생하는 연성 편차.

핵심 연구:

본 연구는 실험과 수치 해석의 두 축으로 진행되었습니다. – 실험 연구: 실제 주조 부품(U-profile, Castasil-37 합금)의 여러 위치에서 다수의 인장 시편을 채취하여 재료 연성의 전역적, 국부적 변동성을 통계적으로 분석했습니다. 또한, 실제 부품 단위의 굽힘 및 압축 시험을 통해 구조적 거동의 편차를 확인했습니다. – 수치 연구: 실험 결과를 바탕으로, Cockcroft-Latham 파괴 기준과 바이불(Weibull)의 최약 링크 이론을 결합한 확률론적 파괴 모델을 개발했습니다. 이 모델을 유한요소 해석 코드에 사용자 정의 재료 루틴(MR#1 ~ MR#4)으로 구현하고, 단일 시뮬레이션을 통한 파괴 확률 예측, 몬테카를로 시뮬레이션, 메쉬 의존성 해결을 위한 비연계 모델링 기법 등 다양한 수치적 기법을 탐구하고 검증했습니다. 최종적으로 개발된 모델이 실제 부품 시험에서 나타난 파괴 확률을 얼마나 정확하게 예측하는지 검증했습니다.

5. 연구 방법론

연구 설계:

본 연구는 실험적 재료 특성 분석과 이를 기반으로 한 수치 모델 개발 및 검증이라는 연계적 구조로 설계되었습니다. 먼저, 실제 HPDC 부품의 기계적 거동, 특히 연성의 통계적 분포를 파악하기 위한 광범위한 실험을 수행했습니다. 이후, 실험에서 얻은 데이터를 사용하여 확률론적 파괴 모델의 매개변수를 식별하고, 이 모델을 유한요소(FE) 시뮬레이션에 적용했습니다. 마지막으로, FE 시뮬레이션 결과를 별도의 부품 단위 실험 결과와 비교하여 개발된 모델의 예측 정확성과 신뢰성을 검증했습니다.

데이터 수집 및 분석 방법:

  • 데이터 수집:
    • 재료 특성 시험: AlSi9Mn(Castasil-37) 합금으로 제작된 U자형 HPDC 부품의 여러 위치(게이트 측, 중간 웹, 진공 측)에서 다수의 표준 인장 시편(UT80, UT75, UT117)을 채취했습니다. 유압식 만능시험기를 사용하여 단축 인장 시험을 수행하고, 각 시편의 응력-변형률 곡선, 파괴 변형률, Cockcroft-Latham 파괴 인자(Wc) 등을 측정했습니다.
    • 부품 단위 시험: 전체 U자형 부품을 대상으로 3점 굽힘 시험과 축 방향 압축 시험을 반복적으로 수행하여 하중-변위 곡선과 파괴 개시 지점을 기록했습니다.
    • 결함 분석: CT 스캐닝과 주사전자현미경(SEM)을 사용하여 파단면의 주조 결함(기공, 산화막 등)을 관찰하고 정성적으로 분석했습니다.
  • 데이터 분석:
    • 기계적 분석: 측정된 하중-변위 곡선으로부터 공칭 응력-변형률, 진응력-변형률, 경화 곡선 등을 계산했습니다.
    • 통계적 분석: 각 추출 위치별로 수집된 파괴 인자(Wc) 데이터에 대해 기술 통계(평균, 표준편차) 및 추론 통계(가설 검정: t-test, F-test, ANOVA, Kruskal-Wallis test)를 적용하여 위치 간의 유의미한 차이를 분석했습니다. 앤더슨-달링(Anderson-Darling) 적합도 검정을 사용하여 데이터가 특정 확률 분포(정규분포, 바이불 분포)를 따르는지 평가했습니다.

연구 주제 및 범위:

  • 연구 주제: 알루미늄 고압 다이캐스팅 부품의 파괴 거동에 대한 확률론적 모델링.
  • 연구 범위:
    • 재료: 주조 상태(F)의 AlSi9Mn(Castasil-37) 합금에 국한됩니다.
    • 하중 조건: 준정적(quasi-static) 하중 조건에서의 단축 인장, 굽힘, 압축을 다룹니다.
    • 모델링: 현상학적 파괴 모델인 Cockcroft-Latham 기준과 바이불의 최약 링크 이론에 기반한 확률론적 모델 개발에 중점을 둡니다. 구성 모델은 등방성 저탄성-소성 모델을 사용하며, 손상 진화가 구성 방정식에 미치는 영향(연계 해석)은 고려하지 않습니다.
    • 수치 해석: 상용 외연적 유한요소 해석 코드(LS-DYNA)를 기반으로 사용자 정의 재료 루틴을 구현하고 검증합니다.

6. 주요 결과:

주요 결과:

  • 실험 결과, HPDC 부품의 재료 연성은 주조 시스템에 따른 전역적/체계적 변동(게이트 측이 진공 측보다 연성이 높음)과 동일 위치 내에서의 국부적/유사-무작위 변동을 동시에 보였습니다.
  • 국부적 연성 편차는 최약 링크 이론에 기반한 바이불(Weibull) 분포로 잘 설명될 수 있음을 통계적으로 확인했습니다.
  • 단일 FE 시뮬레이션으로 파괴 확률을 직접 계산하는 방법(MR#1)이 다수의 시뮬레이션이 필요한 몬테카를로 방법(MR#2)과 동일한 수준의 파괴 확률 예측 결과를 제공함을 입증하여, 계산 효율성을 획기적으로 개선할 수 있는 가능성을 제시했습니다.
  • 재료 물성 메쉬(MS mesh)와 해석용 FE 메쉬를 분리하는 비연계 모델링(uncoupled modeling) 접근법(MR#3, MR#4)을 통해, 확률론적 모델의 고질적인 문제였던 메쉬 의존성을 해결하고 수렴된 파괴 해석 결과를 얻을 수 있었습니다.
  • 개발된 확률론적 파괴 모델(MR#1)을 실제 U-프로파일 부품의 굽힘 및 압축 시험 시뮬레이션에 적용한 결과, 실험에서 측정된 파괴 확률 분포와 매우 높은 상관관계를 보여 모델의 예측 정확성과 신뢰성을 검증했습니다.

Figure List:

  • Figure 1.1.1: Application of two high pressure die-casting components made of the aluminium alloy Castasil-37 in the car body of the current Audi A8 (third generation (D4), production 2010 – present).
  • Figure 2.0.1: Examples of casting products made of metal, concrete and plastic.
  • Figure 2.1.1: Aluminium HPDC gearbox of a KTM motorcycle, see Aluminium Rheinfelden GmbH [6].
  • Figure 2.1.2: Exemplary drawing of cold chamber HPDC machine with vacuum assembly and piston pressure during HPDC process.
  • Figure 2.1.3: Result of an HPDC simulation preformed with MAGMAsoft, see Kleeberg [66].
  • Figure 2.2.1: Characteristic phase diagrams of an Al-Si alloy and an Al-Mg alloy, see Bargel and Schulze [9].
  • Figure 2.2.2: Microstructure of an HPDC Al-Si-Mg alloy, see Dørum et al. [33].
  • Figure 2.3.1: Microstructure of an aluminium HPDC alloy (AlSi9Mg) containing casting defects, see Teng et al. [106].
  • Figure 2.4.1: Car body of the current Audi A8 (third generation (D4), production 2010 – present): Application of aluminium sheets (green), aluminium extrusions (blue) and aluminium die-castings (red).
  • Figure 3.2.1: Two events A and B taken from the sample space Ω.
  • Figure 3.2.2: Bayes’ theorem.
  • Figure 3.3.1: Probability Density Function (PDF) and Cumulative Distribution Function (CDF) of a discrete and a continuous random variable.
  • Figure 3.3.2: Mathematical expectations and statistical measurements.
  • Figure 3.3.3: Examples of uniform PDFs and CDFs (A = 1; B = 2, 4, 6).
  • Figure 3.3.4: Examples of normal PDFs and CDFs (µ = 0;σ = 0.5, 1, 2).
  • Figure 3.3.5: Bivariate normal distributions (σX1X2 = {0, 0.8,−0.8}).
  • Figure 3.3.6: Examples of Weibull PDFs and CDFs (m = 0.5, 1, 2, 4;λ = 4).
  • Figure 3.3.7: Comparison of uniform, normal and Weibull distribution with equal mean and standard deviation (µ = 3.6,σ = 1.0).
  • Figure 3.3.8: Inverse transformation technique.
  • Figure 3.3.9: Influence of Gaussian correlation length d0 on samples of 1D Gaussian random fields.
  • Figure 3.3.10: Influence of Gaussian correlation length d0 on samples of 2D Gaussian random fields.
  • Figure 3.5.1: Graphical representation of sample X and sample Y.
  • Figure 3.5.2: Details of a box-plot.
  • Figure 3.5.3: Distribution estimation of sample X and sample Y.
  • Figure 3.6.1: Illustration of the (1 − α) · 100% confidence interval and the t-distribution.
  • Figure 3.6.2: Estimated normal distribution and Weibull distribution of sample X and sample Y.
  • Figure 4.1.1: Deformation measurements of a solid body.
  • Figure 4.1.2: Illustration of a solid body subjected to of external loads and the Cauchy theorem.
  • Figure 4.1.3: High-exponent yield surface in plane stress and two-terms Voce rule.
  • Figure 4.1.4: Isotropic hypoelastic-plastic material model for metals assuming isothermal conditions.
  • Figure 4.1.5: FEM applied on a structural problem.
  • Figure 4.1.6: Deformation of a four node element.
  • Figure 4.1.7: Discretisation of time t.
  • Figure 4.1.8: Flow chart of the explicit time integration algorithm using the central differences method in the form proposed by Verlet [110].
  • Figure 4.2.1: Characteristic stress-strain curves for brittle, quasi-brittle and ductile materials.
  • Figure 4.2.2: Schematic representation of the fracture mechanisms in brittle and ductile materials.
  • Figure 4.2.3: Stress distribution prior to fracture in a tensile test specimen.
  • Figure 4.3.1: Typical specimen geometries for mechanical material tests.
  • Figure 4.3.2: Schematic representation of the homogenisation procedure.
  • Figure 4.3.3: Uniaxial tensile test: Tensile test set-up and experimental force-elongation curves obtained from the ductile and the quasi-brittle specimen.
  • Figure 4.3.4: Numerical and experimental force-elongation curves: Comparison of the three mesh sizes le = 1.00mm, le = 0.50mm and le = 0.25mm.
  • Figure 4.3.5: W distributions at the moment when the elongation of the gauge section reaches the experimental rupture elongation: Comparison of the three mesh sizes le = 1.00mm, le = 0.50mm and le = 0.25mm.
  • Figure 4.3.6: Influence of mesh size le on critical value Wc and averaged critical value Wc in an experimental-numerical approach.
  • Figure 5.1.1: Failure probability PΛF = 1 − e−cl plotted as function of segment length l for varying weakest-link densities c.
  • Figure 5.1.2: Failure probability PVF = 1 − e−c(f)V plotted as function of material volume V with a constant value of density function c(f).
  • Figure 5.1.3: Failure probability by Weibull plotted as function of uniform loading f for either varying Weibull modulus m or varying volume relation V/V0.
  • Figure 5.1.4: Failure probability according to the approach by Unosson et al. [108] plotted as function of loading f.
  • Figure 5.1.5: Weibull plots including a Weibull curve obtained from a small gauge volume (red) and a Weibull curve obtained from a large gauge volume (blue).
  • Figure 5.1.6: Gauge parts under different loading conditions with equal gauge volumes (VT = VC = VS = VPT).
  • Figure 5.2.1: Randomly distributed failure parameters: The failure parameters are uniformly distributed within the FE mesh.
  • Figure 5.2.2: Range of the middle 95% of a Weibull distributed population.
  • Figure 5.2.3: Randomly distributed failure parameters: The failure parameters are uniformly distributed within the MS mesh, then the MS mesh is discretised into a FE mesh.
  • Figure 5.2.4: Randomly distributed failure parameters: The failure parameters are distributed within the MS mesh according to a uniform random field, then the MS mesh is discretised into a FE mesh.
  • Figure 7.1.1: Images of the aluminium HPDC component U900-1.
  • Figure 7.2.1: Three-point bending test set-up: Technical drawing and images of the test set-up.
  • Figure 7.2.2: Deformed and fractured U900-1 component subjected to three-point bending.
  • Figure 7.2.3: Experimental results obtained from seven parallel three-point bending tests (measured by the testing machine).
  • Figure 7.2.4: Experimental results obtained from six parallel three-point bending tests: Force and displacement measured by testing machine and relative displacements measured by extensometers on gating side and vacuum side.
  • Figure 7.2.5: Drawing of the punch rotation during three-point testing.
  • Figure 7.3.1: Axial compression test set-up: Cutting pattern, technical drawing and image of the test set-up.
  • Figure 7.3.2: Deformed and fractured modified U900-1 component subjected to axial compression.
  • Figure 7.3.3: Experimental force-displacement curves obtained from four parallel axial compression tests (measured by the testing machine).
  • Figure 7.3.4: Experimental results obtained from four parallel axial compression tests: Force and displacement measured by the testing machine and relative displacement measured by the extensometer.
  • Figure 7.3.5: Drawing of the loading plate rotation during axial compression testing.
  • Figure 8.1.1: Technical drawing and image of the applied uniaxial tensile test set-up.
  • Figure 8.1.2: Definition of U900-1 component parts (unfolded geometry).
  • Figure 8.1.3: Mechanical analysis of the result obtained from a uniaxial tensile test.
  • Figure 8.1.4: Mechanical analysis of the result obtained from a uniaxial tensile test.
  • Figure 8.1.5: Approach of statistical hypothesis testing of k samples Xi at a significance level of α = 0.05 using MATLAB [84].
  • Figure 8.2.1: Uniaxial tensile test specimen UT80 (t = 2.5mm).
  • Figure 8.2.2: Engineering stress-strain curves obtained from UT80 specimens machined from an U900-1 component (component #1).
  • Figure 8.2.3: Engineering stress-strain curves obtained from UT80 specimens machined from five U900-1 components presented according to the extraction position.
  • Figure 8.2.4: Averages and COVs of the measured mechanical quantities obtained from UT80 specimens machined from five U900-1 components.
  • Figure 8.2.5: Engineering stress-strain curves obtained from the most ductile specimen and the least ductile specimen and scatter plots of the measured mechanical quantities obtained from UT80 specimens machined from five U900-1 components.
  • Figure 8.2.6: Images of fractured UT80 specimens machined from the fifteen extraction positions of the U900-1 component.
  • Figure 8.2.7: Identification of casting defects in form of porosity using CT scanning of the middle section of three U900-1 components.
  • Figure 8.2.8: Identification of casting defects in form of shrinkage pores, initial cracks and other microstructural irregularities using SEM of fractured UT80 specimens machined from U900-1 components.
  • Figure 8.3.1: Uniaxial tensile test specimen UT75 and uniaxial tensile test specimen UT117.
  • Figure 8.3.2: Engineering stress-strain curves obtained from UT75 and UT117 specimens machined from six U900-1 components presented according to extraction positions.
  • Figure 8.3.3: Average and COVs of the measured mechanical quantities obtained from UT75 and UT117 specimens machined from six U900-1 components.
  • Figure 8.3.4: Scatter plots of the measured mechanical quantities obtained from UT75 and UT117 specimens machined from six U900-1 components.
  • Figure 8.3.5: Measured fracture strain Af obtained from UT75 and UT117 specimens machined from six U900-1 components plotted according to extraction positions in longitudinal direction.
  • Figure 8.3.6: Scatter plots of the measured fracture strain Af obtained from UT75 and UT117 specimens machined from six U900-1 components.
  • Figure 8.3.7: Three fractured UT117 specimens machined from part BF of U900-1 components.
  • Figure 8.3.8: Probability plot of the samples based on measurements of Wc obtained from UT75 and UT117 specimens machined from part OW of six U900-1 components and extendedly fitted Weibull probability function using a considered volume of V = VUT75 and V = VUT117 (m = 5.4829, Wc0 = 0.0206kN/mm2, V0 = 1000.0mm3).
  • Figure 9.3.1: Fortran 95 code of subroutine init_random_seed(t) taken from the course “FORTRAN Programming for Engineers” by D. Hogan [94].
  • Figure 9.4.1: Creation of the MS mesh based on the dimensions of the FE mesh and mapping of the MS mesh onto the FE mesh.
  • Figure 10.1.1: FE model of the uniaxial tensile test using a UT80 specimen.
  • Figure 10.1.2: Fitted two-terms Voce rule based on experimental hardening curves obtained from UT80 specimens machined from part OW.
  • Figure 10.1.3: Comparison of predicted engineering stress-strain curve using material routine MR#1 (red) and experimental engineering stress-strain curves (grey) as well as comparison of predicted failure probability using material routine MR#1 (blue) and experimental failure probability (blue triangles).
  • Figure 10.1.4: Predicted engineering stress-strain curves using material routine MR#2 (red) and comparison of predicted failure probability using material routine MR#1 (blue) and predicted failure probability using material routine MR#2 (blue triangles).
  • Figure 10.1.5: Five deformed and fractured UT80 specimens obtained from FE simulations using material routine MR#2 including the pseudo-random distributions of critical value Wc (le = 1.00mm).
  • Figure 10.1.6: Mesh convergence study of the FE model of the uniaxial tensile test using material routine MR#2 (le = {1.00mm, 0.50mm, 0.25mm, 0.125mm}).
  • Figure 10.1.7: Uncoupled modelling approach applied on the FE model of the UT80 specimen using material routine MR#3 and material routine MR#4.
  • Figure 10.1.8: Mesh convergence study of the FE model of the uniaxial tensile test using material routine MR#3 (le = {1.00mm, 0.50mm, 0.25mm, 0.125mm}).
  • Figure 10.1.9: Mesh convergence study of the FE model of the uniaxial tensile test using material routine MR#4 (le = {1.00mm, 0.50mm, 0.25mm, 0.125mm}).
  • Figure 10.2.1: Image of the three-point bending test set-up and experimental results.
  • Figure 10.2.2: FE model of the U-profile subjected to three-point bending.
  • Figure 10.2.3: Numerical results obtained from a single simulation of the U-profile subjected to three-point bending using material routine MR#1 (le = 3.00mm).
  • Figure 10.2.4: Numerical results obtained from a single simulation of the U-profile subjected to three-point bending using material routine MR#2 (le = 3.00mm).
  • Figure 10.2.5: Comparison of the numerical results obtained from simulations of the U-profile subjected to three-point bending using material routines MR#1 and MR#2 (le = 3.00mm).
  • Figure 10.2.6: Mesh sensitivity analysis of the FE model of the U-profile subjected to three-point bending using material routine MR#3: Predicted force-displacement curves (le = {3.00mm, 1.50mm, 0.75mm, 0.38mm}).
  • Figure 10.2.7: Mesh convergence study of the FE model of the U-profile subjected to three-point bending using material routine MR#3: Prediction of fracture initiation in the vacuum side (le = {3.00mm, 1.50mm, 0.75mm, 0.38mm}).
  • Figure 10.2.8: Through-process modelling approach applied on the FE model of the U-profile (le = 3.00mm).
  • Figure 10.2.9: Comparison of numerical results obtained from simulations (material routine MR#1) of the U-profile subjected to three-point bending without mapping and with mapping (le = 3.00mm).
  • Figure 10.3.1: Discretisation of the cross-section of the U900-1 component using a solid mesh (le ≤ 1.0mm), a shell mesh (le ≤ 8.0mm) and a hybrid mesh (le ≤ 5.0mm).
  • Figure 10.3.2: FE model of the small ejector dome applied for eigenfrequency analysis and numerical results of the first bending eigenfrequency ωB1 and the first torsional eigenfrequency ωT1 (solid mesh).
  • Figure 10.3.3: Part definition of the U900-1 component: Gating side (blue), intermediate part (red) and vacuum side (green).
  • Figure 10.3.4: Fitted two-terms Voce rules based on experimental hardening curves obtained from UT75 specimens machined from gating side (IW), intermediate part (BF) and vacuum side (OW).
  • Figure 10.3.5: Numerical model of the three-point bending test set-up.
  • Figure 10.3.6: Comparison of experimental results and numerical results obtained from solid mesh, shell mesh and hybrid mesh (U900-1 component subjected to three-point bending).
  • Figure 10.3.7: Numerical prediction of the cross-section deformation of the U900-1 component subjected to three-point bending using solid modelling, shell modelling and hybrid modelling.
  • Figure 10.3.8: Numerical modelling of the axial compression test set-up.
  • Figure 10.3.9: Comparison of experimental results and numerical results obtained from solid mesh, shell mesh and hybrid mesh (U900-1 component subjected to axial compression).
  • Figure 10.3.10: Numerical prediction of the deformation of the half U900-1 component subjected to axial compression using solid modelling, shell modelling and hybrid modelling at a loading plate displacement of 7.5mm.
  • Figure A.1.1: Technical drawing of the three-point bending test set-up for the U900-1 component.
  • Figure A.1.2: Technical drawing of the three-point bending test set-up for the U900-1 component: Detail support.
  • Figure A.1.3: Technical drawing of the three-point bending test set-up for the U900-1 component: Detail Punch.
  • Figure A.2.1: Camera images at first fracture initiation obtained from six parallel three-point bending tests on U900-1 components with focus on gating side and vacuum side: Tests #3 – #5.
  • Figure A.2.2: Camera images at first fracture initiation obtained from six parallel three-point bending tests on U900-1 components with focus on gating side and vacuum side: Tests #6 – #8.
  • Figure A.2.3: Images of six deformed and fractured U900-1 components subjected to three-point bending.
  • Figure A.2.4: Experimental measurements obtained from six parallel three-point bending tests on U900-1 components: Force F1(d1) measured by the testing machine (grey), displacement d1(d1) measured by the testing machine (black), displacement d2(d1) measured by the extensometer at gating side (blue), displacement d3(d1) measured by the extensometer at vacuum side (red), mean dµ23(d1) of both extensometer measurements (green) and gap dδ23(d1) between both extensometer measurements (magenta).
  • Figure A.3.1: Technical drawing of the axial compression test set-up for the U900-1 component.
  • Figure A.4.1: Images of four deformed and fractured U900-1 components subjected to axial compression.
  • Figure A.4.2: Experimental measurements obtained from four parallel axial compression tests on U900-1 components: Force F1(d1) measured by the testing machine (grey), displacement d1(d1) measured by the testing machine (black), displacement d2(d1) measured by the extensometer (blue) and gap dδ12(d1) between both displacement measurements (magenta).
  • Figure B.1.1: Uniaxial tensile test specimen UT80 (t = 2.5mm).
  • Figure B.1.2: Extraction plan of UT80 specimens machined from U900-1 components.
  • Figure B.1.3: Labelling system of UT80 specimens machined from U900-1 components.
  • Figure B.2.1: Engineering stress-strain curves obtained from UT80 specimens machined from five U900-1 components presented according to used components.
  • Figure B.2.2: Engineering stress-strain curves obtained from UT80 specimens machined from five U900-1 components presented according to extraction positions.
  • Figure B.2.3: Correlation matrix of the measured mechanical quantities obtained from UT80 specimens machined from five U900-1 components.
  • Figure B.2.4: Averages and COVs of the measured mechanical quantities obtained from UT80 specimens machined from five U900-1 components (Part IF, Part IW and Part BF).
  • Figure B.2.5: Average and COVs of the measured mechanical quantities obtained from UT80 specimens machined from five U900-1 components (Part OW and Part OF).
  • Figure B.3.1: Uniaxial tensile test specimen UT75 and uniaxial tensile test specimen UT117.
  • Figure B.3.2: Extraction plan of UT75 specimens and UT117 specimens machined from U900-1 components.
  • Figure B.3.3: Labelling system of UT75 specimens and UT117 specimens machined from U900-1 components.
  • Figure B.4.1: Engineering stress-strain curves obtained from UT75 and UT117 specimens machined from six U900-1 components presented according to used components (component #1 – #3).
  • Figure B.4.2: Engineering stress-strain curves obtained from UT75 and UT117 specimens machined from six U900-1 components presented according to used components (component #4 – #6).
  • Figure B.4.3: Engineering stress-strain curves obtained from UT75 and UT117 specimens machined from six U900-1 components presented according to extraction positions.
  • Figure B.4.4: Correlation matrix of the measured mechanical quantities obtained from UT75 specimens machined from six U900-1 components.
  • Figure B.4.5: Correlation matrix of the measured mechanical quantities obtained from UT117 specimens machined from six U900-1 components.
  • Figure B.4.6: Average and COVs of the measured mechanical quantities obtained from UT75 specimens machined from six U900-1 components.
  • Figure B.4.7: Average and COVs of the measured mechanical quantities obtained from UT117 specimens machined from six U900-1 components.
  • Figure B.5.1: Average and COVs of the measured thickness obtained from UT80 specimens machined from five U900-1 components.
  • Figure B.5.2: Average and COVs of the measured thickness obtained from UT75 and UT117 specimens machined from six U900-1 components.
  • Figure C.1.1: Stress update algorithm.
  • Figure C.1.2: Element deletion algorithm.
  • Figure C.2.1: Material routine MR#1.
  • Figure C.3.1: Material routine MR#2.
  • Figure C.4.1: Material routine MR#3 (first part).
  • Figure C.4.2: Material routine MR#3 (second part).
  • Figure C.5.1: Material routine MR#4.

7. 결론:

실험 연구의 주요 결과는 HPDC 부품의 재료 연성이 주조 시스템에 따른 전역적 체계적 변동과 공정 변동에 따른 국부적 유사-무작위 변동을 보인다는 것을 확인한 것입니다. 이 두 가지 변동성은 모두 주조 결함에 기인하며, 파괴 모델링 시 반드시 고려되어야 합니다. 상세한 통계 분석을 통해 부품을 기계적 거동이 유사한 세 가지 특징적인 부분(게이트 측, 중간부, 진공 측)으로 나눌 수 있었으며, 각 부분 내의 국부적 변동은 최약 링크 바이불 분포로 설명될 수 있음을 보였습니다.

수치 연구에서는 실험 결과를 바탕으로 확률론적 파괴 모델을 개발하고 검증했습니다. 핵심 성과는 다음과 같습니다. – 단일 시뮬레이션을 통해 파괴 확률을 직접 계산하는 새로운 방법(MR#1)이 계산 비용이 높은 몬테카를로 시뮬레이션(MR#2)과 동일한 예측 결과를 제공함을 입증했습니다. – FE 메쉬와 MS 메쉬를 분리하는 비연계 모델링 접근법(MR#3, MR#4)을 통해 확률론적 해석의 메쉬 의존성 문제를 해결하고 수렴된 결과를 얻을 수 있음을 보였습니다. – 개발된 확률론적 모델(MR#1)과 재료 특성 분석을 통해 식별된 매개변수를 사용하여 실제 부품(U-profile)의 굽힘 및 압축 시험을 시뮬레이션한 결과, 실험적으로 측정된 파괴 확률과 매우 높은 상관관계를 보여 모델의 신뢰성을 최종적으로 검증했습니다.

이 연구는 HPDC 부품의 제조 공정에서 발생하는 불확실성을 설계 단계에 정량적으로 통합할 수 있는 강력하고 효율적인 방법론을 제시하며, 이를 통해 자동차 부품의 충돌 안전성 예측 정확도를 크게 향상시킬 수 있을 것으로 기대됩니다.

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전문가 Q&A: 궁금증 해소

Q1: 확률론적 모델의 기반으로 Cockcroft-Latham 파괴 기준을 선택한 특별한 이유가 있나요?

A1: 네, Cockcroft-Latham 기준은 단일 매개변수(임계값 Wc)만을 필요로 하여 확률론적 모델링에 적용하기 용이하기 때문입니다. 파괴 로커스와 같이 여러 매개변수가 필요한 모델은 각 매개변수의 확률 분포와 상호 상관관계를 모두 정의해야 하므로 복잡성이 크게 증가합니다. 또한, 이 기준은 최대 주응력이 압축일 때 파괴가 발생하지 않는 등 연성 파괴의 물리적 특성을 잘 반영하며, 단축 인장 시험만으로도 임계값을 비교적 쉽게 교정할 수 있다는 장점이 있습니다.

Q2: 논문에서 제안한 ‘비연계 모델링(uncoupled modelling)’ 접근법(MR#3/MR#4)은 기존 방법(MR#2)의 메쉬 의존성 문제를 어떻게 실질적으로 해결하나요?

A2: 기존의 연계(coupled) 접근법(MR#2)에서는 해석용 FE 메쉬가 곧 재료 물성 분포를 정의하는 단위가 됩니다. 따라서 FE 메쉬를 미세하게 나눌수록, 더 작은 체적을 가진 요소들이 최약 링크 이론에 따라 통계적으로 더 넓은 범위의 파괴 임계값을 갖게 되어 결과가 메쉬 크기에 따라 변하게 됩니다. 반면, 비연계 접근법은 재료 물성 분포를 위한 고정된 가상 메쉬(MS Mesh)를 먼저 정의하고, 이 분포를 실제 해석용 FE 메쉬에 ‘매핑’합니다. 따라서 FE 메쉬를 아무리 미세하게 나누어도 재료의 통계적 특성은 변하지 않으므로, 메쉬 크기와 무관하게 일관된 파괴 해석 결과를 얻을 수 있습니다.

Q3: 재료 연성의 ‘전역적 체계적 변동’과 ‘국부적 유사-무작위 변동’의 핵심적인 차이는 무엇이며, 실험 설계에서 이를 어떻게 구분했나요?

A3: ‘전역적 체계적 변동’은 주조 방안과 같이 예측 가능한 요인에 의해 부품의 특정 영역(예: 게이트 측, 진공 측)에 걸쳐 일관되게 나타나는 평균적인 연성 차이를 의미합니다. 반면, ‘국부적 유사-무작위 변동’은 동일한 영역 내에서도 공정의 미세한 흔들림으로 인해 개별 시편마다 무작위적으로 나타나는 연성의 편차를 말합니다. 본 연구에서는 여러 개의 동일 부품에서 시편을 채취하고, 각 부품의 서로 다른 위치(게이트 측, 중간부, 진공 측)에서 시편을 채취하는 ‘계통적 샘플링’을 통해 이 두 가지 변동을 분리하여 분석할 수 있었습니다. 위치 간의 평균값 차이는 전역적 변동을, 동일 위치 내에서의 데이터 분산은 국부적 변동을 나타냅니다.

Q4: 단일 시뮬레이션(MR#1)이 어떻게 전체 몬테카를로 시뮬레이션(MR#2)만큼 정확하게 파괴 확률을 예측할 수 있었나요?

A4: 이는 최약 링크 이론의 수학적 특성을 활용했기 때문입니다. 최약 링크 이론에 따르면, 전체 시스템의 생존 확률은 각 독립적인 하위 시스템(여기서는 각 유한 요소)의 생존 확률의 곱으로 표현됩니다. MR#1은 각 요소에서 계산된 하중(W)과 바이불 분포 함수를 이용해 해당 요소의 ‘생존 확률’을 직접 계산하고, 이 값들을 전체 모델에 걸쳐 곱함으로써 전체 구조물의 총 생존 확률을 구합니다. 최종 파괴 확률은 1에서 이 총 생존 확률을 빼서 얻습니다. 이 방식은 몬테카를로 시뮬레이션이 통계적 샘플링을 통해 근사적으로 찾는 값을 해석적으로 직접 계산하는 것과 같으므로, 단 한 번의 계산으로 동일한 결과를 얻을 수 있습니다.

Q5: 이 연구는 주조 상태(F)의 합금에 초점을 맞췄는데, 만약 열처리(예: T7)된 합금이라면 결과가 어떻게 달라질 수 있을까요?

A5: 논문에서 직접 다루지는 않았지만, 참고 문헌(Dørum et al. [32])에서 열처리된 합금에 대한 유사한 분석이 언급됩니다. 일반적으로 열처리는 주조 결함을 균질화하고 재료의 전반적인 연성을 향상시키는 효과가 있습니다. 따라서 열처리된 합금은 주조 상태의 합금보다 평균 파괴 변형률이 더 높고, 데이터의 편차(바이불 계수 m 값으로 표현)가 더 작을 것으로 예상할 수 있습니다. 하지만 열처리가 모든 결함을 완벽하게 제거하지는 못하므로, 여전히 확률론적 접근법이 결정론적 접근법보다 더 정확한 예측을 제공할 것입니다.

결론: 더 높은 품질과 생산성을 향한 길

알루미늄 고압 다이캐스팅 부품의 신뢰성 예측은 제조 과정에서 필연적으로 발생하는 결함과 그로 인한 물성 편차 때문에 오랫동안 엔지니어링 분야의 어려운 과제였습니다. 본 연구는 이러한 불확실성을 회피하는 대신, 확률론적 파괴 모델링이라는 강력한 도구를 통해 정면으로 마주하고 해결책을 제시했다는 점에서 큰 의미가 있습니다.

실험과 시뮬레이션을 통해 검증된 이 접근법은 HPDC 부품의 파괴 거동을 더 이상 단일한 값이 아닌 ‘확률 분포’로 이해하고 예측할 수 있게 해줍니다. 이는 R&D 및 운영 부서에 다음과 같은 실질적인 가치를 제공합니다. 첫째, 충돌 안전성과 같은 핵심 성능의 신뢰도를 설계 단계에서 정량적으로 평가하고 목표 수준에 맞게 최적화할 수 있습니다. 둘째, 값비싼 물리적 프로토타입 제작 및 테스트 횟수를 줄여 개발 비용과 시간을 절감할 수 있습니다. 마지막으로, 제조 공정의 변동성이 최종 제품의 성능에 미치는 영향을 파악하여 품질 관리를 위한 명확한 기준을 수립할 수 있습니다.

FLOW-3D는 주조 결함의 근본 원인이 되는 용탕의 유동 및 응고 과정을 정밀하게 시뮬레이션하는 데 독보적인 기술력을 보유하고 있습니다. 본 논문에서 논의된 과제들이 귀사의 운영 목표와 일치한다면, FLOW-3D의 엔지니어링 팀에 연락하여 이러한 원칙들이 귀사의 부품에 어떻게 구현될 수 있는지 논의해 보시기 바랍니다.

(주)에스티아이씨앤디에서는 고객이 수치해석을 직접 수행하고 싶지만 경험이 없거나, 시간이 없어서 용역을 통해 수치해석 결과를 얻고자 하는 경우 전문 엔지니어를 통해 CFD consulting services를 제공합니다. 귀하께서 당면하고 있는 연구프로젝트를 최소의 비용으로, 최적의 해결방안을 찾을 수 있도록 지원합니다.

  • 연락처 : 02-2026-0450
  • 이메일 : flow3d@stikorea.co.kr

저작권 정보

  • 이 콘텐츠는 Octavian Knoll의 논문 “A Probabilistic Approach in Failure Modelling of Aluminium High Pressure Die-Castings”을 기반으로 한 요약 및 분석 자료입니다.
  • 출처: https://ntnuopen.ntnu.no/ntnu-xmlui/handle/11250/279895

이 자료는 정보 제공 목적으로만 사용됩니다. 무단 상업적 사용을 금지합니다. Copyright © 2025 STI C&D. All rights reserved.

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(Figure 1) COMPONENT – HORN COVER

CAE 시뮬레이션으로 압력 다이캐스팅 결함 제거: 공정 최적화 가이드

이 기술 요약은 Vinod V Rampur가 작성하여 2016년 IJRET: International Journal of Research in Engineering and Technology에 발표한 “PROCESS OPTIMIZATION OF PRESSURE DIE CASTING TO ELIMINATE DEFECT USING CAE SOFTWARE” 논문을 기반으로 합니다. 이 자료는 STI C&D에 의해 기술 전문가들을 위해 분석 및 요약되었습니다.

키워드

  • Primary Keyword: CAE 시뮬레이션
  • Secondary Keywords: 압력 다이캐스팅, HPDC, Z-cast, 결함 제거, 공정 최적화, 게이팅 시스템

Executive Summary

  • 과제: 알루미늄 합금 부품의 압력 다이캐스팅 공정 중 중요 위치에서 가스 혼입, 수축공 등과 같은 결함이 쉽게 발생합니다.
  • 방법: Z-cast CAE 소프트웨어를 사용하여 금형 충전 및 응고 과정을 시뮬레이션하고, 게이팅 시스템, 러너 및 오버플로우 위치를 최적화했습니다.
  • 핵심 돌파구: 시뮬레이션 결과를 바탕으로 게이팅 시스템과 오버플로우 설계를 수정하여 공기 혼입을 성공적으로 줄이고 용탕 충전 과정을 개선했습니다.
  • 핵심: CAE 시뮬레이션은 생산 전 주조 결함을 예측하고 제거하여 시간과 비용을 절약하고 제품 품질을 향상시키는 필수적인 도구입니다.

과제: 이 연구가 CFD 전문가에게 중요한 이유

압력 다이캐스팅(HPDC)은 높은 치수 정확도와 복잡한 형상을 요구하는 소형 및 중형 부품의 대량 생산에 널리 사용되는 공정입니다. 그러나 이 공정은 가스 결함, 수축공, 금형 재료 결함 등 다양한 결함에 취약합니다. 특히 알루미늄 합금 부품의 경우, 중요 위치에서 결함이 쉽게 형성되어 최종 제품의 품질에 치명적인 영향을 미칠 수 있습니다.

기존의 방식은 실제 금형을 제작하고 시험 주조를 통해 문제점을 파악해야 하므로 시간과 비용이 많이 소요됩니다. 따라서 생산에 들어가기 전에 금형 충전 및 응고 과정을 정확하게 예측하고, 게이팅 시스템과 공정 변수를 최적화하여 결함을 사전에 방지할 수 있는 효율적인 방법이 필요합니다. 이 연구는 CAE 소프트웨어를 활용하여 이러한 산업적 난제를 해결하는 것을 목표로 합니다.

접근 방식: 방법론 분석

본 연구에서는 주조 공정의 결함을 예측하고 최적화하기 위해 체계적인 시뮬레이션 접근법을 채택했습니다. 이 과정은 Z-cast 소프트웨어를 사용하여 자동차 부품인 ‘혼 커버(Horn Cover)’의 압력 다이캐스팅 공정을 분석했습니다.

  1. 데이터 수집: 시뮬레이션의 정확도를 높이기 위해 부품의 3D CAD 모델(STL 형식), 주조 재료(알루미늄 합금 ADC12) 및 금형 재료(HDS BHOLER-W-302)의 물성, 그리고 공정 변수(주입 시간, 온도 등)를 수집했습니다.
  2. 설계 및 모델링: 파팅 라인, 게이팅 시스템, 러너, 라이저 및 금형 캐비티의 초기 설계를 진행했습니다.
  3. 수치 시뮬레이션 (Z-cast 사용):
    • 금형 및 메쉬 생성, 재료 속성 및 온도를 지정했습니다.
    • 주요 공정 변수는 다음과 같이 설정되었습니다.
      • 충전 시간: 0.06초
      • 사출 속도: 1단 0.2m/sec, 2단 2m/sec
      • 사출 압력: 280 Kg/cm²
      • 용탕 온도: 640°C
      • 금형 예열 온도: 초기 150°C, 안정화 후 180°C (고정측), 220°C (이동측)
  4. 최적화: 첫 번째 시뮬레이션 결과를 분석하여 결함의 원인을 파악하고, 게이팅 시스템과 오버플로우 설계를 수정했습니다. 이후 수정된 모델로 다시 시뮬레이션을 수행하여 개선 효과를 검증하는 반복적인 과정을 거쳤습니다.

돌파구: 주요 발견 및 데이터

시뮬레이션 분석을 통해 게이팅 시스템 및 오버플로우 설계가 주조 품질에 미치는 영향을 명확히 파악하고, 이를 개선하여 결함을 제거할 수 있었습니다.

결과 1: 초기 게이팅 시스템 설계

초기 설계에서는 두 개의 부품을 동시에 생산하기 위해 사이드 게이트를 적용한 게이팅 시스템을 구성했습니다. 이 설계는 캐비티의 수와 부품 형상을 고려하여 파팅 라인과 게이팅 위치를 결정한 기본적인 설정입니다. 이 초기 모델은 후속 시뮬레이션 결과와 비교하기 위한 기준선 역할을 합니다.

결과 2: 오버플로우 설계의 문제점 발견

두 번째 시뮬레이션 결과, 오버플로우의 설계에 중대한 문제점이 있음이 밝혀졌습니다. 오버플로우는 미충전 결함을 줄이기 위해 설치되었지만, 시뮬레이션 결과 상단 오버플로우 섹션에 갇힌 공기가 오버플로우의 측면 입구를 통해 다시 금형 캐비티로 역류하는 현상이 관찰되었습니다. 이는 오버플로우가 의도와 달리 오히려 가스 결함의 원인이 될 수 있음을 보여주는 중요한 발견입니다.

결과 3: 오버플로우 설계를 통한 결함 해결

이전 결과에서 발견된 공기 역류 문제를 해결하기 위해 오버플로우 설계를 수정했습니다. 공기가 역류하던 경로에 ‘스텝(step)’ 구조를 추가하여 공기가 부품 내부로 다시 들어오는 것을 물리적으로 차단했습니다. 수정된 설계로 최종 시뮬레이션을 수행한 결과, 공기 혼입 문제가 해결되어 개선된 결과를 얻을 수 있었습니다. 이 시뮬레이션 결과를 바탕으로 제작된 최종 주조품은 분석에서 예측된 것과 거의 일치하는 높은 정확도를 보여주었습니다.

R&D 및 운영을 위한 실질적 시사점

  • 공정 엔지니어: 이 연구는 게이팅 시스템과 특히 오버플로우의 위치 및 설계가 공기 혼입에 직접적인 영향을 미친다는 것을 보여줍니다. 시뮬레이션을 통해 이러한 요소들을 사전에 최적화함으로써 가스 관련 결함을 줄이고 공정 안정성을 높일 수 있습니다.
  • 품질 관리팀: 시뮬레이션 결과(결과 2)는 공기가 재유입될 수 있는 잠재적인 결함 발생 영역을 명확히 보여줍니다. 이는 품질 검사 시 다공성 결함에 대해 집중적으로 확인할 부분을 제시하며, 시뮬레이션이 품질 예측 도구로서 유효함을 입증합니다.
  • 설계 엔지니어: 오버플로우와 같은 기능적 요소의 설계가 얼마나 중요한지를 강조합니다. 잘못 설계된 오버플로우는 오히려 역효과를 낼 수 있습니다. 이는 금형 설계 초기 단계부터 유동 해석을 고려하여 결함 발생 가능성을 최소화해야 함을 시사합니다.

논문 정보

PROCESS OPTIMIZATION OF PRESSURE DIE CASTING TO ELIMINATE DEFECT USING CAE SOFTWARE

1. 개요:

  • 제목: PROCESS OPTIMIZATION OF PRESSURE DIE CASTING TO ELIMINATE DEFECT USING CAE SOFTWARE
  • 저자: Vinod V Rampur
  • 발행 연도: 2016
  • 학술지/학회: IJRET: International Journal of Research in Engineering and Technology
  • 키워드: Casting, HPDC, Z-cast, CAE Software, Simulation

2. 초록:

다이캐스팅은 액체 재료를 원하는 형상의 공동(hallow cavity)을 포함하는 금형에 압력을 가해 주입한 후, 용융 금속을 응고시키는 제조 공정이다. 응고된 부품은 주물(casting)이라고 하며, 공정을 완료하기 위해 배출되거나 분리된다. 이 프로젝트의 목표는 툴, 다이 및 게이팅 시스템을 개발하는 것이다. 가스 결함, 수축공, 금형 재료 결함, 주입 재료 결함, 야금학적 결함 등과 같은 결함을 식별하고 CAE 소프트웨어를 사용하여 결함을 줄이기 위한 조치를 취한다. 게이팅 시스템, 러너 및 오버플로우 위치를 변경하여 금형에 갇히는 공기의 양을 줄이고, 최상의 품질 제품과 향상된 생산성을 위해 게이팅 시스템과 공정 변수를 최적화한다. 알루미늄 합금 부품의 압력 다이캐스팅 중 중요 위치에서 결함이 쉽게 형성될 수 있다. 이는 주물에 결함 효과를 미친다. 부품의 금형 충전 및 응고 과정은 Z-cast 소프트웨어를 사용하여 시뮬레이션되었다.

3. 서론:

다이캐스팅은 액체 재료를 원하는 형상의 공동을 포함하는 금형에 압력을 가해 주입한 후, 용융 금속을 응고시키는 제조 공정이다. 다이캐스팅 합금은 저융점 합금(주석, 납, 아연)부터 고융점 합금(알루미늄, 마그네슘, 구리)까지 다양하다. 저융점 합금에는 열간 챔버 기계를, 고융점 합금에는 냉간 챔버 기계를 사용할 수 있다. 고압 다이캐스팅(HPDC)은 높은 치수 정확도와 복잡한 기하학적 형상을 요구하는 다수의 소형 및 중형 부품 생산에 적합하며, 저비용 부품에도 사용된다.

4. 연구 요약:

연구 주제의 배경:

고압 다이캐스팅(HPDC)은 복잡하고 정밀한 부품을 대량 생산하는 데 효율적이지만, 가스 혼입이나 수축공과 같은 결함이 발생하기 쉬워 제품 품질과 생산성에 영향을 미친다. 이러한 결함을 줄이기 위해 CAE(Computer-Aided Engineering) 시뮬레이션의 필요성이 대두되었다.

이전 연구 현황:

많은 주조 공장에서 CAD/CAM 및 시뮬레이션을 사용하여 특정 제품의 주조 리드 타임을 단축하고 있다. 주조 시뮬레이션은 이제 주조소 운영의 필수적인 부분으로 자리 잡고 있다.

연구 목적:

본 연구의 목적은 CAE 소프트웨어를 사용하여 압력 다이캐스팅 공정에서 발생하는 결함을 식별하고 제거하는 것이다. 구체적으로 게이팅 시스템, 러너, 오버플로우 위치를 변경하여 금형 내 공기 혼입을 줄이고, 충전율과 응고율 분석을 통해 공정을 최적화하여 고품질의 제품을 생산하는 것을 목표로 한다.

(Figure 1) COMPONENT – HORN COVER
(Figure 1) COMPONENT – HORN COVER

핵심 연구:

자동차 부품인 ‘혼 커버’를 대상으로 Z-cast 소프트웨어를 사용하여 다이캐스팅 공정을 시뮬레이션했다. 초기 설계안의 시뮬레이션을 통해 문제점을 파악하고, 특히 오버플로우 설계 수정에 초점을 맞추어 공기 혼입 결함을 해결하는 과정을 분석했다. 수정된 설계를 통해 결함이 없는 시뮬레이션 결과를 도출하고, 이를 통해 최종 제품의 품질을 향상시켰다.

5. 연구 방법론

연구 설계:

본 연구는 데이터 수집, 설계 및 모델링, 수치 시뮬레이션, 최적화의 4단계로 구성된 체계적인 절차를 따랐다. 각 시뮬레이션 라운드 후 결과를 분석하여 설계를 수정하고 다시 시뮬레이션하는 반복적인 접근법을 사용했다.

데이터 수집 및 분석 방법:

  • 데이터 수집: CATIA와 같은 CAD 소프트웨어를 사용하여 부품의 3D 모델(STL)을 개발하고, 주조 금속(ADC12) 및 금형의 재료 속성, 주입 시간 및 온도와 같은 공정 변수를 수집했다.
  • 분석 방법: Z-cast 소프트웨어를 사용하여 금형 생성, 메쉬 생성, 재료 및 온도 설정, 다이캐스트 세부 사항 지정 후 시뮬레이션을 수행했다. 시뮬레이션 완료 후 충전 및 응고 패턴을 분석하여 결함을 식별했다.

연구 주제 및 범위:

연구 대상은 알루미늄 합금(ADC12)으로 제작되는 자동차 부품 ‘혼 커버’이다. 연구 범위는 CAE 시뮬레이션을 통한 게이팅 시스템 및 오버플로우 설계 최적화에 국한되며, 이를 통해 공기 혼입 결함을 제거하고 제품 품질을 개선하는 과정을 다룬다.

6. 주요 결과:

주요 결과:

  • 초기 게이팅 시스템 설계 후 시뮬레이션 결과, 오버플로우 상단에 갇힌 공기가 캐비티로 다시 유입되는 문제점을 발견했다.
  • 오버플로우 설계에 ‘스텝’ 구조를 추가하여 공기의 역류를 차단함으로써 이 문제를 해결했다.
  • 최종 수정된 설계를 통해 얻은 시뮬레이션 결과는 결함이 개선되었음을 보여주었으며, 이를 기반으로 제작된 실제 주조품은 예측과 거의 일치하는 높은 정확도를 보였다.
(Figure 4) Component with gating system with modified overflows
(Figure 4) Component with gating system with modified overflows

그림 목록:

  • (Figure 1) COMPONENT – HORN COVER
  • (Figure 2) Horn cover with proper gating systems
  • (Figure 3) Filling regions in the casting after solidification
  • (Figure 4) Component with gating system with modified overflows
  • (Figure 5) FINAL COMPONENT AFTER CASTING

7. 결론:

  • 주조 공정 중 샷 슬리브에 존재하는 공기를 줄여 제품 품질을 향상시킬 수 있다.
  • HPDC 기계를 사용하여 주조 공정 전 설정 시간을 단축할 수 있다.
  • 플런저 움직임을 통해 주조 공정에서 용탕의 흐름을 제어하여 주조 공정을 최적화할 수 있다.
  • 툴 설계 공정에 소요되는 시간이 단축되고, 주조 공정에 필요한 최소 시간과 재료 낭비가 줄어든다.
  • 시뮬레이션은 사용자에게 제품 품질의 수용 가능 여부에 대한 정보를 제공한다.
  • HPDC 기계와 시뮬레이션 결과를 활용하여 스크랩, 낭비, 생산 시간을 줄이고 제품 품질을 향상시킬 수 있다.
  • 시뮬레이션 결과를 통해 제조업체는 게이트, 러너, 라이저 위치 및 오버플로우 위치를 설계하여 금형 캐비티에 용탕을 채우는 최상의 솔루션을 얻을 수 있다.

8. 참고 문헌:

  1. Dargusch M.S., Dour.G, Schauer.N, Dinnis C.M., Savage G., The influence of pressure during solidification of high pressure die cast aluminium telecommunications components, J. Mater. Process. Technol. 180 (1-3) (2006) 37-43.
  2. Reddy A.P, Pande S.S and Ravi B., IIT – Bombay, “Computer Aided Design of die casting dies”
  3. Muthu kumar. B., “Design and development of pressure die casting”, GT&TC, Bengaluru
  4. Herman E.A, Heat Flow in the Die Casting Process, Society of Die Casting Engineers, 1985.

전문가 Q&A: 자주 묻는 질문

Q1: 이 연구에서 Z-cast 소프트웨어를 사용한 이유는 무엇인가요?

A1: 이 연구는 Z-cast를 사용하여 게이팅 시스템 변경에 따른 금형 내 공기 혼입량 감소와 같은 구체적인 분석을 수행했으며, 이를 통해 공정 최적화를 달성했습니다.

Q2: “최종 결과 3″에서 공기 재유입을 막기 위해 적용된 구체적인 수정 사항은 무엇이었나요?

A2: 논문에 따르면, 이전 결과에서 오버플로우가 파손되었던 부분에 ‘스텝(step)’을 제공했습니다. 이 오버플로우의 변경으로 인해 공기가 부품으로 들어오는 것을 차단할 수 있었습니다. 즉, 공기가 역류하던 경로에 물리적인 장애물을 설치하여 문제를 해결한 것입니다.

Q3: 시뮬레이션에 사용된 핵심 공정 변수들은 무엇이었나요?

A3: 시뮬레이션에 사용된 주요 변수는 다음과 같습니다. 충전 시간은 0.06초, 1단 사출 속도는 0.2m/sec, 2단 사출 속도는 2m/sec였습니다. 사출 압력은 280 Kg/cm², 시스템 압력은 150 Kg/cm²로 설정되었습니다. 또한, 용탕 주입 온도는 640°C, 금형 예열 온도는 150°C(초기)에서 180°C~220°C(안정화)로 설정되었습니다.

Q4: 게이팅 시스템, 러너, 오버플로우 중 이 연구에서 결함 제거에 가장 큰 영향을 미친 요소는 무엇이었나요?

A4: 연구 결과는 오버플로우 설계 수정에 가장 중점을 두고 있습니다. “결과 2″에서 오버플로우 설계로 인한 공기 역류 문제를 명확히 식별했고, “최종 결과 3″에서는 오버플로우 설계를 수정하여 이 문제를 해결했습니다. 따라서 이 연구에서는 오버플로우 설계가 공기 혼입 결함을 제거하는 데 가장 결정적인 역할을 했다고 볼 수 있습니다.

Q5: CAE 시뮬레이션이 제품 주조의 리드 타임을 어떻게 단축시킬 수 있나요?

A5: 논문의 3.1절에 따르면, 시뮬레이션 소프트웨어를 사용하면 “가상 시험(virtual trails)”을 줄일 수 있습니다. 이는 물리적인 금형 제작과 시험 주조를 통한 시행착오 과정을 더 빠르고 비용 효율적인 디지털 시뮬레이션으로 대체할 수 있음을 의미합니다. 이를 통해 결함을 사전에 예측하고 설계를 최적화함으로써 전체 개발 기간과 리드 타임을 단축할 수 있습니다.

결론: 더 높은 품질과 생산성을 향한 길

본 연구는 압력 다이캐스팅 공정에서 발생하는 공기 혼입과 같은 고질적인 문제를 해결하는 데 CAE 시뮬레이션이 얼마나 효과적인지를 명확하게 보여줍니다. 특히 금형 충전 및 응고 과정을 분석하여 게이팅 시스템과 오버플로우 설계를 최적화하는 것이 결함 예방의 핵심임이 입증되었습니다. 이러한 사전 예측 및 최적화 접근 방식은 물리적 시험에 드는 시간과 비용을 절감하고, 최종 제품의 품질과 생산성을 크게 향상시킵니다.

STI C&D는 최신 산업 연구 결과를 적용하여 고객이 더 높은 생산성과 품질을 달성할 수 있도록 최선을 다하고 있습니다. 이 논문에서 논의된 과제가 귀사의 운영 목표와 일치한다면, 저희 엔지니어링 팀에 연락하여 이러한 원칙을 귀사의 부품에 어떻게 구현할 수 있는지 논의해 보십시오.

(주)에스티아이씨앤디에서는 고객이 수치해석을 직접 수행하고 싶지만 경험이 없거나, 시간이 없어서 용역을 통해 수치해석 결과를 얻고자 하는 경우 전문 엔지니어를 통해 CFD consulting services를 제공합니다. 귀하께서 당면하고 있는 연구프로젝트를 최소의 비용으로, 최적의 해결방안을 찾을 수 있도록 지원합니다.

  • 연락처 : 02-2026-0450
  • 이메일 : flow3d@stikorea.co.kr

저작권 정보

  • 이 콘텐츠는 “Vinod V Rampur”의 논문 “PROCESS OPTIMIZATION OF PRESSURE DIE CASTING TO ELIMINATE DEFECT USING CAE SOFTWARE”를 기반으로 한 요약 및 분석 자료입니다.
  • 출처: http://www.ijret.org

이 자료는 정보 제공 목적으로만 사용됩니다. 무단 상업적 사용을 금지합니다. Copyright © 2025 STI C&D. All rights reserved.

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Figure 8. Output image for image resolution of 17 px/μm for (a) a median filter size of 0.1 μm by 0.1 μm and (b) 0.6 μm by 0.6μm. Range filter size was 0.1 μm by 0.1 μm (5 px by 5 px), dilation/erosion disk size was 0.3 μm (10 px), and hole close was 120 μm2 (4096 px2) .The measured α-Al is highlighted in pink.

고압 다이캐스팅 품질 혁신: 자동화된 미세조직 분석으로 수율 극대화

이 기술 요약은 Maria Diana David가 2015년 University of Alabama at Birmingham에서 발표한 논문 “Microstructural Analysis of Aluminum High Pressure Die Castings”를 기반으로 하며, STI C&D의 기술 전문가에 의해 분석 및 요약되었습니다.

키워드

  • Primary Keyword: 고압 다이캐스팅
  • Secondary Keywords: 알루미늄 다이캐스팅, 미세조직 분석, 이미지 분석, 주조 결함, 품질 관리, CFD

Executive Summary

  • 도전 과제: 알루미늄 고압 다이캐스팅(HPDC)의 미세하고 불균일한 미세조직은 수동 분석이 어렵고 시간이 많이 소요되어 품질 관리의 병목 현상을 유발합니다.
  • 해결 방법: SEM 및 광학 현미경 이미지를 사용하여 미세조직 특징(상 분율, 입자 크기 등)을 정량화하는 반자동 이미지 분석 알고리즘을 개발하고 검증했습니다.
  • 핵심 돌파구: 분석 결과의 정확도는 이미지 해상도에 크게 좌우되며, 특정 해상도(본 연구에서는 6 px/µm) 이상에서는 측정값이 안정화되는 ‘플래토’ 구간이 존재함을 발견했습니다.
  • 핵심 결론: 표준화된 자동 분석 기법을 통해 R&D 및 품질 관리 부서는 더 빠르고 일관된 데이터 기반 의사결정을 내려 제품 수율과 신뢰성을 크게 향상시킬 수 있습니다.

도전 과제: 왜 이 연구가 CFD 전문가에게 중요한가?

고압 다이캐스팅(HPDC)은 복잡한 형상의 부품을 빠른 시간 내에 대량 생산할 수 있어 자동차, 전자 등 여러 산업에서 핵심적인 공정입니다. 그러나 극도로 빠른 충전 및 응고 과정은 미세하고 불균일한 미세조직을 형성하며, 이는 부품의 기계적 특성에 결정적인 영향을 미칩니다.

기존의 미세조직 분석은 주로 작업자의 경험에 의존하는 수동 측정 방식으로 이루어졌습니다. 이 방식은 시간이 오래 걸릴 뿐만 아니라, 미세한 특징을 놓치거나 측정값의 일관성이 떨어져 신뢰성 있는 데이터를 확보하기 어렵다는 한계가 있었습니다. 특히, 제품의 품질을 좌우하는 결함이나 미세조직의 정량적 데이터를 신속하게 확보하지 못하면 공정 최적화와 수율 개선에 큰 어려움을 겪게 됩니다. 따라서 정확하고 효율적인 미세조직 정량화 기술의 필요성이 절실한 상황이었습니다.

Figure 1. Backscatter electron SEM image showing the major phases found in the aluminum 380 high pressure die casting examined.
Figure 1. Backscatter electron SEM image showing the major phases found in the aluminum 380 high pressure die casting examined.

접근 방식: 연구 방법론 분석

본 연구는 알루미늄 380 다이캐스팅 부품의 미세조직을 정량적으로 분석하기 위해 반자동화된 이미지 분석 기법을 개발했습니다. 연구진은 주조 표면 근처에서 채취한 시편을 Axioplan 4MP 광학 현미경과 FEI FEG-650 주사전자현미경(SEM)으로 촬영하여 고해상도 이미지를 확보했습니다.

분석의 핵심은 Matlab을 사용하여 개발된 맞춤형 알고리즘입니다. 이 알고리즘은 다음과 같은 체계적인 이미지 처리 단계를 거칩니다.

  1. 노이즈 감소: 미디언 필터(Median Filter)를 적용하여 이미지의 불필요한 노이즈를 제거하면서도 미세한 특징의 손실을 최소화했습니다.
  2. 경계 검출: 레인지 필터(Range Filter)를 사용하여 1차 α-Al상과 공정(eutectic) 조직 간의 경계를 명확히 구분했습니다.
  3. 이미지 이진화 및 형태학적 처리: Otsu의 방법을 통해 이미지를 흑백으로 변환한 후, 팽창(Dilation) 및 침식(Erosion) 연산을 적용하여 각 상(phase)의 영역을 명확히 하고 내부의 미세한 틈을 채웠습니다.
  4. 정량적 측정: 처리된 최종 이미지로부터 1차 α-Al상의 부피 분율(Volume Fraction)과 선 교차 수(Line Intercept Count)를 자동으로 계산했습니다.

연구진은 다양한 이미지 해상도와 알고리즘 파라미터(필터 크기, 팽창/침식 반경 등)가 분석 결과에 미치는 영향을 체계적으로 평가하여 방법론의 신뢰도를 검증했습니다.

핵심 돌파구: 주요 발견 및 데이터

발견 1: 정확한 분석을 위한 임계 이미지 해상도 규명

연구 결과, 미세조직 분석의 정확도는 이미지의 픽셀 해상도(px/µm)에 직접적인 영향을 받는다는 사실이 명확해졌습니다. 해상도가 6 px/µm 미만일 경우, 알고리즘이 미세한 상들을 제대로 구분하지 못해 α-Al상의 부피 분율을 과대 또는 과소평가하는 오류가 발생했습니다.

하지만 그림 21에서 볼 수 있듯이, 해상도가 6 px/µm 이상으로 높아지자 부피 분율 측정값이 약 0.4~0.5 범위에서 안정화되는 ‘플래토(plateau)’ 현상이 나타났습니다. 이는 특정 해상도 이상에서는 이미지 배율에 상관없이 일관되고 신뢰성 있는 결과를 얻을 수 있음을 의미합니다. 이 발견은 효율적인 분석을 위한 최적의 이미지 획득 조건을 설정하는 데 중요한 기준을 제공합니다.

발견 2: 자동화 분석법의 정확성 검증 및 한계점 파악

플래토 구간(6~35 px/µm) 내에서 자동화 알고리즘으로 측정한 부피 분율은 수동으로 측정한 값과 매우 잘 일치하여, 개발된 방법의 높은 정확성을 입증했습니다.

그러나 그림 25에 나타난 바와 같이, 선 교차 수(Line Intercept Count) 측정에서는 자동화 분석 값이 수동 측정 값보다 지속적으로 높게 나타났습니다. 이는 그림 26에서 확인되듯이, 알고리즘이 α-Al상의 거친 표면 경계를 매우 민감하게 감지하여 사람의 눈보다 더 많은 교차점을 계산하기 때문입니다. 이 결과는 자동화 분석이 객관적인 데이터를 제공하는 동시에, 측정 항목에 따라서는 경계 스무딩(edge smoothing)과 같은 추가적인 알고리즘 개선이 필요할 수 있음을 시사합니다.

R&D 및 운영을 위한 실질적 시사점

  • 공정 엔지니어: 이 연구는 이미지 해상도와 분석 파라미터를 표준화함으로써, 냉각 속도나 압력과 같은 공정 변수가 미세조직에 미치는 영향을 정량적으로 추적하고 공정을 최적화하는 데 기여할 수 있음을 보여줍니다.
  • 품질 관리팀: 논문의 그림 21 데이터는 신뢰성 있는 품질 검사를 위해 필요한 최소 이미지 해상도 기준을 제시합니다. 자동화된 분석을 도입하면 검사 속도를 높이고 측정의 일관성을 확보하여, 잠재적 결함을 조기에 발견하고 불량률을 줄일 수 있습니다.
  • 설계 엔지니어: 연구 결과는 주조품의 표면 근처 미세조직이 기계적 특성에 큰 영향을 미친다는 점을 강조합니다. 설계 초기 단계에서 응고 과정 중 미세조직 형성을 고려하면, 결함 발생 가능성이 낮은 최적의 설계를 도출하는 데 도움이 될 수 있습니다.

논문 정보

Microstructural Analysis of Aluminum High Pressure Die Castings

1. 개요:

  • 제목: Microstructural Analysis of Aluminum High Pressure Die Castings
  • 저자: Maria Diana David
  • 발행 연도: 2015
  • 발행 학술지/학회: University of Alabama at Birmingham
  • 키워드: dendrites, stereology, microscopy

2. 초록:

알루미늄 고압 다이캐스팅(HPDC)의 미세조직 분석은 어렵고 시간이 많이 소요됩니다. 입체해석학(stereology) 방법을 자동화하는 것은 정량적 데이터를 얻는 효율적인 방법이지만, 이 기술의 정확성을 검증하는 것 또한 어려운 과제일 수 있습니다. 본 연구에서는 알루미늄 HPDC의 미세조직 특징을 정량화하기 위한 반자동 알고리즘을 개발했습니다. 분석은 미세한 미세조직을 보이는 주조 표면 근처에서 수행되었습니다. 주조물의 특징을 규명하기 위해 광학, 2차 전자(SE), 후방 산란 전자(BSE) SEM 이미지를 사용했습니다. SEM 및 광학 현미경 사진에 적용된 이미지 처리 단계에는 미디언 및 레인지 필터, 팽창, 침식, 홀 클로징 기능이 포함되었습니다. 측정은 3에서 35 pixel/µm 범위의 다양한 이미지 픽셀 해상도에서 수행되었습니다. 6 px/µm 미만의 픽셀 해상도는 알고리즘이 상들을 서로 구별하기에 너무 낮았습니다. 6 px/µm 이상의 해상도에서는 1차 α-Al의 부피 분율과 선 교차 수 곡선이 안정화(plateau)되었습니다. 이 범위 내에서, 입체해석학적 측정이 이미지 해상도와 무관해지는 주조 특징의 크기에 상대적인 이미지 픽셀 해상도 범위가 있다는 가정을 검증하는 유사한 결과를 얻었습니다. 이 곡선 안정 구간 내의 부피 분율은 수동 측정과 일치했지만, 선 교차 수는 모든 해상도에서 컴퓨터화된 기술을 사용했을 때 상당히 높았습니다. 이는 일부 1차 α-Al의 거친 가장자리 때문으로, 알고리즘에 일부 개선이 여전히 필요함을 시사합니다. 알려진 상의 양과 크기를 가진 다른 주조물이나 합금을 사용하여 코드를 추가로 검증하는 것도 유익할 수 있습니다.

3. 서론:

고압 다이캐스팅(HPDC)은 복잡한 부품을 짧은 주조 사이클 시간 내에 생산할 수 있는 장점을 제공합니다. 그러나 공정 중 발생하는 복잡한 유동 및 응고 메커니즘으로 인해 미세조직이 불균일하게 형성되어 비구조적 부품에 주로 사용됩니다. 이러한 미세조직을 정량적으로 분석하는 것은 제품의 기계적 특성을 이해하고 개선하는 데 필수적입니다. 기존의 수동 분석 방법은 시간이 많이 걸리고 작업자의 주관이 개입될 여지가 있어 정밀도와 효율성이 떨어집니다. 따라서 자동화된 정량 분석 기술을 개발하고 검증하여, 더 빠르고 재현성 있는 결과를 얻을 필요가 있습니다.

4. 연구 요약:

연구 주제의 배경:

알루미늄 고압 다이캐스팅은 높은 생산성을 자랑하지만, 급속 냉각으로 인해 형성되는 미세하고 복잡한 미세조직(皮막층, 결함 밴드, 외부 응고 결정 등)이 기계적 특성을 저하 시킬 수 있습니다. 이러한 미세조직 특징을 정확히 정량화하는 것은 품질 관리 및 공정 개선의 핵심입니다.

이전 연구 현황:

기존 연구들은 주로 수동적인 선 교차법이나 비교 차트를 이용해 미세조직을 분석해왔으나, 이는 시간 소모가 크고 재현성이 낮았습니다. 자동화된 이미지 분석법이 대안으로 제시되었지만, HPDC의 미세한 특징에 대한 적용 및 신뢰성 검증 연구는 제한적이었습니다.

연구 목적:

본 연구의 목적은 알루미늄 HPDC의 미세조직(특히 1차 α-Al상의 부피 분율 및 크기)을 신속하고 정확하게 측정할 수 있는 반자동 이미지 분석 알고리즘을 개발하고, 다양한 분석 파라미터와 이미지 해상도가 결과에 미치는 영향을 평가하여 방법론의 신뢰성을 검증하는 것입니다.

핵심 연구:

알루미늄 380 합금을 대상으로 SEM 및 광학 현미경 이미지를 획득하고, Matlab 기반 알고리즘을 통해 미세조직을 분석했습니다. 연구는 (1) 노이즈 감소, (2) 경계 검출, (3) 팽창/침식, (4) 홀 클로징(hole close) 등 각 이미지 처리 단계의 파라미터가 최종 측정값에 미치는 영향을 분석했습니다. 또한, 3~35 px/µm 범위의 다양한 이미지 해상도에서 측정을 수행하여, 결과의 신뢰성이 보장되는 최적의 해상도 범위를 규명했습니다.

5. 연구 방법론

연구 설계:

본 연구는 실험적 설계에 기반하여, 알루미늄 380 다이캐스팅 시편의 미세조직을 정량적으로 분석했습니다. 반자동 이미지 분석 알고리즘의 유효성을 검증하기 위해, 알고리즘으로 얻은 결과를 전통적인 수동 측정 결과와 비교했습니다.

데이터 수집 및 분석 방법:

  • 데이터 수집: Axioplan 4MP 광학 현미경과 FEI FEG-650 SEM을 사용하여 다양한 배율의 미세조직 이미지를 수집했습니다. SEM 분석 시에는 2차 전자(SE) 이미지와 후방 산란 전자(BSE) 이미지를 모두 활용하여 상 구분을 명확히 했습니다.
  • 데이터 분석: 수집된 이미지는 Matlab으로 개발된 반자동 알고리즘을 통해 분석되었습니다. 알고리즘은 미디언 필터, 레인지 필터, 임계값 처리(thresholding), 팽창/침식 등의 이미지 처리 기법을 순차적으로 적용하여 1차 α-Al상과 공정 조직을 분리하고, 각 상의 부피 분율과 선 교차 수를 계산했습니다.

연구 주제 및 범위:

연구는 알루미늄 380 고압 다이캐스팅 부품의 주조 표면으로부터 80~400 µm 이내 영역의 미세조직에 초점을 맞췄습니다. 분석 대상은 1차 α-Al상과 (공정 조직 + 금속간화합물)의 이진(binary) 시스템으로 단순화되었습니다. 주요 연구 내용은 이미지 처리 파라미터와 이미지 해상도가 정량 분석 결과에 미치는 영향을 평가하는 것이었습니다.

6. 주요 결과:

주요 결과:

  • 이미지 분석의 정확성은 픽셀 해상도에 크게 의존하며, 본 연구의 알루미늄 380 합금에서는 6 px/µm 이상의 해상도가 필요함을 확인했습니다.
  • 6 px/µm 이상의 해상도에서는 부피 분율과 선 교차 수 측정값이 특정 값으로 수렴하며 안정화되는 ‘플래토’ 구간이 존재했습니다.
  • 플래토 구간에서 자동화 알고리즘으로 측정한 부피 분율은 수동 측정 결과와 높은 상관관계를 보였습니다.
  • 반면, 선 교차 수는 자동화 알고리즘이 α-Al상의 거친 경계를 민감하게 인식하여 수동 측정보다 일관되게 높은 값을 나타냈습니다.
  • 노이즈 감소, 경계 검출, 팽창/침식 등 각 이미지 처리 단계의 파라미터 값에 따라 분석 결과가 민감하게 변하므로, 분석 대상의 특징에 맞는 최적의 파라미터 범위를 설정하는 것이 중요합니다.
Figure 8. Output image for image resolution of 17 px/μm for (a) a median filter size of 0.1 μm by 0.1 μm and (b) 0.6 μm by 0.6μm. Range filter size was 0.1 μm by 0.1 μm (5 px by 5 px), dilation/erosion disk size was 0.3 μm (10 px), and hole close was 120 μm2 (4096 px2) .The measured α-Al is highlighted in pink.
Figure 8. Output image for image resolution of 17 px/μm for (a) a median filter size of 0.1 μm by 0.1 μm and (b) 0.6 μm by 0.6μm. Range filter size was 0.1 μm by 0.1 μm (5 px by 5 px), dilation/erosion disk size was 0.3 μm (10 px), and hole close was 120 μm2 (4096 px2) .The measured α-Al is highlighted in pink.

Figure 목록:

  • Figure 1. Backscatter electron SEM image showing the major phases found in the aluminum 380 high pressure die casting examined.
  • Figure 2. Schematic diagram of computer-aided microstructural analysis.
  • Figure 3. Detailed schematic diagram of algorithm showing steps done to analyze SEM and optical images.
  • Figure 4. (a) Secondary electron and (b) backscatter electron (right) SEM images used in the parameter studies.
  • Figure 5. (a) Volume fraction of primary a-Al and (b) line intercept count as functions of the noise reduction parameter value.
  • Figure 6. Secondary SEM image with a resolution of 17 px/um after the image noise reduction step for (a) a median filter size of 0.1 µm by 0.1 µm and (b) 0.6 µm by 0.6µm.
  • Figure 7. Secondary SEM image with a resolution of 17 px/um after the median and range filters were applied.
  • Figure 8. Output image for image resolution of 17 px/µm for different median filter sizes.
  • Figure 9. (a) Volume Fraction of primary a-Al and (b) line intercept count as a function of edge detection parameter value.
  • Figure 10. Secondary SEM image after the median and range filters were applied for different range filter sizes.
  • Figure 11. Thresholded image for SEM image after the median and range filters were applied for different range filter sizes.
  • Figure 12. Output image for image resolution for 17 px/µm with different range filter sizes.
  • Figure 13. (a) Volume fraction of primary a-Al and (b) line intercept count as a function of dilation and erosion disk size.
  • Figure 14. Thresholded image for SEM image after the median and range filters were applied.
  • Figure 15. Dilated image for a disk structuring element of different sizes.
  • Figure 16. Output image for image resolution of 17 px/µm with different dilation/erosion disk sizes.
  • Figure 17. (a) Volume fraction of primary a-Al and (b) line intercept count as a function of hole close parameter.
  • Figure 18. Image after the dilation step.
  • Figure 19. Image after small holes/gaps within phases in the dilated image were closed for different hole close areas.
  • Figure 20. Output image for image resolution of 17 px/µm for different hole close areas.
  • Figure 21. Volume fraction of primary a-Al as function of image resolution or length scale.
  • Figure 22. Volume fraction of primary a-Al as function of pixel resolution or length scale for different edge detection technique.
  • Figure 23. Output images for SEM image with a pixel resolution of 3 px/µm for analyses that used (a) range filter and (b) Canny edge as the edge detection technique.
  • Figure 24. Output image of (a) SEM image with pixel resolution of 3 px/µm and (b) optical microscope image with pixel resolution of 3 px/um.
  • Figure 25. Line intercept count as function of image resolution or length scale.
  • Figure 26. (a) Backscatter electron SEM image with pixel resolution of 6 pixel/um of the same location in (b) the output image measured by the algorithm.

7. 결론:

알루미늄 고압 다이캐스팅의 미세조직을 자동화하여 분석하는 것은 전통적인 수동 입체해석학 기법보다 상대적으로 더 효율적입니다. 본 연구에서는 알고리즘에 사용된 함수들을 제시하고 분석했으며, 각 파라미터에 대한 수용 가능한 값의 범위를 제안했습니다.

이미지 분석을 수행해야 하는 해상도는 관심 있는 특징의 크기에 따라 달라집니다. 본 연구에서 조사된 알루미늄 다이캐스팅 샘플의 경우, 6 px/µm 미만의 픽셀 해상도는 알고리즘이 상들을 서로 구별하기에 너무 낮았습니다. 6 px/µm 이상의 해상도에서는 1차 α-Al의 부피 분율과 선 교차 수 곡선이 안정화(plateau)되었습니다. 이 범위 내에서 분석을 수행하면 비교 가능한 결과를 얻을 수 있습니다. 그러나 더 높은 해상도에서는 편차와 5% 변동 계수에 도달하는 데 필요한 이미지 수가 곡선 안정화 시작점의 해상도보다 훨씬 높습니다.

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전문가 Q&A: 자주 묻는 질문

Q1: 이 연구에서 왜 반자동화 알고리즘을 선택했나요? 완전 수동이나 완전 자동 방식에 비해 어떤 장점이 있나요?

A1: 완전 수동 방식은 시간이 많이 걸리고 작업자마다 결과가 달라 일관성이 떨어집니다. 반면, 반자동 방식은 컴퓨터의 빠른 처리 능력으로 효율성을 높이는 동시에, 분석 과정에서 전문가가 개입하여 결과를 검증할 수 있어 신뢰성을 확보할 수 있습니다. 특히 HPDC처럼 미세하고 불균일한 조직을 분석할 때, 자동화의 효율성과 전문가 검증의 정확성을 결합한 이 접근법이 가장 적합합니다.

Q2: 논문에서 이미지 해상도가 6 px/µm 이상일 때 결과가 안정화되는 ‘플래토’ 현상이 언급되었습니다. 이것이 실제 산업 현장에서 의미하는 바는 무엇인가요?

A2: ‘플래토’ 현상은 신뢰할 수 있는 데이터를 얻기 위한 최소한의 이미지 품질 기준을 제시합니다. 즉, 6 px/µm 미만의 저해상도 이미지로는 부정확한 결과를 얻을 수 있으며, 반대로 이보다 훨씬 높은 고해상도로 분석하는 것은 데이터 처리 시간과 저장 공간만 늘릴 뿐 결과의 정확도 향상에는 기여하지 못한다는 의미입니다. 따라서 현장에서는 6 px/µm를 기준으로 분석 효율성과 정확성 사이의 최적점을 찾을 수 있습니다.

Q3: 자동화 분석에서 계산된 선 교차 수가 수동 측정값보다 높게 나온 이유는 무엇이며, 이를 어떻게 해결할 수 있나요?

A3: 이는 자동화 알고리즘이 사람의 눈보다 훨씬 민감하게 α-Al상의 미세하고 거친 경계를 모두 인식하여 더 많은 교차점을 계산하기 때문입니다. 이 문제를 해결하기 위해서는 향후 알고리즘 개발 시, 경계를 부드럽게 만드는 스무딩(smoothing) 기능을 추가하거나, 특정 크기 이하의 미세한 굴곡을 무시하도록 필터링 기준을 설정하는 등의 개선이 필요합니다.

Q4: 1차 α-Al상과 공정 조직을 구분하는 데 가장 중요했던 이미지 처리 단계는 무엇이었나요?

A4: 레인지 필터를 사용한 ‘경계 검출’ 단계와 ‘팽창(Dilation)’ 연산이 가장 중요했습니다. 경계 검출을 통해 두 상의 윤곽을 뚜렷하게 하고, 이후 팽창 연산을 통해 미세하게 흩어져 있는 공정 조직의 라멜라(lamellae) 구조들을 하나의 영역으로 연결했습니다. 이 두 단계의 파라미터를 어떻게 설정하느냐에 따라 각 상을 과대 또는 과소평가할 수 있으므로, 최적의 값을 찾는 것이 분석 정확도의 핵심이었습니다.

Q5: 연구가 주조품의 표면 근처 영역에 집중된 이유는 무엇인가요?

A5: 주조품의 표면, 즉 ‘스킨(skin)층’은 금형과 직접 접촉하여 가장 빠른 냉각 속도를 겪는 부분입니다. 이로 인해 내부보다 훨씬 미세하고 복잡한 미세조직이 형성되며, 이는 부품의 표면 품질, 내마모성, 피로 파괴 시작점 등에 결정적인 영향을 미칩니다. 가장 분석하기 까다로운 이 영역에서 알고리즘의 유효성을 검증함으로써, 다른 영역에서도 충분히 신뢰성 있는 분석이 가능함을 입증한 것입니다.

결론: 더 높은 품질과 생산성을 향한 길

알루미늄 고압 다이캐스팅 공정의 품질과 수율은 눈에 보이지 않는 미세조직에 의해 좌우됩니다. 본 연구는 복잡하고 시간이 많이 소요되던 미세조직 분석을 자동화하고, 신뢰성 있는 데이터를 얻기 위한 핵심 조건(이미지 해상도)을 규명함으로써 R&D 및 품질 관리의 새로운 가능성을 열었습니다. 표준화된 분석 기법은 더 빠른 의사결정을 가능하게 하여 궁극적으로 생산성 향상과 불량률 감소에 기여할 것입니다.

(주)에스티아이씨앤디에서는 고객이 수치해석을 직접 수행하고 싶지만 경험이 없거나, 시간이 없어서 용역을 통해 수치해석 결과를 얻고자 하는 경우 전문 엔지니어를 통해 CFD consulting services를 제공합니다. 귀하께서 당면하고 있는 연구프로젝트를 최소의 비용으로, 최적의 해결방안을 찾을 수 있도록 지원합니다.

  • 연락처 : 02-2026-0450
  • 이메일 : flow3d@stikorea.co.kr

저작권 정보

  • 이 콘텐츠는 Maria Diana David의 논문 “Microstructural Analysis of Aluminum High Pressure Die Castings”를 기반으로 한 요약 및 분석 자료입니다.
  • 출처: https://digitalcommons.library.uab.edu/etd-collection/1478

이 자료는 정보 제공 목적으로만 사용됩니다. 무단 상업적 사용을 금합니다. Copyright © 2025 STI C&D. All rights reserved.

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Figure 9. Pier scour sketch (Anerson et al., 2012)

교량 세굴 해석 정밀도 향상: 1D vs 2D 수리학적 모델링 접근법 비교 분석

이 기술 요약은 Luis Fernando Castaneda Galvis가 2023년 Auburn University에 제출한 석사 학위 논문 “Effect of hydrologic and hydraulic calculation approaches on pier scour estimates”를 기반으로 합니다. STI C&D에서 기술 전문가를 위해 분석하고 요약했습니다.

키워드

  • Primary Keyword: 교량 세굴 해석
  • Secondary Keywords: 수문학적 모델링, 수리학적 모델링, HEC-RAS, 2D 모델링, CFD, 교량 안정성, 홍수 분석

Executive Summary

  • 도전 과제: 교량 기초 주변의 토사 유실 현상인 교각 세굴은 교량 붕괴의 주요 원인이지만, 수문학적 및 수리학적 계산 접근법에 따라 예측치가 크게 달라져 인프라 안전에 심각한 위협이 됩니다.
  • 연구 방법: 4개의 실제 교량을 대상으로 12가지의 수문학적-수리학적 모델링 조합(총 48개 시뮬레이션)을 사용하여 교각 세굴 예측치를 체계적으로 비교 평가했습니다.
  • 핵심 발견: 2D 수리학적 모델은 복잡한 하천 지형에서 1D 모델보다 훨씬 더 현실적인 유속 분포를 보여주며, 결과적으로 더 깊은 세굴 깊이를 예측하여 보수적인 설계에 기여합니다.
  • 핵심 결론: 교량 안전성 평가 시, 특히 복잡한 지형에서는 1D 모델의 한계를 인식하고 2D 수리학적 모델을 채택하는 것이 교량 세굴 해석의 정확도를 높이는 데 필수적입니다.

도전 과제: 왜 이 연구가 CFD 전문가에게 중요한가?

교량 세굴은 전 세계적으로 교량의 안전과 안정성을 위협하는 심각한 문제입니다. 교량 기초 주변의 퇴적물이 침식되어 제거되는 이 현상은 수많은 교량 붕괴 사고의 원인이 되어 막대한 경제적, 인명 피해를 야기했습니다. 따라서 교량 구조물의 복원력과 수명을 보장하기 위해서는 세굴을 정확하게 예측하고 평가하는 것이 무엇보다 중요합니다.

문제는 세굴 깊이를 추정하는 데 사용되는 핵심 변수인 유속과 수심을 계산하는 데 다양한 수문학적, 수리학적 접근법이 존재한다는 것입니다. 각 접근법은 서로 다른 가정, 한계, 경계 조건을 가지므로 동일한 홍수 사상에 대해서도 상당히 다른 유량 결과를 산출할 수 있습니다. 이러한 차이가 최종적인 교각 세굴 예측에 얼마나 큰 영향을 미치는지에 대한 체계적인 연구가 부족한 실정이었습니다. 이는 엔지니어들이 가장 안전하고 정확한 모델링 방법을 선택하는 데 어려움을 겪게 만드는 주된 요인이었습니다.

접근법: 연구 방법론 분석

본 연구는 이러한 기술적 불확실성을 해결하기 위해 4개의 실제 교량을 대상으로 체계적인 비교 연구를 수행했습니다. 총 12가지의 수문학적 및 수리학적 계산법 조합을 적용하여 총 48개의 시뮬레이션을 진행했습니다.

Figure 1. Locations of the Flood regions in Alabama (Anderson, 2020)
Figure 1. Locations of the Flood regions in Alabama (Anderson, 2020)
  • 수문학적 모델링 (최대 유량 산정):
    • 지역 회귀 방정식(RRE): 주 교통국(DOT)에서 일반적으로 사용하는 간편한 방식입니다.
    • 홍수 빈도 분석(FFA): 유량계가 설치된 지점에서 과거 데이터를 기반으로 분석하는 방식입니다.
    • 분산형 수문 모델(HEC-HMS): SCS 유출 곡선 지수법을 사용하여 건조(CNI), 보통(CNII), 습윤(CNIII) 등 다양한 선행 토양 수분 조건을 고려한 강우-유출을 시뮬레이션했습니다.
  • 수리학적 모델링 (유속 및 수심 계산):
    • 1D 모델 (HEC-RAS): WSPRO 및 Energy 방정식을 사용하여 1차원 흐름을 해석했습니다.
    • 2D 모델 (HEC-RAS): SA/2D 연결 방식과 교각을 지형에 직접 반영(raised piers)하는 두 가지 2차원 방식을 사용하여 흐름을 해석했습니다.

이렇게 계산된 유속과 수심 데이터를 사용하여 FHWA의 HEC-18 방정식과 관측 기반 세굴 예측법(OMS)으로 최종 교각 세굴 깊이를 산정하고 그 결과를 비교 분석했습니다. 특히, 2D 지형 수정 모델(raised piers)을 벤치마크로 설정하여 다른 접근법들의 정확도를 평가했습니다.

핵심 발견: 주요 연구 결과 및 데이터

결과 1: 2D 모델이 복잡한 지형에서 더 정확하고 보수적인 세굴 예측을 제공한다

연구 결과, 1D 수리학적 모델(WSPRO, Energy)은 대부분의 경우 서로 유사한 결과를 보였지만, 2D 모델에 비해 세굴 깊이를 과소평가하는 경향이 뚜렷했습니다. 특히 Conecuh 강(BrM 013310)과 같이 유로가 복잡하고 넓은 범람원을 가진 교량의 경우, 2D 모델은 1D 모델보다 훨씬 더 현실적인 유선 분포와 높은 유속을 보여주었습니다.

아래 ‘최대/평균 유속 비율’ 그래프(Figure 63)에서 Conecuh 강(빨간색 막대)의 경우, 1D Energy 모델(1.795)이 비정상적으로 높은 값을 보이는 반면, 2D 모델들(1.431, 1.416)은 상대적으로 안정적인 값을 보입니다. 이는 1D 모델이 복잡한 흐름을 주 수로에만 집중시켜 비현실적인 결과를 낳을 수 있음을 시사합니다. 반면, 2D 모델은 흐름을 더 현실적으로 분산시켜 교각 주변의 실제 유속을 더 잘 예측하고, 이는 더 신뢰성 높은 세굴 해석으로 이어집니다.

결과 2: 표준 계산법(RRE)은 최악의 시나리오를 반영하지 못할 수 있다

주 교통국에서 널리 사용되는 지역 회귀 방정식(RRE)은 간편하지만, 항상 가장 보수적인 최대 유량을 제공하지는 않는 것으로 나타났습니다. 특히 습윤한 선행 토양 수분 조건(CNIII)을 고려한 HEC-HMS 수문 모델은 대부분의 경우 RRE보다 더 높은 최대 유량을 산출했습니다.

예를 들어, BrM 015002 교량의 경우, RRE로 계산된 100년 빈도 홍수 유량은 7,682 cfs였지만, HEC-HMS CNIII 모델은 9,689 cfs를 예측했습니다 (Table 8). 더 나아가, 실제 관측 데이터 기반의 홍수 빈도 분석(FFA) 결과는 14,570 cfs로 훨씬 높았습니다. 이는 RRE가 최악의 홍수 시나리오를 심각하게 과소평가할 수 있음을 보여주며, 특히 습윤 지역에서는 상세한 수문학적 모델링이 교량 세굴 해석에 필수적임을 강조합니다.

R&D 및 운영을 위한 실질적 시사점

  • 토목/수리 엔지니어: 복잡한 하도 형상이나 넓은 범람원을 가진 교량의 세굴을 평가할 때, 1D 모델의 한계를 명확히 인지해야 합니다. 2D 수리학적 모델을 사용하여 교각 주변의 유속 분포를 정밀하게 해석하는 것이 더 안전하고 신뢰할 수 있는 결과를 제공합니다.
  • 인프라 관리 및 교통 부서(DOTs): 최대 유량 산정 시 지역 회귀 방정식(RRE)에만 의존하는 것은 위험할 수 있습니다. 특히 습윤 기후 지역에서는 습윤 선행 토양 수분 조건(CNIII)을 고려한 HEC-HMS와 같은 상세 수문 모델링을 수행하여 더 보수적인 설계 기준을 마련해야 합니다.
  • 품질 및 리스크 관리팀: 본 연구는 수문학적 및 수리학적 모델 선택이 교량 세굴 해석 결과에 지대한 영향을 미친다는 것을 보여줍니다. 교량 인프라에 대한 포괄적인 리스크 평가 프로토콜에는 유량계 데이터가 있는 경우 홍수 빈도 분석(FFA)을 포함하고, 복잡한 현장에는 2D 수리학적 분석을 의무화하는 다중 모델 접근법을 포함해야 합니다.

논문 상세 정보

Effect of hydrologic and hydraulic calculation approaches on pier scour estimates

1. 개요:

  • 제목: Effect of hydrologic and hydraulic calculation approaches on pier scour estimates (수문학적 및 수리학적 계산 접근법이 교각 세굴 추정에 미치는 영향)
  • 저자: Luis Fernando Castaneda Galvis
  • 발행 연도: 2023
  • 학술지/학회: Auburn University (석사 학위 논문)
  • 키워드: HEC-HMS, RRE, SCS Curve Number, HEC-RAS, 1D-models, 2D models, Pier bridge Scour, HEC-18, Hydraulic Toolbox, Observation Method for Scour

2. 초록:

교량 기초 주변의 퇴적물 침식 및 제거 현상인 교량 세굴은 토목 공학 및 인프라 관리 분야에서 중요한 관심사입니다. 세굴 추정에 사용되는 변수인 교량 부근의 수심과 유속을 결정하기 위해 최대 유량을 계산하는 다양한 수문학적 및 수리학적 접근법이 있습니다. 각 접근법은 가정, 한계, 경계 조건에 따라 수심 및 유속 추정에 영향을 미치는 상당히 다른 유량 결과를 낳을 수 있습니다. 또한, 방법들이 유사한 유량 크기를 추정할 때조차도 교량 구성에 따라 다른 유속 분포가 발생할 수 있습니다. 이러한 방법들이 교각 세굴 깊이 추정에 미치는 영향의 정도는 체계적인 조사의 부족으로 잘 알려져 있지 않습니다. 본 연구는 4개의 교량에 대해 12가지의 수문학적 및 수리학적 접근법 조합을 사용하여 총 48개의 시뮬레이션을 통해 교각 세굴을 평가함으로써 이 질문에 답하고자 합니다. 각 시뮬레이션은 FHWA HEC-18 및 관측 기반 세굴 예측법(OMS) 방법론을 사용하여 잠재적인 교각 세굴 깊이를 평가하기 위해 분석되었습니다. 최대 유량을 계산하는 대안으로는 지역 회귀 방정식(RRE), 홍수 빈도 분석(FFA), 그리고 HEC-HMS 4.9를 사용한 분산 모델이 있으며, SCS 유출 곡선 지수법을 사용하여 다양한 선행 수분 조건을 평가했습니다. 100년 주기 사상에 대한 최대 유량이 추정되었고, 수문 모델은 단일 사상 기반으로 시뮬레이션되었습니다. 수리학적 분석에는 HEC-RAS 6.1/6.2가 활용되었으며, 1D-WSPRO, 1D-Energy, 2D SA 연결, 그리고 교각을 높인 2D 지형 수정이 교량 모델링 접근법으로 사용되었습니다. HEC-RAS 모델은 1미터 x 1미터(3.28 x 3.28 ft) 해상도의 Lidar 데이터를 사용하여 생성되었습니다. 결과는 주 교통국에서 자주 사용하는 회귀 방정식이 수문 모델 시뮬레이션과 비교할 때 항상 최악의 수문학적 시나리오를 제공하지는 않는다는 것을 보여주었습니다. 1D 모델의 결과는 매우 유사하며, 대부분의 경우 더 적은 세굴 깊이를 생성합니다. 2D 접근법은 복잡한 구성을 가진 교량의 접근 수로를 더 잘 나타내며, 1D 모델보다 더 큰 유속과 따라서 더 많은 세굴 깊이를 묘사합니다. 마지막으로, 수분 조건이 최대 유량 결정을 위한 최악의 시나리오를 결정하는 데 영향을 미칠 수 있으며, 이는 다시 세굴 계산에 영향을 미친다는 것이 발견되었습니다.

3. 서론:

교량 세굴은 흐르는 하천의 침식 작용으로 인해 발생하는 자연 현상으로, 물, 토양, 구조물이 상호 작용하는 일반적인 문제입니다. 이는 교량의 안전과 안정성에 심각한 위협이 되며, 전 세계적으로 수많은 교량 붕괴를 초래하여 상당한 경제적, 인명 손실을 야기했습니다. 교량 구조물의 복원력과 수명을 보장하기 위해서는 교량 세굴의 예측과 평가가 매우 중요합니다. HEC-18(Hydraulic Engineering Circular No. 18)은 100년 설계 홍수 사상을 기반으로 세굴 깊이를 계산하는 결정론적 절차를 제공합니다. 최대 유량을 계산하는 방법은 다양하며, 계산된 유량을 바탕으로 수리학적 모델링을 통해 교량 부근의 유속과 수심을 추정합니다. 1D 또는 2D 모델링 접근법에 따라 이 변수들의 크기, 방향, 분포가 달라질 수 있습니다. 다양한 최대 유량 계산법과 교량 모델링 접근법이 존재함에도 불구하고, 이들의 조합이 세굴 예측 결과에 미치는 차이를 체계적으로 평가한 연구는 부족했습니다. 이 연구는 “수문학적 및 수리학적 계산 접근법의 다양한 대안이 교각 세굴 추정치에 어느 정도 영향을 미칠 수 있는가?”라는 연구 질문에 답하는 것을 목표로 합니다.

4. 연구 요약:

연구 주제의 배경:

교량 세굴은 교량의 구조적 안전성에 직접적인 영향을 미치는 핵심적인 문제이며, 이를 정확히 예측하는 것은 인프라 관리의 중요한 부분입니다. 세굴 예측은 수문학적 분석(얼마나 많은 물이 오는가?)과 수리학적 분석(물이 어떻게 흐르는가?)의 두 단계로 이루어지는데, 각 단계에서 사용 가능한 여러 방법론 간의 결과 차이가 최종 예측의 불확실성을 증가시킵니다.

이전 연구 현황:

과거 연구들은 개별적인 수문학적 또는 수리학적 모델링 방법에 초점을 맞추었지만, 이 두 가지를 조합했을 때 발생하는 결과의 변동성을 체계적으로 분석한 연구는 드물었습니다. 특히, 간편성 때문에 널리 사용되는 지역 회귀 방정식(RRE)과 물리적 과정을 더 상세히 모사하는 분산형 수문 모델(HEC-HMS) 간의 차이, 그리고 1D와 2D 수리학적 모델 간의 차이가 세굴 예측에 미치는 복합적인 영향을 규명할 필요가 있었습니다.

연구의 목적:

본 연구의 목적은 다양한 수문학적 및 수리학적 계산 접근법 조합이 교각 세굴 예측치에 미치는 영향을 정량적으로 평가하는 것입니다. 이를 통해 엔지니어들이 특정 현장 조건에 가장 적합하고 안전한 모델링 조합을 선택하는 데 과학적 근거를 제공하고자 합니다.

핵심 연구:

알라배마 주에 위치한 4개의 실제 교량을 대상으로, 3가지 수문학적 접근법(RRE, FFA, HEC-HMS)과 4가지 수리학적 접근법(1D WSPRO, 1D Energy, 2D SA connection, 2D terrain modification)을 조합하여 100년 빈도 홍수 사상에 대한 교각 세굴을 시뮬레이션하고 그 결과를 비교 분석했습니다.

Figure 9. Pier scour sketch (Anerson et al., 2012)
Figure 9. Pier scour sketch (Anerson et al., 2012)

5. 연구 방법론:

연구 설계:

본 연구는 비교 분석 연구 설계를 채택했습니다. 4개의 교량(연구 대상)에 대해 독립 변수인 수문학적 접근법(3가지)과 수리학적 접근법(4가지)을 체계적으로 조합하여 종속 변수인 교각 세굴 깊이를 측정하고 비교했습니다. 2D 지형 수정 모델을 벤치마크로 사용하여 다른 모델들의 성능을 평가했습니다.

데이터 수집 및 분석 방법:

  • 데이터 수집: USGS로부터 DEM(Digital Elevation Model) 데이터, Lidar 지형 데이터, NLCD 토지 피복 데이터, SSURGO 토양 데이터를 수집했습니다. 유량계가 있는 지점에서는 과거 유량 데이터를, 강우 데이터는 Atlas 14에서 추출했습니다.
  • 데이터 분석:
    • 수문 분석: StreamStats를 사용하여 유역을 획정하고 RRE 값을 계산했습니다. PeakFQ 소프트웨어로 홍수 빈도 분석(FFA)을 수행했습니다. HEC-HMS 소프트웨어를 사용하여 다양한 선행 토양 수분 조건(CNI, CNII, CNIII)에 대한 강우-유출 모델링을 수행했습니다.
    • 수리 분석: HEC-RAS 소프트웨어를 사용하여 1D 및 2D 수리학적 모델을 구축하고, 각 수문 시나리오에 대한 유속 및 수심을 계산했습니다.
    • 세굴 분석: Hydraulic Toolbox를 사용하여 HEC-18 방정식을 기반으로 교각 세굴 깊이를 계산했으며, OMS 방법론과도 비교했습니다.
Figure 40. Terrain modification with raised piers
Figure 40. Terrain modification with raised piers

연구 주제 및 범위:

본 연구는 알라배마 주에 위치한 4개의 특정 교량을 대상으로 하며, 100년 빈도 홍수 사상에 대한 교각 세굴에 초점을 맞춥니다. 연구에서 사용된 소프트웨어는 HEC-HMS, HEC-RAS, PeakFQ 등이며, 세굴 계산은 HEC-18 방정식을 주로 사용했습니다.

6. 주요 결과:

주요 결과:

  • 주 교통국(DOT)에서 널리 사용하는 지역 회귀 방정식(RRE)은 상세 수문 모델(HEC-HMS)과 비교 시 항상 최악의 시나리오(가장 큰 유량)를 제공하지 않았으며, 일부 교량에서는 유량을 최대 70%까지 과소평가했습니다.
  • 1D 수리학적 모델들은 서로 유사한 결과를 보였으나, 복잡한 하천 지형을 가진 교량에서는 흐름을 제대로 모사하지 못하고 세굴 깊이를 과소평가하는 경향을 보였습니다.
  • 2D 수리학적 모델, 특히 교각을 지형에 직접 반영한 모델(벤치마크)은 더 넓은 범람원, 더 빠른 유속, 그리고 더 얕은 수심을 보여주어, 결과적으로 1D 모델보다 더 깊은 세굴을 예측하는 경향이 있었습니다. 이는 2D 모델이 더 보수적이고 현실적인 결과를 제공함을 의미합니다.
  • 선행 토양 수분 조건은 최대 유량 산정에 큰 영향을 미쳤으며, 습윤 조건(CNIII)이 가장 보수적인(가장 큰) 세굴 예측 결과를 낳았습니다.

Figure 목록:

  • Figure 1. Locations of the Flood regions in Alabama (Anderson, 2020)
  • Figure 2. Calibration process diagram used by HEC-HMS. Feldman (2000)
  • Figure 3. Symbols used. Equations for motion and mass conservation (Brunner et al., 2020)
  • Figure 4. Channel Profile and cross section locations (Brunner and CEIWR-HEC, 2020)
  • Figure 5. Cross Sections Near and Inside the Bridge (Brunner and CEIWR-HEC, 2020)
  • Figure 6. Critical shear stress vs particle grain size (Briaud et al. 2011)
  • Figure 7. Flow around a single pier (Prendergast and Gavin, 2014)
  • Figure 8. Comparison of scour equations for variable depth ratios (y/a) according with Jones (TRB, 1983)
  • Figure 9. Pier scour sketch (Anerson et al., 2012)
  • Figure 10. Methodology Flowchart
  • Figure 11. Location of the selected Bridges in the State of Alabama (Google Earth, 2023)
  • Figure 12. Location of Bridge No 015002. (Google Earth, 2023)
  • Figure 13. USGS station No. 02362240 is located at the Bridge entrance. (USGS, 2023)
  • Figure 14. Bridge No 0150002 configuration. (AASHTOWare BrM, 2023)
  • Figure 15. Location of Bridge No 010738. (Google Earth, 2023)
  • Figure 16. Bridge No 010738 configuration. Source: AASHTOWare BrM
  • Figure 17. Location of Bridge No 013310. (Google Earth, 2023)
  • Figure 18. Bridge No 013310 configuration. (AASHTOWare BrM, 2023)
  • Figure 19. Location of Bridge No 013310. (Google Earth, 2023)
  • Figure 20. Bridge No 013310 configuration. Source: AASHTOWare BrM
  • Figure 21. Area extracted from Streamstats for an example watershed.
  • Figure 22. Peak flow streamflow data for Bridge No 015002
  • Figure 23. Resulted chart using the software PeakFQ
  • Figure 24. Watershed associated with the analyzed bridges (a) BrM No 015002 (b) BrM No 010738 (c) BrM No 007070 (d) BrM 013310
  • Figure 25. DEMs for the watersheds associated with the selected bridges (a) BrM No 015002 (b) BrM No 010738 (c) BrM No 007070 (d) BrM 013310
  • Figure 26. Land cover values for the analyzed watersheds related with the bridges (a) BrM No 015002 (b) BrM No 010738 (c) BrM No 007070 (d) BrM 013310
  • Figure 27. Models created in HEC-HMS for the watersheds associated with the bridges (a) BrM No 015002 (b) BrM No 010738 (c) BrM No 007070 (d) BrM 013310
  • Figure 28. Rain gage deployed in Bridge BrM No 015002
  • Figure 29. Geometry 1D Hydraulic model in HEC-RAS and bridge cross section
  • Figure 30. Geometry 2D Hydraulic model in HEC-RAS and bridge and SA 2D connection
  • Figure 31. Terrain modification with raised piers
  • Figure 32. Geometry 1D Hydraulic model in HEC-RAS and bridge cross section
  • Figure 33. Geometry 2D Hydraulic model in HEC-RAS and bridge and SA 2D connection
  • Figure 34. Terrain modification with raised piers
  • Figure 35. Geometry 1D Hydraulic model in HEC-RAS and bridge cross section
  • Figure 36. Geometry 2D Hydraulic model in HEC-RAS and bridge and SA 2D connection
  • Figure 37. Terrain modification with raised piers
  • Figure 38. Geometry 1D Hydraulic model in HEC-RAS and bridge cross section
  • Figure 39. Geometry 2D Hydraulic model in HEC-RAS and bridge and SA 2D connection
  • Figure 40. Terrain modification with raised piers
  • Figure 41. Calibration results for minimizing the percent error in peak discharge in Little Double Bridges Creek (BrM No 015002)
  • Figure 42. Comparison between the two resultant outflow hydrographs.
  • Figure 43. Outflow hydrographs for watershed associated BrM No 015002 and different antecedent soil moisture conditions, CNI, CNII and CNIII.
  • Figure 44. Outflow hydrographs for watershed associated BrM 0107038 and different antecedent soil moisture conditions, CNI, CNII and CNIII.
  • Figure 45. Outflow hydrographs for watershed associated BrM 013310 and different antecedent soil moisture conditions, CNI, CNII and CNIII
  • Figure 46. Outflow hydrographs for watershed associated BrM 007070 and different antecedent soil moisture conditions, CNI, CNII and CNIII.
  • Figure 47. Velocities for different bridge modeling approaches, Bridge BrM No 015002. (a) WSPRO (b) Energy (c) 2D/SA connection (d) 2D terrain modification with raised piers
  • Figure 48.Velocities comparison for the bridge modeling approaches. Bridge BrM015002
  • Figure 49. Water depth results for different bridge modeling approaches, Bridge BrM No 015002. (a) WSPRO (b) Energy (c) 2D/SA connection (d) 2D terrain modification with raised piers
  • Figure 50.Water depth for the different bridge modeling approach. Bridge BrM015002
  • Figure 51. Velocities results for different bridge modeling approaches, Bridge BrM No 010738. (a) WSPRO (b) Energy (c) 2D/SA connection (d) 2D terrain modification with raised piers
  • Figure 52.Velocities for the different bridge modeling approach. Bridge BrM010738
  • Figure 53. Water depth for different bridge modeling approaches, Bridge BrM No 010738. (a) WSPRO (b) Energy (c) 2D/SA connection (d) 2D terrain modification with raised piers
  • Figure 54.Water depth for the different bridge modeling approach. Bridge BrM010738
  • Figure 55. Velocities for different bridge modeling approaches, Bridge BrM No 013310. (a) WSPRO (b) Energy (c) 2D/SA connection (d) 2D terrain modification with raised piers
  • Figure 56.Velocities for the different bridge modeling approach. Bridge BrM013310
  • Figure 57. Water depth for different bridge modeling approaches, Bridge BrM No 013310. (a) WSPRO (b) Energy (c) 2D/SA connection (d) 2D terrain modification with raised piers
  • Figure 58.Water depth for the different bridge modeling approach. BrM No 013310
  • Figure 59. Velocities results for different bridge modeling approaches, Bridge BrM No 007070. (a) WSPRO (b) Energy (c) 2D/SA connection (d) 2D terrain modification with raised piers
  • Figure 60. Velocity for the different bridge modeling approach. Bridge BrM No 007070
  • Figure 61. Water depth for different bridge modeling approaches, Bridge BrM No 007070. (a) WSPRO (b) Energy (c) 2D/SA connection (d) 2D terrain modification with raised piers
  • Figure 62.Water depth for the different bridge modeling approach. Bridge BrM007070
  • Figure 63.Peak to average velocities by bridge for the different bridge modeling approaches
  • Figure 64.Peak to average for scour depth using RRE
  • Figure 65. Peak to average for scour depth using CNII
  • Figure 66. Peak to average for scour depth using CNIII
  • Figure 67. HEC-18 scour comparison values of the different alternatives to calculate the flow using the Bridge modeling approach (benchmark). Bridge BrM No 015002
  • Figure 68. HEC-18 pier scour comparison of the different alternatives to calculate the flow using the Bridge modeling approach (benchmark). Bridge BrM No 010738
  • Figure 69. HEC-18 pier scour comparison of the different alternatives to calculate the flow using the Bridge modeling approach (benchmark). Bridge BrM No 013310
  • Figure 70. HEC-18 pier scour comparison of the different alternatives to calculate the flow using the Bridge modeling approach (benchmark). Bridge BrM No 007070

7. 결론:

본 연구는 HEC-18 접근법을 사용한 세굴 추정치가 수문학적 및 수리학적 모델링 도구의 선택에 크게 좌우된다는 점을 명확히 보여주었습니다. 1D 모델은 단순한 교량에서는 서로 유사한 결과를 보이지만, 복잡한 교량 횡단면에서는 유용성이 제한적이었습니다. 1D 모델은 교량 상류에서 더 깊은 수심을 예측하고, 교량 입구에서 흐름을 제어하여 유속과 세굴을 감소시키는 경향이 있었습니다. 반면, 2D 모델에서는 더 큰 유속이 관찰되었고 흐름 표현이 더 합리적이어서, 대부분의 경우 세굴 추정치를 개선할 수 있었습니다. 결론적으로, 교량 세굴 해석의 정확성과 안전성을 높이기 위해서는, 특히 복잡한 지형에서는 2D 수리학적 모델을 사용하고, 습윤 지역에서는 보수적인 선행 수분 조건을 고려한 상세 수문 모델링을 수행하는 것이 필수적입니다.

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전문가 Q&A: 자주 묻는 질문

Q1: 이 연구에서 1D와 2D 수리학적 모델을 모두 비교한 이유는 무엇인가요?

A1: 1D와 2D 모델 간의 결과 차이를 체계적으로 평가하기 위함입니다. 1D 모델은 계산이 간단하지만 흐름 방향에 대한 중요한 가정을 포함합니다. 반면, 2D 모델은 더 복잡하지만 교각 주변의 복잡한 흐름 패턴, 유속 분포, 재순환 구역 등을 더 잘 표현할 수 있으며, 이는 정확한 세굴 예측에 매우 중요합니다. 이 연구는 이러한 모델링 상세 수준의 차이가 최종 세굴 추정치에 어떤 영향을 미치는지 정량화하는 것을 목표로 했습니다.

Q2: Conecuh 강 교량(BrM 013310)의 경우, 일반적인 경향과 달리 1D 모델이 2D 모델보다 더 큰 세굴을 예측했습니다. 그 이유는 무엇인가요?

A2: 이는 해당 교량의 복잡한 수리 특성(여러 개의 개구부, 넓은 범람원) 때문인 예외적인 경우입니다. 논문에 따르면, 이 특정 사례에서 1D 모델은 흐름을 비현실적으로 주 수로에만 집중시켜 인위적으로 높은 유속과 세굴을 예측했습니다. 반면, 2D 모델은 흐름을 더 현실적으로 분산시켜 더 낮은(그리고 아마도 더 정확한) 최대 세굴 값을 산출했으며, 이는 복잡한 시나리오에서 1D 모델의 한계를 명확히 보여줍니다.

Q3: HEC-HMS 모델에서 다양한 선행 토양 수분 조건(CNI, CNII, CNIII)을 비교하는 것의 의미는 무엇인가요?

A3: 최대 유출량에 대한 최악의 시나리오를 결정하기 위함입니다. 선행 수분 조건은 강우 사상 이전의 토양 포화도를 반영합니다. 습윤 조건(CNIII)은 토양이 물을 거의 흡수하지 못해 더 높고 빠른 유출을 유발합니다. 연구 결과, CNIII이 일관되게 가장 높은 최대 유량과 세굴 깊이를 예측했으며, 이는 ‘보통’ 조건(CNII)을 가정하는 것이 특히 습윤 기후에서 리스크를 과소평가할 수 있음을 시사합니다.

Q4: 이 연구에서 벤치마크 모델로 ‘교각을 높인 2D 지형 수정 모델’을 선택한 이유는 무엇인가요?

A4: 이 모델이 교각의 물리적 존재와 그로 인한 흐름 방해를 가장 직접적이고 현실적으로 시뮬레이션하기 때문입니다. 교각을 지형 데이터에 직접 통합함으로써, 모델은 교각 주변에서 발생하는 실제 유체 역학적 현상(예: 말발굽 와류, 후류 와류)을 다른 추상적인 방법(예: SA/2D 연결)보다 더 정확하게 재현할 수 있습니다. 따라서 이 모델의 결과를 기준으로 다른 간소화된 모델들의 정확도를 평가하는 것이 합리적입니다.

Q5: 연구 결과가 특정 지역(알라배마)에 국한되는데, 다른 지역에도 이 결론을 적용할 수 있을까요?

A5: 네, 적용 가능합니다. 특히 연구의 핵심 결론인 ‘복잡한 지형에서는 2D 모델이 우수하다’와 ‘단순화된 수문학적 방법은 위험을 과소평가할 수 있다’는 원칙은 보편적입니다. 다만, 습윤 선행 토양 수분 조건(CNIII)의 중요성은 알라배마와 같은 습윤 기후에서 더 두드러집니다. 건조 기후 지역에서는 다른 수분 조건이 최악의 시나리오가 될 수 있으므로, 각 지역의 기후 특성을 고려하여 모델링 조건을 설정하는 것이 중요합니다.

결론: 더 높은 품질과 생산성을 위한 길

이 연구는 교량 세굴 해석의 정확도가 어떤 수문학적, 수리학적 모델링 도구를 선택하는지에 따라 크게 달라질 수 있음을 명확하게 보여주었습니다. 특히 복잡한 교량 횡단면에서는 1D 모델의 한계가 뚜렷하며, 2D 모델이 제공하는 상세한 흐름 정보가 더 안전하고 신뢰성 있는 예측을 가능하게 합니다. 또한, 간편한 표준 계산법에 의존하기보다 현장의 특성을 반영한 상세 모델링을 수행하는 것이 장기적인 인프라 안전 확보에 필수적입니다.

STI C&D는 최신 산업 연구 결과를 적용하여 고객이 더 높은 생산성과 품질을 달성할 수 있도록 최선을 다하고 있습니다. 이 논문에서 논의된 과제가 귀사의 운영 목표와 일치한다면, 저희 엔지니어링 팀에 연락하여 이러한 원칙을 귀사의 구성 요소에 어떻게 구현할 수 있는지 논의해 보십시오.

(주)에스티아이씨앤디에서는 고객이 수치해석을 직접 수행하고 싶지만 경험이 없거나, 시간이 없어서 용역을 통해 수치해석 결과를 얻고자 하는 경우 전문 엔지니어를 통해 CFD consulting services를 제공합니다. 귀하께서 당면하고 있는 연구프로젝트를 최소의 비용으로, 최적의 해결방안을 찾을 수 있도록 지원합니다.

  • 연락처 : 02-2026-0442
  • 이메일 : flow3d@stikorea.co.kr

저작권 정보

  • 이 콘텐츠는 “[Luis Fernando Castaneda Galvis]”의 논문 “[Effect of hydrologic and hydraulic calculation approaches on pier scour estimates]”를 기반으로 한 요약 및 분석 자료입니다.
  • 출처: https://etd.auburn.edu/handle/10415/8904

이 자료는 정보 제공 목적으로만 사용됩니다. 무단 상업적 사용을 금합니다. Copyright © 2025 STI C&D. All rights reserved.

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FLOW-3D HYDRO

FLOW-3D HYDRO를 활용한 CFD 모델링 신뢰도 구축

이 브리핑 문서는 FLOW-3D HYDRO 소프트웨어를 사용한 전산 유체 역학(CFD) 모델링에 대한 신뢰를 구축하는 방법에 중점을 둡니다. 주요 테마는 다음과 같습니다:

  • CFD 모델링의 정의 및 중요성: 유동이 환경과 상호작용하는 방식을 정확하고 상세하며 동적으로 3차원 맥락에서 모델링하는 과정.
  • FLOW-3D HYDRO의 특징 및 이점: 사용자 친화적인 인터페이스, 간소화된 메시 구성, 3D 자유 표면 모델링에 특화된 기능(1-유체 접근 방식)을 통해 다른 CFD 도구와 차별화됩니다.
  • CFD 활용 사례 및 성공 스토리: 실제 프로젝트에서의 다양한 적용 사례를 통해 CFD의 가치와 효과를 입증합니다.
  • FLOW-3D HYDRO 교육 과정 안내: 사용자가 자신의 기술과 CFD 모델링 프로세스에 대한 자신감을 구축할 수 있도록 돕는 새로운 온디맨드 교육 과정을 소개합니다.

복잡한 유체 역학, 더 이상 추측에 맡기지 마세요

현대 엔지니어링 프로젝트에서 유체 역학은 예측 불가능한 변수로 작용하여 설계의 안정성과 효율성에 큰 영향을 미칩니다. 댐, 강, 처리 시설 등 물과 관련된 다양한 환경에서 유체가 어떻게 움직이고 상호작용하는지 정확히 이해하는 것은 성공적인 프로젝트 수행에 필수적입니다. 그러나 기존의 전통적인 방식으로는 이러한 복잡한 유체 거동을 완벽하게 파악하기 어려웠습니다. 이제 우리는 추측이 아닌, 과학적인 분석을 통해 유체 역학의 난제를 해결할 수 있는 시대에 살고 있습니다.

CFD 모델링, 무엇이 다를까요?

CFD(Computational Fluid Dynamics), 즉 전산 유체 역학모델링은 유동이 3차원 환경과 어떻게 상호작용하는지 정확하고 상세하며 동적인 방식으로 모델링하는 과정입니다. 이는 물과 같은 유체가 특정 환경 내에서 어떻게 움직이고 작용하는지 시뮬레이션하는 데 사용됩니다.

CFD모델링이 기존 1D 및 2D 모델과 차별화되는 핵심은 다음과 같습니다:

  • 더 높은 정확도 제공: 기존 1D/2D 모델이 깊이 평균이나 단면 평균과 같은 가정을 포함하고 사용자 계수 입력에 의존하는 반면, 3D CFD모델링은 이러한 가정을 줄여 ‘ 수직 수주’를 고려함으로써 훨씬 높은 정확도를 제공합니다.
  • 복잡한 현상 분석: 고위험 프로젝트, 설계 불확실성 감소, 공기 혼입이나 퇴적물 이동과 같은 다중 물리 현상이 복합적으로 작용하는 경우에 특히 유용합니다.
  • 시각적 커뮤니케이션 도구: 복잡한 상황을 시각적으로 명확하게 설명할 수 있어, 이해 관계자들과의 소통을 위한 강력한 도구가 됩니다.

FLOW-3D HYDRO, 왜 특별할까요?

FLOW-3D HYDRO는 수자원 산업애플리케이션에 특화된 CFD 소프트웨어로, 다음과 같은 독보적인 특징과 이점을 제공합니다.

  • 사용자 친화적인 인터페이스와 효율적인 메시 구성:
    • 쉽게 사용할 수 있는 사용자 인터페이스를 통해 접근성을 높였습니다.
    • ‘ 구조화된 메시’ 방식을 사용하여 지오메트리 포착이 간단하며 효율적인 메시 구성을 가능하게 합니다.
  • 혁신적인 1-유체 접근 방식:
    • 대부분의 수자원 애플리케이션에서 공기 흐름을 명시적으로 모델링하지 않고 자유 표면을 추적하는 ‘ 1-유체 접근 방식’을 사용합니다.
    • 이는 더 빠른 시뮬레이션을 가능하게 하며, 모델 실행에 필요한 하드웨어 요구 사항을 줄여줍니다.
    • 실제로, 동일한 모델에서 1-유체 접근 방식은 1시간이 걸린 반면, 2-유체 접근 방식은 6시간이 소요된 사례가 있습니다.
  • Flow Science의 전문성:
    • Flow Science는 1980년에 설립되었으며, 상용 소프트웨어인 FLOW-3D는 1985년에 출시되었습니다.
    • 이 회사는 로스 알라모스 국립 연구소에서 CFD연구를 시작하며 전문성을 쌓았습니다.

CFD 모델링 워크플로우

일반적인 CFD모델링 워크플로우는 다음과 같은 단계로 진행됩니다.

  • 시뮬레이션 설정: 내장 템플릿을 사용하여 시뮬레이션을 설정합니다.
  • 3D 지오메트리 가져오기: 대부분 3D CAD에서 생성된 지오메트리를 가져옵니다.
  • 메시 적용: 구조화된 메시블록을 사용하여 지오메트리 주변에 메시를 생성하고 셀 해상도를 정의합니다.
  • 경계 조건 및 초기 조건 정의: 유입, 유출, 수위, 초기 수위 등을 정의합니다.
  • 측정 도구 추가: 유속 측정면이나 프로브를 통해 데이터를 수집합니다.
  • 데이터 출력 설정: 데이터 저장 빈도를 제어합니다.
  • 시뮬레이션 실행: 모델을 실행하고 진행 상황을 모니터링합니다.
  • 후처리: 모델 실행 후 결과를 시각화하고 필요한 데이터를 추출하여 프로젝트 정보에 활용합니다.

실제 사례로 본 FLOW-3D HYDRO의 힘

FLOW-3D HYDRO는 전 세계 다양한 프로젝트에서 성공적으로 적용되어 그 가치를 입증하고 있습니다.

  • 자전거 도로 배수 시스템 (브리즈번):
    • ‘곡선 파괴’를 통한 배수 흐름을 시뮬레이션하여 다양한 유량 및 경사 조합에 대한 등급 곡선을 도출하고 설계를 개선했습니다.
    • 물리적 모델링이 불가능한 경우 CFD를 보충적으로 활용하여 효과를 극대화했습니다.
  • 주요 침전 탱크 (빅토리아주):
    • 슬러지 층의 비뉴턴 유체특성을 모델링하여 ‘쥐 구멍’ 현상을 해결하고 슬러지 펌핑을 최적화했습니다.
    • 초기 회의론에도 불구하고, 모델링 결과가 현장 측정과 일치하며 신뢰를 얻었습니다.
  • 어류 통로 (중앙 퀸즐랜드):
    • 혁신적인 계단식 위어디자인의 흐름 패턴을 최적화하여 다양한 수위 조건에서 어류가 원활하게 이동할 수 있도록 설계했습니다.
    • 시뮬레이션후 건설된 어류 통로는 모니터링 기간 동안 거의 3,000마리의 물고기가 통과하는 등 성공적으로 작동했습니다.
  • 터빈 흡입구 게이트 (뉴질랜드):
    • 게이트를 들어 올릴 때 발생하는 ‘불균일한 하중 스파이크’의 원인을 CFD로 파악했습니다.
    • 현장 접근이 어려운 ‘사각 지대’를 밝혀내어 문제 해결책을 찾는 데 중요한 통찰력을 제공했습니다.
  • 생태 해안선 보호 (미국):
    • 연간 10~40피트의 침식을 겪는 해안선 보호를 위해 9가지 다른 제품의 파도 전달을 시뮬레이션했습니다.
    • FLOW-3D HYDRO를 ‘가상 실험실’로 활용하여 비용 효율적으로 제품 성능을 평가하고 최적의 솔루션을 선택했습니다.
    • 결과적으로 파고가 절반으로 줄고, 해안선 침식도 약 절반으로 감소했으며, 모델 예측은 모니터링 결과와 몇 퍼센트 이내로 일치했습니다.
  • 댐 수문 방류량 등급 곡선 (미국):
    • 1950년대에 개발된 댐 수문의 등급 곡선을 업데이트하는 데 CFD를 활용했습니다.
    • 결과는 물리적 모델과 3% 이내로 일치했습니다.

FLOW-3D HYDRO, 직접 경험해보세요: 교육 과정 안내

cfd모델링에 대한 자신감을 얻고 싶다면, FLOW-3D HYDRO교육 과정을 통해 직접 경험해보세요. 이 온디맨드 교육과정은 cfd모델링에 대한 장벽을 없애고 모든 경험 수준의 사용자에게 적합하도록 설계되었습니다.

  • 교육 과정 구성:
    • 파트 1: 간단한 위어위로 흐르는 유동 모델링 (2D에서 3D로 확장)
    • 파트 2: 퇴적물 이동, 하이브리드 메시, 접촉 탱크, 해안선 방어, 비뉴턴 유체, 우수 피트 등 7가지 다양한 응용 분야별 실습
  • 과정의 이점:
    • 실습 중심 학습: 워크플로우를 반복하며 자신감을 얻을 수 있습니다.
    • 유연성: 관심 있는 연습 문제를 자유롭게 선택할 수 있습니다.
    • 라이선스 제공: 30일 동안 FLOW-3D 소프트웨어의 전체 버전을 사용하여 개인 프로젝트에도 적용할 수 있습니다.
    • 전폭적인 지원: 단계별 가이드, 비디오, 온라인 문서 및 라이브 지원을 통해 학습 과정을 돕습니다.
  • 대상자: CFD모델링을 직접 수행하는 실무자는 물론, 관련 보고서를 이해하고 더 많은 정보를 바탕으로 질문을 던지기 원하는 클라이언트에게도 유용합니다.

질의응답 하이라이트: FLOW-3D HYDRO의 다양한 적용 가능성

웨비나 중 질의응답 세션에서 다루어진 중요한 질문들을 통해 FLOW-3D HYDRO의 폭넓은 적용 가능성을 엿볼 수 있습니다.

  • 퇴적물 이동: FLOW-3D HYDRO는 ‘침식 가능한’ 구성 요소를 정의하고 ‘다른 입자 종’을 설정하여 비응집성 퇴적물 모델링이 가능합니다. 바닥 전단 응력에 의해 퇴적물이 유동으로 유입되고 침전 및 퇴적이 모델링됩니다.
  • 비뉴턴 유체: FLOW-3D는 흙탕물, 잔해, 찌꺼기와 같은 비뉴턴 유체를 모델링할 수 있으며, 이를 위해 ‘허셸-버클리(Herschel-Bulkley) 모델’을 사용합니다.
  • 지원되는 데이터 형식: GIS플랫폼에서 래스터 형식(예: GeoTIFF, LAD XML)으로 데이터를 가져올 수 있으며, CAD모델에서 STL 형식으로 지오메트리를 로드할 수 있습니다.
  • 오염물질/열 플룸 전송: ‘ 스칼라 전송 모델’을 사용하여 강이나 해양의 오염물질 또는 열 플룸의 운명을 추적할 수 있습니다.

결론: FLOW-3D HYDRO와 함께 미래를 설계하세요

flow-3d hydro는 다재다능하고 정확하며 위험과 불확실성을 줄이는 데 도움이 되는 강력한 cfd모델링 도구입니다. 기존 1D/2D 모델 및 물리적 모델과 함께 사용될 때 그 가치를 발하며, 특히 복잡한 유체 역학적 상황을 이해하고 시각화하는 데 강력한 커뮤니케이션 도구로 작용합니다.

flow-3d hydro와 함께라면 더 이상 복잡한 유체 역학문제를 추측에만 맡기지 않아도 됩니다. 이 강력한 도구와 함께 더 나은 설계를 하고, 혁신적인 해결책을 찾아 미래를 설계하세요. flow-3d hydro교육 과정은 이러한 여정의 첫걸음을 내딛는 데 필요한 모든 것을 제공할 것입니다. 지금 바로 경험하고, cfd모델링의 무한한 가능성을 탐험해보세요.

Fishway

[Webinar] FLOW-3D HYDRO: 수자원 인프라를 위한 고급 수리 모델링 솔루션

이 문서는 FLOW-3D HYDRO 소프트웨어를 활용한 3d cfd 모델링의 주요 내용과 적용 사례를 소개합니다. CFD는 유체 흐름을 정확하게 시뮬레이션하여 수자원 인프라 설계에 활용될 수 있는 강력한 도구입니다. 특히, 복잡한 유동 현상 분석, 고위험 프로젝트 검증, 비표준 설계 평가, 그리고 다른 모델링 도구와의 연계에 유용합니다. 다양한 사용자 사례 연구를 통해 CFD의 실제 적용 가능성과 효과를 보여줍니다. 이 자료는 수자원 분야에서 CFD 모델링의 잠재력을 이해하고 활용하는 데 도움을 줍니다.

1. 💧 3D CFD 모델링의 개념과 FLOW-3D HYDRO의 주요 기능

  • 3D CFD(전산 유체 역학)는 유체가 환경과 상호 작용하는 방식을 정확하고 상세하게 시뮬레이션하여 다양한 설계 분석에 활용할 수 있는 도구입니다.
  • 3D CFD는 속도의 세 가지 구성 요소를 모두 다루기 때문에 1D/2D 모델의 제한적인 가정과 달리, 복잡한 위어와 같은 수직 유동 가속도가 강한 현상도 직접적으로 해석할 수 있습니다.
  • 가상 실험실처럼 다양한 구조물 형상과 접근 유동 조건을 테스트하고, 높은 정확도가 필요하거나 비표준/고비용 설계, 다중 물리 현상 시뮬레이션 등에 적합합니다.
  • CFD는 물리적 모델링과 연계하여 검증 및 확인 데이터를 제공하며, 구조 설계 등의 복잡한 개념을 효과적으로 전달하는 데 도움이 됩니다.
  • FLOW-3D HYDRO는 토목, 환경, 해안 분야를 포함한 다양한 수자원 인프라 적용을 위한 상업용 3D CFD 솔루션으로, 첨단 자유 수면 해석, 고급 다중 물리 모델링, 전문 지원과 글로벌 적용 사례 등 다양한 특징을 지닙니다.

2. 🛠️ 깊은 터널 시스템의 환경 방류 문제 사례

  • 영국 Mut MacDonald의 노후 복합 하수도 시스템에서 강우 시 처리장 용량을 초과하는 미처리 유량이 발생합니다.
  • 이로 인해 미처리 하수가 환경으로 직접 방류(CSO)되어 환경 오염 문제가 발생합니다.
  • 해당 사례는 CFD 소프트웨어를 적용해 실제 수자원 인프라의 문제를 분석한 사용자 사례입니다.

3. 🏗️ FLOW-3D HYDRO의 실제 적용 사례와 효율성

  • 기존 인프라의 고유 설계와 높은 비용 문제를 CFD로 해결하고, 조절기 및 월류 구조의 수정과 저유속 영역 제거, 에너지 소산 극대화 등의 주요 목표를 달성하였습니다.
  • 수문 게이트 방류량 등급 곡선 개발 및 검증을 통해 유량과 상류 수심의 관계를 제시하고, 1D 모델 검증과 침전물 축적 가능성을 파악하여 설계에 반영하였습니다.
  • CFD 결과는 위험 감소와 이해관계자 정보전달에 탁월한 시각적 자료 제공 등, 복잡한 인프라 설계의 효율적 프로젝트 진행에 기여하였습니다.
  • 루이지애나 해안선 복원에는 인공 암초 적용 및 9가지 대안 시뮬레이션을 실시하여, 최대 파랑 감소와 높은 비용 효율성을 확보하였고, 실제 모니터링 결과와 2% 이내 일치, 해안선 후퇴를 약 50% 감소시켰습니다.
  • 어도 설계에서는 다양한 어종의 수영 속도에 맞춘 정밀한 3D 유동 해석으로 높은 성공률을 달성하였으며, 모든 생활 단계를 만족시키는 설계가 가능함을 보였습니다.
  • 기존 여수로 등급 곡선 개발에서는 87가지 시뮬레이션 자동화를 활용해 31일 소요 작업을 단 4일로 단축하고, 컴퓨팅 비용은 730달러로 절감하였습니다; CFD 결과는 물리적 모델과 3% 이내로 정확히 일치하였습니다.

3.1. ️ FLOW-3D HYDRO를 활용한 기존 인프라 문제 해결 사례

  • 기존 인프라는 비표준 설계 필요성과 높은 비용이 발생하는 문제가 있습니다.
  • FLOW-3D HYDRO를 활용하여 기존 하수도 라인의 조절기 및 월류 구조를 수정하고, 드롭 샤프트에 유량 제어 게이트를 포함한 새로운 구조를 추가했습니다.
  • 주요 목표는 인근 강으로의 방류 이벤트 감소, 침전물 축적 방지를 위한 저유속 영역 제거, 공기 혼입 최소화, 드롭 샤프트 내 에너지 소산 극대화입니다.
  • 시뮬레이션 결과, 1년 유동 피크 이벤트에서도 모든 유량이 드롭 샤프트로 흐르고 강으로의 방류가 발생하지 않음을 확인했습니다.

3.2. ️ 하수도 시스템 개선을 위한 FLOW-3D HYDRO 적용 사례

  • 고유속 영역 및 과도 효과 분석, 1D 모델과의 검증, 그리고 침전물이 쌓일 수 있는 저유속 영역을 식별하여 설계를 조정하였습니다.
  • 25년 유동 피크 이벤트를 고려해, 드롭 샤프트 상류의 조절기 게이트 작동 기준을 정의하였습니다.
  • CFD를 활용해 게이트 방류량 등급 곡선을 개발 및 검증했으며, 유량과 상류 수심 간의 관계를 제시하였습니다.
  • CFD를 통한 결과는 복잡하고 고비용의 인프라 설계 프로젝트에서 위험을 줄이는 데 유용함이 입증되었으며, 다양한 이해관계자에게 정보를 전달하는 시각적 자료로도 효과적입니다.

3.3. 루이지애나 해안선 침식 문제와 인공 암초 CFD 적용

  • 루이지애나 지역은 극심한 파랑 에너지로 심각한 해안선 침식이 발생하고 있습니다.
  • 실제 파랑 감소 성능에 대한 정보는 제한적이며, 물리적 테스트는 비용이 매우 높습니다.
  • FLOW-3D HYDRO로 9가지 인공 암초 디자인과 다양한 구성에 대해, 실제 현장 파랑과 수위 조건을 이용해 시뮬레이션을 진행했습니다.
  • 구조물 유무에 따라 파고를 비교하고, 가장 큰 파랑 감소 효과를 주는 대안을 식별했으며, 비용 효율성도 함께 고려했습니다.
  • CFD 모델 예측값과 모니터링 결과 오차는 2% 이내였으며, 해안선 후퇴가 약 50% 감소하는 성공적 파랑 감쇠가 확인되었습니다.

3.4. 호주 어도의 복잡한 설계 검증과 3D CFD 모델링의 효과

  • FLOW-3D HYDRO는 광범위한 수리 조건에서 다양한 어종과 여러 생활 단계를 모두 수용해야 하는 복잡한 어도 설계 검증에 활용됩니다.
  • 설계의 목표는 암석 경사로 어도와 보육 슬롯이 지정된 설계 기준을 충족하는지 확인하는 것입니다.
  • 대규모 수리학 분석과 개별 보육 슬롯의 수리학 분석을 통해 각 설계 옵션의 효율성을 평가합니다.
  • 시뮬레이션된 유속 데이터를 바탕으로, 대상 어종의 버스트(burst) 및 유지(sustained) 수영 속도와 비교하여 어류 이동 가능성을 분석합니다.
  • 3D CFD 모델링 결과, 13종 2700마리의 모든 생활 단계의 어류가 성공적으로 통과하여 매우 높은 성공률을 보여주었으며, 이는 실제 어류의 규모에서 어도 수리학을 직접 분석하는 데 혁신적인 방법임을 의미합니다.

3.5. FLOW-3D HYDRO 기반 자동화된 여수로 등급 곡선 개발의 혁신

  • 1950년대부터 사용된 기존의 여수로 등급 곡선 업데이트에는 시간과 노력이 많이 드는 수동적 물리적 모델링 방식이 사용되어 왔으며, 반복적이고 비효율적인 문제가 있었습니다.
  • FLOW-3D HYDRO를 활용해 87개의 시뮬레이션 작업을 자동화하여, 수동 설정 대비 소요 시간을 100시간 이상에서 약 하루로 대폭 단축하였습니다.
  • 전체 컴퓨팅 비용은 87건 시뮬레이션에 730달러이며, 오류 발생도 감소하였습니다.
  • 최종적으로 CFD 시뮬레이션 결과는 물리적 모델 데이터와 약 3% 이내로 거의 정확히 일치하여, 전통적 물리적 모델의 31일 작업을 CFD 자동화로 4일만에 달성할 수 있었습니다.

4. 🏞️ CFD 모델링의 주요 추가 기능과 실행 고려사항

  • 침전물 운반 및 침식(Scour) 모델링은 완전한 3D 이동상 침전물 운반 모델을 사용하여 전단 응력 기반의 바닥 하중 운반 및 유출을 계산합니다.
  • Flow-3D는 물고기의 직접 움직임 모델링은 지원하지 않으나, 유속과 난류 특성 등 유압 출력 데이터를 활용해 어류 이동 경로 및 생물학적 기준(예: 수영 속도) 비교에 사용할 수 있습니다.
  • 높은 유속 영역을 시각화함으로써 어류가 이동 가능한 경로를 파악하는 데 유용합니다.
  • 지형 데이터는 GIS 래스터(GeoTIFF), LandXML, 3D CAD(STL) 등 다양한 소스에서 가져올 수 있으며, 정확한 지형 정보 확보가 시뮬레이션의 정확성에 핵심적입니다.
  • 시뮬레이션 런타임은 모델 복잡성, 셀 수, 하드웨어에 따라 수 분에서 수 일로 달라지며, 초기 설정은 빠른 코스 메쉬로 1시간 이내, 생산 실행은 6-12시간이 일반적입니다.
  • 비뉴턴 유체(진흙, 광미, 파편 등)의 특수한 물리적 특성까지 모델링 가능합니다.

5. 🚀 3D CFD 모델링의 장점과 FLOW-3D HYDRO의 미래적 기회

  • 3D CFD 모델링, 특히 FLOW-3D HYDRO는 정확성, 유연성, 위험 감소, 효과적인 의사소통 등 수자원 인프라 프로젝트에 필수적인 여러 이점을 제공합니다.
  • FLOW-3D HYDRO는 자유 수면 모델링, 고급 다중 물리 모듈, 직관적 인터페이스, 체계적 지원 등에서 차별화된 강점을 갖습니다.
  • 이러한 기술 발전과 통합은 앞으로 더욱 보편화될 것으로 예상됩니다.

Q&A

  • Q1: FLOW-3D HYDRO는 어떤 분야의 수자원 인프라 프로젝트에 주로 활용되나요?
  • A1: FLOW-3D HYDRO는 토목, 환경, 해안 공학 분야를 포함한 광범위한 수자원 인프라 프로젝트에 활용됩니다. 댐 및 여수로, 이송 인프라, 강 및 환경 적용, 수처리, 항만 및 해안 적용 등 다양한 문제 해결에 사용될 수 있습니다.
  • Q2: 3D CFD 모델링이 1D/2D 모델링과 비교했을 때 가지는 주요 장점은 무엇인가요?
  • A2: 3d cfd 모델링은 속도의 세 가지 구성 요소를 모두 다루므로, 1D/2D 모델의 제한적인 가정(예: 깊이 평균 유량) 없이 복잡한 유동 현상(예: 수직 유동 가속도가 강한 위어)을 직접 해석할 수 있습니다. 또한, 가상 실험실처럼 다양한 시나리오를 테스트하고, 높은 정확도가 필요한 고위험/고비용 프로젝트에 적합하며, 복잡한 다중 물리 현상을 시뮬레이션할 수 있습니다.
  • Q3: FLOW-3D HYDRO를 활용한 실제 적용 사례 중 가장 인상 깊었던 것은 무엇이며, 그 이유는 무엇인가요?
  • A3: 여러 인상 깊은 사례가 있지만, 특히 ‘자동화된 여수로 등급 곡선 개발’ 사례가 인상 깊습니다. 1950년대부터 사용되던 수동적 물리적 모델링 방식이 31일이 소요되던 작업을 flow-3d hydro를 활용하여 단 4일 만에 완료하고, 컴퓨팅 비용도 730달러로 절감하며 물리적 모델과 3% 이내의 정확도를 보였다는 점이 기술 혁신과 효율성 측면에서 매우 뛰어난 성과를 보여주기 때문입니다.
  • Q4: FLOW-3D HYDRO가 물고기 이동 모델링을 직접 지원하지 않음에도 불구하고, 어도 설계에 어떻게 기여할 수 있나요?
  • A4: FLOW-3D HYDRO는 물고기 자체의 움직임을 직접 모델링하지는 않지만, 유속, 난류 특성 등 유압 출력 데이터를 제공합니다. 이 데이터를 활용하여 대상 어종의 수영 속도와 비교하고, 높은 유속 영역을 시각화함으로써 어류가 이동 가능한 경로를 파악하는 데 유용하게 사용될 수 있습니다. 이를 통해 어류의 모든 생활 단계를 만족시키는 정밀한 어도 설계가 가능해집니다.
Coupled Motion

[Webinar] FLOW-3D HYDRO: 복잡한 수리 모델을 위한 ‘움직이는 객체 통합’ 기능의 모든 것

1. FLOW-3D HYDRO: 움직이는 객체 통합 기능 소개

유체 시뮬레이션 분야에서 ‘움직이는 객체’를 모델링하는 것은 단순히 유체의 흐름만을 파악하는 것을 넘어, 실제 세계의 복잡한 물리적 상호작용을 정확하게 예측하고 분석하는 데 필수적인 요소입니다. 예를 들어, 거대한 파도 속에서 흔들리는 해상 플랫폼의 안정성을 평가하거나, 수문이 개폐될 때 댐의 유량 변화를 예측하는 것 등은 모두 유체와 움직이는 구조물 간의 정교한 상호작용 분석을 요구합니다.

FLOW-3D HYDRO는 이러한 동적 요소를 시뮬레이션에 효과적으로 통합할 수 있는 강력한 기능을 제공하며, 이를 통해 엔지니어와 연구자들은 더욱 현실적이고 심층적인 수리 모델을 구축할 수 있습니다.

2. 움직이는 객체 모델링의 두 가지 핵심 방식

FLOW-3D HYDRO에서 움직이는 객체는 주로 강체(rigid body)로 모델링되며, 최대 6자유도의 움직임을 가질 수 있습니다. 이러한 객체의 움직임을 정의하는 방식은 크게 두 가지로 나뉩니다.

지정된 동작(Prescribed Motion)

객체가 어떻게 움직일지 시뮬레이션 시작 전에 미리 정의하는 방식입니다. “당신이 객체에 움직임을 알려주면, 유체가 그에 반응하여 움직이는 것”이라고 생각할 수 있습니다.

  • 정의: 객체의 움직임 궤적, 속도, 회전 등을 정확하게 입력하여 유체가 그에 따라 어떻게 반응하는지 시뮬레이션합니다.
  • 적용 사례:
    • 웨이브 패들: 위아래로 움직여 파도를 생성하는 시뮬레이션.
    • 개폐 수문: 고정된 축을 중심으로 회전하거나 수직 이동하여 유량을 조절하는 수문.
    • 믹서: 특정 속도로 회전하여 유체를 혼합하는 과정.
  • 특징: 시간 시리즈 입력을 통해 시간에 따라 움직임을 변화시키거나 특정 시간 동안 움직인 후 정지시키는 등의 복잡한 동작도 구현할 수 있습니다.

연동된 동작(Coupled Motion)

유체와 객체가 서로의 움직임에 영향을 미치는 상호작용을 시뮬레이션하는 방식입니다. “유체와 객체가 서로의 움직임을 주고받으며 영향을 미치는 것”이 핵심입니다.

  • 정의: 유체의 힘이 객체를 움직이고, 객체의 움직임이 다시 유체 흐름에 영향을 미치는 복합적인 상호작용을 분석합니다.
  • 적용 사례:
    • 부유하는 플랫폼의 파랑 동역학: 파도 속에서 플랫폼이 어떻게 흔들리고 움직이는지 예측.
    • 수력 터빈: 물의 흐름에 의해 터빈이 회전하는 과정.
    • 계류선(mooring line)에 연결된 부유체: 물속에서 부유체가 계류선에 의해 고정되면서도 유체의 힘에 반응하여 움직이는 상황.
    • 수압에 의해 움직이는 수문: 수위 변화에 따라 수압을 받아 자동으로 개폐되는 수문.
  • 주요 특징:
    • 다중 객체: 하나의 시뮬레이션 모델 안에 여러 개의 움직이는 객체를 포함할 수 있으며, 이들은 지정된 동작과 연동된 동작을 혼합하여 사용할 수도 있습니다 (최대 약 500개).
    • 부가 기능: 스프링, 로프, 계류선에 객체를 부착하여 보다 현실적인 모델링이 가능합니다 (자세한 내용은 이번 웨비나에서 다루지 않음).
    • 메싱(Meshing): 별도의 복잡한 메싱 과정 없이 표준 메싱 접근 방식이 적용됩니다.

3. 왜 움직이는 객체 시뮬레이션이 필요한가?

FLOW-3D HYDRO의 ‘움직이는 객체’ 시뮬레이션은 이름 그대로 “움직이는 무언가”가 존재하고, 그 움직임이 시뮬레이션 결과에 결정적인 영향을 미칠 때 필수적입니다. 이는 주로 물과 관련된 다양한 수자원 및 해양 애플리케이션에서 동적인 요소를 포함합니다.

  • 필요성:
    • 해상 부유 플랫폼: 파도에 의해 흔들리는 해상 구조물의 안정성 및 운동 특성 분석.
    • 플랩 게이트 및 수문: 수위 변화에 따라 자동으로 열리고 닫히는 게이트의 거동 예측.
    • 믹서와 같은 기계 장치: 유체를 혼합하거나 교반하는 과정에서 기계 부품의 움직임이 유체 흐름에 미치는 영향 분석.
  • 고려 사항: 항상 모든 움직임을 시뮬레이션할 필요는 없습니다. 때로는 시뮬레이션 단순화를 위해 움직이는 객체를 고정 상태로 가정하거나 정상(steady) 상태로 모델링하는 것이 효율적일 수 있습니다. 그러나 많은 경우, 특히 위에서 언급된 사례들처럼 유체와 객체 간의 동적인 상호작용이 핵심적인 문제 해결에 필수적일 때, 움직이는 객체 시뮬레이션은 반드시 필요합니다.

4. FLOW-3D HYDRO에서 움직이는 객체 설정하기

FLOW-3D HYDRO에서 움직이는 객체 시뮬레이션을 설정하는 과정은 직관적입니다. 크게 두 단계로 진행됩니다.

  • 물리 활성화(Activating the Physics):FLOW-3D HYDRO의 ‘Physics’ 창에서 ‘Moving Objects’ 기능을 활성화합니다.’Collision model’은 시뮬레이션 목적에 따라 활성화 여부를 선택합니다. 예를 들어, 부유하는 객체들이 서로 부딪히거나 다른 고정된 구조물과 충돌하는 상황을 모델링할 때는 활성화하는 것이 좋습니다.
  • 지오메트리 위젯(Geometry Widget) 설정:객체 정의: FLOW-3D 내에서 직접 실린더와 같은 원시 객체를 생성하거나, 외부 CAD 소프트웨어에서 만든 STL 파일을 가져와서 사용할 수 있습니다.‘Moving Object Properties’ 설정:움직임 유형: ‘Non-moving(비이동)’, ‘Coupled Motion(연동된 동작)’, ‘Prescribed Motion(지정된 동작)’ 중 시뮬레이션 목적에 맞는 유형을 선택합니다.자유도: 연동된 동작의 경우, 최대 6자유도(X, Y, Z 방향 이동 및 3축 회전)를 모두 선택하여 객체의 복합적인 움직임을 모델링할 수 있습니다.질량 매개변수: 객체의 밀도 등을 입력합니다.움직임 매개변수:연동된 동작: 객체의 시작 위치와 밀도 등 초기 조건만 지정하면, 시뮬레이션 과정에서 유체와의 상호작용을 통해 자동으로 움직임이 계산됩니다.지정된 동작: 회전 축 좌표, 회전 속도(각속도) 또는 선형 속도 등 구체적인 움직임 매개변수를 직접 지정해야 합니다. 필요에 따라 시간 시리즈 입력을 통해 시간에 따른 동적인 움직임을 정의할 수도 있습니다.

4. FLOW-3D HYDRO에서 움직이는 객체 설정하기

flow-3d hydro에서 움직이는 객체 시뮬레이션을 설정하는 과정은 직관적입니다. 크게 두 단계로 진행됩니다.

  • 물리 활성화(Activating the Physics):FLOW-3D HYDRO의 ‘Physics’ 창에서 ‘Moving Objects’ 기능을 활성화합니다.’Collision model’은 시뮬레이션 목적에 따라 활성화 여부를 선택합니다. 예를 들어, 부유하는 객체들이 서로 부딪히거나 다른 고정된 구조물과 충돌하는 상황을 모델링할 때는 활성화하는 것이 좋습니다.
  • 지오메트리 위젯(Geometry Widget) 설정:객체 정의: FLOW-3D 내에서 직접 실린더와 같은 원시 객체를 생성하거나, 외부 CAD 소프트웨어에서 만든 STL 파일을 가져와서 사용할 수 있습니다.‘Moving Object Properties’ 설정:움직임 유형: ‘Non-moving(비이동)’, ‘Coupled Motion(연동된 동작)’, ‘Prescribed Motion(지정된 동작)’ 중 시뮬레이션 목적에 맞는 유형을 선택합니다.자유도: 연동된 동작의 경우, 최대 6자유도(X, Y, Z 방향 이동 및 3축 회전)를 모두 선택하여 객체의 복합적인 움직임을 모델링할 수 있습니다.질량 매개변수: 객체의 밀도 등을 입력합니다.움직임 매개변수:연동된 동작: 객체의 시작 위치와 밀도 등 초기 조건만 지정하면, 시뮬레이션 과정에서 유체와의 상호작용을 통해 자동으로 움직임이 계산됩니다.지정된 동작: 회전 축 좌표, 회전 속도(각속도) 또는 선형 속도 등 구체적인 움직임 매개변수를 직접 지정해야 합니다. 필요에 따라 시간 시리즈 입력을 통해 시간에 따른 동적인 움직임을 정의할 수도 있습니다.

5. 실제 적용 사례: 시뮬레이션으로 본 움직이는 객체

FLOW-3D HYDRO 웨비나에서는 ‘움직이는 객체 통합’ 기능의 실제 적용 과정을 명확히 보여주는 두 가지 시뮬레이션 사례가 시연되었습니다.

사례 1: 연동된 동작 – 부유하는 통나무 시뮬레이션

이 시뮬레이션은 연동된 동작의 개념을 잘 보여줍니다. 위어(weir) 상류에 위치한 통나무가 물의 흐름에 따라 위어를 넘어 하류로 이동하는 과정을 모델링했습니다.

  • 목표: 물의 흐름이 통나무의 움직임에 어떻게 영향을 미치는지, 그리고 통나무의 움직임이 다시 유체 흐름에 어떤 변화를 주는지 시뮬레이션합니다.
  • 설정 과정:
    • 이전 웨비나에서 생성된 모델을 재시작 모델로 활용하여 초기 유체 조건을 설정했습니다.
    • ‘Moving Object’ 및 ‘Collision model’을 활성화했습니다.
    • 단순 실린더 형태의 통나무 객체를 생성하고, 위어 상류에 위치시킨 후 ‘Coupled Motion’으로 설정하여 6자유도 부유 밀도를 지정했습니다.
  • 결과: 시뮬레이션을 통해 통나무가 위어를 넘어 하류로 이동하는 것이 명확히 관찰되었습니다. 특히 통나무가 위어를 넘어가는 과정에서 하류의 롤러(roller) 영역에 일시적으로 갇히는 현상이 발생했는데, 이는 실제 저수두 위어(low-head weirs)에서 발생할 수 있는 ‘역회전(reverse rolling)’ 조건과 유사하여 잠재적인 안전 문제를 시사하는 중요한 통찰을 제공했습니다.

사례 2: 지정된 동작 – 회전하는 수문 시뮬레이션

이 시뮬레이션은 지정된 동작의 활용을 보여주며, 두 개의 수문 중 하나가 특정 축을 중심으로 회전하여 열리고 닫히는 과정을 시뮬레이션했습니다.

  • 목표: 고정된 수문의 회전 동작이 상류 수위와 하류 유량에 어떻게 영향을 미치는지 분석합니다.
  • 설정 과정:
    • 시뮬레이션 시작 시 수문이 닫힌 상태를 가정하여 이전 웨비나 모델을 복사하여 사용했습니다.
    • ‘Moving Object’ 물리를 활성화했으며, 이 사례에서는 충돌 모델을 비활성화했습니다.
    • 두 개의 수문 지오메트리를 STL 파일로 가져온 후, 열릴 수문(빨간색 게이트)의 ‘Moving Object Properties’를 ‘Prescribed Motion’으로 설정하고, ‘Rotate about fixed axis’를 선택했습니다.
    • 회전 축 좌표와 각속도를 시간 시리즈 데이터로 입력하여 (예: 5초간 닫힘 유지, 3초간 열림, 이후 정지) 수문의 개폐 동작을 정의했습니다.
    • 수문의 얇은 두께를 고려하여 메시 해상도를 조정하고, 초기 수위를 수문 앞에 위치하도록 설정했습니다.
    • 보조 도구 활용: 수문 상류에 ‘History Probe’를 추가하여 실시간으로 수위를 모니터링하고, 위어 마루에 ‘Flux Surface’를 추가하여 통과하는 유량을 측정했습니다.
  • 결과: 수문이 열리면서 수문 상류의 수위가 변화하고 유량이 증가하는 것을 Probe 및 Flux Surface를 통해 실시간으로 플로팅하여 시각적으로 확인할 수 있었습니다.

6. 결론: 복잡한 수리 모델 구축을 위한 필수 기능

FLOW-3D HYDRO의 ‘움직이는 객체 통합’ 기능은 유체 시뮬레이션에서 ‘움직이는 무언가’를 다루어야 할 때 그 진가를 발휘하는 필수적인 도구입니다. 이 기능은 지정된 동작(Prescribed Motion)과 연동된 동작(Coupled Motion)이라는 두 가지 핵심 방식을 통해 매우 광범위하고 다양한 수리 시뮬레이션 요구사항을 충족시킬 수 있습니다.

초기 모델 설정(예: 첫 번째 웨비나에서 다룬 내용)이 완료되면, 움직이는 객체 물리를 통합하는 과정은 생각보다 복잡하지 않습니다. 또한, 시뮬레이션 중 관심 지점의 데이터를 실시간으로 모니터링할 수 있는 Probe 및 flux surface와 같은 보조 도구들은 모델 분석과 검증에 있어 매우 유용하게 활용될 수 있습니다.

결론적으로, FLOW-3D HYDRO의 ‘움직이는 객체 통합’ 기능은 복잡한 유체-구조물 상호작용 문제를 해결하고, 실제 환경의 동적인 요소를 정밀하게 시뮬레이션하고자 하는 모든 엔지니어와 연구자에게 강력하고 직관적인 솔루션을 제공합니다.

FLOW

[Webinar] FLOW-3D HYDRO 기본 모델 설정 및 활용

FLOW-3D HYDRO는 3D 전산 유체 역학(CFD) 소프트웨어로, 특히 자유 표면(free surface) 애플리케이션에 특화되어 있습니다. 이 문서는FLOW-3D HYDRO의 기본 모델 설정 과정을 검토하고, 주요 기능과 활용 사례를 제시합니다. 수치 모델은 설계 최적화, 미래 조건에서의 성능 예측, 기존 문제의 원인 조사, 위험 완화 및 의사 결정에 대한 신뢰도 향상에 기여합니다. CFD는 문제의 3D 유동 특성, 높은 수준의 정확도 요구, 높은 위험도 프로젝트, 상호 작용하는 복잡한 물리 현상 포함 등의 경우에 유용합니다. 이 소프트웨어는 유체 흐름을 시뮬레이션하여 엔지니어링 판단을 보완하고 설계 최적화에 기여하는 강력한 도구입니다.

1. 📝 FLOW-3D HYDRO의 기본 모델 설정 및 활용 개요

  • 이 문서는 FLOW-3D HYDRO 소프트웨어의 기본 모델 설정 과정을 다룬다.
  • 소프트웨어의 주요 기능, 활용 사례, 그리고 중요 개념을 요약하여 제시한다.
  • 독자는 이 문서를 통해 FLOW-3D HYDRO의 활용 목적과 범위에 대한 전체적인 이해를 얻을 수 있다.

2. 🚀 FLOW-3D HYDRO의 3D 유동 해석과 자유 표면 특화 기능

  • FLOW-3D HYDRO는 Navier-Stokes 방정식을 3D로 풀어 유체 흐름을 시뮬레이션하는 소프트웨어이다.
  • 이 소프트웨어는 특히 공기-물 인터페이스, 예를 들어 하천, 개수로, 댐, 수문, 교량 등에서의 자유 표면 문제 해결에 특화되어 있다.
  • 횡단면 심도 평균 가정 없이 정확한 3D 유동 문제를 다룰 수 있다.
  • 움직이는 객체나 퇴적물 수송 등 다양한 물리 현상과 연동하여 복합 분석이 가능하다.
  • 메시 생성 및 형상 처리가 간단하며, 단일 유체 체적(Volume of Fluid) 접근 방식을 활용하여 계산 효율성이 높다.
  • 자유 표면은 대체로 공기와 물 사이의 경계를 의미한다.

3. 🚀 FLOW-3D HYDRO를 활용한 수치 모델의 목적과 CFD 필요성

  • 수치 모델은 통찰력을 얻고, 설계 및 운영 계획을 최적화하며, 미래 조건에서의 성능 예측, 기존 문제의 원인 조사, 위험 완화 및 의사 결정 신뢰도 향상을 위해 활용된다.
  • FLOW-3D HYDRO는 단순히 도구일 뿐이므로, 최종 판단은 엔지니어가 직접 적용해야 한다.
  • 하지만 이 모델은 위험을 줄이고, 올바른 결정을 내리고 있다는 확신을 부여하는 중요한 수단이다.
  • CFD(전산유체역학)는 문제의 3D 유동 특성, 높은 정확도 요구, 위험도가 높은 프로젝트, 상호 작용하는 복잡한 물리 현상 등이 포함될 때 최적의 선택이다.
  • 3D CFD 모델은 클라이언트 및 이해관계자와의 효과적인 의사소통 도구이고, 1D·2D·물리모델의 보완 도구로 활용될 수 있다.

4. 🏗️ 위어 유동 모델 설정 및 시뮬레이션 목표

  • FLOW-3D HYDRO를 사용하여 단순 위어 유동 모델을 설정하는 과정을 예시로 설명한다.
  • 이 모델 설정 과정은 스필웨이 모델 등 다양한 복잡한 모델에도 똑같이 적용될 수 있다.
  • 시뮬레이션의 목표는 스필웨이의 용량 평가, 유량 변화에 따른 통과 능력 확인, 에너지 소산 시설(dissipator)의 설계 최적화이다.
  • 잠재적인 설계 문제(예: 벽이 너무 짧아 물이 옆으로 넘칠 수 있음)를 식별할 수 있다.
  • 또한 수문(gates), 퇴적물 수송, 공기 혼입, 캐비테이션 등 추가적인 물리 현상도 연구 가능하다.

5. 🖥️ FLOW-3D HYDRO 모델 설정 및 시뮬레이션 준비 과정

  • Simulation Manager 창은 프로그램을 시작할 때 가장 먼저 보이며, 워크스페이스 생성으로 프로젝트를 정리할 수 있다.
  • 모델 설정(Model Setup) 탭은 좌측에 위젯들이 배열되어 있고, 일반적으로 위에서 아래로 순서대로 작업을 진행한다.
  • 전역 설정에서 시뮬레이션 종료 시간을 정의하고, 물리(Physics) 설정에서는 중력과 RNG 난류 모델이 기본 적용되며, 필요시 침식-퇴적, 열전달 등 추가 현상을 활성화할 수 있다.
  • 유체 설정에서는 20°C 물이 자동 로드되며, 밀도 등 속성 변경이 가능하다.
  • 형상(Geometry) 설정에서는 외부 CAD 소프트웨어의 3D STL 파일이나 FLOW-3D 내장 도형을 가져오고, 컴포넌트별 명칭/조직화, 표면 거칠기 적용이 가능하다; 메시는 형상에 맞게 추가 및 크기, 해상도 정의가 가능하고, FAVOR 기법으로 3D 솔리드 표현을 확인할 수 있다.
  • 거친 메시는 빠른 실행이 가능하지만 표면 표현이 단순하며, 모델 검증 후 점차 미세한 해상도로 조정하는 것이 권장된다.
  • 경계 조건에서는 각 메시 면에 조건을 지정하고, 상류·하류 유체의 고도 및 시간 시리즈 입력이 가능하며, 초기 조건으로 빠른 정상 상태 진입을 도울 수 있다.
  • 출력 설정을 통해 저장 변수와 간격을 제어하여, 시뮬레이션 동안 결과 모니터링이 가능하다.

5.1. ️ FLOW-3D HYDRO 사용자 인터페이스와 기본 워크플로우

  • 시뮬레이션 관리자(Simulation Manager) 창은 FLOW-3D HYDRO 실행 시 가장 먼저 보이는 첫 화면이다.
  • 모델 설정(Model Setup) 탭은 주로 사용하는 작업 공간이며, 왼쪽에 위젯들이 배치되어 있고 위에서 아래로 순서대로 진행된다.
  • 워크스페이스(Workspace)는 프로젝트 폴더와 유사한 개념으로, 모델 정리에 사용된다.
  • 새 시뮬레이션을 추가할 때 이름 지정, 단위 선택, 그리고 사전 로드된 템플릿의 활용이 가능하다.

5.2. 기본 모델 설정 및 물리 환경 정의

  • 전역(Global) 설정에서는 시뮬레이션 종료 시간을 사용자가 직접 정의하며, 예를 들어 30초로 설정할 수 있다.
  • 물리(Physics) 설정에서는 템플릿을 통해 중력과 RNG 난류 모델이 기본적으로 활성화되어 있다.
  • 필요에 따라 침식-퇴적, 열전달 등 추가적인 물리 현상을 옵션으로 활성화할 수 있다.
  • 유체(Fluids) 설정에서 20°C의 물이 템플릿을 통해 기본적으로 로드된다.

5.3. ️ 외부 CAD 모델의 시뮬레이션 환경으로의 통합 및 속성 조정

  • 밀도와 같은 속성을 변경할 수 있다.
  • 형상(Geometry) 설정 시 외부 CAD 소프트웨어에서 생성된 3D STL 파일을 가져오는 것이 일반적이다.
  • 외부에서 생성된 3D 모델을 시뮬레이션에 맞게 변환, 조정, 속성 설정 등을 수행해야 한다고 추정된다.
  • 시뮬레이션의 정확도를 높이기 위하여 객체별로 속성 및 세부 설정이 필요하다.

5.4. FLOW-3D HYDRO 메시 생성 및 설정의 핵심

  • FLOW-3D HYDRO에서는 내장 프리미티브 도형, ASC 지형 파일, 여러 STL 파일 등 다양한 형상 파일의 불러오기 및 조작이 가능하다.
  • 객체의 크기 조절이나 이동, 컴포넌트 분리와 이름 변경을 통해 형상 데이터를 효과적으로 조직화하고 속성을 정의할 수 있다.
  • 각 컴포넌트별로 표면 거칠기 값을 다르게 지정함으로써, 예를 들어 지형은 0.01, 콘크리트는 더 부드럽게 설정 가능하다.
  • 메시(Mesh)는 단일 균일 메시로 생성하며, 크기(예: 0.1m)와 해상도를 직접 정의하고, 메시의 확장 범위(extents) 또한 수정할 수 있다.
  • FAVOR(Fractional Area Volume Obstacle Representation) 기법을 통해 3D 솔리드가 메시 내에 어떻게 임베드되는지 확인할 수 있으며, 메시 해상도가 모델의 형상 표현에 중요한 영향을 미친다.

5.5. 시뮬레이션을 위한 경계 조건, 초기 조건, 출력 설정 요약

  • 시뮬레이션 모델은 처음에 거친 메시로 테스트한 후, 기능이 확인되면 점진적으로 미세한 메시로 변경하여 사용한다.
  • 경계 조건은 각 메시 면에 적용하며, 압력 경계에서는 유체 고도(예: 업스트림 4.5m, 다운스트림 2m)를 사용하고, 필요 시 시간에 따른 데이터(시간 시리즈) 입력도 가능하다.
  • 초기 조건으로 모델 내에 초기 물을 설정하면 정상 상태에 더 빠르게 도달할 수 있으며, 전역 수위를 지정하거나 업스트림 유체 영역을 경계 조건에 맞게 추가로 지정할 수 있다.
  • 출력 설정에서는 저장 변수와 저장 간격(예: 0.1초 간격) 등을 지정하여, 시뮬레이션 도중 결과를 모니터링한다.
  • 경계 조건, 초기 조건, 출력 설정을 통해 시뮬레이션의 입력 및 출력 상태를 구체적이고 유연하게 제어할 수 있다.

6. 🖥️ 모델 실행과 실시간 결과 분석 방법

  • 시뮬레이션 관리자의 “시뮬레이션(Simulate)” 버튼을 클릭해 모델 실행이 가능하다.
  • 시뮬레이션은 로컬 컴퓨터에서 실행할 수 있다.
  • 실행 중에는 시간 시리즈 플롯을 추가해 진행 상황(예: 상류 유량)을 모니터링할 수 있다.
  • “분석(Analyze)” 탭에서 3D 플롯으로 실행 중 실시간 결과를 확인할 수 있고, 투명도 조절 및 시간 단계별 확인이 가능하다.
  • 새로운 시간 단계가 저장되면, 이를 다시 로드하여 최신 결과를 확인할 수 있다.

7. 🦾 FLOW-3D HYDRO의 사후 처리와 모델 활용 및 결론

  • 모델 빌드 후 메시 크기, 경계 조건, 수위, 물리 현상, 수치 옵션, 형상 등 다양한 매개변수를 손쉽게 수정하여 여러 시나리오를 테스트할 수 있다.
  • 이러한 매개변수 변경은 대부분 몇 번의 버튼 클릭만으로 간단히 이루어진다.
  • 사후 처리에는 결과 시각화 및 비디오 생성이 포함되며, 이와 관련된 자세한 과정은 별도의 웨비나에서 다뤄질 예정이다.
  • FLOW-3D HYDRO는 3D 유동 문제와 특히 자유 표면 유동 모델링에 매우 강력한 도구이다.
  • 체계적인 기본 모델 설정 과정을 통해, 한 번 모델 구축 후 다양한 설계 변경 및 시나리오 테스트를 효율적으로 수행할 수 있다.
  • 엔지니어링 판단을 보완하여 설계 최적화, 성능 예측, 위험 완화에 실질적으로 기여한다.
Figure 4. Modeling of variant 1 with the movement of waves in the port water area

FLOW-3D를 이용한 항만 수역 배치 설계의 타당성 분석

본 소개 자료는 ‘IOP Conference Series: Materials Science and Engineering’에서 발행한 ‘FLOW-3D software for substantiation the layout of the port water area’ 논문을 기반으로 합니다.

Figure 4. Modeling of variant 1 with the movement of waves in the port water area
Figure 4. Modeling of variant 1 with the movement of waves in the port water area

1. 서론

  • 항만 설계 시, 방파제를 통한 내부 수역의 파랑 차단이 필수적이며, 이를 위해 최적의 항구 입구 배치 및 규모를 결정해야 함.
  • 항만 수역은 파랑, 퇴적물 축적, 그리고 결빙으로부터 보호되어야 하며, 이를 위해 물리적·수치적 모델링이 필요함.
  • 본 연구에서는 FLOW-3D를 활용하여 항만 입구 배치 및 설계 변수들이 항만 내부 수역의 흐름 및 안전성에 미치는 영향을 분석하고자 함.

2. 연구 방법

FLOW-3D 기반 CFD 모델링

  • VOF(Volume of Fluid) 기법을 사용하여 자유 수면을 추적.
  • 유체 해석을 위한 유한체적법(Finite Volume Method, FVM) 기반의 고정 격자 기법 사용.
  • FLOW-3D의 다중 격자(Multi-block Grid) 기능을 활용하여 계산 효율성 향상.
  • 항만 설계를 위한 입력 데이터:
    • 설계 풍속: 20m/s
    • 설계 파고: 1.0m, 주기 T = 5s
    • 설계 수위: 최저 11.50m, 운영 수위 12.00m, 최고 수위 15.00m

3. 연구 결과

다양한 항만 입구 배치에 따른 유동 특성 비교

  • 총 5가지 항만 입구 배치를 고려하여 항만 내부 유속 및 흐름 패턴을 분석.
  • 항만 입구 폭 및 위치에 따른 주요 결과:
    • 입구가 상단(Variant 1) 또는 이중 입구(Variant 2)일 경우, 내부 유속이 불균형하여 계류 안정성이 낮아짐.
    • 입구가 하단(Variant 3)일 경우, 내부 흐름이 균형을 이루며 정박 시 안전성이 가장 높음.
    • 입구 폭이 60m(Variant 5)로 증가할 경우, 외해의 파랑이 거의 그대로 내부로 전달되며, 방파제의 차단 효과가 감소.
    • 입구 폭이 20m(Variant 4)로 좁아질 경우, 항구 내부에서 난류(circulation)가 형성되어 선박 기동성이 저하.

계류 및 선박 기동성 평가

  • 항만 내 특정 지점(A, B, C)에서의 수심 변화를 분석하여 계류 안정성을 평가.
  • Variant 3에서 항만 내 수심 변화가 가장 적고, 계류 안정성이 가장 높음.
  • Variant 4의 경우, 항구 입구 폭이 좁아지면서 난류가 증가하고, 선박 기동성이 제한됨.
  • Variant 5의 경우, 외해 파랑이 내부까지 도달하여 계류 조건이 불안정해짐.

4. 결론 및 제안

결론

  • FLOW-3D 기반 시뮬레이션을 통해 항만 수역 내 유동 특성을 정량적으로 분석할 수 있음.
  • 입구 위치가 하단에 있으며(Variant 3), 폭이 40m일 때 가장 안정적인 계류 환경을 제공.
  • 입구 폭이 과도하게 좁아질 경우(Variant 4), 난류가 증가하여 선박 운항이 어려워지고, 반대로 폭이 과도하게 넓을 경우(Variant 5), 외해 파랑이 항만 내부까지 침투하는 문제가 발생.

향후 연구 방향

  • 다양한 파랑 조건 및 조류 영향에 대한 추가 연구 필요.
  • 실제 항만 데이터를 활용한 모델 검증 연구 수행.
  • 다양한 방파제 형상 및 재료 특성을 고려한 추가 시뮬레이션 진행.

5. 연구의 의의

본 연구는 FLOW-3D를 활용하여 항만 입구 배치 및 방파제 설계가 항만 내부 유동 및 계류 안정성에 미치는 영향을 정량적으로 분석하였다. 이를 통해 향후 항만 설계 및 운영 최적화를 위한 실질적인 설계 지침을 제공할 수 있음.

Figure 1. Sketch map of the port Laozi on Lake Hongze
Figure 1. Sketch map of the port Laozi on Lake Hongze
Figure 3. Port water area plan
Figure 3. Port water area plan
Figure 4. Modeling of variant 1 with the movement of waves in the port water area
Figure 4. Modeling of variant 1 with the movement of waves in the port water area

6. 참고 문헌

  1. SP 350.1326000.2018. 2018 Norms for technological design of sea ports (Moscow: Standartinform) p 226
  2. SP 444.1326000.2019. 2019 Standards for the design of sea channels, fairways and maneuvering areas (Moscow: Standartinform) p 62
  3. SP 38.13330.2012. 2014 Loads and impacts on Hydraulic structures (from wave, ice and ships) (Moscow: Ministry of Regional Development of the Russian Federation) p 112
  4. Rijnsdorp D P Smit PB and Zijlema M 2012 Non-hydrostatic modelling of infragravity waves using SWASH. Proceedings of 33rd Conference on Coastal Engineering. pp 1287-1299
  5. Kantardgi I G Zheleznyak M J 2016 Laboratory and numerical study of waves in the port area. Magazine of Civil Engineering No 6 pp 49-59 DOI: 10.5862/MCE.66.5
  6. Zheleznyak M J Kantardgi I G Sorokin MS and Polyakov A I 2015 Resonance properties of seaport water areas Magazine of Civil Engineering № 5(57) pp 3-19 DOI:10.5862/MCE.57.1
  7. Kantarzhi I Zuev N Shunko N 2014 Numerical and physical modelling of the waves inside the new marina in Gelendjik (Black Sea) Application of physical modelling to port and coastal protection. Proceedings of 5th international conference Coastlab (Varna) Vol 2 pp 253-262
  8. Makarov KN and Chebotarev A G 2015 Breakwater placement at the root of a seawall Magazine of Civil Engineering № 3(55) pp 67-78 DOI: 10.5862/MCE.55.8
  9. Belyaev N D Lebedev V V and Alexeeva A V 2017 Investigation of the soil structure changes under the tsunami waves impact on the marine hydrotechnical structures V 10 № 4 pp 44-52 DOI: 10.7868/S2073667317040049
  10. Lebedev V V Nudner I S and Belyaev N D 2018 The formation of the seabed surface relief near the gravitational object Magazine of Civil Engineering No 79(3) pp 120-131 DOI: 10.18720/MCE.79.13
  11. Kofoed-Hansen H Sloth P Sørensen OR Fuchs J 2000 Combined numerical and physical modelling of seiching in exposed new marina Proceedings of 27th international conference of coastal engineering pp 3600-3614
  12. Smit P Stelling G and Zijlema M 2011 Assessment of nonhydrostatic wave-flow model SWASH for directionally spread waves propagating through a barred basin Proceedings of ACOMEN 2011 pp 1-10
  13. Zijlema M Stelling G Smit P 2011 SWASH: An operational public domain code for simulating wave fields and rapidly varied flows in coastal waters. Coastal Engineering. № 10(58). pp 992-1012
  14. FLOW-3D® 2008 User’s Manual Version 9.3 Flow Science Inc p 821
  15. Pan Bayan and Belyaev N D 2019 Week of Science SPbPU: Proceedings of an international scientific conference The best reports. pp 3-7
  16. Girgidov A A 2011 Hybrid simulation in hydrotechnical facilities design and FLOW-3D as a tool its realization Magazine of Civil Engineering №3 pp 21-27
  17. Girgidov A A 2010 Proceeding of the VNIIG vol 260. pp 12-19
  18. Vasquez J A Walsh B W 2009 CFD simulation of local scour in complex piers under tidal flow, 33rd IAHR Congress: Water Engineering for a Sustainable Environment, © 2009 by International Association of Hydraulic Engineering & Research (IAHR) ISBN: 978-94-90365-01-1.
  19. Shan-Hwei Ou Tai-Wen Hsu and Jian-Feng Lin 2010 Experimental and Numerical Studies on Wave Transformation over Artificial Reefs Proceedings of the International Conference on Coastal Engineering (Shanghai, China) No 32
  20. Hirt C and Nichols B 1980 Volume of Fluid Method for the Dynamics of Free Boundaries Journal Comp. Phys 39 p 201.
Pan_2020_IOP_Conf._Ser.%3A_Mater._Sci._Eng._883_012020Download
Fig. 8. Proposed form of the intake bottom

Verification of a FLOW-3D Mathematical Model by a Physical Hydraulic Model of a Turbine Intake Structure of a Small Hydropower Plant and the Practical Use of the Mathematical Model

FLOW-3D 수치 모델의 검증: 소형 수력 발전소(SHPP) 터빈 취수구 구조의 물리적 유압 모델과의 비교 및 실용적 활용

Fig. 8. Proposed form of the intake bottom
Fig. 8. Proposed form of the intake bottom

연구 배경 및 목적

  • 문제 정의:
    • 드라바 강(Drava River) 유역의 Zlatoličje 수력 발전소(HPP)에서 Melje 소형 수력 발전소(SHPP)의 터빈 취수구 구조물을 건설할 계획이 진행됨.
    • 소형 수력 발전소는 생태 유량(Biological Minimum Discharge)을 활용하여 전력을 생산하므로 효율적인 취수구 설계가 필수적.
    • 물리적 유압 모델은 비용이 높아 대신 FLOW-3D 기반의 3D 수치 모델을 활용하여 취수구 구조 검증 수행.
    • 물리적 모델과 수치 모델을 병행 검증하여 최적 설계 도출.

연구 방법

  1. 물리적 유압 모델 구축
    • 모형 제작:
      • Zlatoličje HPP의 도수로(Headrace Channel) 및 SHPP Melje의 취수구 구조를 1:20 축척으로 제작.
      • 도수로 구간(길이 120m) 중 상류 39m, 하류 54m 포함하여 취수구와 자유 표면 흐름에서 압력 흐름으로 전환되는 구간까지 재현.
    • 경계 조건 설정:
      • Zlatoličje HPP 총 유량(QZLAT) = 530 m³/s.
      • SHPP Melje 최소 유량(QSHPP) = 20 m³/s (해수면 기준 고도 252.90m).
      • SHPP Melje 최대 유량(QSHPP) = 20 m³/s (고도 253.30m).
      • 실험은 2003년 현장 유량 측정 데이터 및 2D 수치 모델(SMS-RMA2) 결과를 반영하여 수행.
    • 연구 목표:
      • 취수구 설계 형태의 유압 효율성 검증 및 최적화 수행.
      • 취수구 각 요소(상류 모서리, 하류 모서리, 피어 배치, 취수구 하부 형상)의 수리적 성능 분석.
      • 유량 측정, 속도 측정, 수두 분포 측정을 통한 최적 설계 도출.
  2. FLOW-3D 기반 수치 모델 구축
    • 3D 지오메트리 생성:
      • ACAD에서 모델링 후 STL 파일로 변환, FLOW-3D 내 유한체적 격자(Finite Volume Mesh) 생성.
      • 모델 영역을 3개 블록으로 구분하여 격자 최적화:
        • 블록 1: 15,000개 셀 (Δx = 1m, Δy = 1m, Δz = 0.2m).
        • 블록 2: 480,000개 셀 (Δx = 0.5m, Δy = 0.5m, Δz = 0.2m).
        • 블록 3: 719,200개 셀 (Δx = 0.25m, Δy = 0.25m, Δz = 0.1m).
    • 경계 조건 설정:
      • 블록 1: 유량 조건 (Vz 유량).
      • 블록 2: 실험 모델의 수위 측정값 반영.
      • 블록 3: 유량 조건 적용하여 최종 배출 경계 설정.
    • 수치 해석 방법:
      • RANS (Reynolds-Averaged Navier-Stokes) 방정식 적용.
      • FAVOR (Fractional Area/Volume Obstacle Representation) 방법을 이용하여 취수구 형상 정밀 재현.
      • VOF (Volume-of-Fluid) 기법을 활용하여 자유 표면 흐름 해석.

주요 결과

  1. 물리적 모델 분석 결과
    • 상류 모서리(Upstream Corner)
      • 초기 설계에서는 소규모 역류(Return Flow) 발생 확인됨.
      • 모서리를 둥글게 수정(Rounding-Off)하면 역류가 감소하고 흐름이 원활해짐.
    • 피어 배치(Orientation of Piers)
      • 초기 설계에서는 중앙 및 하류 피어의 방향이 불규칙하여 난류(Turbulence Zone) 발생.
      • 피어 방향을 조정하면 유동 저항 감소 및 수두 손실 최소화 가능.
    • 하류 모서리(Downstream Corner)
      • 기존 설계에서는 흐름이 분기되면서 정체 영역(Dead Zone) 형성.
      • 하류 벽 기하 구조를 조정하여 유동 저항을 줄이고 정체 영역 제거 가능.
    • 취수구 하부(Intake Bottom)
      • 기존 설계에서는 트래시 랙(Trashrack) 이후 수평 소용돌이(Vortex) 발생.
      • 하부를 완만한 기울기로 변경하면 흐름이 원활해지고 압력 손실 감소.
  2. FLOW-3D 수치 모델 분석 결과
    • 수치 모델 결과가 물리적 모델과 유사한 패턴을 보이며 신뢰성 검증됨.
    • 취수구 하부 유동을 비교한 결과:
      • 기존 설계에서는 트래시 랙 이후 역류 발생.
      • 최적화 설계에서는 유선(Streamline)이 원활하게 진행되며 역류 제거됨.
    • 속도 분포 비교:
      • 3D ADV(Acoustic Doppler Velocimeter) 측정 결과와 FLOW-3D 시뮬레이션 결과 비교 시 평균 오차 5% 이내.
      • 특정 지점에서는 수치 모델이 실측 데이터보다 속도를 과소평가하는 경향 확인됨.

결론 및 향후 연구

  • 결론:
    • FLOW-3D 수치 모델이 취수구 설계 최적화에 유용하게 활용 가능함을 입증.
    • 피어 방향 최적화, 하류 벽 기하 수정, 취수구 하부 형상 변경을 통해 수두 손실 최소화 가능.
    • 물리적 모델을 병행 활용하면 정밀한 취수구 설계 검증이 가능.
    • FLOW-3D는 최적화 도구로 유용하지만, 정밀한 조정에는 물리적 모델 병행 필요.
  • 향후 연구 방향:
    • 곡선 좌표 시스템 적용이 가능한 CFD 모델 개발 필요.
    • 더 정밀한 유량 조건 설정을 위한 추가 데이터 확보 필요.
    • 실제 발전소 운영 데이터와의 비교 연구 수행 필요.

연구의 의의

본 연구는 FLOW-3D 기반 수치 모델을 활용하여 소형 수력 발전소의 취수구 설계를 최적화할 수 있음을 입증하였으며, 물리적 모델과의 비교를 통해 수치 모델의 신뢰성을 검증하였다. 이는 수력 발전소 설계 최적화 및 효율 향상을 위한 실질적인 데이터와 설계 기준을 제공할 수 있다.

Fig. 3. Proposed intake form
Fig. 3. Proposed intake form
Fig. 5. Proposed form of the intake bottom
Fig. 5. Proposed form of the intake bottom
Fig. 8. Proposed form of the intake bottom
Fig. 8. Proposed form of the intake bottom

Reference

  1. Mlačnik, J., Vošnjak, S., “Mathematical model of the intake of the SHPP Melje”, Final research report, 2007,
  2. Vošnjak, S., “Verification of the Flow-3D mathematical model by a physical hydraulic model of a small hydropower plant”, presentation, European FLOW-3D User Meeting 2006, CFD Consultants, Tübingen
  3. Mlačnik, J., Vošnjak, S., “Optimisation of the intake into the headrace channel of the HPP Soteska by means of the mathematical model”, Final research report 2007,
  4. Savage, M., Johnson C., “Flow over ogee spillway: Physical and numerical model case study”, Journal of hydraulic engineering, Vol. 127, No. 8, 2001,
  5. Savage, M., Johnson C., “Physical and Numerical Comparison of Flow over Ogee Spillway in the Presence of Tailwater”, Journal of hydraulic engineering, Vol. 132, No. 12, 2006
  6. Versteeg, H.K., Malalasekera W., “An introduction to computational fluid dynamics”, Longman Scientific and Technical, 1995
Verification-of-a-FLOW-3D-matheDownload
Filling Simulation

Numerical Simulation of Metal Flow and Solidification in Multi-Cavity Casting Moulds of Automotive Components

FLOW-3D를 이용한 자동차 부품 다중 캐비티 주조 금형 내 금속 유동 및 응고의 수치 시뮬레이션

연구 배경 및 목적

  • 문제 정의: 자동차 부품 생산에서 다중 캐비티 주조 금형(Multi-Cavity Casting Mould)을 사용하면 생산 효율을 극대화할 수 있다.
    • 자동차용 회색 주철(Grey Iron) 부품인 브레이크 디스크(Brake Disc)와 플라이휠(Flywheel)을 자동 사형 주조(Automatic Sand Casting) 생산 라인을 통해 제작.
    • 주조 공정 중 금속 유동 및 응고 거동을 예측하는 것은 주조 품질 향상 및 결함 최소화에 중요하다.
  • 연구 목적:
    • FLOW-3D 소프트웨어를 활용하여 자동차 부품 주조 공정의 3차원 수치 시뮬레이션을 수행.
    • 다중 캐비티 금형 설계의 적합성 평가 및 주입 시스템(Running System)과 공급 시스템(Feeding System) 최적화.
    • 실험 데이터와 시뮬레이션 결과 비교를 통해 모델의 신뢰성 검증 및 개선 방안 제시.

연구 방법

  1. 금형 및 시뮬레이션 설정
    • 브레이크 디스크(3개 캐비티) 및 플라이휠(4개 캐비티)의 3D 솔리드 모델(STL 파일 형식)을 생성하고 FLOW-3D 소프트웨어에 적용.
    • 모델링 기법:
      • FAVOR (Fractional Area/Volume Obstacle Representation) 기법을 사용하여 복잡한 형상에서도 정확한 해석 가능.
      • VOF (Volume-of-Fluid) 방법을 통해 용융 금속의 자유 표면 이동 및 변형을 추적.
    • 열 물성(Thermo-Physical Properties) 설정:
      • 주철, 실리카 몰드, 세라믹 필터의 열전도율, 비열, 밀도, 표면 장력 계수 등을 포함 (예: 주철의 밀도 7100 kg/m³, 용융 온도 1504K).
  2. 난류 및 다공성 매체 모델링
    • k-ε 난류 모델을 사용하여 난류 유동(Turbulent Flow) 시뮬레이션.
    • 세라믹 필터를 통한 유동 저항 분석을 위해 D’Arcy 모델을 적용:
      • 다공성 매체 내 흐름 저항은 속도에 선형적으로 비례.
      • 필터 제조업체 제공 데이터를 바탕으로 드래그 계수(Drag Coefficient) 설정.
  3. 실험 설정 및 데이터 검증
    • 정밀 타이머를 이용하여 각 부품의 주입 및 응고 시간 측정:
      • 브레이크 디스크: 주입 시간 9.5초, 응고 시간 300초.
      • 플라이휠: 주입 시간 15초, 응고 시간 250초.
    • 적외선 온도계(Pyrometer)를 사용하여 용탕의 주입 전 온도(1703K) 측정.
    • 주조물 절단 및 현미경 분석을 통해 수축 결함(Shrinkage) 위치 확인.

주요 결과

  1. 브레이크 디스크 (Brake Disc) 결과
    • 주입 시뮬레이션 결과:
      • 주철 용탕이 주입구를 통해 1.0초 만에 1차 러너(Primary Runner) 충전, 6.0초 후 중간 캐비티(Middle Cavity)가 먼저 충전.
      • 시뮬레이션 예측 주입 시간 10.08초, 실험 측정 9.5초와 높은 일치도.
    • 응고 시뮬레이션 결과:
      • 80초 후 게이트(Gate) 부분 완전 응고, 166초 후 2차 러너(Secondary Runner) 응고 완료.
      • 285초 시뮬레이션 응고 시간, 실험 측정 300초와 비교 시 오차 5% 이내.
  2. 플라이휠 (Flywheel) 결과
    • 주입 시뮬레이션 결과:
      • 세라믹 필터를 통과한 용탕이 0.47초 만에 1차 러너 충전, 1.14초 후 게이트를 통해 캐비티 충전 시작.
      • 15.5초 만에 충전 완료, 실험 결과(15초)와 높은 일치도.
    • 응고 시뮬레이션 결과:
      • 50초 후 필터 및 게이트 영역 응고 시작, 100초 후 모든 게이트 응고.
      • 220초에 캐비티 응고 완료, 50초 후 주입 시스템도 응고.

결론 및 향후 연구

  • 결론:
    • FLOW-3D 시뮬레이션을 통한 다중 캐비티 주조 공정의 금속 유동 및 응고 거동 분석이 실제 실험과 높은 일치도를 보임.
    • 4개 캐비티 금형이 3개 캐비티 금형보다 균일한 주조 품질을 제공.
    • 첫 번째 게이트의 단면적을 줄여 기공(Porosity) 발생 가능성을 줄일 수 있음.
    • 모델은 주조 공정 매개변수(예: 용탕 과열 온도, 주입 속도, 금형 표면 거칠기)의 영향을 분석할 수 있음.
  • 향후 연구 방향:
    • 다양한 게이팅 시스템 설계의 적합성 평가.
    • AI 및 머신러닝을 활용한 실시간 주조 공정 최적화 시스템 개발.
    • 산업 현장 적용을 위한 대규모 실증 연구 수행.

연구의 의의

본 연구는 FLOW-3D 시뮬레이션을 활용하여 다중 캐비티 주조 금형의 금속 유동 및 응고 거동을 정량적으로 평가하고, 자동차 부품의 생산 효율성과 품질을 극대화할 수 있는 실질적인 설계 기준을 제공하며, 자동차 및 중공업 산업의 비용 절감과 제품 신뢰성 향상에 기여할 수 있다​.

Reference

  1. Barkhudarov, M.R., 1998. Advanced simulation of the flow and heat transfer in simultaneous engineering, Technical Report, Flow Science, Inc.
  2. Barkhudarov, M.R., Hirt, C.W. Casting simulation: mold filling and solidification—benchmark calculations using FLOW-3D®, Technical Report, Flow Science, Inc., 1993.
  3. Campbell, J., 1991. Castings. Butterworth Heinmann.
  4. Flemings, M.C., 1974. Solidification Processing. McGraw-Hill Book Co., New York.
  5. Flow Science, Inc., 2005. FLOW-3D® User’s Manual, Version 8.2.
  6. Hirt, C.W., Nichols, B.D., 1981. Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39, 201–255.
  7. Hirt, C.W., Sicilian, J.M., 1985. Proceedings of the 4th International Conference on Ship Hydrodynamics, Washington, DC, September 1985.
  8. Kermanpur, A., Mahmoudi, Sh., Hajipour, A., 2006a. Numerical analysis of solidification of the cast iron automotive parts. In: Proceedings of the 8th Symposium of the Iron and Steel Society of Iran, Isfahan University of Technology, Februrary 28–March 1 2006, pp. 188–199.
  9. Kermanpur, A., Hajipour, A., Mahmoudi, Sh., 2006b. Numerical simulation of fluid flow and solidification in the casting of an automotive flywheel part. In: Proceedings of the 14th Annual (International) Mechanical Engineering Conference (ISME2006), Isfahan University of Technology, Isfahan, Iran,
  10. May 2006.Kothe, D.B., Rider, W.J. Comments on modelling interfacial flows with volume-of-fluid methods, Los Alamos National Laboratory Report LA-UR-94-3384, 1994.
Numerical_simulation_of_metal_flow_and_sDownload
Water-Rock interaction

Using Computational Fluid Dynamics (CFD) Simulation with FLOW-3D to Reveal the Origin of the Mushroom Stone in the Xiqiao Mountain of Guangdong, China

FLOW-3D 기반 CFD 시뮬레이션을 통한 광둥성 시차오산 버섯 돌 형성 원인 분석

연구 목적

  • 본 연구는 FLOW-3D® CFD 시뮬레이션을 활용하여 Xiqiao Mountain(시차오산)의 버섯 돌(Mushroom Stone) 형성 과정을 규명함.
  • 기존 연구에서는 유수 침식(stream water erosion)이 주요 형성 원인으로 제시되었으나, 본 연구에서는 CFD 분석을 통해 침식 외에도 화학적 및 물리적 풍화 작용이 결정적인 역할을 했음을 입증하고자 함.
  • 광물 분석 및 현장 조사와 함께 컴퓨터 시뮬레이션을 수행하여 물리적, 화학적 풍화 작용과 유동 역학 간의 관계를 평가함.

연구 방법

  1. 현장 조사 및 샘플링
    • 드론(DJI Phantom 4 RTK)을 활용하여 버섯 돌의 3D 지형 데이터를 정밀 측정.
    • 암석 시료 7개를 서로 다른 위치에서 채취하여 **광물 분석(mineralogical analysis)**을 수행함.
    • 지질 나침반을 사용하여 버섯 돌 곡면의 방향 및 침식 패턴을 기록함.
  2. FLOW-3D® 기반 CFD 시뮬레이션
    • 자유 표면 유동(Free Surface Flow)을 모델링하여 홍수 시 버섯 돌 주변의 유속 및 압력 분포를 분석.
    • 난류 모델 적용: RANS(Reynolds-Averaged Navier-Stokes) 방정식을 사용하여 난류 효과를 고려함.
    • 모의 홍수 실험을 진행하여 홍수 시기 물의 흐름이 버섯 돌에 미치는 영향을 평가함.
  3. 결과 비교 및 검증
    • 광물 분석 데이터 및 현장 조사 결과를 CFD 시뮬레이션과 비교하여 풍화 및 침식 기작을 검증.
    • 침식 패턴, 유속, 압력 분포 등을 종합 분석하여 버섯 돌 형성의 주요 기작을 도출함.

주요 결과

  1. 홍수 시 버섯 돌 주변 유동 특성
    • 시뮬레이션 결과, 최고 유속은 버섯 돌의 측면에서 발생하며, 전·후면에서는 상대적으로 낮은 유속을 보임.
    • 버섯 돌의 전면(상류 방향)에서는 고압력이 발생하여 아래쪽으로 흐름이 집중됨, 이는 하부 침식을 유도함.
    • 그러나 시뮬레이션 결과, 버섯 돌의 좁은 하부 구조는 단순한 유수 침식만으로 형성될 수 없음을 보여줌.
  2. 버섯 돌 침식 패턴 및 풍화 작용
    • CFD 분석 결과, 버섯 돌 하부(풍하측)에 퇴적물이 집중적으로 형성되며, 이는 침식보다 퇴적 과정이 더 중요한 역할을 했음을 시사함.
    • 실험 데이터와 비교 시, 유수 침식만으로는 현장에서 관찰된 곡면 구조를 재현할 수 없음.
    • 대신, 장기간 퇴적물이 축적되면서 화학적 및 물리적 풍화 작용이 진행되었을 가능성이 높음.
  3. 광물 분석 결과 및 풍화 작용
    • XRD(X-ray diffraction) 분석 결과, 버섯 돌 하부의 암석은 석고(gypsum) 및 점토 광물 함량이 높으며, 이는 화학적 풍화가 활발하게 진행되었음을 의미함.
    • 석고 크리스탈이 성장하면서 암석 내부 균열을 유발하는 할로클래스티(haloclasty) 현상이 관찰됨.
    • 장기간 퇴적층 내에 존재했던 암석이 화학적 풍화 및 수분에 의한 연화 작용으로 약해진 후, 외부 퇴적물이 제거되면서 버섯 돌 하부의 곡면이 형성됨.
  4. 버섯 돌 형성 과정 및 주요 기작 정리
    • 1단계: 버섯 돌이 퇴적물 속에 매립됨 → 장기간 퇴적물 내에서 화학적 풍화가 진행됨.
    • 2단계: 퇴적물 제거 후, 풍화된 암석이 노출되면서 내부 곡면이 형성됨.
    • 3단계: 추가적인 기계적 풍화 및 석고 결정 성장이 내부 균열을 유발하며 현재의 버섯 돌 형태가 완성됨.

결론

  • 유수 침식만으로 버섯 돌이 형성되었다는 기존 가설은 CFD 시뮬레이션 결과와 일치하지 않음.
  • 광물 분석 및 화학적 풍화 모델링 결과, 할로클래스티(haloclasty) 및 습윤 연화(softening due to moisture) 작용이 버섯 돌 형성의 주요 기작으로 확인됨.
  • CFD 시뮬레이션을 통한 수력학적 해석과 광물 분석을 결합하여 자연 암석 형성 기작을 정량적으로 분석하는 새로운 접근법을 제시함.
  • 향후 연구에서는 장기적인 풍화 속도 및 추가적인 유체-암석 상호작용 모델링을 수행해야 함.

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  34. Wang W, Huang R (2018) The origin of the “Fairy Stone” on the coast of Dapeng Penisula, Guangdong, China. Quat Sci 38: 427-448. (In Chinese) https://doi.org/10.3760/j.issn:0412-4030.2006.11.029
  35. Wedekind W, López-Doncel R, Dohrmann, R, et al. (2013) Weathering of volcanic tuff rocks caused by moisture expansion. Environ Earth Sci 69: 1203–1224. https://doi.org/10.1007/s12665-012-2158-1
  36. Wei G, Brethour J, Grünzner M, et al. (2014) Sedimentation scour model in FLOW-3D. Flow Sci Rep 03-14: 1-29.
  37. Whipple KX, Hancock GS, Anderson RS (2000) River incision into bedrock: Mechanics and relative efficacy of plucking, abrasion, and cavitation. Geol Soc Am Bull 112: 490–503. https://doi.org/10.1130/0016-7606(2000)112<490:RIIBMA>2.0.CO;2
  38. White AF (2003) Natural Weathering Rates of Silicate Minerals. In: Drever JI (ed.), Treatise on Geochemistry: Surface and Ground Water, Weathering and Soils. Elsevier Science, pp. 133–168. https://doi.org/10.1016/B0-08-043751-6/05076-3
  39. Wu CY, Ren J, Bao Y, et al. (2007) A long-term hybrid morphological modeling study on the evolution of the Pearl River delta network system and estuarine bays since 6000 aBP. In: Harff J, Hay WW, Tetzlaff DF (ed.), Coastline Changes: Interrelation of Climate and Geological Processes; Special Papers – Geological Society of America Spec. Pap 426: 199-214.https://doi.org/10.1130/2007.2426(14)
  40. Zhao L, Zhu Q, Jia S, et al. (2017) Origin of minerals and critical metals in an argillized tuff from the Huayingshan Coalfield, Southwestern China. Minerals 2017: 7: 92. https://doi.org/10.3390/min7060092
Result of Temperature

Comparative Analysis of HPDC Process of an Auto Part with ProCAST and FLOW-3D

ProCAST 및 FLOW-3D를 이용한 자동차 부품 고압 다이캐스팅(HPDC) 공정 비교 분석

연구 배경 및 목적

  • 문제 정의: 고압 다이캐스팅(HPDC, High Pressure Die Casting)은 자동차, 항공우주, 건축 재료 등 다양한 산업에서 ADC12 알루미늄 합금을 사용하여 복잡한 형상의 부품을 대량 생산하는 데 활용된다.
    • HPDC 공정에서는 버블 모델(Bubble Models), 유동 마크(Flow Marks), 콜드 셧(Cold Shuts)과 같은 주조 결함이 자주 발생한다.
    • 이러한 결함은 시제품 제작 비용 증가, 생산 주기 지연, 제품 신뢰성 저하를 초래한다.
  • 연구 목적:
    • ProCAST 및 FLOW-3D 소프트웨어를 사용하여 ADC12 알루미늄 합금 자동차 부품의 HPDC 공정을 시뮬레이션하고, 두 소프트웨어의 충진(Filling) 및 응고(Solidification) 과정 비교.
    • 주조 결함(기포 모델, 수축 캐비티 및 수축 다공성 결함)을 분석하고, 실제 생산과의 정확도 비교를 통해 최적의 시뮬레이션 방법 제시.

연구 방법

  1. 자동차 부품 모델링 및 HPDC 공정 설정
    • ADC12 알루미늄 합금을 사용한 회전체(Rotary Part) 구조의 복잡한 형상 부품을 대상으로 연구.
    • 부품의 순중량 0.45 kg, 최대 직경 68 mm, 평균 벽 두께 3.2 mm.
    • 게이팅 시스템(Gating System) 및 오버플로우 시스템(Overflow System)을 설계하여 CAD 모델 생성(Fig.1, Fig.2).
    • 주조 조건:
      • 주입 온도: 680℃
      • 금형 초기 온도: 200℃
      • 사출 속도: 2.4 m/s
      • 인게이트 속도(Ingate Velocity): 40 m/s
      • 냉각 조건: 공기 냉각
  2. ProCAST 시뮬레이션
    • 유한 요소법(FEM, Finite Element Method)을 사용.
    • 188,107개의 노드, 1,010,920개의 사면체 요소(Tetrahedron Elements)로 메쉬 생성(Fig.3).
    • 온도장(Temperature Field) 변화 분석:
      • 충진 시간 0.052 s 동안 액체 금속이 금형을 완전히 충전.
      • 버블 모델 및 수축 캐비티, 수축 다공성 결함이 A 및 B 영역에서 발생(Fig.4, Fig.5).
  3. FLOW-3D 시뮬레이션
    • 유한 차분법(FDM, Finite Difference Method)을 사용하여 고급 액면 추적 기능 제공.
    • STL 형식의 3D 모델을 사용하여 2개의 그리드 블록으로 분할(Fig.6).
    • 충진 과정 동안 튀김(Splash) 현상 발생(Fig.7):
      • A 영역에서는 고속 및 고압으로 공기를 쉽게 배출하여 기포 결함 발생 억제.
      • B 영역에서는 부드럽게 충진되어 기포 모델 결함 발생하지 않음.
    • 표면 결함 추적 결과(Fig.8):
      • 명확한 표면 결함 없음, 총 충진 시간 0.0455 s로 ProCAST보다 빠른 충진 속도.

주요 결과

  1. ProCAST vs. FLOW-3D 비교
    • ProCAST 시뮬레이션:
      • A 및 B 영역에서 기포 모델 결함 발생, 실제 주조물에서도 동일한 결함이 예상됨.
      • 수축 캐비티 및 다공성 결함의 총 부피 약 0.253 cm³.
    • FLOW-3D 시뮬레이션:
      • 오버플로우 성능이 우수하여 공기 배출 경로를 변경, 기포 모델 결함 발생을 억제.
      • A 및 B 영역에서 결함이 거의 발생하지 않음, 실제 주조물과 높은 일치도(Fig.9).
  2. 정확도 평가
    • FLOW-3D 시뮬레이션 결과가 실제 생산과 더 높은 일치도를 보임.
    • ProCAST는 버블 모델 및 수축 결함을 과대 예측하였으나, FLOW-3D는 결함을 최소화.
    • FLOW-3D의 충진 속도가 더 빠르고 정확하게 금형을 충전할 수 있음을 확인.

결론 및 향후 연구

  • 결론:
    • FLOW-3D 소프트웨어가 ProCAST보다 ADC12 알루미늄 합금 자동차 부품의 HPDC 공정에서 더 높은 정확도를 제공.
    • FLOW-3D는 액체 금속의 충진 과정과 표면 결함을 정밀하게 예측할 수 있으며, 실제 생산 품질을 보장할 수 있음.
    • ProCAST와 FLOW-3D의 알고리즘 차이로 인해 시뮬레이션 결과가 일치하지 않을 수 있음:
      • ProCAST: FEM 기반으로 세부 결함 분석에 유리.
      • FLOW-3D: FDM 기반으로 액체 유동 및 표면 결함 추적에 강점.
  • 향후 연구 방향:
    • 다양한 주조 재료 및 공정 변수에 대한 추가 비교 연구.
    • AI 및 머신러닝을 활용한 주조 결함 예측 모델 개발.
    • 산업 현장 적용을 위한 최적 HPDC 공정 설계 및 실증 실험 수행.

연구의 의의

이 연구는 ProCAST 및 FLOW-3D 시뮬레이션을 통한 HPDC 공정의 비교 분석을 통해 최적의 소프트웨어 선택 가이드라인을 제공하며, 자동차 및 항공우주 산업의 주조 품질 향상 및 생산성 증대에 기여할 수 있다​.

Reference

  1. Jitender K. Rai, Amir M. Lajimi, Paul Xirouchakis, An intelligent system for predicting HPDC process variables in interactive environment, journal of materials processing technology. 203 (2008) 72–79.
  2. A. Krimpenis, P.G. Benardos, G.-C. Vosniakos, A. Koukouvitaki, Simulation-based selection of optimum pressure die-casting process parameters using neural nets and genetic algorithms, Int J Adv Manuf Technol, (2006) 27: 509–517.
  3. Chunmiao Wu, Die casting technical manual[M], Guangdong Science and Technology Press, Guangdong, 2006.
  4. K..Anzai.A Cast CAE System with Flow and Solidification Simulation to Wheel Casting. Proceedings of Modeling of Casting and Solidification Processes[J],1995:279-286.
  5. K.Kubo.SCAST-Integrated Simulation System for Casting Design.Proceedings of Modeling of Casting and Solidification Processes[J],1995:173-181.
  6. M. Ivosevic, V. Gupta, J.A. Baldoni, R.A. Cairncross, T.E. Twardowski, and R. Knight, Effect of Substrate Roughness on Splatting Behavior of HVOF Sprayed Polymer Particles: Modeling and Experiments, Journal of Thermal Spray Technology. Volume 15(4) December 2006:725-730.
  7. Information on http://www.flow3d.com.
Comparative analysis of HPDC process of an auto part with ProCAST and FLOW-3DDownload

pattern

Numerical Modeling of Flow Pattern in Dam Spillway’s Guide Wall. Case Study : Balaroud dam, Iran

댐 방수로(Spillway) 안내벽의 유동 패턴 수치 모델링: 이란 Balaroud 댐 사례 연구

연구 배경

  • 문제 정의: 댐 방수로의 안내벽(Guide Wall)은 흐름 패턴을 조절하는 중요한 구조물로, 최적의 형상을 설계하면 방수로의 성능을 향상할 수 있음.
  • 목표: Balaroud 댐의 방수로 안내벽에 대해 물리적 및 수치적 모델링을 수행하여, 최적의 안내벽 형상을 도출.
  • 접근법: CFD(Computational Fluid Dynamics) 소프트웨어인 FLOW-3D를 활용하여 다양한 안내벽 설계를 비교 분석.

연구 방법

  1. 모델링 개요
    • AutoCAD를 이용하여 3D 모델 생성 후 FLOW-3D로 내보내기(STL 파일 형식).
    • 1:110 축척의 실험실 모델을 구축하고 실험 결과와 수치 해석을 비교.
  2. 수치 모델링 과정
    • 격자 생성(Meshing): 다양한 해상도로 수치 해석을 진행.
    • 경계 조건 설정: 유입 및 유출 조건을 설정하고 난류 모델 선택.
  3. 난류 모델 비교
    • K-epsilon, RNG K-epsilon, LES(Large Eddy Simulation) 모델을 비교.
    • RNG K-epsilon 모델이 가장 적합한 결과를 보임.
  4. 세 가지 안내벽 설계 평가
    • 모델 1: 유동 분리가 심하게 발생하여 부적합.
    • 모델 2: 접근 채널에서 교차파(Cross Waves) 형성.
    • 모델 3: 최소한의 유동 분리 및 교차파 제거 → 최적의 설계로 선정.

주요 결과

  • 모델 3이 가장 우수한 성능을 보이며, 교차파 발생을 최소화하고 유량을 원활하게 전달.
  • 유량-수위 곡선(Rating Curve) 분석을 통해 모델 3이 다른 설계보다 효율적임을 확인.
  • FLOW-3D의 RNG K-epsilon 난류 모델이 유동 패턴 해석에 가장 적합.

결론 및 향후 연구

  • 수치 모델링과 물리적 실험을 결합하여 최적의 안내벽 형상을 도출.
  • 최적 설계(모델 3)를 통해 방수로 성능을 개선하고, 수력 구조물의 안전성을 향상 가능.
  • 향후 연구에서는 다양한 유입 조건과 추가적인 설계 변수를 고려하여 더욱 정밀한 최적화를 수행할 필요.

이 연구는 댐 방수로 안내벽 설계의 최적화를 목표로 하며, 수치 해석 기법을 활용한 CFD 기반 설계 검증 방법론을 제시한다는 점에서 의의가 있다.

Reference

  1. M.C. Aydin, CFD simulation of free-surface flow overtriangular labyrinth side weir, Adv. Eng. Softw. 45 (1) (2012)159–166.
  2. M.C. Aydin, M.E. Emiroglu, Determination of capacity oflabyrinth side weir by CFD, Flow Meas. Instrum. 29 (2013) 1–8.
  3. H. Babaali, A. Shamsai, H. Vosoughifar, Computationalmodeling of the hydraulic jump in the stilling basin withconvergence walls using CFD codes, Arab. J. Sci. Eng. 40 (2)(2015) 381–395.
  4. P.D. Bates, S.N. Lane, R.I. Ferguson, Computational FluidDynamics: Applications in Environmental Hydraulics, Wiley,2005.
  5. T. Cebeci, Turbulence Models and Their Application: EfficientNumerical Methods with Computer Programs, Horizons Pub,2004.
  6. P.G. Chanel, An Evaluation of Computational Fluid Dynamicsfor Spillway Modeling, University of Manitoba, 2008 (Master ofScience).
  7. J. Chatila, M. Tabbara, Computational modeling of flow overan ogee spillway, Comput. Struct. 82 (22) (2004) 1805–1812.
  8. C. Chinnarasri, D. Kositgittiwong, P.Y. Julien, Model of flowover spillways by computational fluid dynamics, Proc. ICE –Water Manage. (2014) 164–175.
  9. R. Ettema, Hydraulic Modeling Concepts and Practice, ASCE,2000.
  10. D. Gessler, CFD modeling of spillway performance, ImpactsGlob. Clim. Change (2005) 1–10.
  11. G. Guyot, H. Maaloul, A. Archer, A Vortex modeling with 3DCFD, in: P. Gourbesville, J. Cunge, G. Caignaert (Eds.),Advances in Hydroinformatics, Springer, Singapore, 2014, pp.433–444.
  12. W.H. Hager, M. Pfister, Hydraulic modelling – an introduction:principles, methods and applications, J. Hydraul. Res. 48 (4)(2010) 557–558.
  13. D. Kim, J. Park, Analysis of flow structure over ogee-spillway inconsideration of scale and roughness effects by using CFDmodel, KSCE J. Civ. Eng. 9 (2) (2005) 161–169.
  14. R. Maghsoodi, M.S. Roozgar, H. Sarkardeh, H.M.Azamathulla, 3D-simulation of flow over submerged weirs,Int. J. Model. Simul. 32 (4) (2012) 237.
  15. B. Mohammadi, O. Pironneau, Analysis of the K-epsilonTurbulence Model, Wiley, 1994.
  16. F. Moukalled, L. Mangani, M. Darwish, The Finite VolumeMethod in Computational Fluid Dynamics: An AdvancedIntroduction with OpenFOAM and Matlab, SpringerInternational Publishing, 2015.
  17. Y. Nakayama, R.F. Boucher, Computational fluid dynamics, in:Y.N.F. Boucher (Ed.), Introduction to Fluid Mechanics,Butterworth-Heinemann, Oxford, 1998, pp. 249–273.
  18. A. Parsaie, A. Haghiabi, Computational modeling of pollutiontransmission in rivers, Appl. Water Sci. (2015) 1–10.
  19. A. Parsaie, A. Haghiabi, Predicting the longitudinal dispersioncoefficient by radial basis function neural network, Model.Earth Syst. Environ. 1 (4) (2015) 1–8.
  20. A. Parsaie, A. Haghiabi, A. Moradinejad, CFD modeling offlow pattern in spillway’s approach channel, Sustain. WaterResour. Manag. 1 (3) (2015) 245–251.Figure 14 Head discharge curve of the model (3).Figure 16 The rating curve of the models for the guide wall.Figure 15 Cross section of the flow through the guide wall at theflood return period 1000 year.472 S. Dehdar-behbahani, A. Parsaie
  21. A. Parsaie, H. Yonesi, S. Najafian, Predictive modeling ofdischarge in compound open channel by support vector machinetechnique, Model. Earth Syst. Environ. 1 (2) (2015) 1–6.
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1-s2.0-S1110016816000107-mainDownload
Welding

A multi-physics CFD study to investigate the impact of laser beam shaping on metal mixing and molten pool dynamics during laser welding of copper to steel for battery terminal-to-casing connections

배터리 단자-케이싱 접합을 위한 구리와 강철 간 레이저 용접 시 레이저 빔 형상이 금속 혼합 및 용융풀 역학에 미치는 영향을 조사하는 다중 물리 CFD 연구

Giovanni Chianese, Qamar Hayat, Sharhid Jabar, Pasquale Franciosa, Darek Ceglarek, Stanislao Patalano

Abstract

This study aims to investigate the impact of laser beam shaping on metal mixing and molten pool dynamics during laser beam welding of Cu-to-steel for battery terminal-to-casing connections. Four beam shapes were tested during LBW of 300 µm Cu to 300 µm nickel-plated steel. Both experiments and simulations were used to study the underlying physics. A CFD model was firstly calibrated against experiments and then deployed to explore the effect of the increasing ring-to-core diameter, as well as a tandem laser spot configuration. The study showed that metal mixing is influenced by the keyhole dynamics and collapse events, but also there is an intricate interplay between keyhole geometry, fluid dynamics via Marangoni forces and buoyancy forces. Notably, the buoyance forces due to the different densities of steel and Cu, along with the recoil pressure contribute to the upward flow of steel towards Cu, and hence impact meaningfully the material mixing. The study pointed-out that the selection of a custom ring-to-core diameter and ring-to-core power is a decision with a trade-off between the need of stabilising the keyhole dynamics and the need to reduce the mixing. Findings indicated that 350 µm ring and 90 µm core with 30% of ring power (weld configuration C3) resulted in more stable dynamics of the keyhole, with significant reduction of collapse events, and ultimately controlled migration of steel towards Cu. Additionally, the pre-heating approach with the tandem beam only led to local fusion of Cu and no significant improvement in keyhole stability was observed.

1. Introduction

The push towards net-zero mobility is globally influencing industrial strategies in the automotive sector as reported by IEA (2022). Manufacturers are introducing new vehicles by replacing internal combustion engines with hybrid or fully electric powertrains. The battery pack is a critical component for un-interrupted supply of electricity to e-drives and other electrical systems in electric vehicles (EV). A battery pack typically consists of several battery modules that are electrically connected in series and parallel based on the desired power and capacity requirements (Zwicker et al., 2020). Battery modules hold the battery cells that store the electrical charge and supply it on-demand to the electrical systems. Electrical connections play a critical role in the entire process of battery pack manufacturing since joints with different electrical resistance may result in uneven current loads that can affect the overall performances of the battery system (Kumar et al., 2021). Joining of dissimilar materials is the most deemed since it complements the properties of the individual materials and allows to develop functionally efficient connections. Joints in EV battery pack involve low-thickness materials (typically 0.3–1 mm) and the welding process is normally performed in lap or fillet configuration. Depending upon design and functional requirements as well as manufacturing costs, research has shown that the following combinations of materials are the most regarded: aluminium (Al) to copper (Cu), steel to Al, Al to steel, Cu to steel (Das et al., 2018).
Connections between Cu and steel have gained much attention in EV applications for joining cells in battery modules. For example, in the cylindrical format, the negative terminals are made of Cu and are generally connected to the steel casing of the cell (Sadeghian and Iqbal, 2022). Several joining processes have been studied for Cu-to-steel welding and they include wire bonding, micro-spot welding, ultrasonic welding, micro-TIG welding, electron beam welding and Laser Beam Welding (LBW) (Zwicker et al., 2020). LBW is an attractive option and has recently gained popularity due to advances in versatile methods for laser beam delivery and associated sensors technology for quality control and process monitoring that make LBW comparatively affordable (Kogel-Hollacher, 2020). Brand et al. (2015) demonstrated that LBW is a suitable process for joining battery terminals since it allows the lowest electrical resistance and the highest joint strength, when compared to micro-spot welding and ultrasonic welding; also, it is potentially applicable to any cell configuration and dissimilar metal combinations.
Despite the benefits of LBW, opening and maintaining a stable molten pool on the Cu-side is challenging when using LBW with infrared sources. The absorptivity of Cu at ambient temperature is approximate 5% and increases with rising temperature, and it suddenly jumps up when the melting temperature is reached. A problem with this is that when fusion of the material does happen, a surplus of energy flows through it, which can vaporise the material and create spatters, as well as pores inside the joint. These defects can reduce the electrical conductivity of the joint. At first sight, the solution to the low coupling efficiency of Cu is to switch from infrared sources to visible sources. The absorption increases drastically up to 60% when using visible sources. Green (515 nm) or blue (450 nm) lasers have been investigated by Kogel-Hollacher et al. (2022) and proved that lower power needed for same penetration achievable with infrared lasers and less thermal damage to enamel and insulators. Hummel et al. (2020) experimentally evaluated and proved the beneficial effects of blue laser during laser micro-welding of Cu, and achieved high welding speed with low input power. Nonetheless, compared to infrared lasers, the higher cost, lower plug efficiency and lower beam quality of visible lasers, push practitioners towards the use of multi-kW infrared sources at very high brightness for Cu welding.
In addition to the challenge posed by the laser beam coupling to the Cu, the welding of Cu to steel presents a series of problems. First, they are quite different in terms of physical properties such as density, melting points and thermal expansion and make defect-free welding difficult. Second, although Cu-Fe alloys are completely miscible in the stable liquid state and do not form brittle intermetallic compounds, the system shows a wide metastable miscibility gap at an undercooling level. The liquid phase separation occurs as the liquid cools in the miscibility gap resulting in the supersaturation of one or both liquids. Jeong et al. (2020) has shown that increasing the content of Fe tends to improve the mechanical properties of alloys but reduce electrical conductivity and ductility. Chen et al. (2013) proved that the toughness and fatigue strength of the joint decreases with the increase in the amount of molten Cu into the steel. Thus, melting of Cu was suggested to be kept at a minimum. Third, excessive penetration of Cu in grain boundaries of steel may result in cracks in the heat affected zone and fusion zone, and ultimately reducing structural performance of the joint. Therefore, to reduce these issues, controlling the mixing of Cu and steel in the molten pool is quite important for producing sound joints.
Laser beam shaping is gaining popularity since it holds the promise to control cooling rates and thermal gradients in and around the molten pool. This theoretically leads to a tailored material response to the heat input both spatially and temporally. A tailored power density profile (Fig. 1 shows typical power density profiles obtained via adjustable ring-mode laser) is generated via adequate insertion of optical components (specially coated lenses of silica substrate) in the optical chain of the welding head; or by electro-optical switching multiple laser beams generated in the laser source itself and enabled by beam combiners with optical phased array. Research has confirmed a positive effect of the laser beam shaping on the control of the weld profile and keyhole stabilization with suppression of spatters and significant reduction of porosity in the weldments. Caprio et al. (2023) investigated the use of beam shaping and beam oscillation to weld 0.2 mm Ni-plated steel sheets in lap joint configuration, which are materials commonly involved in cell to busbar connections. Sokolov et al. (2021) employed the ARM laser coupled with Optical Coherent Tomography (OCT) in Al-to-Cu thin sheets and observed that the use of combined core and ring-shaped laser beams reduced the fluctuations of the keyhole, improved the stability, and ultimately the accuracy of OCT measurements. Rinne et al. (2022) studied the effect of different power distributions between the inner core and outer ring-shaped laser beams on spatter ejection and penetration depth during welding of Cu sheets. Wagner et al. (2022) investigated and proved the influence of dynamic beam shaping on the geometry of the keyhole during welding of Cu by varying the patterns of the intensity distribution in longitudinal and transversal direction. Prieto et al. (2020) implemented dynamic laser beam shaping with infinite pattern and assessed quality of weld seam in 0.8 mm Al thin-sheet and observed that tailored beam with shape frequency over 10 kHz enables welding speed up to 18 m/min with stable keyhole.

Fig. 1. Example of laser beam shapes obtained via an adjustable ring-mode laser.

Despite the benefits, laser beam shaping introduces new set of parameters and finding the optimal combination of number of beams, shape of beams (multiple spots, C-spot, ring-core spots, pyramid, infinity, spiral shapes, etc. (Prieto et al., 2020)) can be expensive and time consuming since it may require dedicated equipment, expertise and experimental setups. In this context, multi-physics computational fluid dynamics (CFD) enable simulations of the process to reproduce mechanisms which are difficult to observe with in-situ investigations. With the raise of computational power and multi-core computing on high performance clusters, advanced simulations of LBW processes are now a close reality. Huang et al. (2020) developed a CFD model in FLOW-3D WELD® to study the metal mixing during linear laser welding of 200 µm Al to 500 µm Cu with different levels of laser power and velocity of the laser spot. They analysed the contribution of recoil pressure and Marangoni effect on the overall mixing process. Chianese et al. (2022) developed a multi-physics model using FLOW-3D and FLOW-3D WELD® to investigate the effect of part-to-part gap in LBW of Cu-to-steel thin sheets with beam wobbling. They showed that the presence of part-to-part gap and mixing mechanism between parent metals are linked, and the occurrence of part-to-part gap influences the temperature and velocity fields in the molten pool resulting in different mixing mechanisms. However, they did not implement any strategies for weld improvement. Drobniak et al. (2020) and Buttazzoni et al. (2021) implemented CFD multi-physics simulations of 1 mm-thick stainless steel plates with adaptive mesh refinement to predict the shape of the weld seam in presence of part-to-part gap, and they predicted the effect on the process of secondary laser beams with different shapes to optimize the weld quality. Recently, Huang et al. (2023) combined experimental approach and CFD simulations in FLOW-3D WELD® to reveal the effect of oscillation frequency and amplitude on fluid-flow and metal mixing during laser welding of 200 µm Al to 500 µm Cu with circular beam wobbling implemented. Additionally, they implemented a Scheil solidification model to predict the phase distributions in the welds based on the predicted thermo-solute conditions.
While significant research has been already developed using linear laser welding or laser welding with wobbling for joining of dissimilar materials, a clear understanding of metal mixing and dynamics of the keyhole during Cu-to-steel welding with beam shaping are not clearly reported. Research into application of beam shaping for Cu-to-steel welding entails a promising prospect for further development and investigation. Furthermore, the use of advanced CFD models is a viable approach to complement experimental investigations and explore weld configurations with different beam shaping profiles that would be difficult to achieve only with experimental work. Therefore, this paper aims to study the impact of laser beam shaping on metal mixing and dynamics of the keyhole during LBW of Cu-to-steel for battery terminal-to-casing connections. Four beam shapes were tested during LBW of 300 µm Cu to 300 µm nickel-plated steel. Both experiments and CFD simulations were used to study the underlying physics. A CFD model was firstly calibrated against experiments and then deployed to explore the effect of the increasing ring-to-core diameter, as well as a tandem laser spot configuration.

2. Experimental design and model description

2.1. Experimental design

Materials used in this work are Copper SE-Cu58 2.0070 and Nickel-plated steel (commercial name: Hilumin TATA STEEL). Experiments consisted of 25 mm long welds in lap joints configuration with 300 µm Cu on top of 300 µm nickel-plated steel.
Dimensions of the specimens were 65 mm × 30 mm. The laser source used was the Lumentum CORELIGHT, having 55 µm core diameter and 220 µm ring diameter, and BPP 1.4 mm·mrad and 11 mm·mrad for core and ring, respectively. The laser fiber was coupled to the Scout-200 (Laser and Control K-lab, South Korea) scanner to deliver the laser power to the specimens via 2D F-theta scanner with telecentric lenses. Fig. 2 shows the welding setup and specifications of the equipment are in Table 1. Caustic parameters were measured using PRIMES GmbH measurement system.

Fig. 2. (a) Welding setup with aluminium fixture; (b) schematical representation of the welding setup; (c) definition of weld features: top weld width, Wtop; width at the interface, Wi; weld penetration depth, Dpen.
Table 1. Specifications of the welding equipment.

Each weld seam was cut and prepared to obtain two cross sections for each experiment – cross sections were positioned at 10 mm and 15 mm away from the weld start. Three replicates were performed for each weld configuration. Sectioned samples were mounted in Bakelite resins and standard metallography procedure was performed for grinding and polishing to reveal weld profile under Nikon Eclipse LV150N optical microscope. To evaluate and characterize metal mixing with parent metals, elemental mapping of cross-sections was performed with an FEI Versa 3D dual beam scanning electron microscope using Energy Dispersive X-ray Spectroscopy (EDS mapping).
Welding experiments were performed in continuous power mode without power modulation. The laser beam was focussed perpendicularly on the upper surface of the Cu sheet, and the motion of the laser was linear (no wobbling). Although the use of shielding gas tends to avoid oxidation in the process and reduce hydrogen entrapment, when using scanners to deliver the laser beam, the gas nozzle cannot be positioned in proximity of the beam. Therefore, in this work, all experiments were conducted with no shielding gas. Part-to-part gap was manually checked and set to a nominal zero.
To study the impact of laser beam shaping on metal mixing and molten pool dynamics, 5 weld configurations (C1 to C5) were designed as shown in Table 2, with 4 beam shapes presented in Fig. 3. LBS#1 is single gaussian spot of 90 µm; LBS#2 super-imposes an inner core of 90 µm with an outer ring-shaped profile of 350 µm, with the ring accounting 30% of the total power. LBS#1 and LBS#2 were experimentally tested and enabled by the static beam shaping system of the Lumentum CORELIGHT source. LBS#3 follows the hollow sinh-Gaussian beam profile as defined in Liu et al. (2019), with 90 µm core and 500 µm ring, with 72% of the total power assigned to the ring. LBS#4 is a tandem beam with primary (90 µm) and secondary beam (150 µm) at a centre-to-centre distance of 300 µm, and 50% split of the power between primary and secondary beams – LBS#4 was introduced with the aim to increase the absorption rate by the pre-heating action of the secondary beam. LBS#3 and LBS#4 were only simulated since the laser beam shaping of the Lumentum CORELIGHT was only capable to work with fixed core-to-ring diameter ratio. Therefore, only a simulation-based approach (with the model pre-validated and calibrated in C1, C2 and C3) was deemed appropriate in this case to explore the effect of the increasing ring-to-core diameter and tandem laser spot configuration on material mixing.

Table 2. Process parameters used for the four selected laser beam shapes in Fig. 3.
Fig. 3. Normalized power density distribution for LBS#1, LBS#2, LBS#3 and LBS#4.

The power and speed of C1, C3, C4 and C5 were selected with an iterative process to ensure weld penetration depth, Dpen, ranging 400 – 500 µm. The choice of this penetration depth is based on the requirement that the temperature at the lower end of the steel sheet remains below 550 K. This precautionary measure aims to prevent any potential damage to the battery cell. Additionally, to minimise the effect of the weld depth on the metal mixing, a uniform depth of penetration was adopted across the different beam shapes for comparative analysis. Welding speeds were kept between 250 mm/s and 375 mm/s which is in line with the experimental work in (Perez Zapico et al., 2021). C2 is a variant of C1 and corresponds to a fully penetrated weld. Although fully penetrated welds must be avoided during LBW of battery terminals due to the risk of fire ignition, this work presents this variant for two reasons: first, to generate an additional weld configuration to validate the simulation; second, to discuss how the metal mixing behaves when transitioning from partial penetration to full penetration.

2.2. Model description

A multi-physics model was developed using the commercial CFD code FLOW-3D® (solver version: 12.0.2.01) and its module FLOW-3D® WELD (release: 7, update: 1). In order to develop a numerical model representing the essential physics during LBW of Cu-to-steel, the following assumptions were considered: (i) the liquid flow is considered Newtonian and incompressible; (ii) volumetric thermal expansion of the liquid metal due to temperature-dependent mass density is accounted; (iii) the air and vaporized metal are modelled as “void” type, with ambient temperature and pressure assigned to model the heat exchange with the metal as a natural convective flux (irradiance is neglected); (iv) the heat sinking effect of the clamping mask is neglected due to the clearance between the weld seam and the mask itself as already presented in (Chianese et al., 2022); (v) the effect of plasma plume on laser absorption is not directly modelled but is accounted in the calibration process as also proposed in previous studies by Lin et al. (2017) and Hao et al. (2021); furthermore, the laser absorption is assumed temperature dependent for Cu, constant for steel, and independent of the incidence angle. This assumption is in-line with the work presented by Huang et al. (2020), where they used the build-in ray-tracing function in FLOW-3D® WELD to predict the laser absorption in the keyhole.

2.2.1. Governing equations, boundary conditions and material properties

To reduce the computational cost of the simulations, the computational domain was divided in two zones (Fig. 4): (1) a process zone which was interested by phase change, and, (2) a thermal diffusion zone that models heat transmission in the sheets. A finer mesh size was used for cells in the process zone, and a mesh size 5 times greater than in the process zone was used for cells in the thermal diffusion zone.

Fig. 4. Top view (a) and side view (b) of a schematic representation of the computational domain and modelling approach with nested meshes (process zone and thermal diffusion zone).

Dimensions of the process zone are 2 mm × 0.8 mm× 0.775 mm. The length (2 mm) of the process zone was chosen to enable the simulation of approx. 1.8 mm weld length, which was experimentally evaluated to be sufficient for reaching the steady-state regime. The width (0.8 mm) of the process zone was selected to ensure that the molten pool was contained in it; the height of the computational domain was chosen equal to 0.8 mm so that, beside the stacked thickness of the processed sheets (0.6 mm), 0.2 mm of air (void type) are included in the computational domain. Extension of the thermal diffusion zone is calculated according to the Eq. (1), where k is the thermal conductivity, cp the specific heat at constant pressure, ρ the mass density, tend the simulation time, T the temperature, and Tamb= 20 °C the ambient temperature. The simulation time, tend, is function of the welding speed and the weld length (1.5 mm).

Four different values of the mesh size in the process zone were considered during sensitivity analysis, namely 40 µm, 20 µm, 15 µm, and 10 µm, that resulted in mesh independent solution for mesh size equal to or below 15 µm, which therefore is the selected size. This led to total number of cells approximatively equal to 528 thousand. The geometry of the thin sheets has been modelled in the computational domain, so that in-plane dimensions were parallel to X and Y axis, as shown in the top and side view in Fig. 4(a) and (b). Welding direction was parallel to X axis.
The following physics have been accounted to model the welding process: continuity, fluid flow via Navier-Stokes equations, energy conservation, evaporation, keyhole formation and evolution, solidification, species conservation and tracking, surface tension with Marangoni and Laplace forces and multiple reflections.
Phase change – Eq. (2) governs the evaporation phenomena which are modelled as mass transfer between the liquid phase and the void type and are proportional to the difference between the saturation pressure Psat and the partial pressure Pvap. In this equation, α is the accommodation coefficient, R is the gas constant, and T is the temperature. The saturation pressure is calculated as a function of the temperature according to the Clapeyron equation (Eq. (3)), in which the couple (Pv, Tv) represents a point on the saturation curve; γ, cv, and ΔHv are the specific heats ratio, the specific heat at constant volume, the latent heat of vaporization, respectively.

Recoil pressure – during laser welding process, intense localised heating of substrate material causes vaporization which results in recoil pressure. This pressure is proportional to the saturated vapor pressure. The relationship between the recoil pressure, Precoil, and the saturated vapor pressure, Psat, depends on the material properties and laser-to-material interaction. Eq. (4) is derived from Eq. (3) with the introduction of two coefficients, Ar and B, that will be calibrated using experimental data.

Tracking of the keyhole – surface of the keyhole is tracked by the volume of fluid (VOF) method (Daligault et al., 2022), which enables the calculation of the interface between the liquid metal and the void type, according to Eq. (5).

The interface between the cell is tracked using a scalar value f that indicates the fraction of fluid in it. A value of f=0 indicates that the cell has only void, conversely, f=1 corresponds to the case of a cell full of liquid, whereas the case of 0<f<1 indicates that the cell has both the liquid and the void type, and therefore the interface between the two falls in it. Similarly, metals involved in the welding process with fluid flow and mixing are tracked in each cell by means of a scalar value f2, which indicates the fraction of second material within the cells. Values of the generic material property ̅φ̅ in each cell is evaluated as weighted sum of the properties φ1 and φ2 of parent metals based on their mixing, as in Eq. (6).

Multiple reflections – Multiple reflections are implemented using a discrete grid cell system through the ray tracing technique. The laser beam is divided into a finite number of rays, which move in the laser beam irradiation direction. When the ray encounters the surface of the material, it is reflected according to vector Eq. (7), in which R→ is the direction of the reflected vector, I→ the direction of the incoming ray, and nˆ the normal direction of the material surface.

Laplace pressure and Marangoni effect – Recoil pressure contributes to the formation of the keyhole and mainly contributes to the velocity field in the fluid; however, surface tension-related phenomena such as Laplace pressure LP and the Marangoni force SM have great influence on the overall welding process. Laplace pressure and the Marangoni force are modelled according to (8), (9) which, σ is the surface tension, RI and RII are the principal curvature radii, and operator ∇t indicates the gradient along the tangent direction at the interface. Eq. (9) explicitly indicates the dependence of the Marangoni effect on the gradient of the surface tension, which in assumed temperature-dependent of the surface tension.

2.2.2. Boundary conditions and material properties

As shown in Fig. (4), the following boundary condition were assigned: wall in the X and Y direction (with constant ambient temperature); assigned pressure and temperature at the boundaries of the computational domain in the Z directions, with natural convective heat flux between the metallic sheets and the air. The heat source was directly imported from the power profiles defined in Fig. 3. Material properties were imported from the JMATPRO® material database. Fig. 5 shows the temperature-dependent plots.

Fig. 5. Temperature-dependent material properties defined in the model.

3. Results and discussion

3.1. Model validation

The model has been applied to simulate all the cases listed in Table 2. Model validation was conducted for the weld configurations C1, C2 and C3 by comparing the weld profile in cross sections and Fe concentration line profiles against the experimental results as shown in Fig. 6. Experimental and simulation results show that welding is done through keyhole mode. The generation of a keyhole is significantly influenced by recoil pressure. In the simulation, the recoil pressure is adjusted through the calibration of coefficients Ar and B, as indicated in Eq. 4. During the model calibration process, a value of Ar was determined to be 55,715 Pa, and the parameter B was set to 4, resulting in comparative results with those obtained in experiments. Five different mesh sizes were tested: 20 µm, 15 µm, 10 µm and 5 µm. The choice of the mesh size was driven by the need to have a minimum of 4 cells to discretise the smallest laser spot (i.e., LSB#1 has the smallest beam diameter of 90 µm among the tested beam shapes in Fig. 3). Mesh-independent solution was achieved with mesh size of 15 µm and this led to approximate a million cells in the whole computational domain.

Fig. 6. Comparison of the experimental and modelling results of the molten pool geometry and elemental maps for weld configurations C1 (a), C2 (b) and C3 (c).

The correlation was conducted looking at two cross-Section (10 mm 15 mm away from the weld start and end) – this was motivated by the need to take into account the experimental errors during the calibration and validation process.

Fig. 6 shows cross sections and elemental maps for experiments C1, C2, and C3, and corresponding simulations. Two representative cross-sections from the same weld seam are shown in each sub-figure to demonstrate the capability of the model to reproduce the geometric shape and the mixing phaenomena at different longitudinal positions along the weld seam. The fusion zones are marked in each cross section and show good correlation with predictions from simulations, as the cases with partial penetration are successfully predicted in for C1 and C3, along with full penetration in C2.

Elemental maps that were measured with EDS, and species concentration that were predicted with simulations, are reported for comparison to show capability of the model to reproduce the mixing mechanism. For each case, plots of the concentration of Fe along with line-scans are reported to quantitatively demonstrate the capability of the model to simulated diffusion of the molten metal from the bottom sheet to the upper one. They show that diffusion of Fe in Cu is well predicted in C1 and C3, as well as presence of Fe-rich clusters in the Cu near the interface between parent materials is reproduced in C2.

Good correlation between measurements and predictions of the weld geometry and metal mixing demonstrates capability of the model to simulate welding scenarios with different laser beam shapes, and weld penetration depth spanning from partial penetration to full penetration. This allows to confidently deploy the simulation model in conjunction with experiments to study the impact of laser beam shaping on metal mixing and molten pool dynamics.

3.2. Keyhole dynamics and impact on metal mixing

As keyhole instabilities have a significant impact on weld quality (Lu et al., 2015), this section highlights the impact of the laser beam shapes on the keyhole dynamics, which ultimately contributes to metal mixing. The discussion is presented by linking the laser power profile to the velocity field within the molten pool and ultimately to the metal mixing between the parent metals and the occurrence of collapse events of the keyhole.

Fig. 7 shows consecutive time frames in each weld configuration and reflects keyhole dynamic mechanisms. The keyhole’s shape and size vary, exhibiting irregularities, asymmetry and fluctuations. These shapes are directly correlated to the laser beam shape profile. The following observations are made:

  • Collapse events terminate in formation of pores and metal mixing. This is visible in the experimental results presented in Fig. 6(a) and (b), where relatively large pores are observed in the experimental cross-section. With a narrow beam profile (weld configuration C1, C2, C3 and C5) and high energy density, once fusion of the Cu does happen, a surplus of energy flows through the keyhole, increasing the temperature at the keyhole bottom. This generates a recoil pressure that pushes the fluid upwards. At the top surface and rear side of the keyhole, the opposing movements of the fluid, both clockwise and counter-clockwise, and driven by the Marangoni force, have an important consequence: they restrict the size of the molten pool. This restriction creates a high viscosity mushy layer that forms a barrier that limits the expansion of the molten pool. As result, closure or narrowing the top neck of the keyhole restricts the ejection of vapours out of keyhole which leads to increase in pressure within keyhole and creates a high-pressure lob. This ultimately results in pores formed to the toe of the keyhole as seen in Fig. 7(a) and (b). Although a collapse event is observed in C3 as shown Fig. 7(c), it does not necessarily create porosity in the solid front as sufficient room is available for gas vapours to escape from the bottom of the keyhole. The introduction of a pre-heat heating beam in weld configuration C5 does not produce any significant change to the keyhole dynamics as observed in Fig. 7(d). In partial penetration, narrow and deep keyhole is more unstable as slight fluctuations in fluid pressure, velocity and temperature on the rear wall of keyhole can create a collapse event. Additionally, the collapse of the keyhole in partial penetration creates a narrower fluid channel, resulting in localized increase of fluid velocity, which, in turn, affects metal mixing.
  • Weld configuration C4 leads to wider opening of the keyhole with greater stability as shown in Fig. 7(e). With the super-imposition of the core beam with the wider ring-shaped beam, the core beam penetrates the steel sheet, while the larger ring keeps the keyhole open at the Cu surface. This weld configuration drastically reduces the collapse events and the development of bubbles. It can be observed that the lower depth-to-width aspect ratio of the melt pool correlates to fewer number of collapse events.
  • Metal mixing is not only influenced by keyhole dynamics and collapse events, but there is an intricate interplay between keyhole geometry, fluid dynamics and buoyancy forces that are dependent upon density which varies with temperature in molten pool, and from top to bottom due to differences in density between Cu and steel. To test the influence of buoyancy forces, a simulation test was performed where the density of Cu and steel were artificially set to be equal. Fig. 8 shows the simulation results and confirm that buoyancy forces have an impact on the metal mixing especially at the interface between the two metals and in the Cu side of the weld. For example, the line-scan B-B in Fig. 8 shows an increase on average of the Fe vol% in the Cu side by 10%, when comparing results with same densities.
Fig. 8. Impact of buoyancy forces on the metal mixing for weld configuration C3. Sections taken at Y= 0.
Fig. 7. Consecutive time steps of the molten pool dynamics for configuration C1 (a), C2 (b), C3 (c) C5 (d) and C4 (e). The plot shows the fluid velocity (both direction and magnitude) visualized by black arrows. Cross sections taken at Y= 0.

The introduction of a ring beam (weld configuration C4 with LBS#3) in the laser welding process alters the shape of the keyhole compared to a single beam scenario (weld configuration C1 with LBS#1). In the single beam case, the keyhole walls develops predominantly in Z direction (schematically illustrated in Fig. 9(a)). The inclusion of a ring beam results in the critical change of the keyhole wall’s curvature, with a pronounced arc-like shape at the rear (Fig. 9(b)). The change of keyhole wall’s curvature plays a critical role and is explained by the complex equilibrium between the fluid pressure, the recoil pressure and the gravity load. A collapse event is associated with the non-equilibrium of the forces in the X direction. To explain this, it is first worth noting that with an idealised static molten pool (no fluid velocity) the fluid pressure would be higher at the bottom and would be governed by the hydrostatic law – with this, the pressure variation occurs linearly downwards and would be a function of the molten pool depth. Under this ideal condition, the keyhole would exhibit a stable equilibrium regime driven by the balanced effect of recoil pressure and fluid flow. With the actual molten pool, the equilibrium state is, however, perturbated by the non-linear variation of the fluid pressure due to the fast upwards motion generated by the recoil pressure itself. A near-equilibrium state is eventually achieved with the change of keyhole wall’s curvature with the resultant of the forces acting predominantly in the Z direction. The shallow angle of the keyhole wall observed at LBS#3 (θ3 < θ1) effectively decomposes the combined forces exerted by the fluid towards the Z direction, hence moving to the near-equilibrium state, with the fluid pushed downwards in Z rather than sidewise in X. It can be observed that the ring-to-core diameter and the ring-to-core power are essential to control the keyhole wall’s curvature and ultimately influence of the stability of the keyhole.

Fig. 9. Schematic representation of forces and pressures acting on the melt pool in case of welding with single laser beam (LBS#1) and ring-core configuration (LBS#3). Arrows represent forces/pressures, and the thickness is proportional of the intensity of the forces/pressures. Arrows are only shown to the rear-side of the keyhole since the physics involved there are more relevant for the dynamics of the keyhole.

3.3. Impact of beam shaping on metal mixing

Cu and steel are generally immiscible as studied by other researchers, such as Shi et al. (2013). This separation means the material solidifies as two separate phases from the liquid state. At this immiscible region a Cu-rich (α phase) and iron-rich (β phase) form FCC and BCC crystal structures, respectively. For the compositional data shown in Fig. 6, the highest amount of mixing for each of the three examples is 60%, 80% and 50% of Fe in the weld pool. When studying the Cu-Fe binary phase diagram, as performed by Chen et al. (2007), these compositions fall within the miscibility gap range. For which no IMCs are expected to form, but instead separate (α and β) phases. However, it is still clear that the formation of these separate phases still creates a mismatch in mechanical properties of the welded joint, both at the interface and enriched regions, which can lead to crack initiation, as reported by Rinne et al. (2020). For this reason, analysing the metal-mixing in dissimilar metals is an important step toward understanding and prevention of cracking mechanisms that can affect the performance of the weld.
Influence of the beam shapes on the metal mixing, can be investigated by analysing velocity fields and fluid flow which are predicted with the validated model. Fig. 10(a) and (b) show that in the weld configuration C1 and C2 (corresponding to LBS#1 – single beam with circular spot and gaussian distribution) the increase in laser power leads to more steel mixing with Cu due to greater recoil pressure and to a larger melt pool with more liquid metal involved. When comparing the parameters in Fig. 11, the increased melting of the bottom steel sheet leads to a greater region of keyhole necking with collapse; this can be due to the increased laser absorption, for which steel has a greater absorptivity than the more reflective Cu (Rinne et al., 2020). The lower density of steel creates an upward buoyancy force which allows the migration of more steel into the Cu-rich region. Fig. 11(c) and (d) show weld configurations C3 and C4 respectively, with combined secondary ring-shaped and primary laser beam (LBS#2 and LBS#3, respectively). They can be compared based on similar levels of weld penetration but different width at the interface between parent metals and at the top of the weld seam. Spread of the laser power over a wider surface due to the use of a ring results in a wider weld pool compared to simulations C1 and C2, which is consistent with results found by Jabar et al. (2023). However, one difference between these two cases is that, due to different power density distributions, to achieve adequate weld penetration depth, different laser power is provided leading to different thermal fields and time that the metal stays liquid. Line-scans of the temperature profiles in the melt pool can be observed in Fig. 12, with higher peak temperature in C4, compared to simulations C1 and C2, and C5; whereas a smaller secondary ring-shaped laser beam in simulation C3 results in intermediate behaviour.

Fig. 10. Plots of metal mixing in the longitudinal and a cross sections predicted with simulations C1 (a), C2 (b), C3 (c), C4 (d) and C5 (e).
Fig. 11. (a) Temperature, (b) velocity, (c) Fe concentration and (d) actual melt pool for all the tested weld configurations C1 to C5. Cross sections taken at Y= 0.
Fig. 12. Temperature profiles for weld configurations C1 (a), C2 (b), C3 (c), C4 (d) and C5 (e). Measurements were taken at X = 1.3 mm (just behind the keyhole wall) and Z = −300 µm (interface between Cu and steel).

The higher peak temperature in C4 eventually leads to a significant thermal gradient that promotes significant upward buoyancy forces and ultimately more migration of steel towards the Cu matrix. Similarity of simulation C5 with C1 can be explained considering that the secondary laser beam pre-heats the metal without widening the keyhole. Additionally, the higher peak temperature and larger size of the melt pool in C4 lead to longer time in which the steel stays in the liquid phase with more time available to migrate toward the Cu matrix due to recoil pressure and buoyancy forces and to diffuse. For these reasons, if use of larger spot helps with keyhole stabilisation, higher laser power required to establish sound connection enhances mixing between parent metal. Therefore, selection of custom ring-to-core diameter and ring-to-core power is a decision with a trade-off between the need of stabilising the keyhole dynamics and the need to reduce the mixing.
Velocity fields in Fig. 11 show also that the use of the ring-shaped secondary beam (C4), results in lower recoil pressure due to less localised laser power and vaporization. For this reason, the fluid flow and velocity of the liquid movements in considerably lower, as shown by contour plots, where regions of the molten pool in red are those in which the flow of the liquid metal is faster. The metal mixing in the molten pool of C3 weld is more homogeneous than in C1 and C2, due to the localised heat input of the ring laser beam. Rinne et al. (2020) found the addition of the ring laser produced a more homogeneous distribution of Cu and steel in the solidified structure. The lower density of the steel can also be used to explain the more even distribution of steel throughout the weld pool of C3. This is also confirmed by the EDS line-scans in Fig. 6(c) that show a significant drop of Fe into the Cu matrix compared to C1 (Fig. 6(a)).
The result of metal mixing has a significant effect on the crack formation in the weld pool and heat-affected zone (HAZ). Two main types of cracking are often referred to as “hot cracking” (Rinne et al., 2020) or “liquation cracking” (Li et al., 2019). During any fusion welding process of Cu to steel the miscibility gap can be identified in the binary phase diagram of Cu-Fe (Chen et al., 2013). When both Cu and steel are melted, there is separation of the liquids during cooling, once the mixture enters the miscibility gap seen on the phase diagram the primary separation of the α and β phases occurs. The secondary separation occurs in the miscibility gap because of a lack of diffusion and a supersaturation of the α and/or β phases. The solidified weld microstructure is found inhomogeneous, consisting of the α and β phases. The difference in the thermal expansion properties of both Cu and steel can create locations of stress concentrations where cracks are often initiated, ad observed by Chen et al. (2013) and Sadeghian and Iqbal (2022). Li et al. (2019) proposed a three-stage mechanism for the formation of liquation cracks in Cu to steel laser welds. The first stage was the penetration of Cu liquid into the grain boundaries of the steel, secondly, the Cu liquid surrounds the Cu phase creating a “film” of liquid in the grain boundary. This drastically reduces the cohesive forces between the grain boundaries due to the presence of the α phase. Cracking can then be initiated in a similar manner to that detailed earlier.

4. Conclusions

A combination of multi-physics CFD modelling results and experiments have been presented to study the impact of laser beam shaping on metal mixing and molten pool dynamics during LBW of Cu-to-steel for battery terminal-to-casing connections. The multi-physics model has been validated with ex-situ EDS element mapping and weld profile’s features. The model has provided useful insights about temperature and velocity fields, mixing mechanisms and dynamics of the keyhole, all of which are difficult to access via experiments due to technological difficulties. The major findings of the work are summarized below:

  • Metal mixing is largely influenced by the fluid dynamics via the Marangoni, buoyancy forces and recoil pressure. With a greater laser power, recoil pressure is increased, and this leads to more weld penetration and melting of steel. Additionally, spread of the laser power results in higher width of the fusion zone. Subsequently, the buoyance forces due to the different densities of steel and Cu contribute to the upward flow of steel towards Cu, and hence impact meaningfully to the mixing. This can be clearly observed in weld configurations C1 and C2.
  • Due to the collapse events of the keyhole wall, porosity formation was found in welds C1, C2 and C5. Furthermore, the collapse events create a narrow fluid channel, which results in localised surges in fluid velocity, therefore, promoting metal mixing. All in all, simulations revealed that increasing depth-to-width aspect ratio is correlated to higher frequency of collapse events in the keyhole. Therefore, stabilisation of the melt pool can be achieved with tailored laser beam shapes.
  • The study has pointed-out that the use of larger ring beam (configuration C4) helps with keyhole stabilisation, but at the same time leads to more laser power and higher temperature that contribute to the enhancement of mixing between parent metals. This poses a trade-off in the definition of a tailored ring-to-core diameter and the ring-to-core power. Analysis of the results showed that ring-to-core diameter (350–90 µm) and 30% of ring power (weld configuration C3) resulted in more stable dynamics of the keyhole, with significant reduction of collapse events, and ultimately controlled migration of steel towards Cu. Furthermore, compared to C4 (2500 W total power), the lower thermal gradient in C3 (1530 W total power) eventually leads to a reduction in the upward buoyancy forces.
  • The pre-heating approach with the tandem beam (C5) only led to local fusion of Cu and no significant improvement in keyhole stability was observed.
  • The combination of experiments and numerical modelling provides a powerful approach to understand complex fluid flow and metal mixing processes during laser keyhole welding. This helps to study mixing behaviour along with weld pool dynamics for selection of laser welding strategies with beam shaping in case of dissimilar material welding, especially in presence of miscibility gap at higher temperature as in case of Cu and steel.

References

F-BW

Determination of Formulae for the Hydrodynamic Performance of a Fixed Box-Type Free Surface Breakwater in the Intermediate Water

중간 수심에서 고정된 박스형 자유 수면 방파제의 유체역학적 성능 공식을 결정하기 위한 연구

Guoxu Niu, Yaoyong Chen, Jiao Lu, Jing Zhang, Ning Fan

Abstract

 two-dimensional viscous numerical wave tank coded mass source function in a computational fluid dynamics (CFD) software Flow-3D 11.2 is built and validated. The effect of the core influencing factors (draft, breakwater width, wave period, and wave height) on the hydrodynamic performance of a fixed box-type free surface breakwater (abbreviated to F-BW in the following texts) are highlighted in the intermediate waters. The results show that four influence factors, except wave period, impede wave transmission; the draft and breakwater width boost wave reflection, and the wave period and wave height are opposite; the draft impedes wave energy dissipation, and the wave height is opposite; the draft and wave height boost the horizontal extreme wave force; four influence factors, except the draft, boost the vertical extreme wave force. Finally, new formulas are provided to determine the transmission, reflection, and dissipation coefficients and extreme wave forces of the F-BW by applying multiple linear regression. The new formulas are verified by comparing with existing literature observation datasets. The results show that it is in good agreement with previous datasets.

1. Introduction

A breakwater dissipates wave energy and reflects waves from the open sea, representing a crucial protective structure for the exploitation and utilization of marine resources. It is also an essential auxiliary marine structure that improves offshore engineering construction conditions and shortens ship berthing times [1,2,3]. With the development and utilization of ocean space and resources, the demand for breakwaters has also varied. The construction of breakwaters has shifted from onshore to offshore. Because most wave energy is concentrated near the water surface, a fixed box-type free surface breakwater (F-BW, Figure 1) was created [4,5]. The F-BW is a type of reflective breakwater with simple structure and high efficiency, which reduces the transmitted wave height by reflecting the incident wave energy [6,7]. Compared with the traditional bottom-founded breakwater, F-BW does not influence water exchange inside and outside the breakwater while maintaining a high wave attenuation efficiency, and has a high application prospect.

Figure 1. Two-dimensional schematic sketch of the F-BW models.

The hydrodynamic performance of the breakwater is important for the research and development of the F-BW, which mainly comprises two aspects. One aspect is the wave attenuation performance, including wave transmission coefficient Ct, reflection coefficient Cr, and dissipation coefficient Cd (hereinafter referred to as RTD coefficients). The other is the wave force, which concerns the safety and stability of the breakwater, including the horizontal wave force and vertical wave force.
In terms of research on the RTD coefficients of an F-BW, some scholars have studied the influence of the breakwater width and draft on the reflection and transmission coefficients when energy dissipation was ignored. [8,9,10,11]. In order to provide some judgement for the needy practitioners, a closed-form formula has been created to predict the transmission coefficient in deep water [8,9,10]. A study by Kolahdoozan et al. [12] showed the poor prediction performance of the formula proposed by Macagno [8] for intermediate water. Therefore, it is necessary to explore a proposed formula for the transmission coefficient under intermediate-water conditions. Different from the analytical solution of potential flow theory, other scholars studied the influence of the draft, breakwater width, and wave height on the performance of wave reflection, transmission, and dissipation of the F-BW via experimental tests conducted in intermediate waters [13,14,15,16]. The computational fluid dynamics (CFD) technique provides us an alternative way to interpret the interaction between wave and F-BW. Koftis and Prinos [16] applied the two-dimensional unsteady Reynolds Averaged Navier–Stokes model to study the influence of the dimensionless draft on the transmission and reflection coefficients of an F-BW. Elsharnouby et al. [17] studied the influence of the draft on the wave transmission of the F-BW by using Flow-3D 11.2 software. Their results showed that the increasing draft impedes wave transmission.
Some researchers carried out earlier work on wave force of F-BW due to concerns regarding safety and stability of the F-BW. Guo et al. [11] confirmed that draft, breakwater width and wave period also influenced the horizontal and vertical wave forces by adopting mathematical analysis based on linear potential flow theory. Chen et al. [18] investigated the effects of wave height and wave period on the horizontal and vertical wave forces of F-BW through a series of experiments. The results showed that the horizontal and vertical wave forces increase with increasing wave height. Limited by the fact that the mathematical analysis tends to ignore flow viscosity [19,20,21] and the physical model test is complicated and costly, considerable effort has been devoted to studying the hydrodynamic performance of an F-BW through numerical simulation in recent years. Zheng et al. [22] and Ren et al. [23] used the smoothed particle hydrodynamics (SPH) method to numerically simulate the horizontal and vertical wave forces of F-BWs under regular waves. Unlike previous studies which overlooked the nonlinearity of wave forces, the positive and negative maximum wave force could be observed in the studies of Zheng et al. [22] and Ren et al. [23].
Human activities are less involved in deep water, and the cost-effectiveness of F-BW construction is poorer in deep water than intermediate water. Reflection coefficient Ct, and dissipation coefficient Cd are also an indispensable part of the wave attenuation performance of F-BW. The horizontal and vertical wave forces are related to the security of the F-BW. However, the prediction formulas based on tests or numerical simulations for horizontal and vertical wave forces of the F-BW in the above studies were rare. Therefore, an attempt is necessary to present a proposed formula for the prediction of RTD coefficients and wave forces, which will provide design judgments for the relevant practitioners in intermediate waters.
The objective of this paper is to provide the prediction formulas for RTD coefficients and wave forces in the intermediate waters under the condition that waves do not overtop the breakwater. With the rapid development of the CFD technique, Kurdistani et al. [24] proposed a formula for submerged homogeneous rubble mound breakwaters based on a large dataset from the CFD model, and the proposed formula was verified by using the literature observation datasets. Inspired by their research method, a numerical wave flume is built through a grid convergence test and validated with the existing experimental results. The prediction equations of RTD coefficients and wave forces are provided by applying multiple linear regression and verified by comparing with existing literature observation datasets. The major conclusions are finally summarized, and some prospects are proposed.

2. Theoretical Introduction

2.1. Governing Equations

Flow-3D 11.2 is widely used in coastal engineering as a powerful CFD software program [25]. The interaction of waves and breakwaters is simulated in a numerical wave tank by using Flow-3D 11.2 software in this paper. The numerical wave tank adopts an incompressible viscous fluid in the wave and F-BW interaction. The Reynolds averaged Navier–Stokes (RANS) equation was applied as the governing equation for turbulent flow. Assuming that the Cartesian coordinate system o-xyz originates from the still water surface, the continuity equation is shown in Equation (1), and the momentum equation is expressed in Equation (2).

where i,j = 1,2 for two-dimensional flows, xi represents the Cartesian coordinate, and ui is the fluid velocity along the x- and z-axes. Ax and Az are the area fractions open to flow in the x and z directions, respectively, ρ is the fluid density, p is the pressure, v is the dynamic viscosity, and g is the gravity force. The Reynolds stresses term, 𝜌𝑢𝑖′𝑢𝑗, is modeled by the renormalized-group (RNG) turbulence model.

2.2. RNG Turbulence Model

The interaction of waves and an F-BW induces turbulence. The RNG turbulence model is adopted to close the governing equations [26], and the discrete governing equations are solved by the finite difference method. The transport equations of turbulent kinetic energy kT and dissipation rate εT in this model are as follows:

The volume of fluid (VOF) method was developed to track the evolution of the free surface [27]. The governing equation is shown as follows:

where F represents the fractional volume of water fluid, F = 1 indicates that the numerical cell is full of water, and F = 0 corresponds to the cell fully occupied by air. Numerical cells with a value of 0 < F < 1 represent a water surface.

Furthermore, the generalized minimal residual (GMRES) method was used to solve the velocity-pressure term [28], and the first-order upwind scheme and Split Lagrangian method were used to solve the volume of fluid advection. The structure of the F-BW is directly imported into Flow-3D 11.2 by the software built-in drawing function. The appearance of an F-BW depicted by the mesh could be viewed with the fractional area volume obstacle representation (FAVOR) method. All numerical simulations were run in parallel using an Intel Core (TM) i5-4460 processor (3.20 GHz). Furthermore, to ensure the accuracy of the numerical solution, the maximum iteration time step was set to 0.001 s, and the results were output at 0.01-s intervals.

2.3. Principle of Mass Source Wavemaker

The present study emerged from the interest shown in the use of F-BW in a specific zone at an actual project in East China Sea. The detailed structural design dimensions of F-BW and wave characteristics are shown in Table 1. All the incident waves are considered to be regular waves. The regular waves used in the study contain a large range of wave periods and wave heights, which represent the majority of wave parameters in real-world problems, making this study of great practical importance. The interaction between the second-order Stokes wave and the current is not considered in the twelve major wave parameters, due to the differing time and spatial scales between the wave and the current [29]. The twelve waves in this research are all in the range of either linear or nonlinear second-order Stokes waves. Figure 2 shows the suitability range of different wave theories. According to Figure 2, the F-BW at this project is located in intermediate waters. Equation (5) presents the wave elevation equation η of the second-order Stokes wave and the wave elevation equation of the linear wave is the first term on the right side of this equation.

where Hi is the incident wave height, k is the wavenumber, σ is the wave frequency, and h is the still water depth.

Figure 2. Wave parameter conditions analyzed in this study and their relations in the Le Méhauté diagram.
Table 1. Summary of the simulated scenarios.

The boundary wavemaker method produces re-reflection waves. Lin and Liu [30] proposed a popular mass source wave generation method [31,32,33,34,35,36]. In the present method, numerical wave generation is achieved by importing a given volume flow rate Vfr into the mass source model. The expression of the volume flow rate Vfr is as follows:

where C is the phase velocity, W is the tank width, η(t) is the wave surface elevation by solving Equation (5).

To effectively reduce the calculation divergence caused by excessive waves in the NWT at the initial stage, the volume flow rate Vfr is multiplied by an increasing envelope function to make the wave increase gradually in the first three wave periods. The equation of the increasing function is as follows:

where t is time and T is the wave period.

2.4. Principle of Numerical Solution

In this paper, the time series of wave elevations were recorded at five different locations (i.e., WG1–WG5) on the onshore and offshore sides of the F-BW (Figure 3a). Furthermore, the current WG spacings are selected according to the water depth and wave period. The distances between the wave source and WG1, WG1 and WG2, WG2 and F-BW, and F-BW and WG5 are set at 1.5 m, 0.2 m, 1.8 m, and 1.435 m, respectively. Note that the distance between wave gauges WG1 and WG2 is more than 0.05 L and less than 0.45 L, and the distances between wave gauges WG2 and F-BW and between WG5 and F-BW are less than 0.25 L and more than 0.2 L (wavelength), as recommended by the two-point method [37]. Two wave gauges (WG1 and WG2) are mounted in a line on the offshore side of the F-BW to separate the incident wave heights Hi and the reflected wave heights Hr by using this method. To prove that the horizontal wave force of the F-BW is related to the free surface onshore and offshore of the breakwater, probe WG3 is placed 0.02 m in front of the F-BW, while probe WG4 is placed 0.02 m behind the F-BW to measure the wave profile at the front (η3) and back (η4) of the F-BW. The wave gauge (WG5) is mounted on the onshore side of the F-BW to obtain the surface elevation of the transmitted wave heights Ht. The wave transmission, reflection, and wave energy dissipation coefficients are defined by solving Equation (8a)–(8c).

where Ct is the transmission coefficient; Cr is the reflection coefficient; and Cd is the wave energy dissipation coefficient.

Figure 3. Schematic layout and mesh sketch of the numerical wave tank for the F-BW.

Furthermore, the horizontal and vertical wave forces are simulated by the integration of the water pressure p at the wet surface of the F-BW. The two kinds of wave forces include the hydrostatic force and hydrodynamic force according to the FLOW-3D theory manual [25]. Because the F-BW is always fixed at the free surface, the vertical wave force needs to remove part of the hydrostatic force (the value up to ρVg, where ρ is the density of water and V is the volume of the F-BW). The shear stress is small enough to be ignored in this paper relative to the wave force. The horizontal wave force and the vertical wave force are denoted by Fx and Fz, respectively. The horizontal wave force is consistent with the direction of wave propagation, and the vertical wave force is vertically upward. To facilitate the research, obtaining the extreme value of the steady part of the wave force time series, we define the average value of the horizontal wave force positive and negative peak as the horizontal positive maximum wave force Fx+max and horizontal negative maximum wave force Fx−max, the vertical wave force positive and negative peak as the vertical positive maximum wave force Fz+max and vertical negative maximum wave force Fz−max. The representative time series of the dimensionless wave elevation, horizontal, and vertical wave forces are shown in Figure 4. The numerical results of Hi, Hr, Ht, Fx±max, Fz±max were acquired based on the stable elevations in this figure. To facilitate discussion, we define Fx±max/0.005 ρgh2 and Fz±max/0.005 ρgh2 as the dimensionless horizontal and vertical maximum wave forces on the F-BW, respectively. The crest and trough values of the time series of the wave forces are studied because the extreme values of the horizontal and vertical wave forces on the F-BW under the Stokes second-order wave have a slightly sharper crest and flatter trough.

Figure 4. Time histories of wave elevation η measured by WG1, WG2, and WG5 and horizontal and vertical wave forces of F-BW at Hi = 0.07 m, T = 1.4 s, B = 0.5 m, dr = 0.14 m, and h = 0.75 m.

The integral formula of the horizontal and vertical wave force is shown in Equation (9).

where 𝑛⃗  is the unit normal vector of the object surface s and the water pressure p is determined by the Bernoulli equation.

3. Model Setup and Validation

3.1. Numerical Wave Tank Setup

The detailed numerical wave tank (NWT) setup is shown in Figure 3b,c. The total length of the NWT was twenty-four wavelengths L long in the x-axis direction, 0.1 m wide in the y-axis direction, and 1 m deep in the z-axis direction. A scale ratio of 1:40 and a constant water depth h of 0.75 m are adopted based on the Froude similarity law. The mesh consisted of two distinct regions. The first region was the computation domain, four wavelengths length, with a width of 0.1 m and a depth of 1 m. The unit grid size of the total NWT was L/100~L/200 in the x and z directions, and ten grids were partitioned in the y directions in this domain. The second region was two identical damping domains with ten wavelength lengths. The Sommerfeld radiation method was employed to bate the secondary reflection of waves at both ends of the NWT. The grid size along the x-axis direction was gradually extended with an identical ratio of 1.01, and one grid was set for the lateral width of the NWT [38].

To describe the F-BW more accurately, nested grids were applied in the domain around the F-BW. The uniform nested grid was equal to half of the compute domain grid in the x, y and z-axis directions. Furthermore, the finer mesh resolution of 0.0035 cm in z direction was nested near the still water level (SWL), The region extends ±0.07 m from the SWL to ensure that the expected wave heights (0.03 m, 0.05 m, 0.07 m, 0.09 m) are encompassed within the region.

The boundary conditions of this NWT were set as follows: both ends of the NWT were defined as outflow boundaries, two sides of the domain were defined as symmetry boundaries, the atmospheric pressure was utilized at the upper boundary, and the lower surface of the computational domain was a no-slip wall boundary without surface roughness.

A mass source model with wide WS and high HS was added to the numerical flume. The symmetry boundaries were used overspreading with the mass source form, and the y-direction width of the mass source block was consistent with the width of the NWT. Pledging each edge of the mass block to coincide with the grid line of the NWT is shown in Figure 3b,c.

3.2. Numerical Model Validation

The present research is mainly implemented under the framework of CFD technology. To demonstrate the accuracy of the simulation results, it is essential to compare them with the extant results. The model is verified by the following three aspects in this section.

3.2.1. Grid Independent Verification

The mesh partition is a crucial procedure in CFD numerical simulation and needs much attention. The number and size of grids are essential criteria for evaluating the convergence of numerical results. Poor grid quality will directly affect the accuracy of numerical results and computation time. Consider that the proposed calculation cases Hi = 0.06 m, T = 1.2 s, and h = 1.2 m by Ren et al. are close to the target cases in this paper [23]. This wave condition is applied to complete the grid independence verification. Different grid arrangements can be seen in Table 2, and the time series of the wave profiles under the three grid sizes are compared with the theoretical results by solving Equation (5), as shown in Figure 5. The error of the numerical simulation results was calculated according to Equation (10). The wave profile deviations among the coarse mesh, medium mesh, and fine mesh are compared. The wave profiles under the medium mesh and the fine mesh are closer, and the deviation from the theoretical value is less than 5%, which meets the requirements of Det Norske Veritas (DNV) [39]. It can be judged that only medium meshes and refined meshes meet the requirements of numerical simulation. Considering the balance between calculation accuracy and calculation efficiency, the following numerical simulations always chose a medium mesh.

where Htheoretical is the wave height of the theoretical result and Hnumerical is the wave height of the numerical result.

Figure 5. Grid independent verification: influence of mesh size on wave profile.
Mesh TypeComputation Domain Grid Size (cm)Nested Domain Grid Size (cm)Cell NumberElapsed Time (×104 s)Wave Height (cm)Error %
Coarse217014600.64965.6425.96
Middle10.534111807.68325.7683.87
Fine0.50.251335096048.14375.7693.85
Theoretical––––6.000–
Table 2. Mesh independence check results.

3.2.2. Validation of Wave Forces

In this section, to further inspect the accuracy of the numerical results of wave forces in this paper, according to the wave conditions of Hi = 0.06 m, T = 1.2 s, h = 1.2 m, and draft dr = 0.2 m, a rectangular box of width B = 0.8 m and wave height Hi = 0.4 m is fixed and semi-immersed, as proposed by Ren et al. [23]. The horizontal and vertical wave forces of the F-BW were verified by comparison with the theoretical results of Mei and Black [40] and the numerical simulation results of Ren et al. [23]. The time series of the wave forces are compared in Figure 6. The total simulation time of this case is 16 wave cycles. Since it takes some time for the progressive wave to arrive at the F-BW from the source, the horizontal and vertical wave forces begin to reach the stable state at t = 7 T seconds in Figure 6. By comparison, the simulated time series of horizontal and vertical wave forces are almost consistent with those presented by Ren et al. [23] and Mei and Black [40]. This result indicated that the present NWT could meet the calculation accuracy.

Figure 6. Comparison of the normalized wave force on an F-BW with previous studies (Mei and Black [40]; Ren et al. [23]). (a) Normalized horizontal wave force; (b) Normalized vertical wave force.

4. Results and Discussion

4.1. Influence Analysis of Four Factors on the Hydrodynamic Performance of F-BW

Among all the influencing factors (refer to Appendix A), the hydrodynamic performance of the F-BW is significantly affected by the following four factors: draft (dr/h), breakwater width (B/h), wave period (T*sqrt(g/h)), and wave height (Hi/h). For the mechanism analysis of the interaction between waves and breakwater, the mechanism study of the horizontal wave force is rather complicated. Since the breakwater is in a semisubmerged state, the Morison formula is no longer applicable to the guidance of the calculation of the horizontal wave force. The horizontal wave force is studied separately from the water particle velocity; see the free surface difference (η3–η4) in the front and back sides of the F-BW and the water particle streamline in Figure 7 and Figure 8 for details. Among them, five representative cases are selected from all cases in this article for comparative analysis corresponding to Figure 7a–e. Note that case (a) T1.2dr0.14B0.5Hi0.07 represents a wave period of 1.2 s, draft of 0.14 m, breakwater width of 0.5 m and incident wave height of 0.07 m. Due to the effect of water blockage, flow separation is generated at the bottom corner of the offshore side of the breakwater, and the generated clockwise vortex destroys the original motion path of the wave water particles without structure in Figure 8a and allows the free surface difference in the front and back of the F-BW to gradually reach a maximum. At time instant t0 in Figure 7, the horizontal wave force also reaches a maximum. It can be seen in Figure 8b that the vertical wave force is easier to analyze. When the vertical wave force is at its maximum, the streamline realizes complete diffraction, and no vortex is generated. Furthermore, to understand the mechanism and contribution of each influencing factor on the hydrodynamic performance of the F-BW in detail, the statistical results are shown in Figure 9, Figure 10, Figure 11 and Figure 12.

Figure 7. Comparative analysis of five different cases under the interaction between waves and breakwater: First column: numerically obtained snapshots of free surface profile and velocity field; Second column: time history of free surface and horizontal wave force.
Figure 8. Snapshots of the velocity streamline field: (a) Time instant of the horizontal positive maximum wave force; (b) Time instant of the vertical positive maximum wave force.
Figure 9. Effect of the draft dr on the hydrodynamic performance of the F-BW at wave heights Hi = 0.05 m and Hi = 0.07 m. (a) Horizontal positive and negative maximum wave forces Fx+max and Fx−max; (b) Vertical positive and negative maximum wave forces Fz+max and Fz−max; (c) Transmission coefficient Ct, reflection coefficient Cr, and dissipation coefficient Cd.
Figure 10. Influence of the breakwater width B on the hydrodynamic performance of the F-BW at wave heights Hi = 0.05 m and Hi = 0.07 m. (a) Horizontal positive and negative maximum wave forces Fx+max and Fx−max; (b) Vertical positive and negative maximum wave forces Fz+max and Fz−max; (c) Transmission coefficient Ct, reflection coefficient Cr, and dissipation coefficient Cd.
Figure 11. Influence of the wave period T on the hydrodynamic performance of the F-BW at wave heights Hi = 0.05 m and Hi = 0.07 m. (a) Horizontal positive and negative maximum wave forces Fx+max and Fx−max; (b) Vertical positive and negative maximum wave forces Fz+max and Fz−max; (c) Transmission coefficient Ct, reflection coefficient Cr, and dissipation coefficient Cd.
Figure 12. Influence of the wave height Hi on the hydrodynamic performance of the F-BW at draft dr = 0.14 m and dr = 0.28 m. (a) Horizontal positive and negative maximum wave forces Fx+max and Fx−max; (b) Vertical positive and negative maximum wave forces Fz+max and Fz−max; (c) Transmission coefficient Ct, reflection coefficient Cr, and dissipation coefficient Cd.

4.1.1. Effect of Draft

Figure 7 lists the distribution diagram of the free surface difference and water particle velocity under cases (a) and (b) at the time instant of the horizontal wave force maximum. Except for the draft being different, the two cases are consistent. Among them, case (a) has a wave period of 1.2 s, draft of 0.14 m, wave height of 0.07 m and breakwater width of 0.5 m. Case (b) has a period of 1.2 s, draft of 0.35 m, wave height of 0.07 m and breakwater width of 0.5 m.

In the second column of Figure 7a, when time t0 = 11.48 s, the maximum free surface difference is 0.068 m, and the maximum horizontal wave force is 7.98 N. In the second column of Figure 7b, when time t0 = 11.52 s, the maximum free surface difference is 0.083 m, and the maximum horizontal wave force is 15.91 N. Obviously, the increase in the draft enhances the water blockage action in front of the F-BW, weakens the diffraction effect of the wave, and delays the time for the horizontal wave force to reach its maximum. Figure 9a shows that Fx+max increases with increasing draft under wave heights of Hi = 0.05 m and Hi = 0.07 m. Similarly, the absolute values of Fx−max exhibit a similar law. The absolute values of Fz−max and Fz+max decrease with increasing draft under wave heights of Hi = 0.05 m and Hi = 0.07 m in Figure 9b, which is related to the exponential decay of the wave kinetic energy along the water depth. It is not difficult to see in Figure 7a,b that the wave hydrodynamic pressure on the lower surface of the F-BW decreases with decreasing wave kinetic energy as the water depth increases. The effective action area increases as the draft reduces the penetration of waves. Figure 9c shows that the transmission coefficient decreases with increasing draft under wave heights of Hi = 0.05 m and Hi = 0.07 m. Due to the increase in the interaction area between waves and F-BW, the reflected wave energy increases in Figure 7, and Figure 7b is more obvious than Figure 7a. The wave energy dissipation coefficient increases with decreasing draft in Figure 9c. Since the wave energy is mainly concentrated on the still water level, the fluid particle velocity maximum at the lower corner of F-BW is 0.30 m/s in Figure 7a is more than the 0.17 m/s in Figure 7b, more wave energy is dissipated when the fluid particle with higher velocity collides with F-BW due to decreasing draft.

Overall, the increasing draft impedes incident waves cross F-BW and promotes the increase in horizontal wave force and wave reflection, which threatens the stability of the structure.

4.1.2. Effect of Breakwater Width

To clarify the mechanism of the breakwater width effect on the hydrodynamic performance of the F-BW, except that the breakwater width is different, cases (a) and (c) in Figure 7 are consistent. In case (c), the period is 1.2 s, the draft is 014 m, the wave height is 0.07 m, and the breakwater width is 0.2 m.

The free surface difference and vortex in Figure 7a,c are similar. Figure 10a shows that the breakwater width effect on Fx−max and Fx+max is not obvious. When the vertical wave force is at its maximum, the streamline realizes complete diffraction, and no vortex is generated in Figure 8b. Therefore, the vertical wave force is related to the acting area of the F-BW lower surface. Figure 10b shows that the absolute values of Fz−max and Fz+max increase with increasing breakwater width. In the second column of Figure 7c, when time t0 = 11.42 s, the free surface difference and the horizontal wave force reach a maximum faster than in case (a). Obviously, the increase in the breakwater width increases the wave diffraction difficulty. Figure 10c shows that the transmission coefficient decreases with increasing breakwater width, and the reflection coefficient increases with increasing breakwater width. Due to fluid particle velocity maximum is similar between Figure 7a,c. The increase in breakwater width has little influence on wave energy dissipation.

In short, the increasing breakwater width is not conducive to incident wave cross F-BW, and promotes the increase of wave reflection and vertical wave force. Obviously, more weights need to be added to ensure the safety of the breakwater when breakwater width increases.

4.1.3. Effect of Wave Period

To clarify the mechanism of the wave period effects on the hydrodynamic performance of the breakwater, except that the wave period is different, cases (a) and (d) are consistent. Figure 7d shows that the wave period is 1.8 s, the draft is 0.14 m, the wave height is 0.07 m and the breakwater width is 0.5 m.

In the second column of Figure 7d, when time t0 = 11.13 s, the maximum free surface difference is 0.051 m, and the maximum horizontal wave force is 6.90 N. According to Equation (9), because the wave energy is more abundant on the two sides of the breakwater in case (4), the horizontal wave force is comparable even if the free surface difference is smaller than that in case (1). Figure 11a shows that Fx−max and Fx+max are weakly related to the wave period under wave heights of Hi = 0.05 m and Hi = 0.07 m. Because the long-period waves possess a large wave energy in Figure 7d, they increase the wave pressure on the lower surface of the F-BW. Therefore, the absolute values of Fz−max and Fz+max increase linearly with the wave period in Figure 11b. Figure 11c shows that the transmission coefficient increases with increasing wave period under wave heights of Hi = 0.05 m and Hi = 0.07 m. Long-period waves have a better diffraction ability at the same depth, and more wave energy passes through the F-BW. The decreasing ratio of the breakwater width to wavelength weakens the ability to block progressive waves, and the reflection coefficient decreases accordingly. The wave energy dissipation coefficient shows an alphabetic symbol “M” distribution with the wave period. This indicates that the wave energy dissipation is more complex and requires further study. When the dimensionless wave period is 5.06, both the transmission and reflection coefficients are close to 0.71, the dissipation coefficient is at the minimum by applying Equation (8c).

In brief, the increasing wave period plays a significant role in increasing the wave transmission and the reducing wave reflection. Although it has little effect on the horizontal wave force, it promotes an increase in the vertical wave force, which is unfavorable to the security of the breakwater.

4.1.4. Effect of Wave Height

To clarify the mechanism of the wave height effects on the hydrodynamic performance of the breakwater, except that the wave height is different, cases (a) and (e) are consistent. Figure 7e shows that the wave period is 1.2 s, the draft is 014 m, the wave height is 0.03 m and the breakwater width is 0.5 m.

In the second column of Figure 7e, when time t0 = 11.44 s, the maximum free surface difference is 0.031 m, and the maximum horizontal wave force is 3.43 N. Obviously, the increase in wave height increases the diffraction difficulty of the wave and delays the time when the horizontal wave force reaches its maximum. The higher the wave height, the more abundant the wave energy in Figure 7a,e. The water particle velocity maximum is 0.11 m/s in Figure 7e, which is much less than the water particle velocity maximum in Figure 7a. The larger wave height causes a larger wave elevation difference, and the larger horizontal wave force under other variable conditions is consistent by comparing Figure 7a,e. Therefore, Fx−max and Fx+max increase linearly with increasing wave height under drafts dr = 0.14 m and dr = 0.28 m in Figure 12a. The increase in wave height leads to increasing dynamic wave pressure, which in turn leads to increasing wave pressure on the F-BW lower surface and an increase in vertical wave force. Therefore, Fz−max and Fz+max increase linearly with increasing wave height under drafts dr = 0.14 m and dr = 0.28 m in Figure 12b. Figure 12c shows that the increasing wave height results in more wave reflection and less transmission due to the increasing blockage effect. The reflection ability weakens with decreasing interaction area (the ratio of the wetted surface height of the front wall of the F-BW to the wave height). The water particle velocity maximum of 0.11 m/s in Figure 7e is less than the water particle velocity maximum of 0.3 m/s in Figure 7a. The increasing water particle velocity with increasing wave height results in better vortex dissipation near the F-BW. Hence, the wave energy dissipation coefficient increases.

In conclusion, the increasing wave height reduces the wave reflection but increases horizontal and vertical wave forces, which is disadvantageous to the security of the breakwater.

4.2. Prediction Equations of F-BW Hydrodynamic Performance Parameters

To understand the contribution of each influencing factor to the hydrodynamic performance of the F-BW in detail, the factors affecting the RTD coefficients and wave force mainly include the wave period T, wave height Hi, draft dr, breakwater width B, and still water depth h. In Equation (11), the RTD coefficients Ct,r,d and wave force extremum Fx,z±max are expressed as follows:

Using the dimensionless analysis method and the numerical simulation results of 30 groups of simulated conditions in Table 1 based on the Origin 2019b software platform, multiple linear regression was performed by the least squares method, and the prediction equations of the RTD coefficients and wave force are given in Equation (12a–g). The detailed formulas are shown in Table 3.

Table 3. Statistics of prediction equation.
Note that 0.0933 ≤ dr/h ≤ 0.4667, 0.26667 ≤ B/h ≤ 0.8, 3.6166 ≤ T*sqrt(g/h) ≤ 6.5099, and 0.04 ≤ Hi/h ≤ 0.12.

4.3. Deviation Analysis of the Prediction Equations

Inspired by Kurdistani et al.’s [24] research method, the current study uses their method to assess the reliability of each predictive formula. The literature observation datasets include the measured RTD coefficients from Koutandos [13] (three cases (R1, R2 and R3) in Figure 16 of his literature) and Liang et al. [14] (six cases in Figures 14a, 19a and 22a of their literature), the wave forces from Mei and Black [40] and Ren et al. [23] (a case in Figure 10 of their literature). The numerical results obtained by Flow-3D are plotted on the x-axis in Figure 13, and predicted values of the predictive equations are plotted on the y-axis in Figure 13. Figure 13a shows a 20% error for the application of Liang et al. [14] transmission coefficient datasets that are mostly lower-estimated values of transmission coefficient with respect to Equation (12a), an almost 10% error for the application of Liang et al.’s [14] reflection coefficient and dissipation coefficient datasets, and Koutandos’s [13] RTD coefficients datasets. Figure 13b shows an almost 10% error for the application of Mei and Black [40] and Ren et al. [23] maximum wave force, which indicates that the present prediction equations are valid.

Figure 13. Comparison of the results between previous studies and the numerical results of this study. (a) Transmission coefficient Ct, reflection coefficient Cr, and dissipation coefficient Cd (Koutandos [13], Liang et al. [14]) and (b) Maximum wave force (Mei and Black [40]; Ren et al. [23]).

It is clearly found that the distribution points of the reflection coefficient and wave energy dissipation coefficient of the F-BW are relatively concentrated in a particular region in Figure 13a, indicating that the F-BW is dominant in reflecting waves and has stable wave dissipation ability. In addition, the horizontal negative maximum wave force of the F-BW is similar to the vertical negative maximum wave force, and the horizontal positive maximum wave force of the F-BW is slightly larger than the vertical positive maximum wave force in Figure 13b.

5. Conclusions

The present study investigated a high-accuracy numerical wave tank (NWT) based on the Flow-3D platform. A series of numerical simulations in the intermediate waters were carried out at a constant water depth (h) of 0.75 m under regular wave conditions, with a wave height range between 0.03–0.09 m, a wave period range between 1–1.8 s, and a breakwater width range between 0.2–0.6 m. The effects of four influencing factors (dr, B, T, Hi) on the hydrodynamic performance (RTD coefficients and wave forces) are highlighted. The vital conclusions are as follows:

  1. The performance of two-dimensional viscous numerical wave tanks (NWTs) with a mass source wave maker and small length scale (1:40) are analyzed. By comparison, the wave model employed in this paper is competent for the numerical simulation of the F-BW.
  2. The results show that the increase in the four influence factors, except the wave period, benefits the decrease in the wave transmission. The increase in draft and breakwater width is beneficial to the increase in the wave reflection, and the wave period and wave height are opposite. The increase in draft benefits the decrease in wave energy dissipation, and the wave height is opposite.
  3. The increase in the draft and wave height benefits the increase in the horizontal positive and negative maximum wave forces. In addition to the draft, the increase in the other three influence factors benefits the increase in the vertical positive and negative maximum wave forces.
  4. Applying multiple linear regression presents the prediction equations of RTD coefficients and the extreme wave force. The prediction equations are verified by comparing them with literature observation datasets.

This study provides insight into the relation of RTD coefficients and wave forces with parameters such as draft, breakwater width, wave period and wave height. The simulated results of the given predicted equations can be generalized to the prototype scale by using Froude’s scaling law and can be used to guide the design of F-BWs in intermediate waters.

Appendix A

The wave period T, wave height Hi, draft dr, breakwater width B, and water depth h are the main factors that affect the wave dissipation performance and wave force of an F-BW in the intermediate waters. Therefore, the wave force of an F-BW can be expressed as a function of the above factors as follows:

Taking water depth h, gravity acceleration g, and water density ρ as the repetitive parameters, the three dimensionless parameters are expressed as follows:

[h] = [M0L1T0], [g] = [M0L1T−2], [ρ] = [M1L−3T0], where wave force per breakwater length in the vertical wave direction 𝐹F, expressed as [F = ρgh2], Equation (A1) can be written as follows:

According to wave theory, there is a nonlinear relationship between the wave force and the four dimensionless parameters in Equation (A2). The relationship between the dependent variable and independent variable in nature is exponential. It can be expressed as follows:

where α, x1, x2, x3, and x4 are the unknown coefficients.

Taking the natural logarithm of both sides of Equation (A3) to obtain the double logarithm function model, the equation can be written in linear form as follows:

Using multiple function linear regression analysis, each unknown coefficient in the equations can be obtained and then substituted into Equation (A3) to obtain the wave force equations. Similarly,

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Wave

Three-Dimensional Simulations of Subaerial Landslide-Generated Waves: Comparing OpenFOAM and FLOW-3D HYDRO Models

지표 산사태로 발생한 파랑의 3차원 시뮬레이션: OpenFOAM과 FLOW-3D HYDRO 모델 비교

Ramtin Sabeti, Mohammad Heidarzadeh, Alessandro Romano, Gabriel Barajas Ojeda & Javier L. Lara

Abstract

The recent destructive landslide tsunamis, such as the 2018 Anak Krakatau event, were fresh reminders for developing validated three-dimensional numerical tools to accurately model landslide tsunamis and to predict their hazards. In this study, we perform Three-dimensional physical modelling of waves generated by subaerial solid-block landslides, and use the data to validate two numerical models: the commercial software FLOW-3D HYDRO and the open-source OpenFOAM package. These models are key representatives of the primary types of modelling tools—commercial and open-source—utilized by scientists and engineers in the field. This research is among a few studies on 3D physical and numerical models for landslide-generated waves, and it is the first time that the aforementioned two models are systematically compared. We show that the two models accurately reproduce the physical experiments and give similar performances in modelling landslide-generated waves. However, they apply different approaches, mechanisms and calibrations to deliver the tasks. It is found that the results of the two models are deviated by approximately 10% from one another. This guide helps engineers and scientists implement, calibrate, and validate these models for landslide-generated waves. The validity of this research is confined to solid-block subaerial landslides and their impact in the near-field zone.

1 Introduction and Literature Review

Subaerial landslide-generated waves represent major threats to coastal areas and have resulted in destruction and casualties in several locations worldwide (Heller et al., 2016; Paris et al., 2021). Interest in landslide-generated tsunamis has risen in the last decade due to a number of devastating events, especially after the December 2018 Anak Krakatau tsunami which left a death toll of more than 450 people (Grilli et al., 2021; Heidarzadeh et al., 2020a). Another significant subaerial landslide tsunami occurred on 16 October 1963 in Vajont dam reservoir (Northern Italy), when an impulsive landslide-generated wave overtopped the dam, killing more than 2000 people (Heller & Spinneken, 2013; Panizzo et al., 2005). The largest tsunami run-up (524 m) was recorded in Lituya Bay landslide tsunami event in 1958 where it killed five people (Fritz et al., 2009).

To achieve a better understanding of subaerial landslide tsunamis, laboratory experiments have been performed using two- and three-dimensional (2D, 3D) set-ups (Bellotti & Romano, 2017; Di Risio et al., 2009; Fritz et al., 2004; Romano et al., 2013; Sabeti & Heidarzadeh, 2022a). Results of physical models are essential to shed light on the nonlinear physical phenomena involved. Furthermore, they can be used to validate numerical models (Fritz et al., 2009; Grilli & Watts, 2005; Liu et al., 2005; Takabatake et al., 2022). However, the complementary development of numerical tools for modelling of landslide-generated waves is inevitable, as these models could be employed to accelerate understanding the nature of the processes involved and predict the detailed outcomes in specific areas (Cremonesi et al. 2011). Due to the high flexibility of numerical models and their low costs in comparison to physical models, validated numerical models can be used to replicate actual events at a fair cost and time (e.g., Cecioni et al., 2011; Grilli et al., 2017; Heidarzadeh et al., 2020b, 2022; Horrillo et al., 2013; Liu et al., 2005; Løvholt et al., 2005; Lynett & Liu, 2005).

Table 1 lists some of the existing numerical models for landslide tsunamis although the list is not exhaustive. Traditionally, Boussinesq-type models, and Shallow water equations have been used to simulate landslide tsunamis, among which are TWO-LAYER (Imamura and Imteaz,1995), LS3D (Ataie-Ashtiani & Najafi Jilani, 2007), GLOBOUSS (Løvholt et al., 2017), and BOUSSCLAW (Kim et al., 2017). Numerical models that solve Navier–Stokes equations showed good capability and reliability to simulate subaerial landslide-generated waves (Biscarini, 2010). Considering the high computational cost of solving the full version of Navier–Stokes equations, a set of methods such as RANS (Reynolds-averaged Navier–Stokes equations) are employed by some existing numerical models (Table 1), which provide an approximate averaged solution to the Navier–Stokes equations in combination with turbulent models (e.g., k–ε, k–ω). Multiphase flow models were used to simulate the complex dynamics of landslide-generated waves, including scenarios where the landslide mass is treated as granular material, as in the work by Lee and Huang (2021), or as a solid block (Abadie et al., 2010). Among the models listed in Table 1, FLOW-3D HYDRO and OpenFOAM solve Navier–Stokes equations with different approaches (e.g., solving the RANS by IHFOAM) (Paris et al., 2021; Rauter et al., 2022). They both offer a wide range of turbulent models (e.g., Large Eddy Simulation—LES, k–ε, k–ω model with Renormalization Group—RNG), and they both use the VOF (Volume of Fluid) method to track the water surface elevation. These similarities are one of the motivations of this study to compare the performance of these two models. Details of governing equations and numerical schemes are discussed in the following.

Numerical modelsApproachDeveloper
FLOW-3D HYDROThis CFD package solves Navier–Stokes equations using finite-difference and finite volume approximations, along with Volume of Fluid (VOF) method for tracking the free surfaceFlow Science, Inc. (https://www.flow3d.com/)
MIKE 21This model is based on the numerical solution of 2D and 3D incompressible RANS equations subject to the assumptions of Boussinesq and hydrostatic pressureDanish Hydraulic Institute (DHI) (https://www.mikepoweredbydhi.com/products/mike-21-3)
OpenFOAM (IHFOAM solver)IHFOAM is a newly developed 3D numerical two-phase flow solver. Its core is based on OpenFOAM®. IHFOAM can also solve two-phase flow within porous media using RANS/VARANS equationsIHCantabria research institute (https://ihfoam.ihcantabria.com/)
NHWAVENHWAVE is a 3D shock-capturing non-Hydrostatic model which solves the incompressible Navier–Stokes equations in terrain and surface-following sigma coordinatesKirby et al. (2022) (https://sites.google.com/site/gangfma/nhwave, https://github.com/JimKirby/NHWAVE)
GLOBOUSSGloBouss is a depth-averaged model based on the standard Boussinesq equations including higher order dispersion terms, Coriolis terms, and numerical hydrostatic correction termsLøvholt et al. (2022) (https://www.duo.uio.no/handle/10852/10184)
BOUSSCLAWBoussClaw is a new hybrid Boussinesq type model which is an extension of the GeoClaw model. It employs a hybrid of finite volume and finite difference methods to solve Boussinesq equationsClawpack Development Team (http://www.clawpack.org/)Kim et al. (2017)
THETIS-MUITHETIS is a multi-fluid Navier–Stokes solver which can be considered a one-fluid model as only one velocity is defined at each point of the mesh and there is no mixing between the three considered fluids (water, air, and slide). It applies VOF methodTREFLE department of the I2M Laboratory at Bordeaux, France (https://www.i2m.u-bordeaux.fr/en)
LS3DA 2D depth-integrated numerical model which applies a fourth-order Boussinesq approximation for an arbitrary time-variable bottom boundaryAtaie-Ashtiani and Najafi Jilani (2007)
LYNETT- Mild-Slope Equation (MSE)MSE is a depth-integrated version of the Laplace equation operating under the assumption of inviscid flow and mildly varying bottom slopesLynett and Martinez (2012)
Tsunami 3DA simplified 3D Navier–Stokes model for two fluids (water and landslide material) using VOF for tracking of water surfaceHorrillo et al. (2013)Kim et al. (2020)
(Cornell Multi-grid Coupled Tsunami Mode (COMCOT)COMCOT adopts explicit staggered leap-frog finite difference schemes to solve Shallow Water Equations in both Spherical and Cartesian CoordinatesLiu et al. (1998); Wang and Liu (2006)
TWO-LAYERA mathematical model for a two-layer flow along a non-horizontal bottom. Conservation of mass and momentum equations are depth integrated in each layer, and nonlinear kinematic and dynamic conditions are specified at the free surface and at the interface between fluidsImamura and Imteaz (1995)
Table 1 Some of the existing numerical models for simulating landslide-generated waves

In this work, we apply two Computational Fluid Dynamic (CFD) frameworks, FLOW-3D HYDRO, and OpenFOAM to simulate waves generated by solid-block subaerial landslides in a 3D set-up. We calibrate and validate both numerical models using our physical experiments in a 3D wave tank and compare the performances of these models systematically. These two numerical models are selected among the existing CFD solvers because they have been reported to provide valuable insights into landslide-generated waves (Kim et al., 2020; Romano et al., 2020a, b ; Sabeti & Heidarzadeh, 2022a). As there is no study to compare the performances of these two models (FLOW-3D HYDRO and OpenFOAM) with each other in reproducing landslide-generated waves, this study is conducted to offer such a comparison, which can be helpful for model selection in future research studies or industrial projects. In the realm of tsunami generation by subaerial landslides, the solid-block approach serves as an effective representative for scenarios where the landslide mass is more cohesive and rigid, rather than granular. This methodology is particularly relevant in cases such as the 2018 Anak Krakatau or 1963 Vajont landslides, where the landslide’s nature aligns closely with the characteristics simulated by a solid-block model (Zaniboni & Tinti, 2014; Heidarzadeh et al., 2020a, 2020b).

The objectives of this research are: (i) To provide a detailed implementation and calibration for simulating solid-block subaerial landslide-generated waves using FLOW-3D HYDRO and OpenFOAM, and (ii) To compare the performance of these two numerical models based on three criteria: free surface elevation of the landslide-generated waves, capabilities of the models in simulating 3D features of the waves in the near-field, velocity fields, and velocity variations at different locations. The innovations of this study are twofold: firstly, it is a 3D study involving physical and numerical modelling and thus the data can be useful for other studies, and secondly, it compares the performance of two popular CFD models in modelling landslide-generated waves for the first time. The validated models such as those reported in this study and comparison of their performances can be useful for engineers and scientists addressing landslide tsunami hazards worldwide.

2 Data and Methods

2.1 Physical Modelling

To validate our numerical models, a series of three-dimensional physical experiments were carried out at the Hydraulic Laboratory of the Brunel University London (UK) in a 3D wave tank 2.40 m long, 2.60 m wide, and 0.60 m high (Figs. 1 and 2). To mitigate experimental errors and enhance the reliability of our results, each physical experiment was conducted three times. The reported data in the manuscript reflects the average of these three trials, assuming no anomalous outliers, thus ensuring an accurate reflection of the experimental tests. One experiment was used for validation of our numerical models. The slope angle (α) and water depth (h) were 45° and 0.246 m, respectively for this experiment. The movement of the sliding mass was recorded by a digital camera with a sampling frequency of 120 frames per second, which was used to calculate the slide impact velocity (vs). The travel distance (D), defined as the distance from the toe of the sliding mass to the water surface, was D=0.045 m. The material of the solid block used in our study was concrete with a density of 2600 kg/m3. Table 2 provides detailed information on the dimensions and kinematics of this solid block used in our physical experiments.

Figure 1. The geometrical and kinematic parameters of a subaerial landslide tsunami. Parameters are: h, water depth; aM, maximum wave amplitude; α, slope angle;vs, slide velocity; ls, length of landslide; bs, width of landslide; s, thickness of landslide; SWL, still water level; D, travel distance (the distance from the toe of the sliding mass to the water surface); L, length of the wave tank; and W, width of the wave tank and H, is the hight of the wave tank

Figure 2. a Wave tank setup of the physical experiments of this study. b Numerical simulation setup for the FLOW-3D HYDRO Model. c The numerical set-up for the OpenFOAM model. The location of the physical wave gauge (represented by numerical gauge WG-3 in the numerical simulations) is at X = 1.03 m, Y = 1.21 m, and Z = 0.046 m. d Top view showing the locations of numerical wave gauges (WG-1, WG-2, WG-3, WG-4, WG-5)
Parameter, unitValue/type
Slide width (bs), m0.26
Slide length (ls), m0.20
Slide thickness (s), m0.10
Slide volume (V), m32.60 × 10–3
Specific gravity, (γs)2.60
Slide weight (ms), kg6.86
Slide impact velocity (vs), m/s1.84
Slide Froude number (Fr)1.18
MaterialConcrete
Table 2 Geometrical and kinematic information of the sliding mass used for physical experiments in this study

We took scale effects into account during physical experiments by considering the study by Heller et al. (2008) who proposed a criterion for avoiding scale effects. Heller et al. (2008) stated that the scale effects can be negligible as long as the Weber number (W=ρgh2/σ; where σ is surface tension coefficient) is greater than 5.0 × 103 and the Reynolds number (R=g0.5h1.5/ν; where ν is kinematic viscosity) is greater than 3.0 × 105 or water depth (h) is approximately above 0.20 m. Considering the water temperature of approximately 20 °C during our experiments, the kinematic viscosity (ν) and surface tension coefficient (σ) of water become 1.01 × 10–6 m2/s and 0.073 N/m, respectively. Therefore, the Reynolds and Weber numbers were as R= 3.8 × 105 and W= 8.1 × 105, indicating that the scale effect can be insignificant in our experiments. To record the waves, we used a twin wire wave gauge provided by HR Wallingford (https://equipit.hrwallingford.com). This wave gauge was placed at X = 1.03 m, Y = 1.21 m based on the coordinate system shown in Fig. 2a.

2.2 Numerical Simulations

The numerical simulations in this work were performed employing two CFD packages FLOW-3D HYDRO, and OpenFOAM which have been widely used in industry and academia (e.g., Bayon et al., 2016; Jasak, 2009; Rauter et al., 2021; Romano et al., 2020a, b; Yin et al., 2015).

2.2.1 Governing Equations and Turbulent Models

2.2.1.1 FLOW-3D HYDRO

The FLOW-3D HYDRO solver is based on the fundamental law of mass, momentum and energy conservation. To estimate the influence of turbulent fluctuations on the flow quantities, it is expressed by adding the diffusion terms in the following mass continuity and momentum transport equations:

quation (1) is the general mass continuity equation, where u is fluid velocity in the Cartesian coordinate directions (x), Ax is the fractional area open to flow in the x direction, VF is the fractional volume open to flow, ρ is the fluid density, R and ξ are coefficients that depend on the choice of the coordinate system. When Cartesian coordinates are used, R is set to unity and ξ is set to zero. RDIF and RSOR are the turbulent diffusion and density source terms, respectively. Uρ=Scμ∗/ρ, in which Sc is the turbulent Schmidt number, μ∗ is the dynamic viscosity, and ρ is fluid density. RSOR is applied to model mass injection through porous obstacle surfaces.

The 3D equations of motion are solved with the following Navier–Stokes equations with some additional terms:

where t is time, Gx is accelerations due to gravity, fx is viscous accelerations, and bx is the flow losses in porous media.

According to Flow Science (2022), FLOW-3D HYDRO’s turbulence models differ slightly from other formulations by generalizing the turbulence production with buoyancy forces at non-inertial accelerations and by including the influence of fractional areas/volumes of the FAVOR method (Fractional Area-Volume Obstacle Representation) method. Here we use k–ω model for turbulence modelling. The k–ω model demonstrates enhanced performance over the k-ε and Renormalization-Group (RNG) methods in simulating flows near wall boundaries. Also, for scenarios involving pressure changes that align with the flow direction, the k–ω model provides more accurate simulations, effectively capturing the effects of these pressure variations on the flow (Flow Science, 2022). The equations for turbulence kinetic energy are formulated as below based on Wilcox’s k–ω model (Flow Science, 2022):

where kT is turbulent kinetic energy, PT is the turbulent kinetic energy production, DiffKT is diffusion of turbulent kinetic energy, GT is buoyancy production, β∗=0.09 is closure coefficient, and ω is turbulent frequency.

2.2.1.2 OpenFOAM

For the simulations conducted in this study, OpenFOAM utilizes the Volume-Averaged RANS equations (VARANS) to enable the representation of flow within porous material, treated as a continuous medium. The momentum equation incorporates supplementary terms to accommodate frictional forces from the porous media. The mass and momentum conservation equations are linked to the VOF equation (Jesus et al., 2012) and are expressed as follows:

where the gravitational acceleration components are denoted bygj. The term u¯i=1Vf∫Vf0ujdV represents the volume averaged ensemble averaged velocity (or Darcy velocity) component, Vf is the fluid volume contained in the average volumeV,τ is the surface tension constant (assumed to be 1 for the water phase and 0 for the air phase), and fσi is surface tension, defined as fσi=σκ∂α∂xi, where σ (N/m) is the surface tension constant and κ (1/m) is the curvature (Brackbill et al., 1992). μeff is the effective dynamic viscosity that is defined as μeff=μ+ρνt and takes into account the dynamic molecular (μ) and the turbulent viscosity effects (ρνt). νt is eddy viscosity, which is provided by the turbulence closure model. n is the porosity, defined as the volume of voids over total volume, and P∗=1Vf∫∂Vf0P∗dS is the ensemble averaged pressure in excess of hydrostatic pressure. The coefficient A accounts for the frictional force induced by laminar Darcy-type flow, B considers the frictional force under turbulent flow conditions, and c accounts for the added mass. These coefficients (A,B, and c) are defined based on the work of Engelund (1953) and later modified by Van Gent (1995) as given below:

where D50 is the mean nominal diameter of the porous material, KC is the Keulegan–Carpenter number, a and b are empirical nondimensional coefficients (see Lara et al., 2011; Losada et al., 2016) and γ = 0.34 is a nondimensional parameter as proposed by Van Gent (1995). The k-ω Shear Stress Transport (SST) turbulence is employed to capture the effect of turbulent flow conditions (Zhang & Zhang, 2023) with the enhancement proposed by Larsen and Fuhrman (2018) for the over-production of turbulence beneath surface waves. Boundary layers are modelled with wall functions. The reader is referred to Larsen and Fuhrman (2018) for descriptions, validations, and discussions of the stabilized turbulence models.

2.2.2 FLOW-3D HYDRO Simulation Procedure

In our specific case in this study, FLOW-3D HYDRO utilizes the finite-volume method to numerically solve the equations described in the previous Sect. 2.2.1.1, ensuring a high level of accuracy in the computational modelling. The use of structured rectangular grids in FLOW-3D HYDRO offers the advantages of easier development of numerical methods, greater transparency in their relation to physical problems, and enhanced accuracy and stability of numerical solutions. (Flow Science, 2022). Curved obstacles, wall boundaries, or other geometric features are embedded in the mesh by defining the fractional face areas and fractional volumes of the cells that are open to flow (the FAVOR method). The VOF method is employed in FLOW-3D HYDRO for accurate capturing of the free-surface dynamics (Hirt and Nichols 1981). This approach then is upgraded to method of the TruVOF which is a split Lagrangian method that typically produces lower cumulative volume error than the alternative methods (Flow Science, 2022).

For numerical simulation using FLOW-3D HYDRO, the entire flow domain was 2.60 m wide, 0.60 m deep and 2.50 m long (Fig. 2b). The specific gravity (γs) for solid blocks was set to 2.60 in our model, aligning closely with the density of the actual sliding mass, which was approximately determined in our physical experiments. The fluid medium was modelled as water with a density of 1000 kg/m3 at 20 °C. A uniform grid comprising of one single mesh plane was applied with a grid size of 0.005 m. The top, front and back of the mesh areas were defined as symmetry, and the other surfaces were of wall type with no-slip conditions around the walls.

To simulate turbulent flows, k-ω model was used because of its accuracy in modelling turbulent flows (Menter 1992). Landslide movement was replicated in simulations using coupled motion objects, which implies that the movement of landslides is based on gravity and the friction between surfaces rather than a specified motion in which the model should be provided by force and torques. The time intervals of the numerical model outputs were set to 0.02 s to be consistent with the actual sampling rates of our wave gauges in the laboratory. In order to calibrate the FLOW-3D HYDRO model, the friction coefficient is set to 0.45, which is consistent with the Coulombic friction measurements in the laboratory. The Courant Number (C=UΔtΔx) is considered as the criterion for the stability of numerical simulations which gives the maximum time step (Δt) for a prespecified mesh size (Δx) and flow speed (U). The Courant number was always kept below one.

2.2.3 OpenFOAM Simulation Procedure

OpenFOAM is an open-source platform containing several C++ libraries which solves both 3D Reynolds-Averaged Navier–Stokes equations (RANS) and Volume-Averaged RANS equations (VARANS) for two-phase flows (https://www.openfoam.com/documentation/user-guide). Its implementation is based on a tensorial approach using object-oriented programming techniques and the Finite Volume Method (McDonald 1971). In order to simulate the subaerial landslide-generated waves, the IHFOAM solver based on interFoam (Higuera et al., 2013a, 2013b), and the overset mesh framework method are employed. The implementation of the overset mesh method for porous mediums in OpenFOAM is described in Romano et al. (2020a, b) for submerged rigid and impermeable landslides.

The overset mesh technique, as outlined by Romano et al. (2020a, b), uses two distinct domains: a moving domain that captures the dynamics of the rigid landslide and a static background domain to characterize the numerical wave tank. The overlapping of these domains results in a composite mesh that accurately depicts complex geometrical transformations while preserving mesh quality. A porous media with a very low permeability (n = 0.001) was used to simulate the impermeable sliding surfaces. RANS equations were solved within the porous media. The Multidimensional Universal Limiter with Explicit Solution (MULES) algorithm is employed for solving the (VOF) equation, ensuring precision in tracking fluid interfaces. Simultaneously, the PIMPLE algorithm is employed for the effective resolution of velocity–pressure coupling in the Eqs. 7 and 8. A background domain was created to reproduce the subaerial landslide waves with dimensions 2.50 m (x-direction) × 2.60 m (y-direction) × 0.6 m (z-direction) (Fig. 2c). The grid size is set to 0.005 m for the background mesh. A moving domain was applied in an area of 0.35 m (x-direction) × 0.46 m (y-direction) × 0.32 m (z-direction) with a grid spacing of 0.005 m and applying a body-fitted mesh approach, which contains the rigid and impermeable wedges. Wall condition with No-slip is defined as the boundary for the four side walls (left, right, front and back, in Fig. 1). Also, a non-slip boundary condition is specified to the bottom, whereas the top boundary is defined as open. The experimental slide movement time series is used to model the landslide motion in OpenFOAM. The applied equation is based on the analytical solution by Pelinovsky and Poplavsky (1996) which was later elaborated by Watts (1998). The motion of a sliding rigid body is governed by the following equation:

where, m represents the mass of the landslide, s is the displacement of the landslide down the slope, t is time elapsed, g stands for the acceleration due to gravity, θ is the slope angle, Cf is the Coulomb friction coefficient, Cm is the added mass coefficient, m0 denotes the mass of the water displaced by the moving landslide, A is the cross-sectional area of the landslide perpendicular to the direction of motion, ρ is the water density, and Cd is the drag coefficient.

2.2.4 Mesh Sensitivity Analysis

In order to find the most efficient mesh size, mesh sensitivity analyses were conducted for both numerical models (Fig. 3). We considered the influence of mesh density on simulated waveforms by considering three mesh sizes (Δx) of 0.0025 m, 0.005 m and 0.010 m. The results of FLOW-3D HYDRO revealed that the largest mesh deviates 9% (Fig. 3a, Δx = 0.0100 m) from two other finer meshes. Since the simulations by FLOW-3D HYDRO for the finest mesh (Δx = 0.0025 m) do not show any improvements in comparison with the 0.005 m mesh, therefore the mesh with the size of Δx = 0.0050 m is used for simulations (Fig. 3a). A similar approach was followed for mesh sensitivity of OpenFOAM mesh grids. The mesh with the grid spacing of Δx = 0.0050 m was selected for further simulations since a satisfactory independence was observed in comparison with the half size mesh (Δx = 0.0025 m). However, results showed that the mesh size with the double size of the selected mesh (Δx = 0.0100 m) was not sufficiently fine to minimize the errors (Fig. 3b).

Figure 3. a, b Sensitivity of numerical simulations to the sizes of the mesh (Δx) for FLOW-3D HYDRO, and OpenFOAM, respectively. The location of the wave gauge 3 (WG-3) is at X = 1.03 m, Y = 1.21 m, and Z = -0.55 m (see Fig. 2d)

In terms of computational cost, the time required for 2 s simulations by FLOW-3D HYDRO is approximately 4.0 h on a PC Intel® Core™ i7-8700 CPU with a frequency of 3.20 GHz equipped with a 32 GB RAM. OpenFOAM requires 20 h to run 2 s of numerical simulation on 2 processors on a PC Intel® Core™ i9-9900KF CPU with a frequency of 3.60 GHz equipped with a 364 GB RAM. Differences in computational time for simulations run with FLOW-3D HYDRO and OpenFOAM reflect the distinct characteristics of each numerical methods, and the specific hardware setups.

2.2.5 Validation

We validated both numerical models based on our laboratory experimental data (Fig. 4). The following criterion was used to assess the level of agreement between numerical simulations and laboratory observations:

where ε is the mismatch error, Obsi is the laboratory observation values, Simi is the simulation values, and the mathematical expression |X| represents the absolute value of X. The slope angle (α), water depth (h) and travel distance (D) were: α = 45°, h = 0.246 m and D = 0.045 m in both numerical models, consistent with the physical model. We find the percentage error between each simulated data point and its corresponding observed value, and subsequently average these errors to assess the overall accuracy of the simulation against the observed time series. Our results revealed that the mismatch errors between physical experiments and numerical models for the FLOW-3D HYDRO and OpenFOAM are 8% and 18%, respectively, indicating that our models reproduce the measured waveforms satisfactorily (Fig. 4). The simulated waveform by OpenFOAM shows a minor mismatch at t = 0.76 s which resulted from a droplet immediately after the slide hits the water surface in the splash zone. In term of the maximum negative amplitude, the simulated waves by OpenFOAM indicates a relatively better performance than FLOW-3D HYDRO, whereas the maximum positive amplitude (aM) simulated by FLOW-3D HYDRO is closer to the experimental value. The recorded maximum positive amplitude in physical experiment is 0.022 m, whereas it is 0.020 m for FLOW-3D HYDRO and 0.017 m for OpenFOAM simulations. In acknowledging the deviations observed, it is pertinent to highlight that while numerical models offer robust insights, the difference in meshing techniques and the distinct computational methods to resolve the governing equations in FLOW-3D HYDRO and OpenFOAM have contributed to the variance. Moreover, the intrinsic uncertainties associated with the physical experimentation process, including the precision of wave gauges and laboratory conditions, are non-negligible factors influencing the results.

Figure 4. Validation of the simulated waves (brown line for FLOW-3D HYDRO and green line for OpenFOAM) using the laboratory-measured waves (black solid diamonds). This physical experiment was conducted for wave gauge 3 (WG-3) located at X = 1.03 m, Y = 1.21 m, and Z = -0.55 m (see Fig. 2d). Here, 
ε shows the errors between simulations and actual physical measurements using Eq. (13)

3 Results

Following the validations of the two numerical models (FLOW-3D HYDRO and OpenFOAM), a series of simulations were performed to compare the performances of these two CFD solvers. The generation process of landslide waves, waveforms, and velocity fields are considered as the basis for comparing the performance of the two models (Figs. 5, 6, 7 and 8).

Figure 5.Comparison between the simulated waveforms by FLOW-3D HYDRO (black) and OpenFOAM (red) at four different locations in the near-field zone (WG-1,2,4 and 5). WG is the abbreviation for wave gauge. The mismatch (Δ) between the two models at each wave gauge is calculated using Eq. (14)
Figure 6. Comparison of water surface elevations produced by solid-block subaerial landslides for the two numerical models FLOW-3D-HYDRO (a–c) and OpenFOAM (e–g) at different times
Figure 7. Snapshots of the simulations at different times for FLOW-3D HYDRO (a–c) and OpenFOAM (e–g) showing velocity fields (colour maps and arrows). The colormaps indicate water particle velocity in m/s, and the lines indicate the velocities of water particles
Figure 8. Comparison of velocity variations at (WG-3) for FLOW-3D HYDRO (light blue) and OpenFOAM (brown)

3.1 Comparison of Waveforms

Five numerical wave gauges were placed in our numerical models to measure water surface oscillations in the near-field zone (Fig. 5). These gauges offer an azimuthal coverage of 60° (Fig. 2d). Figure 5 reveals that the simulated waveforms from two models (FLOW-3D HYDRO and OpenFOAM) are similar. The highest wave amplitude (aM) is recorded at WG-3 for both models, whereas the lowest amplitude is recorded at WG-5 and WG-1 which can be attributed to the longer distances of these gauges from the source region as well as their lateral offsets, resulting in higher wave energy dissipation at these gauges. The sharp peaks observed in the simulated waveforms, such as the red peak between 0.8–1.0 s in Fig. 5a from OpenFOAM, the red peak between 0.6–0.8 s in Fig. 5b also from OpenFOAM, and the black peak between 1.4–1.6 s in Fig. 5d from FLOW-3D HYDRO, are due to the models’ spatial and temporal discretization. They reflect the sensitivity of the models to capturing transient phenomena, where the chosen mesh and time-stepping intervals are key factors in the models’ ability to track rapid changes in the flow field. To quantify the deviations of the two models from one another, we apply the following equation for mismatch calculation:

where Δ is the mismatch error, Sim1 is the simulation values from FLOW-3D HYDRO, Sim2 is the simulation values from OpenFOAM, and the mathematical expression |X| implies the absolute value of X. We calculate the percentage difference for each corresponding pair of simulation results, then take the mean of these percentage differences to determine the average deviation between the two simulation time series. Using Eq. (14), we found a deviation range from 9 to 11% between the two models at various numerical gauges (Fig. 5), further confirming that the two models give similar simulation results.

3.2 Three-Dimensional Vision of Landslide Generation Process by Numerical Models

A sequence of four water surface elevation snapshots at different times is shown in Fig. 6 for both numerical modes. In both simulations, the sliding mass travels a constant distance of 0.045 m before hitting the water surface at t = 0.270 s which induces an initial change in water surface elevation (Figs. 6a and e). At t = 0.420 s, the mass is fully immersed for both simulations and an initial dipole wave is generated (Figs. 6b and f). Based on both numerical models, the maximum positive amplitude (0.020 m for FLOW-3D HYDRO, and 0.017 m for OpenFOAM) is observed at this stage (Fig. 6). The maximum propagation of landslide-simulated waves along with more droplets in the splash zone could be seen at t = 0.670 s for both models (Fig. 6c and g). The observed distinctions in water surface elevation simulations as illustrated in Fig. 6 are rooted in the unique computational methodologies intrinsic to each model. In the OpenFOAM simulations, a more diffused water surface elevation profile is evident. Such diffusion is an outcome of the simulation’s intrinsic treatment of turbulent kinetic energy dissipation, aligning with the solver’s numerical dissipation characteristics. These traits are influenced by the selected turbulence models and the numerical advection schemes, which prioritize computational stability, possibly at the expense of interface sharpness. The diffusion in the wave pattern as rendered by OpenFOAM reflects the application of a turbulence model with higher dissipative qualities, which serves to moderate the energy retained during wave propagation. This approach can provide insights into the potential overestimation of energy loss under specific simulation conditions. In contrast, the simulations from FLOW-3D HYDRO depict a more localized wave pattern, indicative of a different approach to turbulent dissipation. This coherence in wave fronts is a function of the model’s specific handling of the air–water interface and its targeted representation of the energy dynamics resulting from the landslide’s interaction with the water body. They each have specific attributes that cater to different aspects of wave simulation fidelity, thereby contributing to a more comprehensive understanding of the phenomena under study.

3.3 Wave Velocity Analysis

We show four velocity fields at different times during landslide motion in Fig. 7 and one time series of velocity (Fig. 8) for both numerical models. The velocity varies in the range of 0–1.9 m/s for both models, and the spatial distribution of water particle velocity appears to be similar in both. The models successfully reproduce the complex wavefield around the landslide generation area, which is responsible for splashing water and mixing with air around the source zone (Fig. 7). The first snapshot at t = 0.270 s (Fig. 7a and e) shows the initial contact of the sliding mass with water surface for both numerical models which generates a small elevation wave in front of the mass exhibiting a water velocity of approximately 1.2 m/s. The slide fully immerses for the first time at t = 0.420 s producing a water velocity of approximately 1.5 m/s at this time (Fig. 7b and f). The last snapshot (t = 0.670 s) shows 1.20 s after the slide hits the bottom of the wave tank. Both models show similar patterns for the propagation of the waves towards the right side of the wave tank. The differences in water surface profiles close to the slope and solid block at t = 0.67 s, observed in the FLOW-3D HYDRO and OpenFOAM simulations (Figs. 6 and 7), are due to the distinct turbulence models employed by each (RNG and k-ω SST, respectively) which handle the complex interactions of the landslide-induced waves with the structures differently. Additionally, the methods of simulating landslide movement further contribute to this discrepancy, with FLOW-3D HYDRO’s coupled motion objects possibly affecting the waves’ initiation and propagation unlike OpenFOAM’s prescribed motion from experimental data. In addition to the turbulence models, the variations in VOF methodologies between the two models also contribute to the observed discrepancies.

For the simulated time series of velocity, both models give similar patterns and close maximum velocities (Fig. 8). For both models the WG-3 located at X = 1.03 m, Y = 1.21 m, and Z = − 0.55 m (Fig. 2d) were used to record the time series. WG-3 is positioned 5 mm above the wave tank bottom, ensuring that the measurements taken reflect velocities very close to the bottom of the wave tank. The maximum velocity calculated by FLOW-3D HYDRO is 0.162 m/s while it is 0.132 m/s for OpenFOAM, implying a deviation of approximately 19% from one another. Some oscillations in velocity records are observed for both models, but these oscillations are clearer and sharper for OpenFOAM. Although it is hard to see velocity oscillations in the FLOW-3D HYDRO record, a close look may reveal some small oscillations (around t = 0.55 s and 0.9 s in Fig. 8). In fact, velocity oscillations are expected due to the variations in velocity of the sliding mass during the travel as well as due to the interferences of the initial waves with the reflected wave from the beach. In general, it appears that the velocity time series of the two models show similar patterns and similar maximum values although they have some differences in the amplitudes of the velocity oscillations. The differences between the two curves are attributed to factors such as difference in meshing between the two models, turbulence models, as well as the way that two models record the outputs.

4 Discussions

An important step for CFD modelling in academic or industrial projects is the selection of an appropriate numerical model that can deliver the task with satisfactory performance and at a reasonable computational cost. Obviously, the major drivers when choosing a CFD model are cost, capability, flexibility, and accessibility. In this sense, the existing options are of two types as follows:

  • Commercial models, such as FLOW-3D HYDRO, which are optimised to solve free-surface flow problems, with customer support and an intuitive Graphical User Interface (GUI) that significantly facilitates meshing, setup, simulation monitoring, visualization, and post-processing. They usually offer high-quality customer support. Although these models show high capabilities and flexibilities for numerical modelling, they are costly, and thus less accessible.
  • Open-source models, such as OpenFOAM, which come without a GUI but with coded tools for meshing, setup, parallel running, monitoring, post-processing, and visualization. Although these models offer no customer support, they have a big community support and online resources. Open-source models are free and widely accessible, but they may not be necessarily always flexible and capable.

OpenFOAM provides freedom for experimenting and diving through the code and formulating the problem for a user whereas FLOW-3D HYDRO comes with high-level customer supports, tutorial videos and access to an extensive set of example simulations (https://www.flow3d.com/). While FLOW-3D-HYDRO applies a semi-automatic meshing process where users only need to input the 3D model of the structure, OpenFOAM provides meshing options for simple cases, and in many advanced cases, users need to create the mesh in other software (e.g., ANSYS) (Ariza et al., 2018) and then convert it to OpenFOAM format. Auspiciously, there are numerous online resources (https://www.openfoam.com/trainings/about-trainings), and published examples for OpenFOAM (Rauter et al., 2021; Romano et al., 2020a, b; Zhang & Zhang, 2023).

The capabilities of both FLOW-3D HYDRO and OpenFOAM to simulate actual, complex landslide-generated wave events have been showcased in significant case studies. The study by Ersoy et al. (2022) applied FLOW-3D HYDRO to simulate impulse waves originating from landslides near an active fault at the Çetin Dam Reservoir, highlighting the model’s capacity for detailed, site-specific modelling. Concurrently, the work by Alexandre Paris (2021) applied OpenFOAM to model the 2017 Karrat Fjord landslide tsunami events, providing a robust validation of OpenFOAM’s utility in capturing the dynamics of real-world geophysical phenomena. Both instances exemplify the sophisticated computational approaches of these models in aiding the prediction and analysis of natural hazards from landslides.

As for limitations of this study, we acknowledge that our numerical models are validated by one real-world measured wave time series. However, it is believed that this one actual measurement was sufficient for validation of this study because it was out of the scope of this research to fully validate the FLOW-3D HYDRO and OpenFOAM models. These two models have been fully validated by more actual measurements by other researchers in the past (e.g., Sabeti & Heidarzadeh, 2022b). It is also noted that some of the comparisons made in this research were qualitative, such as the 3D wave propagation snapshots, as it was challenging to develop quantitative comparisons for snapshots. Another limitation of this study concerns the number of tests conducted here. We fixed properties such as water depth, slope angle, and travel distance throughout this study because it was out of the scope of this research to perform sensitivity analyses.

5 Conclusions

We configured, calibrated, validated and compared two numerical models, FLOW-3D HYDRO, and OpenFOAM, using physical experiments in a 3D wave tank. These validated models were used to simulate subaerial solid-block landslides in the near-field zone. Our results showed that both models are fully compatible with investigating waves generated by subaerial landslides, although they use different approaches to simulate the phenomenon. The properties of solid-block, water depth, slope angle, and travel distance were kept constant in this study as we focused on comparing the performance of the two models rather than conducting a full sensitivity analysis. The findings are as follows:

  • Different settings were used in the two models for modelling landslide-generated waves. In terms of turbulent flow modelling, we used the Renormalization Group (RNG) turbulence model in FLOW-3D HYDRO, and k-ω (SST) turbulence model in OpenFOAM. Regarding meshing techniques, the overset mesh method was used in OpenFOAM, whereas the structured cartesian mesh was applied in FLOW-3D HYDRO. As for simulation of landslide movement, the coupled motion objects method was used in FLOW-3D HYDRO, and the experimental slide movement time series were prescribed in OpenFOAM.
  • Our modelling revealed that both models successfully reproduced the physical experiments. The two models deviated 8% (FLOW-3D HYDRO) and 18% (OpenFOAM) from the physical experiments, indicating satisfactory performances. The maximum water particle velocity was approximately 1.9 m/s for both numerical models. When the simulated waveforms from the two numerical models are compared with each other, a deviation of 10% was achieved indicating that the two models perform approximately equally. Comparing the 3D snapshots of the two models showed that there are some minor differences in reproducing the details of the water splash in the near field.
  • Regarding computational costs, FLOW-3D HYDRO was able to complete the same simulations in 4 h as compared to nearly 20 h by OpenFOAM. However, the hardware that were used for modelling were not the same; the computer used for the OpenFOAM model was stronger than the one used for running FLOW-3D HYDRO. Therefore, it is challenging to provide a fair comparison for computational time costs.
  • Overall, we conclude that the two models give approximately similar performances, and they are both capable of accurately modelling landslide-generated waves. The choice of a model for research or industrial projects may depend on several factors such as availability of local knowledge of the models, computational costs, accessibility and flexibilities of the model, and the affordability of the cost of a license (either a commercial or an open-source model).

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Three-dimensional flow structure in a confluence-bifurcation unit

합류 분기 유닛의 3차원 유동 구조

Di Wang, Xiaoyong Cheng, Zhixuan Cao, Jinyun Deng

Abstract

Enhanced understanding of flow structure in braided rivers is essential for river regulation, flood control, and infrastructure safety across the river. It has been revealed that the basic morphological element of braided rivers is confluence-bifurcation units. However, flow structure in these units has so far remained poorly understood with previous studies having focused mainly on single confluences/bifurcations. Here, the flow structure in a laboratory-scale confluence-bifurcation unit is numerically investigated based on the FLOW–3D® software platform. Two discharges are considered, with the central bars submerged or exposed respectively when the discharge is high or low. The results show that flow convergence and divergence in the confluence-bifurcation unit are relatively weak when the central bars are submerged. Based on comparisons with a single confluence/bifurcation, it is found that the effects of the upstream central bar on the flow structure in the confluence-bifurcation unit reign over those of the downstream central bar. Concurrently, the high-velocity zone in the confluence-bifurcation unit is less concentrated than that in a single confluence while being more concentrated than that observed in a single bifurcation. The present work unravels the flow structure in a confluence-bifurcation unit and provides a unique basis for further investigating morphodynamics in braided rivers.

1 Introduction

Confluences and bifurcations commonly exist in alluvial rivers and usually are important nodes of riverbed planform (Szupiany et al., 2012; Hackney et al., 2018). Flow convergence and divergence in these junctions result in highly three-dimensional (3D) flow characteristics, which greatly influence sediment transport, and hence riverbed evolution and channel formation (Le et al., 2019; Xie et al., 2020). Braided rivers, characterized by unstable networks of channels separated by central bars (Ashmore, 2013), have confluence-bifurcation units as their basic morphological elements (Ashmore, 1982; 1991; 2013; Federici & Paola, 2003; Jang & Shimizu, 2005). In particular, confluence-bifurcation units exhibit a distinct morphology from single confluences/bifurcations and bifurcation-confluence regions because two adjacent central bars are included. Within a confluence-bifurcation unit, two tributaries converge at the upstream bar tail and soon diverge to two anabranches again at the downstream bar head. Therefore, the flow structure in the unit may be significantly influenced by both the two central bars, and thus considerably different from that in single confluences, single bifurcations, and bifurcation-confluence regions, where the flow is affected by only one central bar. Enhanced understanding of flow structure in confluence-bifurcation units is urgently needed, which is essential for water resources management, river regulation, flood control, protection of river ecosystems and the safety of infrastructures across the rivers such as bridges, oil pipelines and communication cables (Redolfi et al., 2019; Ragno et al., 2021).

The flow dynamics, turbulent coherent structures, and turbulent characteristics in single confluences have been widely studied since the 1980s (Yuan et al., 2022). Flow dynamics at river channel confluences have been systematically and completely analyzed, which can be characterized by six major regions of flow stagnation, flow deflection, flow separation, maximum velocity, flow recovery and distinct shear layers (Best, 1987). For example, the field observation of Roy et al. (1988) and Roy and Bergeron (1990) highlighted the flow separation zones and recirculation at downstream natural confluence corners. Ashmore et al. (1992) measured the flow field in a natural confluence and found flow accelerates suddenly at the confluence junction with two separated high-velocity cores merging into one single core at the channel centre. De Serres et al. (1999) investigated the three-dimensional flow structure at a river confluence and identified the existence of the mixing layer, stagnation zones, separation zones and recovery zones. Sharifipour et al. (2015) numerically studied the flow structure in a 90° single confluence and found that the size of the separation zone decreases with the width ratio between the tributary and the main channel. Recently, three main classes of large-scale turbulent coherent structures (Duguay et al., 2022) have been presented, i.e. vertical-orientated vortices or Kelvin-Helmholtz instabilities (Rhoads & Sukhodolov, 2001; Constantinescu et al., 2011; 2016; Biron et al., 2019), channel-scale ‘back-to-back’ helical cells, (Mosley, 1976; Ashmore, 1982; Ashmore et al., 1992; Ashworth, 1996; Best, 1987; Rhoads & Kenworthy, 1995; Bradbrook et al., 1998; Lane et al., 2000), and smaller, strongly coherent streamwise-orientated vortices (Constantinescu et al., 2011; Sukhodolov & Sukhodolova, 2019; Duguay et al., 2022). However, no consensus on a universal turbulent coherent structure mode has been reached so far (Duguay et al., 2022). In addition, some studies (Ashworth, 1996; Constantinescu et al., 2011; Sukhodolov et al., 2017; Le et al., 2019; Yuan et al., 2023) have focused on turbulent characteristics, e.g. turbulent kinetic energy, turbulent dissipation rate and Reynolds stress, which can be critical parameters to further explaining the diversity of these turbulent coherent structure modes.

Investigations on the flow structure in single bifurcations have mainly focused on hydrodynamics in anabranches (Hua et al., 2009; van der Mark & Mosselman, 2013; Iwantoro et al., 2022) and around bifurcation bars (McLelland et al., 1999; Bertoldi & Tubino, 2005; 2007; Marra et al., 2014), whereas few studies have considered the effects of bifurcations on the upstream flow structure. Thomas et al. (2011) found that the velocity core upstream of the bifurcation is located near the water surface and towards the channel center in experimental investigations of a Y-shaped bifurcation. Miori et al. (2012) simulated flow in a Y-shaped bifurcation and found two circulation cells upstream of the bifurcation with flow converging at the water surface and diverging near the bed. Szupiany et al. (2012) reported velocity decreasing and back-to-back circulation cells upstream of the bifurcation junction in the field observation of a bifurcation of the Rio Parana River. These investigations provide insight into how bifurcations affect the flow patterns upstream, yet there is a need for further research on the dynamics of flow occurring immediately before the bifurcation junction.

Generally, the findings of studies on bifurcation-confluence regions are similar to those concerning single confluences and bifurcations. Hackney et al. (2018) measured the hydrodynamic characteristics in a bifurcation-confluence of the Mekong River and found the velocity cores located at the channel centre and strong secondary current occurring under low discharges. Le et al. (2019) reported a high-turbulent-kinetic-energy (high-TKE) zone located near the bed in their numerical simulation of flow in a natural bifurcation-confluence region. Moreover, a stagnation zone was found upstream of the confluence and back-to-back secondary current cells were detected at the confluence according to Xie et al. (2020) and Xu et al. (2022). Overall, these studies have further unraveled the flow patterns in river confluences and bifurcations.

Unfortunately, limited attention has been paid to the flow structure in confluence-bifurcation units. Parsons et al. (2007) investigated a large confluence-bifurcation unit in Rio Parana, Argentina, and no classical back-to-back secondary current cells were observed under a discharge of 12000 m3·s−1. To date, the differences in flow structure between confluence-bifurcation units and single confluences/bifurcations have remained far from clear. In addition, although the effects of discharge on flow structure have been investigated in several studies on single confluences/bifurcations, (Hua et al., 2009; Le et al., 2019; Luz et al., 2020; Xie et al., 2020; Xu et al., 2022), cases with fully submerged central bars were not considered, which is typical in braided rivers during floods. In-depth studies concerning these issues are urgently needed to gain better insight into the flow structure in confluence-bifurcation units of braided rivers.

This paper aims to (1) reveal the 3D flow structure in a confluence-bifurcation unit under different discharges and (2) elucidate the differences in the flow structure between confluence-bifurcation units and single confluence/bifurcation cases. Using the commercial computational fluid dynamics software FLOW-3D® (Version 11.2; https://www.flow3d.com; Flow Science, Inc.), fixed-bed simulations of a laboratory-scale confluence-bifurcation unit are conducted, and cases of a single confluence/bifurcation are also included for comparison. Two discharges are considered, with the central bars fully submerged or exposed respectively when the discharge is high or low. Based on the computational results, the 3D flow structure in the confluence-bifurcation unit conditions is analyzed from various aspects including free surface elevation, time-averaged flow velocity distribution, recirculation vortex structure, secondary current, and turbulent kinetic energy and dissipation rate. In particular, the flow structure in the confluence-bifurcation unit is compared with that in the single confluence/bifurcation cases to unravel the differences.h

2. Conceptual flume and computational cases

2.1. Conceptual flume

In this paper, a laboratory-scale conceptual flume is designed and used in numerical simulations. Figure 1(a–d) shows the morphological characteristics of the flume. To ensure that the conceptual flume reflects morphology features of natural braided channels, key parameters governing the flume morphology, e.g. unit length, width, and channel width-depth ratio, are determined according to studies on morphological characteristics of natural confluence-bifurcation units (Hundey & Ashmore, 2009; Ashworth, 1996; Orfeo et al., 2006; Parsons et al., 2007; Sambrook Smith et al., 2005; Kelly, 2006; Ashmore, 2013; Egozi & Ashmore, 2009; Redolfi et al., 2016; Ettema & Armstrong, 2019).

Figure 1. The sketch of the conceptual flume: (a) the original flume, (b) the central bar: (c) the sketch of cross-section C-C, (d) the sketch of cross-section D-D, (e) the modified part for the single confluence, (f) the modified part for the single bifurcation, (g) the position of different cross-sections. The red dashed boxes denote the regions of primary concern.

Figure 1. The sketch of the conceptual flume: (a) the original flume, (b) the central bar: (c) the sketch of cross-section C-C, (d) the sketch of cross-section D-D, (e) the modified part for the single confluence, (f) the modified part for the single bifurcation, (g) the position of different cross-sections. The red dashed boxes denote the regions of primary concern.

2.1.1. Length and width scales of the confluence-bifurcation unit

The length and width scales of the flume are first determined. The inner relation among the length LCB and average width B of a confluence-bifurcation unit and the average width Bi of a single branch was statistically studied by Hundey and Ashmore (2009), which indicates the following relations:
𝐿CB =(4∼5)⁢𝐵 (1)
𝐵 =1.41⁢𝐵𝑖 (2)
In addition, Ashworth (1996) gave B = 2Bi in his experimental research on mid-bar formation downstream of a confluence, while the confluence-bifurcation unit of Rio Parana, Argentina has a relation of B≈1.71Bi (Orfeo et al., 2006; Parsons et al., 2007). Accordingly, the following relations are used in the present paper:
𝐿CB =4⁢𝐵 (3)
𝐵 =1.88⁢𝐵𝑖 (4)
where LCB = 6 m, B = 1.5 m and Bi = 0.8 m.

2.1.2. Central bar morphology

The idealized plane pattern of central bars in braided rivers is a slightly fusiform leaf shape with a short upstream side and a long downstream side (Ashworth, 1996; Sambrook Smith et al., 2005; Kelly, 2006; Ashmore, 2013). To simplify the design, the bar is approximated as a combination of two different semi-ellipses (Figure 1(b)). The major axis Lb is two to ten times longer than the minor axis Bb according to the statistical data in Kelly’s study, and the regression equation is given as (Kelly, 2006):
𝐿𝑏=4.62⁢𝐵0.96𝑏 (5)
In this study, the bar width Bb is set as 0.8 m, whilst the lengths of downstream (LT1) and upstream sides (LT2) are 2 and 1.5 m, respectively (Figure 1(b)). Thus, the relation of Lb and Bb is given as:
𝐿𝑏=(𝐿𝑇⁢1+𝐿𝑇⁢2)=4.375⁢𝐵𝑏 (6)
The lengths of the inlet and outlet parts are determined as Lin = Lout = 8 m, which ensures negligible effects of boundary conditions without exceptional computational cost.

2.1.3. Width-depth ratio

Channel flow capacity can be significantly affected by cross-section shapes. For natural rivers, cross-section shapes can be generalized into three sorts based on the following width-depth curve (Redolfi et al., 2016):
𝐵=𝜓⁢𝐻𝜑(7)
Braided rivers usually have ψ = 5∼50 and φ>1, which indicates a rather wide and shallow cross-section. The central bar form should also be taken into account, so a parabolic cross-section shape is used here with ψ = 8 and φ>1 (Figure 1(c,d)).

2.1.4. Bed slope

In addition, natural braided rivers are usually located in mountainous areas and thus have a relatively large bed slope. According to flume experiments and field observations, the bed slope Sb is mostly in the range of 0.01∼0.02, and a few are below 0.01 (Ashworth, 1996; Egozi & Ashmore, 2009; Ashmore, 2013; Redolfi et al., 2016; Ettema & Armstrong, 2019). In this study, Sb takes 0.005.

2.1.5. Complete sketch of the conceptual flume

In summary, the flume is 29 m long, 2.4 m wide, and 0.6 m high. The plane coordinates (x-direction and y-direction) used in the calculation process are shown in Figure 1
(a). Note that the inlet corresponds to x = 0 m, and the centreline of the flume is located at y = 1.3 m. Besides, the thalweg elevation of the outlet is set as z = 0 m.

2.2. Computational cases

As stated before, the first aim of this paper is to reveal the flow structure in the confluence-bifurcation unit under different discharges. Therefore, two basic cases are set first: (1) case 1a under a low discharge (0.05 m3·s−1) with exposed central bars and (2) case 2a under a high discharge (0.30 m3·s−1) with fully submerged central bars. A total of 22 cross-sections are identified to examine the results (Figure 1(g)).

Further, cases of a single confluence/bifurcation are generated by splitting the original confluence-bifurcation unit into two parts. Part 1 only includes the upstream central bar and focuses on the flow convergence downstream of CS04 (Figure 1(e)), while Part 2 only includes the downstream central bar and focuses on the flow divergence upstream of CS19 (Figure 1(f)). Notably, the numbers of corresponding cross-sections in the original flume are reserved to facilitate comparison. The outlet section of the single confluence as well as the inlet section of the single bifurcation is extended to make the total length equivalent to the original flume (29 m). Also, two discharge conditions (0.05 and 0.30 m3·s−1), which correspond to exposed and fully submerged central bars, are considered for the single confluence/bifurcation. In total, six computational cases are conducted, as listed in Table 1. As the conceptual flume is designed to be symmetrical about the centreline, the momentum flux ratio (Mr) of the two branches should be 1 in all six cases. This is confirmed by further examining the computational results.

CaseConfigurationQin (m3·s−1)Zout (m)MrCondition of bars
1aCBU0.050.151Exposed
1bSC0.050.151Exposed
1cSB0.050.151Exposed
2aCBU0.300.341Submerged
2bSC0.300.341Submerged
2cSB0.300.341Submerged
Table 1. Computational cases with inlet and outlet boundary conditions.

3. Numerical method

In this section, the 3D Large Eddy Simulation (LES) model integrated in the FLOW-3D® (Version 11.2; https://www.flow3d.com; Flow Science, Inc.) software platform is introduced, including governing equations and boundary conditions. Information on computational meshes with mesh independence test can be found in the Supplementary material.

3.1. Governing equations

The LES model was applied in the present paper to simulate flow in the laboratory-scale confluence-bifurcation unit. The LES model has been proven to be effective in simulating turbulent flow in river confluences and bifurcations (Constantinescu et al., 2011; Le et al., 2019). The basic idea of the LES model is that one should directly compute all turbulent flow structures that can be resolved by the computational meshes and only approximate those features that are too small to be resolved (Smagorinsky, 1963). Therefore, a filtering operation is applied to the original Navier-Stokes (NS) equations for incompressible fluids to distinguish the large-scale eddies and small-scale eddies (Liu et al., 2018). The filtered NS equations are then generated, which can be expressed in the form of a Cartesian tensor as (Liu, 2012):

(10) where ¯𝑢𝑖 is the resolved velocity component in the i – direction (i goes from 1 to 3, denoting the x-, y – and z-directions, respectively); t is the flow time; ρ is the density of the fluid; ¯𝑝 is the pressure; ν is the kinematic viscosity; τij is the sub-grid scale (SGS) stress; ¯𝐺𝑖 is the body acceleration. In FLOW–3D®, the full NS equations are discretized and solved using the finite-volume/finite-difference method (Bombardelli et al., 2011; Lu et al., 2023).

Due to the filtering process, the velocity can be divided into a resolved part (¯𝑢⁡(𝑥,𝑡)) and an approximate part (𝑢′⁡(𝑥,𝑡)) which is also known as the SGS part (Liu, 2012). To achieve model closure, the standard Smagorinsky SGS stress model is introduced here (Smagorinsky, 1963):
𝜏ij−13⁢𝜏kk⁢𝛿ij=−2⁢𝜈SGS⁢¯𝑆ij(11)
 where νSGS is the SGS turbulent viscosity, and ¯𝑆ij is the resolved rate-of-strain tensor for the resolved scale defined by (Smagorinsky, 1963):
¯𝑆ij=12⁢(∂¯𝑢𝑖∂𝑥𝑗+∂¯𝑢𝑗∂𝑥𝑖)(12) 
In the standard Smagorinsky SGS stress model, the eddy viscosity is modelled by (Smagorinsky, 1963):
𝜈SGS=(𝐶𝑠⁢¯𝛥)2⁢∣¯𝑆∣,∣¯𝑆∣=√2⁢¯𝑆ij⁢¯𝑆ij(13)
¯𝛥=(ΔxΔyΔz⁢)1/3(14) 
where Cs is the Smagorinsky constant, Δx, Δy, and Δz are mesh scales. In FLOW–3D®, Cs is between 0.1 to 0.2 (Smagorinsky, 1963).
One of the key problems in simulating 3D open channel flow is the calculation of free surface. FLOW–3D® uses the Volume of Fluid (VOF) method (Hirt & Nichols, 1981) to track the change of free surface. The VOF method introduces a fluid phase fraction function f to characterize the proportion of a certain fluid in each mesh cell. In that case, the surface position can be precisely located if the mesh cell is fine enough. To monitor the change of f with time and space, the following convection equation is added:

For open channel flow, only two kinds of fluids are involved: water and air. If f is the fraction of water, the state of the fluid in each mesh cell can be defined as:

In FLOW–3D®, the interface between water and air is assumed to be shear-free, which means that the drag force on the water from the air is negligible. Moreover, in most cases, the details of the gas motion are not crucial for the heavier water motion so the computational processes will be more efficient.

3.2. Boundary conditions

Six boundary conditions need to be preset in the 3D numerical simulation process. Discharge boundary conditions are used for the inlet of the flume, where the free surface elevation is automatically calculated based on the free surface elevation boundary conditions set for the outlet. The specific information on the inlet and outlet boundary conditions for all computational cases is shown in Table 1. Moreover, because the free surface moves temporally, the free surface boundary conditions are just set as no shear stress and having a normal pressure, and the position of the free surface will be automatically adjusted over time by the VOF method in FLOW–3D®. Furthermore, the bed and two side walls are all set to be no-slip for fixed bed conditions, and a standard wall function is employed at the wall boundaries for wall treatment.

The inlet turbulent boundary conditions also need to be considered. They are set by default here. The turbulent velocity fluctuations V’ are assumed to be 10% of the mean flow velocity with the turbulent kinetic energy (TKE) (per unit mass) equaling 0.5V’2. The maximum turbulent mixing length is assumed to be 7% of the minimum computational domain scale, and the turbulent dissipation rate is evaluated automatically from the TKE.

4. Results and discussion

4.1. Flow structure in the confluence-bifurcation unit

4.1.1. Free surface elevation

Figure 2 shows the free surface elevation at five different longitudinal profiles (i.e. α = 0.2, 0.4, 0.5, 0.6, 0.8) for cases 1a and 2a. The parameter α was defined as follows:𝛼=𝑠𝐵(17) where s is the transverse distance between a certain profile and the left boundary of the flume. In general, the longitudinal change of free surface in the two cases is very similar despite different discharge levels. The free surface elevation decreases as the channel narrows from the upstream bifurcation to the front of the confluence-bifurcation unit. On the contrary, when the flow diverges again at the end of the confluence-bifurcation unit, the free surface elevation increases with channel widening. However, whether the fall or rise of free surface elevation in case 1a is much sharper than that in case 2a, especially at profiles with α = 0.2 and 0.8 (Figure 2(a)), which indicates there may be distinct flow states between the two cases. To further illustrate this finding, the Froude number Fr at different cross-sections (CS08∼CS15) is examined. In case 2a, the flow remains subcritical within the confluence-bifurcation unit. By contrast, in case 1a, a local supercritical flow is observed near the side banks of CS09 (i.e. α = 0.2 and 0.8), with Fr being about 1.2. This local supercritical flow can lead to a hydraulic drop followed by a hydraulic jump, which accounts for the sharp change of the free surface. The foregoing reveals that when central bars are exposed under relatively low discharge, supercritical flow is more likely to occur near the side banks of the confluence junction due to flow convergence.

Figure 2. Five time-averaged free surface elevation profiles in the confluence-bifurcation unit, in which α denotes the lateral position of the certain profile. Note that the black dashed line denotes the position of CS09, where Fr is about 1.2 near the side banks (α = 0.2 and 0.8) in case 1a. Z’ = z/h2, X’ = x/B, h2 is the maximum flow depth at the outlet boundary of cases 2a, 2b and 2c, h2 = 0.34 m.

Moreover, in both cases 1a and 2a, the free surface is higher at the channel centre than near the side banks, whether at the front or the end of the confluence-bifurcation unit. Thus, lateral free surface slopes from the centre to the side banks are generated. For example, the lateral free surface slopes at CS09 are 0.022 and 0.016 respectively for cases 1a and 2a. These lateral slopes can lead to lateral pressure gradient force whose direction is from the channel centreline to the side banks. Notably, the lateral surface slope in case 1a is steeper than that in case 2a, which may also result from the effect of the supercritical flow.

4.1.2. Time-averaged streamwise flow velocity

Figure 3. Time-averaged flow velocity distribution at three different slices over z-direction in the confluence-bifurcation unit: (a)∼(c) case 1a, (d)∼(f) case 2a. The flow direction is from the left to the right. StZ = Stagnation Zones, MiL = Mixing Layer. X’ = x/B, Y’ = y/B, Ui’ = Ui/Uti, Ui denotes the time-averaged streamwise flow velocity in case series i (i = 1,2), Uti denotes the cross-section-averaged streamwise flow velocity in case series i, Ut1 = 0.385 m/s, for case 2a Ut2 = 0.714 m/s.
Figure 4. Time-averaged flow velocity contours at eight different cross-sections in the confluence-bifurcation unit: (a) case 1a, (b) case 2a.

Besides the shared features described above, some differences between the two cases are also identified. First, flow stagnation zones at the upstream bar tail are found exclusively in case 1a as the central bars are exposed (Figure 3
(a–c)). Second, in case 1a the mixing layer is obvious in both the lower or upper flows (Figure 3
(a–c)), while in case 2a the mixing layer can be inconspicuous in the upper flow (Figure 3
(f)). Third, in case 1a, two high-velocity cores gradually transform into one single core downstream of the confluence [Figure 4
(a), CS08∼CS11] and are divided into two cores again at the downstream bar head [Figure 4
(a), CS15]. By contrast, in case 2a, the two cores merge much more rapidly [Figure 4
(a), CS08∼CS09], and no obvious reseparation of the merged core is found at the downstream bar head (Figure 3
(d–f)). The latter two differences between cases 1a and 2a indicate that the flow convergence and divergence are relatively weak when the central bars are fully submerged. It is noticed that when the central bars are exposed, the flow in branches needs to steer around the central bar, which can cause a large angle between the two flow directions at the confluence, and thus relatively strong flow convergence and divergence may occur. By contrast, when the central bars are fully submerged, the flow behavior resembles that of a straight channel, with flow predominantly moving straight along the main axis of the central bars. Therefore, a small angle between two tributary flow forms, and thus flow convergence and divergence are relatively mild.

4.1.3. Recirculation vortex

A recirculation vortex with a vertical axis is a typical structure usually found where flow steers sharply, and is generated from flow separation (Lu et al., 2023). This vortex structure is found in the confluence-bifurcation unit in the present study, marking several significant flow separation zones. Figure 5 shows the recirculation vortex structure at the bifurcation junction of the confluence-bifurcation unit. In both cases 1a and 2a, two recirculation vortices BV1 and BV2 are found at the bifurcation junction corner. Moreover, BV1 and BV2 seem well-established near the bed but tend to transform into premature ones in the upper flow, and there is also a tendency for the cores of BV1 and BV2 to shift downstream as they transition from the lower to the upper flow (Figure 5(a–c,d–f)). This finding indicates that flow separation zones exist at the bifurcation junction corner, and the vortex structure is similar in the separation zones under low and high discharges. These flow separation zones are generated due to the inertia effect as flow suddenly diverges and steers towards the curved side banks of the channel (Xie et al., 2020). Notably, two additional vortices BV3 and BV4 are found at both sides of the downstream bar in case 1a (Figure 5(a–c)), but no such vortices exist in case 2a. This difference shows that flow separation zones at both sides of the downstream bar are hard to form when the bars are completely submerged under the high discharge.

Figure 5. Recirculation vortices at the bifurcation junction (streamline view at three different slices over z-direction): (a)∼(c) case 1a, (d)∼(f) case 2a. The red solid line marked out the position of these vortices (BV1∼BV4).

Similarly, Figure 6 shows the recirculation vortex structure at the confluence junction of the confluence-bifurcation unit. No noteworthy similarities but a key difference between the two cases are observed at this site. Two vortices CV1 and CV2 are found downstream of the confluence junction corner in case 1a (Figure 6(c)), which mark two separation zones. Conversely, no such separation zones are found in case 2a. In fact, separation zones were reported at similar sites under relatively low discharges in some previous studies (Ashmore et al., 1992, Luz et al., 2020, Sukhodolov & Sukhodolova, 2019; Xie et al., 2020). Nevertheless, the flow separation zones at the confluence corner are very restricted in the present study (Figure 6(c)). Ashmore et al. (1992) also reported that no, or very restricted flow separation zones occur downstream of natural river confluence corners, primarily because of the relatively slow change in bank orientation compared with the sharp corners of laboratory confluences where separation is pronounced (Best & Reid, 1984; Best, 1988). In the present study, the bank orientation also changes slowly, which may explain why flow separation zones are inconspicuous at the confluence corner.

Figure 6. Recirculation vortices at the confluence junction (streamline view at three different slices over z-direction): (a)∼(c) case 1a, (d)∼(f) case 2a. The red solid line marked out the position of these vortices (CV1 & CV2).

The differences in the distribution of recirculation vortices discussed above may be mainly attributed to the difference in the angle between the tributary flows under different discharges. Some previous studies have reported that the confluence/bifurcation angle can significantly influence the flow structure at confluences/bifurcations (Best & Roy, 1991; Ashmore et al., 1992; Miori et al., 2012). Although the confluence/bifurcation angle is fixed due to the determined central bar shape in the present study, the angle between two tributary flows is affected by the varying discharge. When the central bars are exposed under the low discharge, the flow is characterized by a more pronounced curvature of the streamlines, and a large angle between the two tributary flows is noted (Figure 6(b)), causing strong flow convergence and divergence. By contrast, a small angle forms as the central bars are submerged, thereby leading to relatively weak flow convergence/divergence (Figure 6(e)). Overall, the differences mentioned above can be attributed to the differences in the intensity of flow convergence and divergence under different discharges.

It should be noted that some previous studies (Constantinescu et al., 2011; Sukhodolov & Sukhodolova, 2019) presented that there is a wake mode in the mixing layer of two streams at the confluence junction. The wake mode means that in the mixing layer, multiple streamwise coherent vortices moving downstream will form, which is similar to the flow structure around a bluffing body (Constantinescu et al., 2011). However, no such structure has been found within the confluence-bifurcation unit in this study. According to the numerical simulations of Constantinescu et al. (2011), a wake mode was found at a river confluence with a concordant bed and a momentum flux ratio of about 1. The confluence has a much larger angle (∼60°) between the two streams when compared to the confluence junction of the confluence-bifurcation unit in the present study where the angle is about 25°. As flow mechanics at river confluences may include several dominant mechanisms depending on confluence morphology, momentum ratio, the angle between the tributaries and the main channel, and other factors (Constantinescu et al., 2011), the relatively small confluence angle in the present study may explain why the wake mode is absent. The possible effects of the confluence/bifurcation angle are reserved for future study. Additionally, flow separation can lead to reduced local sediment transport capacity, thus causing considerable sediment deposition under natural conditions. Hence, the bank may migrate towards the inner side of the channel at the positions of CV1, CV2, BV1, and BV2, while the bar may expand laterally at the positions of BV3 and BV4.

4.1.4. Secondary current

Secondary current is the flow perpendicular to the mainstream axis (Thorne et al., 1985) and can be categorized into two primary types based on its origin: (1) Secondary current generated by the interaction between centrifugal force and pressure gradient force; (2) Secondary current resulting from turbulence heterogeneity and anisotropy (Lane et al., 2000). There are some widely recognized definitions of secondary current strength (SCS) (Lane et al., 2000). In this paper, the secondary current cells are identified by visible vortex with a streamwise axis, and the definition of SCS proposed by Shukry (1950) is used:

where ux, uy, and uz are flow velocities in x, y, and z directions and ux represents the mainstream flow velocity.

Figure 7 presents contour plots of SCS and the secondary current structure at key cross-sections of the study area. When the central bars are exposed, at the upstream bar tail (CS08), intense transverse flow occurs with flow converging to the centreline, but no secondary current cell is formed (Figure 7(a)). This is consistent with the findings of Hackney et al. (2018). At the confluence junction (CS09), transverse flow still plays a major role in the secondary current structure, with flow converging to the centreline at the surface and diverging to side banks near the bed (Figure 7(b)). Moreover, ‘back-to-back’ helical cells, which are two vortices rotating reversely, tend to generate at CS09 with their cores located near the side banks (Figure 7(b)) (Mosley, 1976; Ashmore, 1982; Ashmore et al., 1992), yet their forms are rather premature. As the flow goes downstream, the cores of the helical cells gradually rise to the upper flow and approach towards the centreline, and the helical cells become well-established (Figure 7(c–e)). When the flow diverges again at the downstream bar head (CS15), the helical cells attenuate rapidly, and the secondary current structure is once again characterized predominantly by transverse flow (Figure 7(f)).

Figure 7. Distribution of secondary current strength and secondary current cells at six different cross-sections: (a)∼(f) case 1a, (g)∼(l) case 2a. The secondary current cells are identified by visible lateral vortices (streamline view). The zero distance of each cross-section is located on the right bank.

When the central bars are fully submerged under the high discharge, the secondary current structure at the upstream bar tail and the confluence junction exhibits a resemblance to that under the low discharge (Figure 7(g,h)). However, at CS09, two pairs of cells with different scales tend to form under the high discharge (Figure 7(h)). The large and premature helical cells are similar to those under the low discharge, whereas the small helical cells are located near side banks possibly due to wall effects. As the flow moves downstream, the large helical cells tend to diminish rapidly and merge with the small ones near both side walls (Figure 7(i–k)). Moreover, the secondary current structure is once again characterized predominantly by transverse flow at CS14 under the high discharge, which occurs earlier than that under the low discharge (Figure 7(k)). At the downstream bar head, transverse flow still takes a dominant place, while the helical cells seem to become premature with increased scale (Figure 7(l)).

In general, in both cases 1a and 2a, the lateral distribution of SCS at all cross-sections is symmetrical about the channel centreline, where SCS is relatively small. A relatively high SCS is detected at both the upstream bar tail and the downstream bar head due to the effects of centrifugal force caused by flow steering. SCS decreases rapidly from the upstream bar tail (CS08) to the entrance of the downstream bifurcation junction (CS14), followed by a sudden increase at the downstream bar head (CS15) (Figure 7
(a–e, g–k)). However, the distribution of high-SCS zones is different between the two discharges. Under the low discharge, high-SCS zones appear along the bottom near the centerline and at the free surface on both sides of the centreline. Although similar high-SCS zones are found along the bottom near the centerline under the high discharge, the high-SCS zones are not found at the free surface. Furthermore, it is noticed that more obvious high-SCS zones appear under the low discharge compared with the high discharge, especially at CS09. This may be attributed to the differences in the intensity of flow convergence and divergence under different submerging conditions of the central bars. When the central bars are exposed, flow convergence and divergence are strong and sharp flow steering occurs, thereby causing large SCS. By contrast, when the central bars are fully submerged, flow convergence and divergence are relatively weak, and thus small SCS is observed.

4.1.5. Turbulent characteristics

Turbulent characteristics reflect the performance of energy and momentum transfer activities in flow (Sukhodolov et al., 2017). Comprehensive analysis of turbulent characteristics is crucial as they greatly impact the incipient motion, settling behavior, diffusion pattern, and transport process of sediment. Here, the TKE and turbulent dissipation rate (TDR) of flow in the confluence-bifurcation unit are analyzed.

Figure 8 shows the distribution of TKE on various cross-sections in cases 1a and 2a. In the same way, Figure 10 shows the distribution of TDR. The values of TKE and TDR are nondimensionalized with mid-values of TKE = 0.005 m2·s−2 and TDR = 0.007 m3·s−2. In both cases 1a and 2a, the distributions of TKE and TDR show symmetrical patterns concerning the channel centreline. High-TKE and high-TDR zones exhibit a belt distribution near the channel bottom (McLelland et al., 1999; Ashworth, 1996; Constantinescu et al., 2011), indicating that turbulence primarily originates at the channel bottom due to the influence of bed shear stress. A sudden increase of TKE (Weber et al., 2001) and TDR occurs near the channel bottom at the confluence junction [Figure 8 and 9, CS08∼CS09] and from the entrance of the bifurcation junction (CS14) to the downstream bar head (CS15) (Figures 8 and 9).

Figure 8. Turbulent kinetic energy contours at eight different cross-sections in the confluence-bifurcation unit: (a) case 1a, (b) case 2a. TKE = turbulent kinetic energy. TKE’ =  dimensionless value of TKE, with regard to a mid-value of TKE = 0.005 m2·s−2.
Figure 9. Turbulent dissipation rate contours at eight different cross-sections in the confluence-bifurcation unit: (a) case 1a, (b) case 2a. TDR = turbulent dissipation rate. TDR’ =  dimensionless value of TDR, with regard to a mid-value of TDR = 0.007 m3·s−2.
Figure 10. Comparison of the distribution of time-averaged streamwise flow velocity along the flow depth at different cross-sections between the confluence-bifurcation unit and the single confluence. (a)∼(f) 1a vs. 1b, (g)∼(l) 2a vs. 2b.

Despite the common turbulent characteristics between cases 1a and 2a, additional high-TKE zones are found in the upper flow at the upstream bar tail (CS08), the confluence junction (CS09) and the downstream bar head (CS15) (Figure 8) when the central bars are fully submerged. The formation mechanism of these high-TKE zones near the water surface is more complicated, which may result from interactions of velocity gradient, secondary current structure and wall shear stress (Engel & Rhoads, 2017; Lu et al., 2023).

4.2. Comparison with single confluence/bifurcation cases

In this section, the results of a single confluence (cases 1b and 2b) and a single bifurcation (cases 1c and 2c) are compared with those of the confluence-bifurcation unit (cases 1a and 2a) under two discharges. Flow structure at CS08∼CS15 is mainly concerned below.

4.2.1. Comparison with single confluence cases

First, the patterns of time-averaged streamwise velocity, TKE and TDR within the single confluence (presented by contour plots in the supplementary materials) are assessed and then compared with those within the confluence-bifurcation unit (Figures 4, 8, and 9). It is found that distributions of these parameters are similar in the confluence-bifurcation unit and the single confluence from the upstream bar tail (CS08) to the entrance of the bifurcation junction (CS14), despite varying discharges. As the existence of the downstream central bar is the main difference between the single confluence and the confluence-bifurcation unit, this finding indicates that the downstream bar may have limited influence on the flow structure in the confluence-bifurcation unit. In other words, the flow structure in the confluence-bifurcation unit appears to be mainly shaped by the presence of the upstream bar, with its impact potentially reaching as far as the entrance of the bifurcation (CS14). Moreover, under the low discharge, the two high-velocity cores seem to merge later (at CS11) in the single confluence than in the confluence-bifurcation unit (at CS10), which indicates the convergence of two tributary flows may achieve a steady state faster in the confluence-bifurcation unit. To further elucidate the differences, results on the distribution of time-averaged streamwise velocity and TKE along the flow depth are discussed below.

4.2.1.1. Time-averaged streamwise velocity

Figure 10 shows the distribution of time-averaged streamwise flow velocity along the flow depth at different cross-sections. Note that α = 0.5 denotes the channel centreline and α = 0.7 denotes a position near the side banks. As only marginal differences are found at α = 0.3 and 0.7, only profiles at α = 0.7 are displayed for clarity.

Under the low discharge, no obvious difference in the distribution of time-averaged streamwise flow velocity is observed at the upstream bar tail (Figure 10(a)). At the confluence junction (Figure 10(b)), the velocities near the side banks (α = 0.7) are larger than those at the centre (α = 0.5) in both the confluence-bifurcation unit and the single confluence, which suggests that the two tributary flows have not sufficiently merged. The two tributary flows achieve convergence at CS11 in both the confluence-bifurcation unit and the single confluence (Figure 10(c)), with the velocity at the centre (α = 0.5) is larger than that near the side banks. Nevertheless, the velocities at the centre (α = 0.5) and near the side banks (α = 0.7) are closer to each other in the confluence-bifurcation unit than those in the single confluence, which represents less sufficient flow convergence in the confluence-bifurcation unit than in the single confluence. Therefore, it can be inferred that the convergence of two tributary flows may achieve a steady state faster in the confluence-bifurcation unit. After reaching the steady state, the velocity near the side banks (α = 0.7) is smaller in the single confluence than in the confluence-bifurcation unit despite close values at the centre (α = 0.5) (Figure 10(d,e)). This leads to a more pronounced disparity between velocities at the centre and near the side banks in the single confluence than that observed in the confluence-bifurcation unit. In other words, the high-velocity zone is more concentrated on the channel centreline in the single confluence, while the lateral distribution of flow velocity tends to be more uniform in the confluence-bifurcation unit. This may be attributed to the influence of the downstream central bar, which is further proved by comparing the velocity profiles at CS15 (Figure 10(e)).

As for the high discharge condition, from CS08 to CS14, the quantitative differences in velocity distribution between the confluence-bifurcation unit and the single confluence seem small. This indicates that the effect of morphology appears to be subdued when the central bars are fully submerged under the high discharge. It should be also noted that under both the low and high discharge, velocity profiles at the corresponding location exhibit the same shapes in the confluence-bifurcation unit and the single confluence, which indicates that the upstream confluence may dominate the flow structure in the confluence-bifurcation unit.

4.2.1.2. Secondary current

Figure 11 shows contour plots of SCS and the secondary current structure for single confluence cases. Compared with Figure 7, under both low and high discharge conditions, the distribution of SCS and the structure of helical cells in the confluence-bifurcation unit and the single confluence are very similar from CS08 to CS12 (Figure 7(a–d, g–j) and Figure 11(a–d, g–j)]. This indicates that the secondary current structure in the confluence-bifurcation unit exhibits certain consistent features when compared to those in the single confluence, thus proving that the effects of the upstream central bar may dominate the flow structure in the confluence-bifurcation unit. However, the secondary current structure at CS14 and CS15 is different between the confluence-bifurcation unit and the single confluence (Figure 7 and 11(e, f, k,l)). Under the low discharge, transverse flow is from the side banks to the centre and relatively high SCS is found near the side banks at CS14 in the single confluence, while the transverse flow is always from the centre to the side banks and SCS is relatively low at the corresponding sites in the confluence-bifurcation unit (Figure 11(e)). Under the high discharge, the helical cells near the side walls almost diminish in the single confluence, while they still exist in the confluence-bifurcation unit at CS14 (Figure 11(k)). Under both low and high discharges, the secondary current pattern at CS15 is similar to that at CS14 in the single confluence, while they are different in the confluence-bifurcation unit due to the existence of the downstream central bar. This comparison indicates that the existence of the downstream central bar can influence the upstream secondary current structure, nevertheless, the effects are fairly limited.

Figure 11. Secondary current at different cross-sections in the single confluence condition: (a)∼(f) case 1b, (g)∼(l) case 2b. The zero distance of each cross-section is located on the right bank.
4.2.1.3. Turbulent kinetic energy

Figure 12 shows TKE distribution along the flow depth at different cross-sections. Under the low discharge, in general, the maximum TKE tends to appear near the channel bottom in both the confluence-bifurcation unit and the single confluence. No obvious difference is observed at the upstream bar tail (CS08) (Figure 12(a)). Downstream this site (at CS09), the maximum TKE near the side banks (α = 0.7) is larger than that at the channel centre in the single confluence, while they are close to each other in the confluence-bifurcation unit (Figure 12(b)). This can also be attributed to the insufficient convergence of the two tributary flows. At CS11, flow convergence achieves a steady state in the confluence-bifurcation unit, while it remains insufficient in the single confluence. As flow convergence reaches a steady state at CS12, the maximum TKE in the single confluence exhibits a more concentrated distribution on the channel centre than that in the confluence-bifurcation unit (Figure 12(d)). This effect becomes more obvious downstream at CS14 (Figure 12(e)). The less-concentrated distribution of the maximum TKE in the confluence-bifurcation unit can be owing to the effects of the downstream central bar as well, which appears analogous to that mentioned in 4.2.1.1.

Figure 12. Comparison of the distribution of TKE along the flow depth at different cross-sections between the confluence-bifurcation unit and the single confluence. (a)∼(f) 1a vs. 1b, (g)∼(l) 2a vs. 2b.

Under the high discharge condition, two peaks of TKE appear in both the confluence-bifurcation unit and the single confluence (Figure 12(g–l)). Moreover, in both the confluence-bifurcation unit and the single confluence, from the upstream bar tail to the downstream bar head, the peak of TKE in the upper flow is larger at the channel centre (α = 0.5), while the peak of TKE in the lower flow is larger near the side banks (α = 0.7). However, the disparity between the TKE near the side banks and at the channel centre seems to be larger in the single confluence, while the TKE in the confluence-bifurcation unit takes a more uniform distribution. Even though, TKE profiles at the corresponding location exhibit highly similar shapes in the confluence-bifurcation unit and the single confluence, suggesting that the effects of channel morphology seem to be inhibited when the central bars are submerged under the high discharge.

4.2.2. Comparison with single bifurcation cases

Distributions of time-averaged streamwise velocity, TKE and TDR at corresponding cross-sections are also compared between the single bifurcation (see the Supplementary material) and the confluence-bifurcation unit (Figures 4, 8 and 9). Unlike the high similarity in flow characteristics exhibited between the confluence-bifurcation unit and the single confluence, significant differences are found between the confluence-bifurcation unit and the single bifurcation, especially at CS08∼CS14. On the one hand, the high-velocity zones are broader and asymmetrical concerning the channel centreline in the single bifurcation, with a belt-like and an approximately elliptic-like distribution respectively under the low and high discharges. By contrast, the high-velocity zone is a core that concentrates on the channel centre in the confluence-bifurcation unit. Moreover, the maximum velocity seems smaller in the single bifurcation than that in the confluence-bifurcation unit. On the other hand, the high-TKE belt near the channel bottom appears to be narrower in the single bifurcation than in the confluence-bifurcation unit, especially at CS08∼CS14 under the low discharge. Furthermore, additional high-TKE zones are found near the side walls at CS08∼CS11 in the single bifurcation, of which the scale is obviously smaller than those in the confluence-bifurcation unit. In addition, TKE at the channel centre is smaller near the free surface in the single bifurcation than that in the confluence-bifurcation unit. Nevertheless, the distributions of velocity, TKE and TDR seem to be similar in the confluence-bifurcation unit and the single bifurcation at CS15. As the existence of the upstream central bar is the main difference between the single confluence and the confluence-bifurcation unit, all the above findings indicate that the upstream central bar greatly influences the flow structure in the confluence-bifurcation unit. On the other hand, the downstream central bar may have a restricted influence on the flow structure in the confluence-bifurcation unit, whose impact may be limited to a range between the entrance of the bifurcation (CS14) and the downstream bar head (CS15). To further elucidate the differences, results on the distribution of time-averaged streamwise velocity and TKE along the flow depth are discussed below.

4.2.2.1. Time-averaged streamwise velocity

Figure 13 shows the distribution of time-averaged streamwise velocity along the flow depth at different cross-sections. Under the low discharge, distinct distribution patterns of flow velocity between the confluence-bifurcation unit and the single bifurcation are found at CS08, CS09 and CS11, which can be attributed to the effects of upstream flow convergence (Figure 13(a–c)). However, when the flow convergence reaches a steady state in the confluence-bifurcation unit (Figure 13(d–f)), the high-velocity zone is more concentrated in the confluence-bifurcation unit than in the single bifurcation due to to the significant influence of the upstream central bar on the flow structure. The velocity profiles at the downstream bar head can be a shred of evidence as well, with the maximum velocity larger at the channel centre but smaller near the side banks in the confluence-bifurcation unit than in the single bifurcation.

Figure 13. Comparison of the distribution of time-averaged streamwise flow velocity along the flow depth at different cross-sections between the confluence-bifurcation unit and the single bifurcation. (a)∼(f) 1a vs. 1c, (g)∼(l) 2a vs. 2c.

Under the high discharge, the distribution of velocity seems to exhibit limited differences between the two kinds of morphology, which indicates that the effects of channel morphology may be less noticeable when the central bars are fully submerged under the high discharge. Nevertheless, the velocity in the lower flow (below a relative depth of 0.45) shows a uniform lateral distribution in the single bifurcation, as the velocity profile at the channel centreline (α = 0.5) is in line with that near the side banks (α = 0.7) (Figure 13(g–l)). However, in the confluence-bifurcation unit, different velocity distributions in the lower flow can be observed at the channel centreline (α = 0.5) and near the side banks (α = 0.7). The foregoing results indicate that when the central bars are fully submerged, the high-velocity zones are more concentrated on the channel centreline in the confluence-bifurcation unit, while the lateral distribution of flow velocity within the single bifurcation tends to be more uniform, especially near the bifurcation junction (Figure 13(j,k)). This can also be attributed to the dominant influence of the upstream central bar over the downstream central bar.

It is also noted that the flow velocity distribution along the flow depth in the confluence-bifurcation unit is of a similar pattern despite varying discharges. As a critical point, the maximum velocity appears in the upper flow. The distribution above the critical point is approximately linear whereas it appears logarithmic below. By contrast, despite the similarity observed under the low discharge, the flow velocity distribution along the flow depth within the single bifurcation exhibits a distinct pattern under the high discharge, especially near the side banks (Figure 13(e–h)). On the one hand, the critical point in the upper flow no longer corresponds to the maximum velocity. On the other hand, the velocity distribution deviates from logarithmic below the critical point, with the maximum velocity appearing at a relative depth of 0.45. Succinctly, the distribution of streamwise velocity along the flow depth may retain the same pattern regardless of discharge levels in the confluence-bifurcation unit, while it may exhibit distinct patterns under different discharge levels in the single bifurcation.

4.2.2.2. Secondary current

Figure 14 shows contour plots of SCS and the distribution of secondary current for single bifurcation cases. In general, the value of SCS near the side banks at CS08∼CS14 (Figure 14(a–d, g–j)) in the single bifurcation seems smaller than that in the confluence-bifurcation unit (Figure 7(a–d, g–j)), especially under the low discharge. SCS distribution at CS14 is similar in the confluence-bifurcation unit and the single bifurcation under both low and high discharges. This difference in SCS distribution between the confluence-bifurcation unit and the single bifurcation indicates that the downstream bifurcation may have a restricted influence on the flow structure in the confluence-bifurcation unit. This influence is limited to a range between the entrance of the bifurcation (CS14) and the downstream bar head (CS15).

Figure 14. Secondary current at different cross-sections in the single bifurcation condition: (a)∼(f) case 1c, (g)∼(l) case 2c. The zero distance of each cross-section is located on the right bank.

In addition, the secondary current structure may also present different patterns in response to varying channel morphologies and discharge conditions. Under the low discharge condition, multiple unstable helical cells with asymmetrical distribution are formed from CS08 to CS12 in the single bifurcation (Figure 14(a–d)), while no obvious helical cells are found at CS14 and CS15 (Figure 14(d,e)). These findings are quite different from the stable and symmetrical helical cells at all cross-sections shown in the confluence-bifurcation unit (Figure 7). This difference may be attributed to the significant influence of the upstream central bar and the limited influence of the downstream central bar. Under the high discharge condition, only one pair of premature helical cells are found from CS08 to CS12 in the single bifurcation with their cores located near the side banks (Figure 14(e,f)). As the flow moves downstream, the helical cells gradually develop and become well-established (Figure 14(g,h)). These helical cells in the single bifurcation show symmetric cross-sectional distribution and a similar longitudinal development as in the confluence-bifurcation unit. However, in the confluence-bifurcation unit, two pairs of helical cells appear upstream of CS12 and CS14 and gradually fuse to one pair under the high discharge. As the ‘two-pairs’ structure in the confluence-bifurcation unit origins from the upstream confluence, the differences in the secondary current structure between the single bifurcation and the confluence-bifurcation unit under the high discharge can also be owing to the effects of the upstream central bar in excess of those of the downstream central bar.

4.2.2.3. Turbulent kinetic energy

Figure 15 shows the TKE distribution along the flow depth at different cross-sections. Under the low discharge, when the two tributary flows have not achieved sufficient convergence in the confluence-bifurcation unit, the maximum TKE is more concentrated in the single bifurcation (Figure 15(a–c)). As flow convergence achieves a steady state, more concentrated high-TKE zones appear at the channel centre within the confluence-bifurcation unit, confirming the finding that the effects of the upstream central bar reign over those of the downstream central bar in the confluence-bifurcation unit. However, things can be very complicated under the high discharge. For TKE distribution at the channel centreline, two peaks appear in the confluence-bifurcation unit with one close to the free surface and the other near the bed (Figure 15(g–l)). By contrast, only one peak near the bed is present in the single bifurcation. Therefore, a larger TKE can be found in the upper flow of the channel centreline in the confluence-bifurcation unit. For TKE distribution near the side banks, two peaks appear in both the confluence-bifurcation unit and the single bifurcation at CS09∼CS14 (Figure 15(h–l)). The upper peak is larger but the lower peak is smaller within the single bifurcation than those within the confluence-bifurcation unit. These significant discordances in TKE distribution under the high discharge further prove that the effects of the upstream bar on the flow structure in the confluence-bifurcation unit are more prominent than those of the downstream central bar.

Figure 15. Comparison of the distribution of TKE along the flow depth at different cross-sections between the confluence-bifurcation unit and the single bifurcation. (a)∼(f) 1a vs. 1c, (g)∼(l) 2a vs. 2c.

4.2.3. Further discussion of the comparisons

The above subsections have revealed significant differences in flow structure within the confluence-bifurcation unit and the single confluence and bifurcation, which directly result from the distinct channel morphologies and vary with the discharge conditions as well. These differences are summarized and further discussed below.

The distinctive morphology of a confluence-bifurcation unit plays a pivotal role in governing streamwise flow velocity distribution, secondary current structure, and turbulent kinetic energy distribution within the channel. Generally, from the upstream bar tail (CS08) to the entrance of the bifurcation (CS14), the flow structure in the confluence-bifurcation unit is highly similar to that in the single confluence, while it exhibits great differences (as shown in 4.2.2) between the confluence-bifurcation unit and the single bifurcation. This indicates that the upstream central bar greatly influences the flow structure in the confluence-bifurcation unit, with the effects spreading to the entrance of the bifurcation. At the downstream bar head (CS15), the flow structure (e.g. the transverse flow patterns) in the confluence-bifurcation unit exhibits high similarity to that in the single bifurcation. However, these similarities do not spread to upstream cross-sections, suggesting that the influence of the downstream central bar is limited at the bifurcation junction. In a word, the effects of the upstream central bar on the flow structure in the confluence-bifurcation unit are in excess of those of the downstream central bar.

However, despite the influence of channel morphology, discharge may also have some important effects on the streamwise flow velocity distribution. On the one hand, when the central bars are exposed under the low discharge, the high-velocity zone is less concentrated in the confluence-bifurcation unit than in the single confluence, while it is more concentrated in the confluence-bifurcation unit than in the single bifurcation. On the other hand, it is noticed that when the central bars are fully submerged under the high discharge, reduced differences in flow structure between the confluence-bifurcation unit and the single confluence/bifurcation are witnessed, and thus the morphology effect seems to be subdued.

4.3. Implications

The present work unravels the flow structure in a laboratory-scale confluence-bifurcation unit and takes the first step to further investigating morphodynamics in such channel morphology. Based on the comparison with a single confluence/bifurcation, the findings provide insight into the complex 3D interactions between water flow and channel morphology. The distinct flow structure in the laboratory-scale confluence-bifurcation unit may appreciably alter sediment transport and morphological evolution, of which research is underway. As the basic morphological element of braided river planform is confluence-bifurcation units, the present work should have direct implications for flow structure in natural braided rivers. This is pivotal for the sustainable management of braided rivers which deals with water and land resources planning, eco-hydrological well-being, and infrastructure safety such as cross-river bridges and oil pipelines (Redolfi et al., 2019; Ragno et al., 2021).

Notably, braided rivers worldwide (e.g. in the Himalayas, North America, and New Zealand) have undergone increased pressures and will continue to evolve due to forces of global climate change and intensified anthropogenic activities (Caruso et al., 2017; Hicks et al., 2021; Lu et al., 2022). In particular, channel aggradation caused by increased sediment supply as well as exploitation of braidplain compromise space for flood conveyance, making the rivers prone to flooding. In this sense, an enhanced understanding of the flow structure under high discharge when central bars are fully submerged is essential for mitigating flooding hazards.

5. Conclusions

This study has numerically investigated the 3D flow structure in a laboratory-scale confluence-bifurcation unit based on the LES model integrated in the FLOW–3D® software platform. Two different discharges are considered with the central bars fully submerged or exposed respectively when the discharge is high or low. Cases of a single confluence/bifurcation are included for comparison. The key findings of this paper are as follows:

  1. Several differences are highlighted in the comparison of the flow structure in the confluence-bifurcation unit between the two discharges. When the central bars are fully submerged under the high discharge, the mixing layer of two tributary flows is less obvious, and two high-velocity cores merge more rapidly as compared with those under the low discharge. Besides, flow separation zones are found neither at the confluence corner nor on both sides of the downstream bar when the central bars are fully submerged. Moreover, SCS seems to be smaller near the side banks under the high discharge than under the low discharge. Therefore, it is suggested that flow convergence/divergence is relatively weak in the confluence-bifurcation unit when central bars are fully submerged under the high discharge.
  2. From the upstream bar tail to the entrance of the bifurcation, the flow structure in the confluence-bifurcation unit is highly similar to that in the single confluence, while it exhibits great differences from that in the single bifurcation. Only at the downstream bar head does the flow structure in the confluence-bifurcation unit exhibit high similarity to that in the single bifurcation. Consequently, the effects of the upstream central bar on the flow structure in the confluence-bifurcation unit reign over those of the downstream central bar.
  3. Despite the influence of channel morphology, discharge may also have significant effects on the distribution of streamwise flow velocity. On the one hand, when the central bars are exposed under the low discharge, the high-velocity zone is less concentrated in the confluence-bifurcation unit than in the single confluence, while it is more concentrated in the confluence-bifurcation unit than in the single bifurcation. On the other hand, when the central bars are fully submerged under the high discharge, reduced differences in flow structure between the confluence-bifurcation unit and the single confluence/bifurcation are witnessed, and thus the morphology effect seems to be subdued.

It is noticed that the effects of other factors (e.g. confluence and bifurcation angles, bed discordance) on the flow structure in the confluence-bifurcation unit are not discussed here. Studies on these issues are warranted and reserved for future work.

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Consumer Products | 소비자 제품의 설계 및 제조

자유 표면 흐름은 가정과 사무실 환경 모두에서 사용되는 소비자 제품의 설계 및 제조에서 일반적입니다. 예를 들어, 병 채우기는 매일 대규모로 이루어지는 프로세스입니다. 생산 속도를 극대화하면서 낭비를 최소화하도록 이러한 프로세스를 설계하면 시간이 지남에 따라 상당한 비용 절감으로 이어질 수 있습니다. FLOW-3D는 또한 스프레이 노즐을 설계하고 다공성 재료 및 기타 소비재 구성 요소의 흡수 기능을 모델링하는 데 사용할 수 있습니다. FLOW-3D 의 공기 유입, 다공성 매체 및 표면 장력을 포함한 고급 다중 물리 모델을 사용하면 소비자 제품 설계를 정확하게 시뮬레이션하고 최적화하는 것이 쉽습니다.

충전재

유입된 공기는 생산 라인에서 용기를 채울 때 액체의 부피를 늘릴 수 있습니다. 아래 왼쪽 이미지는 높이가 약 20cm인 병을 1.2초 동안 채우는 것을 보여줍니다. 색상 음영은 액체에 있는 공기의 부피 분율을 나타냅니다. 병에서 혼합 시간이 짧고 혼합 정도가 높기 때문에 공기가 표면으로 올라가 빠져나갈 시간이 없었습니다. 그러나 오른쪽 이미지에서 볼 수 있듯이 약 1.7초의 추가 시간이 지나면 공기가 표면으로 올라가면서 발생하는 액체 부피 감소가 명확하게 보입니다.  FLOW-3D 의 드리프트 플럭스 모델을 사용하면 액체에 있는 기포와 같은 구성 요소를 분리하여 분리할 수 있습니다.

Tide® 병 충전의 빠른 평가

이 기사에서는  FLOW-3D를  사용하여 새로운 타이드 병 디자인의 충전을 모델링하는 방법을 설명하며,  Procter and Gamble Company의 기술 섹션 책임자인 John McKibben이 기고했습니다 .

지금 오전 9시인데 긴급 이메일을 받았다고 상상해보세요.

 방금 새로운 Tide® 병 디자인 중 하나가 손잡이에 채워지고 충전 장비에 문제가 생길 수 있다는 것을 깨달았습니다. 우리는 프로토타입 병이 없으며 몇 주 동안 없을 것입니다. 디자이너와 소비자는 디자인의 모습을 좋아하지만, 채우는 방식이 생산 시설에 쇼스토퍼가 될 수 있습니다.

이런 상황이 제게 주어졌을 때, 저는 3D 지오메트리(그림 1)의 스테레오 리소그래피(.stl) 파일을 요청하여 응답을 시작했고, 제가 무엇을 할 수 있는지 알아보고자 했습니다. 저는  FLOW-3D가  .stl 파일을 사용하여 지오메트리를 입력하고 충전을 위한 자유 표면 문제를 해결할 수 있을 것이라는 것을 알고 있었습니다. 저는 이것이 잠재적인 문제에 대한 좋은 정성적 이해를 제공할 것으로 기대했지만, 이 애플리케이션에 얼마나 정확할지에 대해 약간 불확실했습니다.

병의 기하학

시뮬레이션 설정 및 실행

오후 1시경에 저는 지오메트리 파일, 유량, 유체 특성을 받았습니다. 몇 시간 이내에 시뮬레이션이 실행되어 예비 결과가 나왔습니다. 저는 제 고객을 초대하여 결과를 잠깐 살펴보게 했고 그는 “사장의 상사”를 데려와서 살펴보게 했습니다. 그래서 저녁 5시경에 예비 결과를 살펴보고 원래 우려했던 것이 문제가 아니라는 것을 확인했습니다.

하지만 결과는 몇 가지 다른 의문을 제기했습니다. 손잡이에 채우면 유입 유체 제트가 많이 깨졌습니다. 이렇게 하면 유입 공기와 거품의 양이 늘어날 것이라는 걸 알았습니다(결국 세탁 세제를 채우고 있으니까요).  FLOW-3D  공기 유입 모델을 테스트하기로 했습니다. 이 모델은 원래 난류 제트용으로 개발되었고, 이 층류 문제를 살펴보면 얼마나 잘 수행될지 확신할 수 없었습니다.

병 채우기 시뮬레이션
그림 2: 채워진 결과
병 채우기 시뮬레이션 및 검증
그림 3: 실험 비교

그림 2는 공기 유입 모델이 있는 경우와 없는 경우 병 충전 모델의 결과를 보여줍니다. 유입 공기가 포함되면 충전 레벨이 상당히 증가한다는 점에 유의하십시오. 유입 공기가 병 상단에서 유체를 강제로 밀어내지는 않지만 공기 유입 정확도를 확인해야 할 만큼 충분히 가깝습니다. 그림 3은 공기 유입 레벨을 몇 주 후에 실행한 실험 이미지와 비교합니다(시제품 병이 출시된 후). 제트 분리 및 충전 레벨의 질적 일치는 우수하며 시뮬레이션이 병 설계를 선별하기에 충분히 정확하다는 것을 확인했습니다.

홍조

변기가 어떻게 작동하는지 궁금한 적이 있나요? 사실 꽤 복잡합니다. 손잡이를 밀면 물이 변기 그릇을 채우기 시작합니다. 변기 그릇의 유체 수위가 트랩 상단(변기 그릇 뒤) 위로 올라가면 웨어 유형의 흐름이 시작됩니다. 흐름이 ​​충분히 빠르면 변기 그릇에 거품이 형성되어 사이펀이 생성됩니다. 그 지점에서 사이펀이 변기 그릇에서 물을 끌어내고 변기가 물을 흘립니다. 많은 지역에서 물 절약은 중요한 문제이며, 저유량 변기는 가정과 상업용 모두에 필요합니다. 하지만 변기가 첫 번째 시도에서 제 역할을 하지 못하면 물 절약 목표는 달성되지 않습니다.  FLOW-3D를  사용하면 다양한 설계를 모델링하여 최적의 결과를 얻을 수 있습니다.

식품 가공

식품 가공 산업은 복잡한 유체, 일반적으로 비뉴턴 유체, 슬러리, 고체와 유체의 혼합물을 관리하여 분배 장비를 최적으로 설계하고 제조하기 위한 다양한 요구 사항이 있습니다. 이는 상업용 장비의 일관성과 내구성 및 품질에 필수적입니다. 또한 포장 디자인의 혁신을 통해 한 제품을 다른 제품과 명확히 구별할 수 있습니다. 예를 들어, 꿀, 케첩 또는 크리머를 깨끗하고 정확하게 분배하는 것은 소비자가 매장에서 내리는 선택일 수 있습니다. 운송 및 보관 요구 사항에는 더 나은 모양 엔지니어링과 더 많은 용기 재료 선택이 필요합니다. 1.5리터 물병이나 세탁 세제를 움직이거나 떨어뜨리는 동안의 유체 하중은 상류 설계의 중요한 부분이 될 수 있습니다.

꿀, 옥수수 시럽, 치약과 같은 점성 유체는 일반적으로 고체 표면에 닿으면 코일을 형성하는 경향이 있습니다. 이 효과는 관찰하기에 흥미롭고 재미있지만, 공기가 제품에 끌려들어 포장이 어려워질 수 있는 포장 공정에서는 환영받지 못할 수 있습니다. 코일링이 발생하는 조건은 유체의 점도, 유체가 떨어지는 거리, 유체의 속도에 따라 달라집니다.  FLOW-3D는  다양한 물리적 공정 매개변수를 연구하여 효율적인 공정을 설계하는 데 도움이 되는 정확한 도구를 제공합니다.

혼입

지난 수십 년 동안 컴퓨터화된 측정 및 시뮬레이션 기술의 발전으로 인해 혼합에 대한 이해가 크게 진전되었습니다. 유동 모델링 기술의 지속적인 발전 덕분에 혼합 장비의 유동 의존적 프로세스에 대한 자세한 통찰력을 CFD 소프트웨어를 사용하여 쉽게 시뮬레이션하고 이해할 수 있습니다. 오늘날 블렌딩에서 고체 현탁액, 재킷 반응기의 열 전달에서 발효에 이르기까지 광범위한 응용 분야가  FLOW-3D 의 혼합 기술을 사용하여 모델링됩니다.  FLOW-3D  시뮬레이션은 임펠러의 모든 구성과 모든 용기 형상의 혼합 조건에서 블렌딩 시간, 순환 및 전력 수와 같은 주요 혼합 매개변수를 평가하는 데 도움이 될 수 있습니다. 이러한 시뮬레이션은 실험적 방법을 사용하여 보완합니다. 이러한 장비의 유동 의존적 프로세스를 예측하고 이해하기 위해 CFD 소프트웨어를 사용하면 제품 품질을 향상시키고 많은 제품의 비용과 출시 시간을 모두 줄일 수 있습니다.

비뉴턴 유체

혈액, 케첩, 치약, 샴푸, 페인트, 로션과 같은 비뉴턴 유체는 다양한 점도를 가진 복잡한 유동학을 가지고 있습니다.  FLOW-3D  는 변형 및/또는 온도에 따라 달라지는 비뉴턴 점도를 가진 이러한 유체를 모델링합니다. 전단 및 온도에 따른 점도는 Carreau, 거듭제곱 법칙 함수 또는 단순히 표 형식의 입력을 통해 설명됩니다. 일부 폴리머, 세라믹 및 반고체 금속의 특징인 시간 종속 또는 틱소트로피 거동도 시뮬레이션할 수 있습니다.

핸드 로션 펌프는 종종 여러 가지 설계 문제와 관련이 있습니다. 펌프가 공기 공극을 가두지 않고 효과적으로 작동하고 로션의 연속적인 흐름을 생성하는 것이 중요합니다. 좋은 설계는 노력이 덜 필요하고 이상적으로는 로션을 원하는 곳으로 향하게 합니다. FLOW-3D 의 이동 객체 모델은 노즐이 아래로 눌리는 것을 시뮬레이션하여 저장소의 로션을 가압하는 데 사용됩니다. 로션의 압력과 로션을 추출하는 데 필요한 힘을 연구할 수 있습니다. 여러 설계 변수는 동일한 고정 구조 메시 내에서 쉽게 분석할 수 있습니다.

다공성 재료

다공성 매체에서 유체의 이동에 대한 수치 모델링은 어려울 수 있지만  FLOW-3D 에는 다공성 재료와 관련된 문제를 해결하는 데 유용한 기능이 많이 포함되어 있습니다. FAVOR™ 기술에는 사용자가 연속적인 다공성 매체를 표현할 수 있도록 하는 데 필요한 다공성 변수가 포함되어 있습니다.  FLOW-3D를 사용하면 사용자가 포화 및 불포화 흐름 조건을 모두 시뮬레이션할 수 있습니다. 거듭제곱 법칙 관계를 사용하면 불포화 흐름 조건에서 모세관 압력 과 포화  사이의 비선형 관계를 모델링  할 수 있습니다. 별도의 충전 및 배수 곡선을 사용하여 히스테리시스 현상을 모델링할 수 있습니다. 서로 직접 접촉하는 경우에도 서로 다른 다공성, 투과성 및 습윤성 속성을 서로 다른 장애물에 할당할 수 있습니다. 투과성은 흐름 방향에 따라 지정할 수 있으므로 사용자가 다공성 매체의 이방성 동작을 모델링할 수 있습니다. 유체와 다공성 매체 간의 열 전달을 고려할 수 있습니다.

분무

소용돌이 분무 노즐은 화학 세정제, 의약품 및 연료에서 액체를 분사하는 일반적인 방법입니다. 액체를 성공적으로 분무하려면 일반적으로 노즐로 침투하는 공기 코어를 형성해야 합니다. CFD는 최적의 분무 콘에 대한 기하학, 소용돌이 속도 및 유체 특성의 영향을 탐색하는 효과적인 방법입니다.

이 예에서 2차원 축대칭 소용돌이 흐름이 시뮬레이션되었습니다. 대칭 축을 따라 공기 코어가 노즐의 전체 길이를 거의 관통했습니다. 왼쪽 플롯은 평면에서 속도 분포를 나타내는 벡터가 있는 압력 분포입니다. 오른쪽 플롯은 속도의 소용돌이 구성 요소로 채색되어 있으며 빨간색은 더 높은 값을 나타냅니다.

분무 콘의 규모와 입자 크기가 너무 광범위하기 때문에 분무의 완전한 분무를 직접 계산하는 것은 불가능합니다. 또한 분무는 외부 교란, 노즐의 미세한 결함 및 기타 영향과 밀접하게 관련된 혼란스러운 프로세스입니다. 그러나 노즐을 떠날 때 분무 콘의 특성(예: 벽 두께, 콘 각도, 축 및 방위 속도)을 예측할 수 있다면 이러한 유형의 흐름 장치를 최적화하는 데 큰 도움이 됩니다.

소용돌이 스프레이 노즐
소용돌이 분무 노즐의 FLOW-3D 시뮬레이션

Products

자유 표면 흐름은 가정과 사무실 환경 모두에서 사용되는 소비자 제품의 설계 및 제조에서 일반적입니다.

예를 들어, 병 채우기는 매일 대규모로 진행되는 프로세스입니다. 생산 속도를 최대화하면서 낭비를 최소화하도록 이러한 프로세스를 설계하면 시간이 지남에 따라 상당한 비용 절감으로 이어질 수 있습니다. FLOW-3D는 또한 스프레이 노즐을 설계하고 다공성 재료 및 기타 소비재 구성 요소의 흡수 기능을 모델링하는 데 사용할 수 있습니다.

공기 혼입, 다공성 매질 및 표면 장력을 포함한 FLOW-3D의 고급 다중 물리 모델을 사용하면 소비자 제품 설계를 정확하게 시뮬레이션하고 최적화 할 수 있습니다.

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stencil

Experimental and numerical investigation of the squeegee process during stencil printing of thick adhesive sealings

두꺼운 접착제 실링의 스텐실 인쇄 중 스퀴지 프로세스에 대한 실험적 및 수치적 조사

 Fabiano I. Indicatti, Bo Cheng, Michael Rädler, Elisabeth Stammen, Klaus Dilger

ABSTRACT

To reliably compensate fuel cell stack tolerances, sealings with a layer thickness of at least 500 µm are necessary. Additionally, threads positioned at the upper region of the stencil apertures need to be integrated to print closed-loop designs under cycle times of as low as 3 seconds. All these requirements can intensify the occurrence of print defects and diminish the process stability. This paper addresses the issues of incomplete regions and air bubbles emerging during the squeegee process. It was detected that the cleanliness state of the stencil directly impacts the formation of incomplete regions by affecting venting conditions inside the aperture. Moreover, it was identified that bubbles are either transferred from the adhesive roll into the aperture or created due to interactions between the moving adhesive and stencil threads. Further, it was shown that bubbles cannot be completely eliminated using a stencil with threads but their size can remain smaller than 300 µm when printing with a new adhesive roll. Finally, distinct strategies were derived and verified experimentally to successfully print a basic sealing design. By introducing a small local gap between substrate and stencil, the entire sealing aperture was reliably filled without the need of a cleaning step.

1. Introduction

The structure of a single low temperature proton exchange membrane fuel cell (LT-PEMFC) fundamentally consists of a membrane electrode assembly (MEA) sandwiched between bipolar plates (BPPs) with sealings between these elements.[Citation1] Up to hundreds of cells can be combined into a stack to provide the required power output, which demands highly reliable manufacturing processes since a single defective cell can compromise the entire stack safety and performance.[Citation2] In light of this, the sealing is one specific component that has been receiving increased attention in the last years. Besides impeding gas and coolant leakages, the sealing is a crucial element in the overall stack concept for compensating assembly tolerances, which can reach up to 300 µm.[Citation3]

To achieve projected market volumes, stencil printing was identified as an attractive technique to meet cycle time requirements for the sealing production, which should be as low as 3 seconds.[Citation4–6] Despite that simple deposit structures achieving heights of up to 500 µm have been reported using solder pastes and conductive adhesives,[Citation7,Citation8] stencil printing is typically not adopted to apply layer thicknesses higher than 200 µm. In comparison, fuel cell sealing concepts demand a minimum layer thickness of 500 µm to safely offset the mentioned stack tolerances under compression ratios of up to 40%.[Citation9–12] Additionally, the sealings are characterized by significantly more complex contour designs to effectively seal ports, flow field and distribution channels of BPPs.

To print closed-loop designs, a so-called double-layer stencil can be adopted to apply the desired structure using a single print cycle.[Citation12–15] As shown in Figure 1, it consists of an upper layer with patterned threads that link different regions of the stencil and provide sufficient mechanical stability. These threads also support the second lower layer, which delineates the print design. This same stencil concept was previously tested using distinct configurations for the threads to print sealings for fuel cells.[Citation5,Citation6] These studies were mainly focused on investigating phenomena and print inconsistencies occurring during the separation process, such as the formation of air bubbles, filaments and excessive spreading. In contrast, print defects emerging during the squeegee process have not been thoroughly explored using this stencil concept.

Figure 1. Schematic of the stencil printing process consisting of a squeegee process (a) and a separation process (b). Perspective view of an aperture segment of a double-layer stencil made from stainless steel, based on.[Citation5,Citation6]

In this paper, a basic sealing design was used to identify relevant printing problems during the squeegee process, as shown in Figure 2. It presents approximate dimensions of 60 mm x 60 mm that should resemble the sealing design in the ports region of typical fuel cells. The squeegee direction corresponds to the indicated x-direction and the three sealing lines perpendicular to the squeegee direction were marked with the letters A, B and C for the sake of better differentiation. With this design, potential printing difficulties closer to the real application can be identified and evaluated more effectively. Based on preliminary experiments, two main print defects during the squeegee process were identified: incomplete regions and bubble formation.

Figure 2. Representative specimen of the basic sealing design with highlighted print defects (printed at 160 mm/s using condition SS–R1). The used squeegee direction corresponds to the indicated positive x-direction.

Incomplete regions are a known issue in stencil printing.[Citation16–20] Typically, small aperture dimensions and an insufficient pressure inside the print material are the main reported reasons for the emergence of this defect. In contrast, the formation of bubbles during the squeegee process is a less recognized phenomenon in stencil printing but can considerably impact the process reproducibility. In the field of screen printing, the presence of bubbles inside specimens was already reported by several studies.[Citation20–27] The mechanical agitation of the print material before the squeegee process and inherent interactions with the mesh were indicated as driving mechanisms for bubbles to appear.[Citation24–28] Yet, there is still very little consensus and a general lack of correlation with experimental data on describing how these bubbles are produced. Several computational fluid dynamics (CFD) simulations were developed to estimate the pressure distribution within the print material in front of the moving squeegee[Citation29–32] and the filling completeness of a given aperture volume,[Citation17,Citation18,Citation33,Citation34] where the latter has the additional advantage of being experimentally measurable. However, more comprehensive simulative approaches demonstrating the print material motion are still missing in the literature, which could provide valuable information to optimize the aperture filling behaviour and avoid print defects.

Based on this scenario, comprehensive print experiments were conducted to determine how print and stencil parameters influence the formation of incomplete regions and bubbles during the squeegee process. Characterisation methods using microscope images and micro-CT scans were applied to quantify and analyse these defects. Here, a stencil containing a lines design with and without threads was adopted, which allows to isolate the impact of threads in the print results. In addition, a new CFD model of the squeegee process was developed in FLOW–3D[Citation35] to visualize how these print defects emerge. The squeegee process was recorded in slow motion to analyse the adhesive roll behaviour and provide additional validation for the simulations. Based upon the combined experimental and simulation results, potential approaches to avoid these printing problems using the basic sealing design were derived and tested. Ultimately, the collected findings in this paper should enhance the understanding on decisive process and stencil parameters during the squeegee step, increasing the attractiveness of this technique for the application of sealings and adhesives in the industry.

2. Materials and methods

All preparation steps and experiments were conducted in laboratory conditions, at 23°C.

2.1. Stencil design

Two different stencils made from stainless steel (Christian Koenen GmbH, Ottobrunn, Germany) were used for the experiments. As illustrated in Figure 3, both stencils presented apertures with a 680 µm thick step and 120 µm thick threads, resulting in a stencil thickness of 800 µm. Here, a thicker stencil than the minimum layer thickness of 500 µm is required since a certain degree of spreading (height loss) of the applied material over the substrate always occurs. A very similar configuration was previously used to reliably reach the same layer thickness using several distinct adhesives as print material.[Citation6] The first stencil (a) corresponds to the one used to print the mentioned sealing design, and the second stencil (b) consists of 80 mm length lines with two different widths: 1.52 and 2.34 mm, which correspond to aperture aspect ratios (AR = width/height) of 1.90 and 2.93, respectively. A second pair of lines without threads was included in this stencil to separately examine how the addition of threads influences the print results. The line orientation relative to the squeegee direction was primarily adjusted at 0°. This considerably reduces the modelling and computational effort for the numerical simulations but still allows to capture the basic formation mechanisms of desired print defects.

Figure 3. Schematic of used stencils and detailed views of the aperture threads design.

2.2. Adhesive selection and print parameters

An ultraviolet (UV) curable acrylic was selected for all experiments, and it corresponds to adhesive B3, which was thoroughly characterized and tested previously by Indicatti et al.[Citation6] It exhibited very good printability, and its transparency facilitates the characterisation of bubbles inside the specimen. Moreover, this adhesive presented a reduced filament-stretching tendency, which avoided the formation of bubbles during the separation process.

The rheological properties of this adhesive required for the simulation model are reported in Table 1. The viscosity values were obtained with a stepped flow approach using a rheometer (MCR 500, Anton-Paar GmbH, Ostfildern, Germany) equipped with a plate-plate setup (25 mm diameter) and a 0.4 mm gap. The adhesive surface tension was measured with the Wilhelmy plate method (K100 Force Tensiometer, KRÜSS GmbH, Hamburg, Germany) using a platin-iridium Wilhelmy-plate (10 × 20 x 0.2 mm). These measurements were carried out at a constant speed of 0.01 mm/s and an immersion depth of 2 mm. An optical contact angle measurement system (DSA 10, KRÜSS GmbH, Hamburg, Germany) was used to determine the adhesive equilibrium contact angle with the stencil surface. The surface tension and contact angle measurements were conducted with adhesive B3 without fumed silica since the filled one used for the print experiments exhibited an apparent yield stress that prevented wetting and thereby reliable measurements with these methods. For additional information about this adhesive and rheological characterisations, see reference.[Citation6]

Equilibrium surface tension [mN/m]28.6 ± 0.1
Equilibrium contact angle of the adhesive on the stencil surface (smooth untreated stainless steel) [°]20.0 ± 1.5
Density [g/cm3]0.970
Shear rate [1/s]Steady-state viscosity [Pa∙s]
1021.1
15.615.4
25.111.5
39.88.9
63.17.1
1005.8
Table 1. Average and corresponding standard deviation of the adhesive properties incorporated into the model. The contact angle and surface tension measurements were repeated five times. The viscosity standard deviation remained below 5%, based upon three measurements.

The print experiments were performed with a commercial stencil printer (EKRA STS E5, ASYS Group, Dornstadt, Germany). Squeegee speeds of 40 and 160 mm/s were tested, and the separation speed kept unchanged at 1 mm/s to minimize the risk of print defects emerging during separation. A squeegee pressure of 0.5 N/mm was adopted to leave the stencil topside completely free of adhesive remains after the squeegee process, which is a required condition to not affect the final layer thickness. The used squeegee (RKS Carbon S HQ/30 65 Shore, RK Siebdrucktechnik GmbH, Rösrath, Germany) presented a length of 120 mm and a 4 mm chamfer (45°) at the tip. A squeegee holder of 60° was adopted, resulting in a nominal squeegee angle of 15°. This squeegee configuration was selected based on previous experiments to enhance the aperture filling and process reproducibility.

An adhesive roll was manually dispensed over the stencil using an adhesive gun to ensure comparable initial conditions. Every new adhesive roll was completely free of bubbles and its height was always between 8 and 12 mm. Large adhesive residues on the squeegee after printing were also removed when a new roll was added to prevent any further sources of bubbles. Another additional parameter evaluated was the aperture state and cleanliness of the stencil underside before printing. Considering the adhesive roll state, four different print conditions were investigated, as illustrated in Figure 4
: cleaned aperture with cleaned stencil and a new adhesive roll (CA–R1), pre-wetted aperture with cleaned stencil and a new adhesive roll (CS–R1), pre-wetted aperture with smeared stencil and a new adhesive roll (SS–R1), and pre-wetted aperture with smeared stencil and a three-times used adhesive roll (SS–R3).

Figure 4. Simplified illustration of the aperture cross section describing the four tested print conditions considering the state of the aperture, stencil underside and adhesive roll.

With exception of condition CA–R1, these correspond to relevant operation modes that have direct impact on the production cycle time and process efficiency. The cleaning procedure of the stencil was conducted manually by hand using absorbent wipes. It is important to emphasize that the illustrated smearings in Figure 4 were not considered as a print defect since these remained roughly smaller than 0.2 mm throughout the performed experiments. Moreover, the extent of smearings observed did not cause instabilities during the separation process, nor did it significantly affect print resolution due to the relatively large dimensions of the printed structures.

2.3. Specimens characterisation

All specimens were scanned using a light microscope (VHX-2000, Keyence, Osaka, Japan) with a resolution of 5.2 µm/pixel. To analyse the bubbles inside the specimens, ImageJ[Citation36,Citation37] was used for image processing and extracting the quantity and area of bubbles, as depicted in Figure 5
. Since the majority of the bubbles exhibited a circular shape, the measured bubble area was converted to an equivalent bubble diameter, which is a more convenient indicator. Frequency distribution histograms of the bubble diameter were derived from this data by combining the quantity of bubbles of three different specimens printed at identical conditions. Furthermore, micro-CT measurements (voxel-size: 10 µm) were conducted with a few representative specimens to obtain the precise position of the bubbles along the specimen height, which could not be assessed using the microscope.

Figure 5. Developed approach using ImageJ to characterize bubbles formed during the squeegee process.

3. Experimental results and discussion

3.1. Incomplete regions

The gap between stencil and substrate was measured and set to zero in order to keep the smearings at a minimum. Prominent smearings were not observed during all experiments. However, it was identified that the cleanliness state of the stencil before printing was associated with the emergence of incomplete regions, as reported in Figure 6. When the stencil was not cleaned before printing (conditions SS–R1 and SS–R3), 95.8% of the specimens exhibited incomplete regions. In contrast, only 6.3% of the specimens printed with a cleaned stencil (conditions CA–R1 and CS–R1) presented this defect. The incomplete regions were located exclusively at the line extremity that was last filled by the squeegee and appeared either as a large bubble that extends almost throughout the entire line width (Figure 7(a)) or as an empty space (Figure 7(b)).

Figure 6. Number of specimens exhibiting incomplete regions printed at 40 and 160 mm/s.
Figure 7. Representative specimens with incomplete regions at the line extremity (last part to be filled by the squeegee).

The occurrence of this defect was attributed to the lack of air venting at the line extremity due to the smearings at the stencil underside. Despite being small, the smearings can act like an additional seal between the stencil and substrate that impedes air to be expelled from the aperture during the squeegee process. This deduction is supported by the fact that large air bubbles were transferred into the adhesive roll when printing with a smeared stencil whereas such bubbles were not observed when it was cleaned. Figure 8 displays this phenomenon with two image sequences from the squeegee process recorded at a frame rate of 120 fps using a cleaned (a) and a smeared stencil (b). As can be seen, both adhesive rolls are completely free of bubbles before reaching the line extremity. The gap between stencil and substrate is intended to be zero, however, it still allows air to escape when the stencil is cleaned, which most of the time is sufficient to avoid filling defects and the formation of bubbles inside the adhesive roll. This phenomenon was identified using all four print conditions and was consistently replicated using both squeegee speeds.

Figure 8. Image sequences of the squeegee process using a cleaned (a) and smeared stencil (b) to compare the formation of bubbles inside the adhesive roll when the squeegee (40 mm/s) passes through the line extremity.

The same effect was observed when printing the sealing design, where large bubbles formed inside the adhesive roll when it was passing by the T-intersections and the line C of the sealing. Here, the detection of these bubbles was correlated with the presence of incomplete regions as well. The T-intersections can be considered as a more critical part to be completely filled due to their geometry and larger volume compared to the lines. Thus, the aperture design and its orientation relative to the squeegee direction can be considered as an additional influencing parameter, which directly determine the available time for filling. For instance, a few small incomplete regions were also formed at lines A and B, as shown in Figure 2. In this case, large bubbles did not appear inside the adhesive roll when passing through these lines, and the formation of these incomplete regions can be further associated with an insufficient time for the adhesive to fill the aperture or air to be expelled from it. This is reinforced by the observation that lines A and B of sealing specimens printed at 40 mm/s exhibited a better or even complete filling of those lines. Therefore, additional approaches to provide sufficient venting and time for filling are required to reliably fill all critical regions, which will be discussed later in section 5.

Variations of the squeegee speed and aperture AR or the presence of stencil threads did not notably impact the formation of incomplete regions, see Figure 6. All specimens were printed with a nominal squeegee angle of 15°, and experiments performed with larger (30°) and shallower (5°) angles did not result in any significant improvement of the aperture filling completeness. Increasing the vertical squeegee pressure to minimize the extent of smearings at the stencil underside also did not avoid incomplete regions. Indeed, an excessive squeegee pressure (>1 N/mm) might even enhance the restriction on air flow between stencil and substrate, leading to the emergence of incomplete regions using a cleaned stencil as well. This description better indicates the ‘cleanliness state’ as the decisive parameter on the formation of the print defect.

3.2. Bubble formation

Figure 9 reports frequency distribution histograms of the bubble diameter from specimens printed at two different squeegee speeds and aperture ARs. The measured quantity of bubbles was normalized by the total considered length of three specimens (240 mm) to enhance comparability. The histograms of specimens printed without threads were included as well. Yet, the following explanations are only considered for the specimens printed with threads if not indicated.

Figure 9. Frequency histograms of the diameter of the bubbles produced during the squeegee process.

Overall, the diameter of the bubbles did not surpass 1000 µm and the majority of them remained below 300 µm. By increasing the squeegee speed from 40 to 160 mm/s, the quantity of bubbles more than doubled in average considering the four tested print conditions. When the aperture AR is increased from 1.90 to 2.93, the average quantity of bubbles increased about 44%. In all considered cases, the cleaned aperture (CA–R1) produced the smallest quantity of bubbles. The bubble formation drastically increased with a pre-wetted aperture, as represented by the profiles of the cleaned (CS–R1) and smeared stencil (SS–R1). Here, the quantity of bubbles stayed relatively constant independent of the cleanliness state of the stencil (CS–R1 or SS–R1), and the distribution of the bubble diameter maintained a similar range as well. In this case, the largest discrepancy was notable in bubbles of up to 50 µm in diameter. Specimens printed with a smeared stencil (SS–R1) presented about twice the quantity of bubbles of this size when compared to those printed with the cleaned stencil (CS–R1). When printing with the same adhesive roll for the third time (SS–R3), the quantity of bubbles kept in about the same level of specimens printed with a new adhesive roll (SS–R1). One exception here was observed using the larger aperture AR at 160 mm/s, which produced approximately 50% more bubbles with the three times used adhesive roll. In addition, SS–R3 specimens were the only ones that exhibited very large bubbles with more than 300 µm in diameter.

By combining the results from the diagrams with the recordings of the squeegee process and specimens characteristics, three main mechanisms for bubble formation were identified, as shown in Figure 10. The first mechanism corresponds to bubbles that are not created due to the stencil threads but transferred from the adhesive roll into the aperture during the squeegee process. These bubbles are in general smaller than 300 µm and they hardly interact with stencil threads due to their size. This was confirmed by the fact that lines printed with the aperture without threads still presented bubbles but in considerable smaller quantities. In this case, lines printed with a new adhesive roll did not exhibit a significant quantity of bubbles independent of the squeegee speed. However, if a new adhesive roll was not added, the quantity of bubbles increased with the number of print cycles. Figure 11 presents an adhesive roll free of air bubbles before the squeegee process (a) and the same adhesive roll after three print cycles (b). The visible bubbles in the roll correspond to the ones that can be transferred into the aperture during the squeegee process. These bubbles might be created by random local instabilities during filling, but the main sources appear to be the air entrapment due to the lack of venting at the aperture extremity, as mentioned earlier, and due to the first contact or recontact between the squeegee and the adhesive over the stencil.

Figure 10. Identified bubble formation mechanisms during the squeegee process. The shown specimen segments were printed with an aperture AR of 2.93.
Figure 11. Adhesive roll over the stencil free of air bubbles before printing (a) and after three print cycles (b). In this case, the aperture with threads was used but very similar bubble characteristics inside the adhesive roll were observed when printing with the aperture without threads.

The second mechanism is very similar to the first one, with the difference that the stencil threads interact with large bubbles from the adhesive roll (shown in Figure 11(b)) when these are entering the aperture. This was deduced considering the regular position of large bubbles coinciding with the threads pitch and by comparing specimens printed with and without threads. This mechanism was responsible for producing the largest bubbles identified (>300 µm), which solely emerged inside specimens printed with threads. Thus, it is plausible to say that the interactions with the threads might increase the final air volume of bubbles coming from the adhesive roll since the characteristics of bubbles produced inside the adhesive roll were very similar independent of the threads presence. Alternatively, the threads might also locally change flow conditions, which could facilitate the transfer of larger bubbles from the adhesive roll.

Finally, the third mechanism is exclusively related to the presence of stencil threads, as these bubbles presented a very uniform pattern correlated with the threads pitch. Here, bubbles having a broad size range between 50 and 300 µm appearing near the centreline were the main type responsible for increasing the quantity of bubbles when a higher squeegee speed was used. Moreover, bubbles typically smaller than 100 µm in diameter emerged very close to the aperture walls and mostly in pairs. These are the primary contributors to the increase of the bubbles quantity when printing with a pre-wetted aperture (CS–R1 and SS–R1) instead with a cleaned aperture (CA–R1). The formation mechanisms of these two types of bubbles could not be captured experimentally but were assessed by the numerical simulations.

During the experiments it was also observed that bubbles can disappear after the separation process, as shown in Figure 12. Bubbles close to the aperture walls and threads might stay in the aperture or break due to the separation process since filaments are stretched near these regions. However, this phenomenon happened only occasionally and has a considerable smaller impact than the mechanisms previously presented. Yet, this phenomenon should be still mentioned since these bubbles might remain inside the aperture after separation and reappear in the following printed specimen. Thus, considering this and the three bubble formation mechanisms shown in Figure 10, it can be stated that all bubbles inside specimens printed with condition CA–R1 emerge due to the presence of stencil threads (Mechanism 3). Specimens produced with conditions CS–R1 and SS–R1 present bubbles that are majorly originated from Mechanism 3 since a new adhesive roll is used for these two conditions as well. Finally, specimens printed with condition SS–R3 exhibit bubbles from all mechanisms described before. It is possible to infer that all bubbles larger than 300 µm emerge due to Mechanism 2. However, excepting the small bubbles (<100 µm) close to the lateral walls exhibiting a uniform relative distance (Mechanism 3), the remaining bubbles cannot be categorized into their corresponding formation mechanism with certainty.

Figure 12. Comparison of the aperture before the separation process (left) and the final specimen (right) demonstrating how bubbles can disappear when located near the aperture walls and threads. This specimen was printed using condition SS–R1.

4. Modelling approach

This numerical study is focused on reproducing the basic formation mechanisms of incomplete regions and bubbles during the squeegee process. The simulations were performed only at a constant squeegee speed of 40 mm/s since it was already sufficient for both print defects to emerge. As previously discussed, a higher squeegee speed solely increased the quantity of bubbles but did not drastically change other characteristics of these print defects. For validation, the position and relative size of these defects were assessed alongside real specimens using microscope images and micro-CT scans. In addition, recordings of the adhesive motion during the squeegee process were compared with the simulation results to identify possible similarities. The CFD model was implemented in the commercially available software FLOW–3D,[Citation35] which applies the finite volume method (FVM) to numerically solve the conservation equations for mass and momentum. By neglecting turbulence effects and mass generation, these two equations can be described by the following expressions, respectively:

∂𝜌∂t+∇⋅(𝜌⁢𝒖)=0 (1)

∂𝒖∂𝑡+(𝒖⋅∇)⁢𝒖=1𝜌∇𝑝+𝜈∇2𝒖+𝒇 (2)

where 𝜌 is the adhesive density, 𝑡 is the time, ∇ is the divergence, 𝒖 is the velocity vector, and 𝑝 is the static pressure. 𝜈 corresponds to the kinematic viscosity and 𝒇 to the external body forces, such as gravitational and surface tension forces. To describe the free interface between the two fluids (adhesive and air), the volume of fluid (VOF) method is used:

∂𝛼∂t+∇⋅(𝛼⁢𝒖)=0 (3)

The variable 𝛼 represents the proportion of the cell volume occupied by adhesive, with 𝛼=0 signifying a cell entirely filled with air and 𝛼=1 indicating a cell entirely filled with adhesive. Consequently, a partially filled cell is defined as 0<𝛼<1. At each step time, the interface between the fluids can be dynamically reconstructed based on this cell information and is iteratively recalculated considered the updated moving squeegee location. For further details about the model implementation, we refer here to the software’s user manual.[Citation38]

4.1. Model description and assumptions

The same squeegee and threads dimensions from the experiments were incorporated into the model. To reduce computational effort, the aperture with 2.34 mm width (AR = 2.93) was modelled using an axisymmetric geometry, and only a line segment with 9.96 mm length was considered, as shown in Figure 13. A 3D model was adopted since a 2D model is not able to capture the adhesive flow perpendicular to the squeegee direction, which is a decisive phenomenon inside the aperture during the filling process. In order to investigate the impact of venting on the formation of incomplete regions and bubbles, two different simulation cases were established. In the first case, a 50 µm gap between stencil and substrate was integrated to allow air to escape from the aperture during filling. This should be equivalent to condition CA–R1 tested experimentally. In the second case, the model did not include a gap and should correspond to condition SS–R1. Here, it is important to note that the simulation model did not contain pre-wetted aperture walls or threads, which has to be considered when comparing it with experimental results.

Figure 13. Model overview with relevant dimensions and mesh details.

The following assumptions have been further considered for the model:

  1. The simulation domain contains only two phases (adhesive and air) with constant volumes, where the adhesive motion is simulated as an incompressible and laminar fluid flow.
  2. The stencil and squeegee are modelled as rigid bodies and exhibit no-slip boundary conditions. A horizontal translational speed is given to the squeegee to simulate the filling process, and the stencil remains stationary. There is no gap between the squeegee tip and the stencil.
  3. The shear thinning viscosity of the adhesive was defined in a tabular form between the shear rates of 10 and 100 s−1, see Table 1.
  4. The measured adhesive surface tension and its equilibrium contact angle with the stencil surface were included in the material model. The same equilibrium contact angle was adopted for the squeegee surface in the simulation.

The entire simulation domain was meshed with regular block shaped cells adopting a commonly used meshing strategy, where the cells exhibit reducing dimensions towards the aperture region and remain unchanged throughout the entire simulation time, as shown in Figure 12. To minimize repeated calculations, the squeegee process was modelled using a two-step approach. In the first step, the adhesive over the stencil rolls for about 25 mm up to near the aperture, reproducing the initial conditions from the experiments. The rolling motion of the adhesive reduces the viscosity due its shear thinning properties, which can impact the filling behaviour. This step was identical in both simulation cases, and the adhesive roll remained free of air bubbles. A coarser mesh with cell sides of up to 750 µm was applied for this step resulting in a simulation domain with about 1.8 million cells. In the second step, the adhesive starts entering the aperture, which corresponds to the simulation stage of main interest. Inside the aperture, the cells exhibited equal sides of 40 µm, which was adopted as a balance between computational time and accuracy. Using this mesh approach, the second domain contained about 3 million cells. The time step was automatically adjusted and ranged from 1 × 103 to 1 × 104 s during the first step while in the second one it stayed between 1 × 10−4 and 1 × 10−5 s.

4.2. Simulation results and validation

Figure 14 shows two simultaneous views from the symmetry plane and aperture bottom over the simulation time during the aperture filling with (a) and without (b) a gap between stencil and substrate. As can be seen, the adhesive is able to completely fill the aperture when a gap for venting is available. When the gap is removed, the right aperture extremity remains unfilled due to the enclosed volume formed between substrate, aperture walls and adhesive (t = 1.44 s). In this case, the formation of an air bubble inside the adhesive roll (t = 1.53 s) was captured by the simulation as well, agreeing with the experiment results presented in Figure 8(b). Another important phenomenon observed in the experiments and replicated by the model was the adhesive infiltrating the gap between the stencil and substrate, resulting in the formation of smearings that remained smaller than 0.15 mm in the simulation.

Figure 14. Simultaneous views (∆t = 0.09 s) from the symmetry plane and aperture bottom of the simulated squeegee process with (a) and without (b) a gap between stencil and substrate.

The simulations were also able to reproduce the formation of bubbles due to the presence of threads, as previously described by the third mechanism shown in Figure 10
. In the simulation case without a gap, bubbles with size ranging between 50 and 100 µm formed at the aperture walls and substrate surface with their relative distance coinciding with the threads pitch. When entering the aperture, the adhesive front is split by the threads into two smaller fronts that entrap air when reencountering at the substrate surface (t = 1.35 s). As the squeegee advances, the air is pushed towards the lateral walls but remains inside the aperture due to lack of venting. From micro-CT scans, it was possible to verify that these bubbles are touching the substrate surface as well, see Figure 15(b)
. Thus, these simulation results correlate very well with real specimens printed using condition SS–R1. Here is important to stress that the bubbles in the simulation are directly touching the aperture walls and would disappear in a subsequent separation process. In the real specimens, these bubbles are not contacting the aperture walls before separation, as shown in Figure 12
. This difference can be explained by the fact that the aperture in the simulation is not pre-wetted with adhesive before being filled, which differs from real SS–R1 conditions. Hence, the formation of these bubbles near the aperture walls results from the interplay between the incoming adhesive pushed by the squeegee and the adhesive that is pre-wetting the aperture walls. For comparison, these bubbles near the aperture walls did not appear when venting was available in the simulation, which also correlates with real specimens printed with CA–R1 conditions.

Figure 15. Qualitative comparison of representative specimens (scanned with microscope and micro-CT) and corresponding simulation exhibiting the final state of the aperture after the squeegee process with (a) and without (b) a venting gap. Bubbles produced due to the presence of threads (Mechanism 3) are visible in both experimental and simulation results, as indicated by the arrows. Two additional views (perspective and symmetry plane showing mesh cell size) of the two last threads (aperture extremity) from the simulated cases were included with the adhesive showing transparent properties to better visualize the generated bubbles.

Bubbles along the aperture centreline were formed in both simulation cases as well, see Figure 15. These bubbles are located close to or on the threads and exhibited sizes in the range of 100 to 200 µm, which fairly correlates with the experimental results. In the model, these bubbles only remained at the two last threads of the aperture. However, it is possible to observe bubbles forming around the other threads during filling (t = 1.44 s) but are broken after the squeegee tip passes through them (t = 1.62 s). In the experiments, these bubbles were visible all along the line length using conditions CA–R1 and SS–R1. Hence, the formation of these bubbles is unaffected by whether the threads are pre-wetted with adhesive or not. This discrepancy can be related to the apparent higher difficulty for the bubbles to detach from the threads in the model, which might be associated with insufficient small cell elements or simplifications in the material model.

To better understand this behaviour, Figure 16 presents the resulting adhesive velocity during the aperture filling for the case with a venting gap. The bubbles around the threads are formed approximately 4 to 6 mm in front of the squeegee tip (t = 1.46 s) and remain attached up until the squeegee tip reaches them (t = 1.55 s). The generated adhesive flow around the bubbles is not sufficient to release these from the threads. About 1 mm in front of the squeegee tip, a region with practically zero velocity is formed due to the flow direction change inside the aperture (t = 1.46 s). Immediately below the squeegee tip, the adhesive flow follows the squeegee direction but is gradually reorientated towards the substrate surface up until reaching the opposite direction of the squeegee. This reorientation leads to the formation of a backflow behind the squeegee tip, which causes a local overfilling of the aperture and contributes to break the bubbles around the threads (t = 1.55 s). When approaching the aperture extremity, the backflow region is affected by the aperture wall, which can explain why these bubbles only formed near the last two threads in the simulation.

Figure 16. Detailed symmetry plane view (∆t = 0.03 s) showing the resulting adhesive velocity for the simulation case with a venting gap between the stencil and substrate. The velocity vectors and fields are represented for a stationary observer fixed on the stencil.

This backflow was also observed experimentally but not in the same intensity as in the simulations. This difference can be related to the reduced viscosity range adopted and calibrated for the model, which used the viscosity value at 10 s−1 for lower shear rates. In addition, the neglected thixotropic properties of the adhesive might also have an impact on this response. Simulations using a larger range for the shear thinning viscosity of up to 0.1 and 1 s−1 were carried out but the higher viscosity avoided the reliable filling of the aperture, preventing any assessment of bubble formation during this step. Thus, the model is sensitive to changes in the viscosity range and should be recalibrated when, for instance, the squeegee speed is considerably increased. Additional simulation cases were not conducted since the formation of incomplete regions and bubbles was already detected and an appropriate investigation of the mentioned models deviations would go beyond the scope of this paper.

5. Sealing design with optimized print conditions

In this section, new strategies based on the presented experimental and numerical results were assessed to enhance the print conditions of the sealing design. Primary focus was placed on minimizing the process cycle time and on reducing print defects. The exhibited findings indicate that bubbles cannot be completely eliminated when using a stencil with threads. However, when using a new adhesive roll, the bubble diameter generally did not surpass 300 µm independent of the squeegee speed. Therefore, for every new specimen, a new adhesive roll was used. Despite producing more bubbles, the higher squeegee speed of 160 mm/s was favoured since these marginally impacted the process reliability. Yet, it should be emphasized that the influence of such bubbles on other sealing characteristics still needs to be quantified experimentally. For instance, previous studies have shown that voids inside composite and polymeric materials can notably diminish gas permeability, which on the other hand might be also compensated by increasing the sealing width or altering material properties.[Citation39–43] Hence, systematic investigations should be conducted in the future to assess the real performance of sealings printed with stencil printing and determine how process parameters can be actively adjusted to control gas permeability.

It is possible to reduce the number of stencil threads and consequently the quantity of bubbles. However, the mechanical stability of the stencil must be re-evaluated when altering the threads design. In this case, the stencil was not changed but the orientation of the sealing design relative to the squeegee direction was rotated by 20°. This angle was selected based on previous experiments to shift the position of incomplete regions to the sealing edges highlighted in Figure 17. Yet, solely adjusting the sealing orientation was not sufficient to prevent all filling defects, which can be considered the major cause for print inconsistencies. For this reason, four different approaches were investigated to achieve a completely filled sealing, as reported in Table 2. Here, only approaches using the least amount of cleaning were considered since adding a cleaning step before printing every single specimen can substantially increase cycle time and production costs. Thus, all approaches were conducted using a pre-wetted aperture with a smeared stencil (SS–R1 condition), and three specimens were printed in sequence to confirm the observations. It is also important to note that, despite rotating the sealing design at 20° or adding a second squeegee stroke, the observed quantity and size of bubbles did not notably change compared to sealings printed at 0° with a single squeegee stroke. Thereby, further bubble characterisations were not conducted to analyse the influence of these parameters.

Figure 17. Illustration of the rotated stencil with the sealing design and indication of regions exhibiting filling problems.
Approach descriptionSnap-off distance [mm]Formation of incomplete regions
(a) Single squeegee stroke with snap-off distance0.2Yes
(b) Double squeegee stroke0Yes
(c) Double squeegee stroke with snap-off distance0.2Yes
(d) Single squeegee stroke with local tape pieces (0.2 mm)0.2No
Table 2. Overview of evaluated approaches to eliminate incomplete regions in the sealing design.

The first approach was based on introducing a gap of 0.2 mm between stencil and substrate, also sometimes referred as snap-off distance.[Citation44,Citation45] It was expected that this gap could provide sufficient venting to fill the aperture entirely. However, no significant improvement in avoiding incomplete regions was observed compared to sealings printed without a gap, see Figure 18(a)
. Here, the squeegee vertical pressure closes the gap when it advances towards the aperture, and the smearings at the stencil underside act, as previously described, as an additional seal that inhibit air being expelled through it. Additional tests including the cleaning of the stencil enhanced the filling completeness of the T-intersection, but the last sealing edge (at line C) still remained incomplete.

Figure 18. Representative specimens printed with four different approaches to avoid the formation of incomplete regions: (a) single squeegee stroke with snap-off distance, (b) double squeegee stroke, (c) double squeegee stroke with snap-off distance, and (d) single squeegee stroke with local tape pieces.

The second and third approaches relied on using two squeegee strokes moving forwards and backwards. The idea here was that a second squeegee stroke could eliminate the incomplete regions by pushing adhesive from the opposite direction. However, this approach was insufficient to completely prevent this print defect as well. Adding a gap of 0.2 mm between stencil and substrate also did not improve the filling completeness. Instead of an incomplete filling, large bubbles usually larger than 1000 µm formed at these regions, see cases (b) and (c) in Figure 18. The main disadvantage of this approach is that it requires at least twice the time for the squeegee process. Yet, an additional squeegee stroke can be considered to have a smaller impact on production efficiency compared to introducing a cleaning step before every single specimen.

For the fourth approach, local gaps of about 0.2 mm height were introduced between the stencil and substrate by adding a small piece of adhesive tape near the edges with filling problems. The main difference to the first approach is that the gap created by the piece of tape does not close due to the squeegee vertical pressure or due to smearings. Thus, a small venting channel is maintained during the squeegee process that allows air to escape the aperture at those edges, ensuring the complete filling of the entire sealing, see Figure 18(d)
. The use of a tape piece was solely a simple method to prove the effectiveness of a local gap and more sophisticated approaches can be used, such as integrating a local elevation or channel on the substrate or stencil.[Citation46–48]

6. Conclusions

The squeegee process to print a basic sealing including relevant design features close to real fuel cell applications was optimized using experimental and numerical approaches. First, incomplete regions and bubbles forming during the squeegee process were detected as the main print defects. An additional stencil containing only lines with and without threads was used to isolate the formation mechanisms of these two defects. It was shown that the stencil cleanliness state considerably impacts the venting conditions inside the aperture during filling and thereby is determinant on the emergence of incomplete regions. Moreover, three main formation mechanisms of bubbles were proposed, evidencing that pre-existing bubbles inside the adhesive roll might be transferred into the aperture by the squeegee movement or produced due to interactions between the adhesive and stencil threads. The developed numerical model presented an overall good agreement with experimental observations and was able to reproduce the formation of incomplete regions and bubbles as well.

By combining experiment and simulation results it was verified that bubbles cannot be completely avoided when using a stencil with threads. However, by adding a new adhesive roll for every new print cycle, the quantity of bubbles can be reduced, and their diameter remained generally smaller than 300 µm, which was considered to have a minor impact on the process reliability. Based on these findings, four different print strategies focused on minimizing the print cycle time were assessed to eliminate incomplete regions emerging in the sealing design. By reorienting the aperture relative to the squeegee direction and maintaining a local gap during the squeegee process, this printing issue was prevented and the reproducible filling of the entire sealing was successfully achieved.

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Melt pool EBSD and X-ray computed tomography analysis results.

High-speed synchrotron X-ray imaging of melt pool dynamics during ultrasonic melt processing of Al6061

알루미늄 6061의 초음파 용융 처리 중 용융 풀 역학에 대한 고속 동기화된 X선 영상 촬영

Lovejoy Mutswatiwa, Lauren Katch, Nathan J Kizer, Judith A Todd, Tao Sun, Samuel J Clark, Kamel Fezzaa, Jordan S Lum, David M Stobbe, Griffin Jones, Kenneth C Meinert Jr., Andrea P Argüelles, Christopher M Kube

Abstract

Ultrasonic processing of solidifying metals in additive manufacturing can provide grain refinement and advantageous mechanical properties. However, the specific physical mechanisms of microstructural refinement relevant to laser-based additive manufacturing have not been directly observed because of sub-millimeter length scales and rapid solidification rates associated with melt pools. Here, high-speed synchrotron X-ray imaging is used to observe the effect of ultrasonic vibration directly on melt pool dynamics and solidification of Al6061 alloy. The high temporal and spatial resolution enabled direct observation of cavitation effects driven by a 20.2 kHz ultrasonic source. We utilized multiphysics simulations to validate the postulated connection between ultrasonic treatment and solidification. The X-ray results show a decrease in melt pool and keyhole depth fluctuations during melting and promotion of pore migration toward the melt pool surface with applied sonication. Additionally, the simulation results reveal increased localized melt pool flow velocity, cooling rates, and thermal gradients with applied sonication. This work shows how ultrasonic treatment can impact melt pools and its potential for improving part quality.

Introduction

Laser-based metal additive manufacturing (AM), a three-dimensional printing technique, can manufacture single components and structures with highly complex geometries, functionally graded alloys1, tailored microstructures2, and enhanced mechanical properties3. However, for most alloys, thermal cracking, porosity, and columnar grains4 reduce mechanical properties and prevent the widespread adoption of AM parts5. Establishing techniques for influencing solidification toward grain refinement could lead to parts with better mechanical properties and, ultimately, improve the reliability and quality of AM components6. The variation of AM process parameters, such as laser power, scan speed, and energy density7 allows control of thermal gradients and cooling rates, resulting in location-specific microstructural refinement2. However, process parameter optimization can be challenging, especially for alloys that are difficult to print. In addition to process parameter adjustment, inoculants can be added to the AM process to promote heterogeneous nucleation in the melt pool, resulting in grain refinement8. However, inoculants unavoidably change the chemical composition of the material, which can impact the mechanical strength of AM components9. In addition, inoculants can cause inclusions due to settlement and agglomeration10.

Other techniques for solidification control can be achieved by applying external fields such as electromagnetic11, mechanical12, or acoustic13 fields. In casting, electromagnetic fields were reported to increase cooling rates14, which resulted in reduced alloying element segregation and a more homogeneous macrostructure. Low-frequency mold vibration also succeeded in solidification manipulation during casting, resulting in a refined as-cast grain structure15. The application of high-intensity ultrasound on solidifying metals for molten metal processing during welding resulted in grain refinement and improved weld joint strength16. Nonetheless, using these techniques in laser-based metal AM is challenging because of the short length and time scales involved in melt pool dynamics and solidification17.

Following the work of Eskin18 and Abramov19, and applying successful grain refinement techniques in welding20, Todaro et al.21 recently demonstrated that high-intensity ultrasound can promote columnar to equiaxed grain transitions (CET) in laser AM fabricated Ti-6Al-4V and Inconel 625. As a result, components built with a fine, equiaxed grain structure exhibited increased yield and tensile strengths. One form of ultrasonic melt processing in AM involves laser metal powder consolidation on a substrate vibrating at ultrasonic frequencies (i.e., sonicated substrates). An applied ultrasonic frequency of 20 kHz on an AM-fabricated 316L stainless steel plate resulted in a noticeable decrease in grain sizes and an increase in random grain orientations22. Similarly, a reduction in mechanical property anisotropy and grain refinement along the build direction in wire arc AM was recently observed after ultrasonic treatment23. Ivanov et al.24 and Yoon et al.25 leveraged high-frequency pulsed laser irradiation to introduce high-intensity ultrasonic waves in the melt pool, resulting in microstructural refinement. Wang et al.26 used ultrasonic vibration-assisted AM to fabricate Inconel 718 parts and investigated the influence of four ultrasonic frequencies (i.e., 0, 25, 33, and 41 kHz) on microstructural refinement and mechanical properties. While ultrasonic melt processing at 25 kHz increased mechanical strength, the use of higher ultrasonic frequencies was observed to increase porosity and hardness. Wang et al.26 elucidated the effects of frequency, yet the effect of other ultrasonic wave parameters, such as vibration amplitude and acoustic intensity, on grain refinement, remained unclear.

The observed microstructural refinement in AM ultrasonic melt processing reported in the literature is hypothesized to result from increased nucleation rates and sites caused by acoustic cavitation and streaming induced in the melt pool. Acoustic cavitation and streaming have been suggested to compete with Marangoni convection, recoil pressure, and surface tension forces in the melt pool27, influencing solidification rates and thermal gradients and promoting columnar to fine equiaxed grain transitions28. Cavitation was observed in high-speed synchrotron X-ray imaging experiments within a controlled casting with ultrasonic treatment by Wang et al.29. They observed acoustic cavitation bubbles imploding in a Bi-8%Zn alloy on the solid-liquid interface, causing fragmentation of the solid phase in the mushy zone. Moreover, acoustic streaming was observed to disperse solid particles in the liquid, which have been reported to later act as solidification nuclei30. In AM, however, the melting and solidification processes occur rapidly, presenting spatial and temporal resolution challenges in direct cavitation observation. In their study focused on observing grain refinement mechanisms in ultrasound-assisted AM, Ji et al.31 stated that because of extremely high temperature, opacity, and short survival time, it is hardly possible to directly observe the process of ultrasound effect on the molten metal pool in AM through experiments. While direct observation of dendrite fracture would be challenging, recent high-speed X-ray imaging of keyhole dynamics in AM32 allows observation of cavitation bubbles directly during ultrasound-assisted AM.

In this work, high-speed synchrotron X-ray imaging at the Advanced Photon Source, Argonne National Laboratory was used to capture acoustic cavitation in high-temperature, viscous, and opaque sub-millimeter scale melt pools within an Al6061 sample. Ultrasonic treatment was observed to alter keyhole morphology, which could potentially reduce or eliminate porosity generated from keyhole tip collapse, in addition to reducing dynamic keyhole instabilities. Ultrasonic treatment influenced bubble dynamics, causing pore migration toward the melt pool surface. The reported results demonstrated the existence and influence of cavitation on laser-generated melt pool dynamics during ultrasonic melt processing, which was previously hypothesized by Todaro et al.21,22, Feilong et al.23, and Wang et al.26. The multiphysics Computational fluid dynamics (CFD) simulations using the Flow-3DⓇ platform showed an increase in melt pool flow velocity, thermal gradients, and cooling rates with applied ultrasonic treatment. This study provides direct evidence that acoustic cavitation effects are present in laser-generated melt pools and can be studied using high-speed X-ray imaging and CFD simulations. Thus, controlling acoustic cavitation, microstructure, and, henceforth, mechanical properties and part quality is now a closer reality33.

Results

In-situ synchrotron X-ray imaging of acoustic cavitation in melt pools

Figure 1 shows the primary features of the experimental setup. The experiment consisted of a continuous-wave ytterbium fiber laser with user set powers ranging from 100 to 560 W, the high-speed X-ray imaging system (see details in29), and an Al6061 sample mounted vertically on top of a Langevin transducer driven at its lowest order extensional resonance frequency of 20.2 kHz. Single-pulse X-ray images were collected at a rate of 50 kHz to observe melt pool dynamics, cavitation bubble dynamics, and solidification. X-ray computed tomography (CT) and electron backscattered diffraction (EBSD) were used to further characterize the pore structure ex-situ.

Fig. 1: Experimental setup.
Schematic diagram illustrating the experimental setup for high-speed X-ray imaging of melt pools on a vibrating substrate.

A representative X-ray image showing annotated melt pool features and vibration direction is shown in Fig. 2. X-ray absorption and phase contrast allowed easy identification of the solid/liquid transition region, vapor depression area, and microscale bubbles from cavitation. Supplementary Movie 1 shows the entire single-point melt pool and solidification process when the 350 W laser is applied for 3.34 ms without sonication. In addition, the video shows highly dynamic features such as bubble motion, melt pool size fluctuation, and keyhole initiation, growth, and fluctuation. The high spatial (i.e., 2 μm/pixel) and temporal (i.e., 50,000 frames per second) resolutions afforded by the high-energy synchrotron facility enabled direct quantifiable observation of the microscale bubble dynamics within the melt pool. The effect of the vibration could then be easily observed by conducting measurements with and without the active ultrasonic transducer. While the vibration was active, the X-ray imaging allowed direct measurement of the vibration amplitude of approximately 8 μm (more details on image processing and measurements are provided in the “Methods” section).

Fig. 2: Melt pool X-ray frame.
An X-ray frame showing the melt pool boundary at the solid/liquid interface, the keyhole or vapor depression morphology, the keyhole rim, hot spatter, a microbubble, and vibration direction. The video from which this frame was extracted is found in Supplementary Movie 1.

Figure 3a, b depict real-time X-ray image sequences of stationary laser-generated molten Al6061 pool dynamics without and with sonication, respectively. Supplementary Movie 2 is the associated high-speed videos containing the frames seen in Fig. 3a, b. In Fig. 3a, a narrow and deep vapor depression or keyhole can be observed in melt pools without sonication. Keyhole melt pools with these characteristics are known to be susceptible to keyhole porosity in AM when the tip of the vapor depression pinches off and forms a bubble32,34. Without sonication, bubbles were observed to settle at the bottom of the melt pool, where the solidification front could quickly freeze them, resulting in porosity. Figure 3a also shows strong fluctuations in keyhole depth, which is a characteristic of keyhole instability35.

Fig. 3: X-ray image sequences showing laser-generated molten Al6061 pools.
Melt pools (a) without and (b) with sonication. The six X-ray frames were taken at 0.02 ms intervals, beginning at 2.96 ms after the laser was turned on. The video from which these frames were extracted is found in Supplementary Movie 2.

The bubble density is shown to increase due to sonication as depicted in Fig. 3b and Supplementary Movie 2, proving the sonication leads to bubble nucleation in the liquid phase separate from the keyhole region. The bubbles in the melt pool with sonication rapidly nucleate, grow, oscillate, and sometimes implode, demonstrating cavitation bubble behavior. In addition, acoustic streaming effects were observed, where the molten metal flows in the vibration direction36,37. Sonication increased the average bubble diameter and promoted bubble migration towards the melt pool surface (Supplementary Movie 2). Bubbles with larger diameters were observed to implode at the melt pool surface, demonstrating degassing characteristics. In conventional AM, the melt flow-induced drag force dominates bubble dynamics38. Based on the observed bubble dynamics in melt pools with sonication, it can be pointed out that bubble growth due to cavitation increases the buoyancy force, overcoming the drag force that usually traps pores38, steering the bubbles toward the melt pool surface, and promoting degassing39. In addition, we speculate that primary and secondary Bjerknes acoustic radiation forces may exist in the melt pool, facilitating bubble translation toward the melt pool surface and causing degassing40. The concentration of porosity toward the melt pool surface induced by sonication might be convenient in metal AM because the remelting between successive layers could eliminate the residual porosity from previous layers.

Figure 3b also shows a reduction in the keyhole depth fluctuations and an increase in the keyhole tip radius with sonication. These phenomena resulted in the elimination of the keyhole tip pinch-off porosity32. However, sonication was observed to eject molten metal from the melt pool, as shown in the X-ray frame at 2.96 ms with sonication in Fig. 3b. Further investigation on the influence of substrate vibration directions (i.e., in-plane or out-of-plane vibration) and vibration amplitudes and frequencies could help minimize potential spatter in laser-based AM with ultrasonic melt processing and will be explored in our future research.

Influence of ultrasonic treatment on melt pool geometry and dynamics

The variations in the keyhole and melt pool depths, with and without sonication, are illustrated in Fig. 4. The melt pool depths, keyhole depths, and melt pool widths were measured from the point where sizable contrast difference between the liquid/solid and gas/liquid phases could be observed in the X-ray images. From Fig. 4a, it can be observed that the keyhole depth without sonication was larger than the sonicated keyhole. Melt pool and keyhole depths were shown to fluctuate at constant laser power41, indicative of instabilities34. The depth fluctuations were quantified as one standard deviation about the mean of the measured depths. With sonication, the melt pool depth standard deviation was 66.3 μm, whereas it was 111.6 μm without. Similarly, the keyhole depth standard deviation was 31.6 μm compared to 57.6 μm with and without sonication, respectively. This indicates ultrasonic treatment reduces fluctuations, leading to more stable dynamics. Without sonication, the melt pool began in conduction mode as shown in Fig. 4c from 2.8 to 4.25 ms, after which the melt pool transitioned into the keyhole mode. Conversely, with sonication, the melt pool started directly in keyhole mode. In both cases, the transition from conduction to keyhole mode occurred rapidly until stabilizing after about 5.5 ms.

Fig. 4: Influence of ultrasonic treatment on melt pool and keyhole geometry.
a Keyhole depth, b Keyhole aspect ratios (keyhole depth divided by fixed laser beam diameter of 80 μm), c Melt pool depths, and d Melt pool aspect ratios (melt pool width divided by depth based on measurements from X-ray images) with and without sonication. Red plain line shows measurements without sonication while black line with circular markers shows measurements with sonication.

Keyhole morphology also plays a role in melt pool dynamics and defect formation during laser-based metal AM processes. Fig. 4b shows the Keyhole aspect ratios calculated from measured depths divided by the 80 μm laser diameter35. These results show lower keyhole aspect ratios in sonicated melt pools. A high aspect ratio represents a deep and narrow keyhole with a needle-like tip, while a low keyhole aspect ratio represents a wide keyhole with an observable tip radius. A deep and narrow keyhole traps laser beam reflections at the bottom, leading to a J-shaped keyhole in moving laser scenarios32, which are susceptible to keyhole tip pinch-off porosity38,42. Therefore, ultrasonic treatment in metal AM can potentially eliminate one of the major keyhole porosity driving mechanisms by decreasing the keyhole aspect ratio and increasing keyhole-tip radius. Figure 4 d depicts the melt pool aspect ratio with and without sonication. In the absence of sonication, a high melt pool aspect ratio was observed when the melt pool was in conduction mode (i.e., from 2.7 to 4.4 ms) compared to the keyhole mode. There was not a significant difference in the melt pool aspect ratio due to sonication.

Laser energy absorptivity is known to be influenced by melt pool and keyhole depths43. Thus, the difference in melt pool geometries in ultrasonically treated melt pools relative to non-ultrasonically treated melt pools could result from the variation in the position of the laser focal point relative to the melt surface caused by the back-and-forth motion of the vibrating sample, promoting multiple laser beam reflections, resulting in improved laser energy absorptivity. This is possible at high vibration amplitudes to laser spot size ratios. However, in our case, a 16 μm peak-to-peak vibration amplitude and a laser spot size of 80 μm will not significantly influence laser energy absorptivity. Therefore, we speculate that the increased absorptivity could be due to the raised melt pool surface above the sample due to ultrasonic vibration causing the keyhole rim to rise while the recoil pressure keeps the bottom of the keyhole stationary. Hence, it results in deeper keyholes that promote multiple laser beam reflections on the vapor/liquid interface and increased absorptivity. In addition, the melt pool temperature could have increased because of bubble implosions, resulting in a larger melt region with applied ultrasound. Improved laser energy absorptivity and large melt pools are advantageous in metal AM to potentially reduce component build time. To investigate these claims further, CFD simulations were conducted to explain the impact of sonication on thermal gradients and cooling rates.

Multiphysics modeling of melt pool dynamics and solidification in ultrasound-assisted AM

High-speed X-ray imaging was able to provide real-time evidence of acoustic cavitation and melt pool dynamics in laser-generated melt pools driven by an external ultrasonic field. Additional insight into pressure distributions, thermal gradients, and cooling rate information is available through bridging the experiments with CFD simulations. In particular, CFD offers the ability to connect thermal properties to microstructural development. To further investigate the influence of ultrasonic treatment on solidification, we conducted multiphysics simulations of single-spot laser-generated melt pools with and without ultrasonic vibration using Flow-3DⓇ. Identical laser and ultrasonic parameters and substrate material used in the X-ray imaging experiments were adopted in the simulations. To reduce the simulation time, the laser duration was set to 0.8 ms compared to 3.4 ms in the experiments. The X-ray images were used to validate the simulations by directly observing melt pool and keyhole morphologies, cavitation bubbles, and solidification structures. Fig. 5a, b compare CFD simulated melt pools to melt pool geometries directly captured in X-ray imaging for the cases of without and with sonication. Deep and narrow keyholes observed with high-speed X-ray imaging in melt pools without sonication were replicated in the simulations. Similarly, an increased keyhole tip radius observed with X-ray imaging in melt pools with sonication was captured in the Flow-3DⓇ simulation. Supplementary Movies 3 and 4 show simulated keyhole dynamics for the two cases. Furthermore, Supplementary Movies 5 and 6 show the results of simulated melt pool dynamics. Similar to the melt pool dynamics undergoing sonication captured by X-ray imaging (i.e., Supplementary Movie 2), the simulated melt pools (i.e., Supplementary Movie 5) showed acoustic cavitation-driven bubble nucleation and implosion caused by pressure variation in the melt pool. Furthermore, the simulated solidification structure with ultrasonic treatment shows frozen cavitation-induced pores like those observed in X-ray imaging and X-ray CT. To further validate the simulations, the measured melt pool aspect ratios (width/depth) from X-ray images were compared with the simulated melt pool aspect ratios. Figs. 5c, d show melt pool aspect ratios, which were found to be closely consistent between simulations and experiments. The close agreement in aspect ratios speaks to the simulations accurately representing the laser energy transfer into the pool

Fig. 5: CFD melt pool simulation comparison with X-ray results.
a Melt pool simulation without and with sonication, b comparable experimental results without and with sonication, c Aspect ratios (depth/width) observed in the simulations, and d corresponding experimental aspect ratios.

Melt pool flow dynamics are primarily driven by surface tension, Marangoni convection, and recoil pressure. The application of ultrasound introduces acoustic streaming as an additional driving force. Simulations allowed us to quantify acoustic streaming by comparing velocity vectors at points in the fluid with and without applied ultrasonic treatment. Fig. 6a shows melt pool speed contours and velocity vectors with and without sonication. Supplementary Movies 7 and 8 show additional melt pool dynamics. The higher melt pool velocities in melt pools with sonication confirm that acoustic streaming is a major factor in fluid flow. Figure 6b shows the pressure distribution. Large pressure fluctuations are observed in the presence of sonication. The frames shown in Fig. 6b were taken from the simulation results during solidification and when the laser was switched off. This was done to decouple the sonication from thermal energy input. Supplementary Movies 9 and 10 show animations of pressure distribution in solidifying melt pools with and without sonication, respectively. It can be seen from Fig. 6b that the pressure variation in the melt pool with sonication promoted bubble nucleation. In addition, the influence of ultrasonic vibration can be observed in Fig. 6b with sonication, as ripples of high and low-pressure regions captured by the solidification. Without sonication, no significant pressure variation was observed during solidification. Acoustic cavitation bubble nucleation occurs when the localized pressure within a liquid drops below the vapor pressure of that liquid. Therefore, in Al6061 laser-generated melt pools, it can be seen that if the localized pressure within the melt pool drops below the vapor pressure of molten Al6061, nucleation of bubbles will occur. To investigate the influence of pressure variation on bubble nucleation during melting, the image sequence in Fig. 6c shows the pressure contours at a bubble nucleation site within the melt pool. A decrease in melt pool pressure was observed to result in bubble nucleation, while an increase in pressure promoted bubble implosion.

Fig. 6: CFD melt pool simulation results with and without sonication.
a Simulation frames showing velocity vectors of points in the liquid, b pressure distributions, c pressure field at the nucleation of a cavitation bubble and after the collapse.

Microstructure development is directly linked to solidification rates and thermal gradients. To investigate the influence of ultrasonic treatment on solidification conditions, we collected time history temperature gradients and cooling rates at a point within the melt pools with and without sonication. Figure 7a shows the point data probing location at which the time history of parameters that can be related to microstructural development was collected. Figure 7b shows the time history of pressure, cooling rate, thermal gradient, and velocity at the data probing point, with and without sonication. It can be observed that high pressure was observed in melt pools without compared to those with sonication. Conversely, higher cooling rates were observed in melt pools with sonication. Similarly, higher thermal gradients and fluid velocities were observed in melt pools with compared to those without sonication. Figure 7c shows the overall cooling rates and thermal gradients at each simulation time frame over the entire simulation. It can be observed that the overall thermal gradient did not respond to ultrasonic treatment. However, the overall melt pool cooling rate increased with the applied ultrasonic treatment.

Fig. 7: Melt pool thermal history from CFD simulation.
a Point data probing location. b The time history of fluid pressure, cooling rates, thermal gradients, and fluid velocities at the data probing point with and without sonication. c Melt pool thermal gradients and cooling rates at each time frame during the entire simulation with (red line plain line) and without sonication (black line with circular markers).

Acoustic cavitation characterization and influence on microstructural development

The primary aim of this article is to unveil the physics associated with ultrasonically driving the melt pool. A secondary aim and a topic of future work is to unveil conditions that lead to refined or tailored microstructures toward improved quality and performance of AM parts. Nevertheless, the solidification microstructures formed in melt pools with and without sonication were characterized using electron backscatter diffraction (EBSD). Fig. 8 a, b show the microstructures and crystallographic orientations of the grains in melt pools without and with sonication, respectively. Since EBSD is destructive, it is noted that the non-sonicated case is a different sample having a single point melt with the same laser power and duration as the sonicated melt pool case. For both samples, the melt pool boundary was traced using standard optical images, in which the melt region was clear (see Supplementary Figs. 6 and 7) and then superimposed on the EBSD grain map. Epitaxial grain growth and cracking along grain boundaries were evident in both cases. A qualitative reduction in grain size is observed in the sonication case but is difficult to ascertain because of the large pore structure as seen by the dark features in Fig. 8b.

Fig. 8: Melt pool EBSD and X-ray computed tomography analysis results.
EBSD grain map showing the solidification microstructure (a) without and (b) with sonication. c High-speed X-ray frame showing the final solidification structure and corresponding X-ray computed tomography visualization showing the porosity features and indications of the sonication-driven vibrations (seen by the red arrows).

Moreover, X-ray computed tomography analysis was performed on the final solidification structure (prior to EBSD) to characterize the influence of cavitation and acoustic streaming in sonicated laser-generated melt pools. An X-ray frame from the high-speed imaging showing the final solidification structure and a 3D isosurface of cavitation-induced porosity in the melt pool is shown in Fig. 8c. The X-ray computed tomography reveals evidence of frozen cavitation bubbles and ultrasonic vibration-induced-ripples in the melt pool (i.e., labeled by arrows in the X-ray computed tomography scan image). The ultrasonic wavelength in Al6061 at a frequency of 20.2 kHz was calculated to be 0.32 m, which is orders of magnitude higher than the melt pool depth and width. Thus, the micron scale ripples observed resulted from the sinusoidal variation in pressure from the ultrasonic vibration, which we have also observed in CFD simulations. This discovery calls attention to the influence of vibration amplitudes on cavitation in laser-based AM with ultrasonic treatment, which has not been previously explored. Figure 8c also shows a higher concentration of pores near the sample surface relative to the bottom of the melt pool. Thus, it is further corroborated that ultrasonic treatment causes bubble migration toward the melt pool surface.

Cavitation in ultrasonic molten metal processing has been explored by several researchers28,39,44,45, who conducted casting experiments on light metallic alloys. High-temperature cavitometry46,47 and high-speed imaging48 were used to establish a cavitation threshold in terms of acoustic intensity49. The first-order linear approximation of ultrasonic intensity, I, in an acoustic field is44

where ρ is the fluid density, c is the speed of sound in the fluid, A is the wave amplitude and f is the ultrasonic frequency. An acoustic intensity cavitation threshold of 100 W/cm2 was established for light metal alloys through casting experiments with ultrasonic melt processing44. In the experiments described in the literature29,45, an ultrasonic transducer horn was immersed in molten metal to introduce a propagating wave directly into the solidifying metal. Hence, the cavitation threshold could be established for sizable molten metal pools, and solidification rates would be significantly lower than those in AM processes. Nevertheless, the 100 W/cm2 cavitation threshold has been proposed for laser-based AM printing of light metallic alloys on sonicated substrates21,22,23,31,37,50,51,52,53,54,55,56. However, laser AM fundamentally differs from casting because of the submillimeter-size melt pools that exist for milliseconds owing to the associated rapid solidification rates. In casting, metal melting and solidification are separate processes, whereas melting, molten metal agitation, and solidification occur simultaneously in laser AM with sonication to generate acoustic cavitation. In addition, ultrasonic melt processing in casting involves wave propagation in a solidifying molten metal, while in AM, it involves local vibration of the molten metal. Such factors indicate different physical environments for cavitation in casting and AM. Therefore, validation of acoustic cavitation thresholds in laser-generated melt pools is needed, underpinning the importance of our technique.

Using a wave speed of 4718 m/s, density of 2586 kg/m3, wave amplitude of 8 μm, and frequency of 20.2 kHz in Equation (1) resulted in an acoustic intensity of 628.9 W/cm2. Our calculated acoustic intensity is above the established 100 W/cm2 cavitation threshold. However, cavitation was observed in the CFD simulations at an average acoustic intensity of 10 W/cm2, which is much lower than the established cavitation intensity threshold and the calculated intensity from Equation (1). Therefore, the established cavitation threshold from casting light metals with sonication overestimates the acoustic intensity required to induce cavitation in laser-generated melt pools on vibrating substrates. In the future, we will explore the influence of acoustic intensity on cavitation, porosity, and microstructure refinement.

Discussion

The application of ultrasound in solidifying melt pools in laser-based AM has been shown to promote columnar to equiaxed grain transition57,58 resulting in improved and homogenized mechanical properties and random crystallographic orientations50. By adopting observed microstructural refinement mechanisms in casting with ultrasonic treatment, acoustic cavitation and streaming28 have been hypothesized as the primary driving mechanisms of microstructural refinement in laser-based AM. Unambiguous evidence of cavitation in sub-millimeter scale and opaque laser-generated melt pools has been elusive until now. Here, the real-time influence of ultrasonic vibration on melt pool, keyhole, and bubble dynamics and the solidification of laser-generated melt pools was revealed. We also elucidated the impact of ultrasonic vibration at 20.2 kHz on melt pool and keyhole morphologies. Furthermore, we explained the potential influence of ultrasonic vibration on laser energy absorptivity and its benefits in AM. EBSD and XCT techniques were used to analyze the microstructures and solidification structures with and without applied sonication. The influence of ultrasonic vibration on melt pool flow velocity, pressure distribution, and solidification conditions with and without sonication was investigated using Flow-3DⓇ multiphysics CFD simulation software.

Melt pool and keyhole dynamics in laser-based AM processes influence porosity formation mechanisms38 and dictate the resulting solidification microstructures59 and mechanical properties60 of AM components. Marangoni flow, recoil pressure, and surface tension are some of the major driving forces governing melt pool and keyhole dynamics27. Generating melt pools on a substrate vibrating at ultrasonic frequencies introduces an additional force that drives melt pool flow in the wave propagation direction (i.e., acoustic streaming)37, which competes with existing forces in the melt pool. We used high-speed synchrotron X-ray imaging and Flow-3DⓇ simulations to show that acoustic streaming dominates the melt pool and keyhole dynamics in the laser-generated melt pool with sonication. Moreover, physical evidence of real-time acoustic cavitation in submillimeter-sized laser-generated melt pools was revealed in situ using high-speed X-ray imaging. Ultrasonic vibration was observed to increase bubble density in the melt pool and promote bubble migration toward the melt pool surface. X-ray computed tomography scan of the final solidification structure further demonstrated that ultrasonic vibration drives pores toward the melt pool surface and that vibration amplitude influences molten metal flow rather than ultrasonic wavelength.

Keyhole morphology analysis from high-speed X-ray images revealed a wide and shallow keyhole with applied sonication. A deep and narrow keyhole was observed in the case without sonication. Deep and narrow keyhole geometries are susceptible to keyhole tip collapse porosity32; therefore, by changing the keyhole morphology, ultrasonic treatment could potentially eliminate one of the major porosity formation mechanisms in laser AM. It is important, however, to note that sonication-induced cavitation resulted in porosity, as revealed by post-process EBSD and X-ray computed tomography scan results Therefore, these observations spark interest in further investigations on ultrasonic wave parameter optimization to leverage cavitation for porosity reduction and location-specific microstructural refinement. Furthermore, cavitation-induced porosity in AM ultrasonic melt processing could be used to manufacture porous structures for biomedical applications. Frequency modulation and the use of multiple ultrasound sources could potentially provide a certain degree of control over cavitation in laser-generated metal pools.

The application of ultrasonic vibration in laser-based AM was considered to increase the laser beam reflection from the liquid/gas interface in the melt pool because of increased keyhole depth caused by the raised keyhole rim. Increased laser beam reflection can potentially improve laser energy absorptivity61, resulting in larger melt volumes. On the other hand, applying ultrasonic treatment through out-of-plane vibration increased hot spattering due to the molten metal droplets pinching off the melt pool at peak positive and negative vibration amplitudes. Further optimizing vibration frequency, amplitudes, and direction can help mitigate hot spattering.

To investigate the influence of ultrasonic treatment on solidification and microstructural development, we utilized Flow-3DⓇ multiphysics simulations validated with real-time high-speed synchrotron X-ray images of melt pool dynamics. Flow-3DⓇ simulation results showed pressure variation-driven acoustic cavitation in melt pools with applied ultrasonic treatment. The pressure variation in melt pools with and without applied ultrasound was analyzed during the solidification phase (i.e., after the laser was switched off) using color maps. Ultrasonic treatment was also observed to promote high melt pool velocities, cooling rates, and thermal gradients. Higher thermal gradients and melt pool velocities create stronger cooling effects and promote heterogeneous nucleation and grain refinement.

In summary, we provided evidence of acoustic cavitation in laser-generated molten metal pools on sonicated substrates using both high-speed X-ray imaging and CFD simulations. We further showed that ultrasonic treatment influenced melt pool and keyhole dynamics and could potentially eliminate some major keyhole porosity driving mechanisms. We also demonstrated through simulations that ultrasonic treatment creates favorable conditions for heterogeneous nucleation and grain refinement. These results facilitate further investigation into the influence of ultrasonic treatment on microstructural refinement and mechanical property improvement in laser-based AM processes.

Methods

Materials and sample preparation

Al6061 alloy was chosen as the material of interest because of its widespread usage in lightweight material industries such as automotive, aerospace, and many others. Unfortunately, Al6061 is extremely challenging to use in welding or AM because of thermal cracking. Thus, this research has a broader goal of investigating techniques to improve the printability of such alloys. Moreover, manufacturing methods, processes, and conditions highly influence Al6061 grain sizes and mechanical properties, as demonstrated by Eskin44 in the ultrasonic treatment of light metallic alloys. Secondly, applications of Al6061 as an additive manufacturing material have been limited because of residual stress build-up62. Lastly, Al6061 has liquidus and solidus temperatures of 660 °C and 595 °C, respectively, enabling sizable mushy zones necessary for effective and efficient ultrasonic treatment. Al6061 samples with a length of 20 mm, a height of 12 mm, and a thickness of 1.5 mm were used in our experiments. A thickness of 1.5 mm allowed adequate X-ray absorption contrast between the solid, liquid, and gaseous phases during laser melting, making it easy to identify melt pool features (i.e., vapor/gas depression, bubbles, solid-liquid interfaces.).

Ultrasonic wave generation system

Al6061 specimens were adhered to an ultrasonic transducer horn using an adhesive, as illustrated in Supplementary Fig. 1. A 20.2 kHz high-power ultrasonic transducer by Hangzhou Altrasonic Technology Co., Ltd., with a maximum power of 2000 W, was used in this study. The ultrasonic system consisted of a horn, piezoelectric elements, and an ultrasonic generator. The ultrasonic generator converts the power source into high-frequency and high-voltage alternating current and transmits it to the piezoelectric elements, which convert the input electrical energy into mechanical energy (i.e., ultrasonic waves). In our experiments, the transducer generated a continuous longitudinal wave and was operated at the horn’s resonant frequency of 20.2 kHz, with a power of 600 W and vibration amplitude of 8 μm. The transducer power and short time intervals of ultrasonic wave application were chosen to prevent the transducer horn overheating, which may influence melt pool solidification rates and thermal gradients. A custom-designed relay apparatus operated from outside the experimental hutch controlled the transducer on/off switching and the duration of ultrasonic vibration.

X-ray imaging and laser melting system

Experiments were conducted using the high-energy ultrafast synchrotron X-ray imaging system available at the Advanced Photon Source, Argonne National Laboratory, USA. The 32-ID-B beamline at the Advanced Photon Source offers a state-of-the-art high-speed X-ray imaging technique. The intense undulator white beam allows ultrafast image acquisition rates of 50 kHz with a spatial resolution of 2 μm/pixel in a field of view of 1.8 × 1 mm. In addition, a continuous-wave ytterbium fiber laser (IPG YLR-500-AC, IPG Photonics, Oxford, USA, wavelength of 1070 nm, maximum output power of 560 W) and a galvanometer scanner (IntelliSCANde 30, SCANLAB GmbH., Germany)38 were integrated to perform stationary laser melting on bare Al6061 samples. A laser power of 350 W was used in the experiments. Experiments were conducted in the following sequence: the X-ray shutter and camera were first opened to initiate image acquisition. Secondly, the ultrasonic transducer was switched on, and lastly, the laser was turned on. The experimental setup and sequence allowed the sample melting, vapor depression development, and melt pool solidification occurring in an acoustic field to be captured via X-ray imaging. The laser was switched on for 3.34 ms for both cases with and without ultrasonic treatment.

EBSD and X-ray computed tomography analysis

Electron backscattered diffraction patterns (EBSPs) were obtained in the Oxford scanning electron microscope (SEM) instrument by focusing an electron beam on the Al6061 sample. The final polishing of the Al6061 sample was conducted using the Final A polishing pad with 0.04-micron colloidal silica suspension for 12 h. The sample was tilted to approximately 70 degrees with respect to the horizontal, and the diffraction patterns were imaged on a phosphor screen. The images were captured using a low-light CMOS camera. A 1.5-micron step size was used for both samples with and without ultrasonic treatment. The X-ray computed tomography scan was conducted with a Zeiss Xradia Versa 620 CT system using a source accelerating voltage of 80 kV. Images were acquired over 2 h at a voxel size of 1.5 μm and reconstructed using Zeiss proprietary software. The dicom image files were then processed using MATLAB to reveal the influence of ultrasonic vibration on the final solidification structure of the melt pools. A 3D view of sonication-induced pores showing the influence of ultrasonic vibration amplitude on the melt pool solidification was captured using the 3D volume viewer tool in MATLAB.

Image processing

MATLAB image processing toolkit and ImageJ were utilized in the X-ray image analysis. MATLAB codes were developed to normalize a sequence of X-ray images with their average pixel values. To create an X-ray image sequence with a uniform gray value, images within a 5% range of gray values were grouped together. A normalization operation was applied to each distinct group, which allowed enhanced visualization of melt pool features, keyhole dynamics, and bubble motion. Measurements of the melt pool and keyhole depth changes and bubble motion characterization were conducted using ImageJ. Maximum depths and widths on each X-ray frame measured in ImageJ were used to characterize melt pool and keyhole dynamics. The peak-to-peak vibration amplitude on the Al6061 sample surface was also measured as 16 μm using ImageJ.

Multiphysics computational fluid dynamic simulations

A 1 mm2 domain with a 4-μm mesh size was used in the CFD simulations on the Flow-3DⓇ platform. The simulation finish time was set at 1.3 ms, and the laser on time was set at 0.8 ms. Similar to our experiments, the laser power used in the simulations was 350 W, with a laser spot size of 80-μm. Ultrasonic vibration was introduced by defining a non-inertial reference frame with harmonic oscillations on the melt volume (i.e., substrate). The oscillation frequency was set at 20.2 kHz and an amplitude of 8-μm. The execution time for each simulation with and without ultrasonic treatment was one day and 16 h, with each model generating a 2.5 TB output data file (More details on the simulation setup, boundary conditions, and governing equations are provided in Supplementary Material Section 2).

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Propagation Velocity of Excitation Waves Caused by Turbidity Currents

혼탁류에 의한 자극파의 전파 속도

Guohui Xu, Shiqing Sun, Yupeng Ren, Meng Li, Zhiyuan Chen

Abstract

Turbidity currents are important carriers for transporting terrestrial sediment into the deep sea, facilitating the transfer of matter and energy between land and the deep sea. Previous studies have suggested that turbidity currents can exhibit high velocities during their movement in submarine canyons. However, the maximum vertical descent velocity of high-concentration turbid water simulating turbidity currents does not exceed 1 m/s, which does not support the understanding that turbidity currents can reach speeds of over twenty meters per second in submarine canyons. During their movement, turbidity currents can compress and push the water ahead, generating propagating waves. These waves, known as excitation waves, exert a force on the seafloor, resuspending bottom sediments and potentially leading to the generation of secondary turbidity currents downstream. Therefore, the propagation distance of excitation waves is not the same as the initial journey of the turbidity currents, and the velocity of excitation waves within this journey has been mistakenly regarded as the velocity of the turbidity currents. Research on the propagation velocity of excitation waves is of great significance for understanding the sediment supply patterns of turbidity currents and the transport patterns of deep-sea sediments. In this study, numerical simulations were conducted to investigate the velocity of excitation waves induced by turbidity currents and to explore the factors that can affect their propagation velocity and amplitude. The relationship between the velocity and amplitude of excitation waves and different influencing factors was determined. The results indicate that the propagation velocity of excitation waves induced by turbidity currents is primarily determined by the water depth, and an expression (v2 = 0.63gh) for the propagation velocity of excitation waves is provided.

Keywords

turbidity current; excitation wave; propagation speed; flume test; FLOW-3D

1. Introduction

Submarine turbidity currents, often referred to as underwater rivers, are important carriers that transport terrestrial sediments to the deep sea [1,2,3,4,5,6,7]. These turbidity currents, carrying a large amount of silt and sand, not only have strong erosive capabilities on the seabed [8,9,10], but also pose a threat to underwater communication cables, resulting in significant economic losses [11,12,13]. For example, the 2006 Pingdong earthquake in Taiwan caused the rupture of 11 submarine cables within the Kaoping Canyon, resulting in a slowdown in network speed in Southeast Asia for 49 days and requiring the deployment of 11 cable ships for repairs [13,14,15]. Investigating the velocity and patterns of turbidity currents in submarine canyons is of great significance for the protection of infrastructure such as pipelines and cables in these canyons.
One of the main methods for quantitatively studying the velocity of turbidity currents in submarine canyons is to infer their speed through cable ruptures. The first confirmed occurrence of cable rupture caused by a turbidity current was in 1929, when the Grand Banks earthquake triggered the continuous rupture of 12 submarine cables. Inferred maximum turbidity current velocities reached 28 m/s [16,17,18]. Subsequently, multiple cable rupture incidents caused by turbidity currents have occurred worldwide. Table 1 summarizes the inferred maximum turbidity current velocities from these cable rupture incidents.

EventMaximum Turbidity VelocityReferences
18 November 1929 Grand Banks earthquake28 m/s[16,19,20,21]
1953 Suva earthquake in the Fiji Islands5.1 m/s[22]
The Orleansville earthquake of 9 September 1954, Algeria20.6 m/s[23]
Earthquake, Solomon Islands, Western Pacific, 23 December 196610.3 m/s[24]
Incident at Nice airport, France, 16 October 19797 m/s[25]
Taitung earthquake, 22 August 20029.8 m/s[26]
21 May 2003 earthquake in Algeria15.8 m/s[27]
The Taitung earthquake of 10 December 200316.5 m/s[26]
The Taitung earthquake of 18 December 200318.6 m/s[26]
Pingtung earthquake on 26 December 200620 m/s[28]
Typhoon Morakot on 7–9 August 200916.6 m/s[29]
The 15 January 2022 eruption of Hunga volcano33.9 m/s[30]
Table 1. Cable breakage events caused by turbidity currents worldwide.

Previous studies have shown that the maximum vertical velocity of high-concentration turbidity currents in water does not exceed 1 m/s, and the maximum downward velocity of spherical particles in water does not exceed 10 m/s [31]. The maximum velocity of professional athlete Usain Bolt in the 100 m sprint on land is 9.58 m/s, while dolphins in the ocean can reach speeds of up to 20 m/s. Deep-sea turbidity currents, characterized by a small density difference compared to water, are primarily driven by the gravitational component along the direction of flow. However, factors such as bed friction also need to be considered. The driving force behind turbidity currents is primarily the density difference between the turbulent flow and the surrounding water, as well as the gravitational downslope component. Previous studies have detected a maximum sediment concentration of 12% in the basal layer of turbidity currents [32]. However, even high concentrations of suspended sediment, such as 1720 g/L, in seawater with a density of 1020 g/L, do not exceed a maximum vertical velocity of 1 m/s [33]. Similarly, spherical particles also have a maximum settling velocity in water of less than 10 m/s [33]. Turbidity currents, being density-driven flows, have relatively low density differences compared to water, and the gentle slope of submarine canyons also contributes to a smaller gravitational downslope force. Additionally, the influence of bed friction and other factors related to sediment deposition needs to be considered. It is incredible to think that turbidity currents can achieve flow velocities as high as 28 m/s [16,18,28,34,35].
When submarine landslides occur on continental slopes, the sliding mass entering the bottom of submarine canyons can cause the destruction of soft sediment beds. The mixing of sliding or flowing sediment with water forms turbidity currents. Turbidity currents exert pressure and propel the water ahead, forming an excitation wave. This aligns with Paull’s hypothesis that in the course of turbidity currents, a high-pressure zone is formed ahead, capable of causing an increase in pore water pressure in the sediment ahead [36]. Similar to surging waves, the excitation waves generated can propagate downstream along the submarine canyon, with a propagation velocity much greater than the velocity of turbidity currents [31]. The rapid propagation of excitation waves can exert a force on the seafloor of the submarine canyon, causing the resuspension of sediment in front of the head of the turbidity currents, which may lead to the formation of secondary turbidity currents at some downstream locations. The distance between the secondary and initial turbidity currents is actually the propagation distance of the excitation waves, rather than the journey of the initial turbidity currents. Therefore, the speed of the excitation waves within this distance is mistakenly considered as the velocity of the turbidity currents (see Figure 1). This may explain why the velocity of the turbidity currents as deduced from cable breakages is so high.

Figure 1. Diagram of excitation wave propagation due to turbidity current (v1 is the velocity of turbidity current. This refers to the ratio of distance to time experienced by a turbidity current mass moving underwater. v2 is the velocity of secondary turbidity current: the rapidly propagating excitation wave applies a force on the submarine canyon floor, leading to the destruction of the soft sediment floor and the secondary turbidity current. v is the propagation velocity of the excitation wave; this refers to the propagation velocity of the turbidity current excitation wave. This speed is not the velocity of the motion of the water mass. At time t0, the initial turbidity current moves underwater, pushing the stationary water in front to generate an excitation wave. At time t1, the excitation wave is propagating. At time t2, the rapidly propagating excitation wave exerts pressure on the soft bottom bed, resulting in the destruction of the bottom bed and secondary turbidity current).

Turbidity currents are mass movements composed of sediment particles, with a high concentration of the dense basal layer near the seabed. Depending on their density and granulometric composition, turbidity currents can move along submarine canyons through mechanisms such as diffusion, collapse, and flow [37], which differ from the downward movement as a single entity of landslide bodies after slope failure (this distinguishes them from surges). Additionally, during the long-distance movement of turbidity currents in canyons, the completion of subsequent water replenishment may generate multiple excitation waves. Furthermore, secondary excitation waves may also occur during the movement of secondary turbidity currents triggered by the initial turbidity current, which differs significantly from the surges caused by submarine landslides. Furthermore, previous studies [38,39,40,41] on sediment supply during turbidity current movements have mostly focused on the scouring action on the seabed, whereas the resuspension of sedimentary deposits in front of the initial turbidity current caused by excitation waves may serve as an effective mode of sediment supply during the long-distance transport of turbidity currents.
In 2023, Ren et al. proposed that the cause of the long-distance high-speed motion of turbidity currents is due to the excitation waves caused by the primary turbidity currents. However, only preliminary research has been conducted on the comparison of excitation wave velocity and solitary wave velocity, and there has been no specific discussion on the reasons for the excitation wave velocity being much greater than that of the turbidity current. In an experiment conducted using an indoor flume, it was observed that the wavelength of the excitation waves was much larger than the water depth, similar to shallow water waves [33]. The amplitude of excitation waves in proportion to their wavelength was small, consistent with the theory of small-amplitude waves. Similar to the velocity model of shallow water waves, it is expected that the propagation speed of excitation waves is also influenced by the water depth. However, since excitation waves are triggered by sediment-laden turbidity currents, the velocity model may differ from that of surface waves induced by gravitational flows.
The purpose of this study is to simulate and investigate the effects of different factors on the propagation velocity and amplitude of excitation waves through a validated numerical model based on laboratory experiments. The study aims to determine the maximum propagation velocity of excitation waves at a field scale and whether there is attenuation in the long-distance propagation after their formation. In recent studies, seafloor sediment flows have been collectively referred to as turbidity currents [42]. Therefore, we simulated the movement of turbidity currents by sediment flow.
This study uses the CFD-based fluid computation software FLOW-3D to simulate the underwater movement process of turbidity currents. The numerical model is validated against indoor experimental results. During the simulation process, a velocity model for surging wave generation triggered by submarine landslides is used as a reference, and multiple factors that may affect the propagation velocity of the excitation wave are considered. By controlling a single variable, the main factors influencing the excitation wave propagation velocity are determined, and the corresponding expression for excitation wave propagation velocity is provided. The results indicate that the propagation velocity of the excitation wave induced by turbidity currents is primarily determined by the water depth. This research provides a new perspective for understanding the high-speed movement of turbidity currents in submarine canyons and enriches the understanding of the movement patterns of turbidity currents in submarine canyons. In addition, studying the propagation speed of excitation waves is highly significant for the resuspension of underwater sediments, as well as the re-circulation of carbon sequestration, nutrients, heavy metals, and microplastics.

2. Experimental Study on Excitation Waves Induced by Turbidity Currents

2.1. Experimental Design and Apparatus

The experimental apparatus used for the turbidity current-induced excitation wave tests is a straight water tank [33]. The water tank is 12.5 m long, 0.5 m wide, and 0.7 m high. A turbidity source area is located on the right side of the tank to generate turbidity currents. The tank is equipped with a terrain with a certain slope.
Turbidity currents are generated underwater using a weir. The mass ratio of silt and clay used in the experimental turbid water solution was 8:2, with a density of 1600 kg/m3. Previous experiments have shown that this turbid mixture can reach a maximum flow velocity of 18.7 cm/s [31]. Three pressure sensors are placed along the straight section of the tank at intervals of 0.4 m. These sensors continuously monitor the bottom shear stress caused by the turbidity current-induced excitation wave, as well as the force exerted by the turbidity current itself on the bed. The monitoring frequency is set at 100 Hz.

2.2. Experimental Phenomenon and Results

In the laboratory water tank experiments, it was observed that as the turbidity current propagates, a wave is generated ahead of the turbidity front, moving in the same direction as the current and with a velocity greater than the turbidity current velocity [33]. By monitoring the pressure changes on the bed during the turbidity current motion [33], the propagation velocity of the excitation wave, the head movement velocity of the turbidity current, and the amplitude of the excitation wave (obtained from the measured surface elevation changes caused by the wave) can be estimated based on the distances between the sensors and the time when the pressure change peaks occur.
The results of indoor experiments on turbidity currents indicate that they can compress and propel the water ahead of them, generating excitation waves similar to pulses. The propagation speed of these excitation waves caused by turbidity currents is found to be much greater than the velocity of the turbidity current movement at its head, as determined by pressure sensors installed on the seabed.

3. Numerical Simulation of Excitation Waves Induced by Turbidity Currents

FLOW-3D is a powerful computational fluid dynamics (CFD) software that excels in making accurate calculations of free surface and six-degrees-of-freedom motions of objects. Similar to other CFD software, FLOW-3D consists of three modules: pre-processing, solver, and post-processing. In recent years, there have been many simulations of turbidity currents using FLOW-3D due to its superior capabilities. For example, Heimsund (2007) simulated turbidity currents in the Monterey Canyon system using FLOW-3D based on high-resolution bathymetry and flow data [43]. Zhou et al. (2017) used FLOW-3D software to simulate turbidity currents in a flume with obstacles, analyzing the impact of the proportion between obstacle height and flume height on the movement of turbidity currents, including their velocity, flow state, and morphological evolution [44]. In this study, using the CFD software FLOW-3D, the underwater motion process of turbidity currents is simulated. The model is validated by comparing it with experimental results, and the motion of the waves induced by turbidity currents is simulated based on this validation.

3.1. Control Equations

FLOW-3D, a mature three-dimensional fluid simulation software, is used in this study. It employs the RNG turbulence model, which is capable of handling high strain rate flows and is suitable for simulating excitation waves. The research focus of this paper is on sediment gravity flows (turbulent flows), and the control equations used in the calculations include the basic continuity equation, the momentum equation, the turbulent kinetic energy k equation, and the turbulent kinetic energy dissipation rate ε equation.

The continuity equation:

The momentum equation:

The turbulence model:

k equation:

ε equation:

where u, v and w is the flow velocity component in x, y and z directions; Ax, Ay and Az represent the area fraction that can flow in x, y and z directions; Gx, Gy and Gz are the gravitational acceleration in x, y and z directions; fx, fy and fz are the viscous forces in the three directions; VF is the fraction of the volume that can flow; ρ is the fluid density; p is the pressure acting on the fluid element; k is the turbulence energy; ε is the turbulence kinetic energy dissipation rate; μ is turbulence viscosity coefficient

where u, v and w is the flow velocity component in x, y and z directions; Ax, Ay and Az represent the area fraction that can flow in x, y and z directions; Gx, Gy and Gz are the gravitational acceleration in x, y and z directions; fx, fy and fz are the viscous forces in the three directions; VF is the fraction of the volume that can flow; ρ is the fluid density; p is the pressure acting on the fluid element; k is the turbulence energy; ε is the turbulence kinetic energy dissipation rate; 

 μ is turbulence viscosity coefficient μ t = ρ C μ k 2 ε where Cμ = 0.0845;

Gk is the turbulent kinetic energy generation term, expressed as G k = μ t ∂ u i ∂ x j + ∂ u j ∂ x i ∂ u i ∂ x j

and σk and σε are the Prandtl numbers corresponding to the turbulent kinetic energy and dissipation rate, respectively, both of which are 1.39.

In addition, C ε 1 * = C ε 1 − η 1 − η / η 0 1 + β η 3 where Cε1 and Cε2 are the empirical constants, 1.42 and 1.68, respectively.

Furthermore, η = 2 E i j E i j 1 / 2 k ε

where E i j = 1 2 ∂ u i ∂ x j + ∂ u j ∂ x i , η0 = 4.377, β = 0.012.

The general mass continuity equation is as follows:

where VF is the fractional volume open to flow, ρ is the fluid density, RDIF is a turbulent diffusion term, and RSOR is the mass source.

3.2. Model Validation

To determine the factors affecting the velocity of the turbidity-induced excitation wave and its velocity expression, first, the indoor flume test was taken as the prototype. Then, a 1:1 geometric solid model was established, and the simulation parameters were set to be consistent with the flume test parameters [33]. Finally, the simulation results were compared with the laboratory test results.

The computational domain employs the method of unstructured grid and is entirely divided into structured orthogonal grids. Nested grids are used for local refinement at the interfaces of straight sections, resulting in a total of 800,000 grid cells after refinement.

The simulation results were compared with the indoor experimental results, with the velocity of the excitation wave and the turbidity current head being represented by changes in surface elevation and water density. The experimental and simulation results are shown in Table 2, and the calculation formula for the error is |Calculated value−Test value|Test value×100%Calculated value-Test valueTest value×100%.

ResultPropagation Velocity of Excitation Wave (m/s)Velocity of Turbidity Current (m/s)Excitation Wave Amplitude (m)
Sensor 1 to 2Sensor 2 to 3Sensor 1 to 2Sensor 2 to 3Sensor 1 to 2Sensor 2 to 3
Test results1.541.480.240.230.0290.03
Computed results1.551.520.250.230.030.03
Error range0.6%2.7%4.2%0%3.4%0%
Table 2. The test results of the propagation velocity of the excitation wave, the turbidity current velocity, and the excitation wave amplitude are compared with the simulation results.

From the above comparison, it can be observed that the simulated velocities of the excitation wave and the head of the turbidity current align well with the experimental results, indicating the rationality of using the numerical model established in this study for simulating the propagation velocity of the excitation wave induced by turbidity currents.

3.3. Analysis of Factors Affecting the Propagation Velocity of Excitation Waves

An analysis of the factors influencing the propagation velocity of excitation waves was conducted using numerical simulation. The reference model for wave velocity was based on the surge velocity model. The main factors affecting the propagation velocity of excitation waves were summarized, including the turbidity current density ρ, the thickness of the turbidity current source area d, the length of the turbidity current source area L, the depth at the initial flow of turbidity currents h, the canyon width l, and the initial velocity of the turbidity current v0 (as shown in Figure 2). The simulations were performed using a controlled variable approach for different parameters, and the velocity changes of the excitation wave were obtained, as shown in Table 3. The slope angle was fixed at 3°, and sensors were placed at intervals of 100 m starting from a distance of 500 m from the turbidity current source area (named Sensors 1, 2, 3). These sensors were used to extract surface elevation, density, and other relevant parameters at their respective locations. We can obtain the propagating velocity of excitation waves by measuring the time difference in surface elevation changes at the monitoring points. Similarly, we can determine the propagation velocity of turbidity currents by measuring the time difference in density changes.

Figure 2. Excitation wave velocity simulation model and parameters.
Group OrderTurbidity Current Density (kg/m3)Length of Turbidity Source Area
(m)		Canyon Width
(m)		Thickness of Turbidity Source Area
(m)		Depth (m)Initial Velocity of Turbidity Current (m/s)Propagation Velocity of Excitation Wave (m/s)Excitation Wave Amplitude (m)Velocity of Turbidity Current (m/s)
11600100020020200033.430.3455.88
21500100020020200033.090.3045.41
31400100020020200033.350.2234.99
41300100020020200033.330.1774.35
51200100020020200033.860.0923.74
61600100020040200033.051.1099.09
71600100020060200033.392.68910.79
81600100020080200033.214.82812.91
916001000200100200036.437.74413.79
10160020020020200032.930.1815.58
11160040020020200033.490.255.71
12160060020020200033.060.2785.79
13160080020020200033.170.315.72
141600100020020100026.670.565.72
151600100020020300039.650.1695.80
161600100020020400045.980.125.80
171600100020020500049.970.085.96
181600100010020200033.600.3545.72
191600100030020200032.980.3385.97
201600100040020200033.270.3565.87
211600100050020200033.310.3655.86
221600100020020200233.500.5324.35
231600100020020200533.121.3896.56
241600100020020200833.522.2718.10
2516001000200202001033.332.8788.99
Table 3. Simulation results under different variables conditions.

The variations in surface elevation at three sensor locations in the simulated results of five different turbidity current density groups are presented in Figure 3.

Figure 3. Simulation of propagating velocity of excitation wave under the sole variable condition of turbulent current density. (Length of turbidity source area: 1000 m; canyon width: 200 m; thickness of turbidity source area: 20 m; depth: 200 m; initial velocity of turbidity current: 0 m/s).

Based on the simulation results described above, while keeping all other conditions constant, the impact of a single variable, namely, the turbidity current density, on the propagation velocity and amplitude of the excitation wave was analyzed. By fitting the data, the relationship between turbidity current density and the propagation velocity of turbidity currents as well as the amplitude of the excitation wave was obtained, as shown in Figure 4.

Figure 4. Relationship between turbidity current density and turbidity current velocity, as well as excitation wave amplitude.

The simulation results indicate that changes in turbidity current density, while keeping the other conditions constant, do not result in a change in the propagation velocity of the excitation waves. However, they do affect the amplitude of the excitation waves and the velocity of the turbidity current itself. The simulation reveals that within the selected density range, both the amplitude of the excitation waves and the velocity of the turbidity current increase with increasing turbidity current density. When the turbidity current density is equal to that of water (ρTurbidity current = ρWater), there is no turbidity current or excitation wave generation. Thus, the relationship between the turbidity current velocity (v) and density (ρ) is expressed as v = −34.80643 + 0.05082•ρ − 1.59286 × 10−5 ρ2 (ρ > 1000, R2 = 0.994). Additionally, the relationship between the amplitude of the excitation waves (A) caused by turbidity currents and density (ρ) is expressed as A = −0.6021 + 5.9729 × 10−4 ρ (ρ > 1000, R2 = 0.991).

3.3.2. The Influence of the Thickness of the Turbidity Source Area on the Propagation Velocity and Amplitude of Excitation Waves

The variations in surface elevation at three sensor locations in the simulated results of five different thickness of turbidity source area groups are presented in Figure 5.

Figure 5. Simulation of propagating velocity of excitation wave under the sole variable condition of thickness of turbidity source area. (Turbidity current density: 1600 kg/m3; length of turbidity source area: 1000 m; canyon width: 200 m; depth: 200 m; initial velocity of turbidity current: 0 m/s).

Based on the simulation results described above, while keeping all other conditions constant, the impact of a single variable, namely, the thickness of the turbidity source area, on the propagation velocity and amplitude of the excitation wave was analyzed. By fitting the data, the relationship between the thickness of the turbidity source area and the propagation velocity of the turbidity current as well as the amplitude of the excitation wave was obtained, as shown in Figure 6.

Figure 6. Relationship between thickness of turbidity source area and turbidity current velocity, as well as excitation wave amplitude.

Based on the simulated results mentioned above, it can be concluded that, while keeping the other conditions constant, changing only the thickness of the turbidity current source area does not affect the propagation velocity of the excitation waves. However, it does impact both the amplitude of the excitation waves and the velocity of the turbidity current itself. The simulation reveals that within the selected range of thickness values for the turbidity current source area, both the amplitude of the excitation waves and the velocity of the turbidity current increase with an increase in the thickness of the source area. Additionally, it is observed that when the length of the turbidity current source area is zero, neither the turbidity current nor the excitation waves are generated (i.e., no turbidity current is produced when hTurbidity current = 0). Therefore, the relationship between the velocity (v) of the turbidity current and its thickness (h) is expressed as v = 0.27983•h − 0.00146•h2 (h ≥ 0, R2 = 0.999). Similarly, the relationship between the amplitude (A) of the excitation waves caused by the turbidity current and its thickness (h) is A = −0.00375•h − 0.0008•h2 (h ≥ 0, R2 = 0.999).

3.3.3. The Influence of the Length of the Turbidity Source Area on the Propagation Velocity and Amplitude of Excitation Waves

The variations in surface elevation at three sensor locations in the simulated results of five different length of turbidity source area groups are presented in Figure 7.

Figure 7. Simulation of propagating velocity of excitation wave under the sole variable condition of length of turbidity source area. (Turbidity current density: 1600 kg/m3; canyon width: 200 m; thickness of turbidity source area: 20 m; depth: 200 m; initial velocity of turbidity current: 0 m/s).

Based on the simulation results described above, while keeping all other conditions constant, the impact of a single variable, namely, the length of the turbidity source area, on the propagation velocity and amplitude of the excitation wave was analyzed. By fitting the data, the relationship between the length of the turbidity source area and the amplitude of the excitation wave was obtained, as shown in Figure 8.

Figure 8. Relationship between length of turbidity source area and excitation wave amplitude.(Amplitude refers to the surface elevation change caused by the excitation wave).

Through simulations, it has been determined that within the chosen range of the length of the turbidity source area, the amplitude of the excitation waves increases with an increase in the length of the turbidity source area. When the length of the turbidity source area is zero, there is no turbidity current and no generation of excitation waves (i.e., when LTurbidity current = 0). Additionally, for large lengths of the turbidity source area, under the condition of sufficient sediment supply, the variations in surface elevation caused by the waves generated by turbidity currents are negligible. Therefore, the relationship between the amplitude of the excitation waves (A) generated by turbidity currents and the length of the turbidity source area (L) is expressed as follows: A = −0.3624 + 0.10305•ln(L − 6.15619) (L ≥ 0, R2 = 0.997).

3.3.4. The Influence of Depth on the Propagation Velocity and Amplitude of Excitation Waves

The variations in surface elevation at three sensor locations in the simulated results of five different depth groups are presented in Figure 9.

Figure 9. Simulation of propagation velocity of excitation wave under the sole variable condition of depth. (Turbidity current density: 1600 kg/m3; length of turbidity source area: 1000 m; canyon width: 200 m; thickness of turbidity source area: 20 m; initial velocity of turbidity current: 0 m/s).

Based on the simulation results described above, while keeping all other conditions constant, the impact of a single variable, namely, depth, on the propagation velocity and amplitude of the excitation wave was analyzed. By fitting the data, the relationship between depth and the propagation velocity of the excitation wave as well as the amplitude of the excitation wave was obtained, as shown in Figure 10.

Figure 10. Relationship between depth and propagating velocity of excitation wave, as well as excitation wave amplitude.

As the water depth approaches infinity, the excitation wave amplitude can only approach zero but cannot reach zero. Therefore, the characteristics of the excitation wave amplitude change with the water depth are similar to those of the velocity propagation of the excitation wave. The relationship between the velocity of the excitation wave induced by turbidity currents (vExcitation wave) and the water depth (H) can be described as vExcitation wave = −287.05446 + 48.59211•ln(H + 535.14863) (R2 = 0.998). The relationship between the excitation wave amplitude (A) and the water depth (H) can be expressed as A = 1.46573 − 0.22816•ln(H − 47.67563) (R2 = 0.985).

3.3.5. The Influence of the Canyon Width on the Propagation Velocity and Amplitude of Excitation Waves

The variations in surface elevation at three sensor locations in the simulated results of five different canyon width groups are presented in Figure 11.

Figure 11. Simulation of propagating velocity of excitation wave under the sole variable condition of canyon width. (Turbidity current density: 1600 kg/m3; length of turbidity source area: 1000 m; thickness of turbidity source area: 20 m; depth: 200 m; initial velocity of turbidity current: 0 m/s).

When the canyon width is taken as the single variable condition, changing the canyon width does not significantly affect the propagation velocity of excitation waves, the amplitude of excitation waves, and the velocity of turbidity currents. Therefore, it can be concluded that, without considering the impact of the differences in the terrain and sediment on the canyon width, the canyon width has no impact on the propagation of excitation waves and the movement of turbidity currents.

3.3.6. The Influence of the Initial Velocity of the Turbidity Current on the Propagation Velocity and Amplitude of Excitation Waves

The variations in surface elevation at three sensor locations in the simulated results of five different initial velocity of turbidity current groups are presented in Figure 12.

Figure 12. Simulation of propagating velocity of excitation wave under the sole variable condition of initial velocity of turbidity current. (Turbidity current density: 1600 kg/m3; length of turbidity source area: 1000 m; canyon width: 200 m; thickness of turbidity source area: 20 m; depth: 200 m).

Based on the simulation results described above, while keeping all other conditions constant, the impact of a single variable, namely, the initial velocity of the turbidity current, on the propagation velocity and amplitude of the excitation wave was analyzed. By fitting the data, the relationship between the initial velocity of the turbidity current and the amplitude of the excitation wave was obtained, as shown in Figure 13.

Figure 13. Relationship between initial velocity of turbidity current and excitation wave amplitude.

Based on the simulation, it is observed that within the selected range of the initial velocity of the turbidity current, the amplitude of the excitation wave increases linearly with the increase in the initial velocity of the turbidity current. Therefore, the relationship between the amplitude (A) of the excitation wave caused by the turbidity current and the initial velocity of the turbidity current (v0) can be expressed as A = 0.34 + 0.24084•v0 (A ≥ 0, R2 = 0.992).

Through controlling the simulation calculation of a single variable, it was found that there are several factors that can affect the amplitude of the excitation wave. These factors include the turbidity current density ρ, the thickness of the turbidity current source area d, the length of the turbidity current source area L, the water depth h, and the initial velocity of the turbidity current v0. In contrast, there are relatively few factors that influence the propagation velocity of the excitation wave. Within the selected parameter range, only the water depth can affect the propagation velocity of the excitation wave. The physical parameters of the turbidity current, including the turbidity current density ρ, the thickness of the turbidity current source area d, the length of the turbidity current source area L, the canyon width l, and the initial velocity of the turbidity current v0, have no direct influence on the propagation velocity of the excitation wave. Therefore, the turbidity current only serves as a triggering factor for the excitation wave and is not directly related to the propagation velocity of the excitation wave.

3.4. Analyze the Changes in Propagation Velocity of Excitation Waves along a Path

In order to further investigate the underlying truth behind the variation in the propagation velocity of the excitation wave, a discussion on whether there is velocity attenuation along the propagation path of the excitation wave is conducted. Since the seventh group of the excitation wave causes significant changes in surface elevation, the seventh group of the excitation wave is selected as the research object in order to study the variations in surface elevation along the propagation path of the excitation wave. The changes in surface elevation are extracted every 200 m along the sediment slope (with the first extraction point located 400 m away from the source area of the turbidity current). A total of six sets of surface elevation data are extracted (ranging from 400 m to 1400 m distance from the source area of the turbidity current), as shown in Figure 14.

Figure 14. Surface elevation changes during excitation wave propagation along sediment slopes.

The amplitudes and propagation velocities of the excitation wave at each point are shown in Table 4.

Distance from Turbidity Current Source Area (m)Propagation Velocity of Excitation Wave (m/s)Excitation Wave Amplitude (m)
40033.342.524
60036.792.596
80037.132.589
100039.992.566
120040.042.542
140040.132.523
Table 4. Excitation wave velocity during the excitation wave propagation along the sediment slope.

From the table above, it can be observed that the amplitude of the excitation wave does not change while traveling along the slope. This indicates that the change in surface elevation caused by the propagation of the excitation wave does not attenuate. Furthermore, the propagation velocity of the excitation wave gradually increases, although the change is not very pronounced. This variation may be attributed to the change in the water depth caused by the sloping bed. To investigate this, a simulation was conducted in a straight channel with a length of 3000 m. Six sampling points were established from 400 m to 1400 m away from the turbidity current source area to extract the amplitude of the excitation wave. The results of the simulation are presented in Figure 15.

Figure 15. Surface elevation changes during wave propagation along a straight channel.

The amplitudes and propagation velocities of the excitation wave at each point are shown in Table 5.

Distance from Turbidity Current Source Area (m)Propagation Velocity of Excitation Wave (m/s)Excitation Wave Amplitude (m)
40033.892.559
60037.662.692
80037.122.712
100036.922.717
120037.092.715
140037.482.718
Table 5. Excitation wave velocity during the propagation along the straight channel.

The data from the table above indicate that during the propagation of the excitation wave along a straight water channel, its velocity remains constant, except for a slight decrease at the initial point. This phenomenon may be attributed to the fact that in the starting phase, the excitation wave is not fully developed, and hence its velocity is relatively smaller. However, once it is fully developed, the propagation velocity of the excitation wave does not decrease in subsequent processes. Therefore, the propagation velocity of the excitation wave is only dependent on the real-time water depth of the wave. In future studies, we aim to explore the relationships between these influencing factors and other physical parameters, such as the speed of wave propagation, using the effective and accurate method of machine learning algorithms [45].

3.5. Expression of the Propagation Velocity of the Excitation Wave

The propagation of the excitation wave along a long distance does not experience an attenuation in velocity, as is the case with the propagation velocity of solitary waves. Referring to the estimated wave propagation velocity (the square of the propagation velocity is directly proportional to the water depth amplitude) [46], the wavelengths under different water depth conditions were extracted, as shown in Table 6.

Depth (m)Propagation Velocity of Excitation Wave (m/s)Excitation Wave Amplitude (m)Excitation Wave Length (m)
10026.670.562580
20033.430.352850
30039.650.173250
40045.980.123600
50049.970.084150
100066.670.046000
200090.910.029500
4000165.840.317600
Table 6. Physical parameters of excitation wave under different water depth conditions.

From the simulation results of a single variable, the water depth, it could be seen that the wavelengths of the excitation waves were much larger than the water depth. Therefore, further simulations were conducted under water depth conditions ranging from 1000 m to 4000 m. Due to the minimal change in wave amplitude when the water depth reached 4000 m, it was not possible to observe a distinct waveform. However, through simulations with the thickness of the turbidity current source area as the single variable, it was found that an increase in the thickness of the source region led to a larger amplitude of the excitation waves, but it did not affect the wavelength of the excitation waves. Therefore, in order to better extract the wavelength of the excitation waves, the thickness of the source region in the simulation with a water depth of 4000 m was set to 200 m.

Through simulations at water depths of 1000 m and 4000 m, it is observed that the wavelengths of the excitation waves are much larger than the water depth, indicating that these waves belong to the category of shallow water waves. The amplitude of the excitation waves is relatively small compared to their wavelength, aligning with the small amplitude wave theory [47]. According to this theory, the wave velocity of shallow water waves is only dependent on the water depth (h) and gravity acceleration (g), regardless of the wave period. In the case of excitation waves induced by turbidity currents in deep water, the amplitudes of these waves are relatively small compared to the water depth. Referring to the expression for shallow water waves (when the relative water depth, which is the ratio of water depth to wavelength, is much smaller than 1/2), the wave velocity is denoted as 𝐶𝑠=√𝑔ℎ. This implies that the propagation velocity of the excitation waves is also solely related to the water depth. Therefore, a fitting of the square of the propagation velocity of the excitation waves (v2) and the water depth (h) was conducted (Figure 16).

Figure 16. The relationship between the propagation velocity of excitation wave and the depth.

Through fitting, the following can be obtained:

Through fitting, it can be discovered that the propagation model of the velocity of excitation waves is different from the shallow water wave theory. This is because turbidity currents, as granular materials, generate excitation waves by pushing the water in front of them with sediment particles underwater, which is different from the surges formed by solid blocks entering the ocean. Additionally, excitation waves formed by turbidity currents occur in an underwater environment, which may be the reason why the propagation velocity equation for the excitation waves behaves as if the velocity squared is equal to half the Earth’s gravity. This equation reveals the variation in the propagation velocity of the excitation wave with depth, explaining why the average velocity between the monitoring points in the field is greater than the instantaneous velocity measured at these points [41]. Further theoretical research on the propagation velocity of excitation waves requires subsequent field monitoring and the deployment of monitoring systems to more thoroughly investigate the fundamental causes.

4. Conclusions

This study aimed to investigate the velocity of turbidity current-induced excitation waves through numerical simulation. By fixing a single variable, different factors that could affect the propagation velocity and amplitude of the excitation waves were analyzed and discussed, leading to the following three conclusions:

  1. Within the selected parameter range, there are several factors that can influence the amplitude of the excitation waves, including the turbidity current density ρ, the thickness of the turbidity current source area d, the length of the turbidity current source area L, the water depth h, and the initial velocity of the turbidity current v0.The amplitude of the excitation waves is positively correlated with the turbidity density, the thickness of the source area, the length of the source area, and the initial velocity, while it is negatively correlated with the water depth.
  2. Within the selected parameter range, only the water depth can affect the propagation velocity of the excitation waves. As the water depth increases, the propagation velocity of the excitation waves also increases, and a relationship of v2 = 0.63gh (R2 = 0.967) is established between the square of the propagation velocity v2 and the water depth h.
  3. During the propagation of the excitation waves, both the propagation velocity and the changes in surface elevation caused by the waves do not attenuate. Considering the relatively calm deep-sea environment, the high-speed propagation of the excitation waves and the resuspension of bottom sediments they cause not only complement the understanding of turbidity current motion patterns in canyons, but also provide new research directions for deep-sea sediment transport.

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river depth

Ecological inferences on invasive carp survival using hydrodynamics and egg drift models

수리역학 및 알 이동 모델을 활용한 외래종 잉어 생존에 대한 생태적
추론

Ruichen Xu, Duane C. Chapman, Caroline M. Elliott, Bruce C. Call, Robert B. Jacobson, Binbin Wang

Abstract

Bighead carp (Hypophthalmichthys nobilis), silver carp (H. molitrix), black carp (Mylopharyngodon piceus), and grass carp (Ctenopharyngodon idella), are invasive species in North America. However, they hold significant economic importance as food sources in China. The drifting stage of carp eggs has received great attention because egg survival rate is strongly affected by river hydrodynamics. In this study, we explored egg-drift dynamics using computational fluid dynamics (CFD) models to infer potential egg settling zones based on mechanistic criteria from simulated turbulence in the Lower Missouri River. Using an 8-km reach, we simulated flow characteristics with four different discharges, representing 45–3% daily flow exceedance. The CFD results elucidate the highly heterogeneous spatial distribution of flow velocity, flow depth, turbulence kinetic energy (TKE), and the dissipation rate of TKE. The river hydrodynamics were used to determine potential egg settling zones using criteria based on shear velocity, vertical turbulence intensity, and Rouse number. Importantly, we examined the difference between hydrodynamic-inferred settling zones and settling zones predicted using an egg-drift transport model. The results indicate that hydrodynamic inference is useful in determining the ‘potential’ of egg settling, however, egg drifting paths should be taken into account to improve prediction. Our simulation results also indicate that the river turbulence does not surpass the laboratory-identified threshold to pose a threat to carp eggs.

Introduction

Bighead carp (Hypophthalmichthys nobilis), silver carp (H. molitrix), black carp (Mylopharyngodon piceus), and grass carp (Ctenopharyngodon idella), are considered invasive in North America. These species were imported into North America in the 1970’s to support aquaculture and escaped into the wild where they alter aquatic environments and food webs, resulting in undesirable ecological consequences1,2,3. On the other hand, these carp species are important food sources in China, yet their populations in their native environment have been declining due to over-fishing and the negative effects on fish habitats resulting from dam construction4,5. As either native or invasive species, it is of great importance to understand their life cycles in order to identify potential intervention strategies to control their populations6.

These rheophilic, broadcast-spawning carps exhibit prolific reproduction, with a single female carp capable of producing between 100,000 and one million eggs annually7. Carps typically engage in spawning during the spring and summer months when the temperature is within a range favorable for successful reproduction (peaking at roughly 20–24 ∘C) and during periods of high flows8,9. They select specific locations for spawning characterized by high turbulence, including rocky rapids, riffles, islands, river confluences, and bends. This choice helps prevent the settling of eggs onto the riverbed, as sediment burial causes high mortality10. Within 3–5 h after spawning, eggs absorb a large amount of water in a process known as water hardening, leading to an increase in egg size and decrease in egg density. The water-hardening process leads to a decrease in settling velocity by approximately 70%, making eggs more likely to suspension in the water column10,11.

After spawning and fertilization, the drift stage of carp eggs begins, a critical early-life stage in carp recruitment. Eggs hatch in approximately 30 h at optimal temperatures10,12. During the drift stage before hatching, eggs are susceptible to predation, relying entirely on river currents and turbulence to remain suspended until hatch. After hatching, larval carp remain in the drift for a period, but they can behaviorally avoid settling10,12. Because hydrodynamics plays a critical role in the suspension, dispersion, and transport of carp eggs across various scales in rivers, numerous studies have been conducted to explore river hydraulics and turbulence in relation to suitable carp spawning grounds, survival potential, and hatch locations13,14,15,16. A key survival condition is the necessity for eggs to remain suspended in the water column throughout the entire egg drift stage, or at the very least, to avoid settling and being buried by sediment. Consequently, assessing whether river hydrodynamics can support this condition is a fundamental step in gauging recruitment success.

Flow velocity has been used as a simple indicator for assessing the suspension of eggs in rivers. For instance, Kocovsky et al.17 used a threshold velocity of 0.7 m/s as suitable for the spawn-to-hatch environment. Selection of 0.7 m/s is based on early literature with limited mechanistic studies9,18. Lower critical flow velocities were also reported in the literature. Tang et al.19 suggested a value of 0.25 m/s based on a flume experiment, which agreed with some early field observations in the Yangtze River. Murphy and Jackson20 found that mean velocities of 0.15–0.25 m/s allowed for egg suspension in four tributary rivers of the Great Lakes. Guo et al.21 suggested a critical flow velocity of 0.3 m/s in a flume experiment. Because rivers are largely non-uniform and vary in size and morphology, selecting a specific flow velocity as the sole empirical indicator for assessing suitability of carp recruitment is rather challenging.

While using flow velocity as an indicator for examining egg suspension or settling might be practical, it does not fully represent the underlying physics, especially in areas where turbulence is not well correlated with mean flow velocity. To account for the mechanism of egg suspension, Garcia et al.22 proposed three different criteria involving the ratio of shear velocity and egg settling velocity, the ratio of vertical turbulence intensity and egg settling velocity, and the Rouse number to predict the suspension and settling of carp eggs. In their laboratory experiment, they observed that 65% of eggs remained in suspension with a mean flow velocity of 0.07 m/s, corresponding to a Rouse number of 1.32 and shear velocity of 0.004 m/s. At higher flow velocities of 0.2 and 0.4 m/s, with Rouse numbers of 0.57 and 0.58 and shear velocity of 0.008 and 0.016 m/s, respectively, all eggs were in suspension. These observations agree well with the empirical values of Rouse number classification for sediment transport for bedload, partial suspension, full suspension, and washload23. Therefore, using these parameters is better supported by the mechanism of particle suspension compared to velocity alone.

Given the above simple criteria of using shear velocity or Rouse number, hydraulic models or measurements can be used to infer whether a stream or a river reach can support a favorable environment for egg suspension in the egg-drift stage17. In addition, three dimensional hydrodynamic models can provide additional insights into the spatial distributions of potential egg settling zones, given the strong spatial heterogeneity of river turbulence24,25,26. In this paper, we use an 8-km reach in the Lower Missouri River as representative of channelized segments of the Upper Mississippi River basin where carps are established. We used computational fluid dynamics (CFD) modeling to explore the overall suitability for egg drift and to infer potential egg settling zones, with an emphasis on understanding the spatial distributions of hydrodynamics associated with in-stream hydraulic structures, river morphology, and strong topographic gradients on the riverbed. Specifically, we examine the criteria of egg suspension and evaluate the locations where the hydrodynamics are unfavorable for suspending eggs. Our objective is to evaluate whether the potential egg settling zones based on hydrodynamic inference would agree with entrapment locations that can be estimated using drift models. We additionally evaluate whether turbulence conditions indicated in the model approach criteria for turbulence-induced damage to carp eggs as determined in laboratory studies.

Methods

Study site

The study site is a selected reach in the Lower Missouri River near Lexington, Missouri (Fig. 1). The reach is approximately 8 km long with a sinuosity index of 1.12. The mean bankful width is 331.4 m. The bed is mostly covered by medium and coarse sand (D50 = 0.55 mm) with fine muddy materials (< 0.125 mm) near the banks and close to the dike fields27,28. The mean annual discharge is approximately 1700 m3/s measured at a U.S. Geological Survey (USGS) gaging station approximately 24 km downstream (station no. 06895500, Waverly, Missouri, USGS). The reach is representative of rivers that have been highly engineered to support navigation and bank stability, with complex hydraulic conditions where water flows around and over the rock channel-training structures29,30. This reach has been used as the main site for model development stage of SDrift31,32, an egg drift model used in this study. The previous studies have accumulated substantial data for the bathymetric-topographic digital elevation model (DEM), water surface elevations, and cross-channel velocity profiles33, which have been used for calibration and validation of our CFD model.

Figure 1. Bathymetry map of the study site in the Lower Missouri River. Black line represents the measurement of water surface elevation. Black triangles represent the river miles measured from the confluence with the Mississippi River near St. Louis, Missouri. Twelve red lines represent the cross sectional transects of velocity measurement at Q=2282 m3/s. Ten blue lines represent the cross sectional transects of velocity measurement at Q=3060 m3/s. Map was generated with ArcGIS Pro v. 3.2 https://www.esri.com/en-us/home. Basemap is U.S. Army Corps of Engineers Imagery, 2012. River miles are from the U.S. Army Corps of Engineers, 1960, https://www.nwk.usace.army.mil/Missions/Civil-Works/Navigation/.

Hydrodynamic model

The flow was simulated using FLOW-3D HYDRO with a Reynolds-averaged Navier-Stokes (RANS) solver and a Re-Normalization Group (RNG) modified k−ε turbulence sub-model. The model was set up for solving the steady-state flows under four discharge conditions ( Q = 1342, 2282, 3060 and 4219 m3/s, referred to as Q1 to Q4 conditions), which correspond to approximately 45–3% daily flow exceedance during spawning season. A Cartesian mesh with a final size of 4×4×0.4 m in the east-north-up coordinate system was used after a mesh independence study to evaluate optimal mesh dimensions31.

The upstream and downstream boundary conditions were set to the measured flow discharge and calculated hydrostatic pressure from the measured water-surface elevation, respectively. The model was calibrated by adjusting the roughness coefficient until the simulated water-surface elevations agree with the measured data, where the water-surface elevations were measured using a ship-mounted, real-time corrected kinematic global navigation satellite system (RTK-GNSS). The measured cross-channel velocities at 22 locations at two flow conditions (Q=2282 and 3060 m3/s) were used to evaluate model performance, where the velocities were measured using a ship-board acoustic Doppler current profiler (ADCP, Workhorse Rio Grande, Teledyne, Inc) at each cross section with four repeated transects. The ADCP had a vertical resolution of 0.5 m and horizontal resolution of 1 m. The velocities within 1 m below the water surface and within 1 m above the river bed were not measured due to instrument blanking distance and measurement noise. Additional details on model calibration and evaluation are in Li et al.31.

Egg drift model

The egg drift model SDrift was used for egg transport modeling in this study31. This model uses Lagrangian particle tracking to simulate the transport of carp eggs, where turbulent fluctuations are modeled using an explicit solution for the Langevin equation, i.e., the Markov-chain continuous random walk (CRW) algorithm34,35,36. The density and diameter of carp eggs were determined as a function of post-fertilization time and water temperature based on the regression equation to the laboratory measured data11. The details of regression can be found in31. The time-varying characteristics of eggs result in evolving egg settling velocity in the water, which is determined based on the drag law for spherical particles37.

SDrift was incorporated with the CFD model outputs to predict transport of silver carp eggs in the selected reach. A broad surface-spawning event across the entire cross section at an upstream location in the model (x= 427,130 m, near River Mile 314) was simulated by releasing 6600 model eggs on the water surface at 33 locations31. All eggs were tracked until they were transported outside the downstream boundary or ‘entrapped’ in the model domain determined by the model criterion.

Criterion of egg entrapment from the egg drift model

SDrift allows the simulated eggs to be ‘entrapped’ if they are stationary for a pre-defined duration. The entrapment would occur if a simulated egg is transported into a low velocity zone and eventually loses its momentum. From the model evaluation, entrapment primarily occurs in the region with high topographic gradients, e.g., near the bank and hydraulic structures. A duration of 30 s was used here to determine the entrapment, i.e., if a simulated egg does not move for 30 s, it would be considered entrapped and would no longer be tracked. Although the entrapment does not necessarily provide a certain prediction of egg settling, it offers insight into locations where the eggs may be stopped and eventually buried by bed sediment. The selection of a 30-s duration is somewhat arbitrary. From a physics standpoint, this duration should ideally exceed the largest turbulent time scale. However, due to the extensive spatial scale of the modeled reach and the river-training structures, the turbulent time scale varies significantly across space. Furthermore, both the spatial resolution in the CFD simulation and the temporal resolution in particle tracking have the potential to influence particle movements and their entrapment. Therefore, determining the optimal duration requires further investigation in future studies.

Criterion of egg suspension and settling from the hydrodynamic model

Suspension of carp eggs depends on whether the flow can provide adequate upward motions that overcome their settling. Analogous to sediment suspension and transport38, several means have been used to quantify the settling and suspension of carp eggs in turbulent flows. Here we analyze three parameters following Garcia et al.22: the ratio between shear velocity and settling velocity, the ratio between vertical turbulence intensity and settling velocity, and the Rouse number.

Shear velocity

Shear velocity (u∗) is a velocity scale defined from the bed shear stress. The ratio of shear velocity and particle terminal velocity (wt), a so-called movability number (M∗=u∗/wt), has been used to classify sediment transport39. Different critical values have been proposed to define particle suspension38,39. Here, the critical value of 1.0 is used following the studies of carp eggs20,22: locations with u∗/wt<1 are the potential settling zones of carp eggs, where particle terminal velocity is the egg settling velocity (wt=Vegg).

Because shear velocity only represents the bed shear but does not provide the vertical variability in the water column, we applied a scaling method so that potential egg suspension and settling can be evaluated in the entire water column. Using the relationship between bed shear and turbulence kinetic energy (TKE)40,41, i.e., τb=C1ρk with C1=0.1940, the movability number can be estimated at every grid point using the TKE determined from the CFD simulation:

The potential egg settling zones were then determined based on M∗<1.

Vertical turbulence intensity

The vertical turbulence intensity (wrms′) is a direct parameter to quantify the turbulent velocity scale in the vertical direction, which can be used to define the initiation of particle suspension38. Therefore, we also calculated the ratio between wrms′ and V{egg} as the second indicator for egg settling: locations with wrms′/Vegg<1 are the potential settling zones of carp eggs. Here, we estimated w′ based on anisotropy of turbulent fluctuations in open channel flows:

with Du=2.30, Dv=1.27, and Dw=1.6342. This gives wrms′/Vegg=0.75TKE/Vegg where TKE was obtained from the CFD simulations.

Rouse number

In sediment transport, the Rouse number has been used to describe the suspended load38. The Rouse number is defined as Ro=wt/(βκu∗) with wt=Vegg for carp eggs, where κ is von Kárman constant and β is a coefficient related to diffusion of particles22,23:

The Rouse number (Ro, also used as Z or P in the literature), can be used to classify the sediment transport similar to the movability number. Hearn23 suggested that sediment particles are in 100% suspension or wash load when Ro<1.2; particles are partially suspended when 1.2<Ro<2.5; particles are predominantly transported by bedload if Ro>2.5. Here, we use 1.2 as the criterion, such that the potential egg settling zones were determined based on Ro>1.2.

Results and discussion

Model calibration and evaluation

The model calibration results for water-surface elevation are shown in Fig. 2 for four flow conditions31. The elevation of river bed in the main channel is also plotted for reference. The root-mean-square-error (RMSE) in the water surface elevation between the measurement and modeling is 0.07, 0.03, 0.04, and 0.03 m, for Q1 to Q4, respectively. The RMSE is considered to be small compared to the length of the reach and the water depths.

Figure 2. Result of model calibration using the measured water surface elevation for four discharge conditions from Li et al.31 and Elliott et al.33. Black solid lines are measured data. Red dashed lines are modeled results.

The measurement-modeling comparison of double-averaged velocities over the flow depth and the cross section in both streamwise (Us) and transverse (Ut) directions is given in Fig. 3 for two measured conditions (Q2 and Q3). The RMSE of Us and Ut is 0.055 and 0.028 m/s, much smaller than the mean flow of 1.29 and 1.38 m/s in the measured cross sections for Q2 and Q3, respectively. The direct measurement-modeling comparison in all 22 cross sections is given in the supplementary file (Figs. S1 and S2).

Figure 3. Comparison between computational fluid dynamics (CFD) modeled and acoustic Doppler current profiler (ADCP) measured velocities in the streamwise direction (Us) and transverse direction (Ut) at 22 cross sections under the two surveyed conditions Q2 and Q333. The 1:1 dashed line represents perfect agreement.

Mean flow characteristics

The CFD simulated flow depth and depth-averaged flow velocity for two out of four conditions are shown in Figures 4 and 5. Greater depths are located downstream from the dikes (i.e., in scour holes) and near the right bank at the upstream bend (i.e., Easting 431,000–432,000 m, downstream of river mile 311). Shallower depths are located upstream from the dikes and along the left bank in the downstream bend (i.e., Easting 432,000–433,500 m, in the vicinity of river mile 310).

Flow velocities are greater at a higher discharge, and are strongly related to the in-stream hydraulic structures: high velocities are located within the main channel and low velocities are located close to the dike areas and both sides of the bank. For Q1, the L-head dikes on the left bank around Easting 430,500–431,000 m (upstream of river mile 311) block the flow into the left bank, resulting in channel narrowing and an area of localized higher velocity. Relatively faster velocities are also located close to the right bank from Easting 432,000–433,500 m (in the vicinity of river mile 310) and then shaped by the L-head dike at Easting 433,500–434,500 m (between river miles 309 and 310). When water enters the L-head dike area at Easting 430,500–431,000 m (between river miles 311 and 312) in high discharge conditions (e.g., Q4), the localized fast flow is not observed.

Figure 4. Flow depth in the reach: (a) Q1; (b) Q4. River miles 309–313 are indicated in the plot by black triangles.
Figure 5. Depth-averaged flow velocity in the reach: (a) Q1; (b) Q
4. River miles 309–313 are indicated in the plot by black triangles.

Turbulence quantities

Two turbulence quantities were selected to elucidate the turbulence in the reach: the depth-averaged TKE (Fig. 6) and the depth-averaged dissipation rate of TKE (Fig. 7). For Q1, TKE shows a similar spatial pattern as the flow velocity, indicating that the high TKE is usually associated with high velocities. For Q4, additional high TKE regions are located within the low velocity zones near the dikes. These high turbulence regions are caused by the interaction of flow with the hydraulic structures. For instance, enhanced turbulence may occur within wakes downstream from the flows over the dikes. Strong shear-induced turbulence may also occur at the water surface near the edge of the dikes close to the main channel. Similar to TKE, the locations of high TKE dissipation rate are coincident with high velocity in the main channel and near the dikes where strong flow-structure interactions occur.

Figure 6. Depth-averaged turbulence kinetic energy (TKE): (a) Q1; (b) Q4. River miles 309–313 are indicated in the plot by black triangles.
Figure 7. Depth-averaged turbulence dissipation rate: (a) Q1; (b) Q4. River miles
309–313 are indicated in the plot by black triangles.

To examine the correlation between turbulence and the mean flow in the reach, Fig. 8 elucidates the ratio between TKE and the mean kinetic energy (MKE) where MKE is defined based on mean velocity values, MKE = 0.5(U2+V2+W2). The data show that the TKE/MKE ratio is much smaller than 1 in the main channel, a typical open-channel feature. However, near the river bank and in the dike fields, greater TKE than MKE is common, with the spatial distribution of TKE/MKE>1 being dependent on discharge. This result documents strong interactions between water flow and the solid boundaries, which generate substantial turbulence comparing to the reduced mean velocity in these regions. Within these regions, particles would be expected to have longer residence times32.

Figure 8. The ratio between turbulent kinetic energy (TKE) and mean kinetic energy (MKE) in the reach: (a) Q1; (b) Q4. River miles 309–313 are indicated in the plot by black triangles.

Egg suspension and settling

The CFD modeling results allow for analysis of potential egg settling zones based on the criteria of particle suspension outlined in section “Criterion of egg suspension and settling from the hydrodynamic model”. In Fig. 9, the potential egg settling locations are plotted based on the Rouse number criterion for all four discharge conditions. The plot shows that potential settling zones are located near the river banks, in dike fields, and even in the channel at locations with strong gradients in the bed morphology. We note that the criterion was applied to all data points simulated in the CFD. Therefore, the settling zones represent the x–y locations where turbulence is inadequate to suspend eggs. Not surprisingly, the estimated potential settling zones become smaller with increasing discharge. Results using shear velocity and vertical turbulence intensity criteria show similar results, which are plotted in the supplementary file (Figs. S3 and S4).

Figure 9. Predicted egg settling locations using the criterion of Rouse number. Black dots show the locations where the turbulence is inadequate to keep eggs suspended, i.e., inferring egg settling. Note that the egg settling is evaluated at all nodes in the three-dimensional computational fluid dynamics (CFD) simulation results. River miles 309–313 are indicated in the plot by red triangles.
Figure 10. Predicted egg settling location using the egg drift model, SDrift31. River miles 309–313 are indicated in the plot by red triangles.

Figure 10 shows the predicted locations of entrapped eggs using the egg drift model, SDrift31. Comparing Fig. 10 with Fig. 9, we found that both hydrodynamic-inferred potential settling locations and drift-model predicted locations include the regions near the dike fields and the sparse areas in the channel where strong topographic gradients are present. However, careful examination of the wing dike areas (Fig. 11 under Q1 condition and Fig. 12 under Q4 condition), shows that the predicted egg settling zones using two methods are located in different regions near the dike areas. SDrift results indicate that egg entrapment is mainly located adjacent to the dikes, whereas the hydrodynamic inference indicates strong egg settling potential downstream from the dikes under low-flow conditions, such as the discharge condition Q1 (Fig. 11). The potential egg settling zones are substantially decreased by increasing discharge (Fig. 12). SDrift results indicate that egg entrapment is primarily due to interception of egg movement due to strong topographic gradients near the dikes while being tracked in the model under these hydrodynamic conditions. Although this does not directly imply that the eggs would settle in these areas, higher probability of egg-dike interaction would occur that could potentially affect egg survival. In contrast, the hydrodynamic inference only suggests hydrodynamic conditions that are favorable for egg settling, which differs from the drift models.

Figure 11. Zoom-in view of estimated egg settling zone under discharge condition Q1 using (a) SDrift model and (b) hydrodynamic inference based on Rouse number criterion. River miles 312 and 313 are indicated in the plot by red triangles.
Figure 12. Zoom-in view of estimated egg settling zone under discharge condition Q4 using (a) SDrift model and (b) hydrodynamic inference based on Rouse number criterion. River miles 312 and 313 are indicated in the plot by red triangles.

In addition, the drift model predicts substantial egg entrapment near the left bank upstream of the bend located around x=43,100 m (upstream of river mile 311), where these regions were not inferred from hydrodynamic data. The differences indicate that eggs can be entrapped within locations where hydrodynamics would indicate suspension. The potential entrapment in the drift model is likely due to the reduction in egg-drift speed close to the left bank, which increases the probability of egg settling. In curved rivers reaches, the unevenly distributed flow in the cross section and secondary flow may push eggs towards the outer side of the channel, which can increase the probability of the particle-bank interaction.

Figure 13. Trajectories of 200 SDrift simulated eggs near the left bank at the release point at two discharges: (a) Q1, (b) Q4. River miles 309–313 are indicated in the plot by red triangles.

The drift trajectories of 200 simulated eggs released near the left bank for discharge Q1 and Q4 can be used to visualize drift dynamics simulated in SDrift (Fig. 13). The modeling results show that, under Q1, there is minimal egg drift into the low-flow region between the L-head dikes and the left bank in Area 1, as well as into the high-riverbed region close to the left bank in Area 2. This restriction occurs because the elevation of the dikes in Area 1 are higher than the water surface elevation during low-flow conditions, preventing eggs from entering these areas. As a result, the drift model predicts minimal entrapment of eggs in these areas. However, the hydrodynamic inference only takes into account favorable conditions for egg settling, implying significant settling in these regions even when trajectories would fail to transport eggs into the areas. Nevertheless, under higher-flow conditions that permit eggs to enter these areas (see Fig. 13b), particularly in Area 1, entrapment of eggs can occur (see Fig. 10), even though the hydrodynamic inference does not indicate significant settling compared to other low-velocity areas.

Vertical distribution of potential egg settling zones

To examine the likelihood of egg settling based on vertical position in the water column, the number of cells were counted that satisfy the criterion of egg settling based on hydrodynamic inference at the same vertical height above the riverbed (z) under the four simulated discharges. Figure 14 illustrates an example based on Rouse number criterion. The results show that the flow condition of Q1 has substantially more counts (about one order of magnitude) due to weaker turbulence compared to the other three flow conditions (Fig. 14a and b). We interpret this large change between Q1 and higher discharges as a threshold resulting when flows begin to overtop the wing dikes. Overtopping flows substantially decrease low-turbulence areas downstream and landward of wing dikes.

The modeling data also indicate that egg settling is more likely to occur in the lower part of water column but not near the riverbed. Taking Q1 as an example, the peak of the number of counts are located about 2 m above the riverbed, with the number of counts decreasing both towards surface and towards the riverbed (Fig. 14a). In the normalized water column profile (Fig. 14b), substantial counts are located within the bottom 20% of the water column. We note that various water depths occur across the river reach, and hence the number of counts on the x-axis of the plots (Fig. 14a and b) are different before and after the water column normalization.

Examining the probability distribution function (PDF), we found that four discharge conditions show similar vertical profiles: egg settling has more than 10% probability within approximately the bottom 5 m (Fig. 14c), corresponding to approximately the bottom 20% of water depth (Fig. 14d). This result suggests that when eggs are transported to the bottom 20% layer, the hydrodynamic condition is less favorable for them to be re-suspended compared to higher-up in the water column. Similar results of profiles were found for the criterion using shear velocity and the vertical turbulence intensity, albeit the number of counts and the PDF values are different due to different criteria (see supplementary file, Figs. S5 and S6).

Figure 14. Vertical distribution of hydrodynamic-inferred egg settling locations using the criterion of Rouse number. (a) Number of counts as a function of different heights (z) above the riverbed; (b) number of counts as a function of the normalized heights which are normalized using flow depth (H); (c) probability distribution function (PDF) of the occurrence as a function of z; (d) PDF of the occurrence as a function of z/H.

Discussion on the egg survival

Examining river hydrodynamics in three dimensions through well-calibrated models yields valuable insights into the spatial distribution of flow velocity, water depth, and associated turbulence. These parameters can be used to identify potential locations where carp eggs may settle. However, using and interpreting results based on hydrodynamic criteria must be exercised with careful consideration. For instance, the Rouse number classification for particle suspension involves a broad range of values. In this study, we adopted Ro>1.2 as an indicator of egg settling, with Ro=1.2 representing the lower Rouse number bound for partial suspension. Conservatively, a critical value of Ro=2.523 is recommended for assessing predominantly bedload particle transport, indicating minimal to no suspension in the water column. Hence, at Rouse numbers between 1.2 and 2.5, partial suspension would be expected. In addition, the analysis using three-dimensional drift model results indicates that carp eggs would not drift into the egg settling zones within the L-head dikes and left bank (Area 1 in Fig. 13), for example, which would have predicted settling using hydrodynamic inference under the low-flow condition. This is because the actual egg drift pathway is governed by various parameters including egg spawning locations, streamlines of water flows, and interactions of flow and hydraulic structures. Consequently, predictions relevant to invasive carp management would improve when using the hydrodynamic-inferred egg settling zones if these additional parameters were taken into account.

Although egg settling zones based on hydrodynamic inference may not represent the actual conditions for egg settling, those predictions provide valuable information about the local hydrodynamics and suitability for egg settling at lower computational cost compared to drift modeling (for example SDrift). Therefore, this information could be useful for managers in determining the desirability of implementing hydraulic controls for egg settling. For example, if flow patterns can be adjusted to guide eggs into low-turbulence zones with adequate residence time, the hydrodynamics would facilitate the desired settling of eggs, aligning with management objectives for controlling aquatic invasive species. However we noted that solely using hydrodynamic inference may be misleading in invasive carp management without knowledge of drift pathways.

While high turbulence zones are the necessary environment for carp eggs to be suspended, eggs can be damaged or killed if turbulence exceeds a certain threshold. Prada et al.43 found an increased mortality in drifting grass carp eggs when exposed to turbulence with TKE greater than 2 m2/s2 for 1 minute in a grid-stirred turbulence tank. When TKE reaches 2.7 m2/s2, the mortality rate increased by nearly 30%. The corresponding maximal shear stresses were found to be 20 and 30 N/m2 near the grid for these two TKE values respectively. From our hydrodynamic model, mean TKE in the simulated reach under discharges Q1 to Q4 ranges from 0.01 to 0.02 m2/s2, with maximal depth-averaged TKE ranging from 0.16 to 0.21 m2/s2. The maximal TKE in the water column is found within 0.31–0.38 m2/s2 under four discharge conditions. These values are much smaller than the reported values that are harmful for carp eggs. Therefore, in a typical egg drift process, it is unlikely for eggs to experience persistent, extreme turbulence that could cause direct damage or mortality.

However, strong turbulence often generates high suspension and transport of sediment in the river. The abrasion between carp eggs and the suspended sediment may affect the egg survival rate. In the laboratory experiment conducted by Prada et al.15, carp eggs were found to drift within the lower 75% of the water column with lower flow velocity in the flume (0.08 m/s). When the flow velocity was increased to 0.22 m/s, the egg distribution in the water column was uniform, indicating a well-suspended condition for carp eggs. With further increasing flow velocity, Prada et al.15 observed that eggs were drifting more towards the bottom where they collided with the sediment particles. This indicates that the suspension of sediment could affect the vertical distribution of suspended eggs. They also observed reduced survival rate in medium and high flows compared to the control, while the survival rate was almost the same in low flow compared to the control. They also observed different larvae behaviors in different flow velocities, which may also contribute to the survival of carps. In our simulated Missouri River reach, the river turbulence may not pose a threat to carp eggs, but the suspended sediment could have negative effects. There has been limited study on the quantitative effects of sediment abrasion on egg mortality, indicating a fruitful subject for future studies.

Conclusions

In this study, we analyzed the simulated hydrodynamics of an 8-km reach in the Lower Missouri River, a site characterized by extensive channelization and river training. Four discharges representing 45–3% daily flow exceedance were examined. Calibration and validation of the simulations were conducted based on field observations. Flow depth, mean flow velocity, and turbulence quantities were investigated through computational fluid dynamics modeling. Simulated results show highly varied spatial distributions of mean flow and turbulence characteristics, primarily attributed to the curvature of the channel, variation in bed morphology, and the presence of river-training hydraulic structures, including wing dikes and L-head dikes.

To investigate the use of hydrodynamics for inferring the settling and suspension of carp eggs, we applied three criteria established in previous carp egg studies to analyze the spatial distribution of potential settling zones. The simulation results enabled the identification of low turbulence zones where insufficient suspension may hinder carp egg development. When comparing these hydrodynamic-inferred egg settling zones with the entrapment predicted by a Lagrangian egg-drift model, we observed that egg drift paths significantly influenced the locations where eggs may settle or be intercepted by in-stream hydraulic structures. Therefore, it is crucial to consider additional factors, such as spawning locations and drift paths, when using hydrodynamic inference to identify potential egg settling zones and larval nursery locations for invasive carp management.

Lastly, river turbulence may also influence carp egg survival through shear stresses and interactions with suspended sediment. Our data indicate that turbulence kinetic energy in the river does not surpass the laboratory-identified threshold associated with direct egg damage. However, abrasion from suspended sediment and the complex interactions between eggs and hydraulic structures, riverbed, and banks, accentuated by high morphological variations as demonstrated in the entrapment areas in the egg drift model, could affect the overall survival rate of carp eggs.

Data availibility

The data of field measurements and modeling are available in the online repository doi:10.5066/P9X5M3WH33.

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Velocity of pipe

Dynamic Performance of Suspended Pipelines with Permeable Wrappers under Solitary Waves

단일 파동 하에서 투과성 포장지가 있는 현수 파이프라인의 동적 성능

Youkou Dong, Enjin Zhao, Lan Cui, Yizhe Li, Yang Wang

Abstract

Submarine pipelines are widely adopted around the world for transporting oil and gas from offshore fields. They tend to be severely ruined by the extreme waves induced by the natural disaster, such as hurricanes and tsunamis. To maintain the safety and function integrity of the pipelines, porous media have been used to wrap them from the external loads by the submarine environment. The functions of the porous wrappers under the hydrodynamic impact remain to be uncovered before they are widely accepted by the industry. In this study, a numerical wave tank is established with the immersed boundary method as one of the computational fluid dynamics. The submarine pipelines and their porous wrappers are two-way-coupled in terms of displacement and pressure at their interfaces. The impact from the solitary waves, which approximately represent the extreme waves in the reality, on the pipelines with different configurations of the porous wrapper is investigated. The results present significant protective functions of the wrappers on the internal pipelines, transferring the impact forces from the pipelines to the wrappers. The protective effects tend to be enhanced by the porosity and thickness of the wrappers. The influence of the pipeline configurations and the marine environment are then analysed. As for the front pipeline, an increase in the gap leads to a slight increase in the horizontal forces on both the wrapper and the pipeline, but a significant increase in the vertical forces. As for the rear pipeline, because of the shield function of the front pipeline, the velocity within the gap space and the forces on the pipes are decreased with the decrease in the gap size. The complex flow fields around the pipelines with wrappers are also illuminated, implying that the protection function of the wrapper is enhanced by the wave height reduction.

Keywords

extreme wave; submarine pipeline; external wrapper; coupling analysis; computational fluid dynamics

1. Introduction

Pipelines that are laid on or below the seabed and continuously transport large amounts of oil (or gas) are collectively referred to as submarine pipelines. They constitute the main transporting structures and currently they are the most economical and reliable selections in the design of transportation tools. Pipelines are usually installed within the seabed sediments under the protection of rock berms [1]. However, the sediments around the pipelines may be scoured by contour currents and internal waves, which expose the pipelines to the threat of complex marine environments [2]. The scour mechanism and its evolution process around the in-position pipelines were investigated by many scholars, such as Reference [3]. Occasionally, segments of a pipeline may be suspended between high points through continental slopes due to an uneven seabed profile. For example, suspended pipelines were widely used in the Ormen Lange projects, with massive depressions and landslide blocks scattered along the 120-km-long route [4].
Natural disaster, such as hurricanes and tsunamis, may induce extreme waves that generate enormous impact loads on the pipelines and may cause serious ruins to the whole production and transportation system [5,6,7]. Tsunamis, one of the major marine disasters caused by earthquakes and submarine landslides [8,9], send surges of water with extremely long waves that are not especially steep [10]. The tsunami triggered by a 9.0-Mw earthquake in 2011 extensively destroyed 70% of the total 200,000 structures along the Miyagi coastline, including submarine pipelines, seawalls, and coastal bridges. A tsunami is typically composed of several transient waves with varying amplitudes, wave-lengths, and wave periods during propagation. Solitary waves were proposed to simulate the tsunami waves by decomposing them into N-waves through the Korteweg-de Vries equation [11,12,13,14]. Since then, the run-up process of the tsunami waves along the shoreline was investigated with the depth-averaged smooth particle hydrodynamics method [15,16]. References [17,18] quantified the impact loads over cylinders from a tsunami wave.
To protect the marine structures from potential damages due to extreme marine conditions, engineers have developed outer protections in terms of wrappers made of porous media. A porous medium enhances the buffering performance of the structures and dissipates part of the incoming wave energy [19]. For example, the turbulent intensities on a permeable breakwater were significantly attenuated in the numerical analysis by References [20,21,22]. Naturally, porous media are expected to be protective to submarine pipelines under extreme marine conditions, although thermal insulation and erosion prevention were mainly considered in designing pipeline coatings in the industry [23,24]. Reference [25] quantified the wave forces on pipelines buried in an impermeable bed with coverings of porous media. References [26,27] evaluated the protective performance of a porous polymer coating on subsea pipelines under sudden impacts. The drag reduction function of the porous coatings over cylinders were then quantified by Reference [28]. Two factors were considered to influence the stabilization effect of the porous coatings on pipelines: the production of an entrainment layer through the coating and the triggering of turbulent transition of the detaching shear layers. In engineering practice, applications of porous coatings on submarine pipelines are limited. Concrete wrappers, mainly designed to counteract the buoyancy forces of pipelines, can be considered as one kind of porous wrapper with medium permeability. In addition, porous wrappers made with woven carbon-fiber materials or polyurethane foam may be designed in future for pipeline protection.
The above literature review revealed that few studies were performed to examine the protective effect by the porous media on submarine pipelines, which is the main aim of this study. The porous wrapper and the submarine pipeline modules are simulated in a numerical wave tank (NWT) with the immersed boundary (IB) method. The numerical methods and equations will be provided in Section 2. Verification of the numerical model is provided in Section 3. The parametric simulations are in Section 4, in which the effects of different waves on various pipelines with porous wrappers are analysed. The conclusions are given in Section 5.

2. Numerical Methods

For simulating the interactions between pipelines and waves, the finite volume methods have been widely used. In this study, the commercial finite volume package FLOW-3D® (version 11.1.0; 2014; https://www.flow3d.com (accessed on 10 December 2022); Flow Science, Inc., Santa Fe, NM, USA). Flow-3D aims to solve the transient response of fluids under interactions with structures, internal and external loads and multi-physical processes. It features some advantages in terms of a high level of accuracy in solving the Navier-Stokes equation with the volume of fluid (VOF) method, efficient meshing techniques for complex geometries, and high efficiency level for large-scale problems. Also, Flow-3D provides the flexibility and utility for flowing through porous media. A two-dimensional numerical wave tank was constructed by using the immersed boundary (IB) method and an in-house subroutine termed as IFS_IB. A submarine pipeline and porous medium were two-way coupled at the interface described by the individual volume fractions [29]. The pipeline was wrapped with a layer of a porous medium. A solitary wave was generated at the inlet boundary of the tank to simulate an approaching tsunami. Non-slip wall conditions were assigned at the bottom of the tank and the pipe surface, which was also specified with a roughness coefficient. The top boundary was defined as a free boundary and configured with the atmospheric pressure. A Neumann-type absorbing boundary condition, a stable, local, and absorbing numerical boundary condition for discretized transport equations [30], was imposed on the outlet boundary to attenuate the reflections of the outgoing waves. A transition zone is set within a certain range from the boundary to reduce the horizontal gradient force of the elements near the boundary and suppress the calculation wave caused by this boundary condition. Through the relaxation coefficient, the predicted value on the inner boundary of the transition zone and the initial value on the outer boundary are continuously transitioned to achieve the purpose of reducing the reflection of propagating waves. The CUSTOMIZATION function of the software FLOW-3D was utilised to impose the Neumann-type absorbing boundary condition. The FLOW-3D distribution includes a variety of FORTRAN source subroutines that allow the user to customize FLOW-3D to meet their requirements. The FORTRAN subroutines provided allow the user to customize boundary conditions, include their own material property correlations, specify custom fluid forces (i.e., electromagnetic forces), add physical models to FLOW-3D, and have additional benefits. Several “dummy” variables have been provided in the input file namelists that users may use for custom options. A user definable namelist has also been provided for customization. Makefiles are provided for Linux and Windows distributions and Visual Studio solution files are provided for Windows distributions to allow users to recompile the FLOW-3D code with their customizations.

2.1. Governing Equations

The governing equations involved include the continuity equations and Reynolds-averaged Navier-Stokes equations. The mass and momentum are conserved in a two-dimensional zone [31]:

where U is the velocity vector, X is the Cartesian position vector, g denotes the gravitational acceleration vector, and ρ represents the weighted averaged density. The term μ is the viscosity. σκ∇α identifies the surface tension effects with σ as the surface tension and α as the fluid volume fraction. Each cell in the fluid domain has a water volume fraction (α) ranging between 0 and 1, where 1 represents cells that are fully occupied with water, while 0 represents cells that fully occupied with air. Values between 1 and 0 represent free surface between air and water. The free surface elevation is defined by using the volume of fluid (VOF) function:

where VF is the volume of fluid fraction, FSOR is the source function, FDIF is the diffusion function; Ax, Ay, and Az represent the fractional areas; and u, v, and w are the velocity components in the x, y, and z directions.

2.2. Porous Media Module

In FLOW-3D, the porous medium’s flow resistance is modelled by the inclusion of a drag term in the momentum equations (Equation (2)). Coarse granular material is used in most coastal engineering applications, in which case the Forchheimer model is suitable. Using this model, a drag term Fdui is added to the righthand-side of Equation (2):

where |U| is the norm of the velocity vector, n the porosity, and a and b are the factors.

2.3. Solitary Wave Boundary

The solitary wave is generated in terms of variations of the surface elevation η and velocities u and v by following McCowan’s theory [32]:

where h is the still water depth; Q is the reference value

where X = x − c0t; 𝑐0=√𝑔𝐻+ℎ; H is the wave height; and t is the elapsed time.

3. Validation

3.1. Propagation over a Porous Breakwater

An experimental test on the propagation process of a solitary wave over a permeable breakwater was performed by Reference [20], which was simulated in this study to validate the adopted two-way coupling model (Figure 1a). The length, width, and depth of the flume tank were 25, 0.5, and 0.6 m, respectively. A permeable breakwater was mounted at the bottom of the flume, which had dimensions of 13 cm and 6.5 cm in the length and height, respectively. The porous breakwater with an average porosity of 0.52 was configured by glass beads with a constant diameter of 1.5 cm. Two wave gauges were fixed before (WG1) and behind (WG2) the breakwater, respectively. The initial still water depth h was assumed to be 10.6 cm. Height of the solitary wave H was considered to be 4.77 cm. In the numerical model, the calculation zone had dimensions of 5 m in length and 0.25 m in height. The second order quadrilateral mesh elements were adopted. The grid around the breakwater was the finest of 0.001 m. The adopted time step size was 0.05 s. The numerical predictions of the water elevations at the locations WG1 and WG2 by the adopted numerical tool FLOW-3D are close to both the experimental measurements and the numerical predictions from another CFD FLUENT version 14.0.1 [33] (Figure 1). Figure 1b,c show the comparison of monitored water levels at the two water level monitoring points in Figure 1a. It can be seen that the experimental results of the two monitoring points are consistent with the numerical simulation results, indicating that the propagating solitary wave energy is basically completely dissipated and then flows out. If the propagating wave energy is not dissipated, the phenomenon of wave reflection will occur. The waves monitored at the two monitoring points will appear superposition of propagating waves and reflected waves. The numerical simulation results do not agree with the physical experiment results. The fluctuations of the water surface elevation after the bypass of the incoming wave are due to its residual reflection at the right absorbing boundary condition, which arrives at WG2 at an earlier time than WG1. Evolution of the wave surfaces was also compared between the experimental and the numerical models (Figure 2), which demonstrates that the numerical tool is sufficiently reliable. The velocity of the wave is reduced by the porous medium as it partially infiltrates into the breakwater, which is shown as in Figure 3 by comparing the horizontal velocity distributions between the experimental and numerical results at times of 1.5 s and 2 s. The numerical predictions of the flow velocities have slight discrepancies with the experimental measurements, which are attributed to the material assumptions made in the numerical model for the glass beads in the experimental setup.

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Figure 1. The diagrammatic sketch of the numerical setup (non–scaled) (a) and the temporal evolution comparison of water surface between experimental and numerical results (b,c).

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Figure 2. Water surface comparison between experimental and numerical results.

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Figure 3. Comparison of horizontal velocity distribution between experimental and numerical results.

3.2. Forces on Pipeline

Another experimental test of a solitary wave impacting a pipeline was performed by Reference [34], which was also reproduced in this study for validation purposes. The calculation zone had dimensions of 40 m in length and 0.6 m in height. The solitary wave had a height of 0.0555 m with the initial water depth of 0.192 m. The pipe had a diameter of 0.048 m, which had a distance of 0.136 m over the bottom boundary of the model. A dense mesh consisting of 413,411 cells was employed with a mesh size of 0.1 mm around the pipe, which proved to be sufficiently fine through convergence studies. History of the horizontal and vertical forces, normalized by ρgL(πD2/4) with L as the unit length of 1 m, is compared between the experimental and numerical results (Figure 4). Both the peak values and the transient variations of the forces predicted by the numerical analysis converge to the measured values in the experimental test. The slight discrepancy between the numerical and experimental results at 2.5 s and 3.1 s, which may be induced by the error of the numerical model simulating the complicated turbulence behaviour, is acceptable in relation to the requirements of this study as our concern is mainly the peak values of forces.

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Figure 4. Force comparison between the experimental and numerical results.

Therefore, the adopted numerical tool is sufficiently reliable to simulate the interactions between solitary waves and the permeable structure through the above validation cases.

4. Results and Discussion

Influence of the solitary waves on the performance of wrapped pipelines was investigated by considering different wave heights (H) and thicknesses (T) and wrapper porosities (n). The still water depth (h) was taken to be 6 m (Figure 5). The diameter of the porous medium was assumed to be 0.05 m. The pipeline diameter D was set at 1 m. In Figure 5 the variable G represents the gap between the permeable wrapper and the seabed. The scouring process had been completed before the simulation; therefore, the seabed boundary was taken as a rigid wall. The tandem pipelines had a distance of S between each other. The whole model had dimensions of 400 m in length and 12 m in height. The finest mesh around the pipeline was configured as 0.0025 m, which was verified to be sufficiently fine through trial calculations with finer meshes.

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Figure 5. Layout for solitary wave impinging on the submarine pipeline encased in porous media.

4.1. Effect of Porous Wrapper

4.1.1. Wrapper Porosity

The pipeline was put on the seabed. The gap (G) between the wrapper and the seabed was considered to be zero. The height (H) of the solitary wave was considered to be 2 m. The porosity (n) was taken to be 0.0, 0.4, 0.6, and 1.0. Note that n = 0.0 indicates the impervious condition, while n = 1.0 corresponds to the non-wrapping condition. The thickness of the permeable wrapper remained at 0.5 m. In calculation, the wave approaches the pipe at around 6.3 s and departs from it at 10.2 s. When the wave approaches, the kinematic performance over the pipe is enhanced (Figure 6). Due to the wave disturbance, a number of small vortices are generated around the pipe (Figure 7). At the departure of the wave, the disturbance to the flow field seems to be more intense than that at its arrival, which further generates vortices around the pipeline. Without a wrapper, the pipe is fully exposed to the disturbance of the incoming wave, which maximises the velocity and vorticity values around the pipe. When the pipeline is wrapped by a porous medium, some water seeps into the wrapper, and the velocity in the wrapper is reduced to a very low value, which implies that the porous medium is capable of absorbing the dynamic energy of the flowing fluid. With an external coverage (n < 1.0), the disturbance is generated mainly at the outer surface of the wrapper. As the wrapper porosity increases, the domain of the low-speed flow underneath the pipeline expands.

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Figure 6. The velocity contours of the flow fields under different porosities; (a) n = 0.0; (b) n = 0.4; (c) n = 0.6; (d) n = 1.0; left to right: arrival, departure.

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Figure 7. The vorticity contours of the flow fields under different porosities; (a) n = 0.0; (b) n = 0.4; (c) n = 0.6; (d) n = 1.0; left to right: arrival, departure.

The peak velocity around the pipeline without a wrapper (1.9 m/s) is larger than that with a wrapper (1.6 m/s) (Figure 8). For pipes with wrappers, the peak velocities around them are similar to one another. In contrast, the velocity profiles at x = 23 m are quite different. When the pipeline has no wrapper (i.e., n = 1.0), the change in velocity is fairly moderate. When the pipeline has a wrapper, the porous wrapper causes a secondary fluctuation in the rear water body after the primary fluctuation due to the peak of the wave passing through the pipeline. This generates a series of velocity peaks. The secondary velocity peaks for a porosity coefficient of 0.4 are higher than those for a porosity coefficient of 0.6. Accordingly, the turbulent kinetic energy (TKE) also changes with the porosities, as shown in Figure 9. The TKE is expressed as

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Figure 8. Comparison of horizontal and vertical velocities at front and rear of pipeline under different porosities.

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Figure 9. Comparison of turbulent kinetic energy at front and rear of wrapper under different porosities.

With the propagation of the wave, the TKE increases gradually in front of the pipeline. The TKE value under the pipeline without a wrapper (n = 1.0) (0.0008 kJ) is nearly half of that with a wrapper (0.0015 kJ). In comparison, the TKE values for the wrapped pipelines (n < 1.0) are very close to each other. After the wave leaves the pipeline, the TKE in front of the pipeline decreases for around 50%. Then, the TKE in the rear of the pipeline with a porous wrapper increases intensively because the porous media perturb the flow field. Compared with the pipeline without the wrapper, the interaction between the wrapped pipeline with the flow field is more severe. Furthermore, the solid wrapper can cause a strong disturbance to the flow, but the interference of the solid wrapper (n = 0.0) in the rear flow is still weaker than the wrapper with the porosity of 0.4.
The hydrodynamic forces (F), including the pressure and shear stress, are normalized by ρgL(πD2/4) (Figure 10). With a fully solid (i.e., n = 0.0) wrapper, the pipeline tends to be unaffected by the external flow. Hence, the hydrodynamic forces are zero while the forces on the wrapper reach their maximum. With porous wrappers, water seeps into the wrapper, buffering the impact of the incoming waves on the pipe. As the porosity coefficient increases, the induced forces on the pipeline increase while those on the wrapper decrease. When the porosity coefficient is 0.4, the forces on the external wrapper become higher than that on the internal pipeline. Therefore, the porous wrapper is capable of protecting the pipeline. The smaller the porosity coefficient the better protection the wrapper provides to the pipeline. The pressure gradient and shear stress forces are also shown in Figure 11.

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Figure 10. Comparisons of the maximum hydrodynamic forces on the pipeline and wrapper.

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Figure 11. Decomposed pressure gradient force (a) and shear stress (b) force on the pipeline.

4.1.2. Thickness of Wrapper

Seven wrapper thicknesses are considered: T = 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, and 0.5 m. The porosity coefficient is taken to be 0.6. At the moment that the wave goes through the pipe, the transient evolution of the vorticity contours around the pipeline with a wrapper thickness of 0.25 m is depicted in Figure 12. A couple of vortices emerge on the upper and lower vertices of the pipeline as the wave approaches the pipeline. As the wave propagates, many vortices flow along the wrapper and then shed off. Compared with the top vortices, the bottom vortices are shed off faster for two reasons. Firstly, as the friction at the seabed is small, the bottom flow velocity is higher than that on the top. Secondly, when the wave peak departs from the pipeline, a strong disturbance by the water body occurs behind the pipeline, followed by the irregular swing and fall off of the vortices. After the wave travels far away, the water flow near the pipeline becomes weak, and the vortices are scattered around the pipeline.

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Figure 12. Temporal evolutions of vorticity contours around pipeline with wrapper thickness of 0.25 m (a) 6.0 s (b) 6.6 s (c) 7.2 s (d) 7.8 s (e) 8.1 s (f) 8.7 s (g) 9.0 s (h) 10.2 s (i) 12.6 s.

Figure 13 shows a comparison of flow field stream traces and the velocity contours. When the fluid penetrates the wrapper, the streamline starts to diverge, which indicates that the free flow is hindered. Therefore, the flow becomes slower and the flow direction becomes non-uniform. For the fluid flows out of the wrapper, the stream traces are quite complex and chaotic. The reason is that the seeping fluid mixes with the bypass flows and causes strong interference in the water body behind the pipeline. The streamlines passing through the wrapper indicates frequent water exchange at the wrapper surface. Along with the small-attached vortices on the wrapper surface, more fluid passes over the wrapper and causes a large vortex behind the wrapper.

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Figure 13. Comparisons of flow field streamtraces and velocity contours under different wrapper thicknesses; (a) T = 0.2 m; (b) T = 0.3 m; (c) T = 0.4 m; (d) T = 0.5 m.

The highest free surface elevations and velocities at the front and at the rear of the pipeline with different wrapper thicknesses are depicted in Figure 14. As the wrapper thickness increases, the highest elevation at the front of the pipeline seems to be quite stable, although the peak velocity increases by around 6%. At the moment that the wave bypasses the pipeline, the maximum elevation reduces with an increase in the wrapper thickness. This is because the pipeline blocks the wave propagation. However, due to the strong mixing effect of the seepage and bypass water, the maximum velocity rises to be higher than that in front of the pipe. The maximum forces on the wrapper and the pipeline for different wrapper thicknesses are shown in Figure 15. With an increase in the wrapper thickness from 0.2 to 0.5 m, the normalized forces on the wrapper are doubled as a larger interaction area is involved. In contrast, the vertical forces on the pipeline decrease by 12.5%. Therefore, the larger the thickness of the wrapper the safer the pipeline.

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Figure 14. Comparisons of the maximum elevations and velocities in front and rear of the pipelines with different wrapper thicknesses; (a) free surface elevation (note: original water depth is 6 m); (b) velocity.

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Figure 15. Hydrodynamic forces on the pipeline and wrapper.

4.2. Effect of Pipeline Structure

The in-situ pipelines may be under various suspended conditions since the seabed topography is often uneven. Some pipelines are also laid in tandem for the sake of the transportation efficiency. In order to examine the effects of porous wrappers on pipelines under different conditions, a study was carried out considering two scenarios, namely, suspended pipelines and pipelines in tandem. In the numerical models, the porosity coefficient (n) remained at 0.6, the thickness (T) of the wrapper was kept at 0.5 m, and the wave height (H) was assumed to be 2.0 m.

4.2.1. Suspended Pipelines

Six gaps (G) between the wrapper and the seabed (0.0, 0.2, 0.4, 0.6, 0.8, and 1.0 m) were considered [35,36,37]. The representative flow field at three points in time (6.3, 7.2, and 10.2 s) are shown in Figure 16. At the arrival of the wave at the pipeline (at 6.3 s), the flow is accelerated and the velocities over and beneath the pipe reach the maximum values due to the bypass effect of the fluid. At the moment that the wave peak is above the pipe (at 7.2 s), all the velocities around the pipe reach their highest values. After the wave passes over the pipe (at 10.2 s), the velocity decreases and several vortices are formed behind the pipeline. With a tiny wrapper-seabed gap, the velocity within the gap is very high while the flux is relatively small. An increase in the gap will result in an increase in the flux and a decrease in the velocity. A symmetric velocity distribution similar to a fisheye is observed behind the pipeline, which becomes more obvious when the gap increases (Figure 16c).

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Figure 16. The velocity contours of the flow fields under different gaps; (a) G = 0.2 m; (b) G = 0.6 m; (c) G = 1.0 m. Left to right: 6.3 s, 7.2 s, and 10.2 s. Left to right: arrival, stay, departure.

With the bypass of the wave, the vortices generated around the pipeline become larger. The vorticity contours and the streamlines of the flow field are shown in Figure 17. As the solitary wave approaches, a pair of whirlpools shed off from the wrapper with a gap of 0.2 m. With an increase in the gap, the two whirlpools gradually disappear and are replaced with two smaller vortices. Due to the internal pores within the wrapper, the streamlines in the wrapper are dispersed, and it is hard for a vortex to be generated. With an increase in the gap, two anti-symmetric vortices shed off from the wrapper. Besides, some tiny vortices remain adhered to the wrapper due to the interaction by the seepage and the external flow. When the gap is very small, a few small vortices are generated between the wrapper and the seabed. In contrast to the interface of vortex from the flow around a solid cylinder, the vortex interface at the wrapper is not fully smooth. Because of the strong interactions of fluid over the wrapper surface, several small vortices mingle with the large shedding vortices. The flow direction also varies greatly according to the streamline mobilisation.

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Figure 17. The vorticity contours of the flow fields under different gaps; (a) G = 0.2 m; (b) G = 0.6 m; (c) G = 1.0 m. Left to right: 6.3 s, 7.2 s and 10.2 s.

The gap is normalized by the pipeline diameter as β = G/D. With a small gap (β < 0.2), the horizontal forces on both the wrapper and the pipeline are slightly smaller than those on the wrapper and pipeline without a gap (Figure 18). With a further rise of the gap width, the horizontal forces are accordingly enlarged due to higher velocity around the pipeline as shown in Figure 16.

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Figure 18. Comparisons of the maximum horizontal and vertical hydrodynamic forces on the pipeline and wrapper under different gaps.

In contrast, an increase in the gap width may inversely cause the reduction of vertical forces on both the wrapper and the pipeline. The vertical forces can be considered to consist of two parts. One is caused by the weight of the water body at the bypass of the wave from the pipeline, while the other can be caused by the velocity difference between the flow above and below the pipeline after the flow passes over. In summary, as the gap increases, the flow velocity within the gap initially increases when β < 0.2 and then decreases when β > 0.2. In contrast, the vertical forces caused by the wave’s weight always decrease with an increase in the gap.

4.2.2. Pipelines in Tandem

The hydrodynamic forces on pipelines in tandem are investigated considering five different distances (S) between the two pipeline centres (2.5, 3.0, 3.5, 4.0, and 4.5 m). The velocity and vorticity fields at 6.3, 7.2, and 10.2 s around the tandem pipelines with distances of 2.5, 3.5, and 4.5 m are depicted (Figure 19 and Figure 20). As the wave approaches the pipeline, the velocity within the pipeline gap is very small due to the blockage effect of the pipeline in front. As the distance increases, the velocity field within gap space is enhanced as more water flow is allowed. The velocity above the pipeline has its maximum value, and part of the high-speed fluid flows into the gap through the space underneath the pipeline. With a small distance, the vortices shedding off from the front pipeline impinge directly on the rear pipeline without any stretching. When the distance is increased, noticeable vortex shedding emerges in the middle space (Figure 20c). Similar vortex shedding behind the rear pipeline is observed for different distances. After the wave bypasses the pipeline, the increase in the distance between the pipelines will cause an increase in the velocity magnitudes in the space among the pipelines. As the distance increases, the flow becomes more chaotic due to the seepage from the wrapper and the limited flow space. In summary, influence of the distance between the pipelines over the whole kinematic field is not significant, although the local flow field around the pipelines is severely affected. When the wave bypasses the tandem pipelines, the largest forces on structures (i.e., the pipelines and wrappers) are shown in Figure 21, in which the distance ratio (θ) is calculated as θ = S/D.

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Figure 19. The velocity contours of the flow fields under different spacings; (a) S = 2.5 m; (b) S = 3.5 m; (c) S = 4.5 m. Left to right: 6.3 s, 7.2 s and 10.2 s.

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Figure 20. The vorticity contours of the flow fields under different porosities; (a) S = 2.5 m; (b) S = 3.5 m; (c) S = 4.5 m. Left to right: 6.3 s, 7.2 s and 10.2 s.

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Figure 21. The maximum forces on the pipeline and wrapper under different distances.

As for the pipeline in front, as the distance ratio increases, the horizontal loads on the wrapper and pipeline increase slightly, while the vertical forces are almost doubled. As for the rear pipeline, as the distance reduces, the velocity in the gap becomes smaller and the forces on the pipelines and wrappers are also reduced, which is mainly attributed to the shield effect from the front pipeline. With an increase in the distance, the forces increase due to the increase in the turbulence energy in the gap.
Different ratios of the forces on the front and rear pipelines are depicted in Figure 22. The difference ratio is defined as ΔFn = (ff,max−fr,max)/ff,max, where ff,max and fr,max are the maximum forces on the pipeline or wrapper. It is found that the horizontal loads on the rear pipe and wrapper tend to be always higher than their counterparts on the front pipe. This means that a turbulent flow in the horizontal direction on rear pipe is more intense than that on the front pipe. For different distances, deviations for the forces on the pipelines and wrappers are also different. The deviation is found to be maximized at a distance of 1 m and this indicates that the pipeline is not well protected and needs to be avoided in engineering practice.

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Figure 22. The deviation of the forces on the front and rear pipelines and wrappers under different distances.

4.3. Effect of Wave Height

Six groups of wave heights (H), i.e., 1.6, 1.8, 2.0, 2.2, 2.4, and 2.6 m, are selected to consider different marine environment. After bypassing the pipeline, the height of the wave decreases because of the blockage effect of the pipeline and the dissipation of the flow energy (Figure 23a). The deviation ratio of the wave heights before and after the wave passes over the pipeline is shown in Figure 23b and is defined as δ = (Hf,max − Hr,max)/Hf,max. The wave height attenuation becomes more significant as the wave height increases. This means that waves with larger heights are more easily affected by the pipelines.

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Figure 23. Waves with different wave heights; (a) temporal evolutions; (b) attenuation deviation.

At the bypass of the wave through the pipe, the loads are increased until they reach the maximum values at the moment that the wave peak appears above pipeline (Figure 24). The forces gradually decrease as the wave propagates. Because of some reflux after the wave bypasses the pipeline, the flow is in the opposite direction to that of the wave propagation, resulting in a negative force. The vibration of the water body by the wave propagation induces oscillations of the forces on the pipeline and wrapper. When the wave height is larger, the force oscillation becomes fiercer and the maximum loads on the pipeline and the wrapper increase (Figure 25). The vertical forces on the pipeline are the largest compared with other forces under the same conditions. Besides, as the wave height increases, the increased amplitude of vertical forces on the pipeline is the most significant change since the weight of the water above the pipeline increases. Therefore, given that the wave height is very high, the protective function of wrapper on the pipeline tends to be weakened compared with that of the wrapper for a low wave height.

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Figure 24. The temporal evolutions of forces on the pipeline and wrapper; (a) Horizontal maximum force on pipeline; (b) Vertical maximum force on pipeline; (c) Horizontal maximum force on wrapper; (d) Vertical maximum force on wrapper.

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Figure 25. Variation of hydrodynamic forces on the pipeline and wrapper under different distances.

5. Conclusions

The effect of porous media on the dynamic performance of submarine pipelines under solitary waves was investigated. The porosity of the wrapper, the seabed topography, the structure of the pipeline, and the marine environment were considered. The study had a limitation of the model sizes due to the limited computational resource and the simplification of the solitary wave due to its mathematical complication, which will be tackled in future works. The following main conclusions have been made.

(1) When a pipe is wrapped by a porous medium, the velocity in the wrapper is relatively small because the porous medium can consume the water energy and weaken the flow. With an increase in the porosity, the range of the low-speed flow at the bottom of the pipeline expands. This indicates that the porous wrapper can slow down the flow and affect a wider region of the surrounding water. After the bypass of the wave through the pipe, the number and volume of the vortices behind the porous wrapper are larger than those for a pipeline with a solid wrapper or without a wrapper. As the porosity coefficient increases, the impact forces on the pipe increase, while those on the wrapper decrease. This implies that the porous wrapper is capable of protecting the pipeline.

With an increase in the wrapper’s thickness, the hydrodynamic forces on the wrapper tend to increase. In particular, the horizontal forces on the pipeline decrease with an increase in the thickness due to the protection of the wrapper, while the vertical forces are increased because of variations in the fluid’s stagnation point.

(2) For a wave bypassing a pipe with different heights, a symmetric speed change similar to a fisheye appears behind the pipeline, along with two antisymmetric vortices shedding off from the wrapper.

As the internal seepage interacts with the external fluid flow, several small vortices are still attached to the wrapper. The hydrodynamic vertical forces on both the wrapper and the pipeline decrease with the pipeline distance. With an increase in the suspension of the pipe, the velocity and TKE within the gap space increase and both the vortex intensity and the number of vortices increase. Therefore, the flow pattern appears to be chaotic. As for the front pipeline, an increase in the gap leads to a slight increase in the horizontal forces on both the wrapper and the pipeline, but a significant increase in the vertical forces. As for the rear pipeline, because of the shield function of the front pipeline, the velocity within the gap space and the forces on the pipes decrease with a decrease in the gap size.

(3)When the waves with different heights pass over the pipeline, the height of the wave is reduced because of the blockage function from the pipeline and the dissipation characteristic of the flow energy. When the wave height is increased, the velocity around the pipeline increases, inducing an increase in the TKE. As the wave height increases, all the maximum forces on the pipeline and wrapper also increase. Note that an increase in the vertical forces on the pipeline is the most significant change because the weight of the water above the pipeline increases, which implies that the protection function of the wrapper is enhanced by the reduction in the wave height.

From the above investigation, the mechanism of load transfer from the pipeline to the external wrapper has been presented. This encourages industrial experts and academic scholars to arrange more investigations of the functions and cost-efficiency of porous wrappers, which could form a new branch of the pipeline design practice.

Author Contributions

Contributor Roles Taxonomy: E.Z.: Conceptualization, Methodology, Validation, Investigation and Writing—Original Draft; Y.D.: Data Curation, Formal analysis; Y.D.: Visualization, Project administration; Y.D., L.C., Y.W. and Y.L.: Writing—Review & Editing. All authors have read and agreed to the published version of the manuscript.

Funding

The paper was supported by the National Natural Science Foundations of China (Grants No. 52001286 and No. 42272328), GuangDong Basic and Applied Basic Research Foundation (Grant No. 2022A1515240002) and Comprehensive Survey of Natural Resources in Huizhou-Shanwei Coastal Zone (Grant No. DD20230415).

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflict of interest.

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Concrete 3D Printing

Computational fluid dynamics modelling and experimental analysis of reinforcement bar integration in 3D concrete printing

3D 콘크리트 프린팅에서 철근 통합에 대한 전산 유체 역학 모델링 및 실험적 분석

Md Tusher Mollah, Raphaël Comminal, Wilson Ricardo Leal da Silva, Berin Šeta, Jon Spangenberg

Abstract

A challenge for 3D Concrete Printing is to incorporate reinforcement bars without compromising the concrete-rebar bonding. In this paper, a Computational Fluid Dynamics (CFD) model is used to analyze the deposition of concrete around pre-installed rebars. The concrete is modelled with a yield-stress dependent elasto-viscoplastic constitutive model. The simulated cross-sections of the deposited layers are compared with experiments under different configurations and rebar sizes, and found capable of capturing the air void formation with high accuracy. This proves model robustness and provides a tool for running digital experiments prior to full-scale tests. Additionally, the model is employed to conduct a parametric study under three different rebar-configurations: i) no-rebar; ii) horizontal rebar; and iii) cross-shaped (horizontal and vertical) rebars. The results illustrate that air voids can be eliminated in all investigated cases by changing the toolpath, process parameters, and rebar joint geometry, which emphasizes the great potential of the digital model.

Keywords

3D Concrete Printing (3DCP); Reinforcement bars (rebars); Computational Fluid Dynamics (CFD); Multilayer deposition; Air voids

1. Introduction

3D Concrete Printing (3DCP) [1] is an extrusion-based automated construction process that belongs to Digital Fabrication with Concrete (DFC) [2,3]. The 3DCP offers high-quality built-structures with customizable structural design in a cost- and time-efficient manner [[4], [5], [6], [7]]. Structures in 3DCP are fabricated in a layer-by-layer approach, where a concrete extrusion nozzle is controlled by a robotic arm, cylindrical robot, gantry system, or delta system [[8], [9], [10], [11]]. Despite the enormous potential of 3DCP, one of its crucial limitations is the integration of reinforcement for the production of load-bearing structures.
Most structural applications require the use of reinforcement to withstand tensile forces and introduce structural ductility [[12], [13], [14], [15]]. However, the introduction of reinforcement with 3DCP has never been an easy task, and difficulties were recognized at early stages of the technology [4] and various design solutions have been tested in practice to either circumvent the need for reinforcement or integrate reinforcement after the concrete is printed [[16], [17], [18], [19], [20]]. As a result, several reinforcement techniques have been proposed, such as bar reinforcement [21], micro-cable reinforcement [22,23], fiber reinforcement into the cementitious material [[24], [25], [26]], steel reinforcement using robotic arc welding [27,28], and in-process mesh reinforcement [29]. For comprehensive details on the reinforcement strategies, refer to [30]. Nevertheless, these reinforcement strategies are still rudimentary in many instances.
This study focuses on bar reinforcement methods, where rebars are integrated with freshly deposited cementitious material. A few approaches can be found in the literature, for example, penetration of vertical bars through multiple printed layers [31,32], placement of horizontal bars into a printed layer along the printing direction and then covered by the next layer on top [33,34], and depositing around pre-installed bi-directional rebars [35]. However, in most approaches, the bonding between the rebar and concrete was compromised by the air void around the rebar [21,36]. To overcome this constraint, a large amount of trial and error is required, which is costly and time-consuming.
An approach to mitigate extensive experimental campaigns is to apply numerical models. In the context of 3D printing technologies, like Fused Filament Fabrication (FFF), Robocasting, and 3DCP, CFD modelling has been found to be very beneficial [[37], [38], [39], [40], [41], [42], [43], [44]]. The morphology of the deposited strands in FFF was studied by Comminal et al. [45]. Furthermore, Serdeczny et al. [46] addressed how to reduce the porosities and enhance the bonding between subsequent layers. Mollah et al. [[47], [48], [49]] studied ways to minimize the deformation and thereby stabilize layers printed by Robocasting, while for 3DCP, the geometrical shapes of the single- and multiple-deposited layers have been investigated in detail in [[50], [51], [52]].
This paper uses the CFD model and extends the preliminary results recently published in [53]. The model uses elasto-viscoplastic constitutive equations to approximate the rheology of the concrete. The CFD model is validated by comparison with a number of experiments, and the model is subsequently exploited to make an in-depth analysis of air void formation between rebars and concrete using the cross-sections of the deposited part and the calculated volume fraction of air voids. Different material properties, such as yield stress and plastic viscosity, and processing parameters, like the rebar diameter, nozzle-rebar distance, a geometric ratio (i.e., the distance from nozzle to the substrate divided by the nozzle diameter), as well as a speed ratio (i.e., the printing speed divided by the extrusion speed) are varied. Section 2 describes the methodology of the study, along with the experimental and numerical details. Next, Section 3 presents and discusses the results. Finally, Section 4 summarizes the results with the conclusion.

2. Methodology

2.1. Materials’ properties and 3DCP experiments

A fresh cement-based mortar was used to perform the 3DCP experiment around the rebars. The mortar includes a binder system with white cement CEM I 52.5 R-SR 5 (EA), limestone filler with sand of maximum particle size 0.5 mm, admixtures, and water. The binder was prepared with a 75 L Eirich Intensive Mixer Type Ro8W. The water to cement ratio was 0.39. The admixtures dosage (by weight of cement) was set at 0.1 % high-range water-reducing agent, 0.1 % viscosity-modifying agent, and 0.5 % hydration retarder.

The rheological characterization of the mortar was done using an Anton Paar rheometer MCR 502, as used in [50,54]. The rotational and oscillatory tests were performed with a vane-in-cup measuring device. The obtained flow curve of the mortar from the rotational rheometric tests, with a ramp-down controlled shear rate (CSR), was fitted by a linear regression to determine the yield stress τ0= 630 Pa and plastic viscosity ηP= 7.5 Pa·s. The oscillatory test showed that the constitutive behavior of the unyielded mortar had a factorized relationship between the storage modulus G′ and loss modulus G′′ within the linear viscoelastic (LVE) region, where G′= 200 kPa was captured. Therefore, the mortar’s rheology was modelled as a yield stress limited elasto-viscoplastic material, where the storage modulus is used as the linear elastic shear modulus of the unyielded mortar. Furthermore, the rheological characterization showed that the mortar exhibited time-independent rheological characteristics within the actual printing process, see [50] for more details.

The setup for 3DCP experiments around ribbed rebars is presented in Fig. 1. It comprised a 6-axis industrial robot (Fanuc R-2000iC/165F) with a custom-designed nozzle ∅20 mm (i.e., nozzle diameter, Dn= 20 mm) made by fused filament fabrication of ABS thermoplastic, cf. Fig. 1-a. The robot also included a progressive cavity pump (NETZSCH) equipped with a hopper and a long steel-wire rubber hose (cf. Refs. [50, 52] for details). A 25 mm thick plywood plate was used as the built substrate as seen in Fig. 1-b. The 1000 mm long rebars of diameter Dr= 8 and 12 mm were placed horizontally on top of the substrate at a distance Hr= 14 mm. The horizontal rebars were held in place by two vertical rebars with a height of 37 mm. The setup was used to print a structure of four successive layers of parallel strands around the rebars. Details on the printing toolpath around the rebars are illustrated in the subsections below.

Fig. 1

Fig. 1. 3DCP experiment around rebars: (a) 6-axis robotic arm [50]; (b) plywood built platform with integrated rebars; (c) example of printing (picture is taken during printing of the third layer).

The extrusion nozzle was placed above the substrate with a nozzle height Dn/2 for the first layer, whereas for subsequent number of layers (Nl), the nozzle height was set at Nl∗Dn/2. Thus, the nominal height of a layer was h=Dn/2. The print was done with a material extrusion rate 0.91 dm3/min and nozzle speed 35 mm/s. An example of a physical print is presented in Fig. 1-c. After the prints hardened, cross-sections were collected to investigate the rebar-concrete bonding. The cross-section slices were taken at specific positions to analyze the print around the horizontal rebar and cross-shaped rebar (i.e., horizontal and vertical rebars). To avoid destroying the specimens while cutting them, the printed part were impregnated with epoxy resin in a vacuum chamber.

2.2. Computational models and governing equations

Three different CFD models are built. The first model only simulated the mortar flow to understand the void formation pattern without rebars. The last two models simulated the 3DCP experiment around rebars: one model simulated the mortar flow around the horizontal rebar, while the other considered the cross-shaped rebar. This subdivision enabled the CFD models to consider a smaller computational domain than if the two scenarios were combined.

The CFD models comprised a cylindrical nozzle, a solid-substrate, and an artificial solid component (at the top) within the computational domain of size 8.5D×6D×2D+4h as shown in Fig. 2 (top), where Model 1 excluded rebars (left), Model 2 included the horizontal rebar (middle), and Model 3 considered the cross-shaped rebar (right). The printing toolpath of the models are illustrated in Fig. 2. The toolpath for Models 1 and 2 are presented in 3D (left bottom figure), where the only difference was the presence of the horizontal rebar. The toolpath in 2D presented at the bottom right is for Model 3. For all the models, the toolpath of the extrusion nozzle kept a distance of Dnr from the axis of the nearest rebar. The lengths of the horizontal and vertical rebars were 50 and 40 mm, respectively. The other printing parameters were similar to the ones used in the experiment, cf. Section 2.1. Finally, the models were used to simulate four successive layers with a length of 125 mm. Note that the rebars are modelled as cylindrical solid objects (i.e., smooth rebar).

Fig. 2

Fig. 2. Model geometry with the extrusion nozzle, substrate, integrated rebars, and computational domain (top) and toolpath (bottom).

The computational domain was meshed by a uniform Cartesian grid. A mesh sensitivity test was performed for different meshes with cell sizes 0.9, 1.0, and 1.1 μm. Even if the change in absolute size of the cells were small, the total number of cells within the domain was 1.1, 1.5, and 2.0 million, respectively. A cell size of 1.0 μm was chosen as that was found to be time-efficient and had a negligible effect on the accuracy of the results. The top plane of the domain was an inlet boundary, where the artificial solid component was defined in order to prevent material flow outside the nozzle orifice, cf. Fig. 2 (top). On the bottom plane, a wall boundary was applied to represent the solid substrate. The other planes were assigned continuative boundary conditions, but had no influence on the results. Furthermore, no-slip boundary conditions were applied between fluids and solids.

Table 1 lists the printing parameters and their values for each of the investigated cases. All the models and cases are simulated for 4 successive layers.

Table 1. Description of case IDs with printing parameters and accompanying values. The reference values (corresponding to the experimental print) are written in bold, while the parameter change for each case is highlighted by underlining the value.

Empty CellModel/case ID
ParametersModel 1 (no rebar), Model 2 (horizontal rebar), and Model 3 (cross-shaped rebar)
Case 1
(reference)		Case 2Case 3Case 4Case 5Case 6Case 7Case 8Case 9
Nozzle diameter Dn (mm)202020202020202020
Rebar diameter Dr (mm)8612888888
Nozzle-rebar distance Dnr (mm)202020191820202020
Layer height h (mm)1010101010981010
Geometric ratio Gr=h/Dn0.50.50.50.50.50.450.40.50.5
Printing speed V (mm/s)353535353535353535
Extrusion speed U (mm/s)48.4248.4248.4248.4248.4248.4248.4251.4753.84
Speed ratio Sr=V/U0.720.720.720.720.720.720.720.680.65

The cementitious mortar flow was assumed transient and isothermal. Thus, the flow dynamics of the mortar are governed by the mass and momentum conservation equations of incompressible fluid:

where u is the velocity vector, ρ is the density, g=00−g is the gravitational acceleration vector, t is the time, p is the pressure, and σ is the deviatoric stress tensor.

The rheological behavior of the mortar was modelled by the following elasto-viscoplastic constitutive equation that represents σ as the sum of the deviatoric part of the viscous stress σV and elastic stress σE tensors; i.e.:

The deviatoric viscous stress tensor was predicted as:

is the deformation rate tensor, and T represents the transpose notation.

The deviatoric elastic stress tensor was modelled by the Hookean assumption of a small strain rate tensor E between each small time steps Δt=t−t0, to represent the elastic response of unyielded materials 

Ewhere G is the shear modulus and Et=Et0+ΔtDT is the incremental strain rate tensor approximated by integrating the deformation rate tensor over Δt.

The incremental representation of Eq. (5) can be written as:

 is the vorticity tensor. The first term of the left-hand side of Eq. (6) represents the change in stress at a fixed location in space. The change in stress due to advection and rotation of material particle is approximated by the second and third terms, respectively. The right-hand side takes into account the change in stress due to shearing.

The elastic stress tensor of the yielded material was approximated by imposing the yield stress τ0 limit as follows:

where σvM is the von Mises stress predicted as:

where IIσE∗=trσE∗2 is the second invariant of σE∗. The material was yielded when σvM exceeded the yield stress. The properties of the material used in the different models and cases are presented in Table 2. Note that the CFD model does not include the solidifications of the printed layers.

Table 2. Material properties.

Parameter with symbolUnitValueValue for reference simulation
Density, ρkg·m−321122112
Shear modulus, GkPa20–10020
Dynamic yield stress, τ0Pa400–800630
Plastic viscosity, ηPPa·s3.5–107.5

2.3. Numerical method

The computational model was developed in the commercial CFD tool FLOW-3D® (V12.0; Flow Science Inc.) [55]. It uses the FAVOR technique (Fractional Area/Volume Obstacle Representation) to embed solid objects (i.e., the nozzle, rebars, substrate, etc.) in the computational domain. The computational domain was meshed with a Cartesian grid and discretized with the Finite Volume Method.
The governing equations of the mortar flow were solved by the implicit pressure-velocity solver GMRES (Generalized Minimum Residual) [[56], [57], [58]]. The predictions of pressure and forces near solid objects were modelled by the immersed boundary method [59]. The yield stress limited elasto-viscoplastic criterion was built in the software, and the elastic stress was calculated explicitly. An implicit technique, successive under-relaxation, was used to solve the viscous stress of the momentum equation (Eq. (2)). The free surface of the mortar was captured by the Volume-of-Fluid technique, see details in Ref. [60, 61]. The momentum advection was calculated explicitly by an upwind-difference technique and ensured first-order accuracy. The time step size was controlled dynamically with a stability limit in order to avoid numerical instabilities [55]. All the simulations were run with 20 cores on a high-performance computing cluster. The study was carried out with a first-order accuracy in both space and time in order to reduce the computational time, which was extensive due to the elasto-viscoplastic material model that computes both viscous and elastic stresses (e.g., the computational time was six days for model 1 case 1). In this regard, one should note that the model can simulate a multitude of scenarios simultaneous.

2.4. Results post-processing

The simulated results were processed in two steps. The first step was to show the cross-sectional shapes which were done in the post-processing tool FLOW-3D®POST, and the second step was to calculate the volume fraction of air voids inside the printed structure. The cross-sectional shapes were used to investigate the interior of the structure and the rebar-concrete bonding. The cross-sectional shapes were obtained in the plane parallel to the yz-plane at the middle of the layer’s length, as shown in Fig. 3-d. Fig. 3-c sketches the nominal positions of the air void creation in a four-layered structure. The positions of the air voids were defined as outer-bottom, bottom, mid, top, and outer-top in this study. The presence of the air void was quantified by calculating the volume fraction of air voids around the middle of the layer’s length. The calculation enabled to capture the presence of air voids for Model 3, i.e., around the vertical rebar, as seen in the dashed-box of Fig. 3-b.

Fig. 3

Fig. 3. Post-processing of results; (a) introduction of volume sampling cuboid to calculate the volume fraction of air voids; (b) presence of air voids around the vertical rebar in the experiment; (c) schematic of air void creation; (d) cross-sectional shapes and void sampling area for the different models.

In order to calculate the volume fraction of air voids, a cuboid of size 20×25×3h mm3 was introduced to the CFD models as a volume sampling object, as seen in Fig. 3-a. Note that the size and position of the object were the same for all the models. The volume sampling was a three dimensional data collection tool built in the software that enabled calculating the amount of material as well as air void inside of it. Finally, the volume fraction of air voids VV was calculated as below:

3. Results and discussions

his section compares the simulated and experimental results of 3DCP around the rebars. Furthermore, it discusses the influence of different parameters on the air void formation in the cross-sectional shapes of printed parts and the volume fraction of air voids inside the structure. The parametric study includes the material properties (i.e., yield stress and plastic viscosity) and the printing properties (i.e., rebar diameter, rebar-nozzle distance, geometric ratio, and speed ratio).

3.1. Experiments and validation of the CFD model

The CFD models (Models 2 and 3) are compared and validated with the experiments. The results are presented in Fig. 4. Two rebar diameters, i.e., Dr= 8 and 12 mm, are taken into account, where the nozzle-rebar distances are 20 and 24 mm, respectively. The other printing and material parameters are kept constant in the experiments with different rebar diameters, see Table 1 (cases 1 and 3). In the case of the simulations, all parametric details are the same as implemented in the experiments except for the elastic shear modulus. The choice of shear modulus is subject to the analysis presented in Appendix A. The shear modulus is reduced to 100 kPa from the measured value (i.e., 200 kPa) to compare the simulated results with experiments. Furthermore, a shear modulus of 20 kPa is chosen for the parametric study in the later sections. These assumptions seem reasonable to avoid extensive computational time consumption since the differences found in void formation are limited (see Fig. A.1).

Fig. 4

Fig. 4. 3DCP experiments (left column), simulations (middle column), and comparison (right column). (a) Horizontal rebar with Dr= 8 mm and Dnr= 20 mm; (b) horizontal rebar with Dr= 12 mm and Dnr= 24 mm; (c) cross-shaped rebar with Dr= 8 mm and Dnr= 20 mm; and (d) cross-shaped rebar with Dr= 12 mm and Dnr= 24 mm. The blue part in the experiments is epoxy resin. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

The cross-sectional shapes of the 3DCP experiments around the horizontal rebar of
8 mm in Fig. 4-a illustrate the presence of a top air void as well as mid and bottom air voids positioned respectively above and below the horizontal rebar. The mid and bottom air voids are found to be smaller than the top one. This is due to the presence of the rebar that occupies the mortar’s flowable space as well as the deformation of the previously printed layers. For a detailed analysis of the deformation pattern, refer to [53]. The air voids at the top and bottom are significant when the rebar diameter is increased to 12 mm (Fig. 4-b). This is due to the fact that the nozzle-rebar distance was increased, which enhances the flowable space between the strands. In addition, the larger size of the rebar creates larger channels below and above itself, where the mortar of the second and third layers is forced to be squeezed into. The mid-air void is found to be absent as its area is fully occupied by the larger rebar. In the case of the cross-shaped rebars, the existence of the vertical rebar seems to restrict the merging of parallel strands, and therefore, the presence of air void content increases, cf. Fig. 4-c, d. This limitation is found to be pronounced for the larger rebar diameter with the larger nozzle-rebar distance.
The cross-sectional shapes of the simulations (middle column in Fig. 4) illustrate high accuracy predictions of the position and size of the air voids when compared with the experiments. Particularly, the models capture small details around the vertical rebar for both diameters. This can clearly be seen in the comparison of experiments and simulation, cf. right column in Fig. 4. A discrepancy is found in the strand’s width of the bottom layer as well as the shape of the printed part, specifically in the shape of strands of all the layers next to the vertical rebar and the height of the part for the smaller rebar diameter. These could be due to a combined effect of the idealized rheological model, as well as slight differences in the processing parameters, e.g. nozzle height above the printing surface, nozzle-rebar distance, as well as printing- and extrusion-speed. Note that the height of the vertical rebar in the experiments is a bit shorter than the one in the simulations (40 mm), although it does not influence the results.

3.2. Influence of materials properties

The influence of the material properties, yield stress and plastic viscosity, on the air void formation is presented in Fig. 5, Fig. 6, Fig. 7. The process parameters of Case 1 (cf. Table 1) are utilized.

Fig. 5

Fig. 5. Air void formation in the cross-sections of the printed parts for different yield stress.

Fig. 6

Fig. 6. Air void formation in the cross-sections of the printed parts for different plastic viscosity.

Fig. 7

Fig. 7. Volume fraction of air voids for different models as a function of (a) yield stress and (b) plastic viscosity.

Yield stress

Fig. 5 presents cross-sectional shapes for different yield stress, 400, 630, and 800 Pa. It can be seen that Models 1 and 2 predict a top air void, while for Model 3 the two topmost strands to the left are not in contact with the vertical rebar. The cross-sections illustrate that an increased yield stress causes less deformation of the printed layers and create stands with less round shape. This is due to the reduced effective gap (i.e., the distance between the nozzle and previous printed layer), which results in a reduced air void content for most models as seen quantitatively in Fig. 7-a. This behavior is converse to conventional concrete castings where a more fluid material (e.g. self-compacting concrete) can lead to a lower void content. An exception to the observed behavior that a higher yield stress leads to less voids formation is seen in case of Model 2 with
800 Pa, where the top air void is slightly larger as compared to the one for
630 Pa. Another exception is that an outer bottom air void appears for Models 1 and 2 when increasing the yield stress to 800 Pa. Both exceptions are a consequence of the yield stress now restricting the flow in confined spaces, which illustrates that it is a non-trivial task to fully eradicate air voids only by increasing the yield stress.

Plastic viscosity

As the plastic viscosity is varied, cross-sections for Model 1 show a slight change in air voids, see Fig. 6. A mid-air void is produced when the plastic viscosity is small, while the two largest plastic viscosities only produce the top air void. This is due to the increase in extrusion pressure that leads to larger deformation of the printed layers when the plastic viscosity is increased, cf. details in ref. [47]. When integrating a horizontal rebar (see Model 2), the air void formation increases at higher plastic viscosities. This could be due to the fact that the sideway flow of the depositing material (i.e., y-velocity) is limited by the flow resistance that comes from both the larger plastic viscosity and the presence of the solid rebar. No noticeable change can be seen in the cross-sections of Model 3 for different plastic viscosities. The same findings are quantitatively highlighted in Fig. 7-b, which illustrates that the volume fraction of air voids is not influenced much by the plastic viscosity except for Model 2.

3.3. Influence of processing conditions

The influence of processing conditions such as rebar diameter, nozzle-rebar distance, geometric ratio, and speed ratio on air void formation is presented in terms of cross-sectional shapes and volume fraction of air void, see Fig. 8, Fig. 9, Fig. 10, Fig. 11, Fig. 12. Models 1 to 3 are simulated with the reference material properties, cf. Table 2.

Fig. 8

Fig. 8. Air void formation in the cross-sections of the printed parts for different rebar diameters.

Fig. 9

Fig. 9. Air void formation in the cross-sections of the printed parts for different nozzle-rebar distances.

Fig. 10

Fig. 10. Air void formation in the cross-sections of the printed parts for different geometric ratios.

Fig. 11

Fig. 11. Air void formation in the cross-sections of the printed parts for different speed ratios.

Fig. 12

Fig. 12. Volume fraction of air voids for different models as a function of (a) rebar diameter, (b) nozzle-rebar distance, (c) geometric ratio, and (d) speed ratio.

Rebar diameter

The influence of the rebar diameter on the air void formation is presented in Fig. 8, Fig. 12-a. Models 2 and 3 are simulated (Model 1 does not contain a rebar) for Cases 1, 2, and 3, cf. Table 1. Fig. 8 illustrates that the top air void appears almost constant for Model 2, whereas the air void below the rebar increases with an enlarged rebar diameter. Two phenomena with opposite effects on the void formation play a role in this regard. On the one hand, increasing the rebar size reduces the space that the strands need to occupy to fully merge and thereby eliminate voids. On the other hand, the resistance towards flow and merging of the parallel strands next to the rebar increases proportionally with the size of the reinforcement. The latter effect is dominating in this case. For Model 3, the air void formation also increases when increasing the reinforcement. In addition to the previously mentioned argument, this is due to the left strands having to flow longer to reach the vertical rebar (i.e., Dnr+Dr/2). Conversely, additional air voids take place on the right-hand side of the vertical rebar for the smallest rebar diameter, because the nozzle-rebar distance Dnr= 20 mm is kept constant. Fig. 12-a underlines quantitatively that the volume fraction of air voids reduces when the rebar diameter is small. The trend is more pronounced for the cross-shaped rebar (Model 3), but in absolute values the air voids are substantially less for Model 2.

Nozzle-rebar distance

Fig. 9, Fig. 12-b show the effect of different nozzle-rebar distances on the formation of air voids. All the models are simulated for Cases 1, 4, and 5, cf. Table 1. Fig. 9 shows that the presence of air voids is reduced when the nozzle-rebar distance reduces. This is because the flowable space around the rebars shrinks. Interestingly, no significant air voids are present in Model 1 and 2 when Dnr= 18 mm, see Fig. 12-b. Fig. 12-b also depicts that the trend is more pronounced for the cross-shaped rebar (Model 3). One should be careful though about decreasing the nozzle-rebar distance too much, as a ridge is forming on the top layer since material from the left strand starts to flow on top of the right strand (Fig. 9), which potentially could affect the final shape of the structure. In case of the cross-shaped rebar model, air voids are formed for all investigated Dnr. One could potentially with benefit reduce the Dnr further, but not more than the sum of half of the nozzle diameter (10 mm), the nozzle wall thickness (2.5 mm), and half of the rebar diameter (4 mm), i.e., 16.5 mm, otherwise the nozzle will collide with the rebar.

Geometric ratio

The effect of the geometric ratio on the formation of air voids is presented in Fig. 10, Fig. 12-c. The considered simulations are Cases 1, 6, and 7 cf. Table 1. Fig. 10 illustrates that decreasing the geometric ratio can reduce the presence of air voids in the cross-sections. This is because a smaller geometric ratio results in wider strands, which then occupy more of the flowable space around the rebars. Note that when Gr= 0.50, 0.45, and 0.40 the layer height is 10, 9, and 8 mm, respectively. No air voids are formed for Model 1 and 2 when Gr= 0.45, and 0.40. However, for the smallest ratio ridges are obtained on either side of the strands as clearly seen for the top layer. These ridges can as previously mentioned have a negative effect on the final shape of the structure. Consequently, Gr= 0.45 is preferable for these two models. In the case of Model 3, air voids are still present next to the vertical rebar, even for the smallest investigated geometric ratio. The volume fraction of air voids is approximately 1.5 %, see Fig. 12-c. The geometric ratio could be reduced further in order to decrease the air voids even more, but the ridges already form at Gr= 0.40. Consequently, it is not possible to fully eliminate air voids while at the same time avoiding ridges when only varying the geometric ratio for Model 3.

Speed ratio

Fig. 11, Fig. 12-d illustrate the formation of air voids for different speed ratios. The considered simulations are Case 1, Case 8, and Case 9, cf. Table 1. The three speed ratios are obtained by applying an extrusion speed of 48.4 mm/s, 51.5 mm/s, and 53.8 mm/s. Fig. 11 show that less air voids are formed when decreasing the speed ratio (i.e., higher extrusion speed). Reducing the speed ratio increases the cross-sectional area of the strands proportionally, thereby decreasing the air voids. Model 1 obtains no air voids for the two smallest ratios, and the same is almost the case for Model 2; only a very small air void is formed when Sr= 0.68, see Fig. 12-d. Model 3 forms air voids for all speed ratios. For the lowest speed ratio, the third strand to the left is in contact with the vertical rebar, but air voids are still formed around the horizontal reinforcement, which underlines the fact that it is difficult to fully eliminate air voids for the cross-shaped rebars.

3.4. Cross-shaped reinforcement

Based on the above analysis, it is clear that the air voids around the horizontal rebar can be eliminated by changing some of the processing conditions, such as the nozzle-rebar distance, geometric ratio, and speed ratio. However, it remains unsolved to fully omit the presence of air voids around the cross-shaped rebar, although the processing conditions can reduce the volume fraction of air voids. A parametric study was conducted by varying some combinations of processing conditions; however, the same conclusion was achieved that the air voids could not be fully eliminated. In order to solve this predicament, a new stepped toolpath is investigated (see Fig. 13) along with three different rebar geometries: 1) cylindrical rebars as in the previous analysis, see Fig. 14-a; 2) a squared horizontal rebar, cf. Fig. 14-b; and 3) cylindrical rebars with a smooth transition between them, see Fig. 14-c. In all scenarios, the speed ratio is 0.665, the size (i.e., diameter or side of square) of the rebars are 6 mm, and the horizontal rebar is placed at a height of 8 mm from the substrate. The other processing parameters are the same as for Case 2 and reference material properties are applied. For scenarios one and two small air voids are formed, but for scenario three air voids are eliminated, see Fig. 14. This numerical analysis illustrates that although it is difficult to get rid of air voids for the cross-shaped rebars, one can do it when carefully selecting the material- and processing-parameters and remembering to have a smooth transition between the rebars.

Fig. 13

Fig. 13. New toolpath planning around the cross-shaped rebar.

Fig. 14

Fig. 14. Simulated structure with new toolpath and different rebar geometries. (a) Cylindrical horizontal- and vertical-rebar, (b) square horizontal rebar and cylindrical vertical rebar, (c) cylindrical horizontal- and vertical-rebar with smooth transition. Note that Dr= 6 mm, Sr= 0.665, and Hr= 8 mm.

4. Conclusions

A CFD model was used to predict the morphology of strands and the formation of air voids around reinforcement bars when integrated with 3DCP. The model used an elasto-viscoplastic constitutive model to mimic the cementitious mortar flow. The CFD model was compared with experiments that constituted a horizontal and a cross-shaped rebar configuration. The results illustrated that the model with high-accuracy could predict the air void formation in the structures. The simulations had though slightly less wide bottom strands as compared to the experimental counterpart, which was attributed to small differences in material behavior and processing parameters.
The CFD model was exploited to investigate the effect of material properties on the air void formation. The results illustrated that by increasing the yield stress less air voids were formed due to the reduced effective gap. However, the air voids could not be eliminated as the increased yield stress also restricted the flow in confined spaces. In contrast to the effect of the yield stress, the void formation decreased somewhat when decreasing the plastic viscosity (although not enough to omit air voids fully).
The process parameters were found to have a substantial effect on the air void formation. The air void formation increased when increasing the rebar diameter, because the resistance towards flow around the reinforcement and thereby merging of the strands increased proportional with the size of the rebars. The air voids could be reduced and in some of the horizontal cases fully avoided by reducing the nozzle-rebar distance, but it could come with the expense of ridges (which could affect the final geometry of the structure), since material from one strand would flow on top of a previously deposited stand. Similarly, decreasing the geometric ratio was found to reduce the presence of air voids, because a smaller geometric ratio resulted in wider stands that occupied more of the space around the rebars. However, the smallest ratios also resulted in ridges. It was also found that less air voids were formed when decreasing the speed ratio, since the cross-sectional area of the strands increased proportionally, thereby occupying more space around the rebars.
By decreasing the nozzle-rebar distance, geometric ratio, and speed ratio, voids were omitted around the horizontal rebar, but air voids would still be introduced for the cross-shaped rebar. Those air voids could be eliminated by changing the toolpath and some processing parameters, as well as altering the geometry of the reinforcement joint to a smooth transition between the horizontal and vertical rebar. The results highlight that it is non-trivial to avoid air voids when integrating rebars in 3DCP, but that the CFD model is a very strong digital tool when it comes to securing a good bonding between the reinforcement and concrete.
A limitation of the CFD model is that with the current computational power it is not possible to simulate a full 3DCP structure. Nevertheless, the CFD model is powerful when it comes to understanding and optimizing printing strategies for individual reinforcement details. In future research, it would be interesting to exploit the CFD model to systematically investigate various reinforcement setups and based on the model results generate response surfaces or lookup tables, which can be coupled with the 3DCP toolpath software. This approach would have several benefits: 1) the computational heavy CFD model could run all scenarios in parallel, thereby minimizing the physical time spent on calculations; 2) one could avoid repetition of individual reinforcement studies; and 3) the response surfaces or lookup tables could in a computational light manner come up with printing strategies for all reinforcement details in a full 3DCP structure.

CRediT authorship contribution statement

Md Tusher Mollah: Conceptualization, Methodology, Investigation, Formal analysis, Visualization, Writing – original draft, Writing – review & editing. Raphaël Comminal: Conceptualization, Formal analysis, Writing – review & editing, Supervision. Wilson Ricardo Leal da Silva: Conceptualization, Formal analysis, Writing – review & editing, Resources. Berin Šeta: Investigation, Formal analysis, Writing – review & editing. Jon Spangenberg: Conceptualization, Investigation, Formal analysis, Writing – review & editing, Supervision, Resources, Project administration.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors would like to acknowledge the support of the Danish Council for Independent Research (DFF) | Technology and Production Sciences (FTP) (Contract No. 8022-00042B). Also, the authors would like to acknowledge the support of the Innovation Fund Denmark (Grant No. 8055-00030B: Next Generation of 3D-printed Concrete Structures and Grant no. 0223-00084B: ThermoForm – Robotic ThermoSetting Printing of Large-Scale Construction Formwork), Moreover, the support of FLOW-3D® regarding licenses is acknowledged.

Appendix A.

This analysis varies the shear modulus (i.e., 20, 50, and 100 kPa) in the case Dr= 8 mm, as seen in Fig. A.1, which presents the cross-sectional shapes (top) and the volume fraction of air voids (bottom). It can be seen that increasing the shear modulus slightly reduces the air void formation. This is because the larger shear modulus enhances the ability of the material to act against the shear deformation. However, an increase in shear modulus also extensively increases the computational time of solving the non-linear elastic response of the elasto-viscoplastic material. For example, the computational time of Model 3 is about 6, 12, and 18 days for a shear modulus of 20, 50, and 100 kPa, respectively. Therefore, the shear modulus is reduced to 100 kPa from the measured value (i.e., 200 kPa) to compare the simulated results with experiments. Furthermore, the shear modulus 20 kPa is chosen for the parametric study in 3.2 Influence of materials properties, 3.3 Influence of processing conditions, 3.4 Cross-shaped reinforcement. These assumptions seem reasonable to avoid extensive computational time consumption since the differences found in Fig. A.1 are not substantial.

Fig. A.1

Fig. A.1. Air void formation in the cross-sections of the printed parts (top) and the volume fraction of air voids (bottom) for different shear modulus.

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Influences of the Powder Size and Process Parameters on the Quasi-Stability of Molten Pool Shape in Powder Bed Fusion-Laser Beam of Molybdenum

Influences of the Powder Size and Process Parameters on the Quasi-Stability of Molten Pool Shape in Powder Bed Fusion-Laser Beam of Molybdenum

몰리브덴 분말층 융합-레이저 빔의 용융 풀 형태의 준안정성에 대한 분말 크기 및 공정 매개변수의 영향

Abstract

Formation of a quasi-steady molten pool is one of the necessary conditions for achieving excellent quality in many laser processes. The influences of distribution characteristics of powder sizes on quasi-stability of the molten pool shape during single-track powder bed fusion-laser beam (PBF-LB) of molybdenum and the underlying mechanism were investigated.

The feasibility of improving quasi-stability of the molten pool shape by increasing the laser energy conduction effect and preheating was explored. Results show that an increase in the range of powder sizes does not significantly influence the average laser energy conduction effect in PBF-LB process. Whereas, it intensifies fluctuations of the transient laser energy conduction effect.

It also leads to fluctuations of the replenishment rate of metals, difficulty in formation of the quasi-steady molten pool, and increased probability of incomplete fusion and pores defects. As the laser power rises, the laser energy conduction effect increases, which improves the quasi-stability of the molten pool shape. When increasing the laser scanning speed, the laser energy conduction effect grows.

However, because the molten pool size reduces due to the decreased heat input, the replenishment rate of metals of the molten pool fluctuates more obviously and the quasi-stability of the molten pool shape gets worse. On the whole, the laser energy conduction effect in the PBF-LB process of Mo is low (20-40%). The main factor that affects quasi-stability of the molten pool shape is the amount of energy input per unit length of the scanning path, rather than the laser energy conduction effect.

Moreover, substrate preheating can not only enlarge the molten pool size, particularly the length, but also reduce non-uniformity and discontinuity of surface morphologies of clad metals and inhibit incomplete fusion and pores defects.

준안정 용융 풀의 형성은 많은 레이저 공정에서 우수한 품질을 달성하는 데 필요한 조건 중 하나입니다. 몰리브덴의 단일 트랙 분말층 융합 레이저 빔(PBF-LB) 동안 용융 풀 형태의 준안정성에 대한 분말 크기 분포 특성의 영향과 그 기본 메커니즘을 조사했습니다.

레이저 에너지 전도 효과와 예열을 증가시켜 용융 풀 형태의 준안정성을 향상시키는 타당성을 조사했습니다. 결과는 분말 크기 범위의 증가가 PBF-LB 공정의 평균 레이저 에너지 전도 효과에 큰 영향을 미치지 않음을 보여줍니다. 반면, 과도 레이저 에너지 전도 효과의 변동이 강화됩니다.

이는 또한 금속 보충 속도의 변동, 준안정 용융 풀 형성의 어려움, 불완전 융합 및 기공 결함 가능성 증가로 이어집니다. 레이저 출력이 증가함에 따라 레이저 에너지 전도 효과가 증가하여 용융 풀 모양의 준 안정성이 향상됩니다. 레이저 스캐닝 속도를 높이면 레이저 에너지 전도 효과가 커집니다.

그러나 열 입력 감소로 인해 용융 풀 크기가 줄어들기 때문에 용융 풀의 금속 보충 속도의 변동이 더욱 뚜렷해지고 용융 풀 형태의 준안정성이 악화됩니다.

전체적으로 Mo의 PBF-LB 공정에서 레이저 에너지 전도 효과는 낮다(20~40%). 용융 풀 형상의 준안정성에 영향을 미치는 주요 요인은 레이저 에너지 전도 효과보다는 스캐닝 경로의 단위 길이당 입력되는 에너지의 양입니다.

또한 기판 예열은 용융 풀 크기, 특히 길이를 확대할 수 있을 뿐만 아니라 클래드 금속 표면 형태의 불균일성과 불연속성을 줄이고 불완전한 융합 및 기공 결함을 억제합니다.

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Lab-on-a-Chip 시스템의 혈류 역학에 대한 검토: 엔지니어링 관점

Review on Blood Flow Dynamics in Lab-on-a-Chip Systems: An Engineering Perspective

  • Bin-Jie Lai
  • , 
  • Li-Tao Zhu
  • , 
  • Zhe Chen*
  • , 
  • Bo Ouyang*
  • , and 
  • Zheng-Hong Luo*

Abstract

다양한 수송 메커니즘 하에서, “LOC(lab-on-a-chip)” 시스템에서 유동 전단 속도 조건과 밀접한 관련이 있는 혈류 역학은 다양한 수송 현상을 초래하는 것으로 밝혀졌습니다.

본 연구는 적혈구의 동적 혈액 점도 및 탄성 거동과 같은 점탄성 특성의 역할을 통해 LOC 시스템의 혈류 패턴을 조사합니다. 모세관 및 전기삼투압의 주요 매개변수를 통해 LOC 시스템의 혈액 수송 현상에 대한 연구는 실험적, 이론적 및 수많은 수치적 접근 방식을 통해 제공됩니다.

전기 삼투압 점탄성 흐름에 의해 유발되는 교란은 특히 향후 연구 기회를 위해 혈액 및 기타 점탄성 유체를 취급하는 LOC 장치의 혼합 및 분리 기능 향상에 논의되고 적용됩니다. 또한, 본 연구는 보다 정확하고 단순화된 혈류 모델에 대한 요구와 전기역학 효과 하에서 점탄성 유체 흐름에 대한 수치 연구에 대한 강조와 같은 LOC 시스템 하에서 혈류 역학의 수치 모델링의 문제를 식별합니다.

전기역학 현상을 연구하는 동안 제타 전위 조건에 대한 보다 실용적인 가정도 강조됩니다. 본 연구는 모세관 및 전기삼투압에 의해 구동되는 미세유체 시스템의 혈류 역학에 대한 포괄적이고 학제적인 관점을 제공하는 것을 목표로 한다.

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1. Introduction

1.1. Microfluidic Flow in Lab-on-a-Chip (LOC) Systems

Over the past several decades, the ability to control and utilize fluid flow patterns at microscales has gained considerable interest across a myriad of scientific and engineering disciplines, leading to growing interest in scientific research of microfluidics. 

(1) Microfluidics, an interdisciplinary field that straddles physics, engineering, and biotechnology, is dedicated to the behavior, precise control, and manipulation of fluids geometrically constrained to a small, typically submillimeter, scale. 

(2) The engineering community has increasingly focused on microfluidics, exploring different driving forces to enhance working fluid transport, with the aim of accurately and efficiently describing, controlling, designing, and applying microfluidic flow principles and transport phenomena, particularly for miniaturized applications. 

(3) This attention has chiefly been fueled by the potential to revolutionize diagnostic and therapeutic techniques in the biomedical and pharmaceutical sectorsUnder various driving forces in microfluidic flows, intriguing transport phenomena have bolstered confidence in sustainable and efficient applications in fields such as pharmaceutical, biochemical, and environmental science. The “lab-on-a-chip” (LOC) system harnesses microfluidic flow to enable fluid processing and the execution of laboratory tasks on a chip-sized scale. LOC systems have played a vital role in the miniaturization of laboratory operations such as mixing, chemical reaction, separation, flow control, and detection on small devices, where a wide variety of fluids is adapted. Biological fluid flow like blood and other viscoelastic fluids are notably studied among the many working fluids commonly utilized by LOC systems, owing to the optimization in small fluid sample volumed, rapid response times, precise control, and easy manipulation of flow patterns offered by the system under various driving forces. 

(4)The driving forces in blood flow can be categorized as passive or active transport mechanisms and, in some cases, both. Under various transport mechanisms, the unique design of microchannels enables different functionalities in driving, mixing, separating, and diagnosing blood and drug delivery in the blood. 

(5) Understanding and manipulating these driving forces are crucial for optimizing the performance of a LOC system. Such knowledge presents the opportunity to achieve higher efficiency and reliability in addressing cellular level challenges in medical diagnostics, forensic studies, cancer detection, and other fundamental research areas, for applications of point-of-care (POC) devices. 

(6)

1.2. Engineering Approach of Microfluidic Transport Phenomena in LOC Systems

Different transport mechanisms exhibit unique properties at submillimeter length scales in microfluidic devices, leading to significant transport phenomena that differ from those of macroscale flows. An in-depth understanding of these unique transport phenomena under microfluidic systems is often required in fluidic mechanics to fully harness the potential functionality of a LOC system to obtain systematically designed and precisely controlled transport of microfluids under their respective driving force. Fluid mechanics is considered a vital component in chemical engineering, enabling the analysis of fluid behaviors in various unit designs, ranging from large-scale reactors to separation units. Transport phenomena in fluid mechanics provide a conceptual framework for analytically and descriptively explaining why and how experimental results and physiological phenomena occur. The Navier–Stokes (N–S) equation, along with other governing equations, is often adapted to accurately describe fluid dynamics by accounting for pressure, surface properties, velocity, and temperature variations over space and time. In addition, limiting factors and nonidealities for these governing equations should be considered to impose corrections for empirical consistency before physical models are assembled for more accurate controls and efficiency. Microfluidic flow systems often deviate from ideal conditions, requiring adjustments to the standard governing equations. These deviations could arise from factors such as viscous effects, surface interactions, and non-Newtonian fluid properties from different microfluid types and geometrical layouts of microchannels. Addressing these nonidealities supports the refining of theoretical models and prediction accuracy for microfluidic flow behaviors.

The analytical calculation of coupled nonlinear governing equations, which describes the material and energy balances of systems under ideal conditions, often requires considerable computational efforts. However, advancements in computation capabilities, cost reduction, and improved accuracy have made numerical simulations using different numerical and modeling methods a powerful tool for effectively solving these complex coupled equations and modeling various transport phenomena. Computational fluid dynamics (CFD) is a numerical technique used to investigate the spatial and temporal distribution of various flow parameters. It serves as a critical approach to provide insights and reasoning for decision-making regarding the optimal designs involving fluid dynamics, even prior to complex physical model prototyping and experimental procedures. The integration of experimental data, theoretical analysis, and reliable numerical simulations from CFD enables systematic variation of analytical parameters through quantitative analysis, where adjustment to delivery of blood flow and other working fluids in LOC systems can be achieved.

Numerical methods such as the Finite-Difference Method (FDM), Finite-Element-Method (FEM), and Finite-Volume Method (FVM) are heavily employed in CFD and offer diverse approaches to achieve discretization of Eulerian flow equations through filling a mesh of the flow domain. A more in-depth review of numerical methods in CFD and its application for blood flow simulation is provided in Section 2.2.2.

1.3. Scope of the Review

In this Review, we explore and characterize the blood flow phenomena within the LOC systems, utilizing both physiological and engineering modeling approaches. Similar approaches will be taken to discuss capillary-driven flow and electric-osmotic flow (EOF) under electrokinetic phenomena as a passive and active transport scheme, respectively, for blood transport in LOC systems. Such an analysis aims to bridge the gap between physical (experimental) and engineering (analytical) perspectives in studying and manipulating blood flow delivery by different driving forces in LOC systems. Moreover, the Review hopes to benefit the interests of not only blood flow control in LOC devices but also the transport of viscoelastic fluids, which are less studied in the literature compared to that of Newtonian fluids, in LOC systems.

Section 2 examines the complex interplay between viscoelastic properties of blood and blood flow patterns under shear flow in LOC systems, while engineering numerical modeling approaches for blood flow are presented for assistance. Sections 3 and 4 look into the theoretical principles, numerical governing equations, and modeling methodologies for capillary driven flow and EOF in LOC systems as well as their impact on blood flow dynamics through the quantification of key parameters of the two driving forces. Section 5 concludes the characterized blood flow transport processes in LOC systems under these two forces. Additionally, prospective areas of research in improving the functionality of LOC devices employing blood and other viscoelastic fluids and potentially justifying mechanisms underlying microfluidic flow patterns outside of LOC systems are presented. Finally, the challenges encountered in the numerical studies of blood flow under LOC systems are acknowledged, paving the way for further research.

2. Blood Flow Phenomena

ARTICLE SECTIONS

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2.1. Physiological Blood Flow Behavior

Blood, an essential physiological fluid in the human body, serves the vital role of transporting oxygen and nutrients throughout the body. Additionally, blood is responsible for suspending various blood cells including erythrocytes (red blood cells or RBCs), leukocytes (white blood cells), and thrombocytes (blood platelets) in a plasma medium.Among the cells mentioned above, red blood cells (RBCs) comprise approximately 40–45% of the volume of healthy blood. 

(7) An RBC possesses an inherent elastic property with a biconcave shape of an average diameter of 8 μm and a thickness of 2 μm. This biconcave shape maximizes the surface-to-volume ratio, allowing RBCs to endure significant distortion while maintaining their functionality. 

(8,9) Additionally, the biconcave shape optimizes gas exchange, facilitating efficient uptake of oxygen due to the increased surface area. The inherent elasticity of RBCs allows them to undergo substantial distortion from their original biconcave shape and exhibits high flexibility, particularly in narrow channels.RBC deformability enables the cell to deform from a biconcave shape to a parachute-like configuration, despite minor differences in RBC shape dynamics under shear flow between initial cell locations. As shown in Figure 1(a), RBCs initiating with different resting shapes and orientations displaying display a similar deformation pattern 

(10) in terms of its shape. Shear flow induces an inward bending of the cell at the rear position of the rim to the final bending position, 

(11) resulting in an alignment toward the same position of the flow direction.

Figure 1. Images of varying deformation of RBCs and different dynamic blood flow behaviors. (a) The deforming shape behavior of RBCs at four different initiating positions under the same experimental conditions of a flow from left to right, (10) (b) RBC aggregation, (13) (c) CFL region. (18) Reproduced with permission from ref (10). Copyright 2011 Elsevier. Reproduced with permission from ref (13). Copyright 2022 The Authors, under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/. Reproduced with permission from ref (18). Copyright 2019 Elsevier.

The flexible property of RBCs enables them to navigate through narrow capillaries and traverse a complex network of blood vessels. The deformability of RBCs depends on various factors, including the channel geometry, RBC concentration, and the elastic properties of the RBC membrane. 

(12) Both flexibility and deformability are vital in the process of oxygen exchange among blood and tissues throughout the body, allowing cells to flow in vessels even smaller than the original cell size prior to deforming.As RBCs serve as major components in blood, their collective dynamics also hugely affect blood rheology. RBCs exhibit an aggregation phenomenon due to cell to cell interactions, such as adhesion forces, among populated cells, inducing unique blood flow patterns and rheological behaviors in microfluidic systems. For blood flow in large vessels between a diameter of 1 and 3 cm, where shear rates are not high, a constant viscosity and Newtonian behavior for blood can be assumed. However, under low shear rate conditions (0.1 s

–1) in smaller vessels such as the arteries and venules, which are within a diameter of 0.2 mm to 1 cm, blood exhibits non-Newtonian properties, such as shear-thinning viscosity and viscoelasticity due to RBC aggregation and deformability. The nonlinear viscoelastic property of blood gives rise to a complex relationship between viscosity and shear rate, primarily influenced by the highly elastic behavior of RBCs. A wide range of research on the transient behavior of the RBC shape and aggregation characteristics under varied flow circumstances has been conducted, aiming to obtain a better understanding of the interaction between blood flow shear forces from confined flows.

For a better understanding of the unique blood flow structures and rheological behaviors in microfluidic systems, some blood flow patterns are introduced in the following section.

2.1.1. RBC Aggregation

RBC aggregation is a vital phenomenon to be considered when designing LOC devices due to its impact on the viscosity of the bulk flow. Under conditions of low shear rate, such as in stagnant or low flow rate regions, RBCs tend to aggregate, forming structures known as rouleaux, resembling stacks of coins as shown in Figure 1(b). 

(13) The aggregation of RBCs increases the viscosity at the aggregated region, 

(14) hence slowing down the overall blood flow. However, when exposed to high shear rates, RBC aggregates disaggregate. As shear rates continue to increase, RBCs tend to deform, elongating and aligning themselves with the direction of the flow. 

(15) Such a dynamic shift in behavior from the cells in response to the shear rate forms the basis of the viscoelastic properties observed in whole blood. In essence, the viscosity of the blood varies according to the shear rate conditions, which are related to the velocity gradient of the system. It is significant to take the intricate relationship between shear rate conditions and the change of blood viscosity due to RBC aggregation into account since various flow driving conditions may induce varied effects on the degree of aggregation.

2.1.2. Fåhræus-Lindqvist Effect

The Fåhræus–Lindqvist (FL) effect describes the gradual decrease in the apparent viscosity of blood as the channel diameter decreases. 

(16) This effect is attributed to the migration of RBCs toward the central region in the microchannel, where the flow rate is higher, due to the presence of higher pressure and asymmetric distribution of shear forces. This migration of RBCs, typically observed at blood vessels less than 0.3 mm, toward the higher flow rate region contributes to the change in blood viscosity, which becomes dependent on the channel size. Simultaneously, the increase of the RBC concentration in the central region of the microchannel results in the formation of a less viscous region close to the microchannel wall. This region called the Cell-Free Layer (CFL), is primarily composed of plasma. 

(17) The combination of the FL effect and the following CFL formation provides a unique phenomenon that is often utilized in passive and active plasma separation mechanisms, involving branched and constriction channels for various applications in plasma separation using microfluidic systems.

2.1.3. Cell-Free Layer Formation

In microfluidic blood flow, RBCs form aggregates at the microchannel core and result in a region that is mostly devoid of RBCs near the microchannel walls, as shown in Figure 1(c). 

(18) The region is known as the cell-free layer (CFL). The CFL region is often known to possess a lower viscosity compared to other regions within the blood flow due to the lower viscosity value of plasma when compared to that of the aggregated RBCs. Therefore, a thicker CFL region composed of plasma correlates to a reduced apparent whole blood viscosity. 

(19) A thicker CFL region is often established following the RBC aggregation at the microchannel core under conditions of decreasing the tube diameter. Apart from the dependence on the RBC concentration in the microchannel core, the CFL thickness is also affected by the volume concentration of RBCs, or hematocrit, in whole blood, as well as the deformability of RBCs. Given the influence CFL thickness has on blood flow rheological parameters such as blood flow rate, which is strongly dependent on whole blood viscosity, investigating CFL thickness under shear flow is crucial for LOC systems accounting for blood flow.

2.1.4. Plasma Skimming in Bifurcation Networks

The uneven arrangement of RBCs in bifurcating microchannels, commonly termed skimming bifurcation, arises from the axial migration of RBCs within flowing streams. This uneven distribution contributes to variations in viscosity across differing sizes of bifurcating channels but offers a stabilizing effect. Notably, higher flow rates in microchannels are associated with increased hematocrit levels, resulting in higher viscosity compared with those with lower flow rates. Parametric investigations on bifurcation angle, 

(20) thickness of the CFL, 

(21) and RBC dynamics, including aggregation and deformation, 

(22) may alter the varying viscosity of blood and its flow behavior within microchannels.

2.2. Modeling on Blood Flow Dynamics

2.2.1. Blood Properties and Mathematical Models of Blood Rheology

Under different shear rate conditions in blood flow, the elastic characteristics and dynamic changes of the RBC induce a complex velocity and stress relationship, resulting in the incompatibility of blood flow characterization through standard presumptions of constant viscosity used for Newtonian fluid flow. Blood flow is categorized as a viscoelastic non-Newtonian fluid flow where constitutive equations governing this type of flow take into consideration the nonlinear viscometric properties of blood. To mathematically characterize the evolving blood viscosity and the relationship between the elasticity of RBC and the shear blood flow, respectively, across space and time of the system, a stress tensor (τ) defined by constitutive models is often coupled in the Navier–Stokes equation to account for the collective impact of the constant dynamic viscosity (η) and the elasticity from RBCs on blood flow.The dynamic viscosity of blood is heavily dependent on the shear stress applied to the cell and various parameters from the blood such as hematocrit value, plasma viscosity, mechanical properties of the RBC membrane, and red blood cell aggregation rate. The apparent blood viscosity is considered convenient for the characterization of the relationship between the evolving blood viscosity and shear rate, which can be defined by Casson’s law, as shown in eq 1.

𝜇=𝜏0𝛾˙+2𝜂𝜏0𝛾˙⎯⎯⎯⎯⎯⎯⎯√+𝜂�=�0�˙+2��0�˙+�

(1)where τ

0 is the yield stress–stress required to initiate blood flow motion, η is the Casson rheological constant, and γ̇ is the shear rate. The value of Casson’s law parameters under blood with normal hematocrit level can be defined as τ

0 = 0.0056 Pa and η = 0.0035 Pa·s. 

(23) With the known property of blood and Casson’s law parameters, an approximation can be made to the dynamic viscosity under various flow condition domains. The Power Law model is often employed to characterize the dynamic viscosity in relation to the shear rate, since precise solutions exist for specific geometries and flow circumstances, acting as a fundamental standard for definition. The Carreau and Carreau–Yasuda models can be advantageous over the Power Law model due to their ability to evaluate the dynamic viscosity at low to zero shear rate conditions. However, none of the above-mentioned models consider the memory or other elastic behavior of blood and its RBCs. Some other commonly used mathematical models and their constants for the non-Newtonian viscosity property characterization of blood are listed in Table 1 below. 

(24−26)Table 1. Comparison of Various Non-Newtonian Models for Blood Viscosity 

(24−26)

ModelNon-Newtonian ViscosityParameters
Power Law(2)n = 0.61, k = 0.42
Carreau(3)μ0 = 0.056 Pa·s, μ∞ = 0.00345 Pa·s, λ = 3.1736 s, m = 2.406, a = 0.254
Walburn–Schneck(4)C1 = 0.000797 Pa·s, C2 = 0.0608 Pa·s, C3 = 0.00499, C4 = 14.585 g–1, TPMA = 25 g/L
Carreau–Yasuda(5)μ0 = 0.056 Pa·s, μ∞ = 0.00345 Pa·s, λ = 1.902 s, n = 0.22, a = 1.25
Quemada(6)μp = 0.0012 Pa·s, k∞ = 2.07, k0 = 4.33, γ̇c = 1.88 s–1

The blood rheology is commonly known to be influenced by two key physiological factors, namely, the hematocrit value (H

t) and the fibrinogen concentration (c

f), with an average value of 42% and 0.252 gd·L

–1, respectively. Particularly in low shear conditions, the presence of varying fibrinogen concentrations affects the tendency for aggregation and rouleaux formation, while the occurrence of aggregation is contingent upon specific levels of hematocrit. 

(27) The study from Apostolidis et al. 

(28) modifies the Casson model through emphasizing its reliance on hematocrit and fibrinogen concentration parameter values, owing to the extensive knowledge of the two physiological blood parameters.The viscoelastic response of blood is heavily dependent on the elasticity of the RBC, which is defined by the relationship between the deformation and stress relaxation from RBCs under a specific location of shear flow as a function of the velocity field. The stress tensor is usually characterized by constitutive equations such as the Upper-Convected Maxwell Model 

(29) and the Oldroyd-B model 

(30) to track the molecule effects under shear from different driving forces. The prominent non-Newtonian features, such as shear thinning and yield stress, have played a vital role in the characterization of blood rheology, particularly with respect to the evaluation of yield stress under low shear conditions. The nature of stress measurement in blood, typically on the order of 1 mPa, is challenging due to its low magnitude. The occurrence of the CFL complicates the measurement further due to the significant decrease in apparent viscosity near the wall over time and a consequential disparity in viscosity compared to the bulk region.In addition to shear thinning viscosity and yield stress, the formation of aggregation (rouleaux) from RBCs under low shear rates also contributes to the viscoelasticity under transient flow 

(31) and thixotropy 

(32) of whole blood. Given the difficulty in evaluating viscoelastic behavior of blood under low strain magnitudes and limitations in generalized Newtonian models, the utilization of viscoelastic models is advocated to encompass elasticity and delineate non-shear components within the stress tensor. Extending from the Oldroyd-B model, Anand et al. 

(33) developed a viscoelastic model framework for adapting elasticity within blood samples and predicting non-shear stress components. However, to also address the thixotropic effects, the model developed by Horner et al. 

(34) serves as a more comprehensive approach than the viscoelastic model from Anand et al. Thixotropy 

(32) typically occurs from the structural change of the rouleaux, where low shear rate conditions induce rouleaux formation. Correspondingly, elasticity increases, while elasticity is more representative of the isolated RBCs, under high shear rate conditions. The model of Horner et al. 

(34) considers the contribution of rouleaux to shear stress, taking into account factors such as the characteristic time for Brownian aggregation, shear-induced aggregation, and shear-induced breakage. Subsequent advancements in the model from Horner et al. often revolve around refining the three aforementioned key terms for a more substantial characterization of rouleaux dynamics. Notably, this has led to the recently developed mHAWB model 

(35) and other model iterations to enhance the accuracy of elastic and viscoelastic contributions to blood rheology, including the recently improved model suggested by Armstrong et al. 

(36)

2.2.2. Numerical Methods (FDM, FEM, FVM)

Numerical simulation has become increasingly more significant in analyzing the geometry, boundary layers of flow, and nonlinearity of hyperbolic viscoelastic flow constitutive equations. CFD is a powerful and efficient tool utilizing numerical methods to solve the governing hydrodynamic equations, such as the Navier–Stokes (N–S) equation, continuity equation, and energy conservation equation, for qualitative evaluation of fluid motion dynamics under different parameters. CFD overcomes the challenge of analytically solving nonlinear forms of differential equations by employing numerical methods such as the Finite-Difference Method (FDM), Finite-Element Method (FEM), and Finite-Volume Method (FVM) to discretize and solve the partial differential equations (PDEs), allowing for qualitative reproduction of transport phenomena and experimental observations. Different numerical methods are chosen to cope with various transport systems for optimization of the accuracy of the result and control of error during the discretization process.FDM is a straightforward approach to discretizing PDEs, replacing the continuum representation of equations with a set of finite-difference equations, which is typically applied to structured grids for efficient implementation in CFD programs. 

(37) However, FDM is often limited to simple geometries such as rectangular or block-shaped geometries and struggles with curved boundaries. In contrast, FEM divides the fluid domain into small finite grids or elements, approximating PDEs through a local description of physics. 

(38) All elements contribute to a large, sparse matrix solver. However, FEM may not always provide accurate results for systems involving significant deformation and aggregation of particles like RBCs due to large distortion of grids. 

(39) FVM evaluates PDEs following the conservation laws and discretizes the selected flow domain into small but finite size control volumes, with each grid at the center of a finite volume. 

(40) The divergence theorem allows the conversion of volume integrals of PDEs with divergence terms into surface integrals of surface fluxes across cell boundaries. Due to its conservation property, FVM offers efficient outcomes when dealing with PDEs that embody mass, momentum, and energy conservation principles. Furthermore, widely accessible software packages like the OpenFOAM toolbox 

(41) include a viscoelastic solver, making it an attractive option for viscoelastic fluid flow modeling. 

(42)

2.2.3. Modeling Methods of Blood Flow Dynamics

The complexity in the blood flow simulation arises from deformability and aggregation that RBCs exhibit during their interaction with neighboring cells under different shear rate conditions induced by blood flow. Numerical models coupled with simulation programs have been applied as a groundbreaking method to predict such unique rheological behavior exhibited by RBCs and whole blood. The conventional approach of a single-phase flow simulation is often applied to blood flow simulations within large vessels possessing a moderate shear rate. However, such a method assumes the properties of plasma, RBCs and other cellular components to be evenly distributed as average density and viscosity in blood, resulting in the inability to simulate the mechanical dynamics, such as RBC aggregation under high-shear flow field, inherent in RBCs. To accurately describe the asymmetric distribution of RBC and blood flow, multiphase flow simulation, where numerical simulations of blood flows are often modeled as two immiscible phases, RBCs and blood plasma, is proposed. A common assumption is that RBCs exhibit non-Newtonian behavior while the plasma is treated as a continuous Newtonian phase.Numerous multiphase numerical models have been proposed to simulate the influence of RBCs on blood flow dynamics by different assumptions. In large-scale simulations (above the millimeter range), continuum-based methods are wildly used due to their lower computational demands. 

(43) Eulerian multiphase flow simulations offer the solution of a set of conservation equations for each separate phase and couple the phases through common pressure and interphase exchange coefficients. Xu et al. 

(44) utilized the combined finite-discrete element method (FDEM) to replicate the dynamic behavior and distortion of RBCs subjected to fluidic forces, utilizing the Johnson–Kendall–Roberts model 

(45) to define the adhesive forces of cell-to-cell interactions. The iterative direct-forcing immersed boundary method (IBM) is commonly employed in simulations of the fluid–cell interface of blood. This method effectively captures the intricacies of the thin and flexible RBC membranes within various external flow fields. 

(46) The study by Xu et al. 

(44) also adopts this approach to bridge the fluid dynamics and RBC deformation through IBM. Yoon and You utilized the Maxwell model to define the viscosity of the RBC membrane. 

(47) It was discovered that the Maxwell model could represent the stress relaxation and unloading processes of the cell. Furthermore, the reduced flexibility of an RBC under particular situations such as infection is specified, which was unattainable by the Kelvin–Voigt model 

(48) when compared to the Maxwell model in the literature. The Yeoh hyperplastic material model was also adapted to predict the nonlinear elasticity property of RBCs with FEM employed to discretize the RBC membrane using shell-type elements. Gracka et al. 

(49) developed a numerical CFD model with a finite-volume parallel solver for multiphase blood flow simulation, where an updated Maxwell viscoelasticity model and a Discrete Phase Model are adopted. In the study, the adapted IBM, based on unstructured grids, simulates the flow behavior and shape change of the RBCs through fluid-structure coupling. It was found that the hybrid Euler–Lagrange (E–L) approach 

(50) for the development of the multiphase model offered better results in the simulated CFL region in the microchannels.To study the dynamics of individual behaviors of RBCs and the consequent non-Newtonian blood flow, cell-shape-resolved computational models are often adapted. The use of the boundary integral method has become prevalent in minimizing computational expenses, particularly in the exclusive determination of fluid velocity on the surfaces of RBCs, incorporating the option of employing IBM or particle-based techniques. The cell-shaped-resolved method has enabled an examination of cell to cell interactions within complex ambient or pulsatile flow conditions 

(51) surrounding RBC membranes. Recently, Rydquist et al. 

(52) have looked to integrate statistical information from macroscale simulations to obtain a comprehensive overview of RBC behavior within the immediate proximity of the flow through introduction of respective models characterizing membrane shape definition, tension, bending stresses of RBC membranes.At a macroscopic scale, continuum models have conventionally been adapted for assessing blood flow dynamics through the application of elasticity theory and fluid dynamics. However, particle-based methods are known for their simplicity and adaptability in modeling complex multiscale fluid structures. Meshless methods, such as the boundary element method (BEM), smoothed particle hydrodynamics (SPH), and dissipative particle dynamics (DPD), are often used in particle-based characterization of RBCs and the surrounding fluid. By representing the fluid as discrete particles, meshless methods provide insights into the status and movement of the multiphase fluid. These methods allow for the investigation of cellular structures and microscopic interactions that affect blood rheology. Non-confronting mesh methods like IBM can also be used to couple a fluid solver such as FEM, FVM, or the Lattice Boltzmann Method (LBM) through membrane representation of RBCs. In comparison to conventional CFD methods, LBM has been viewed as a favorable numerical approach for solving the N–S equations and the simulation of multiphase flows. LBM exhibits the notable advantage of being amenable to high-performance parallel computing environments due to its inherently local dynamics. In contrast to DPD and SPH where RBC membranes are modeled as physically interconnected particles, LBM employs the IBM to account for the deformation dynamics of RBCs 

(53,54) under shear flows in complex channel geometries. 

(54,55) However, it is essential to acknowledge that the utilization of LBM in simulating RBC flows often entails a significant computational overhead, being a primary challenge in this context. Krüger et al. 

(56) proposed utilizing LBM as a fluid solver, IBM to couple the fluid and FEM to compute the response of membranes to deformation under immersed fluids. This approach decouples the fluid and membranes but necessitates significant computational effort due to the requirements of both meshes and particles.Despite the accuracy of current blood flow models, simulating complex conditions remains challenging because of the high computational load and cost. Balachandran Nair et al. 

(57) suggested a reduced order model of RBC under the framework of DEM, where the RBC is represented by overlapping constituent rigid spheres. The Morse potential force is adapted to account for the RBC aggregation exhibited by cell to cell interactions among RBCs at different distances. Based upon the IBM, the reduced-order RBC model is adapted to simulate blood flow transport for validation under both single and multiple RBCs with a resolved CFD-DEM solver. 

(58) In the resolved CFD-DEM model, particle sizes are larger than the grid size for a more accurate computation of the surrounding flow field. A continuous forcing approach is taken to describe the momentum source of the governing equation prior to discretization, which is different from a Direct Forcing Method (DFM). 

(59) As no body-conforming moving mesh is required, the continuous forcing approach offers lower complexity and reduced cost when compared to the DFM. Piquet et al. 

(60) highlighted the high complexity of the DFM due to its reliance on calculating an additional immersed boundary flux for the velocity field to ensure its divergence-free condition.The fluid–structure interaction (FSI) method has been advocated to connect the dynamic interplay of RBC membranes and fluid plasma within blood flow such as the coupling of continuum–particle interactions. However, such methodology is generally adapted for anatomical configurations such as arteries 

(61,62) and capillaries, 

(63) where both the structural components and the fluid domain undergo substantial deformation due to the moving boundaries. Due to the scope of the Review being blood flow simulation within microchannels of LOC devices without deformable boundaries, the Review of the FSI method will not be further carried out.In general, three numerical methods are broadly used: mesh-based, particle-based, and hybrid mesh–particle techniques, based on the spatial scale and the fundamental numerical approach, mesh-based methods tend to neglect the effects of individual particles, assuming a continuum and being efficient in terms of time and cost. However, the particle-based approach highlights more of the microscopic and mesoscopic level, where the influence of individual RBCs is considered. A review from Freund et al. 

(64) addressed the three numerical methodologies and their respective modeling approaches of RBC dynamics. Given the complex mechanics and the diverse levels of study concerning numerical simulations of blood and cellular flow, a broad spectrum of numerical methods for blood has been subjected to extensive review. 

(64−70) Ye at al. 

(65) offered an extensive review of the application of the DPD, SPH, and LBM for numerical simulations of RBC, while Rathnayaka et al. 

(67) conducted a review of the particle-based numerical modeling for liquid marbles through drawing parallels to the transport of RBCs in microchannels. A comparative analysis between conventional CFD methods and particle-based approaches for cellular and blood flow dynamic simulation can be found under the review by Arabghahestani et al. 

(66) Literature by Li et al. 

(68) and Beris et al. 

(69) offer an overview of both continuum-based models at micro/macroscales and multiscale particle-based models encompassing various length and temporal dimensions. Furthermore, these reviews deliberate upon the potential of coupling continuum-particle methods for blood plasma and RBC modeling. Arciero et al. 

(70) investigated various modeling approaches encompassing cellular interactions, such as cell to cell or plasma interactions and the individual cellular phases. A concise overview of the reviews is provided in Table 2 for reference.

Table 2. List of Reviews for Numerical Approaches Employed in Blood Flow Simulation

ReferenceNumerical methods
Li et al. (2013) (68)Continuum-based modeling (BIM), particle-based modeling (LBM, LB-FE, SPH, DPD)
Freund (2014) (64)RBC dynamic modeling (continuum-based modeling, complementary discrete microstructure modeling), blood flow dynamic modeling (FDM, IBM, LBM, particle-mesh methods, coupled boundary integral and mesh-based methods, DPD)
Ye et al. (2016) (65)DPD, SPH, LBM, coupled IBM-Smoothed DPD
Arciero et al. (2017) (70)LBM, IBM, DPD, conventional CFD Methods (FDM, FVM, FEM)
Arabghahestani et al. (2019) (66)Particle-based methods (LBM, DPD, direct simulation Monte Carlo, molecular dynamics), SPH, conventional CFD methods (FDM, FVM, FEM)
Beris et al. (2021) (69)DPD, smoothed DPD, IBM, LBM, BIM
Rathnayaka (2022) (67)SPH, CG, LBM

3. Capillary Driven Blood Flow in LOC Systems

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3.1. Capillary Driven Flow Phenomena

Capillary driven (CD) flow is a pivotal mechanism in passive microfluidic flow systems 

(9) such as the blood circulation system and LOC systems. 

(71) CD flow is essentially the movement of a liquid to flow against drag forces, where the capillary effect exerts a force on the liquid at the borders, causing a liquid–air meniscus to flow despite gravity or other drag forces. A capillary pressure drops across the liquid–air interface with surface tension in the capillary radius and contact angle. The capillary effect depends heavily on the interaction between the different properties of surface materials. Different values of contact angles can be manipulated and obtained under varying levels of surface wettability treatments to manipulate the surface properties, resulting in different CD blood delivery rates for medical diagnostic device microchannels. CD flow techniques are appealing for many LOC devices, because they require no external energy. However, due to the passive property of liquid propulsion by capillary forces and the long-term instability of surface treatments on channel walls, the adaptability of CD flow in geometrically complex LOC devices may be limited.

3.2. Theoretical and Numerical Modeling of Capillary Driven Blood Flow

3.2.1. Theoretical Basis and Assumptions of Microfluidic Flow

The study of transport phenomena regarding either blood flow driven by capillary forces or externally applied forces under microfluid systems all demands a comprehensive recognition of the significant differences in flow dynamics between microscale and macroscale. The fundamental assumptions and principles behind fluid transport at the microscale are discussed in this section. Such a comprehension will lay the groundwork for the following analysis of the theoretical basis of capillary forces and their role in blood transport in LOC systems.

At the macroscale, fluid dynamics are often strongly influenced by gravity due to considerable fluid mass. However, the high surface to volume ratio at the microscale shifts the balance toward surface forces (e.g., surface tension and viscous forces), much larger than the inertial force. This difference gives rise to transport phenomena unique to microscale fluid transport, such as the prevalence of laminar flow due to a very low Reynolds number (generally lower than 1). Moreover, the fluid in a microfluidic system is often assumed to be incompressible due to the small flow velocity, indicating constant fluid density in both space and time.Microfluidic flow behaviors are governed by the fundamental principles of mass and momentum conservation, which are encapsulated in the continuity equation and the Navier–Stokes (N–S) equation. The continuity equation describes the conservation of mass, while the N–S equation captures the spatial and temporal variations in velocity, pressure, and other physical parameters. Under the assumption of the negligible influence of gravity in microfluidic systems, the continuity equation and the Eulerian representation of the incompressible N–S equation can be expressed as follows:

∇·𝐮⇀=0∇·�⇀=0

(7)

−∇𝑝+𝜇∇2𝐮⇀+∇·𝝉⇀−𝐅⇀=0−∇�+�∇2�⇀+∇·�⇀−�⇀=0

(8)Here, p is the pressure, u is the fluid viscosity, 

𝝉⇀�⇀ represents the stress tensor, and F is the body force exerted by external forces if present.

3.2.2. Theoretical Basis and Modeling of Capillary Force in LOC Systems

The capillary force is often the major driving force to manipulate and transport blood without an externally applied force in LOC systems. Forces induced by the capillary effect impact the free surface of fluids and are represented not directly in the Navier–Stokes equations but through the pressure boundary conditions of the pressure term p. For hydrophilic surfaces, the liquid generally induces a contact angle between 0° and 30°, encouraging the spread and attraction of fluid under a positive cos θ condition. For this condition, the pressure drop becomes positive and generates a spontaneous flow forward. A hydrophobic solid surface repels the fluid, inducing minimal contact. Generally, hydrophobic solids exhibit a contact angle larger than 90°, inducing a negative value of cos θ. Such a value will result in a negative pressure drop and a flow in the opposite direction. The induced contact angle is often utilized to measure the wall exposure of various surface treatments on channel walls where different wettability gradients and surface tension effects for CD flows are established. Contact angles between different interfaces are obtainable through standard values or experimental methods for reference. 

(72)For the characterization of the induced force by the capillary effect, the Young–Laplace (Y–L) equation 

(73) is widely employed. In the equation, the capillary is considered a pressure boundary condition between the two interphases. Through the Y–L equation, the capillary pressure force can be determined, and subsequently, the continuity and momentum balance equations can be solved to obtain the blood filling rate. Kim et al. 

(74) studied the effects of concentration and exposure time of a nonionic surfactant, Silwet L-77, on the performance of a polydimethylsiloxane (PDMS) microchannel in terms of plasma and blood self-separation. The study characterized the capillary pressure force by incorporating the Y–L equation and further evaluated the effects of the changing contact angle due to different levels of applied channel wall surface treatments. The expression of the Y–L equation utilized by Kim et al. 

(74) is as follows:

𝑃=−𝜎(cos𝜃b+cos𝜃tℎ+cos𝜃l+cos𝜃r𝑤)�=−�(cos⁡�b+cos⁡�tℎ+cos⁡�l+cos⁡�r�)

(9)where σ is the surface tension of the liquid and θ

b, θ

t, θ

l, and θ

r are the contact angle values between the liquid and the bottom, top, left, and right walls, respectively. A numerical simulation through Coventor software is performed to evaluate the dynamic changes in the filling rate within the microchannel. The simulation results for the blood filling rate in the microchannel are expressed at a specific time stamp, shown in Figure 2. The results portray an increasing instantaneous filling rate of blood in the microchannel following the decrease in contact angle induced by a higher concentration of the nonionic surfactant treated to the microchannel wall.

Figure 2. Numerical simulation of filling rate of capillary driven blood flow under various contact angle conditions at a specific timestamp. (74) Reproduced with permission from ref (74). Copyright 2010 Elsevier.

When in contact with hydrophilic or hydrophobic surfaces, blood forms a meniscus with a contact angle due to surface tension. The Lucas–Washburn (L–W) equation 

(75) is one of the pioneering theoretical definitions for the position of the meniscus over time. In addition, the L–W equation provides the possibility for research to obtain the velocity of the blood formed meniscus through the derivation of the meniscus position. The L–W equation 

(75) can be shown below:

𝐿(𝑡)=𝑅𝜎cos(𝜃)𝑡2𝜇⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√�(�)=��⁡cos(�)�2�

(10)Here L(t) represents the distance of the liquid driven by the capillary forces. However, the generalized L–W equation solely assumes the constant physical properties from a Newtonian fluid rather than considering the non-Newtonian fluid behavior of blood. Cito et al. 

(76) constructed an enhanced version of the L–W equation incorporating the power law to consider the RBC aggregation and the FL effect. The non-Newtonian fluid apparent viscosity under the Power Law model is defined as

𝜇=𝑘·(𝛾˙)𝑛−1�=�·(�˙)�−1

(11)where γ̇ is the strain rate tensor defined as 

𝛾˙=12𝛾˙𝑖𝑗𝛾˙𝑗𝑖⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√�˙=12�˙���˙��. The stress tensor term τ is computed as τ = μγ̇

ij. The updated L–W equation by Cito 

(76) is expressed as

𝐿(𝑡)=𝑅[(𝑛+13𝑛+1)(𝜎cos(𝜃)𝑅𝑘)1/𝑛𝑡]𝑛/𝑛+1�(�)=�[(�+13�+1)(�⁡cos(�)��)1/��]�/�+1

(12)where k is the flow consistency index and n is the power law index, respectively. The power law index, from the Power Law model, characterizes the extent of the non-Newtonian behavior of blood. Both the consistency and power law index rely on blood properties such as hematocrit, the appearance of the FL effect, the formation of RBC aggregates, etc. The updated L–W equation computes the location and velocity of blood flow caused by capillary forces at specified time points within the LOC devices, taking into account the effects of blood flow characteristics such as RBC aggregation and the FL effect on dynamic blood viscosity.Apart from the blood flow behaviors triggered by inherent blood properties, unique flow conditions driven by capillary forces that are portrayed under different microchannel geometries also hold crucial implications for CD blood delivery. Berthier et al. 

(77) studied the spontaneous Concus–Finn condition, the condition to initiate the spontaneous capillary flow within a V-groove microchannel, as shown in Figure 3(a) both experimentally and numerically. Through experimental studies, the spontaneous Concus–Finn filament development of capillary driven blood flow is observed, as shown in Figure 3(b), while the dynamic development of blood flow is numerically simulated through CFD simulation.

Figure 3. (a) Sketch of the cross-section of Berthier’s V-groove microchannel, (b) experimental view of blood in the V-groove microchannel, (78) (c) illustration of the dynamic change of the extension of filament from FLOW 3D under capillary flow at three increasing time intervals. (78) Reproduced with permission from ref (78). Copyright 2014 Elsevier.

Berthier et al. 

(77) characterized the contact angle needed for the initiation of the capillary driving force at a zero-inlet pressure, through the half-angle (α) of the V-groove geometry layout, and its relation to the Concus–Finn filament as shown below:

𝜃<𝜋2−𝛼sin𝛼1+2(ℎ2/𝑤)sin𝛼<cos𝜃{�<�2−�sin⁡�1+2(ℎ2/�)⁡sin⁡�<cos⁡�

(13)Three possible regimes were concluded based on the contact angle value for the initiation of flow and development of Concus–Finn filament:

𝜃>𝜃1𝜃1>𝜃>𝜃0𝜃0no SCFSCF without a Concus−Finn filamentSCF without a Concus−Finn filament{�>�1no SCF�1>�>�0SCF without a Concus−Finn filament�0SCF without a Concus−Finn filament

(14)Under Newton’s Law, the force balance with low Reynolds and Capillary numbers results in the neglect of inertial terms. The force balance between the capillary forces and the viscous force induced by the channel wall is proposed to derive the analytical fluid velocity. This relation between the two forces offers insights into the average flow velocity and the penetration distance function dependent on time. The apparent blood viscosity is defined by Berthier et al. 

(78) through Casson’s law, 

(23) given in eq 1. The research used the FLOW-3D program from Flow Science Inc. software, which solves transient, free-surface problems using the FDM in multiple dimensions. The Volume of Fluid (VOF) method 

(79) is utilized to locate and track the dynamic extension of filament throughout the advancing interface within the channel ahead of the main flow at three progressing time stamps, as depicted in Figure 3(c).

4. Electro-osmotic Flow (EOF) in LOC Systems

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The utilization of external forces, such as electric fields, has significantly broadened the possibility of manipulating microfluidic flow in LOC systems. 

(80) Externally applied electric field forces induce a fluid flow from the movement of ions in fluid terms as the “electro-osmotic flow” (EOF).Unique transport phenomena, such as enhanced flow velocity and flow instability, induced by non-Newtonian fluids, particularly viscoelastic fluids, under EOF, have sparked considerable interest in microfluidic devices with simple or complicated geometries within channels. 

(81) However, compared to the study of Newtonian fluids and even other electro-osmotic viscoelastic fluid flows, the literature focusing on the theoretical and numerical modeling of electro-osmotic blood flow is limited due to the complexity of blood properties. Consequently, to obtain a more comprehensive understanding of the complex blood flow behavior under EOF, theoretical and numerical studies of the transport phenomena in the EOF section will be based on the studies of different viscoelastic fluids under EOF rather than that of blood specifically. Despite this limitation, we believe these studies offer valuable insights that can help understand the complex behavior of blood flow under EOF.

4.1. EOF Phenomena

Electro-osmotic flow occurs at the interface between the microchannel wall and bulk phase solution. When in contact with the bulk phase, solution ions are absorbed or dissociated at the solid–liquid interface, resulting in the formation of a charge layer, as shown in Figure 4. This charged channel surface wall interacts with both negative and positive ions in the bulk sample, causing repulsion and attraction forces to create a thin layer of immobilized counterions, known as the Stern layer. The induced electric potential from the wall gradually decreases with an increase in the distance from the wall. The Stern layer potential, commonly termed the zeta potential, controls the intensity of the electrostatic interactions between mobile counterions and, consequently, the drag force from the applied electric field. Next to the Stern layer is the diffuse mobile layer, mainly composed of a mobile counterion. These two layers constitute the “electrical double layer” (EDL), the thickness of which is directly proportional to the ionic strength (concentration) of the bulk fluid. The relationship between the two parameters is characterized by a Debye length (λ

D), expressed as

𝜆𝐷=𝜖𝑘B𝑇2(𝑍𝑒)2𝑐0⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√��=��B�2(��)2�0

(15)where ϵ is the permittivity of the electrolyte solution, k

B is the Boltzmann constant, T is the electron temperature, Z is the integer valence number, e is the elementary charge, and c

0 is the ionic density.

Figure 4. Schematic diagram of an electro-osmotic flow in a microchannel with negative surface charge. (82) Reproduced with permission from ref (82). Copyright 2012 Woodhead Publishing.

When an electric field is applied perpendicular to the EDL, viscous drag is generated due to the movement of excess ions in the EDL. Electro-osmotic forces can be attributed to the externally applied electric potential (ϕ) and the zeta potential, the system wall induced potential by charged walls (ψ). As illustrated in Figure 4, the majority of ions in the bulk phase have a uniform velocity profile, except for a shear rate condition confined within an extremely thin Stern layer. Therefore, EOF displays a unique characteristic of a “near flat” or plug flow velocity profile, different from the parabolic flow typically induced by pressure-driven microfluidic flow (Hagen–Poiseuille flow). The plug-shaped velocity profile of the EOF possesses a high shear rate above the Stern layer.Overall, the EOF velocity magnitude is typically proportional to the Debye Length (λ

D), zeta potential, and magnitude of the externally applied electric field, while a more viscous liquid reduces the EOF velocity.

4.2. Modeling on Electro-osmotic Viscoelastic Fluid Flow

4.2.1. Theoretical Basis of EOF Mechanisms

The EOF of an incompressible viscoelastic fluid is commonly governed by the continuity and incompressible N–S equations, as shown in eqs 7 and 8, where the stress tensor and the electrostatic force term are coupled. The electro-osmotic body force term F, representing the body force exerted by the externally applied electric force, is defined as 

𝐹⇀=𝑝𝐸𝐸⇀�⇀=���⇀, where ρ

E and 

𝐸⇀�⇀ are the net electric charge density and the applied external electric field, respectively.Numerous models are established to theoretically study the externally applied electric potential and the system wall induced potential by charged walls. The following Laplace equation, expressed as eq 16, is generally adapted and solved to calculate the externally applied potential (ϕ).

∇2𝜙=0∇2�=0

(16)Ion diffusion under applied electric fields, together with mass transport resulting from convection and diffusion, transports ionic solutions in bulk flow under electrokinetic processes. The Nernst–Planck equation can describe these transport methods, including convection, diffusion, and electro-diffusion. Therefore, the Nernst–Planck equation is used to determine the distribution of the ions within the electrolyte. The electric potential induced by the charged channel walls follows the Poisson–Nernst–Plank (PNP) equation, which can be written as eq 17.

∇·[𝐷𝑖∇𝑛𝑖−𝑢⇀𝑛𝑖+𝑛𝑖𝐷𝑖𝑧𝑖𝑒𝑘𝑏𝑇∇(𝜙+𝜓)]=0∇·[��∇��−�⇀��+����������∇(�+�)]=0

(17)where D

i, n

i, and z

i are the diffusion coefficient, ionic concentration, and ionic valence of the ionic species I, respectively. However, due to the high nonlinearity and numerical stiffness introduced by different lengths and time scales from the PNP equations, the Poisson–Boltzmann (PB) model is often considered the major simplified method of the PNP equation to characterize the potential distribution of the EDL region in microchannels. In the PB model, it is assumed that the ionic species in the fluid follow the Boltzmann distribution. This model is typically valid for steady-state problems where charge transport can be considered negligible, the EDLs do not overlap with each other, and the intrinsic potentials are low. It provides a simplified representation of the potential distribution in the EDL region. The PB equation governing the EDL electric potential distribution is described as

∇2𝜓=(2𝑒𝑧𝑛0𝜀𝜀0)sinh(𝑧𝑒𝜓𝑘b𝑇)∇2�=(2���0��0)⁡sinh(����b�)

(18)where n

0 is the ion bulk concentration, z is the ionic valence, and ε

0 is the electric permittivity in the vacuum. Under low electric potential conditions, an even further simplified model to illustrate the EOF phenomena is the Debye–Hückel (DH) model. The DH model is derived by obtaining a charge density term by expanding the exponential term of the Boltzmann equation in a Taylor series.

4.2.2. EOF Modeling for Viscoelastic Fluids

Many studies through numerical modeling were performed to obtain a deeper understanding of the effect exhibited by externally applied electric fields on viscoelastic flow in microchannels under various geometrical designs. Bello et al. 

(83) found that methylcellulose solution, a non-Newtonian polymer solution, resulted in stronger electro-osmotic mobility in experiments when compared to the predictions by the Helmholtz–Smoluchowski equation, which is commonly used to define the velocity of EOF of a Newtonian fluid. Being one of the pioneers to identify the discrepancies between the EOF of Newtonian and non-Newtonian fluids, Bello et al. attributed such discrepancies to the presence of a very high shear rate in the EDL, resulting in a change in the orientation of the polymer molecules. Park and Lee 

(84) utilized the FVM to solve the PB equation for the characterization of the electric field induced force. In the study, the concept of fractional calculus for the Oldroyd-B model was adapted to illustrate the elastic and memory effects of viscoelastic fluids in a straight microchannel They observed that fluid elasticity and increased ratio of viscoelastic fluid contribution to overall fluid viscosity had a significant impact on the volumetric flow rate and sensitivity of velocity to electric field strength compared to Newtonian fluids. Afonso et al. 

(85) derived an analytical expression for EOF of viscoelastic fluid between parallel plates using the DH model to account for a zeta potential condition below 25 mV. The study established the understanding of the electro-osmotic viscoelastic fluid flow under low zeta potential conditions. Apart from the electrokinetic forces, pressure forces can also be coupled with EOF to generate a unique fluid flow behavior within the microchannel. Sousa et al. 

(86) analytically studied the flow of a standard viscoelastic solution by combining the pressure gradient force with an externally applied electric force. It was found that, at a near wall skimming layer and the outer layer away from the wall, macromolecules migrating away from surface walls in viscoelastic fluids are observed. In the study, the Phan-Thien Tanner (PTT) constitutive model is utilized to characterize the viscoelastic properties of the solution. The approach is found to be valid when the EDL is much thinner than the skimming layer under an enhanced flow rate. Zhao and Yang 

(87) solved the PB equation and Carreau model for the characterization of the EOF mechanism and non-Newtonian fluid respectively through the FEM. The numerical results depict that, different from the EOF of Newtonian fluids, non-Newtonian fluids led to an increase of electro-osmotic mobility for shear thinning fluids but the opposite for shear thickening fluids.Like other fluid transport driving forces, EOF within unique geometrical layouts also portrays unique transport phenomena. Pimenta and Alves 

(88) utilized the FVM to perform numerical simulations of the EOF of viscoelastic fluids considering the PB equation and the Oldroyd-B model, in a cross-slot and flow-focusing microdevices. It was found that electroelastic instabilities are formed due to the development of large stresses inside the EDL with streamlined curvature at geometry corners. Bezerra et al. 

(89) used the FDM to numerically analyze the vortex formation and flow instability from an electro-osmotic non-Newtonian fluid flow in a microchannel with a nozzle geometry and parallel wall geometry setting. The PNP equation is utilized to characterize the charge motion in the EOF and the PTT model for non-Newtonian flow characterization. A constriction geometry is commonly utilized in blood flow adapted in LOC systems due to the change in blood flow behavior under narrow dimensions in a microchannel. Ji et al. 

(90) recently studied the EOF of viscoelastic fluid in a constriction microchannel connected by two relatively big reservoirs on both ends (as seen in Figure 5) filled with the polyacrylamide polymer solution, a viscoelastic fluid, and an incompressible monovalent binary electrolyte solution KCl.

Figure 5. Schematic diagram of a negatively charged constriction microchannel connected to two reservoirs at both ends. An electro-osmotic flow is induced in the system by the induced potential difference between the anode and cathode. (90) Reproduced with permission from ref (90). Copyright 2021 The Authors, under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/.

In studying the EOF of viscoelastic fluids, the Oldroyd-B model is often utilized to characterize the polymeric stress tensor and the deformation rate of the fluid. The Oldroyd-B model is expressed as follows:

𝜏=𝜂p𝜆(𝐜−𝐈)�=�p�(�−�)

(19)where η

p, λ, c, and I represent the polymer dynamic viscosity, polymer relaxation time, symmetric conformation tensor of the polymer molecules, and the identity matrix, respectively.A log-conformation tensor approach is taken to prevent convergence difficulty induced by the viscoelastic properties. The conformation tensor (c) in the polymeric stress tensor term is redefined by a new tensor (Θ) based on the natural logarithm of the c. The new tensor is defined as

Θ=ln(𝐜)=𝐑ln(𝚲)𝐑Θ=ln(�)=�⁡ln(�)�

(20)in which Λ is the diagonal matrix and R is the orthogonal matrix.Under the new conformation tensor, the induced EOF of a viscoelastic fluid is governed by the continuity and N–S equations adapting the Oldroyd-B model, which is expressed as

∂𝚯∂𝑡+𝐮·∇𝚯=𝛀Θ−ΘΩ+2𝐁+1𝜆(eΘ−𝐈)∂�∂�+�·∇�=�Θ−ΘΩ+2�+1�(eΘ−�)

(21)where Ω and B represent the anti-symmetric matrix and the symmetric traceless matrix of the decomposition of the velocity gradient tensor ∇u, respectively. The conformation tensor can be recovered by c = exp(Θ). The PB model and Laplace equation are utilized to characterize the charged channel wall induced potential and the externally applied potential.The governing equations are numerically solved through the FVM by RheoTool, 

(42) an open-source viscoelastic EOF solver on the OpenFOAM platform. A SIMPLEC (Semi-Implicit Method for Pressure Linked Equations-Consistent) algorithm was applied to solve the velocity-pressure coupling. The pressure field and velocity field were computed by the PCG (Preconditioned Conjugate Gradient) solver and the PBiCG (Preconditioned Biconjugate Gradient) solver, respectively.Ranging magnitudes of an applied electric field or fluid concentration induce both different streamlines and velocity magnitudes at various locations and times of the microchannel. In the study performed by Ji et al., 

(90) notable fluctuation of streamlines and vortex formation is formed at the upper stream entrance of the constriction as shown in Figure 6(a) and (b), respectively, due to the increase of electrokinetic effect, which is seen as a result of the increase in polymeric stress (τ

xx). 

(90) The contraction geometry enhances the EOF velocity within the constriction channel under high E

app condition (600 V/cm). Such phenomena can be attributed to the dependence of electro-osmotic viscoelastic fluid flow on the system wall surface and bulk fluid properties. 

(91)

Figure 6. Schematic diagram of vortex formation and streamlines of EOF depicting flow instability at (a) 1.71 s and (b) 1.75 s. Spatial distribution of the elastic normal stress at (c) high Eapp condition. Streamline of an electro-osmotic flow under Eapp of 600 V/cm (90) for (d) non-Newtonian and (e) Newtonian fluid through a constriction geometry. Reproduced with permission from ref (90). Copyright 2021 The Authors, under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/.

As elastic normal stress exceeds the local shear stress, flow instability and vortex formation occur. The induced elastic stress under EOF not only enhances the instability of the flow but often generates an irregular secondary flow leading to strong disturbance. 

(92) It is also vital to consider the effect of the constriction layout of microchannels on the alteration of the field strength within the system. The contraction geometry enhances a larger electric field strength compared with other locations of the channel outside the constriction region, resulting in a higher velocity gradient and stronger extension on the polymer within the viscoelastic solution. Following the high shear flow condition, a higher magnitude of stretch for polymer molecules in viscoelastic fluids exhibits larger elastic stresses and enhancement of vortex formation at the region. 

(93)As shown in Figure 6(c), significant elastic normal stress occurs at the inlet of the constriction microchannel. Such occurrence of a polymeric flow can be attributed to the dominating elongational flow, giving rise to high deformation of the polymers within the viscoelastic fluid flow, resulting in higher elastic stress from the polymers. Such phenomena at the entrance result in the difference in velocity streamline as circled in Figure 6(d) compared to that of the Newtonian fluid at the constriction entrance in Figure 6(e). 

(90) The difference between the Newtonian and polymer solution at the exit, as circled in Figure 6(d) and (e), can be attributed to the extrudate swell effect of polymers 

(94) within the viscoelastic fluid flow. The extrudate swell effect illustrates that, as polymers emerge from the constriction exit, they tend to contract in the flow direction and grow in the normal direction, resulting in an extrudate diameter greater than the channel size. The deformation of polymers within the polymeric flow at both the entrance and exit of the contraction channel facilitates the change in shear stress conditions of the flow, leading to the alteration in streamlines of flows for each region.

4.3. EOF Applications in LOC Systems

4.3.1. Mixing in LOC Systems

Rather than relying on the micromixing controlled by molecular diffusion under low Reynolds number conditions, active mixers actively leverage convective instability and vortex formation induced by electro-osmotic flows from alternating current (AC) or direct current (DC) electric fields. Such adaptation is recognized as significant breakthroughs for promotion of fluid mixing in chemical and biological applications such as drug delivery, medical diagnostics, chemical synthesis, and so on. 

(95)Many researchers proposed novel designs of electro-osmosis micromixers coupled with numerical simulations in conjunction with experimental findings to increase their understanding of the role of flow instability and vortex formation in the mixing process under electrokinetic phenomena. Matsubara and Narumi 

(96) numerically modeled the mixing process in a microchannel with four electrodes on each side of the microchannel wall, which generated a disruption through unstable electro-osmotic vortices. It was found that particle mixing was sensitive to both the convection effect induced by the main and secondary vortex within the micromixer and the change in oscillation frequency caused by the supplied AC voltage when the Reynolds number was varied. Qaderi et al. 

(97) adapted the PNP equation to numerically study the effect of the geometry and zeta potential configuration of the microchannel on the mixing process with a combined electro-osmotic pressure driven flow. It was reported that the application of heterogeneous zeta potential configuration enhances the mixing efficiency by around 23% while the height of the hurdles increases the mixing efficiency at most 48.1%. Cho et al. 

(98) utilized the PB model and Laplace equation to numerically simulate the electro-osmotic non-Newtonian fluid mixing process within a wavy and block layout of microchannel walls. The Power Law model is adapted to describe the fluid rheological characteristic. It was found that shear-thinning fluids possess a higher volumetric flow rate, which could result in poorer mixing efficiency compared to that of Newtonian fluids. Numerous studies have revealed that flow instability and vortex generation, in particular secondary vortices produced by barriers or greater magnitudes of heterogeneous zeta potential distribution, enhance mixing by increasing bulk flow velocity and reducing flow distance.To better understand the mechanism of disturbance formed in the system due to externally applied forces, known as electrokinetic instability, literature often utilize the Rayleigh (Ra) number, 

(1) as described below:

𝑅𝑎𝑣=𝑢ev𝑢eo=(𝛾−1𝛾+1)2𝑊𝛿2𝐸el2𝐻2𝜁𝛿Ra�=�ev�eo=(�−1�+1)2��2�el2�2��

(22)where γ is the conductivity ratio of the two streams and can be written as 

𝛾=𝜎el,H𝜎el,L�=�el,H�el,L. The Ra number characterizes the ratio between electroviscous and electro-osmotic flow. A high Ra

v value often results in good mixing. It is evident that fluid properties such as the conductivity (σ) of the two streams play a key role in the formation of disturbances to enhance mixing in microsystems. At the same time, electrokinetic parameters like the zeta potential (ζ) in the Ra number is critical in the characterization of electro-osmotic velocity and a slip boundary condition at the microchannel wall.To understand the mixing result along the channel, the concentration field can be defined and simulated under the assumption of steady state conditions and constant diffusion coefficient for each of the working fluid within the system through the convection–diffusion equation as below:

∂𝑐𝒊∂𝑡+∇⇀(𝑐𝑖𝑢⇀−𝐷𝑖∇⇀𝑐𝒊)=0∂��∂�+∇⇀(���⇀−��∇⇀��)=0

(23)where c

i is the species concentration of species i and D

i is the diffusion coefficient of the corresponding species.The standard deviation of concentration (σ

sd) can be adapted to evaluate the mixing quality of the system. 

(97) The standard deviation for concentration at a specific portion of the channel may be calculated using the equation below:

𝜎sd=∫10(𝐶∗(𝑦∗)−𝐶m)2d𝑦∗∫10d𝑦∗⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯�sd=∫01(�*(�*)−�m)2d�*∫01d�*

(24)where C*(y*) and C

m are the non-dimensional concentration profile and the mean concentration at the portion, respectively. C* is the non-dimensional concentration and can be calculated as 

𝐶∗=𝐶𝐶ref�*=��ref, where C

ref is the reference concentration defined as the bulk solution concentration. The mean concentration profile can be calculated as 

𝐶m=∫10(𝐶∗(𝑦∗)d𝑦∗∫10d𝑦∗�m=∫01(�*(�*)d�*∫01d�*. With the standard deviation of concentration, the mixing efficiency 

(97) can then be calculated as below:

𝜀𝑥=1−𝜎sd𝜎sd,0��=1−�sd�sd,0

(25)where σ

sd,0 is the standard derivation of the case of no mixing. The value of the mixing efficiency is typically utilized in conjunction with the simulated flow field and concentration field to explore the effect of geometrical and electrokinetic parameters on the optimization of the mixing results.

5. Summary

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5.1. Conclusion

Viscoelastic fluids such as blood flow in LOC systems are an essential topic to proceed with diagnostic analysis and research through microdevices in the biomedical and pharmaceutical industries. The complex blood flow behavior is tightly controlled by the viscoelastic characteristics of blood such as the dynamic viscosity and the elastic property of RBCs under various shear rate conditions. Furthermore, the flow behaviors under varied driving forces promote an array of microfluidic transport phenomena that are critical to the management of blood flow and other adapted viscoelastic fluids in LOC systems. This review addressed the blood flow phenomena, the complicated interplay between shear rate and blood flow behaviors, and their numerical modeling under LOC systems through the lens of the viscoelasticity characteristic. Furthermore, a theoretical understanding of capillary forces and externally applied electric forces leads to an in-depth investigation of the relationship between blood flow patterns and the key parameters of the two driving forces, the latter of which is introduced through the lens of viscoelastic fluids, coupling numerical modeling to improve the knowledge of blood flow manipulation in LOC systems. The flow disturbances triggered by the EOF of viscoelastic fluids and their impact on blood flow patterns have been deeply investigated due to their important role and applications in LOC devices. Continuous advancements of various numerical modeling methods with experimental findings through more efficient and less computationally heavy methods have served as an encouraging sign of establishing more accurate illustrations of the mechanisms for multiphase blood and other viscoelastic fluid flow transport phenomena driven by various forces. Such progress is fundamental for the manipulation of unique transport phenomena, such as the generated disturbances, to optimize functionalities offered by microdevices in LOC systems.

The following section will provide further insights into the employment of studied blood transport phenomena to improve the functionality of micro devices adapting LOC technology. A discussion of the novel roles that external driving forces play in microfluidic flow behaviors is also provided. Limitations in the computational modeling of blood flow and electrokinetic phenomena in LOC systems will also be emphasized, which may provide valuable insights for future research endeavors. These discussions aim to provide guidance and opportunities for new paths in the ongoing development of LOC devices that adapt blood flow.

5.2. Future Directions

5.2.1. Electro-osmosis Mixing in LOC Systems

Despite substantial research, mixing results through flow instability and vortex formation phenomena induced by electro-osmotic mixing still deviate from the effective mixing results offered by chaotic mixing results such as those seen in turbulent flows. However, recent discoveries of a mixing phenomenon that is generally observed under turbulent flows are found within electro-osmosis micromixers under low Reynolds number conditions. Zhao 

(99) experimentally discovered a rapid mixing process in an AC applied micromixer, where the power spectrum of concentration under an applied voltage of 20 V

p-p induces a −5/3 slope within a frequency range. This value of the slope is considered as the O–C spectrum in macroflows, which is often visible under relatively high Re conditions, such as the Taylor microscale Reynolds number Re > 500 in turbulent flows. 

(100) However, the Re value in the studied system is less than 1 at the specific location and applied voltage. A secondary flow is also suggested to occur close to microchannel walls, being attributed to the increase of convective instability within the system.Despite the experimental phenomenon proposed by Zhao et al., 

(99) the range of effects induced by vital parameters of an EOF mixing system on the enhanced mixing results and mechanisms of disturbance generated by the turbulent-like flow instability is not further characterized. Such a gap in knowledge may hinder the adaptability and commercialization of the discovery of micromixers. One of the parameters for further evaluation is the conductivity gradient of the fluid flow. A relatively strong conductivity gradient (5000:1) was adopted in the system due to the conductive properties of the two fluids. The high conductivity gradients may contribute to the relatively large Rayleigh number and differences in EDL layer thickness, resulting in an unusual disturbance in laminar flow conditions and enhanced mixing results. However, high conductivity gradients are not always achievable by the working fluids due to diverse fluid properties. The reliance on turbulent-like phenomena and rapid mixing results in a large conductivity gradient should be established to prevent the limited application of fluids for the mixing system. In addition, the proposed system utilizes distinct zeta potential distributions at the top and bottom walls due to their difference in material choices, which may be attributed to the flow instability phenomena. Further studies should be made on varying zeta potential magnitude and distribution to evaluate their effect on the slip boundary conditions of the flow and the large shear rate condition close to the channel wall of EOF. Such a study can potentially offer an optimized condition in zeta potential magnitude through material choices and geometrical layout of the zeta potential for better mixing results and manipulation of mixing fluid dynamics. The two vital parameters mentioned above can be varied with the aid of numerical simulation to understand the effect of parameters on the interaction between electro-osmotic forces and electroviscous forces. At the same time, the relationship of developed streamlines of the simulated velocity and concentration field, following their relationship with the mixing results, under the impact of these key parameters can foster more insight into the range of impact that the two parameters have on the proposed phenomena and the microfluidic dynamic principles of disturbances.

In addition, many of the current investigations of electrokinetic mixers commonly emphasize the fluid dynamics of mixing for Newtonian fluids, while the utilization of biofluids, primarily viscoelastic fluids such as blood, and their distinctive response under shear forces in these novel mixing processes of LOC systems are significantly less studied. To develop more compatible microdevice designs and efficient mixing outcomes for the biomedical industry, it is necessary to fill the knowledge gaps in the literature on electro-osmotic mixing for biofluids, where properties of elasticity, dynamic viscosity, and intricate relationship with shear flow from the fluid are further considered.

5.2.2. Electro-osmosis Separation in LOC Systems

Particle separation in LOC devices, particularly in biological research and diagnostics, is another area where disturbances may play a significant role in optimization. 

(101) Plasma analysis in LOC systems under precise control of blood flow phenomena and blood/plasma separation procedures can detect vital information about infectious diseases from particular antibodies and foreign nucleic acids for medical treatments, diagnostics, and research, 

(102) offering more efficient results and simple operating procedures compared to that of the traditional centrifugation method for blood and plasma separation. However, the adaptability of LOC devices for blood and plasma separation is often hindered by microchannel clogging, where flow velocity and plasma yield from LOC devices is reduced due to occasional RBC migration and aggregation at the filtration entrance of microdevices. 

(103)It is important to note that the EOF induces flow instability close to microchannel walls, which may provide further solutions to clogging for the separation process of the LOC systems. Mohammadi et al. 

(104) offered an anti-clogging effect of RBCs at the blood and plasma separating device filtration entry, adjacent to the surface wall, through RBC disaggregation under high shear rate conditions generated by a forward and reverse EOF direction.

Further theoretical and numerical research can be conducted to characterize the effect of high shear rate conditions near microchannel walls toward the detachment of binding blood cells on surfaces and the reversibility of aggregation. Through numerical modeling with varying electrokinetic parameters to induce different degrees of disturbances or shear conditions at channel walls, it may be possible to optimize and better understand the process of disrupting the forces that bind cells to surface walls and aggregated cells at filtration pores. RBCs that migrate close to microchannel walls are often attracted by the adhesion force between the RBC and the solid surface originating from the van der Waals forces. Following RBC migration and attachment by adhesive forces adjacent to the microchannel walls as shown in Figure 7, the increase in viscosity at the region causes a lower shear condition and encourages RBC aggregation (cell–cell interaction), which clogs filtering pores or microchannels and reduces flow velocity at filtration region. Both the impact that shear forces and disturbances may induce on cell binding forces with surface walls and other cells leading to aggregation may suggest further characterization. Kinetic parameters such as activation energy and the rate-determining step for cell binding composition attachment and detachment should be considered for modeling the dynamics of RBCs and blood flows under external forces in LOC separation devices.

Figure 7. Schematic representations of clogging at a microchannel pore following the sequence of RBC migration, cell attachment to channel walls, and aggregation. (105) Reproduced with permission from ref (105). Copyright 2018 The Authors under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/.

5.2.3. Relationship between External Forces and Microfluidic Systems

In blood flow, a thicker CFL suggests a lower blood viscosity, suggesting a complex relationship between shear stress and shear rate, affecting the blood viscosity and blood flow. Despite some experimental and numerical studies on electro-osmotic non-Newtonian fluid flow, limited literature has performed an in-depth investigation of the role that applied electric forces and other external forces could play in the process of CFL formation. Additional studies on how shear rates from external forces affect CFL formation and microfluidic flow dynamics can shed light on the mechanism of the contribution induced by external driving forces to the development of a separate phase of layer, similar to CFL, close to the microchannel walls and distinct from the surrounding fluid within the system, then influencing microfluidic flow dynamics.One of the mechanisms of phenomena to be explored is the formation of the Exclusion Zone (EZ) region following a “Self-Induced Flow” (SIF) phenomenon discovered by Li and Pollack, 

(106) as shown in Figure 8(a) and (b), respectively. A spontaneous sustained axial flow is observed when hydrophilic materials are immersed in water, resulting in the buildup of a negative layer of charges, defined as the EZ, after water molecules absorb infrared radiation (IR) energy and break down into H and OH

+–.

Figure 8. Schematic representations of (a) the Exclusion Zone region and (b) the Self Induced Flow through visualization of microsphere movement within a microchannel. (106) Reproduced with permission from ref (106). Copyright 2020 The Authors under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/.

Despite the finding of such a phenomenon, the specific mechanism and role of IR energy have yet to be defined for the process of EZ development. To further develop an understanding of the role of IR energy in such phenomena, a feasible study may be seen through the lens of the relationships between external forces and microfluidic flow. In the phenomena, the increase of SIF velocity under a rise of IR radiation resonant characteristics is shown in the participation of the external electric field near the microchannel walls under electro-osmotic viscoelastic fluid flow systems. The buildup of negative charges at the hydrophilic surfaces in EZ is analogous to the mechanism of electrical double layer formation. Indeed, research has initiated the exploration of the core mechanisms for EZ formation through the lens of the electrokinetic phenomena. 

(107) Such a similarity of the role of IR energy and the transport phenomena of SIF with electrokinetic phenomena paves the way for the definition of the unknown SIF phenomena and EZ formation. Furthermore, Li and Pollack 

(106) suggest whether CFL formation might contribute to a SIF of blood using solely IR radiation, a commonly available source of energy in nature, as an external driving force. The proposition may be proven feasible with the presence of the CFL region next to the negatively charged hydrophilic endothelial glycocalyx layer, coating the luminal side of blood vessels. 

(108) Further research can dive into the resonating characteristics between the formation of the CFL region next to the hydrophilic endothelial glycocalyx layer and that of the EZ formation close to hydrophilic microchannel walls. Indeed, an increase in IR energy is known to rapidly accelerate EZ formation and SIF velocity, depicting similarity to the increase in the magnitude of electric field forces and greater shear rates at microchannel walls affecting CFL formation and EOF velocity. Such correlation depicts a future direction in whether SIF blood flow can be observed and characterized theoretically further through the lens of the relationship between blood flow and shear forces exhibited by external energy.

The intricate link between the CFL and external forces, more specifically the externally applied electric field, can receive further attention to provide a more complete framework for the mechanisms between IR radiation and EZ formation. Such characterization may also contribute to a greater comprehension of the role IR can play in CFL formation next to the endothelial glycocalyx layer as well as its role as a driving force to propel blood flow, similar to the SIF, but without the commonly assumed pressure force from heart contraction as a source of driving force.

5.3. Challenges

Although there have been significant improvements in blood flow modeling under LOC systems over the past decade, there are still notable constraints that may require special attention for numerical simulation applications to benefit the adaptability of the designs and functionalities of LOC devices. Several points that require special attention are mentioned below:

1.The majority of CFD models operate under the relationship between the viscoelasticity of blood and the shear rate conditions of flow. The relative effect exhibited by the presence of highly populated RBCs in whole blood and their forces amongst the cells themselves under complex flows often remains unclearly defined. Furthermore, the full range of cell populations in whole blood requires a much more computational load for numerical modeling. Therefore, a vital goal for future research is to evaluate a reduced modeling method where the impact of cell–cell interaction on the viscoelastic property of blood is considered.
2.Current computational methods on hemodynamics rely on continuum models based upon non-Newtonian rheology at the macroscale rather than at molecular and cellular levels. Careful considerations should be made for the development of a constructive framework for the physical and temporal scales of micro/nanoscale systems to evaluate the intricate relationship between fluid driving forces, dynamic viscosity, and elasticity.
3.Viscoelastic fluids under the impact of externally applied electric forces often deviate from the assumptions of no-slip boundary conditions due to the unique flow conditions induced by externally applied forces. Furthermore, the mechanism of vortex formation and viscoelastic flow instability at laminar flow conditions should be better defined through the lens of the microfluidic flow phenomenon to optimize the prediction of viscoelastic flow across different geometrical layouts. Mathematical models and numerical methods are needed to better predict such disturbance caused by external forces and the viscoelasticity of fluids at such a small scale.
4.Under practical situations, zeta potential distribution at channel walls frequently deviates from the common assumption of a constant distribution because of manufacturing faults or inherent surface charges prior to the introduction of electrokinetic influence. These discrepancies frequently lead to inconsistent surface potential distribution, such as excess positive ions at relatively more negatively charged walls. Accordingly, unpredicted vortex formation and flow instability may occur. Therefore, careful consideration should be given to these discrepancies and how they could trigger the transport process and unexpected results of a microdevice.

Author Information

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  • Corresponding Authors
    • Zhe Chen – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Email: zaccooky@sjtu.edu.cn
    • Bo Ouyang – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Email: bouy93@sjtu.edu.cn
    • Zheng-Hong Luo – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Orcidhttps://orcid.org/0000-0001-9011-6020; Email: luozh@sjtu.edu.cn
  • Authors
    • Bin-Jie Lai – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Orcidhttps://orcid.org/0009-0002-8133-5381
    • Li-Tao Zhu – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Orcidhttps://orcid.org/0000-0001-6514-8864
  • NotesThe authors declare no competing financial interest.

Acknowledgments

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This work was supported by the National Natural Science Foundation of China (No. 22238005) and the Postdoctoral Research Foundation of China (No. GZC20231576).

Vocabulary

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Microfluidicsthe field of technological and scientific study that investigates fluid flow in channels with dimensions between 1 and 1000 μm
Lab-on-a-Chip Technologythe field of research and technological development aimed at integrating the micro/nanofluidic characteristics to conduct laboratory processes on handheld devices
Computational Fluid Dynamics (CFD)the method utilizing computational abilities to predict physical fluid flow behaviors mathematically through solving the governing equations of corresponding fluid flows
Shear Ratethe rate of change in velocity where one layer of fluid moves past the adjacent layer
Viscoelasticitythe property holding both elasticity and viscosity characteristics relying on the magnitude of applied shear stress and time-dependent strain
Electro-osmosisthe flow of fluid under an applied electric field when charged solid surface is in contact with the bulk fluid
Vortexthe rotating motion of a fluid revolving an axis line

References

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Predicting solid-state phase transformations during metal additive manufacturing: A case study on electron-beam powder bed fusion of Inconel-738

Predicting solid-state phase transformations during metal additive manufacturing: A case study on electron-beam powder bed fusion of Inconel-738

금속 적층 제조 중 고체 상 변형 예측: Inconel-738의 전자빔 분말층 융합에 대한 사례 연구

Nana Kwabena Adomako a, Nima Haghdadi a, James F.L. Dingle bc, Ernst Kozeschnik d, Xiaozhou Liao bc, Simon P. Ringer bc, Sophie Primig a

Abstract

Metal additive manufacturing (AM) has now become the perhaps most desirable technique for producing complex shaped engineering parts. However, to truly take advantage of its capabilities, advanced control of AM microstructures and properties is required, and this is often enabled via modeling. The current work presents a computational modeling approach to studying the solid-state phase transformation kinetics and the microstructural evolution during AM. Our approach combines thermal and thermo-kinetic modelling. A semi-analytical heat transfer model is employed to simulate the thermal history throughout AM builds. Thermal profiles of individual layers are then used as input for the MatCalc thermo-kinetic software. The microstructural evolution (e.g., fractions, morphology, and composition of individual phases) for any region of interest throughout the build is predicted by MatCalc. The simulation is applied to an IN738 part produced by electron beam powder bed fusion to provide insights into how γ′ precipitates evolve during thermal cycling. Our simulations show qualitative agreement with our experimental results in predicting the size distribution of γ′ along the build height, its multimodal size character, as well as the volume fraction of MC carbides. Our findings indicate that our method is suitable for a range of AM processes and alloys, to predict and engineer their microstructures and properties.

Graphical Abstract

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Keywords

Additive manufacturing, Simulation, Thermal cycles, γ′ phase, IN738

1. Introduction

Additive manufacturing (AM) is an advanced manufacturing method that enables engineering parts with intricate shapes to be fabricated with high efficiency and minimal materials waste. AM involves building up 3D components layer-by-layer from feedstocks such as powder [1]. Various alloys, including steel, Ti, Al, and Ni-based superalloys, have been produced using different AM techniques. These techniques include directed energy deposition (DED), electron- and laser powder bed fusion (E-PBF and L-PBF), and have found applications in a variety of industries such as aerospace and power generation [2], [3], [4]. Despite the growing interest, certain challenges limit broader applications of AM fabricated components in these industries and others. One of such limitations is obtaining a suitable and reproducible microstructure that offers the desired mechanical properties consistently. In fact, the AM as-built microstructure is highly complex and considerably distinctive from its conventionally processed counterparts owing to the complicated thermal cycles arising from the deposition of several layers upon each other [5], [6].

Several studies have reported that the solid-state phases and solidification microstructure of AM processed alloys such as CMSX-4, CoCr [7], [8], Ti-6Al-4V [9], [10], [11], IN738 [6], 304L stainless steel [12], and IN718 [13], [14] exhibit considerable variations along the build direction. For instance, references [9], [10] have reported that there is a variation in the distribution of α and β phases along the build direction in Ti-alloys. Similarly, the microstructure of an L-PBF fabricated martensitic steel exhibits variations in the fraction of martensite [15]. Furthermore, some of the present authors and others [6], [16], [17], [18], [19], [20] have recently reviewed and reported that there is a difference in the morphology and fraction of nanoscale precipitates as a function of build height in Ni-based superalloys. These non-uniformities in the as-built microstructure result in an undesired heterogeneity in mechanical and other important properties such as corrosion and oxidation [19], [21], [22], [23]. To obtain the desired microstructure and properties, additional processing treatments are utilized, but this incurs extra costs and may lead to precipitation of detrimental phases and grain coarsening. Therefore, a through-process understanding of the microstructure evolution under repeated heating and cooling is now needed to further advance 3D printed microstructure and property control.

It is now commonly understood that the microstructure evolution during printing is complex, and most AM studies concentrate on the microstructure and mechanical properties of the final build only. Post-printing studies of microstructure characteristics at room temperature miss crucial information on how they evolve. In-situ measurements and modelling approaches are required to better understand the complex microstructural evolution under repeated heating and cooling. Most in-situ measurements in AM focus on monitoring the microstructural changes, such as phase transformations and melt pool dynamics during fabrication using X-ray scattering and high-speed X-ray imaging [24], [25], [26], [27]. For example, Zhao et al. [25] measured the rate of solidification and described the α/β phase transformation during L-PBF of Ti-6Al-4V in-situ. Also, Wahlmann et al. [21] recently used an L-PBF machine coupled with X-ray scattering to investigate the changes in CMSX-4 phase during successive melting processes. Although these techniques provide significant understanding of the basic principles of AM, they are not widely accessible. This is due to the great cost of the instrument, competitive application process, and complexities in terms of the experimental set-up, data collection, and analysis [26], [28].

Computational modeling techniques are promising and more widely accessible tools that enable advanced understanding, prediction, and engineering of microstructures and properties during AM. So far, the majority of computational studies have concentrated on physics based process models for metal AM, with the goal of predicting the temperature profile, heat transfer, powder dynamics, and defect formation (e.g., porosity) [29], [30]. In recent times, there have been efforts in modeling of the AM microstructure evolution using approaches such as phase-field [31], Monte Carlo (MC) [32], and cellular automata (CA) [33], coupled with finite element simulations for temperature profiles. However, these techniques are often restricted to simulating the evolution of solidification microstructures (e.g., grain and dendrite structure) and defects (e.g., porosity). For example, Zinovieva et al. [33] predicted the grain structure of L-PBF Ti-6Al-4V using finite difference and cellular automata methods. However, studies on the computational modelling of the solid-state phase transformations, which largely determine the resulting properties, remain limited. This can be attributed to the multi-component and multi-phase nature of most engineering alloys in AM, along with the complex transformation kinetics during thermal cycling. This kind of research involves predictions of the thermal cycle in AM builds, and connecting it to essential thermodynamic and kinetic data as inputs for the model. Based on the information provided, the thermokinetic model predicts the history of solid-state phase microstructure evolution during deposition as output. For example, a multi-phase, multi-component mean-field model has been developed to simulate the intermetallic precipitation kinetics in IN718 [34] and IN625 [35] during AM. Also, Basoalto et al. [36] employed a computational framework to examine the contrasting distributions of process-induced microvoids and precipitates in two Ni-based superalloys, namely IN718 and CM247LC. Furthermore, McNamara et al. [37] established a computational model based on the Johnson-Mehl-Avrami model for non-isothermal conditions to predict solid-state phase transformation kinetics in L-PBF IN718 and DED Ti-6Al-4V. These models successfully predicted the size and volume fraction of individual phases and captured the repeated nucleation and dissolution of precipitates that occur during AM.

In the current study, we propose a modeling approach with appreciably short computational time to investigate the detailed microstructural evolution during metal AM. This may include obtaining more detailed information on the morphologies of phases, such as size distribution, phase fraction, dissolution and nucleation kinetics, as well as chemistry during thermal cycling and final cooling to room temperature. We utilize the combination of the MatCalc thermo-kinetic simulator and a semi-analytical heat conduction model. MatCalc is a software suite for simulation of phase transformations, microstructure evolution and certain mechanical properties in engineering alloys. It has successfully been employed to simulate solid-state phase transformations in Ni-based superalloys [38], [39], steels [40], and Al alloys [41] during complex thermo-mechanical processes. MatCalc uses the classical nucleation theory as well as the so-called Svoboda-Fischer-Fratzl-Kozeschnik (SFFK) growth model as the basis for simulating precipitation kinetics [42]. Although MatCalc was originally developed for conventional thermo-mechanical processes, we will show that it is also applicable for AM if the detailed time-temperature profile of the AM build is known. The semi-analytical heat transfer code developed by Stump and Plotkowski [43] is used to simulate these profile throughout the AM build.

1.1. Application to IN738

Inconel-738 (IN738) is a precipitation hardening Ni-based superalloy mainly employed in high-temperature components, e.g. in gas turbines and aero-engines owing to its exceptional mechanical properties at temperatures up to 980 °C, coupled with high resistance to oxidation and corrosion [44]. Its superior high-temperature strength (∼1090 MPa tensile strength) is provided by the L12 ordered Ni3(Al,Ti) γ′ phase that precipitates in a face-centered cubic (FCC) γ matrix [45], [46]. Despite offering great properties, IN738, like most superalloys with high γ′ fractions, is challenging to process owing to its propensity to hot cracking [47], [48]. Further, machining of such alloys is challenging because of their high strength and work-hardening rates. It is therefore difficult to fabricate complex INC738 parts using traditional manufacturing techniques like casting, welding, and forging.

The emergence of AM has now made it possible to fabricate such parts from IN738 and other superalloys. Some of the current authors’ recent research successfully applied E-PBF to fabricate defect-free IN738 containing γ′ throughout the build [16], [17]. The precipitated γ′ were heterogeneously distributed. In particular, Haghdadi et al. [16] studied the origin of the multimodal size distribution of γ′, while Lim et al. [17] investigated the gradient in γ′ character with build height and its correlation to mechanical properties. Based on these results, the present study aims to extend the understanding of the complex and site-specific microstructural evolution in E-PBF IN738 by using a computational modelling approach. New experimental evidence (e.g., micrographs not published previously) is presented here to support the computational results.

2. Materials and Methods

2.1. Materials preparation

IN738 Ni-based superalloy (59.61Ni-8.48Co-7.00Al-17.47Cr-3.96Ti-1.01Mo-0.81W-0.56Ta-0.49Nb-0.47C-0.09Zr-0.05B, at%) gas-atomized powder was used as feedstock. The powders, with average size of 60 ± 7 µm, were manufactured by Praxair and distributed by Astro Alloys Inc. An Arcam Q10 machine by GE Additive with an acceleration voltage of 60 kV was used to fabricate a 15 × 15 × 25 mm3 block (XYZ, Z: build direction) on a 316 stainless steel substrate. The block was 3D-printed using a ‘random’ spot melt pattern. The random spot melt pattern involves randomly selecting points in any given layer, with an equal chance of each point being melted. Each spot melt experienced a dwell time of 0.3 ms, and the layer thickness was 50 µm. Some of the current authors have previously characterized the microstructure of the very same and similar builds in more detail [16], [17]. A preheat temperature of ∼1000 °C was set and kept during printing to reduce temperature gradients and, in turn, thermal stresses [49], [50], [51]. Following printing, the build was separated from the substrate through electrical discharge machining. It should be noted that this sample was simultaneously printed with the one used in [17] during the same build process and on the same build plate, under identical conditions.

2.2. Microstructural characterization

The printed sample was longitudinally cut in the direction of the build using a Struers Accutom-50, ground, and then polished to 0.25 µm suspension via standard techniques. The polished x-z surface was electropolished and etched using Struers A2 solution (perchloric acid in ethanol). Specimens for image analysis were polished using a 0.06 µm colloidal silica. Microstructure analyses were carried out across the height of the build using optical microscopy (OM) and scanning electron microscopy (SEM) with focus on the microstructure evolution (γ′ precipitates) in individual layers. The position of each layer being analyzed was determined by multiplying the layer number by the layer thickness (50 µm). It should be noted that the position of the first layer starts where the thermal profile is tracked (in this case, 2 mm from the bottom). SEM images were acquired using a JEOL 7001 field emission microscope. The brightness and contrast settings, acceleration voltage of 15 kV, working distance of 10 mm, and other SEM imaging parameters were all held constant for analysis of the entire build. The ImageJ software was used for automated image analysis to determine the phase fraction and size of γ′ precipitates and carbides. A 2-pixel radius Gaussian blur, following a greyscale thresholding and watershed segmentation was used [52]. Primary γ′ sizes (>50 nm), were measured using equivalent spherical diameters. The phase fractions were considered equal to the measured area fraction. Secondary γ′ particles (<50 nm) were not considered here. The γ′ size in the following refers to the diameter of a precipitate.

2.3. Hardness testing

A Struers DuraScan tester was utilized for Vickers hardness mapping on a polished x-z surface, from top to bottom under a maximum load of 100 mN and 10 s dwell time. 30 micro-indentations were performed per row. According to the ASTM standard [53], the indentations were sufficiently distant (∼500 µm) to assure that strain-hardened areas did not interfere with one another.

2.4. Computational simulation of E-PBF IN738 build

2.4.1. Thermal profile modeling

The thermal history was generated using the semi-analytical heat transfer code (also known as the 3DThesis code) developed by Stump and Plotkowski [43]. This code is an open-source C++ program which provides a way to quickly simulate the conductive heat transfer found in welding and AM. The key use case for the code is the simulation of larger domains than is practicable with Computational Fluid Dynamics/Finite Element Analysis programs like FLOW-3D AM. Although simulating conductive heat transfer will not be an appropriate simplification for some investigations (for example the modelling of keyholding or pore formation), the 3DThesis code does provide fast estimates of temperature, thermal gradient, and solidification rate which can be useful for elucidating microstructure formation across entire layers of an AM build. The mathematics involved in the code is as follows:

In transient thermal conduction during welding and AM, with uniform and constant thermophysical properties and without considering fluid convection and latent heat effects, energy conservation can be expressed as:(1)��∂�∂�=�∇2�+�̇where � is density, � specific heat, � temperature, � time, � thermal conductivity, and �̇ a volumetric heat source. By assuming a semi-infinite domain, Eq. 1 can be analytically solved. The solution for temperature at a given time (t) using a volumetric Gaussian heat source is presented as:(2)��,�,�,�−�0=33�����32∫0�1������exp−3�′�′2��+�′�′2��+�′�′2����′(3)and��=12��−�′+��2for�=�,�,�(4)and�′�′=�−���′Where � is the vector �,�,� and �� is the location of the heat source.

The numerical integration scheme used is an adaptive Gaussian quadrature method based on the following nondimensionalization:(5)�=��xy2�,�′=��xy2�′,�=��xy,�=��xy,�=��xy,�=���xy

A more detailed explanation of the mathematics can be found in reference [43].

The main source of the thermal cycling present within a powder-bed fusion process is the fusion of subsequent layers. Therefore, regions near the top of a build are expected to undergo fewer thermal cycles than those closer to the bottom. For this purpose, data from the single scan’s thermal influence on multiple layers was spliced to represent the thermal cycles experienced at a single location caused by multiple subsequent layers being fused.

The cross-sectional area simulated by this model was kept constant at 1 × 1 mm2, and the depth was dependent on the build location modelled with MatCalc. For a build location 2 mm from the bottom, the maximum number of layers to simulate is 460. Fig. 1a shows a stitched overview OM image of the entire build indicating the region where this thermal cycle is simulated and tracked. To increase similarity with the conditions of the physical build, each thermal history was constructed from the results of two simulations generated with different versions of a random scan path. The parameters used for these thermal simulations can be found in Table 1. It should be noted that the main purpose of the thermal profile modelling was to demonstrate how the conditions at different locations of the build change relative to each other. Accurately predicting the absolute temperature during the build would require validation via a temperature sensor measurement during the build process which is beyond the scope of the study. Nonetheless, to establish the viability of the heat source as a suitable approximation for this study, an additional sensitivity analysis was conducted. This analysis focused on the influence of energy input on γ′ precipitation behavior, the central aim of this paper. This was achieved by employing varying beam absorption energies (0.76, 0.82 – the values utilized in the simulation, and 0.9). The direct impact of beam absorption efficiency on energy input into the material was investigated. Specifically, the initial 20 layers of the build were simulated and subsequently compared to experimental data derived from SEM. While phase fractions were found to be consistent across all conditions, disparities emerged in the mean size of γ′ precipitates. An absorption efficiency of 0.76 yielded a mean size of approximately 70 nm. Conversely, absorption efficiencies of 0.82 and 0.9 exhibited remarkably similar mean sizes of around 130 nm, aligning closely with the outcomes of the experiments.

Fig. 1

Table 1. A list of parameters used in thermal simulation of E-PBF.

ParameterValue
Spatial resolution5 µm
Time step0.5 s
Beam diameter200 µm
Beam penetration depth1 µm
Beam power1200 W
Beam absorption efficiency0.82
Thermal conductivity25.37 W/(m⋅K)
Chamber temperature1000 °C
Specific heat711.756 J/(kg⋅K)
Density8110 kg/m3

2.4.2. Thermo-kinetic simulation

The numerical analyses of the evolution of precipitates was performed using MatCalc version 6.04 (rel 0.011). The thermodynamic (‘mc_ni.tdb’, version 2.034) and diffusion (‘mc_ni.ddb’, version 2.007) databases were used. MatCalc’s basic principles are elaborated as follows:

The nucleation kinetics of precipitates are computed using a computational technique based on a classical nucleation theory [54] that has been modified for systems with multiple components [42], [55]. Accordingly, the transient nucleation rate (�), which expresses the rate at which nuclei are formed per unit volume and time, is calculated as:(6)�=�0��*∙�xp−�*�∙�∙exp−��where �0 denotes the number of active nucleation sites, �* the rate of atomic attachment, � the Boltzmann constant, � the temperature, �* the critical energy for nucleus formation, τ the incubation time, and t the time. � (Zeldovich factor) takes into consideration that thermal excitation destabilizes the nucleus as opposed to its inactive state [54]. Z is defined as follows:(7)�=−12�kT∂2∆�∂�2�*12where ∆� is the overall change in free energy due to the formation of a nucleus and n is the nucleus’ number of atoms. ∆�’s derivative is evaluated at n* (critical nucleus size). �* accounts for the long-range diffusion of atoms required for nucleation, provided that the matrix’ and precipitates’ composition differ. Svoboda et al. [42] developed an appropriate multi-component equation for �*, which is given by:(8)�*=4��*2�4�∑�=1��ki−�0�2�0��0�−1where �* denotes the critical radius for nucleation, � represents atomic distance, and � is the molar volume. �ki and �0� represent the concentration of elements in the precipitate and matrix, respectively. The parameter �0� denotes the rate of diffusion of the ith element within the matrix. The expression for the incubation time � is expressed as [54]:(9)�=12�*�2

and �*, which represents the critical energy for nucleation:(10)�*=16�3�3∆�vol2where � is the interfacial energy, and ∆Gvol the change in the volume free energy. The critical nucleus’ composition is similar to the γ′ phase’s equilibrium composition at the same temperature. � is computed based on the precipitate and matrix compositions, using a generalized nearest neighbor broken bond model, with the assumption of interfaces being planar, sharp, and coherent [56], [57], [58].

In Eq. 7, it is worth noting that �* represents the fundamental variable in the nucleation theory. It contains �3/∆�vol2 and is in the exponent of the nucleation rate. Therefore, even small variations in γ and/or ∆�vol can result in notable changes in �, especially if �* is in the order of �∙�. This is demonstrated in [38] for UDIMET 720 Li during continuous cooling, where these quantities change steadily during precipitation due to their dependence on matrix’ and precipitate’s temperature and composition. In the current work, these changes will be even more significant as the system is exposed to multiple cycles of rapid cooling and heating.

Once nucleated, the growth of a precipitate is assessed using the radius and composition evolution equations developed by Svoboda et al. [42] with a mean-field method that employs the thermodynamic extremal principle. The expression for the total Gibbs free energy of a thermodynamic system G, which consists of n components and m precipitates, is given as follows:(11)�=∑���0��0�+∑�=1�4���33��+∑�=1��ki�ki+∑�=1�4���2��.

The chemical potential of component � in the matrix is denoted as �0�(�=1,…,�), while the chemical potential of component � in the precipitate is represented by �ki(�=1,…,�,�=1,…,�). These chemical potentials are defined as functions of the concentrations �ki(�=1,…,�,�=1,…,�). The interface energy density is denoted as �, and �� incorporates the effects of elastic energy and plastic work resulting from the volume change of each precipitate.

Eq. (12) establishes that the total free energy of the system in its current state relies on the independent state variables: the sizes (radii) of the precipitates �� and the concentrations of each component �ki. The remaining variables can be determined by applying the law of mass conservation to each component �. This can be represented by the equation:(12)��=�0�+∑�=1�4���33�ki,

Furthermore, the global mass conservation can be expressed by equation:(13)�=∑�=1���When a thermodynamic system transitions to a more stable state, the energy difference between the initial and final stages is dissipated. This model considers three distinct forms of dissipation effects [42]. These include dissipations caused by the movement of interfaces, diffusion within the precipitate and diffusion within the matrix.

Consequently, �̇� (growth rate) and �̇ki (chemical composition’s rate of change) of the precipitate with index � are derived from the linear system of equation system:(14)�ij��=��where �� symbolizes the rates �̇� and �̇ki [42]. Index i contains variables for precipitate radius, chemical composition, and stoichiometric boundary conditions suggested by the precipitate’s crystal structure. Eq. (10) is computed separately for every precipitate �. For a more detailed description of the formulae for the coefficients �ij and �� employed in this work please refer to [59].

The MatCalc software was used to perform the numerical time integration of �̇� and �̇ki of precipitates based on the classical numerical method by Kampmann and Wagner [60]. Detailed information on this method can be found in [61]. Using this computational method, calculations for E-PBF thermal cycles (cyclic heating and cooling) were computed and compared to experimental data. The simulation took approximately 2–4 hrs to complete on a standard laptop.

3. Results

3.1. Microstructure

Fig. 1 displays a stitched overview image and selected SEM micrographs of various γ′ morphologies and carbides after observations of the X-Z surface of the build from the top to 2 mm above the bottom. Fig. 2 depicts a graph that charts the average size and phase fraction of the primary γ′, as it changes with distance from the top to the bottom of the build. The SEM micrographs show widespread primary γ′ precipitation throughout the entire build, with the size increasing in the top to bottom direction. Particularly, at the topmost height, representing the 460th layer (Z = 22.95 mm), as seen in Fig. 1b, the average size of γ′ is 110 ± 4 nm, exhibiting spherical shapes. This is representative of the microstructure after it solidifies and cools to room temperature, without experiencing additional thermal cycles. The γ′ size slightly increases to 147 ± 6 nm below this layer and remains constant until 0.4 mm (∼453rd layer) from the top. At this position, the microstructure still closely resembles that of the 460th layer. After the 453rd layer, the γ′ size grows rapidly to ∼503 ± 19 nm until reaching the 437th layer (1.2 mm from top). The γ′ particles here have a cuboidal shape, and a small fraction is coarser than 600 nm. γ′ continue to grow steadily from this position to the bottom (23 mm from the top). A small fraction of γ′ is > 800 nm.

Fig. 2

Besides primary γ′, secondary γ′ with sizes ranging from 5 to 50 nm were also found. These secondary γ′ precipitates, as seen in Fig. 1f, were present only in the bottom and middle regions. A detailed analysis of the multimodal size distribution of γ′ can be found in [16]. There is no significant variation in the phase fraction of the γ′ along the build. The phase fraction is ∼ 52%, as displayed in Fig. 2. It is worth mentioning that the total phase fraction of γ′ was estimated based on the primary γ′ phase fraction because of the small size of secondary γ′. Spherical MC carbides with sizes ranging from 50 to 400 nm and a phase fraction of 0.8% were also observed throughout the build. The carbides are the light grey precipitates in Fig. 1g. The light grey shade of carbides in the SEM images is due to their composition and crystal structure [52]. These carbides are not visible in Fig. 1b-e because they were dissolved during electro-etching carried out after electropolishing. In Fig. 1g, however, the sample was examined directly after electropolishing, without electro-etching.

Table 2 shows the nominal and measured composition of γ′ precipitates throughout the build by atom probe microscopy as determined in our previous study [17]. No build height-dependent composition difference was observed in either of the γ′ precipitate populations. However, there was a slight disparity between the composition of primary and secondary γ′. Among the main γ′ forming elements, the primary γ′ has a high Ti concentration while secondary γ′ has a high Al concentration. A detailed description of the atom distribution maps and the proxigrams of the constituent elements of γ′ throughout the build can be found in [17].

Table 2. Bulk IN738 composition determined using inductively coupled plasma atomic emission spectroscopy (ICP-AES). Compositions of γ, primary γ′, and secondary γ′ at various locations in the build measured by APT. This information is reproduced from data in Ref. [17] with permission.

at%NiCrCoAlMoWTiNbCBZrTaOthers
Bulk59.1217.478.487.001.010.813.960.490.470.050.090.560.46
γ matrix
Top50.4832.9111.591.941.390.820.440.80.030.030.02–0.24
Mid50.3732.6111.931.791.540.890.440.10.030.020.020.010.23
Bot48.1034.5712.082.141.430.880.480.080.040.030.01–0.12
Primary γ′
Top72.172.513.4412.710.250.397.780.56–0.030.020.050.08
Mid71.602.573.2813.550.420.687.040.73–0.010.030.040.04
Bot72.342.473.8612.500.260.447.460.500.050.020.020.030.04
Secondary γ′
Mid70.424.203.2314.190.631.035.340.790.03–0.040.040.05
Bot69.914.063.6814.320.811.045.220.650.05–0.100.020.11

3.2. Hardness

Fig. 3a shows the Vickers hardness mapping performed along the entire X-Z surface, while Fig. 3b shows the plot of average hardness at different build heights. This hardness distribution is consistent with the γ′ precipitate size gradient across the build direction in Fig. 1, Fig. 2. The maximum hardness of ∼530 HV1 is found at ∼0.5 mm away from the top surface (Z = 22.5), where γ′ particles exhibit the smallest observed size in Fig. 2b. Further down the build (∼ 2 mm from the top), the hardness drops to the 440–490 HV1 range. This represents the region where γ′ begins to coarsen. The hardness drops further to 380–430 HV1 at the bottom of the build.

Fig. 3

3.3. Modeling of the microstructural evolution during E-PBF

3.3.1. Thermal profile modeling

Fig. 4 shows the simulated thermal profile of the E-PBF build at a location of 23 mm from the top of the build, using a semi-analytical heat conduction model. This profile consists of the time taken to deposit 460 layers until final cooling, as shown in Fig. 4a. Fig. 4b-d show the magnified regions of Fig. 4a and reveal the first 20 layers from the top, a single layer (first layer from the top), and the time taken for the build to cool after the last layer deposition, respectively.

Fig. 4

The peak temperatures experienced by previous layers decrease progressively as the number of layers increases but never fall below the build preheat temperature (1000 °C). Our simulated thermal cycle may not completely capture the complexity of the actual thermal cycle utilized in the E-PBF build. For instance, the top layer (Fig. 4c), also representing the first deposit’s thermal profile without additional cycles (from powder heating, melting, to solidification), recorded the highest peak temperature of 1390 °C. Although this temperature is above the melting range of the alloy (1230–1360 °C) [62], we believe a much higher temperature was produced by the electron beam to melt the powder. Nevertheless, the solidification temperature and dynamics are outside the scope of this study as our focus is on the solid-state phase transformations during deposition. It takes ∼25 s for each layer to be deposited and cooled to the build temperature. The interlayer dwell time is 125 s. The time taken for the build to cool to room temperature (RT) after final layer deposition is ∼4.7 hrs (17,000 s).

3.3.2. MatCalc simulation

During the MatCalc simulation, the matrix phase is defined as γ. γ′, and MC carbide are included as possible precipitates. The domain of these precipitates is set to be the matrix (γ), and nucleation is assumed to be homogenous. In homogeneous nucleation, all atoms of the unit volume are assumed to be potential nucleation sites. Table 3 shows the computational parameters used in the simulation. All other parameters were set at default values as recommended in the version 6.04.0011 of MatCalc. The values for the interfacial energies are automatically calculated according to the generalized nearest neighbor broken bond model and is one of the most outstanding features in MatCalc [56], [57], [58]. It should be noted that the elastic misfit strain was not included in the calculation. The output of MatCalc includes phase fraction, size, nucleation rate, and composition of the precipitates. The phase fraction in MatCalc is the volume fraction. Although the experimental phase fraction is the measured area fraction, it is relatively similar to the volume fraction. This is because of the generally larger precipitate size and similar morphology at the various locations along the build [63]. A reliable phase fraction comparison between experiment and simulation can therefore be made.

Table 3. Computational parameters used in the simulation.

Precipitation domainγ
Nucleation site γ′Bulk (homogenous)
Nucleation site MC carbideBulk (Homogenous)
Precipitates class size250
Regular solution critical temperature γ′2500 K[64]
Calculated interfacial energyγ′ = 0.080–0.140 J/m2 and MC carbide = 0.410–0.430 J/m2
3.3.2.1. Precipitate phase fraction

Fig. 5a shows the simulated phase fraction of γ′ and MC carbide during thermal cycling. Fig. 5b is a magnified view of 5a showing the simulated phase fraction at the center points of the top 70 layers, whereas Fig. 5c corresponds to the first two layers from the top. As mentioned earlier, the top layer (460th layer) represents the microstructure after solidification. The microstructure of the layers below is determined by the number of thermal cycles, which increases with distance to the top. For example, layers 459, 458, 457, up to layer 1 (region of interest) experience 1, 2, 3 and 459 thermal cycles, respectively. In the top layer in Fig. 5c, the volume fraction of γ′ and carbides increases with temperature. For γ′, it decreases to zero when the temperature is above the solvus temperature after a few seconds. Carbides, however, remain constant in their volume fraction reaching equilibrium (phase fraction ∼ 0.9%) in a short time. The topmost layer can be compared to the first deposit, and the peak in temperature symbolizes the stage where the electron beam heats the powder until melting. This means γ′ and carbide precipitation might have started in the powder particles during heating from the build temperature and electron beam until the onset of melting, where γ′ dissolves, but carbides remain stable [28].

Fig. 5

During cooling after deposition, γ′ reprecipitates at a temperature of 1085 °C, which is below its solvus temperature. As cooling progresses, the phase fraction increases steadily to ∼27% and remains constant at 1000 °C (elevated build temperature). The calculated equilibrium fraction of phases by MatCalc is used to show the complex precipitation characteristics in this alloy. Fig. 6 shows that MC carbides form during solidification at 1320 °C, followed by γ′, which precipitate when the solidified layer cools to 1140 °C. This indicates that all deposited layers might contain a negligible amount of these precipitates before subsequent layer deposition, while being at the 1000 °C build temperature or during cooling to RT. The phase diagram also shows that the equilibrium fraction of the γ′ increases as temperature decreases. For instance, at 1000, 900, and 800 °C, the phase fractions are ∼30%, 38%, and 42%, respectively.

Fig. 6

Deposition of subsequent layers causes previous layers to undergo phase transformations as they are exposed to several thermal cycles with different peak temperatures. In Fig. 5c, as the subsequent layer is being deposited, γ′ in the previous layer (459th layer) begins to dissolve as the temperature crosses the solvus temperature. This is witnessed by the reduction of the γ′ phase fraction. This graph also shows how this phase dissolves during heating. However, the phase fraction of MC carbide remains stable at high temperatures and no dissolution is seen during thermal cycling. Upon cooling, the γ′ that was dissolved during heating reprecipitates with a surge in the phase fraction until 1000 °C, after which it remains constant. This microstructure is similar to the solidification microstructure (layer 460), with a similar γ′ phase fraction (∼27%).

The complete dissolution and reprecipitation of γ′ continue for several cycles until the 50th layer from the top (layer 411), where the phase fraction does not reach zero during heating to the peak temperature (see Fig. 5d). This indicates the ‘partial’ dissolution of γ′, which continues progressively with additional layers. It should be noted that the peak temperatures for layers that underwent complete dissolution were much higher (1170–1300 °C) than the γ′ solvus.

The dissolution and reprecipitation of γ′ during thermal cycling are further confirmed in Fig. 7, which summarizes the nucleation rate, phase fraction, and concentration of major elements that form γ′ in the matrix. Fig. 7b magnifies a single layer (3rd layer from top) within the full dissolution region in Fig. 7a to help identify the nucleation and growth mechanisms. From Fig. 7b, γ′ nucleation begins during cooling whereby the nucleation rate increases to reach a maximum value of approximately 1 × 1020 m−3s−1. This fast kinetics implies that some rearrangement of atoms is required for γ′ precipitates to form in the matrix [65], [66]. The matrix at this stage is in a non-equilibrium condition. Its composition is similar to the nominal composition and remains unchanged. The phase fraction remains insignificant at this stage although nucleation has started. The nucleation rate starts declining upon reaching the peak value. Simultaneously, diffusion-controlled growth of existing nuclei occurs, depleting the matrix of γ′ forming elements (Al and Ti). Thus, from (7), (11), ∆�vol continuously decreases until nucleation ceases. The growth of nuclei is witnessed by the increase in phase fraction until a constant level is reached at 27% upon cooling to and holding at build temperature. This nucleation event is repeated several times.

Fig. 7

At the onset of partial dissolution, the nucleation rate jumps to 1 × 1021 m−3s−1, and then reduces sharply at the middle stage of partial dissolution. The nucleation rate reaches 0 at a later stage. Supplementary Fig. S1 shows a magnified view of the nucleation rate, phase fraction, and thermal profile, underpinning this trend. The jump in nucleation rate at the onset is followed by a progressive reduction in the solute content of the matrix. The peak temperatures (∼1130–1160 °C) are lower than those in complete dissolution regions but still above or close to the γ′ solvus. The maximum phase fraction (∼27%) is similar to that of the complete dissolution regions. At the middle stage, the reduction in nucleation rate is accompanied by a sharp drop in the matrix composition. The γ′ fraction drops to ∼24%, where the peak temperatures of the layers are just below or at γ′ solvus. The phase fraction then increases progressively through the later stage of partial dissolution to ∼30% towards the end of thermal cycling. The matrix solute content continues to drop although no nucleation event is seen. The peak temperatures are then far below the γ′ solvus. It should be noted that the matrix concentration after complete dissolution remains constant. Upon cooling to RT after final layer deposition, the nucleation rate increases again, indicating new nucleation events. The phase fraction reaches ∼40%, with a further depletion of the matrix in major γ′ forming elements.

3.3.2.2. γ′ size distribution

Fig. 8 shows histograms of the γ′ precipitate size distributions (PSD) along the build height during deposition. These PSDs are predicted at the end of each layer of interest just before final cooling to room temperature, to separate the role of thermal cycles from final cooling on the evolution of γ′. The PSD for the top layer (layer 460) is shown in Fig. 8a (last solidified region with solidification microstructure). The γ′ size ranges from 120 to 230 nm and is similar to the 44 layers below (2.2 mm from the top).

Fig. 8

Further down the build, γ′ begins to coarsen after layer 417 (44th layer from top). Fig. 8c shows the PSD after the 44th layer, where the γ′ size exhibits two peaks at ∼120–230 and ∼300 nm, with most of the population being in the former range. This is the onset of partial dissolution where simultaneously with the reprecipitation and growth of fresh γ′, the undissolved γ′ grows rapidly through diffusive transport of atoms to the precipitates. This is shown in Fig. 8c, where the precipitate class sizes between 250 and 350 represent the growth of undissolved γ′. Although this continues in the 416th layer, the phase fractions plot indicates that the onset of partial dissolution begins after the 411th layer. This implies that partial dissolution started early, but the fraction of undissolved γ′ was too low to impact the phase fraction. The reprecipitated γ′ are mostly in the 100–220 nm class range and similar to those observed during full dissolution.

As the number of layers increases, coarsening intensifies with continued growth of more undissolved γ′, and reprecipitation and growth of partially dissolved ones. Fig. 8d, e, and f show this sequence. Further down the build, coarsening progresses rapidly, as shown in Figs. 8d, 8e, and 8f. The γ′ size ranges from 120 to 1100 nm, with the peaks at 160, 180, and 220 nm in Figs. 8d, 8e, and 8f, respectively. Coarsening continues until nucleation ends during dissolution, where only the already formed γ′ precipitates continue to grow during further thermal cycling. The γ′ size at this point is much larger, as observed in layers 361 and 261, and continues to increase steadily towards the bottom (layer 1). Two populations in the ranges of ∼380–700 and ∼750–1100 nm, respectively, can be seen. The steady growth of γ′ towards the bottom is confirmed by the gradual decrease in the concentration of solute elements in the matrix (Fig. 7a). It should be noted that for each layer, the γ′ class with the largest size originates from continuous growth of the earliest set of the undissolved precipitates.

Fig. 9, Fig. 10 and supplementary Figs. S2 and S3 show the γ′ size evolution during heating and cooling of a single layer in the full dissolution region, and early, middle stages, and later stages of partial dissolution, respectively. In all, the size of γ′ reduces during layer heating. Depending on the peak temperature of the layer which varies with build height, γ′ are either fully or partially dissolved as mentioned earlier. Upon cooling, the dissolved γ′ reprecipitate.

Fig. 9
Fig. 10

In Fig. 9, those layers that underwent complete dissolution (top layers) were held above γ′ solvus temperature for longer. In Fig. 10, layers at the early stage of partial dissolution spend less time in the γ′ solvus temperature region during heating, leading to incomplete dissolution. In such conditions, smaller precipitates are fully dissolved while larger ones shrink [67]. Layers in the middle stages of partial dissolution have peak temperatures just below or at γ′ solvus, not sufficient to achieve significant γ′ dissolution. As seen in supplementary Fig. S2, only a few smaller γ′ are dissolved back into the matrix during heating, i.e., growth of precipitates is more significant than dissolution. This explains the sharp decrease in concentration of Al and Ti in the matrix in this layer.

The previous sections indicate various phenomena such as an increase in phase fraction, further depletion of matrix composition, and new nucleation bursts during cooling. Analysis of the PSD after the final cooling of the build to room temperature allows a direct comparison to post-printing microstructural characterization. Fig. 11 shows the γ′ size distribution of layer 1 (460th layer from the top) after final cooling to room temperature. Precipitation of secondary γ′ is observed, leading to the multimodal size distribution of secondary and primary γ′. The secondary γ′ size falls within the 10–80 nm range. As expected, a further growth of the existing primary γ′ is also observed during cooling.

Fig. 11
3.3.2.3. γ′ chemistry after deposition

Fig. 12 shows the concentration of the major elements that form γ′ (Al, Ti, and Ni) in the primary and secondary γ′ at the bottom of the build, as calculated by MatCalc. The secondary γ′ has a higher Al content (13.5–14.5 at% Al), compared to 13 at% Al in the primary γ′. Additionally, within the secondary γ′, the smallest particles (∼10 nm) have higher Al contents than larger ones (∼70 nm). In contrast, for the primary γ′, there is no significant variation in the Al content as a function of their size. The Ni concentration in secondary γ′ (71.1–72 at%) is also higher in comparison to the primary γ′ (70 at%). The smallest secondary γ′ (∼10 nm) have higher Ni contents than larger ones (∼70 nm), whereas there is no substantial change in the Ni content of primary γ′, based on their size. As expected, Ti shows an opposite size-dependent variation. It ranges from ∼ 7.7–8.7 at% Ti in secondary γ′ to ∼9.2 at% in primary γ′. Similarly, within the secondary γ′, the smallest (∼10 nm) have lower Al contents than the larger ones (∼70 nm). No significant variation is observed for Ti content in primary γ′.

Fig. 12

4. Discussion

A combined modelling method is utilized to study the microstructural evolution during E-PBF of IN738. The presented results are discussed by examining the precipitation and dissolution mechanism of γ′ during thermal cycling. This is followed by a discussion on the phase fraction and size evolution of γ′ during thermal cycling and after final cooling. A brief discussion on carbide morphology is also made. Finally, a comparison is made between the simulation and experimental results to assess their agreement.

4.1. γ′ morphology as a function of build height

4.1.1. Nucleation of γ′

The fast precipitation kinetics of the γ′ phase enables formation of γ′ upon quenching from higher temperatures (above solvus) during thermal cycling [66]. In Fig. 7b, for a single layer in the full dissolution region, during cooling, the initial increase in nucleation rate signifies the first formation of nuclei. The slight increase in nucleation rate during partial dissolution, despite a decrease in the concentration of γ′ forming elements, may be explained by the nucleation kinetics. During partial dissolution and as the precipitates shrink, it is assumed that the regions at the vicinity of partially dissolved precipitates are enriched in γ′ forming elements [68], [69]. This differs from the full dissolution region, in which case the chemical composition is evenly distributed in the matrix. Several authors have attributed the solute supersaturation of the matrix around primary γ′ to partial dissolution during isothermal ageing [69], [70], [71], [72]. The enhanced supersaturation in the regions close to the precipitates results in a much higher driving force for nucleation, leading to a higher nucleation rate upon cooling. This phenomenon can be closely related to the several nucleation bursts upon continuous cooling of Ni-based superalloys, where second nucleation bursts exhibit higher nucleation rates [38], [68], [73], [74].

At middle stages of partial dissolution, the reduction in the nucleation rate indicates that the existing composition and low supersaturation did not trigger nucleation as the matrix was closer to the equilibrium state. The end of a nucleation burst means that the supersaturation of Al and Ti has reached a low level, incapable of providing sufficient driving force during cooling to or holding at 1000 °C for further nucleation [73]. Earlier studies on Ni-based superalloys have reported the same phenomenon during ageing or continuous cooling from the solvus temperature to RT [38], [73], [74].

4.1.2. Dissolution of γ′ during thermal cycling

γ′ dissolution kinetics during heating are fast when compared to nucleation due to exponential increase in phase transformation and diffusion activities with temperature [65]. As shown in Fig. 9, Fig. 10, and supplementary Figs. S2 and S3, the reduction in γ′ phase fraction and size during heating indicates γ′ dissolution. This is also revealed in Fig. 5 where phase fraction decreases upon heating. The extent of γ′ dissolution mostly depends on the temperature, time spent above γ′ solvus, and precipitate size [75], [76], [77]. Smaller γ′ precipitates are first to be dissolved [67], [77], [78]. This is mainly because more solute elements need to be transported away from large γ′ precipitates than from smaller ones [79]. Also, a high temperature above γ′ solvus temperature leads to a faster dissolution rate [80]. The equilibrium solvus temperature of γ′ in IN738 in our MatCalc simulation (Fig. 6) and as reported by Ojo et al. [47] is 1140 °C and 1130–1180 °C, respectively. This means the peak temperature experienced by previous layers decreases progressively from γ′ supersolvus to subsolvus, near-solvus, and far from solvus as the number of subsequent layers increases. Based on the above, it can be inferred that the degree of dissolution of γ′ contributes to the gradient in precipitate distribution.

Although the peak temperatures during later stages of partial dissolution are much lower than the equilibrium γ′ solvus, γ′ dissolution still occurs but at a significantly lower rate (supplementary Fig. S3). Wahlmann et al. [28] also reported a similar case where they observed the rapid dissolution of γ′ in CMSX-4 during fast heating and cooling cycles at temperatures below the γ′ solvus. They attributed this to the γ′ phase transformation process taking place in conditions far from the equilibrium. While the same reasoning may be valid for our study, we further believe that the greater surface area to volume ratio of the small γ′ precipitates contributed to this. This ratio means a larger area is available for solute atoms to diffuse into the matrix even at temperatures much below the solvus [81].

4.2. γ′ phase fraction and size evolution

4.2.1. During thermal cycling

In the first layer, the steep increase in γ′ phase fraction during heating (Fig. 5), which also represents γ′ precipitation in the powder before melting, has qualitatively been validated in [28]. The maximum phase fraction of 27% during the first few layers of thermal cycling indicates that IN738 theoretically could reach the equilibrium state (∼30%), but the short interlayer time at the build temperature counteracts this. The drop in phase fraction at middle stages of partial dissolution is due to the low number of γ′ nucleation sites [73]. It has been reported that a reduction of γ′ nucleation sites leads to a delay in obtaining the final volume fraction as more time is required for γ′ precipitates to grow and reach equilibrium [82]. This explains why even upon holding for 150 s before subsequent layer deposition, the phase fraction does not increase to those values that were observed in the previous full γ′ dissolution regions. Towards the end of deposition, the increase in phase fraction to the equilibrium value of 30% is as a result of the longer holding at build temperature or close to it [83].

During thermal cycling, γ′ particles begin to grow immediately after they first precipitate upon cooling. This is reflected in the rapid increase in phase fraction and size during cooling in Fig. 5 and supplementary Fig. S2, respectively. The rapid growth is due to the fast diffusion of solute elements at high temperatures [84]. The similar size of γ′ for the first 44 layers from the top can be attributed to the fact that all layers underwent complete dissolution and hence, experienced the same nucleation event and growth during deposition. This corresponds with the findings by Balikci et al. [85], who reported that the degree of γ′ precipitation in IN738LC does not change when a solution heat treatment is conducted above a certain critical temperature.

The increase in coarsening rate (Fig. 8) during thermal cycling can first be ascribed to the high peak temperature of the layers [86]. The coarsening rate of γ′ is known to increase rapidly with temperature due to the exponential growth of diffusion activity. Also, the simultaneous dissolution with coarsening could be another reason for the high coarsening rate, as γ′ coarsening is a diffusion-driven process where large particles grow by consuming smaller ones [78], [84], [86], [87]. The steady growth of γ′ towards the bottom of the build is due to the much lower layer peak temperature, which is almost close to the build temperature, and reduced dissolution activity, as is seen in the much lower solute concentration in γ′ compared to those in the full and partial dissolution regions.

4.2.2. During cooling

The much higher phase fraction of ∼40% upon cooling signifies the tendency of γ′ to reach equilibrium at lower temperatures (Fig. 4). This is due to the precipitation of secondary γ′ and a further increase in the size of existing primary γ′, which leads to a multimodal size distribution of γ′ after cooling [38], [73], [88], [89], [90]. The reason for secondary γ′ formation during cooling is as follows: As cooling progresses, it becomes increasingly challenging to redistribute solute elements in the matrix owing to their lower mobility [38], [73]. A higher supersaturation level in regions away from or free of the existing γ′ precipitates is achieved, making them suitable sites for additional nucleation bursts. More cooling leads to the growth of these secondary γ′ precipitates, but as the temperature and in turn, the solute diffusivity is low, growth remains slow.

4.3. Carbides

MC carbides in IN738 are known to have a significant impact on the high-temperature strength. They can also act as effective hardening particles and improve the creep resistance [91]. Precipitation of MC carbides in IN738 and several other superalloys is known to occur during solidification or thermal treatments (e.g., hot isostatic pressing) [92]. In our case, this means that the MC carbides within the E-PBF build formed because of the thermal exposure from the E-PBF thermal cycle in addition to initial solidification. Our simulation confirms this as MC carbides appear during layer heating (Fig. 5). The constant and stable phase fraction of MC carbides during thermal cycling can be attributed to their high melting point (∼1360 °C) and the short holding time at peak temperatures [75], [93], [94]. The solvus temperature for most MC carbides exceeds most of the peak temperatures observed in our simulation, and carbide dissolution kinetics at temperatures above the solvus are known to be comparably slow [95]. The stable phase fraction and random distribution of MC carbides signifies the slight influence on the gradient in hardness.

4.4. Comparison of simulations and experiments

4.4.1. Precipitate phase fraction and morphology as a function of build height

A qualitative agreement is observed for the phase fraction of carbides, i.e. ∼0.8% in the experiment and ∼0.9% in the simulation. The phase fraction of γ′ differs, with the experiment reporting a value of ∼51% and the simulation, 40%. Despite this, the size distribution of primary γ′ along the build shows remarkable consistency between experimental and computational analyses. It is worth noting that the primary γ′ morphology in the experimental analysis is observed in the as-fabricated state, whereas the simulation (Fig. 8) captures it during deposition process. The primary γ′ size in the experiment is expected to experience additional growth during the cooling phase. Regardless, both show similar trends in primary γ′ size increments from the top to the bottom of the build. The larger primary γ’ size in the simulation versus the experiment can be attributed to the fact that experimental and simulation results are based on 2D and 3D data, respectively. The absence of stereological considerations [96] in our analysis could have led to an underestimation of the precipitate sizes from SEM measurements. The early starts of coarsening (8th layer) in the experiment compared to the simulation (45th layer) can be attributed to a higher actual γ′ solvus temperature than considered in our simulation [47]. The solvus temperature of γ′ in a Ni-based superalloy is mainly determined by the detailed composition. A high amount of Cr and Co are known to reduce the solvus temperature, whereas Ta and Mo will increase it [97], [98], [99]. The elemental composition from our experimental work was used for the simulation except for Ta. It should be noted that Ta is not included in the thermodynamic database in MatCalc used, and this may have reduced the solvus temperature. This could also explain the relatively higher γ′ phase fraction in the experiment than in simulation, as a higher γ′ solvus temperature will cause more γ′ to precipitate and grow early during cooling [99], [100].

Another possible cause of this deviation can be attributed to the extent of γ′ dissolution, which is mainly determined by the peak temperature. It can be speculated that individual peak temperatures at different layers in the simulation may have been over-predicted. However, one needs to consider that the true thermal profile is likely more complicated in the actual E-PBF process [101]. For example, the current model assumes that the thermophysical properties of the material are temperature-independent, which is not realistic. Many materials, including IN738, exhibit temperature-dependent properties such as thermal conductivity, specific heat capacity, and density [102]. This means that heat transfer simulations may underestimate or overestimate the temperature gradients and cooling rates within the powder bed and the solidified part. Additionally, the model does not account for the reduced thermal diffusivity through unmelted powder, where gas separating the powder acts as insulation, impeding the heat flow [1]. In E-PBF, the unmelted powder regions with trapped gas have lower thermal diffusivity compared to the fully melted regions, leading to localized temperature variations, and altered solidification behavior. These limitations can impact the predictions, particularly in relation to the carbide dissolution, as the peak temperatures may be underestimated.

While acknowledging these limitations, it is worth emphasizing that achieving a detailed and accurate representation of each layer’s heat source would impose tough computational challenges. Given the substantial layer count in E-PBF, our decision to employ a semi-analytical approximation strikes a balance between computational feasibility and the capture of essential trends in thermal profiles across diverse build layers. In future work, a dual-calibration strategy is proposed to further reduce simulation-experiment disparities. By refining temperature-independent thermophysical property approximations and absorptivity in the heat source model, and by optimizing interfacial energy descriptions in the kinetic model, the predictive precision could be enhanced. Further refining the simulation controls, such as adjusting the precipitate class size may enhance quantitative comparisons between modeling outcomes and experimental data in future work.

4.4.2. Multimodal size distribution of γ′ and concentration

Another interesting feature that sees qualitative agreement between the simulation and the experiment is the multimodal size distribution of γ′. The formation of secondary γ′ particles in the experiment and most E-PBF Ni-based superalloys is suggested to occur at low temperatures, during final cooling to RT [16], [73], [90]. However, so far, this conclusion has been based on findings from various continuous cooling experiments, as the study of the evolution during AM would require an in-situ approach. Our simulation unambiguously confirms this in an AM context by providing evidence for secondary γ′ precipitation during slow cooling to RT. Additionally, it is possible to speculate that the chemical segregation occurring during solidification, due to the preferential partitioning of certain elements between the solid and liquid phases, can contribute to the multimodal size distribution during deposition [51]. This is because chemical segregation can result in variations in the local composition of superalloys, which subsequently affects the nucleation and growth of γ′. Regions with higher concentrations of alloying elements will encourage the formation of larger γ′ particles, while regions with lower concentrations may favor the nucleation of smaller precipitates. However, it is important to acknowledge that the elevated temperature during the E-PBF process will largely homogenize these compositional differences [103], [104].

A good correlation is also shown in the composition of major γ′ forming elements (Al and Ti) in primary and secondary γ′. Both experiment and simulation show an increasing trend for Al content and a decreasing trend for Ti content from primary to secondary γ′. The slight composition differences between primary and secondary γ′ particles are due to the different diffusivity of γ′ stabilizers at different thermal conditions [105], [106]. As the formation of multimodal γ′ particles with different sizes occurs over a broad temperature range, the phase chemistry of γ′ will be highly size dependent. The changes in the chemistry of various γ′ (primary, secondary, and tertiary) have received significant attention since they have a direct influence on the performance [68], [105], [107], [108], [109]. Chen et al. [108], [109], reported a high Al content in the smallest γ′ precipitates compared to the largest, while Ti showed an opposite trend during continuous cooling in a RR1000 Ni-based superalloy. This was attributed to the temperature and cooling rate at which the γ′ precipitates were formed. The smallest precipitates formed last, at the lowest temperature and cooling rate. A comparable observation is evident in the present investigation, where the secondary γ′ forms at a low temperature and cooling rate in comparison to the primary. The temperature dependence of γ′ chemical composition is further evidenced in supplementary Fig. S4, which shows the equilibrium chemical composition of γ′ as a function of temperature.

5. Conclusions

A correlative modelling approach capable of predicting solid-state phase transformations kinetics in metal AM was developed. This approach involves computational simulations with a semi-analytical heat transfer model and the MatCalc thermo-kinetic software. The method was used to predict the phase transformation kinetics and detailed morphology and chemistry of γ′ and MC during E-PBF of IN738 Ni-based superalloy. The main conclusions are:

  • 1.The computational simulations are in qualitative agreement with the experimental observations. This is particularly true for the γ′ size distribution along the build height, the multimodal size distribution of particles, and the phase fraction of MC carbides.
  • 2.The deviations between simulation and experiment in terms of γ′ phase fraction and location in the build are most likely attributed to a higher γ′ solvus temperature during the experiment than in the simulation, which is argued to be related to the absence of Ta in the MatCalc database.
  • 3.The dissolution and precipitation of γ′ occur fast and under non-equilibrium conditions. The level of γ′ dissolution determines the gradient in γ′ size distribution along the build. After thermal cycling, the final cooling to room temperature has further significant impacts on the final γ′ size, morphology, and distribution.
  • 4.A negligible amount of γ′ forms in the first deposited layer before subsequent layer deposition, and a small amount of γ′ may also form in the powder induced by the 1000 °C elevated build temperature before melting.

Our findings confirm the suitability of MatCalc to predict the microstructural evolution at various positions throughout a build in a Ni-based superalloy during E-PBF. It also showcases the suitability of a tool which was originally developed for traditional thermo-mechanical processing of alloys to the new additive manufacturing context. Our simulation capabilities are likely extendable to other alloy systems that undergo solid-state phase transformations implemented in MatCalc (various steels, Ni-based superalloys, and Al-alloys amongst others) as well as other AM processes such as L-DED and L-PBF which have different thermal cycle characteristics. New tools to predict the microstructural evolution and properties during metal AM are important as they provide new insights into the complexities of AM. This will enable control and design of AM microstructures towards advanced materials properties and performances.

CRediT authorship contribution statement

Primig Sophie: Writing – review & editing, Supervision, Resources, Project administration, Funding acquisition, Conceptualization. Adomako Nana Kwabena: Writing – original draft, Writing – review & editing, Visualization, Software, Investigation, Formal analysis, Conceptualization. Haghdadi Nima: Writing – review & editing, Supervision, Project administration, Methodology, Conceptualization. Dingle James F.L.: Methodology, Conceptualization, Software, Writing – review & editing, Visualization. Kozeschnik Ernst: Writing – review & editing, Software, Methodology. Liao Xiaozhou: Writing – review & editing, Project administration, Funding acquisition. Ringer Simon P: Writing – review & editing, Project administration, Funding acquisition.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This research was sponsored by the Department of Industry, Innovation, and Science under the auspices of the AUSMURI program – which is a part of the Commonwealth’s Next Generation Technologies Fund. The authors acknowledge the facilities and the scientific and technical assistance at the Electron Microscope Unit (EMU) within the Mark Wainwright Analytical Centre (MWAC) at UNSW Sydney and Microscopy Australia. Nana Adomako is supported by a UNSW Scientia PhD scholarship. Michael Haines’ (UNSW Sydney) contribution to the revised version of the original manuscript is thankfully acknowledged.

Appendix A. Supplementary material

Download : Download Word document (462KB)

Supplementary material.

Data Availability

Data will be made available on request.

References

Study on the critical sediment concentration determining the optimal transport capability of submarine sediment flows with different particle size composition

Study on the critical sediment concentration determining the optimal transport capability of submarine sediment flows with different particle size composition

Yupeng Ren abc, Huiguang Zhou cd, Houjie Wang ab, Xiao Wu ab, Guohui Xu cd, Qingsheng Meng cd

Abstract

해저 퇴적물 흐름은 퇴적물을 심해로 운반하는 주요 수단 중 하나이며, 종종 장거리를 이동하고 수십 또는 수백 킬로미터에 걸쳐 상당한 양의 퇴적물을 운반합니다. 그것의 강력한 파괴력은 종종 이동 과정에서 잠수함 유틸리티에 심각한 손상을 초래합니다.

퇴적물 흐름의 퇴적물 농도는 주변 해수와의 밀도차를 결정하며, 이 밀도 차이는 퇴적물 흐름의 흐름 능력을 결정하여 이송된 퇴적물의 최종 퇴적 위치에 영향을 미칩니다. 본 논문에서는 다양한 미사 및 점토 중량비(미사/점토 비율이라고 함)를 갖는 다양한 퇴적물 농도의 퇴적물 흐름을 수로 테스트를 통해 연구합니다.

우리의 테스트 결과는 특정 퇴적물 구성에 대해 퇴적물 흐름이 가장 빠르게 이동하는 임계 퇴적물 농도가 있음을 나타냅니다. 4가지 미사/점토 비율 각각에 대한 임계 퇴적물 농도와 이에 상응하는 최대 속도가 구해집니다. 결과는 점토 함량이 임계 퇴적물 농도와 선형적으로 음의 상관 관계가 있음을 나타냅니다.

퇴적물 농도가 증가함에 따라 퇴적물의 흐름 거동은 흐름 상태에서 붕괴된 상태로 변환되고 흐름 거동이 변화하는 두 탁한 현탁액의 유체 특성은 모두 Bingham 유체입니다.

또한 본 논문에서는 퇴적물 흐름 내 입자 배열을 분석하여 위에서 언급한 결과에 대한 미시적 설명도 제공합니다.

Submarine sediment flows is one of the main means for transporting sediment to the deep sea, often traveling long-distance and transporting significant volumes of sediment for tens or even hundreds of kilometers. Its strong destructive force often causes serious damage to submarine utilities on its course of movement. The sediment concentration of the sediment flow determines its density difference with the ambient seawater, and this density difference determines the flow ability of the sediment flow, and thus affects the final deposition locations of the transported sediment. In this paper, sediment flows of different sediment concentration with various silt and clay weight ratios (referred to as silt/clay ratio) are studied using flume tests. Our test results indicate that there is a critical sediment concentration at which sediment flows travel the fastest for a specific sediment composition. The critical sediment concentrations and their corresponding maximum velocities for each of the four silt/clay ratios are obtained. The results further indicate that the clay content is linearly negatively correlated with the critical sediment concentration. As the sediment concentration increases, the flow behaviors of sediment flows transform from the flow state to the collapsed state, and the fluid properties of the two turbid suspensions with changing flow behaviors are both Bingham fluids. Additionally, this paper also provides a microscopic explanation of the above-mentioned results by analyzing the arrangement of particles within the sediment flow.

Introduction

Submarine sediment flows are important carriers for sea floor sediment movement and may carry and transport significant volumes of sediment for tens or even hundreds of kilometers (Prior et al., 1987; Pirmez and Imran, 2003; Zhang et al., 2018). Earthquakes, storms, and floods may all trigger submarine sediment flow events (Hsu et al., 2008; Piper and Normark, 2009; Pope et al., 2017b; Gavey et al., 2017). Sediment flows have strong forces during the movement, which will cause great harm to submarine structures such as cables and pipelines (Pope et al., 2017a). It was first confirmed that the cable breaking event caused by the sediment flow occurred in 1929. The sediment flow triggered by the Grand Banks earthquake damaged 12 cables. According to the time sequence of the cable breaking, the maximum velocity of the sediment flow is as high as 28 m/s (Heezen and Ewing, 1952; Kuenen, 1952; Heezen et al., 1954). Subsequent research shows that the lowest turbidity velocity that can break the cable also needs to reach 19 m/s (Piper et al., 1988). Since then, there have been many damage events of submarine cables and oil and gas pipelines caused by sediment flows in the world (Hsu et al., 2008; Carter et al., 2012; Cattaneo et al., 2012; Carter et al., 2014). During its movement, the sediment flow will gradually deposit a large amount of sediment carried by it along the way, that is, the deposition process of the sediment flow. On the one hand, this process brings a large amount of terrestrial nutrients and other materials to the ocean, while on the other hand, it causes damage and burial to benthic organisms, thus forming the largest sedimentary accumulation on Earth – submarine fans, which are highly likely to become good reservoirs for oil and gas resources (Daly, 1936; Yuan et al., 2010; Wu et al., 2022). The study on sediment flows (such as, the study of flow velocity and the forces acting on seabed structures) can provide important references for the safe design of seabed structures, the protection of submarine ecosystems, and exploration of turbidity sediments related oil and gas deposits. Therefore, it is of great significance to study the movement of sediment flows.

The sediment flow, as a highly sediment-concentrated fluid flowing on the sea floor, has a dense bottom layer and a dilute turbulent cloud. Observations at the Monterey Canyon indicated that the sediment flow can maintain its movement over long distances if its bottom has a relatively high sediment concentration. This dense bottom layer can be very destructive along its movement path to any facilities on the sea floor (Paull et al., 2018; Heerema et al., 2020; Wang et al., 2020). The sediment flow mentioned in this research paper is the general term of sediment density flow.

The sediment flow, which occurs on the seafloor, has the potential to cause erosion along its path. In this process, the suspended sediment is replenished, allowing the sediment flow to maintain its continuous flow capacity (Zhao et al., 2018). The dynamic force of sediment flow movement stem from its own gravity and density difference with surrounding water. In cases that the gravity drive of the slope is absent (on a flat sea floor), the flow velocity and distance of sediment flows are essentially determined by the sediment composition and concentration of the sediment flows as previous studies have demonstrated. Ilstad et al. (2004) conducted underwater flow tests in a sloped tank and employed high speed video camera to perform particle tracking. The results indicated that the premixed sand-rich and clay-rich slurries demonstrated different flow velocity and flow behavior. Using mixed kaolinite(d50 = 6 μm) and silica flour(d50 = 9 μm) in three compositions with total volumetric concentration ranged 22% or 28%, Felix and Peakall (2006) carried out underwater flow tests in a 5° slope Perspex channel and found that the flow ability of sediment flows is different depending on sediment compositions and concentrations. Sumner et al. (2009) used annular flume experiments to investigate the depositional dynamics and deposits of waning sediment-laden flows, finding that decelerating fast flows with fixed sand content and variable mud content resulted in four different deposit types. Chowdhury and Testik (2011) used lock-exchange tank, and experimented the kaolin clay sediment flows in the concentration range of 25–350 g/L, and predicted the fluid mud sediment flows propagation characteristics, but this study focused on giving sediment flows propagate phase transition time parameters, and is limited to clay. Lv et al. (2017) found through experiments that the rheological properties and flow behavior of kaolin clay (d50 = 3.7 μm) sediment flows were correlated to clay concentrations. In the field monitoring conducted by Liu et al. (2023) at the Manila Trench in the South China Sea in 2021, significant differences in the velocity, movement distance, and flow morphology of turbidity currents were observed. These differences may be attributed to variations in the particle composition of the turbidity currents.

On low and gentle slopes, although sediment flow with sand as the main sediment composition moves faster, it is difficult to propagate over long distances because sand has greater settling velocity and subaqueous angle of repose. Whereas the sediment flows with silt and clay as main composition may maintain relatively stable currents. Although its movement speed is slow, it has the ability to propagate over long distances because of the low settling rate of the fine particles (Ilstad et al., 2004; Liu et al., 2023). In a field observation at the Gaoping submarine canyon, the sediments collected from the sediment flows exhibited grain size gradation and the sediment was mostly composed of silt and clay (Liu et al., 2012). At the largest deltas in the world, for instance, the Mississippi River Delta, the sediments are mainly composed of silt and clay, which generally distributed along the coast in a wide range and provided the sediment sources for further distribution. The sediment flows originated and transported sediment from the coast to the deep sea are therefore share the same sediment compositions as delta sediments. To study the sediment flows composed of silt and clay is of great importance.

The sediment concentration of the sediment flows determines the density difference between the sediment flows and the ambient water and plays a key role in its flow ability. For the sediment flow with sediment composed of silt and clay, low sediment concentration means low density and therefore leads to low flow ability; however, although high sediment concentration results in high density, since there is cohesion between fine particles, it changes fluid properties and leads to low flow ability as well. Therefore, there should be a critical sediment concentration with mixed composition of silt and clay, at which the sediment flow maintains its strongest flow capacity and have the highest movement speed. In other words, the two characteristics of particle diameter and concentration of the sediment flow determine its own motion ability, which, if occurs, may become the most destructive force to submarine structures.

The objectives of this work was to study how the sediment composition (measured in relative weight of silt and clay, and referred as silt/clay ratio) and sediment concentration affect flow ability and behavior of the sediment flows, and to quantify the critical sediment concentration at which the sediment flows reached the greatest flow velocity under the experiment setting. We used straight flume without slope and conducted a series of flume tests with varying sediment compositions (silt-rich or clay-rich) and concentrations (96 to 1212 g/L). Each sediment flow sample was tested and analyzed for rheological properties using a rheometer, in order to characterize the relationship between flow behavior and rheological properties. Combined with the particle diameter, density and viscosity characteristics of the sediment flows measured in the experiment, a numerical modeling study is conducted, which are mutually validated with the experimental results.

The sediment concentration determines the arrangements of the sediment particles in the turbid suspension, and the arrangement impacts the fluid properties of the turbid suspension. The microscopic mode of particle arrangement in the turbid suspension can be constructed to further analyze the relationship between the fluid properties of turbid suspension and the flow behaviors of the sediment flow, and then characterize the critical sediment concentration at which the sediment flow runs the fastest. A simplified microscopic model of particle arrangement in turbid suspension was constructed to analyze the microscopic arrangement characteristics of sediment particles in turbid suspension with the fastest velocity.

Section snippets

Equipment and materials

The sediment flows flow experiments were performed in a Perspex channel with smooth transparent walls. The layout and dimensions of the experimental set-up were shown in Fig. 1. The bottom of the channel was flat and straight, and a gate was arranged to separate the two tanks. In order to study the flow capacity of turbidity currents from the perspective of their own composition (particle size distribution and concentration), we used a straight channel instead of an inclined one, to avoid any

Relationship between sediment flow flow velocity and sediment concentration

After the sediment flow is generated, its movement in the first half (50 cm) of the channel is relatively stable, and there is obvious shock diffusion in the second half. The reason is that the excitation wave (similar to the surge) will be formed during the sediment flow movement, and its speed is much faster than the speed of the sediment flow head. When the excitation wave reaches the tail of the channel, it will be reflected, thus affecting the subsequent flow of the sediment flow.

Sediment flows motion simulation based on FLOW-3D

As a relatively mature 3D fluid simulation software, FLOW-3D can accurately predict the free surface flow, and has been used to simulate the movement process of sediment flows for many times (Heimsund, 2007). The model adopted in this paper is RNG turbulence model, which can better deal with the flow with high strain rate and is suitable for the simulation of sediment flows with variable shape during movement. The governing equations of the numerical model involved include continuity equation,

Conclusions

In this study, we conducted a series of sediment flow flume tests with mixed silt and clay sediment samples in four silt/clay ratios on a flat slope. Rheological measurements were carried out on turbid suspension samples and microstructure analysis of the sediment particle arrangements was conducted, we concluded that:

  • (1)The flow velocity of the sediment flow is controlled by the sediment concentration and its own particle diameter composition, the flow velocity increased with the increase of the

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by the National Natural Science Foundation of China [Grant no. 42206055]; the National Natural Science Foundation of China [Grant no. 41976049]; and the National Natural Science Foundation of China [Grant no. 42272327].

References (39)

There are more references available in the full text version of this article.

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Figure 11. Sketch of scour mechanism around USAF under random waves.

Scour Characteristics and Equilibrium Scour Depth Prediction around Umbrella Suction Anchor Foundation under Random Waves

by Ruigeng Hu 1,Hongjun Liu 2,Hao Leng 1,Peng Yu 3 andXiuhai Wang 1,2,*

1College of Environmental Science and Engineering, Ocean University of China, Qingdao 266000, China

2Key Lab of Marine Environment and Ecology (Ocean University of China), Ministry of Education, Qingdao 266000, China

3Qingdao Geo-Engineering Survering Institute, Qingdao 266100, China

*Author to whom correspondence should be addressed.

J. Mar. Sci. Eng. 2021, 9(8), 886; https://doi.org/10.3390/jmse9080886

Received: 6 July 2021 / Revised: 8 August 2021 / Accepted: 13 August 2021 / Published: 17 August 2021

(This article belongs to the Section Ocean Engineering)

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Abstract

A series of numerical simulation were conducted to study the local scour around umbrella suction anchor foundation (USAF) under random waves. In this study, the validation was carried out firstly to verify the accuracy of the present model. Furthermore, the scour evolution and scour mechanism were analyzed respectively. In addition, two revised models were proposed to predict the equilibrium scour depth Seq around USAF. At last, a parametric study was carried out to study the effects of the Froude number Fr and Euler number Eu for the Seq. The results indicate that the present numerical model is accurate and reasonable for depicting the scour morphology under random waves. The revised Raaijmakers’s model shows good agreement with the simulating results of the present study when KCs,p < 8. The predicting results of the revised stochastic model are the most favorable for n = 10 when KCrms,a < 4. The higher Fr and Eu both lead to the more intensive horseshoe vortex and larger Seq.

Keywords: 

scour; numerical investigation; random waves; equilibrium scour depth; KC number

1. Introduction

The rapid expansion of cities tends to cause social and economic problems, such as environmental pollution and traffic jam. As a kind of clean energy, offshore wind power has developed rapidly in recent years. The foundation of offshore wind turbine (OWT) supports the upper tower, and suffers the cyclic loading induced by waves, tides and winds, which exerts a vital influence on the OWT system. The types of OWT foundation include the fixed and floating foundation, and the fixed foundation was used usually for nearshore wind turbine. After the construction of fixed foundation, the hydrodynamic field changes in the vicinity of the foundation, leading to the horseshoe vortex formation and streamline compression at the upside and sides of foundation respectively [1,2,3,4]. As a result, the neighboring soil would be carried away by the shear stress induced by vortex, and the scour hole would emerge in the vicinity of foundation. The scour holes increase the cantilever length, and weaken the lateral bearing capacity of foundation [5,6,7,8,9]. Moreover, the natural frequency of OWT system increases with the increase of cantilever length, causing the resonance occurs when the system natural frequency equals the wave or wind frequency [10,11,12]. Given that, an innovative foundation called umbrella suction anchor foundation (USAF) has been designed for nearshore wind power. The previous studies indicated the USAF was characterized by the favorable lateral bearing capacity with the low cost [6,13,14]. The close-up of USAF is shown in Figure 1, and it includes six parts: 1-interal buckets, 2-external skirt, 3-anchor ring, 4-anchor branch, 5-supporting rod, 6-telescopic hook. The detailed description and application method of USAF can be found in reference [13].

Jmse 09 00886 g001 550

Figure 1. The close-up of umbrella suction anchor foundation (USAF).

Numerical and experimental investigations of scour around OWT foundation under steady currents and waves have been extensively studied by many researchers [1,2,15,16,17,18,19,20,21,22,23,24]. The seabed scour can be classified as two types according to Shields parameter θ, i.e., clear bed scour (θ < θcr) or live bed scour (θ > θcr). Due to the set of foundation, the adverse hydraulic pressure gradient exists at upstream foundation edges, resulting in the streamline separation between boundary layer flow and seabed. The separating boundary layer ascended at upstream anchor edges and developed into the horseshoe vortex. Then, the horseshoe vortex moved downstream gradually along the periphery of the anchor, and the vortex shed off continually at the lee-side of the anchor, i.e., wake vortex. The core of wake vortex is a negative pressure center, liking a vacuum cleaner. Hence, the soil particles were swirled into the negative pressure core and carried away by wake vortexes. At the same time, the onset of scour at rear side occurred. Finally, the wake vortex became downflow when the turbulence energy could not support the survival of wake vortex. According to Tavouktsoglou et al. [25], the scale of pile wall boundary layer is proportional to 1/ln(Rd) (Rd is pile Reynolds), which means the turbulence intensity induced by the flow-structure interaction would decrease with Rd increases, but the effects of Rd can be neglected only if the flow around the foundation is fully turbulent [26]. According to previous studies [1,15,27,28,29,30,31,32], the scour development around pile foundation under waves was significantly influenced by Shields parameter θ and KC number simultaneously (calculated by Equation (1)). Sand ripples widely existed around pile under waves in the case of live bed scour, and the scour morphology is related with θ and KC. Compared with θ, KC has a greater influence on the scour morphology [21,27,28]. The influence mechanism of KC on the scour around the pile is reflected in two aspects: the horseshoe vortex at upstream and wake vortex shedding at downstream.

KC=UwmTD��=�wm��(1)

where, Uwm is the maximum velocity of the undisturbed wave-induced oscillatory flow at the sea bottom above the wave boundary layer, T is wave period, and D is pile diameter.

There are two prerequisites to satisfy the formation of horseshoe vortex at upstream pile edges: (1) the incoming flow boundary layer with sufficient thickness and (2) the magnitude of upstream adverse pressure gradient making the boundary layer separating [1,15,16,18,20]. The smaller KC results the lower adverse pressure gradient, and the boundary layer cannot separate, herein, there is almost no horseshoe vortex emerging at upside of pile. Sumer et al. [1,15] carried out several sets of wave flume experiments under regular and irregular waves respectively, and the experiment results show that there is no horseshoe vortex when KC is less than 6. While the scale and lifespan of horseshoe vortex increase evidently with the increase of KC when KC is larger than 6. Moreover, the wake vortex contributes to the scour at lee-side of pile. Similar with the case of horseshoe vortex, there is no wake vortex when KC is less than 6. The wake vortex is mainly responsible for scour around pile when KC is greater than 6 and less than O(100), while horseshoe vortex controls scour nearly when KC is greater than O(100).

Sumer et al. [1] found that the equilibrium scour depth was nil around pile when KC was less than 6 under regular waves for live bed scour, while the equilibrium scour depth increased with the increase of KC. Based on that, Sumer proposed an equilibrium scour depth predicting equation (Equation (2)). Carreiras et al. [33] revised Sumer’s equation with m = 0.06 for nonlinear waves. Different with the findings of Sumer et al. [1] and Carreiras et al. [33], Corvaro et al. [21] found the scour still occurred for KC ≈ 4, and proposed the revised equilibrium scour depth predicting equation (Equation (3)) for KC > 4.

Rudolph and Bos [2] conducted a series of wave flume experiments to investigate the scour depth around monopile under waves only, waves and currents combined respectively, indicting KC was one of key parameters in influencing equilibrium scour depth, and proposed the equilibrium scour depth predicting equation (Equation (4)) for low KC (1 < KC < 10). Through analyzing the extensive data from published literatures, Raaijmakers and Rudolph [34] developed the equilibrium scour depth predicting equation (Equation (5)) for low KC, which was suitable for waves only, waves and currents combined. Khalfin [35] carried out several sets of wave flume experiments to study scour development around monopile, and proposed the equilibrium scour depth predicting equation (Equation (6)) for low KC (0.1 < KC < 3.5). Different with above equations, the Khalfin’s equation considers the Shields parameter θ and KC number simultaneously in predicting equilibrium scour depth. The flow reversal occurred under through in one wave period, so sand particles would be carried away from lee-side of pile to upside, resulting in sand particles backfilled into the upstream scour hole [20,29]. Considering the backfilling effects, Zanke et al. [36] proposed the equilibrium scour depth predicting equation (Equation (7)) around pile by theoretical analysis, and the equation is suitable for the whole range of KC number under regular waves and currents combined.

S/D=1.3(1−exp([−m(KC−6)])�/�=1.3(1−exp(−�(��−6))(2)

where, m = 0.03 for linear waves.

S/D=1.3(1−exp([−0.02(KC−4)])�/�=1.3(1−exp(−0.02(��−4))(3)

S/D=1.3γKwaveKhw�/�=1.3��wave�ℎw(4)

where, γ is safety factor, depending on design process, typically γ = 1.5, Kwave is correction factor considering wave action, Khw is correction factor considering water depth.

S/D=1.5[tanh(hwD)]KwaveKhw�/�=1.5tanh(ℎw�)�wave�ℎw(5)

where, hw is water depth.

S/D=0.0753(θθcr−−−√−0.5)0.69KC0.68�/�=0.0753(��cr−0.5)0.69��0.68(6)

where, θ is shields parameter, θcr is critical shields parameter.

S/D=2.5(1−0.5u/uc)xrelxrel=xeff/(1+xeff)xeff=0.03(1−0.35ucr/u)(KC−6)⎫⎭⎬⎪⎪�/�=2.5(1−0.5�/��)��������=����/(1+����)����=0.03(1−0.35�cr/�)(��−6)(7)

where, u is near-bed orbital velocity amplitude, uc is critical velocity corresponding the onset of sediment motion.

S/D=1.3{1−exp[−0.03(KC2lnn+36)1/2−6]}�/�=1.31−exp−0.03(��2ln�+36)1/2−6(8)

where, n is the 1/n’th highest wave for random waves

For predicting equilibrium scour depth under irregular waves, i.e., random waves, Sumer and Fredsøe [16] found it’s suitable to take Equation (2) to predict equilibrium scour depth around pile under random waves with the root-mean-square (RMS) value of near-bed orbital velocity amplitude Um and peak wave period TP to calculate KC. Khalfin [35] recommended the RMS wave height Hrms and peak wave period TP were used to calculate KC for Equation (6). References [37,38,39,40] developed a series of stochastic theoretical models to predict equilibrium scour depth around pile under random waves, nonlinear random waves plus currents respectively. The stochastic approach thought the 1/n’th highest wave were responsible for scour in vicinity of pile under random waves, and the KC was calculated in Equation (8) with Um and mean zero-crossing wave period Tz. The results calculated by Equation (8) agree well with experimental values of Sumer and Fredsøe [16] if the 1/10′th highest wave was used. To author’s knowledge, the stochastic approach proposed by Myrhaug and Rue [37] is the only theoretical model to predict equilibrium scour depth around pile under random waves for the whole range of KC number in published documents. Other methods of predicting scour depth under random waves are mainly originated from the equation for regular waves-only, waves and currents combined, which are limited to the large KC number, such as KC > 6 for Equation (2) and KC > 4 for Equation (3) respectively. However, situations with relatively low KC number (KC < 4) often occur in reality, for example, monopile or suction anchor for OWT foundations in ocean environment. Moreover, local scour around OWT foundations under random waves has not yet been investigated fully. Therefore, further study are still needed in the aspect of scour around OWT foundations with low KC number under random waves. Given that, this study presents the scour sediment model around umbrella suction anchor foundation (USAF) under random waves. In this study, a comparison of equilibrium scour depth around USAF between this present numerical models and the previous theoretical models and experimental results was presented firstly. Then, this study gave a comprehensive analysis for the scour mechanisms around USAF. After that, two revised models were proposed according to the model of Raaijmakers and Rudolph [34] and the stochastic model developed by Myrhaug and Rue [37] respectively to predict the equilibrium scour depth. Finally, a parametric study was conducted to study the effects of the Froude number (Fr) and Euler number (Eu) to equilibrium scour depth respectively.

2. Numerical Method

2.1. Governing Equations of Flow

The following equations adopted in present model are already available in Flow 3D software. The authors used these theoretical equations to simulate scour in random waves without modification. The incompressible viscous fluid motion satisfies the Reynolds-averaged Navier-Stokes (RANS) equation, so the present numerical model solves RANS equations:

∂u∂t+1VF(uAx∂u∂x+vAy∂u∂y+wAz∂u∂z)=−1ρf∂p∂x+Gx+fx∂�∂�+1��(���∂�∂�+���∂�∂�+���∂�∂�)=−1�f∂�∂�+��+��(9)

∂v∂t+1VF(uAx∂v∂x+vAy∂v∂y+wAz∂v∂z)=−1ρf∂p∂y+Gy+fy∂�∂�+1��(���∂�∂�+���∂�∂�+���∂�∂�)=−1�f∂�∂�+��+��(10)

∂w∂t+1VF(uAx∂w∂x+vAy∂w∂y+wAz∂w∂z)=−1ρf∂p∂z+Gz+fz∂�∂�+1��(���∂�∂�+���∂�∂�+���∂�∂�)=−1�f∂�∂�+��+��(11)

where, VF is the volume fraction; u, v, and w are the velocity components in x, y, z direction respectively with Cartesian coordinates; Ai is the area fraction; ρf is the fluid density, fi is the viscous fluid acceleration, Gi is the fluid body acceleration (i = x, y, z).

2.2. Turbulent Model

The turbulence closure is available by the turbulent model, such as one-equation, the one-equation k-ε model, the standard k-ε model, RNG k-ε turbulent model and large eddy simulation (LES) model. The LES model requires very fine mesh grid, so the computational time is large, which hinders the LES model application in engineering. The RNG k-ε model can reduce computational time greatly with high accuracy in the near-wall region. Furthermore, the RNG k-ε model computes the maximum turbulent mixing length dynamically in simulating sediment scour model. Therefore, the RNG k-ε model was adopted to study the scour around anchor under random waves [41,42].

∂kT∂T+1VF(uAx∂kT∂x+vAy∂kT∂y+wAz∂kT∂z)=PT+GT+DiffkT−εkT∂��∂�+1��(���∂��∂�+���∂��∂�+���∂��∂�)=��+��+������−���(12)

∂εT∂T+1VF(uAx∂εT∂x+vAy∂εT∂y+wAz∂εT∂z)=CDIS1εTkT(PT+CDIS3GT)+Diffε−CDIS2ε2TkT∂��∂�+1��(���∂��∂�+���∂��∂�+���∂��∂�)=����1����(��+����3��)+�����−����2��2��(13)

where, kT is specific kinetic energy involved with turbulent velocity, GT is the turbulent energy generated by buoyancy; εT is the turbulent energy dissipating rate, PT is the turbulent energy, Diffε and DiffkT are diffusion terms associated with VF, Ai; CDIS1, CDIS2 and CDIS3 are dimensionless parameters, and CDIS1, CDIS3 have default values of 1.42, 0.2 respectively. CDIS2 can be obtained from PT and kT.

2.3. Sediment Scour Model

The sand particles may suffer four processes under waves, i.e., entrainment, bed load transport, suspended load transport, and deposition, so the sediment scour model should depict the above processes efficiently. In present numerical simulation, the sediment scour model includes the following aspects:

2.3.1. Entrainment and Deposition

The combination of entrainment and deposition determines the net scour rate of seabed in present sediment scour model. The entrainment lift velocity of sand particles was calculated as [43]:

ulift,i=αinsd0.3∗(θ−θcr)1.5∥g∥di(ρi−ρf)ρf−−−−−−−−−−−−√�lift,i=�����*0.3(�−�cr)1.5���(��−�f)�f(14)

where, αi is the entrainment parameter, ns is the outward point perpendicular to the seabed, d* is the dimensionless diameter of sand particles, which was calculated by Equation (15), θcr is the critical Shields parameter, g is the gravity acceleration, di is the diameter of sand particles, ρi is the density of seabed species.

d∗=di(∥g∥ρf(ρi−ρf)μ2f)1/3�*=��(��f(��−�f)�f2)1/3(15)

where μf is the fluid dynamic viscosity.

In Equation (14), the entrainment parameter αi confirms the rate at which sediment erodes when the given shear stress is larger than the critical shear stress, and the recommended value 0.018 was adopted according to the experimental data of Mastbergen and Von den Berg [43]. ns is the outward pointing normal to the seabed interface, and ns = (0,0,1) according to the Cartesian coordinates used in present numerical model.

The shields parameter was obtained from the following equation:

θ=U2f,m(ρi/ρf−1)gd50�=�f,m2(��/�f−1)��50(16)

where, Uf,m is the maximum value of the near-bed friction velocity; d50 is the median diameter of sand particles. The detailed calculation procedure of θ was available in Soulsby [44].

The critical shields parameter θcr was obtained from the Equation (17) [44]

θcr=0.31+1.2d∗+0.055[1−exp(−0.02d∗)]�cr=0.31+1.2�*+0.0551−exp(−0.02�*)(17)

The sand particles begin to deposit on seabed when the turbulence energy weaken and cann’t support the particles suspending. The setting velocity of the particles was calculated from the following equation [44]:

usettling,i=νfdi[(10.362+1.049d3∗)0.5−10.36]�settling,�=�f��(10.362+1.049�*3)0.5−10.36(18)

where νf is the fluid kinematic viscosity.

2.3.2. Bed Load Transport

This is called bed load transport when the sand particles roll or bounce over the seabed and always have contact with seabed. The bed load transport velocity was computed by [45]:

ubedload,i=qb,iδicb,ifb�bedload,�=�b,����b,��b(19)

where, qb,i is the bed load transport rate, which was obtained from Equation (20), δi is the bed load thickness, which was calculated by Equation (21), cb,i is the volume fraction of sand i in the multiple species, fb is the critical packing fraction of the seabed.

qb,i=8[∥g∥(ρi−ρfρf)d3i]1/2�b,�=8�(��−�f�f)��31/2(20)

δi=0.3d0.7∗(θθcr−1)0.5di��=0.3�*0.7(��cr−1)0.5��(21)

2.3.3. Suspended Load Transport

Through the following transport equation, the suspended sediment concentration could be acquired.

∂Cs,i∂t+∇(us,iCs,i)=∇∇(DfCs,i)∂�s,�∂�+∇(�s,��s,�)=∇∇(�f�s,�)(22)

where, Cs,i is the suspended sand particles mass concentration of sand i in the multiple species, us,i is the sand particles velocity of sand i, Df is the diffusivity.

The velocity of sand i in the multiple species could be obtained from the following equation:

us,i=u¯¯+usettling,ics,i�s,�=�¯+�settling,��s,�(23)

where, u¯�¯ is the velocity of mixed fluid-particles, which can be calculated by the RANS equation with turbulence model, cs,i is the suspended sand particles volume concentration, which was computed from Equation (24).

cs,i=Cs,iρi�s,�=�s,���(24)

3. Model Setup

The seabed-USAF-wave three-dimensional scour numerical model was built using Flow-3D software. As shown in Figure 2, the model includes sandy seabed, USAF model, sea water, two baffles and porous media. The dimensions of USAF are shown in Table 1. The sandy bed (210 m in length, 30 m in width and 11 m in height) is made up of uniform fine sand with median diameter d50 = 0.041 cm. The USAF model includes upper steel tube with the length of 20 m, which was installed in the middle of seabed. The location of USAF is positioned at 140 m from the upstream inflow boundary and 70 m from the downstream outflow boundary. Two baffles were installed at two ends of seabed. In order to eliminate the wave reflection basically, the porous media was set at the outflow side on the seabed.

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Figure 2. (a) The sketch of seabed-USAF-wave three-dimensional model; (b) boundary condation:Wv-wave boundary, S-symmetric boundary, O-outflow boundary; (c) USAF model.

Table 1. Numerical simulating cases.

Table

3.1. Mesh Geometric Dimensions

In the simulation of the scour under the random waves, the model includes the umbrella suction anchor foundation, seabed and fluid. As shown in Figure 3, the model mesh includes global mesh grid and nested mesh grid, and the total number of grids is 1,812,000. The basic procedure for building mesh grid consists of two steps. Step 1: Divide the global mesh using regular hexahedron with size of 0.6 × 0.6. The global mesh area is cubic box, embracing the seabed and whole fluid volume, and the dimensions are 210 m in length, 30 m in width and 32 m in height. The details of determining the grid size can see the following mesh sensitivity section. Step 2: Set nested fine mesh grid in vicinity of the USAF with size of 0.3 × 0.3 so as to shorten the computation cost and improve the calculation accuracy. The encryption range is −15 m to 15 m in x direction, −15 m to 15 m in y direction and 0 m to 32 m in z direction, respectively. In order to accurately capture the free-surface dynamics, such as the fluid-air interface, the volume of fluid (VOF) method was adopted for tracking the free water surface. One specific algorithm called FAVORTM (Fractional Area/Volume Obstacle Representation) was used to define the fractional face areas and fractional volumes of the cells which are open to fluid flow.

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Figure 3. The sketch of mesh grid.

3.2. Boundary Conditions

As shown in Figure 2, the initial fluid length is 210 m as long as seabed. A wave boundary was specified at the upstream offshore end. The details of determining the random wave spectrum can see the following wave parameters section. The outflow boundary was set at the downstream onshore end. The symmetry boundary was used at the top and two sides of the model. The symmetric boundaries were the better strategy to improve the computation efficiency and save the calculation cost [46]. At the seabed bottom, the wall boundary was adopted, which means the u = v = w= 0. Besides, the upper steel tube of USAF was set as no-slip condition.

3.3. Wave Parameters

The random waves with JONSWAP wave spectrum were used for all simulations as realistic representation of offshore conditions. The unidirectional JONSWAP frequency spectrum was described as [47]:

S(ω)=αg2ω5exp[−54(ωpω)4]γexp[−(ω−ωp)22σ2ω2p]�(�)=��2�5exp−54(�p�)4�exp−(�−�p)22�2�p2(25)

where, α is wave energy scale parameter, which is calculated by Equation (26), ω is frequency, ωp is wave spectrum peak frequency, which can be obtained from Equation (27). γ is wave spectrum peak enhancement factor, in this study γ = 3.3. σ is spectral width factor, σ equals 0.07 for ω ≤ ωp and 0.09 for ω > ωp respectively.

α=0.0076(gXU2)−0.22�=0.0076(���2)−0.22(26)

ωp=22(gU)(gXU2)−0.33�p=22(��)(���2)−0.33(27)

where, X is fetch length, U is average wind velocity at 10 m height from mean sea level.

In present numerical model, the input key parameters include X and U for wave boundary with JONSWAP wave spectrum. The objective wave height and period are available by different combinations of X and U. In this study, we designed 9 cases with different wave heights, periods and water depths for simulating scour around USAF under random waves (see Table 2). For random waves, the wave steepness ε and Ursell number Ur were acquired form Equations (28) and (29) respectively

ε=2πgHsT2a�=2���s�a2(28)

Ur=Hsk2h3w�r=�s�2ℎw3(29)

where, Hs is significant wave height, Ta is average wave period, k is wave number, hw is water depth. The Shield parameter θ satisfies θ > θcr for all simulations in current study, indicating the live bed scour prevails.

Table 2. Numerical simulating cases.

Table

3.4. Mesh Sensitivity

In this section, a mesh sensitivity analysis was conducted to investigate the influence of mesh grid size to results and make sure the calculation is mesh size independent and converged. Three mesh grid size were chosen: Mesh 1—global mesh grid size of 0.75 × 0.75, nested fine mesh grid size of 0.4 × 0.4, and total number of grids 1,724,000, Mesh 2—global mesh grid size of 0.6 × 0.6, nested fine mesh grid size of 0.3 × 0.3, and total number of grids 1,812,000, Mesh 3—global mesh grid size of 0.4 × 0.4, nested fine mesh grid size of 0.2 × 0.2, and total number of grids 1,932,000. The near-bed shear velocity U* is an important factor for influencing scour process [1,15], so U* at the position of (4,0,11.12) was evaluated under three mesh sizes. As the Figure 4 shown, the maximum error of shear velocity ∆U*1,2 is about 39.8% between the mesh 1 and mesh 2, and 4.8% between the mesh 2 and mesh 3. According to the mesh sensitivity criterion adopted by Pang et al. [48], it’s reasonable to think the results are mesh size independent and converged with mesh 2. Additionally, the present model was built according to prototype size, and the mesh size used in present model is larger than the mesh size adopted by Higueira et al. [49] and Corvaro et al. [50]. If we choose the smallest cell size, it will take too much time. For example, the simulation with Mesh3 required about 260 h by using a computer with Intel Xeon Scalable Gold 4214 CPU @24 Cores, 2.2 GHz and 64.00 GB RAM. Therefore, in this case, considering calculation accuracy and computation efficiency, the mesh 2 was chosen for all the simulation in this study.

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Figure 4. Comparison of near-bed shear velocity U* with different mesh grid size.

The nested mesh block was adopted for seabed in vicinity of the USAF, which was overlapped with the global mesh block. When two mesh blocks overlap each other, the governing equations are by default solved on the mesh block with smaller average cell size (i.e., higher grid resolution). It is should be noted that the Flow 3D software used the moving mesh captures the scour evolution and automatically adjusts the time step size to be as large as possible without exceeding any of the stability limits, affecting accuracy, or unduly increasing the effort required to enforce the continuity condition [51].

3.5. Model Validation

In order to verify the reliability of the present model, the results of present study were compared with the experimental data of Khosronejad et al. [52]. The experiment was conducted in an open channel with a slender vertical pile under unidirectional currents. The comparison of scour development between the present results and the experimental results is shown in Figure 5. The Figure 5 reveals that the present results agree well with the experimental data of Khosronejad et al. [52]. In the first stage, the scour depth increases rapidly. After that, the scour depth achieves a maximum value gradually. The equilibrium scour depth calculated by the present model is basically corresponding with the experimental results of Khosronejad et al. [52], although scour depth in the present model is slightly larger than the experimental results at initial stage.

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Figure 5. Comparison of time evolution of scour between the present study and Khosronejad et al. [52], Petersen et al. [17].

Secondly, another comparison was further conducted between the results of present study and the experimental data of Petersen et al. [17]. The experiment was carried out in a flume with a circular vertical pile in combined waves and current. Figure 4 shows a comparison of time evolution of scour depth between the simulating and the experimental results. As Figure 5 indicates, the scour depth in this study has good overall agreement with the experimental results proposed in Petersen et al. [17]. The equilibrium scour depth calculated by the present model is 0.399 m, which equals to the experimental value basically. Overall, the above verifications prove the present model is accurate and capable in dealing with sediment scour under waves.

In addition, in order to calibrate and validate the present model for hydrodynamic parameters, the comparison of water surface elevation was carried out with laboratory experiments conducted by Stahlmann [53] for wave gauge No. 3. The Figure 6 depicts the surface wave profiles between experiments and numerical model results. The comparison indicates that there is a good agreement between the model results and experimental values, especially the locations of wave crest and trough. Comparison of the surface elevation instructs the present model has an acceptable relative error, and the model is a calibrated in terms of the hydrodynamic parameters.

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Figure 6. Comparison of surface elevation between the present study and Stahlmann [53].

Finally, another comparison was conducted for equilibrium scour depth or maximum scour depth under random waves with the experimental data of Sumer and Fredsøe [16] and Schendel et al. [22]. The Figure 7 shows the comparison between the numerical results and experimental data of Run01, Run05, Run21 and Run22 in Sumer and Fredsøe [16] and test A05 and A09 in Schendel et al. [22]. As shown in Figure 7, the equilibrium scour depth or maximum scour depth distributed within the ±30 error lines basically, meaning the reliability and accuracy of present model for predicting equilibrium scour depth around foundation in random waves. However, compared with the experimental values, the present model overestimated the equilibrium scour depth generally. Given that, a calibration for scour depth was carried out by multiplying the mean reduced coefficient 0.85 in following section.

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Figure 7. Comparison of equilibrium (or maximum) scour depth between the present study and Sumer and Fredsøe [16], Schendel et al. [22].

Through the various examination for hydrodynamic and morphology parameters, it can be concluded that the present model is a validated and calibrated model for scour under random waves. Thus, the present numerical model would be utilized for scour simulation around foundation under random waves.

4. Numerical Results and Discussions

4.1. Scour Evolution

Figure 8 displays the scour evolution for case 1–9. As shown in Figure 8a, the scour depth increased rapidly at the initial stage, and then slowed down at the transition stage, which attributes to the backfilling occurred in scour holes under live bed scour condition, resulting in the net scour decreasing. Finally, the scour reached the equilibrium state when the amount of sediment backfilling equaled to that of scouring in the scour holes, i.e., the net scour transport rate was nil. Sumer and Fredsøe [16] proposed the following formula for the scour development under waves

St=Seq(1−exp(−t/Tc))�t=�eq(1−exp(−�/�c))(30)

where Tc is time scale of scour process.

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Figure 8. Time evolution of scour for case 1–9: (a) Case 1–5; (b) Case 6–9.

The computing time is 3600 s and the scour development curves in Figure 8 kept fluctuating, meaning it’s still not in equilibrium scour stage in these cases. According to Sumer and Fredsøe [16], the equilibrium scour depth can be acquired by fitting the data with Equation (30). From Figure 8, it can be seen that the scour evolution obtained from Equation (30) is consistent with the present study basically at initial stage, but the scour depth predicted by Equation (30) developed slightly faster than the simulating results and the Equation (30) overestimated the scour depth to some extent. Overall, the whole tendency of the results calculated by Equation (30) agrees well with the simulating results of the present study, which means the Equation (30) is applicable to depict the scour evolution around USAF under random waves.

4.2. Scour Mechanism under Random Waves

The scour morphology and scour evolution around USAF are similar under random waves in case 1~9. Taking case 7 as an example, the scour morphology is shown in Figure 9.

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Figure 9. Scour morphology under different times for case 7.

From Figure 9, at the initial stage (t < 1200 s), the scour occurred at upstream foundation edges between neighboring anchor branches. The maximum scour depth appeared at the lee-side of the USAF. Correspondingly, the sediments deposited at the periphery of the USAF, and the location of the maximum accretion depth was positioned at an angle of about 45° symmetrically with respect to the wave propagating direction in the lee-side of the USAF. After that, when t > 2400 s, the location of the maximum scour depth shifted to the upside of the USAF at an angle of about 45° with respect to the wave propagating direction.

According to previous studies [1,15,16,19,30,31], the horseshoe vortex, streamline compression and wake vortex shedding were responsible for scour around foundation. The Figure 10 displays the distribution of flow velocity in vicinity of foundation, which reflects the evolving processes of horseshoe vertex.

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Figure 10. Velocity profile around USAF: (a) Flow runup and down stream at upstream anchor edges; (b) Horseshoe vortex at upstream anchor edges; (c) Flow reversal during wave through stage at lee side.

As shown in Figure 10, the inflow tripped to the upstream edges of the USAF and it was blocked by the upper tube of USAF. Then, the downflow formed the horizontal axis clockwise vortex and rolled on the seabed bypassing the tube, that is, the horseshoe vortex (Figure 11). The Figure 12 displays the turbulence intensity around the tube on the seabed. From Figure 12, it can be seen that the turbulence intensity was high-intensity with respect to the region of horseshoe vortex. This phenomenon occurred because of drastic water flow momentum exchanging in the horseshoe vortex. As a result, it created the prominent shear stress on the seabed, causing the local scour at the upstream edges of USAF. Besides, the horseshoe vortex moved downstream gradually along the periphery of the tube and the wake vortex shed off continually at the lee-side of the USAF, i.e., wake vortex.

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Figure 11. Sketch of scour mechanism around USAF under random waves.

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Figure 12. Turbulence intensity: (a) Turbulence intensity of horseshoe vortex; (b) Turbulence intensity of wake vortex; (c) Turbulence intensity of accretion area.

The core of wake vortex is a negative pressure center, liking a vacuum cleaner [11,42]. Hence, the soil particles were swirled into the negative pressure core and carried away by wake vortex. At the same time, the onset of scour at rear side occurred. Finally, the wake vortex became downflow at the downside of USAF. As is shown in Figure 12, the turbulence intensity was low where the downflow occurred at lee-side, which means the turbulence energy may not be able to support the survival of wake vortex, leading to accretion happening. As mentioned in previous section, the formation of horseshoe vortex was dependent with adverse pressure gradient at upside of foundation. As shown in Figure 13, the evaluated range of pressure distribution is −15 m to 15 m in x direction. The t = 450 s and t = 1800 s indicate that the wave crest and trough arrived at the upside and lee-side of the foundation respectively, and the t = 350 s was neither the wave crest nor trough. The adverse gradient pressure reached the maximum value at t = 450 s corresponding to the wave crest phase. In this case, it’s helpful for the wave boundary separating fully from seabed, which leads to the formation of horseshoe vortex with high turbulence intensity. Therefore, the horseshoe vortex is responsible for the local scour between neighboring anchor branches at upside of USAF. What’s more, due to the combination of the horseshoe vortex and streamline compression, the maximum scour depth occurred at the upside of the USAF with an angle of about 45° corresponding to the wave propagating direction. This is consistent with the findings of Pang et al. [48] and Sumer et al. [1,15] in case of regular waves. At the wave trough phase (t = 1800 s), the pressure gradient became positive at upstream USAF edges, which hindered the separating of wave boundary from seabed. In the meantime, the flow reversal occurred (Figure 10) and the adverse gradient pressure appeared at downstream USAF edges, but the magnitude of adverse gradient pressure at lee-side was lower than the upstream gradient pressure under wave crest. In this way, the intensity of horseshoe vortex behind the USAF under wave trough was low, which explains the difference of scour depth at upstream and downstream, i.e., the scour asymmetry. In other words, the scour asymmetry at upside and downside of USAF was attributed to wave asymmetry for random waves, and the phenomenon became more evident for nonlinear waves [21]. Briefly speaking, the vortex system at wave crest phase was mainly related to the scour process around USAF under random waves.

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Figure 13. Pressure distribution around USAF.

4.3. Equilibrium Scour Depth

The KC number is a key parameter for horseshoe vortex emerging and evolving under waves. According to Equation (1), when pile diameter D is fixed, the KC depends on the maximum near-bed velocity Uwm and wave period T. For random waves, the Uwm can be denoted by the root-mean-square (RMS) value of near-bed velocity amplitude Uwm,rms or the significant value of near-bed velocity amplitude Uwm,s. The Uwm,rms and Uwm,s for all simulating cases of the present study are listed in Table 3 and Table 4. The T can be denoted by the mean up zero-crossing wave period Ta, peak wave period Tp, significant wave period Ts, the maximum wave period Tm, 1/10′th highest wave period Tn = 1/10 and 1/5′th highest wave period Tn = 1/5 for random waves, so the different combinations of Uwm and T will acquire different KC. The Table 3 and Table 4 list 12 types of KC, for example, the KCrms,s was calculated by Uwm,rms and Ts. Sumer and Fredsøe [16] conducted a series of wave flume experiments to investigate the scour depth around monopile under random waves, and found the equilibrium scour depth predicting equation (Equation (2)) for regular waves was applicable for random waves with KCrms,p. It should be noted that the Equation (2) is only suitable for KC > 6 under regular waves or KCrms,p > 6 under random waves.

Table 3. Uwm,rms and KC for case 1~9.

Table

Table 4. Uwm,s and KC for case 1~9.

Table

Raaijmakers and Rudolph [34] proposed the equilibrium scour depth predicting model (Equation (5)) around pile under waves, which is suitable for low KC. The format of Equation (5) is similar with the formula proposed by Breusers [54], which can predict the equilibrium scour depth around pile at different scour stages. In order to verify the applicability of Raaijmakers’s model for predicting the equilibrium scour depth around USAF under random waves, a validation of the equilibrium scour depth Seq between the present study and Raaijmakers’s equation was conducted. The position where the scour depth Seq was evaluated is the location of the maximum scour depth, and it was depicted in Figure 14. The Figure 15 displays the comparison of Seq with different KC between the present study and Raaijmakers’s model.

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Figure 14. Sketch of the position where the Seq was evaluated.

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Figure 15. Comparison of the equilibrium scour depth between the present model and the model of Raaijmakers and Rudolph [34]: (a) KCrms,s, KCrms,a; (b) KCrms,p, KCrms,m; (c) KCrms,n = 1/10, KCrms,n = 1/5; (d) KCs,s, KCs,a; (e) KCs,p, KCs,m; (f) KCs,n = 1/10, KCs,n = 1/5.

As shown in Figure 15, there is an error in predicting Seq between the present study and Raaijmakers’s model, and Raaijmakers’s model underestimates the results generally. Although the error exists, the varying trend of Seq with KC obtained from Raaijmakers’s model is consistent with the present study basically. What’s more, the error is minimum and the Raaijmakers’s model is of relatively high accuracy for predicting scour around USAF under random waves by using KCs,p. Based on this, a further revision was made to eliminate the error as much as possible, i.e., add the deviation value ∆S/D in the Raaijmakers’s model. The revised equilibrium scour depth predicting equation based on Raaijmakers’s model can be written as

S′eq/D=1.95[tanh(hD)](1−exp(−0.012KCs,p))+ΔS/D�eq′/�=1.95tanh(ℎ�)(1−exp(−0.012��s,p))+∆�/�(31)

As the Figure 16 shown, through trial-calculation, when ∆S/D = 0.05, the results calculated by Equation (31) show good agreement with the simulating results of the present study. The maximum error is about 18.2% and the engineering requirements have been met basically. In order to further verify the accuracy of the revised model for large KC (KCs,p > 4) under random waves, a validation between the revised model and the previous experimental results [21]. The experiment was conducted in a flume (50 m in length, 1.0 m in width and 1.3 m in height) with a slender vertical pile (D = 0.1 m) under random waves. The seabed is composed of 0.13 m deep layer of sand with d50 = 0.6 mm and the water depth is 0.5 m for all tests. The significant wave height is 0.12~0.21 m and the KCs,p is 5.52~11.38. The comparison between the predicting results by Equation (31) and the experimental results of Corvaro et al. [21] is shown in Figure 17. From Figure 17, the experimental data evenly distributes around the predicted results and the prediction accuracy is favorable when KCs,p < 8. However, the gap between the predicting results and experimental data becomes large and the Equation (31) overestimates the equilibrium scour depth to some extent when KCs,p > 8.

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Figure 16. Comparison of Seq between the simulating results and the predicting values by Equation (31).

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Figure 17. Comparison of Seq/D between the Experimental results of Corvaro et al. [21] and the predicting values by Equation (31).

In ocean environment, the waves are composed of a train of sinusoidal waves with different frequencies and amplitudes. The energy of constituent waves with very large and very small frequencies is relatively low, and the energy of waves is mainly concentrated in a certain range of moderate frequencies. Myrhaug and Rue [37] thought the 1/n’th highest wave was responsible for scour and proposed the stochastic model to predict the equilibrium scour depth around pile under random waves for full range of KC. Noteworthy is that the KC was denoted by KCrms,a in the stochastic model. To verify the application of the stochastic model for predicting scour depth around USAF, a validation between the simulating results of present study and predicting results by the stochastic model with n = 2,3,5,10,20,500 was carried out respectively.

As shown in Figure 18, compared with the simulating results, the stochastic model underestimates the equilibrium scour depth around USAF generally. Although the error exists, the varying trend of Seq with KCrms,a obtained from the stochastic model is consistent with the present study basically. What’s more, the gap between the predicting values by stochastic model and the simulating results decreases with the increase of n, but for large n, for example n = 500, the varying trend diverges between the predicting values and simulating results, meaning it’s not feasible only by increasing n in stochastic model to predict the equilibrium scour depth around USAF.

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Figure 18. Comparison of Seq between the simulating results and the predicting values by Equation (8).

The Figure 19 lists the deviation value ∆Seq/D′ between the predicting values and simulating results with different KCrms,a and n. Then, fitted the relationship between the ∆S′and n under different KCrms,a, and the fitting curve can be written by Equation (32). The revised stochastic model (Equation (33)) can be acquired by adding ∆Seq/D′ to Equation (8).

ΔSeq/D=0.052*exp(−n/6.566)+0.068∆�eq/�=0.052*exp(−�/6.566)+0.068(32)

S′eq¯/D=S′eq/D+0.052*exp(−n/6.566)+0.068�eq′¯/�=�eq′/�+0.052*exp(−�/6.566)+0.068(33)

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Figure 19. The fitting line between ∆S′and n.

The comparison between the predicting results by Equation (33) and the simulating results of present study is shown in Figure 20. According to the Figure 20, the varying trend of Seq with KCrms,a obtained from the stochastic model is consistent with the present study basically. Compared with predicting results by the stochastic model, the results calculated by Equation (33) is favorable. Moreover, comparison with simulating results indicates that the predicting results are the most favorable for n = 10, which is consistent with the findings of Myrhaug and Rue [37] for equilibrium scour depth predicting around slender pile in case of random waves.

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Figure 20. Comparison of Seq between the simulating results and the predicting values by Equation (33).

In order to further verify the accuracy of the Equation (33) for large KC (KCrms,a > 4) under random waves, a validation was conducted between the Equation (33) and the previous experimental results of Sumer and Fredsøe [16] and Corvaro et al. [21]. The details of experiments conducted by Corvaro et al. [21] were described in above section. Sumer and Fredsøe [16] investigated the local scour around pile under random waves. The experiments were conducted in a wave basin with a slender vertical pile (D = 0.032, 0.055 m). The seabed is composed of 0.14 m deep layer of sand with d50 = 0.2 mm and the water depth was maintained at 0.5 m. The JONSWAP wave spectrum was used and the KCrms,a was 5.29~16.95. The comparison between the predicting results by Equation (33) and the experimental results of Sumer and Fredsøe [16] and Corvaro et al. [21] are shown in Figure 21. From Figure 21, contrary to the case of low KCrms,a (KCrms,a < 4), the error between the predicting values and experimental results increases with decreasing of n for KCrms,a > 4. Therefore, the predicting results are the most favorable for n = 2 when KCrms,a > 4.

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Figure 21. Comparison of Seq between the experimental results of Sumer and Fredsøe [16] and Corvaro et al. [21] and the predicting values by Equation (33).

Noteworthy is that the present model was built according to prototype size, so the errors between the numerical results and experimental data of References [16,21] may be attribute to the scale effects. In laboratory experiments on scouring process, it is typically impossible to ensure a rigorous similarity of all physical parameters between the model and prototype structure, leading to the scale effects in the laboratory experiments. To avoid a cohesive behaviour, the bed material was not scaled geometrically according to model scale. As a consequence, the relatively large-scaled sediments sizes may result in the overestimation of bed load transport and underestimation of suspended load transport compared with field conditions. What’s more, the disproportional scaled sediment presumably lead to the difference of bed roughness between the model and prototype, and thus large influences for wave boundary layer on the seabed and scour process. Besides, according to Corvaro et al. [21] and Schendel et al. [55], the pile Reynolds numbers and Froude numbers both affect the scour depth for the condition of non fully developed turbulent flow in laboratory experiments.

4.4. Parametric Study

4.4.1. Influence of Froude Number

As described above, the set of foundation leads to the adverse pressure gradient appearing at upstream, leading to the wave boundary layer separating from seabed, then horseshoe vortex formatting and the horseshoe vortex are mainly responsible for scour around foundation (see Figure 22). The Froude number Fr is the key parameter to influence the scale and intensity of horseshoe vortex. The Fr under waves can be calculated by the following formula [42]

Fr=UwgD−−−√�r=�w��(34)

where Uw is the mean water particle velocity during 1/4 cycle of wave oscillation, obtained from the following formula. Noteworthy is that the root-mean-square (RMS) value of near-bed velocity amplitude Uwm,rms is used for calculating Uwm.

Uw=1T/4∫0T/4Uwmsin(t/T)dt=2πUwm�w=1�/4∫0�/4�wmsin(�/�)��=2��wm(35)

Jmse 09 00886 g022 550

Figure 22. Sketch of flow field at upstream USAF edges.

Tavouktsoglou et al. [25] proposed the following formula between Fr and the vertical location of the stagnation y

yh∝Fer�ℎ∝�r�(36)

where e is constant.

The Figure 23 displays the relationship between Seq/D and Fr of the present study. In order to compare with the simulating results, the experimental data of Corvaro et al. [21] was also depicted in Figure 23. As shown in Figure 23, the equilibrium scour depth appears a logarithmic increase as Fr increases and approaches the mathematical asymptotic value, which is also consistent with the experimental results of Corvaro et al. [21]. According to Figure 24, the adverse pressure gradient pressure at upstream USAF edges increases with the increase of Fr, which is benefit for the wave boundary layer separating from seabed, resulting in the high-intensity horseshoe vortex, hence, causing intensive scour around USAF. Based on the previous study of Tavouktsoglou et al. [25] for scour around pile under currents, the high Fr leads to the stagnation point is closer to the mean sea level for shallow water, causing the stronger downflow kinetic energy. As mentioned in previous section, the energy of downflow at upstream makes up the energy of the subsequent horseshoe vortex, so the stronger downflow kinetic energy results in the more intensive horseshoe vortex. Therefore, the higher Fr leads to the more intensive horseshoe vortex by influencing the position of stagnation point y presumably. Qi and Gao [19] carried out a series of flume tests to investigate the scour around pile under regular waves, and proposed the fitting formula between Seq/D and Fr as following

lg(Seq/D)=Aexp(B/Fr)+Clg(�eq/�)=�exp(�/�r)+�(37)

where A, B and C are constant.

Jmse 09 00886 g023 550

Figure 23. The fitting curve between Seq/D and Fr.

Jmse 09 00886 g024 550

Figure 24. Sketch of adverse pressure gradient at upstream USAF edges.

Took the Equation (37) to fit the simulating results with A = −0.002, B = 0.686 and C = −0.808, and the results are shown in Figure 23. From Figure 23, the simulating results evenly distribute around the Equation (37) and the varying trend of Seq/D and Fr in present study is consistent with Equation (37) basically, meaning the Equation (37) is applicable to express the relationship of Seq/D with Fr around USAF under random waves.

4.4.2. Influence of Euler Number

The Euler number Eu is the influencing factor for the hydrodynamic field around foundation. The Eu under waves can be calculated by the following formula. The Eu can be represented by the Equation (38) for uniform cylinders [25]. The root-mean-square (RMS) value of near-bed velocity amplitude Um,rms is used for calculating Um.

Eu=U2mgD�u=�m2��(38)

where Um is depth-averaged flow velocity.

The Figure 25 displays the relationship between Seq/D and Eu of the present study. In order to compare with the simulating results, the experimental data of Sumer and Fredsøe [16] and Corvaro et al. [21] were also plotted in Figure 25. As shown in Figure 25, similar with the varying trend of Seq/D and Fr, the equilibrium scour depth appears a logarithmic increase as Eu increases and approaches the mathematical asymptotic value, which is also consistent with the experimental results of Sumer and Fredsøe [16] and Corvaro et al. [21]. According to Figure 24, the adverse pressure gradient pressure at upstream USAF edges increases with the increasing of Eu, which is benefit for the wave boundary layer separating from seabed, inducing the high-intensity horseshoe vortex, hence, causing intensive scour around USAF.

Jmse 09 00886 g025 550

Figure 25. The fitting curve between Seq/D and Eu.

Therefore, the variation of Fr and Eu reflect the magnitude of adverse pressure gradient pressure at upstream. Given that, the Equation (37) also was used to fit the simulating results with A = 8.875, B = 0.078 and C = −9.601, and the results are shown in Figure 25. From Figure 25, the simulating results evenly distribute around the Equation (37) and the varying trend of Seq/D and Eu in present study is consistent with Equation (37) basically, meaning the Equation (37) is also applicable to express the relationship of Seq/D with Eu around USAF under random waves. Additionally, according to the above description of Fr, it can be inferred that the higher Fr and Eu both lead to the more intensive horseshoe vortex by influencing the position of stagnation point y presumably.

5. Conclusions

A series of numerical models were established to investigate the local scour around umbrella suction anchor foundation (USAF) under random waves. The numerical model was validated for hydrodynamic and morphology parameters by comparing with the experimental data of Khosronejad et al. [52], Petersen et al. [17], Sumer and Fredsøe [16] and Schendel et al. [22]. Based on the simulating results, the scour evolution and scour mechanisms around USAF under random waves were analyzed respectively. Two revised models were proposed according to the model of Raaijmakers and Rudolph [34] and the stochastic model developed by Myrhaug and Rue [37] to predict the equilibrium scour depth around USAF under random waves. Finally, a parametric study was carried out with the present model to study the effects of the Froude number Fr and Euler number Eu to the equilibrium scour depth around USAF under random waves. The main conclusions can be described as follows.(1)

The packed sediment scour model and the RNG k−ε turbulence model were used to simulate the sand particles transport processes and the flow field around UASF respectively. The scour evolution obtained by the present model agrees well with the experimental results of Khosronejad et al. [52], Petersen et al. [17], Sumer and Fredsøe [16] and Schendel et al. [22], which indicates that the present model is accurate and reasonable for depicting the scour morphology around UASF under random waves.(2)

The vortex system at wave crest phase is mainly related to the scour process around USAF under random waves. The maximum scour depth appeared at the lee-side of the USAF at the initial stage (t < 1200 s). Subsequently, when t > 2400 s, the location of the maximum scour depth shifted to the upside of the USAF at an angle of about 45° with respect to the wave propagating direction.(3)

The error is negligible and the Raaijmakers’s model is of relatively high accuracy for predicting scour around USAF under random waves when KC is calculated by KCs,p. Given that, a further revision model (Equation (31)) was proposed according to Raaijmakers’s model to predict the equilibrium scour depth around USAF under random waves and it shows good agreement with the simulating results of the present study when KCs,p < 8.(4)

Another further revision model (Equation (33)) was proposed according to the stochastic model established by Myrhaug and Rue [37] to predict the equilibrium scour depth around USAF under random waves, and the predicting results are the most favorable for n = 10 when KCrms,a < 4. However, contrary to the case of low KCrms,a, the predicting results are the most favorable for n = 2 when KCrms,a > 4 by the comparison with experimental results of Sumer and Fredsøe [16] and Corvaro et al. [21].(5)

The same formula (Equation (37)) is applicable to express the relationship of Seq/D with Eu or Fr, and it can be inferred that the higher Fr and Eu both lead to the more intensive horseshoe vortex and larger Seq.

Author Contributions

Conceptualization, H.L. (Hongjun Liu); Data curation, R.H. and P.Y.; Formal analysis, X.W. and H.L. (Hao Leng); Funding acquisition, X.W.; Writing—original draft, R.H. and P.Y.; Writing—review & editing, X.W. and H.L. (Hao Leng); The final manuscript has been approved by all the authors. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Fundamental Research Funds for the Central Universities (grant number 202061027) and the National Natural Science Foundation of China (grant number 41572247).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data presented in this study are available on request from the corresponding author.

Conflicts of Interest

The authors declare no conflict of interest.

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Hu, R.; Liu, H.; Leng, H.; Yu, P.; Wang, X. Scour Characteristics and Equilibrium Scour Depth Prediction around Umbrella Suction Anchor Foundation under Random Waves. J. Mar. Sci. Eng. 2021, 9, 886. https://doi.org/10.3390/jmse9080886

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Hu R, Liu H, Leng H, Yu P, Wang X. Scour Characteristics and Equilibrium Scour Depth Prediction around Umbrella Suction Anchor Foundation under Random Waves. Journal of Marine Science and Engineering. 2021; 9(8):886. https://doi.org/10.3390/jmse9080886Chicago/Turabian Style

Hu, Ruigeng, Hongjun Liu, Hao Leng, Peng Yu, and Xiuhai Wang. 2021. “Scour Characteristics and Equilibrium Scour Depth Prediction around Umbrella Suction Anchor Foundation under Random Waves” Journal of Marine Science and Engineering 9, no. 8: 886. https://doi.org/10.3390/jmse9080886

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Figure 5. Schematic view of flap and support structure [32]

Design Optimization of Ocean Renewable Energy Converter Using a Combined Bi-level Metaheuristic Approach

결합된 Bi-level 메타휴리스틱 접근법을 사용한 해양 재생 에너지 변환기의 설계 최적화

Erfan Amini a1, Mahdieh Nasiri b1, Navid Salami Pargoo a, Zahra Mozhgani c, Danial Golbaz d, Mehrdad Baniesmaeil e, Meysam Majidi Nezhad f, Mehdi Neshat gj, Davide Astiaso Garcia h, Georgios Sylaios i

Abstract

In recent years, there has been an increasing interest in renewable energies in view of the fact that fossil fuels are the leading cause of catastrophic environmental consequences. Ocean wave energy is a renewable energy source that is particularly prevalent in coastal areas. Since many countries have tremendous potential to extract this type of energy, a number of researchers have sought to determine certain effective factors on wave converters’ performance, with a primary emphasis on ambient factors. In this study, we used metaheuristic optimization methods to investigate the effects of geometric factors on the performance of an Oscillating Surge Wave Energy Converter (OSWEC), in addition to the effects of hydrodynamic parameters. To do so, we used CATIA software to model different geometries which were then inserted into a numerical model developed in Flow3D software. A Ribed-surface design of the converter’s flap is also introduced in this study to maximize wave-converter interaction. Besides, a Bi-level Hill Climbing Multi-Verse Optimization (HCMVO) method was also developed for this application. The results showed that the converter performs better with greater wave heights, flap freeboard heights, and shorter wave periods. Additionally, the added ribs led to more wave-converter interaction and better performance, while the distance between the flap and flume bed negatively impacted the performance. Finally, tracking the changes in the five-dimensional objective function revealed the optimum value for each parameter in all scenarios. This is achieved by the newly developed optimization algorithm, which is much faster than other existing cutting-edge metaheuristic approaches.

Keywords

Wave Energy Converter

OSWEC

Hydrodynamic Effects

Geometric Design

Metaheuristic Optimization

Multi-Verse Optimizer

1. Introduction

The increase in energy demand, the limitations of fossil fuels, as well as environmental crises, such as air pollution and global warming, are the leading causes of calling more attention to harvesting renewable energy recently [1], [2], [3]. While still in its infancy, ocean wave energy has neither reached commercial maturity nor technological convergence. In recent decades, remarkable progress has been made in the marine energy domain, which is still in the early stage of development, to improve the technology performance level (TPL) [4], [5]and technology readiness level (TRL) of wave energy converters (WECs). This has been achieved using novel modeling techniques [6], [7], [8], [9], [10], [11], [12], [13], [14] to gain the following advantages [15]: (i) As a source of sustainable energy, it contributes to the mix of energy resources that leads to greater diversity and attractiveness for coastal cities and suppliers. [16] (ii) Since wave energy can be exploited offshore and does not require any land, in-land site selection would be less expensive and undesirable visual effects would be reduced. [17] (iii) When the best layout and location of offshore site are taken into account, permanent generation of energy will be feasible (as opposed to using solar energy, for example, which is time-dependent) [18].

In general, the energy conversion process can be divided into three stages in a WEC device, including primary, secondary, and tertiary stages [19], [20]. In the first stage of energy conversion, which is the subject of this study, the wave power is converted to mechanical power by wave-structure interaction (WSI) between ocean waves and structures. Moreover, the mechanical power is transferred into electricity in the second stage, in which mechanical structures are coupled with power take-off systems (PTO). At this stage, optimal control strategies are useful to tune the system dynamics to maximize power output [10], [13], [12]. Furthermore, the tertiary energy conversion stage revolves around transferring the non-standard AC power into direct current (DC) power for energy storage or standard AC power for grid integration [21], [22]. We discuss only the first stage regardless of the secondary and tertiary stages. While Page 1 of 16 WECs include several categories and technologies such as terminators, point absorbers, and attenuators [15], [23], we focus on oscillating surge wave energy converters (OSWECs) in this paper due to its high capacity for industrialization [24].

Over the past two decades, a number of studies have been conducted to understand how OSWECs’ structures and interactions between ocean waves and flaps affect converters performance. Henry et al.’s experiment on oscillating surge wave energy converters is considered as one of the most influential pieces of research [25], which demonstrated how the performance of oscillating surge wave energy converters (OSWECs) is affected by seven different factors, including wave period, wave power, flap’s relative density, water depth, free-board of the flap, the gap between the tubes, gap underneath the flap, and flap width. These parameters were assessed in their two models in order to estimate the absorbed energy from incoming waves [26], [27]. In addition, Folly et al. investigated the impact of water depth on the OSWECs performance analytically, numerically, and experimentally. According to this and further similar studies, the average annual incident wave power is significantly reduced by water depth. Based on the experimental results, both the surge wave force and the power capture of OSWECs increase in shallow water [28], [29]. Following this, Sarkar et al. found that under such circumstances, the device that is located near the coast performs much better than those in the open ocean [30]. On the other hand, other studies are showing that the size of the converter, including height and width, is relatively independent of the location (within similar depth) [31]. Subsequently, Schmitt et al. studied OSWECs numerically and experimentally. In fact, for the simulation of OSWEC, OpenFOAM was used to test the applicability of Reynolds-averaged Navier-Stokes (RANS) solvers. Then, the experimental model reproduced the numerical results with satisfying accuracy [32]. In another influential study, Wang et al. numerically assessed the effect of OSWEC’s width on their performance. According to their findings, as converter width increases, its efficiency decreases in short wave periods while increases in long wave periods [33]. One of the main challenges in the analysis of the OSWEC is the coupled effect of hydrodynamic and geometric variables. As a result, numerous cutting-edge geometry studies have been performed in recent years in order to find the optimal structure that maximizes power output and minimizes costs. Garcia et al. reviewed hull geometry optimization studies in the literature in [19]. In addition, Guo and Ringwood surveyed geometric optimization methods to improve the hydrodynamic performance of OSWECs at the primary stage [14]. Besides, they classified the hull geometry of OSWECs based on Figure 1. Subsequently, Whittaker et al. proposed a different design of OSWEC called Oyster2. There have been three examples of different geometries of oysters with different water depths. Based on its water depth, they determined the width and height of the converter. They also found that in the constant wave period the less the converter’s width, the less power captures the converter has [34]. Afterward, O’Boyle et al. investigated a type of OSWEC called Oyster 800. They compared the experimental and numerical models with the prototype model. In order to precisely reproduce the shape, mass distribution, and buoyancy properties of the prototype, a 40th-scale experimental model has been designed. Overall, all the models were fairly accurate according to the results [35].

Inclusive analysis of recent research avenues in the area of flap geometry has revealed that the interaction-based designs of such converters are emerging as a novel approach. An initiative workflow is designed in the current study to maximizing the wave energy extrication by such systems. To begin with, a sensitivity analysis plays its role of determining the best hydrodynamic values for installing the converter’s flap. Then, all flap dimensions and characteristics come into play to finalize the primary model. Following, interactive designs is proposed to increase the influence of incident waves on the body by adding ribs on both sides of the flap as a novel design. Finally, a new bi-level metaheuristic method is proposed to consider the effects of simultaneous changes in ribs properties and other design parameters. We hope this novel approach will be utilized to make big-scale projects less costly and justifiable. The efficiency of the method is also compared with four well known metaheuristic algorithms and out weight them for this application.

This paper is organized as follows. First, the research methodology is introduced by providing details about the numerical model implementation. To that end, we first introduced the primary model’s geometry and software details. That primary model is later verified with a benchmark study with regard to the flap angle of rotation and water surface elevation. Then, governing equations and performance criteria are presented. In the third part of the paper, we discuss the model’s sensitivity to lower and upper parts width (we proposed a two cross-sectional design for the flap), bottom elevation, and freeboard. Finally, the novel optimization approach is introduced in the final part and compared with four recent metaheuristic algorithms.

2. Numerical Methods

In this section, after a brief introduction of the numerical software, Flow3D, boundary conditions are defined. Afterwards, the numerical model implementation, along with primary model properties are described. Finally, governing equations, as part of numerical process, are discussed.

2.1. Model Setup

FLOW-3D is a powerful and comprehensive CFD simulation platform for studying fluid dynamics. This software has several modules to solve many complex engineering problems. In addition, modeling complex flows is simple and effective using FLOW-3D’s robust meshing capabilities [36]. Interaction between fluid and moving objects might alter the computational range. Dynamic meshes are used in our modeling to take these changes into account. At each time step, the computational node positions change in order to adapt the meshing area to the moving object. In addition, to choose mesh dimensions, some factors are taken into account such as computational accuracy, computational time, and stability. The final grid size is selected based on the detailed procedure provided in [37]. To that end, we performed grid-independence testing on a CFD model using three different mesh grid sizes of 0.01, 0.015, and 0.02 meters. The problem geometry and boundary conditions were defined the same, and simulations were run on all three grids under the same conditions. The predicted values of the relevant variable, such as velocity, was compared between the grids. The convergence behavior of the numerical solution was analyzed by calculating the relative L2 norm error between two consecutive grids. Based on the results obtained, it was found that the grid size of 0.02 meters showed the least error, indicating that it provided the most accurate and reliable solution among the three grids. Therefore, the grid size of 0.02 meters was selected as the optimal spatial resolution for the mesh grid.

In this work, the flume dimensions are 10 meters long, 0.1 meters wide, and 2.2 meters high, which are shown in figure2. In addition, input waves with linear characteristics have a height of 0.1 meters and a period of 1.4 seconds. Among the linear wave methods included in this software, RNGk-ε and k- ε are appropriate for turbulence model. The research of Lopez et al. shows that RNGk- ε provides the most accurate simulation of turbulence in OSWECs [21]. We use CATIA software to create the flap primary model and other innovative designs for this project. The flap measures 0.1 m x 0.65 m x 0.360 m in x, y and z directions, respectively. In Figure 3, the primary model of flap and its dimensions are shown. In this simulation, five boundaries have been defined, including 1. Inlet, 2. Outlet, 3. Converter flap, 4. Bed flume, and 5. Water surface, which are shown in figure 2. Besides, to avoid wave reflection in inlet and outlet zones, Flow3D is capable of defining some areas as damping zones, the length of which has to be one to one and a half times the wavelength. Therefore, in the model, this length is considered equal to 2 meters. Furthermore, there is no slip in all the boundaries. In other words, at every single time step, the fluid velocity is zero on the bed flume, while it is equal to the flap velocity on the converter flap. According to the wave theory defined in the software, at the inlet boundary, the water velocity is called from the wave speed to be fed into the model.

2.2. Verification

In the current study, we utilize the Schmitt experimental model as a benchmark for verification, which was developed at the Queen’s University of Belfast. The experiments were conducted on the flap of the converter, its rotation, and its interaction with the water surface. Thus, the details of the experiments are presented below based up on the experimental setup’s description [38]. In the experiment, the laboratory flume has a length of 20m and a width of 4.58m. Besides, in order to avoid incident wave reflection, a wave absorption source is devised at the end of the left flume. The flume bed, also, includes two parts with different slops. The flap position and dimensions of the flume can be seen in Figure4. In addition, a wave-maker with 6 paddles is installed at one end. At the opposite end, there is a beach with wire meshes. Additionally, there are 6 indicators to extract the water level elevation. In the flap model, there are three components: the fixed support structure, the hinge, and the flap. The flap measures 0.1m x 0.65m x 0.341m in x, y and z directions, respectively. In Figure5, the details are given [32]. The support structure consists of a 15 mm thick stainless steel base plate measuring 1m by 1.4m, which is screwed onto the bottom of the tank. The hinge is supported by three bearing blocks. There is a foam centerpiece on the front and back of the flap which is sandwiched between two PVC plates. Enabling changes of the flap, three metal fittings link the flap to the hinge. Moreover, in this experiment, the selected wave is generated based on sea wave data at scale 1:40. The wave height and the wave period are equal to 0.038 (m) and 2.0625 (s), respectively, which are tantamount to a wave with a period of 13 (s) and a height of 1.5 (m).

Two distinct graphs illustrate the numerical and experi-mental study results. Figure6 and Figure7 are denoting the angle of rotation of flap and surface elevation in computational and experimental models, respectively. The two figures roughly represent that the numerical and experimental models are a good match. However, for the purpose of verifying the match, we calculated the correlation coefficient (C) and root mean square error (RMSE). According to Figure6, correlation coefficient and RMSE are 0.998 and 0.003, respectively, and in Figure7 correlation coefficient and RMSE are respectively 0.999 and 0.001. Accordingly, there is a good match between the numerical and empirical models. It is worth mentioning that the small differences between the numerical and experimental outputs may be due to the error of the measuring devices and the calibration of the data collection devices.

Including continuity equation and momentum conserva- tion for incompressible fluid are given as [32], [39]:(1)

where P represents the pressure, g denotes gravitational acceleration, u represents fluid velocity, and Di is damping coefficient. Likewise, the model uses the same equation. to calculate the fluid velocity in other directions as well. Considering the turbulence, we use the two-equation model of RNGK- ε. These equations are:

(3)��t(��)+����(����)=����[�eff�������]+��-��and(4)���(��)+����(����)=����[�eff�������]+�1�∗����-��2��2�Where �2� and �1� are constants. In addition, �� and �� represent the turbulent Prandtl number of � and k, respectively.

�� also denote the production of turbulent kinetic energy of k under the effect of velocity gradient, which is calculated as follows:(5)��=�eff[�����+�����]�����(6)�eff=�+��(7)�eff=�+��where � is molecular viscosity,�� represents turbulence viscosity, k denotes kinetic energy, and ∊∊ is energy dissipation rate. The values of constant coefficients in the two-equation RNGK ∊-∊ model is as shown in the Table 1 [40].Table 2.

Table 1. Constant coefficients in RNGK-∊ model

Factors��0�1�2������
Quantity0.0124.381.421.681.391.390.084

Table 2. Flap properties

Joint height (m)0.476
Height of the center of mass (m)0.53
Weight (Kg)10.77

It is worth mentioning that the volume of fluid method is used to separate water and air phases in this software [41]. Below is the equation of this method [40].(8)����+����(���)=0where α and 1 − α are portion of water phase and air phase, respectively. As a weighting factor, each fluid phase portion is used to determine the mixture properties. Finally, using the following equations, we calculate the efficiency of converters [42], [34], [43]:(9)�=14|�|2�+�2+(�+�a)2(�n2-�2)2where �� represents natural frequency, I denotes the inertia of OSWEC, Ia is the added inertia, F is the complex wave force, and B denotes the hydrodynamic damping coefficient. Afterward, the capture factor of the converter is calculated by [44]:(10)��=�1/2��2����gw where �� represents the capture factor, which is the total efficiency of device per unit length of the wave crest at each time step [15], �� represent the dimensional amplitude of the incident wave, w is the flap’s width, and Cg is the group velocity of the incident wave, as below:(11)��=��0·121+2�0ℎsinh2�0ℎwhere �0 denotes the wave number, h is water depth, and H is the height of incident waves.

According to previous sections ∊,����-∊ modeling is used for all models simulated in this section. For this purpose, the empty boundary condition is used for flume walls. In order to preventing wave reflection at the inlet and outlet of the flume, the length of wave absorption is set to be at least one incident wavelength. In addition, the structured mesh is chosen, and the mesh dimensions are selected in two distinct directions. In each model, all grids have a length of 2 (cm) and a height of 1 (cm). Afterwards, as an input of the software for all of the models, we define the time step as 0.001 (s). Moreover, the run time of every simulation is 30 (s). As mentioned before, our primary model is Schmitt model, and the flap properties is given in table2. For all simulations, the flume measures 15 meters in length and 0.65 meters in width, and water depth is equal to 0.335 (m). The flap is also located 7 meters from the flume’s inlet.

Finally, in order to compare the results, the capture factor is calculated for each simulation and compared to the primary model. It is worth mentioning that capture factor refers to the ratio of absorbed wave energy to the input wave energy.

According to primary model simulation and due to the decreasing horizontal velocity with depth, the wave crest has the highest velocity. Considering the fact that the wave’s orbital velocity causes the flap to move, the contact between the upper edge of the flap and the incident wave can enhance its performance. Additionally, the numerical model shows that the dynamic pressure decreases as depth increases, and the hydrostatic pressure increases as depth increases.

To determine the OSWEC design, it is imperative to understand the correlation between the capture factor, wave period, and wave height. Therefore, as it is shown in Figure8, we plot the change in capture factor over the variations in wave period and wave height in 3D and 2D. In this diagram, the first axis features changes in wave period, the second axis displays changes in wave height, and the third axis depicts changes in capture factor. According to our wave properties in the numerical model, the wave period and wave height range from 2 to 14 seconds and 2 to 8 meters, respectively. This is due to the fact that the flap does not oscillate if the wave height is less than 2 (m), and it does not reverse if the wave height is more than 8 (m). In addition, with wave periods more than 14 (s), the wavelength would be so long that it would violate the deep-water conditions, and with wave periods less than 2 (s), the flap would not oscillate properly due to the shortness of wavelength. The results of simulation are shown in Figure 8. As it can be perceived from Figure 8, in a constant wave period, the capture factor is in direct proportion to the wave height. It is because of the fact that waves with more height have more energy to rotate the flap. Besides, in a constant wave height, the capture factor increases when the wave period increases, until a given wave period value. However, the capture factor falls after this point. These results are expected since the flap’s angular displacement is not high in lower wave periods, while the oscillating motion of that is not fast enough to activate the power take-off system in very high wave periods.

As is shown in Figure 9, we plot the change in capture factor over the variations in wave period (s) and water depth (m) in 3D. As it can be seen in this diagram, the first axis features changes in water depth (m), the second axis depicts the wave period (s), and the third axis displays OSWEC’s capture factor. The wave period ranges from 0 to 10 seconds based on our wave properties, which have been adopted from Schmitt’s model, while water depth ranges from 0 to 0.5 meters according to the flume and flap dimensions and laboratory limitations. According to Figure9, for any specific water depth, the capture factor increases in a varying rate when the wave period increases, until a given wave period value. However, the capture factor falls steadily after this point. In fact, the maximum capture factor occurs when the wave period is around 6 seconds. This trend is expected since, in a specific water depth, the flap cannot oscillate properly when the wavelength is too short. As the wave period increases, the flap can oscillate more easily, and consequently its capture factor increases. However, the capture factor drops in higher wave periods because the wavelength is too large to move the flap. Furthermore, in a constant wave period, by changing the water depth, the capture factor does not alter. In other words, the capture factor does not depend on the water depth when it is around its maximum value.

3. Sensitivity Analysis

Based on previous studies, in addition to the flap design, the location of the flap relative to the water surface (freeboard) and its elevation relative to the flume bed (flap bottom elevation) play a significant role in extracting energy from the wave energy converter. This study measures the sensitivity of the model to various parameters related to the flap design including upper part width of the flap, lower part width of the flap, the freeboard, and the flap bottom elevation. Moreover, as a novel idea, we propose that the flap widths differ in the lower and upper parts. In Figure10, as an example, a flap with an upper thickness of 100 (mm) and a lower thickness of 50 (mm) and a flap with an upper thickness of 50 (mm) and a lower thickness of 100 (mm) are shown. The influence of such discrepancy between the widths of the upper and lower parts on the interaction between the wave and the flap, or in other words on the capture factor, is evaluated. To do so, other parameters are remained constant, such as the freeboard, the distance between the flap and the flume bed, and the wave properties.

In Figure11, models are simulated with distinct upper and lower widths. As it is clear in this figure, the first axis depicts the lower part width of the flap, the second axis indicates the upper part width of the flap, and the colors represent the capture factor values. Additionally, in order to consider a sufficient range of change, the flap thickness varies from half to double the value of the primary model for each part.

According to this study, the greater the discrepancy in these two parts, the lower the capture factor. It is on account of the fact that when the lower part of the flap is thicker than the upper part, and this thickness difference in these two parts is extremely conspicuous, the inertia against the motion is significant at zero degrees of rotation. Consequently, it is difficult to move the flap, which results in a low capture factor. Similarly, when the upper part of the flap is thicker than the lower part, and this thickness difference in these two parts is exceedingly noticeable, the inertia is so great that the flap can not reverse at the maximum degree of rotation. As the results indicate, the discrepancy can enhance the performance of the converter if the difference between these two parts is around 20%. As it is depicted in the Figure11, the capture factor reaches its own maximum amount, when the lower part thickness is from 5 to 6 (cm), and the upper part thickness is between 6 and 7 (cm). Consequently, as a result of this discrepancy, less material will be used, and therefore there will be less cost.

As illustrated in Figure12, this study examines the effects of freeboard (level difference between the flap top and water surface) and the flap bottom elevation (the distance between the flume bed and flap bottom) on the converter performance. In this diagram, the first axis demonstrates the freeboard and the second axis on the left side displays the flap bottom elevation, while the colors indicate the capture factor. In addition, the feasible range of freeboard is between -15 to 15 (cm) due to the limitation of the numerical model, so that we can take the wave slamming and the overtopping into consideration. Additionally, based on the Schmitt model and its scaled model of 1:40 of the base height, the flap bottom should be at least 9 (cm) high. Since the effect of surface waves is distributed over the depth of the flume, it is imperative to maintain a reasonable flap height exposed to incoming waves. Thus, the maximum flap bottom elevation is limited to 19 (cm). As the Figure12 pictures, at constant negative values of the freeboard, the capture factor is in inverse proportion with the flap bottom elevation, although slightly.

Furthermore, at constant positive values of the freeboard, the capture factor fluctuates as the flap bottom elevation decreases while it maintains an overall increasing trend. This is on account of the fact that increasing the flap bottom elevation creates turbulence flow behind the flap, which encumbers its rotation, as well as the fact that the flap surface has less interaction with the incoming waves. Furthermore, while keeping the flap bottom elevation constant, the capture factor increases by raising the freeboard. This is due to the fact that there is overtopping with adverse impacts on the converter performance when the freeboard is negative and the flap is under the water surface. Besides, increasing the freeboard makes the wave slam more vigorously, which improves the converter performance.

Adding ribs to the flap surface, as shown in Figure13, is a novel idea that is investigated in the next section. To achieve an optimized design for the proposed geometry of the flap, we determine the optimal number and dimensions of ribs based on the flap properties as our decision variables in the optimization process. As an example, Figure13 illustrates a flap with 3 ribs on each side with specific dimensions.

Figure14 shows the flow velocity field around the flap jointed to the flume bed. During the oscillation of the flap, the pressure on the upper and lower surfaces of the flap changes dynamically due to the changing angle of attack and the resulting change in the direction of fluid flow. As the flap moves upwards, the pressure on the upper surface decreases, and the pressure on the lower surface increases. Conversely, as the flap moves downwards, the pressure on the upper surface increases, and the pressure on the lower surface decreases. This results in a cyclic pressure variation around the flap. Under certain conditions, the pressure field around the flap can exhibit significant variations in magnitude and direction, forming vortices and other flow structures. These flow structures can affect the performance of the OSWEC by altering the lift and drag forces acting on the flap.

4. Design Optimization

We consider optimizing the design parameters of the flap of converter using a nature-based swarm optimization method, that fall in the category of metaheuristic algorithms [45]. Accordingly, we choose four state-of-the-art algorithms to perform an optimization study. Then, based on their performances to achieve the highest capture factor, one of them will be chosen to be combined with the Hill Climb algorithm to carry out a local search. Therefore, in the remainder of this section, we discuss the search process of each algorithm and visualize their performance and convergence curve as they try to find the best values for decision variables.

4.1. Metaheuristic Approaches

As the first considered algorithm, the Gray Wolf Optimizer (GWO) algorithm simulates the natural leadership and hunting performance of gray wolves which tend to live in colonies. Hunters must obey the alpha wolf, the leader, who is responsible for hunting. Then, the beta wolf is at the second level of the gray wolf hierarchy. A subordinate of alpha wolf, beta stands under the command of the alpha. At the next level in this hierarchy, there are the delta wolves. They are subordinate to the alpha and beta wolves. This category of wolves includes scouts, sentinels, elders, hunters, and caretakers. In this ranking, omega wolves are at the bottom, having the lowest level and obeying all other wolves. They are also allowed to eat the prey just after others have eaten. Despite the fact that they seem less important than others, they are really central to the pack survival. Since, it has been shown that without omega wolves, the entire pack would experience some problems like fighting, violence, and frustration. In this simulation, there are three primary steps of hunting including searching, surrounding, and finally attacking the prey. Mathematically model of gray wolves’ hunting technique and their social hierarchy are applied in determined by optimization. this study. As mentioned before, gray wolves can locate their prey and surround them. The alpha wolf also leads the hunt. Assuming that the alpha, beta, and delta have more knowledge about prey locations, we can mathematically simulate gray wolf hunting behavior. Hence, in addition to saving the top three best solutions obtained so far, we compel the rest of the search agents (also the omegas) to adjust their positions based on the best search agent. Encircling behavior can be mathematically modeled by the following equations: [46].(12)�→=|�→·��→(�)-�→(�)|(13)�→(�+1)=��→(�)-�→·�→(14)�→=2.�2→(15)�→=2�→·�1→-�→Where �→indicates the position vector of gray wolf, ��→ defines the vector of prey, t indicates the current iteration, and �→and �→are coefficient vectors. To force the search agent to diverge from the prey, we use �→ with random values greater than 1 or less than -1. In addition, C→ contains random values in the range [0,2], and �→ 1 and �2→ are random vectors in [0,1]. The second considered technique is the Moth Flame Optimizer (MFO) algorithm. This method revolves around the moths’ navigation mechanism, which is realized by positioning themselves and maintaining a fixed angle relative to the moon while flying. This effective mechanism helps moths to fly in a straight path. However, when the source of light is artificial, maintaining an angle with the light leads to a spiral flying path towards the source that causes the moth’s death [47]. In MFO algorithm, moths and flames are both solutions. The moths are actual search agents that fly in hyper-dimensional space by changing their position vectors, and the flames are considered pins that moths drop when searching the search space [48]. The problem’s variables are the position of moths in the space. Each moth searches around a flame and updates it in case of finding a better solution. The fitness value is the return value of each moth’s fitness (objective) function. The position vector of each moth is passed to the fitness function, and the output of the fitness function is assigned to the corresponding moth. With this mechanism, a moth never loses its best solution [49]. Some attributes of this algorithm are as follows:

  • •It takes different values to converge moth in any point around the flame.
  • •Distance to the flame is lowered to be eventually minimized.
  • •When the position gets closer to the flame, the updated positions around the flame become more frequent.

As another method, the Multi-Verse Optimizer is based on a multiverse theory which proposes there are other universes besides the one in which we all live. According to this theory, there are more than one big bang in the universe, and each big bang leads to the birth of a new universe [50]. Multi-Verse Optimizer (MVO) is mainly inspired by three phenomena in cosmology: white holes, black holes, and wormholes. A white hole has never been observed in our universe, but physicists believe the big bang could be considered a white hole [51]. Black holes, which behave completely in contrast to white holes, attract everything including light beams with their extremely high gravitational force [52]. In the multiverse theory, wormholes are time and space tunnels that allow objects to move instantly between any two corners of a universe (or even simultaneously from one universe to another) [53]. Based on these three concepts, mathematical models are designed to perform exploration, exploitation, and local search, respectively. The concept of white and black holes is implied as an exploration phase, while the concept of wormholes is considered as an exploitation phase by MVO. Additionally, each solution is analogous to a universe, and each variable in the solution represents an object in that universe. Furthermore, each solution is assigned an inflation rate, and the time is used instead of iterations. Following are the universe rules in MVO:

  • •The possibility of having white hole increases with the inflation rate.
  • •The possibility of having black hole decreases with the inflation rate.
  • •Objects tend to pass through black holes more frequently in universes with lower inflation rates.
  • •Regardless of inflation rate, wormholes may cause objects in universes to move randomly towards the best universe. [54]

Modeling the white/black hole tunnels and exchanging objects of universes mathematically was accomplished by using the roulette wheel mechanism. With every iteration, the universes are sorted according to their inflation rates, then, based on the roulette wheel, the one with the white hole is selected as the local extremum solution. This is accomplished through the following steps:

Assume that

(16)���=����1<��(��)����1≥��(��)

Where ��� represents the jth parameter of the ith universe, Ui indicates the ith universe, NI(Ui) is normalized inflation rate of the ith universe, r1 is a random number in [0,1], and j xk shows the jth parameter of the kth universe selected by a roulette wheel selection mechanism [54]. It is assumed that wormhole tunnels always exist between a universe and the best universe formed so far. This mechanism is as follows:(17)���=if�2<���:��+���×((���-���)×�4+���)�3<0.5��-���×((���-���)×�4+���)�3≥0.5����:���where Xj indicates the jth parameter of the best universe formed so far, TDR and WEP are coefficients, where Xj indicates the jth parameter of the best universelbjshows the lower bound of the jth variable, ubj is the upper bound of the jth variable, and r2, r3, and r4 are random numbers in [1], [54].

Finally, one of the newest optimization algorithms is WOA. The WOA algorithm simulates the movement of prey and the whale’s discipline when looking for their prey. Among several species, Humpback whales have a specific method of hunting [55]. Humpback whales can recognize the location of prey and encircle it before hunting. The optimal design position in the search space is not known a priori, and the WOA algorithm assumes that the best candidate solution is either the target prey or close to the optimum. This foraging behavior is called the bubble-net feeding method. Two maneuvers are associated with bubbles: upward spirals and double loops. A unique behavior exhibited only by humpback whales is bubble-net feeding. In fact, The WOA algorithm starts with a set of random solutions. At each iteration, search agents update their positions for either a randomly chosen search agent or the best solution obtained so far [56], [55]. When the best search agent is determined, the other search agents will attempt to update their positions toward that agent. It is important to note that humpback whales swim around their prey simultaneously in a circular, shrinking circle and along a spiral-shaped path. By using a mathematical model, the spiral bubble-net feeding maneuver is optimized. The following equation represents this behavior:(18)�→(�+1)=�′→·�bl·cos(2��)+�∗→(�)

Where:(19)�′→=|�∗→(�)-�→(�)|

X→(t+ 1) indicates the distance of the it h whale to the prey (best solution obtained so far),� is a constant for defining the shape of the logarithmic spiral, l is a random number in [−1, 1], and dot (.) is an element-by-element multiplication [55].

Comparing the four above-mentioned methods, simulations are run with 10 search agents for 400 iterations. In Figure 15, there are 20 plots the optimal values of different parameters in optimization algorithms. The five parameters of this study are freeboard, bottom elevations, number of ribs on the converter, rib thickness, and rib Height. The optimal value for each was found by optimization algorithms, naming WOA, MVO, MFO, and GWO. By looking through the first row, the freeboard parameter converges to its maximum possible value in the optimization process of GWO after 300 iterations. Similarly, MFO finds the same result as GWO. In contrast, the freeboard converges to its minimum possible value in MVO optimizing process, which indicates positioning the converter under the water. Furthermore, WOA found the optimal value of freeboard as around 0.02 after almost 200 iterations. In the second row, the bottom elevation is found at almost 0.11 (m) in all algorithms; however, the curves follow different trends in each algorithm. The third row shows the number of ribs, where results immediately reveal that it should be over 4. All algorithms coincide at 5 ribs as the optimal number in this process. The fourth row displays the trends of algorithms to find optimal rib thickness. MFO finds the optimal value early and sets it to around 0.022, while others find the same value in higher iterations. Finally, regarding the rib height, MVO, MFO, and GWO state that the optimal value is 0.06 meters, but WOA did not find a higher value than 0.039.

4.2. HCMVO Bi-level Approach

Despite several strong search characteristics of MVO and its high performance in various optimization problems, it suffers from a few deficiencies in local and global search mechanisms. For instance, it is trapped in the local optimum when wormholes stochastically generate many solutions near the best universe achieved throughout iterations, especially in solving complex multimodal problems with high dimensions [57]. Furthermore, MVO needs to be modified by an escaping strategy from the local optima to enhance the global search abilities. To address these shortages, we propose a fast and effective meta-algorithm (HCMVO) to combine MVO with a Random-restart hill-climbing local search. This meta-algorithm uses MVO on the upper level to develop global tracking and provide a range of feasible and proper solutions. The hill-climbing algorithm is designed to develop a comprehensive neighborhood search around the best-found solution proposed by the upper-level (MVO) when MVO is faced with a stagnation issue or falling into a local optimum. The performance threshold is formulated as follows.(20)Δ����THD=∑�=1�����TH��-����TH��-1�where BestTHDis the best-found solution per generation, andM is related to the domain of iterations to compute the average performance of MVO. If the proposed best solution by the local search is better than the initial one, the global best of MVO will be updated. HCMVO iteratively runs hill climbing when the performance of MVO goes down, each time with an initial condition to prepare for escaping such undesirable situations. In order to get a better balance between exploration and exploitation, the search step size linearly decreases as follows:(21)��=��-����Ma�iter��+1where iter and Maxiter are the current iteration and maximum number of evaluation, respectively. �� stands for the step size of the neighborhood search. Meanwhile, this strategy can improve the convergence rate of MVO compared with other algorithms.

Algorithm 1 shows the technical details of the proposed optimization method (HCMVO). The initial solution includes freeboard (�), bottom elevation (�), number of ribs (Nr), rib thickness (�), and rib height(�).

5. Conclusion

The high trend of diminishing worldwide energy resources has entailed a great crisis upon vulnerable societies. To withstand this effect, developing renewable energy technologies can open doors to a more reliable means, among which the wave energy converters will help the coastal residents and infrastructure. This paper set out to determine the optimized design for such devices that leads to the highest possible power output. The main goal of this research was to demonstrate the best design for an oscillating surge wave energy converter using a novel metaheuristic optimization algorithm. In this regard, the methodology was devised such that it argued the effects of influential parameters, including wave characteristics, WEC design, and interaction criteria.

To begin with, a numerical model was developed in Flow 3D software to simulate the response of the flap of a wave energy converter to incoming waves, followed by a validation study based upon a well-reputed experimental study to verify the accuracy of the model. Secondly, the hydrodynamics of the flap was investigated by incorporating the turbulence. The effect of depth, wave height, and wave period are also investigated in this part. The influence of two novel ideas on increasing the wave-converter interaction was then assessed: i) designing a flap with different widths in the upper and lower part, and ii) adding ribs on the surface of the flap. Finally, four trending single-objective metaheuristic optimization methods

Empty CellAlgorithm 1: Hill Climb Multiverse Optimization
01:procedure HCMVO
02:�=30,�=5▹���������������������������������
03:�=〈F1,B1,N,R,H1〉,…〈FN,B2,N,R,HN〉⇒lb1N⩽�⩽ubN
04:Initialize parameters�ER,�DR,�EP,Best�,���ite��▹Wormhole existence probability (WEP)
05:��=����(��)
06:��=Normalize the inflation rate��
07:for iter in[1,⋯,���iter]do
08:for�in[1,⋯,�]do
09:Update�EP,�DR,Black����Index=�
10:for���[1,⋯,�]��
11:�1=����()
12:if�1≤��(��)then
13:White HoleIndex=Roulette�heelSelection(-��)
14:�(Black HoleIndex,�)=��(White HoleIndex,�)
15:end if
16:�2=����([0,�])
17:if�2≤�EPthen
18:�3=����(),�4=����()
19:if�3<0.5then
20:�1=((��(�)-��(�))�4+��(�))
21:�(�,�)=Best�(�)+�DR�
22:else
23:�(�,�)=Best�(�)-�DR�
24:end if
25:end if
26:end for
27:end for
28:�HD=����([�1,�2,⋯,�Np])
29:Bes�TH�itr=����HD
30:ΔBestTHD=∑�=1�BestTII��-BestTII��-1�
31:ifΔBestTHD<��then▹Perform hill climbing local search
32:BestTHD=����-�lim��������THD
33:end if
34:end for
35:return�,BestTHD▹Final configuration
36:end procedure

The implementation details of the hill-climbing algorithm applied in HCMPA can be seen in Algorithm 2. One of the critical parameters isg, which denotes the resolution of the neighborhood search around the proposed global best by MVO. If we set a small step size for hill-climbing, the convergence speed will be decreased. On the other hand, a large step size reinforces the exploration ability. Still, it may reduce the exploitation ability and in return increase the act of jumping from a global optimum or surfaces with high-potential solutions. Per each decision variable, the neighborhood search evaluates two different direct searches, incremental or decremental. After assessing the generated solutions, the best candidate will be selected to iterate the search algorithm. It is noted that the hill-climbing algorithm should not be applied in the initial iteration of the optimization process due to the immense tendency for converging to local optima. Meanwhile, for optimizing largescale problems, hill-climbing is not an appropriate selection. In order to improve understanding of the proposed hybrid optimization algorithm’s steps, the flowchart of HCMVO is designed and can be seen in Figure 16.

Figure 17 shows the observed capture factor (which is the absorbed energy with respect to the available energy) by each optimization algorithm from iterations 1 to 400. The algorithms use ten search agents in their modified codes to find the optimal solutions. While GWO and MFO remain roughly constant after iterations 54 and 40, the other three algorithms keep improving the capture factor. In this case, HCMVO and MVO worked very well in the optimizing process with a capture factor obtained by the former as 0.594 and by the latter as 0.593. MFO almost found its highest value before the iteration 50, which means the exploration part of the algorithm works out well. Similarly, HCMVO does the same. However, it keeps finding the better solution during the optimization process until the last iteration, indicating the strong exploitation part of the algorithm. GWO reveals a weakness in exploration and exploitation because not only does it evoke the least capture factor value, but also the curve remains almost unchanged throughout 350 iterations.

Figure 18 illustrates complex interactions between the five optimization parameters and the capture factor for HCMVO (a), MPA (b), and MFO (c) algorithms. The first interesting observation is that there is a high level of nonlinear relationships among the setting parameters that can make a multi-modal search space. The dark blue lines represent the best-found configuration throughout the optimisation process. Based on both HCMVO (a) and MVO (b), we can infer that the dark blue lines concentrate in a specific range, showing the high convergence ability of both HCMVO and MVO. However, MFO (c) could not find the exact optimal range of the decision variables, and the best-found solutions per generation distribute mostly all around the search space.

Empty CellAlgorithm 1: Hill Climb Multiverse Optimization
01:procedure HCMVO
02:Initialization
03:Initialize the constraints��1�,��1�
04:�1�=Mi�1�+���1�/�▹Compute the step size,�is search resolution
05:So�1=〈�,�,�,�,�〉▹���������������
06:�������1=����So�1▹���������ℎ���������
07:Main loop
08:for iter≤���ita=do
09:���=���±��
10:while�≤���(Sol1)do
11:���=���+�,▹����ℎ���ℎ��������ℎ
12:fitness��iter=�������
13:t = t+1
14:end while
15:〈�����,������max〉=����������
16:���itev=���Inde�max▹�������ℎ�������������������������������ℎ�������
17:��=��-����Max��+1▹�����������������
18:end for
19:return���iter,����
20:end procedure

were utilized to illuminate the optimum values of the design parameters, and the best method was chosen to develop a new algorithm that performs both local and global search methods.

The correlation between hydrodynamic parameters and the capture factor of the converter was supported by the results. For any given water depth, the capture factor increases as the wave period increases, until a certain wave period value (6 seconds) is reached, after which the capture factor gradually decreases. It is expected since the flap cannot oscillate effectively when the wavelength is too short for a certain water depth. Conversely, when the wavelength is too long, the capture factor decreases. Furthermore, under a constant wave period, increasing the water depth does not affect the capture factor. Regarding the sensitivity analysis, the study found that increasing the flap bottom elevation causes turbulence flow behind the flap and limitation of rotation, which leads to less interaction with the incoming waves. Furthermore, while keeping the flap bottom elevation constant, increasing the freeboard improves the capture factor. Overtopping happens when the freeboard is negative and the flap is below the water surface, which has a detrimental influence on converter performance. Furthermore, raising the freeboard causes the wave impact to become more violent, which increases converter performance.

In the last part, we discussed the search process of each algorithm and visualized their performance and convergence curves as they try to find the best values for decision variables. Among the four selected metaheuristic algorithms, the Multi-verse Optimizer proved to be the most effective in achieving the best answer in terms of the WEC capture factor. However, the MVO needed modifications regarding its escape approach from the local optima in order to improve its global search capabilities. To overcome these constraints, we presented a fast and efficient meta-algorithm (HCMVO) that combines MVO with a Random-restart hill-climbing local search. On a higher level, this meta-algorithm employed MVO to generate global tracking and present a range of possible and appropriate solutions. Taken together, the results demonstrated that there is a significant degree of nonlinearity among the setup parameters that might result in a multimodal search space. Since MVO was faced with a stagnation issue or fell into a local optimum, we constructed a complete neighborhood search around the best-found solution offered by the upper level. In sum, the newly-developed algorithm proved to be highly effective for the problem compared to other similar optimization methods. The strength of the current findings may encourage future investigation on design optimization of wave energy converters using developed geometry as well as the novel approach.

CRediT authorship contribution statement

Erfan Amini: Conceptualization, Methodology, Validation, Data curation, Writing – original draft, Writing – review & editing, Visualization. Mahdieh Nasiri: Conceptualization, Methodology, Validation, Data curation, Writing – original draft, Writing – review & editing, Visualization. Navid Salami Pargoo: Writing – original draft, Writing – review & editing. Zahra Mozhgani: Conceptualization, Methodology. Danial Golbaz: Writing – original draft. Mehrdad Baniesmaeil: Writing – original draft. Meysam Majidi Nezhad: . Mehdi Neshat: Supervision, Conceptualization, Writing – original draft, Writing – review & editing, Visualization. Davide Astiaso Garcia: Supervision. Georgios Sylaios: Supervision.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This research has been carried out within ILIAD (Inte-grated Digital Framework for Comprehensive Maritime Data and Information Services) project that received funding from the European Union’s H2020 programme.

Data availability

Data will be made available on request.

References

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Figure 1: Mold drawings

3D Flow and Temperature Analysis of Filling a Plutonium Mold

플루토늄 주형 충전의 3D 유동 및 온도 분석

Authors: Orenstein, Nicholas P. [1]

Publication Date:2013-07-24
Research Org.: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.: DOE/LANL
OSTI Identifier: 1088904
Report Number(s): LA-UR-13-25537
DOE Contract Number: AC52-06NA25396
Resource Type: Technical Report
Country of Publication: United States
Language: English
Subject: Engineering(42); Materials Science(36); Radiation Chemistry, Radiochemistry, & Nuclear Chemistry(38)

Introduction

The plutonium foundry at Los Alamos National Laboratory casts products for various special nuclear applications. However, plutonium’s radioactivity, material properties, and security constraints complicate the ability to perform experimental analysis of mold behavior. The Manufacturing Engineering and Technologies (MET-2) group previously developed a graphite mold to vacuum cast small plutonium disks to be used by the Department of Homeland Security as point sources for radiation sensor testing.

A two-stage pouring basin consisting of a funnel and an angled cavity directs the liquid into a vertical runner. A stack of ten disk castings connect to the runner by horizontal gates. Volumetric flow rates were implemented to limit overflow into the funnel and minimize foundry returns. Models using Flow-3D computational fluid dynamics software are employed here to determine liquid Pu flow paths, optimal pour regimes, temperature changes, and pressure variations.

Setup

Hardcopy drawings provided necessary information to create 3D .stl models for import into Flow-3D (Figs. 1 and 2). The mesh was refined over several iterations to isolate the disk cavities, runner, angled cavity, funnel, and input pour. The final flow and mold-filling simulation utilizes a fine mesh with ~5.5 million total cells. For the temperature study, the mesh contained 1/8 as many cells to reduce computational time and set temperatures to 850 °C for the molten plutonium and 500 °C for the solid graphite mold components (Fig. 3).

Flow-3D solves mass continuity and Navier-Stokes momentum equations over the structured rectangular grid model using finite difference and finite volume numerical algorithms. The solver includes terms in the momentum equation for body and viscous accelerations and uses convective heat transfer.

Simulation settings enabled Flow-3D physics calculations for gravity at 980.665 cm/s 2 in the negative Z direction (top of mold to bottom); viscous, turbulent, incompressible flow using dynamically-computed Renormalized Group Model turbulence calculations and no-slip/partial slip wall shear, and; first order, full energy equation heat transfer.

Mesh boundaries were all set to symmetric boundary conditions except for the Zmin boundary set to outflow and the Zmax boundary set to a volume flow. Vacuum casting conditions and the high reactivity of remaining air molecules with Pu validate the assumption of an initially fluidless void.

Results

The flow follows a unique three-dimensional path. The mold fills upwards with two to three disks receiving fluid in a staggered sequence. Figures 5-9 show how the fluid fills the cavity, and Figure 7 includes the color scale for pressure levels in these four figures. The narrow gate causes a high pressure region which forces the fluid to flow down the cavity centerline.

It proceeds to splash against the far wall and then wrap around the circumference back to the gate (Figs. 5 and 6). Flow in the angled region of the pouring basin cascades over the bottom ledge and attaches to the far wall of the runner, as seen in Figure 7.

This channeling becomes less pronounced as fluid volume levels increase. Finally, two similar but non-uniform depressed regions form about the centerline. These regions fill from their perimeter and bottom until completion (Fig. 8). Such a pattern is counter, for example, to a steady scenario in which a circle of molten Pu encompassing the entire bottom surface rises as a growing cylinder.

Cavity pressure becomes uniform when the cavity is full. Pressure levels build in the rising well section of the runner, where impurities were found to settle in actual casting. Early test simulations optimized the flow as three pours so that the fluid would never overflow to the funnel, the cavities would all fill completely, and small amounts of fluid would remain as foundry returns in the angled cavity.

These rates and durations were translated to the single 2.7s pour at 100 cm 3 per second used here. Figure 9 shows anomalous pressure fluctuations which occurred as the cavities became completely filled. Multiple simulations exhibited a rapid change in pressure from positive to negative and back within the newly-full disk and surrounding, already-full disks.

The time required to completely fill each cavity is plotted in Figure 10. Results show negligible temperature change within the molten Pu during mold filling and, as seen in Figure 11, at fill completion.

Figure 1: Mold drawings
Figure 1: Mold drawings
Figure 2: Mold Assembly
Figure 2: Mold Assembly
Figure 4: Actual mold and cast Pu
Figure 4: Actual mold and cast Pu
Figure 5: Bottom cavity filling from runner
Figure 5: Bottom cavity filling from runner
Figure 6: Pouring and filling
Figure 6: Pouring and filling
Figure 8: Edge detection of cavity fill geometry. Two similar depressed areas form about the centerline. Top cavity shown; same pressure scale as other figures
Figure 8: Edge detection of cavity fill geometry. Two similar depressed areas form about the centerline. Top cavity shown; same pressure scale as other figures
Figure 10: Cavity fill times,from first fluid contact with pouring basin, Figure 11:Fluid temperature remains essentially constant
Figure 10: Cavity fill times,from first fluid contact with pouring basin, Figure 11:Fluid temperature remains essentially constant

Conclusions

Non-uniform cavity filling could cause crystal microstructure irregularities during solidification. However, the small temperature changes seen – due to large differences in specific heat between Pu and graphite – over a relatively short time make such problems unlikely in this case.

In the actual casting, cooling required approximately ten minutes. This large difference in time scales further reduces the chance for temperature effects in such a superheated scenario. Pouring basin emptying decreases pressure at the gate which extends fill time of the top two cavities.

The bottom cavity takes longer to fill because fluid must first enter the runner and fill the well. Fill times continue linearly until the top two cavities. The anomalous pressure fluctuations may be due to physical attempts by the system to reach equilibrium, but they are more likely due to numerical errors in the Flow3D solver.

Unsuccessful tests were performed to remove them by halving fluid viscosity. The fine mesh reduced, but did not eliminate, the extent of the fluctuations. Future work is planned to study induction and heat transfer in the full Pu furnace system, including quantifying temporal lag of the cavity void temperature to the mold wall temperature during pre-heat and comparing heat flux levels between furnace components during cool-down.

Thanks to Doug Kautz for the opportunity to work with MET-2 and for assigning an interesting unclassified project. Additional thanks to Mike Bange for CFD guidance, insight of the project’s history, and draft review.

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Sketch of approach channel and spillway of the Kamal-Saleh dam

CFD modeling of flow pattern in spillway’s approach channel

Sustainable Water Resources Management volume 1, pages245–251 (2015)Cite this article

Abstract

Analysis of behavior and hydraulic characteristics of flow over the dam spillway is a complicated task that takes lots of money and time in water engineering projects planning. To model those hydraulic characteristics, several methods such as physical and numerical methods can be used. Nowadays, by utilizing new methods in computational fluid dynamics (CFD) and by the development of fast computers, the numerical methods have become accessible for use in the analysis of such sophisticated flows. The CFD softwares have the capability to analyze two- and three-dimensional flow fields. In this paper, the flow pattern at the guide wall of the Kamal-Saleh dam was modeled by Flow 3D. The results show that the current geometry of the left wall causes instability in the flow pattern and making secondary and vortex flow at beginning approach channel. This shape of guide wall reduced the performance of weir to remove the peak flood discharge.

댐 여수로 흐름의 거동 및 수리학적 특성 분석은 물 공학 프로젝트 계획에 많은 비용과 시간이 소요되는 복잡한 작업입니다. 이러한 수력학적 특성을 모델링하기 위해 물리적, 수치적 방법과 같은 여러 가지 방법을 사용할 수 있습니다. 요즘에는 전산유체역학(CFD)의 새로운 방법을 활용하고 빠른 컴퓨터의 개발로 이러한 정교한 흐름의 해석에 수치 방법을 사용할 수 있게 되었습니다. CFD 소프트웨어에는 2차원 및 3차원 유동장을 분석하는 기능이 있습니다. 본 논문에서는 Kamal-Saleh 댐 유도벽의 흐름 패턴을 Flow 3D로 모델링하였다. 결과는 왼쪽 벽의 현재 형상이 흐름 패턴의 불안정성을 유발하고 시작 접근 채널에서 2차 및 와류 흐름을 만드는 것을 보여줍니다. 이러한 형태의 안내벽은 첨두방류량을 제거하기 위해 둑의 성능을 저하시켰다.

Introduction

Spillways are one of the main structures used in the dam projects. Design of the spillway in all types of dams, specifically earthen dams is important because the inability of the spillway to remove probable maximum flood (PMF) discharge may cause overflow of water which ultimately leads to destruction of the dam (Das and Saikia et al. 2009; E 2013 and Novak et al. 2007). So study on the hydraulic characteristics of this structure is important. Hydraulic properties of spillway including flow pattern at the entrance of the guide walls and along the chute. Moreover, estimating the values of velocity and pressure parameters of flow along the chute is very important (Chanson 2004; Chatila and Tabbara 2004). The purpose of the study on the flow pattern is the effect of wall geometry on the creation transverse waves, flow instability, rotating and reciprocating flow through the inlet of spillway and its chute (Parsaie and Haghiabi 2015a, b; Parsaie et al. 2015; Wang and Jiang 2010). The purpose of study on the values of velocity and pressure is to calculate the potential of the structure to occurrence of phenomena such as cavitation (Fattor and Bacchiega 2009; Ma et al. 2010). Sometimes, it can be seen that the spillway design parameters of pressure and velocity are very suitable, but geometry is considered not suitable for conducting walls causing unstable flow pattern over the spillway, rotating flows at the beginning of the spillway and its design reduced the flood discharge capacity (Fattor and Bacchiega 2009). Study on spillway is usually conducted using physical models (Su et al. 2009; Suprapto 2013; Wang and Chen 2009; Wang and Jiang 2010). But recently, with advances in the field of computational fluid dynamics (CFD), study on hydraulic characterist–ics of this structure has been done with these techniques (Chatila and Tabbara 2004; Zhenwei et al. 2012). Using the CFD as a powerful technique for modeling the hydraulic structures can reduce the time and cost of experiments (Tabbara et al. 2005). In CFD field, the Navier–Stokes equation is solved by powerful numerical methods such as finite element method and finite volumes (Kim and Park 2005; Zhenwei et al. 2012). In order to obtain closed-form Navier–Stokes equations turbulence models, such k − ε and Re-Normalisation Group (RNG) models have been presented. To use the technique of computational fluid dynamics, software packages such as Fluent and Flow 3D, etc., are provided. Recently, these two software packages have been widely used in hydraulic engineering because the performance and their accuracy are very suitable (Gessler 2005; Kim 2007; Kim et al. 2012; Milési and Causse 2014; Montagna et al. 2011). In this paper, to assess the flow pattern at Kamal-Saleh guide wall, numerical method has been used. All the stages of numerical modeling were conducted in the Flow 3D software.

Materials and methods

Firstly, a three-dimensional model was constructed according to two-dimensional map that was prepared for designing the spillway. Then a small model was prepared with scale of 1:80 and entered into the Flow 3D software; all stages of the model construction was conducted in AutoCAD 3D. Flow 3D software numerically solved the Navier–Stokes equation by finite volume method. Below is a brief reference on the equations that used in the software. Figure 1 shows the 3D sketch of Kamal-Saleh spillway and Fig. 2 shows the uploading file of the Kamal-Saleh spillway in Flow 3D software.

figure 1
Fig. 1
figure 2
Fig. 2

Review of the governing equations in software Flow 3D

Continuity equation at three-dimensional Cartesian coordinates is given as Eq (1).

vf∂ρ∂t+∂∂x(uAx)+∂∂x(vAy)+∂∂x(wAz)=PSORρ,vf∂ρ∂t+∂∂x(uAx)+∂∂x(vAy)+∂∂x(wAz)=PSORρ,

(1)

where u, v, z are velocity component in the x, y, z direction; A x, A y, A z cross-sectional area of the flow; ρ fluid density; PSOR the source term; v f is the volume fraction of the fluid and three-dimensional momentum equations given in Eq (2).

∂u∂t+1vf(uAx∂u∂x+vAy∂u∂y+wAz∂u∂z)=−1ρ∂P∂x+Gx+fx∂v∂t+1vf(uAx∂v∂x+vAy∂v∂y+wAz∂v∂z)=−1ρ∂P∂y+Gy+fy∂w∂t+1vf(uAx∂w∂x+vAy∂w∂y+wAz∂w∂z)=−1ρ∂P∂y+Gz+fz,∂u∂t+1vf(uAx∂u∂x+vAy∂u∂y+wAz∂u∂z)=−1ρ∂P∂x+Gx+fx∂v∂t+1vf(uAx∂v∂x+vAy∂v∂y+wAz∂v∂z)=−1ρ∂P∂y+Gy+fy∂w∂t+1vf(uAx∂w∂x+vAy∂w∂y+wAz∂w∂z)=−1ρ∂P∂y+Gz+fz,

(2)

where P is the fluid pressure; G x, G y, G z the acceleration created by body fluids; f x, f y, f z viscosity acceleration in three dimensions and v f is related to the volume of fluid, defined by Eq. (3). For modeling of free surface profile the VOF technique based on the volume fraction of the computational cells has been used. Since the volume fraction F represents the amount of fluid in each cell, it takes value between 0 and 1.

∂F∂t+1vf[∂∂x(FAxu)+∂∂y(FAyv)+∂∂y(FAzw)]=0∂F∂t+1vf[∂∂x(FAxu)+∂∂y(FAyv)+∂∂y(FAzw)]=0

(3)

Turbulence models

Flow 3D offers five types of turbulence models: Prantl mixing length, k − ε equation, RNG models, Large eddy simulation model. Turbulence models that have been proposed recently are based on Reynolds-averaged Navier–Stokes equations. This approach involves statistical methods to extract an averaged equation related to the turbulence quantities.

Steps of solving a problem in Flow 3D software

(1) Preparing the 3D model of spillway by AutoCAD software. (2) Uploading the file of 3D model in Flow 3D software and defining the problem in the software and checking the final mesh. (3) Choosing the basic equations that should be solved. (4) Defining the characteristics of fluid. (5) Defining the boundary conditions; it is notable that this software has a wide range of boundary conditions. (6) Initializing the flow field. (7) Adjusting the output. (8) Adjusting the control parameters, choice of the calculation method and solution formula. (9) Start of calculation. Figure 1 shows the 3D model of the Kamal-Saleh spillway; in this figure, geometry of the left and right guide wall is shown.

Figure 2 shows the uploading of the 3D spillway dam in Flow 3D software. Moreover, in this figure the considered boundary condition in software is shown. At the entrance and end of spillway, the flow rate or fluid elevation and outflow was considered as BC. The bottom of spillway was considered as wall and left and right as symmetry.

Model calibration

Calibration of the Flow 3D for modeling the effect of geometry of guide wall on the flow pattern is included for comparing the results of Flow 3D with measured water surface profile. Calibration the Flow 3D software could be conducted in two ways: first, changing the value of upstream boundary conditions is continued until the results of water surface profile of the Flow 3D along the spillway successfully covered the measurement water surface profile; second is the assessment the mesh sensitivity. Analyzing the size of mesh is a trial-and-error process where the size of mesh is evaluated form the largest to the smallest. With fining the size of mesh the accuracy of model is increased; whereas, the cost of computation is increased. In this research, the value of upstream boundary condition was adjusted with measured data during the experimental studies on the scaled model and the mesh size was equal to 1 × 1 × 1 cm3.

Results and discussion

The behavior of water in spillway is strongly affected by the flow pattern at the entrance of the spillway, the flow pattern formation at the entrance is affected by the guide wall, and choice of an optimized form for the guide wall has a great effect on rising the ability of spillway for easy passing the PMF, so any nonuniformity in flow in the approach channel can cause reduction of spillway capacity, reduction in discharge coefficient of spillway, and even probability of cavitation. Optimizing the flow guiding walls (in terms of length, angle and radius) can cause the loss of turbulence and flow disturbances on spillway. For this purpose, initially geometry proposed for model for the discharge of spillway dam, Kamal-Saleh, 80, 100, and 120 (L/s) were surveyed. These discharges of flow were considered with regard to the flood return period, 5, 100 and 1000 years. Geometric properties of the conducting guidance wall are given in Table 1.Table 1 Characteristics and dimensions of the guidance walls tested

Full size table

Results of the CFD simulation for passing the flow rate 80 (L/s) are shown in Fig. 3. Figure 3 shows the secondary flow and vortex at the left guide wall.

figure 3
Fig. 3

For giving more information about flow pattern at the left and right guide wall, Fig. 4 shows the flow pattern at the right side guide wall and Fig. 5 shows the flow pattern at the left side guide wall.

figure 4
Fig. 4
figure 5
Fig. 5

With regard to Figs. 4 and 5 and observing the streamlines, at discharge equal to 80 (L/s), the right wall has suitable performance but the left wall has no suitable performance and the left wall of the geometric design creates a secondary and circular flow, and vortex motion in the beginning of the entrance of spillway that creates cross waves at the beginning of spillway. By increasing the flow rate (Q = 100 L/s), at the inlet spillway secondary flows and vortex were removed, but the streamline is severely distorted. Results of the guide wall performances at the Q = 100 (L/s) are shown in Fig. 6.

figure 6
Fig. 6

Also more information about the performance of each guide wall can be derived from Figs. 7 and 8. These figures uphold that the secondary and vortex flows were removed, but the streamlines were fully diverted specifically near the left side guide wall.

figure 7
Fig. 7
figure 8
Fig. 8

As mentioned in the past, these secondary and vortex flows and diversion in streamline cause nonuniformity and create cross wave through the spillway. Figure 9 shows the cross waves at the crest of the spillway.

figure 9
Fig. 9

The performance of guide walls at the Q = 120 (L/s) also was assessed. The result of simulation is shown in Fig. 10. Figures 11 and 12 show a more clear view of the streamlines near to right and left side guide wall, respectively. As seen in Fig. 12, the left side wall still causes vortex flow and creation of and diversion in streamline.

figure 10
Fig. 10
figure 11
Fig. 11
figure 12
Fig. 12

The results of the affected left side guide wall shape on the cross wave creation are shown in Fig. 13. As seen from Fig. 3, the left side guide wall also causes cross wave at the spillway crest.

figure 13
Fig. 13

As can be seen clearly in Figs. 9 and 13, by moving from the left side to the right side of the spillway, the cross waves and the nonuniformity in flow is removed. By reviewing Figs. 9 and 13, it is found that the right side guide wall removes the cross waves and nonuniformity. With this point as aim, a geometry similar to the right side guide wall was considered instead of the left side guide wall. The result of simulation for Q = 120 (L/s) is shown in Fig. 14. As seen from this figure, the proposed geometry for the left side wall has suitable performance smoothly passing the flow through the approach channel and spillway.

figure 14
Fig. 14

More information about the proposed shape for the left guide wall is shown in Fig. 15. As seen from this figure, this shape has suitable performance for removing the cross waves and vortex flows.

figure 15
Fig. 15

Figure 16 shows the cross section of flow at the crest of spillway. As seen in this figure, the proposed shape for the left side guide wall is suitable for removing the cross waves and secondary flows.

figure 16
Fig. 16

Conclusion

Analysis of behavior and hydraulic properties of flow over the spillway dam is a complicated task which is cost and time intensive. Several techniques suitable to the purposes of study have been undertaken in this research. Physical modeling, usage of expert experience, usage of mathematical models on simulation flow in one-dimensional, two-dimensional and three-dimensional techniques, are some of the techniques utilized to study this phenomenon. The results of the modeling show that the CFD technique is a suitable tool for simulating the flow pattern in the guide wall. Using this tools helps the designer for developing the optimal shape for hydraulic structure which the flow pattern through them are important.

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  1. Department of Water Engineering, Lorestan University, Khorram Abad, IranAbbas Parsaie, Amir Hamzeh Haghiabi & Amir Moradinejad

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Correspondence to Abbas Parsaie.

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Parsaie, A., Haghiabi, A.H. & Moradinejad, A. CFD modeling of flow pattern in spillway’s approach channel. Sustain. Water Resour. Manag. 1, 245–251 (2015). https://doi.org/10.1007/s40899-015-0020-9

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  • Received28 April 2015
  • Accepted28 August 2015
  • Published15 September 2015
  • Issue DateSeptember 2015
  • DOIhttps://doi.org/10.1007/s40899-015-0020-9

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Keywords

  • Approach channel
  • Kamal-Saleh dam
  • Guide wall
  • Flow pattern
  • Numerical modeling
  • Flow 3D software
    원문 보기
    Effect of tailwater depth on non-cohesive earth dam failure due to overtopping

    Effect of tailwater depth on non-cohesive earth dam failure due to overtopping

    범람으로 인한 비점착성 흙댐 붕괴에 대한 테일워터 깊이의 영향

    ShaimaaAmanaMohamedAbdelrazek RezkbRabieaNasrc

    Abstract

    본 연구에서는 범람으로 인한 토사댐 붕괴에 대한 테일워터 깊이의 영향을 실험적으로 조사하였다. 테일워터 깊이의 네 가지 다른 값을 검사합니다. 각 실험에 대해 댐 수심 측량 프로파일의 진화, 고장 기간, 침식 체적 및 유출 수위곡선을 관찰하고 기록합니다.

    결과는 tailwater 깊이를 늘리면 고장 시간이 최대 57% 감소하고 상대적으로 침식된 마루 높이가 최대 77.6% 감소한다는 것을 보여줍니다. 또한 상대 배수 깊이가 3, 4, 5인 경우 누적 침식 체적의 감소는 각각 23, 36.5 및 75%인 반면 최대 유출량의 감소는 각각 7, 14 및 17.35%입니다.

    실험 결과는 침식 과정을 복제할 때 Flow 3D 소프트웨어의 성능을 평가하는 데 활용됩니다. 수치 모델은 비응집성 흙댐의 침식 과정을 성공적으로 시뮬레이션합니다.

    The influence of tailwater depth on earth dam failure due to overtopping is investigated experimentally in this work. Four different values of tailwater depths are examined. For each experiment, the evolution of the dam bathymetry profile, the duration of failure, the eroded volume, and the outflow hydrograph are observed and recorded. The results reveal that increasing the tailwater depth reduces the time of failure by up to 57% and decreases the relative eroded crest height by up to 77.6%. In addition, for relative tailwater depths equal to 3, 4, and 5, the reduction in the cumulative eroded volume is 23, 36.5, and 75%, while the reduction in peak discharge is 7, 14, and 17.35%, respectively. The experimental results are utilized to evaluate the performance of the Flow 3D software in replicating the erosion process. The numerical model successfully simulates the erosion process of non-cohesive earth dams.

    Keywords

    Earth dam, Eroded volume, Flow 3D model, Non-cohesive soil, Overtopping failure, Tailwater depth

    Notation

    d50

    Mean partical diameterWc

    Optimum water contentZo

    Dam height (cm)do

    Tailwater depth (cm)Zeroded

    Eroded height of the dam measured at distance of 0.7 m from the dam heel (cm)t

    Total time of failure (sec)t1

    Time of crest width erosion (sec)Zcrest

    The crest height (cm)Vtotal

    Total volume of the dam (m3)Veroded

    Cumulative eroded volume (m3)RMSE

    The statistical variable root- mean- square errord

    Degree of agreement indexyu.s.

    The upstream water depth (cm)yd.s

    The downstream water depth (cm)H

    Water surface elevation over sharp crested weir (cm)Q

    Outflow discharge (liter/sec)Qpeak

    Peak discharge (liter/sec)

    1. Introduction

    Earth dams are compacted structures composed of natural materials that are usually mined or quarried from local locations. The failures of the earth dams have proven to be deadly, destructive, and costly. According to People’s Daily, two earthen dams, Yong’an Dam and Xinfa Dam located in Hulun Buir City in North China’s Inner Mongolia failed on 2021, due to a surge in the water level of the Nuomin River caused by heavy rain. The dam breach affected 16,660 people, flooded 325,622 mu of farmland (21708.1 ha), and destroyed 22 bridges, 124 culverts, and 15.6 km of roadways. Also, the failure of south fork dam (earth and rock fill dam) near Johnstown on 1889 is considered the worst U.S dam disaster in terms of loss of life. The dam was overtopped and washed away due to unexpected heavy rains, releasing 20 million tons of water which destroyed Johnstown and resulted in 2209 deaths, [1], [2]. Piping or shear sliding, failure due to natural factors, and failure due to overtopping are all possible causes of earth dam failure. However, overtopping failure is the most frequent cause of dam failure. According to The International Committee on Large Dams (ICOLD, 1995), and [3], more than one-third of the total known dam failures were caused by dam overtopping.

    Overtopping occurs as the result of insufficient flood design or freeboard in some cases. Extreme rainstorms can cause floods which can overtop the dam and cause it to fail. The size and geometry of the reservoir or the dam (side slopes, top width, height, etc.), the homogeneity of the material used in the construction of the dam, overtopping depth, and the presence or absence of tailwater are all elements that influence this type of failure which will be illustrated in the following literature. Overtopping failures of earth dams may be divided into several failure mechanisms based on the material composition and the inner structure of the dam. For cohesive earth dams because of low permeability, no seepage exists on the slopes. Erosion often begins at the earth dam toe during turbulent erosion and moves upstream, undercutting the slope, causing the removal of large chunks of materials. While for non-cohesive earth dams the downstream face of the dam flattens progressively and is often said to rotate around a point near the downstream toe [4], [5], [6] In the last few decades, the study of failures due to overtopping has gained popularity among researchers. The overtopping failure, in fact, has been widely investigated in coastal and river hydraulics and morpho dynamic. In addition, several laboratory experimental studies have been conducted in this field in order to better understand different involved factors. Also, many numerical types of research have been conducted to investigate the process of overtopping failure as well as the elements that influence this type of failure.

    Tabrizi et al. [5] conducted a series of embankment overtopping tests to find the effect of compaction on the failure of a homogenous sand embankment. A plane breach process occurred across the flume width due to the narrow flume width. They measured the downstream hydrographs and embankment surface profile for every case. They concluded that the peak discharge decreased with a high compaction level, while the time to peak increased. Kansoh et al. [6] studied experimentally the failure of compacted homogeneous non-cohesive earthen embankment due to overtopping. They investigated the influence of different shape parameters including the downstream slope, the crest width, and the height of the embankment on the erosion process. The erosion process was initiated by carving a pilot channel into the embankment crest. They evaluated the time of embankment failure for different shape parameters. They concluded that the failure time increases with increasing the downstream slope and the crest width. Zhu et al. [7] investigated experimentally the breaching of five embankments, one constructed with pure sand, and four with different sand-silt–clay mixtures. The erosion pattern was similar across the flume width. They stated that for cohesive soil mixtures the head cut erosion was the most important factor that affected the breach growth, while for non-cohesive soil the breach erosion was affected by shear erosion.

    Amaral et al. [8] studied experimentally the failure by overtopping for two embankments built from silt sand material. They studied the effect of the degree of compaction of the embankment and the geometry of the pilot channel carved at the centre of the dam crest. They studied two shapes of pilot channel a rectangular shape and triangular shape. They stated that the breach development is influenced by a higher degree of compaction, however, the pilot channel geometry did not influence the breach’s final form. Bereta et al. [9] studied experimentally the breach formation of five dam models, three of them were homogenous clay soil while two were sandy-clay mixtures. The erosion process was initiated by cutting a pilot channel at the centre of the dam crest. They observed the initiation of erosion, flow shear erosion, sidewall bottom erosion, and distinguished the soil mechanical slope mass failure from the head cut vertically and laterally during these tests. Verma et al. [10] investigated experimentally a two-dimensional erosion phenomenon due to overtopping by using a wooden fuse plug model and five different soils. They concluded that the erosion process was affected mostly by cohesiveness and degree of compaction. For cohesive soils, a head cut erosion was observed, while for non-cohesive soils surface erosion occurred gradually. Also, the dimensions of fuse plug, type of fill material, reservoir capacity, and inflow were found to affect the behaviour of the overall breaching process.

    Wu and Qin [11] studied the effect of adding coarse grains to the downstream face of a non-cohesive dam as a result of tailings deposition. The process of overtopping during tailings dam failures is analyzed and its effect on delaying the dam-break process and disaster mitigation are investigated. They found that the tested protective measures decreased the breach area, the maximum breaching flow discharge and flow velocity, and the downstream inundated area. Khankandi et al. [12] studied experimentally the effect of reservoir geometry on dam break flow in case of dry and wet bed conditions. They considered four different reservoir shapes, a long reservoir, a wide, a trapezoidal shaped and one with a 90◦ bend all with identical water volume and horizontal bed. The dam break is simulated by the sudden gate removal using a pneumatic jack. They measured the variation of water level over time with ultrasonic sensors and flow velocity component with an acoustic Doppler velocimeter. Also, the experimental results of water level variation are compared with Ritters solution (1892) [13]. They stated that for dry bed condition the long and 90 bend reservoirs results are close to the analytical solution by ritter also in these two shapes a 1D flow is noticed. However, for wide and trapezoidal reservoirs a 2D effect is significant due to flow contraction at channel entrance.

    Rifai et al. [14] conducted a series of experiments to investigate the effect of tailwater depth on the outflow discharge and breach geometry during non-cohesive homogenous fluvial dikes overtopping failure. They cut an initial notch in the crest at 0.8 m from the upstream end of the dike to initiate overtopping. They compared their results to previous experiments under different main channel inflow discharges combined with a free floodplain. They divided the dike breaching process into three stages: gradual start of overtopping flow resulting in slow initiation of dike erosion, deepening and widening breach due to large flow depth and velocity, finally the flow depth starts stabilizing at its minimal level with or without sustained breach expansion. They stated that breach discharge has lower values than in free floodplain tests. Jiang [15] studied the effect of bed slope on breach parameters and peak discharge in non-cohesive embankment failure. An initial triangular breach with a depth and width of 4 cm was pre-set on one side of the dam. He stated that peak discharge increases with the increase of bed slope and then decreases.

    Ozmen-cagatay et al. [16] studied experimentally flood wave propagation resulted from a sudden dam break event. For dam-break modelling, they used a mechanism that permitted the rapid removal of a vertical plate with a thickness of 4 mm and made of rigid plastic. They conducted three tests, one with dry bed condition and two tests with tailwater depths equal 0.025 m and 0.1 m respectively. They recorded the free surface profile during initial stages of dam break by using digital image processing. Finally, they compared the experimental results with the with a commercially available VOF-based CFD program solving the Reynolds-averaged Navier –Stokes equations (RANS) with the k– Ɛ turbulence model and the shallow water equations (SWEs). They concluded that Wave breaking was delayed with increasing the tailwater depth to initial reservoir depth ratio. They also stated that the SWE approach is sufficient more to represent dam break flows for wet bed condition. Evangelista [17] investigated experimentally and numerically using a depth-integrated two-phase model, the erosion of sand dike caused by the impact of a dam break wave. The dam break is simulated by a sudden opening of an upstream reservoir gate resulting in the overtopping of a downstream trapezoidal sand dike. The evolution of the water wave caused from the gate opening and dike erosion process are recorded by using a computer-controlled camera. The experimental results demonstrated that the progression of the wave front and dike erosion have a considerable influence on each other during the process. In addition, the dike constructed from fine sands was more resistant to erosion than the one built with coarse sand. They also stated that the numerical model can is capable of accurately predicting wave front position and dike erosion. Also, Di Cristo et al. [18] studied the effect of dam break wave propagation on a sand embankment both experimentally and numerically using a two-phase shallow-water model. The evolution of free surface and of the embankment bottom are recorded and used in numerical model assessment. They stated that the model allows reasonable simulation of the experimental trends of the free surface elevation regardeless of the geofailure operator.

    Lots of numerical models have been developed over the past few years to simulate the dam break flooding problem. A one-dimensional model, such as Hec-Ras, DAMBRK and MIKE 11, ect. A two-dimensional model such as iRIC Nay2DH is used in earth embankment breach simulation. Other researchers studied the failure process numerically using (3D) computational fluid dynamics (CFD) models, such as FLOW-3D, and FLUENT. Goharnejad et al. [19] determined the outflow hydrograph which results from the embankment dam break due to overtopping. Hu et al. [20] performed a comparison between Flow-3D and MIKE3 FM numerical models in simulating a dam break event under dry and wet bed conditions with different tailwater depths. Kaurav et al. [21] simulated a planar dam breach process due to overtopping. They conducted a sensitivity analysis to find the effect of dam material, dam height, downstream slope, crest width, and inlet discharge on the erosion process and peak discharge through breach. They concluded that downstream slope has a significant influence on breaching process. Yusof et al. [22] studied the effect of embankment sediment sizes and inflow rates on breaching geometric and hydrodynamic parameters. They stated that the peak outflow hydrograph increases with increasing sediment size and inflow rates while time of failure decreases.

    In the present work, the effect of tailwater depth on earth dam failure during overtopping is studied experimentally. The relation between the eroded volume of the dam and the tailwater depth is presented. Also, the percentage of reduction in peak discharge due to tailwater existence is calculated. An assessment of Flow 3D software performance in simulating the erosion process during earth dam failure is introduced. The statistical variable root- mean- square error, RMSE, and the agreement degree index, d, are used in model assessment.

    2. Material and methods

    The tests are conducted in a straight rectangular flume in the laboratory of Irrigation Engineering and Hydraulics Department, Faculty of Engineering, Alexandria University, Egypt. The flume dimensions are 10 m long, 0.86 m wide, and 0.5 m deep. The front part of the flume is connected to a storage basin 1 m long by 0.86 m wide. The storage basin is connected to a collecting tank for water recirculation during the experiments as shown in Fig. 1, Fig. 2. A sharp-crested weir is placed at a distance of 4 m downstream the constructed dam to keep a constant tailwater depth in each experiment and to measure the outflow discharge.

    To measure the eroded volume with time a rods technique is used. This technique consists of two parallel wooden plates with 10 cm distance in between and five rows of stainless-steel rods passing vertically through the wooden plates at a spacing of 20 cm distributed across flume width. Each row consists of four rods with 15 cm spacing between them. Also, a graph board is provided to measure the drop in each rod with time as shown in Fig. 3, Fig. 4. After dam construction the rods are carefully rested on the dam, with the first line of rods resting in the middle of the dam crest and then a constant distance of 15 cm between rods lines is maintained.

    A soil sample is taken and tested in the laboratory of the soil mechanics to find the soil geotechnical parameters. The soil particle size distribution is also determined by sieve analysis as shown in Fig. 5. The soil mean diameter d50,equals 0.38 mm and internal friction angle equals 32.6°.

    2.1. Experimental procedures

    To investigate the effect of the tailwater depth (do), the tailwater depth is changed four times 5, 15, 20, and 25 cm on the sand dam model. The dam profile is 35 cm height, with crest width = 15 cm, the dam base width is 155 cm, and the upstream and downstream slopes are 2:1 as shown in Fig. 6. The dam dimensions are set as the flume permitted to allow observation of the dam erosion process under the available flume dimensions and conditions. All of the conducted experiments have the same dimensions and configurations.

    The optimum water content, Wc, from the standard proctor test is found to be 8 % and the maximum dry unit weight is 19.42 kN/m3. The soil and water are mixed thoroughly to ensure consistency and then placed on three horizontal layers. Each layer is compacted according to ASTM standard with 25 blows by using a rammer (27 cm × 20.5 cm) weighing 4 kg. Special attention is paid to the compaction of the soil to guarantee the repeatability of the tests.

    After placing and compacting the three layers, the dam slopes are trimmed carefully to form the trapezoidal shape of the dam. A small triangular pilot channel with 1 cm height and 1:1 side slopes is cut into the dam crest to initiate the erosion process. The position of triangular pilot channel is presented in Fig. 1. Three digital video cameras with a resolution of 1920 × 1080 pixels and a frame rate of 60 fps are placed in three different locations. One camera on one side of the flume to record the progress of the dam profile during erosion. Another to track the water level over the sharp-crested rectangular weir placed at the downstream end of the flume. And the third camera is placed above the flume at the downstream side of the dam and in front of the rods to record the drop of the tip of the rods with time as shown previously in Fig. 1.

    Before starting the experiment, the water is pumped into the storage basin by using pump with capacity 360 m3/hr, and then into the upstream section of the flume. The upstream boundary is an inflow condition. The flow discharge provided to the storage basin is kept at a constant rate of 6 L/sec for all experiments, while the downstream boundary is an outflow boundary condition.

    Also, the required tailwater depth for each experiment is filled to the desired depth. A dye container valve is opened to color the water upstream of the dam to make it easy to distinguish the dam profile from the water profile. A wooden board is placed just upstream of the dam to prevent water from overtopping the dam until the water level rises to a certain level above the dam crest and then the wooden board is removed slowly to start the experiment.

    2.2. Repeatability

    To verify the accuracy of the results, each experiment is repeated two times under the same conditions. Fig. 7 shows the relative eroded crest height, Zeroded / Zo, with time for 5 cm tailwater depth. From the Figure, it can be noticed that results for all runs are consistent, and accuracy is achieved.

    3. Numerical model

    The commercially available numerical model, Flow 3D is used to simulate the dam failure due to overtopping for the cases of 15 cm, 20 cm and 25 cm tailwater depths. For numerical model calibration, experimental results for dam surface evolution are used. The numerical model is calibrated for selection of the optimal turbulence model (RNG, K-e, and k-w) and sediment scour equations (Van Rin, Meyer- peter and Muller, and Nielsen) that produce the best results. In this, the flow field is solved by the RNG turbulence model, and the van Rijn equation is used for the sediment scour model. A geometry file is imported before applying the mesh.

    A Mesh sensitivity is analyzed and checked for various cell sizes, and it is found that decreasing the cell size significantly increases the simulation time with insignificant differences in the result. It is noticed that the most important factor influencing cell size selection is the value of the dam’s upstream and downstream slopes. For example, the slopes in the dam model are 2:1, thus the cell size ratio in X and Z directions should be 2:1 as well. The cell size in a mesh block is set to be 0.02 m, 0.025 m, and 0.01 m in X, Y and Z directions respectively.

    In the numerical computations, the boundary conditions employed are the walls for sidewalls and the channel bottom. The pressure boundary condition is applied at the top, at the air–water interface, to account for atmospheric pressure on the free surface. The upstream boundary is volume flow rate while the downstream boundary is outflow discharge.

    The initial condition is a fluid region, which is used to define fluid areas both upstream and downstream of the dam. To assess the model accuracy, the statistical variable root- mean- square error, RMSE, and the agreement degree index, d, are calculated as(1)RMSE=1N∑i=1N(Pi-Mi)2(2)d=1-∑Mi-Pi2∑Mi-M¯+Pi-P¯2

    where N is the number of samples, Pi and Mi are the models and experimental values, P and M are the means of the model and experimental values. The best fit between the experimental and model results would have an RMSE = 0 and degree of agreement, d = 1.

    4. Results of experimental work

    The results of the total time of failure, t (defined as the time from when the water begins to overtop the dam crest until the erosion reaches a steady state, when no erosion occurs), time of crest width erosion t1, cumulative eroded volume Veroded, and peak discharge Qpeak for each experiment are listed in Table 1. The case of 5 cm tailwater depth is considered as a reference case in this work.

    Table 1. Results of experimental work.

    Tailwater depth, do (cm)Total time of failure, t (sec)Time of crest width erosion, t1 (sec)cumulative eroded volume, Veroded (m3)Peak discharge, Qpeak (liter/sec)
    5255220.2113.12
    15165300.1612.19
    20140340.1311.29
    25110390.0510.84

    5. Discussion

    5.1. Side erosion

    The evolution of the bathymetry of the erosion line recorded by the video camera1. The videos are split into frames (60 frames/sec) by the Free Video to JPG Converter v.5.063 build and then converted into an excel spreadsheet using MATLAB code as shown in Fig. 8.

    Fig. 9 shows a sample of numerical model output. Fig. 10, Fig. 11, Fig. 12 show a dam profile development for different time steps from both experimental and numerical model, for tailwater depths equal 15 cm, 20 cm and 25 cm. Also, the values of RMSE and d for each figure are presented. The comparison shows that the Flow 3D software can simulate the erosion process of non-cohesive earth dam during overtopping with an RMSE value equals 0.023, 0.0218, and 0.0167 and degree of agreement, d, equals 0.95, 0.968, and 0.988 for relative tailwater depths, do/(do)ref, = 3, 4 and 5, respectively. The low values of RMSE and high values of d show that the Flow 3D can effectively simulate the erosion process. From Fig. 10, Fig. 11, Fig. 12, it can be noticed that the model is not capable of reproducing the head cut, while it can simulate well the degradation of the crest height with a minor difference from experimental work. The reason of this could be due to inability of simulation of all physical conditions which exists in the experimental work, such as channel friction and the grain size distribution of the dam soil which is surely has a great effect on the erosion process and breach development. In the experimental work the grain size distribution is shown in Fig. 5, while the numerical model considers that the soil is uniform and exactly 50 % of the dam particles diameter are equal to the d50 value. Another reason is that the model is not considering the increased resistance of the dam due to the apparent cohesion which happens due to dam saturation [23].

    It is clear from both the experimental and numerical results that for a 5 cm tailwater depth, do/(do)ref = 1.0, erosion begins near the dam toe and continues upward on the downstream slope until it reaches the crest. After eroding the crest width, the crest is lowered, resulting in increased flow rates and the speeding up of the erosion process. While for relative tailwater depths, do/(do)ref = 3, 4, and 5 erosion starts at the point of intersection between the downstream slope and tailwater. The existence of tailwater works as an energy dissipater for the falling water which reduces the erosion process and prevents the dam from failure as shown in Fig. 13. It is found that the time of the failure decreases with increasing the tailwater depth because most of the dam height is being submerged with water which decreases the erosion process. The reduction in time of failure from the referenced case is found to be 35.3, 45, and 57 % for relative tailwater depth, do /(do)ref equals 3, 4, and 5, respectively.

    The relation between the relative eroded crest height, Zeroded /Zo, with time is drawn as shown in Fig. 14. It is found that the relative eroded crest height decreases with increasing tailwater depth by 10, 41, and 77.6 % for relative tailwater depth, do /(do)ref equals 3, 4, and 5, respectively. The time required for the erosion of the crest width, t1, is calculated for each experiment. The relation between relative tailwater depth and relative time of crest width erosion is shown in Fig. 15. It is found that the time of crest width erosion increases linearly with increasing, do /Zo. The percent of increase is 36.4, 54.5 and 77.3 % for relative tailwater depth, do /(do)ref = 3, 4 and 5, respectively.

    Crest height, Zcrest is calculated from the experimental results and the Flow 3D results for relative tailwater depths, do/(do)ref, = 3, 4, and 5. A relation between relative crest height, Zcrest/Zo with time from experimental and numerical results is presented in Fig. 16. From Fig. 16, it is seen that there is a good consistency between the results of numerical model and the experimental results in the case of tracking the erosion of the crest height with time.

    5.2. Upstream and downstream water depths

    It is noticed that at the beginning of the erosion process, both upstream and downstream water depths increase linearly with time as long as erosion of the crest height did not take place. However, when the crest height starts to lower the upstream water depth decreases with time while the downstream water depth increases. At the end of the experiment, the two depths are nearly equal. A relation between relative downstream and upstream water depths with time is drawn for each experiment as shown in Fig. 17.

    5.3. Eroded volume

    A MATLAB code is used to calculate the cumulative eroded volume every time interval for each experiment. The total volume of the dam, Vtotal is 0.256 m3. The cumulative eroded volume, Veroded is 0.21, 0.16, 0.13, and 0.05 m3 for tailwater depths, do = 5, 15, 20, and 25 cm, respectively. Fig. 18 presents the relation between cumulative eroded volume, Veroded and time. From Fig. 18, it is observed that the cumulative eroded volume decreases with increasing the tailwater depth. The reduction in cumulative eroded volume is 23, 36.5, and 75 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The relative remained volume of the dam equals 0.18, 0.375, 0.492, and 0.8 for tailwater depths = 5, 15, 20, and 25 cm, respectively. Fig. 19 shows a relation between relative tailwater depth and relative cumulative eroded volume from experimental results. From that figure, it is noticed that the eroded volume decreases exponentially with increasing relative tailwater depth.

    5.4. The outflow discharge

    The inflow discharge provided to the storage tank is maintained constant for all experiments. The water surface elevation, H, over the sharp-crested weir placed at the downstream side is recorded by the video camera 2. For each experiment, the outflow discharge is then calculated by using the sharp-crested rectangular weir equation every 10 sec.

    The outflow discharge is found to increase rapidly until it reaches its peak then it decreases until it is constant. For high values of tailwater depths, the peak discharge becomes less than that in the case of small tailwater depth as shown in Fig. 20 which agrees well with the results of Rifai et al. [14] The reduction in peak discharge is 7, 14, and 17.35 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively.

    The scenario presented in this article in which the tailwater depth rises due to unexpected heavy rainfall, is investigated to find the effect of rising tailwater depth on earth dam failure. The results revealed that rising tailwater depth positively affects the process of dam failure in terms of preventing the dam from complete failure and reducing the outflow discharge.

    6. Conclusions

    The effect of tailwater depth on earth dam failure due to overtopping is investigated experimentally in this work. The study focuses on the effect of tailwater depth on side erosion, upstream and downstream water depths, eroded volume, outflow hydrograph, and duration of the failure process. The Flow 3D numerical software is used to simulate the dam failure, and a comparison is made between the experimental and numerical results to find the ability of this software to simulate the erosion process. The following are the results of the investigation:

    The existence of tailwater with high depths prevents the dam from completely collapsing thereby turning it into a broad crested weir. The failure time decreases with increasing the tailwater depth and the reduction from the reference case is found to be 35.3, 45, and 57 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The difference between the upstream and downstream water depths decreases with time till it became almost negligible at the end of the experiment. The reduction in cumulative eroded volume is 23, 36.5, and 75 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The peak discharge decreases by 7, 14, and 17.35 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The relative eroded crest height decreases linearly with increasing the tailwater depth by 10, 41, and 77.6 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The numerical model can reproduce the erosion process with a minor deviation from the experimental results, particularly in terms of tracking the degradation of the crest height with time.

    Declaration of Competing Interest

    The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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    Cited by (0)

    My name is Shaimaa Ibrahim Mohamed Aman and I am a teaching assistant in Irrigation and Hydraulics department, Faculty of Engineering, Alexandria University. I graduated from the Faculty of Engineering, Alexandria University in 2013. I had my MSc in Irrigation and Hydraulic Engineering in 2017. My research interests lie in the area of earth dam Failures.

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    Extratropical cyclone damage to the seawall in Dawlish, UK: eyewitness accounts, sea level analysis and numerical modelling

    영국 Dawlish의 방파제에 대한 온대 저기압 피해: 목격자 설명, 해수면 분석 및 수치 모델링

    Extratropical cyclone damage to the seawall in Dawlish, UK: eyewitness accounts, sea level analysis and numerical modelling

    Natural Hazards (2022)Cite this article

    Abstract

    2014년 2월 영국 해협(영국)과 특히 Dawlish에 영향을 미친 온대 저기압 폭풍 사슬은 남서부 지역과 영국의 나머지 지역을 연결하는 주요 철도에 심각한 피해를 입혔습니다.

    이 사건으로 라인이 두 달 동안 폐쇄되어 5천만 파운드의 피해와 12억 파운드의 경제적 손실이 발생했습니다. 이 연구에서는 폭풍의 파괴력을 해독하기 위해 목격자 계정을 수집하고 해수면 데이터를 분석하며 수치 모델링을 수행합니다.

    우리의 분석에 따르면 이벤트의 재난 관리는 성공적이고 효율적이었으며 폭풍 전과 도중에 인명과 재산을 구하기 위해 즉각적인 조치를 취했습니다. 파도 부이 분석에 따르면 주기가 4–8, 8–12 및 20–25초인 복잡한 삼중 봉우리 바다 상태가 존재하는 반면, 조위계 기록에 따르면 최대 0.8m의 상당한 파도와 최대 1.5m의 파도 성분이 나타났습니다.

    이벤트에서 가능한 기여 요인으로 결합된 진폭. 최대 286 KN의 상당한 임펄스 파동이 손상의 시작 원인일 가능성이 가장 높았습니다. 수직 벽의 반사는 파동 진폭의 보강 간섭을 일으켜 파고가 증가하고 최대 16.1m3/s/m(벽의 미터 너비당)의 상당한 오버탑핑을 초래했습니다.

    이 정보와 우리의 공학적 판단을 통해 우리는 이 사고 동안 다중 위험 계단식 실패의 가장 가능성 있는 순서는 다음과 같다고 결론을 내립니다. 조적 파괴로 이어지는 파도 충격력, 충전물 손실 및 연속적인 조수에 따른 구조물 파괴.

    The February 2014 extratropical cyclonic storm chain, which impacted the English Channel (UK) and Dawlish in particular, caused significant damage to the main railway connecting the south-west region to the rest of the UK. The incident caused the line to be closed for two months, £50 million of damage and an estimated £1.2bn of economic loss. In this study, we collate eyewitness accounts, analyse sea level data and conduct numerical modelling in order to decipher the destructive forces of the storm. Our analysis reveals that the disaster management of the event was successful and efficient with immediate actions taken to save lives and property before and during the storm. Wave buoy analysis showed that a complex triple peak sea state with periods at 4–8, 8–12 and 20–25 s was present, while tide gauge records indicated that significant surge of up to 0.8 m and wave components of up to 1.5 m amplitude combined as likely contributing factors in the event. Significant impulsive wave force of up to 286 KN was the most likely initiating cause of the damage. Reflections off the vertical wall caused constructive interference of the wave amplitudes that led to increased wave height and significant overtopping of up to 16.1 m3/s/m (per metre width of wall). With this information and our engineering judgement, we conclude that the most probable sequence of multi-hazard cascading failure during this incident was: wave impact force leading to masonry failure, loss of infill and failure of the structure following successive tides.

    Introduction

    The progress of climate change and increasing sea levels has started to have wide ranging effects on critical engineering infrastructure (Shakou et al. 2019). The meteorological effects of increased atmospheric instability linked to warming seas mean we may be experiencing more frequent extreme storm events and more frequent series or chains of events, as well as an increase in the force of these events, a phenomenon called storminess (Mölter et al. 2016; Feser et al. 2014). Features of more extreme weather events in extratropical latitudes (30°–60°, north and south of the equator) include increased gusting winds, more frequent storm squalls, increased prolonged precipitation and rapid changes in atmospheric pressure and more frequent and significant storm surges (Dacre and Pinto 2020). A recent example of these events impacting the UK with simultaneous significant damage to coastal infrastructure was the extratropical cyclonic storm chain of winter 2013/2014 (Masselink et al. 2016; Adams and Heidarzadeh 2021). The cluster of storms had a profound effect on both coastal and inland infrastructure, bringing widespread flooding events and large insurance claims (RMS 2014).

    The extreme storms of February 2014, which had a catastrophic effect on the seawall of the south Devon stretch of the UK’s south-west mainline, caused a two-month closure of the line and significant disruption to the local and regional economy (Fig. 1b) (Network Rail 2014; Dawson et al. 2016; Adams and Heidarzadeh 2021). Restoration costs were £35 m, and economic effects to the south-west region of England were estimated up to £1.2bn (Peninsula Rail Taskforce 2016). Adams and Heidarzadeh (2021) investigated the disparate cascading failure mechanisms which played a part in the failure of the railway through Dawlish and attempted to put these in the context of the historical records of infrastructure damage on the line. Subsequent severe storms in 2016 in the region have continued to cause damage and disruption to the line in the years since 2014 (Met Office 2016). Following the events of 2014, Network Rail Footnote1 who owns the network has undertaken a resilience study. As a result, it has proposed a £400 m refurbishment of the civil engineering assets that support the railway (Fig. 1) (Network Rail 2014). The new seawall structure (Fig. 1a,c), which is constructed of pre-cast concrete sections, encases the existing Brunel seawall (named after the project lead engineer, Isambard Kingdom Brunel) and has been improved with piled reinforced concrete foundations. It is now over 2 m taller to increase the available crest freeboard and incorporates wave return features to minimise wave overtopping. The project aims to increase both the resilience of the assets to extreme weather events as well as maintain or improve amenity value of the coastline for residents and visitors.

    figure 1
    Fig. 1

    In this work, we return to the Brunel seawall and the damage it sustained during the 2014 storms which affected the assets on the evening of the 4th and daytime of the 5th of February and eventually resulted in a prolonged closure of the line. The motivation for this research is to analyse and model the damage made to the seawall and explain the damage mechanisms in order to improve the resilience of many similar coastal structures in the UK and worldwide. The innovation of this work is the multidisciplinary approach that we take comprising a combination of analysis of eyewitness accounts (social science), sea level and wave data analysis (physical science) as well as numerical modelling and engineering judgement (engineering sciences). We investigate the contemporary wave climate and sea levels by interrogating the real-time tide gauge and wave buoys installed along the south-west coast of the English Channel. We then model a typical masonry seawall (Fig. 2), applying the computational fluid dynamics package FLOW3D-Hydro,Footnote2 to quantify the magnitude of impact forces that the seawall would have experienced leading to its failure. We triangulate this information to determine the probable sequence of failures that led to the disaster in 2014.

    figure 2
    Fig. 2

    Data and methods

    Our data comprise eyewitness accounts, sea level records from coastal tide gauges and offshore wave buoys as well as structural details of the seawall. As for methodology, we analyse eyewitness data, process and investigate sea level records through Fourier transform and conduct numerical simulations using the Flow3D-Hydro package (Flow Science 2022). Details of the data and methodology are provided in the following.

    Eyewitness data

    The scale of damage to the seawall and its effects led the local community to document the first-hand accounts of those most closely affected by the storms including residents, local businesses, emergency responders, politicians and engineering contractors involved in the post-storm restoration work. These records now form a permanent exhibition in the local museum in DawlishFootnote3, and some of these accounts have been transcribed into a DVD account of the disaster (Dawlish Museum 2015). We have gathered data from the Dawlish Museum, national and international news reports, social media tweets and videos. Table 1 provides a summary of the eyewitness accounts. Overall, 26 entries have been collected around the time of the incident. Our analysis of the eyewitness data is provided in the third column of Table 1 and is expanded in Sect. 3.Table 1 Eyewitness accounts of damage to the Dawlish railway due to the February 2014 storm and our interpretations

    Full size table

    Sea level data and wave environment

    Our sea level data are a collection of three tide gauge stations (Newlyn, Devonport and Swanage Pier—Fig. 5a) owned and operated by the UK National Tide and Sea Level FacilityFootnote4 for the Environment Agency and four offshore wave buoys (Dawlish, West Bay, Torbay and Chesil Beach—Fig. 6a). The tide gauge sites are all fitted with POL-EKO (www.pol-eko.com.pl) data loggers. Newlyn has a Munro float gauge with one full tide and one mid-tide pneumatic bubbler system. Devonport has a three-channel data pneumatic bubbler system, and Swanage Pier consists of a pneumatic gauge. Each has a sampling interval of 15 min, except for Swanage Pier which has a sampling interval of 10 min. The tide gauges are located within the port areas, whereas the offshore wave buoys are situated approximately 2—3.3 km from the coast at water depths of 10–15 m. The wave buoys are all Datawell Wavemaker Mk III unitsFootnote5 and come with sampling interval of 0.78 s. The buoys have a maximum saturation amplitude of 20.5 m for recording the incident waves which implies that every wave larger than this threshold will be recorded at 20.5 m. The data are provided by the British Oceanographic Data CentreFootnote6 for tide gauges and the Channel Coastal ObservatoryFootnote7 for wave buoys.

    Sea level analysis

    The sea level data underwent quality control to remove outliers and spikes as well as gaps in data (e.g. Heidarzadeh et al. 2022; Heidarzadeh and Satake 2015). We processed the time series of the sea level data using the Matlab signal processing tool (MathWorks 2018). For calculations of the tidal signals, we applied the tidal package TIDALFIT (Grinsted 2008), which is based on fitting tidal harmonics to the observed sea level data. To calculate the surge signals, we applied a 30-min moving average filter to the de-tided data in order to remove all wind, swell and infra-gravity waves from the time series. Based on the surge analysis and the variations of the surge component before the time period of the incident, an error margin of approximately ± 10 cm is identified for our surge analysis. Spectral analysis of the wave buoy data is performed using the fast Fourier transform (FFT) of Matlab package (Mathworks 2018).

    Numerical modelling

    Numerical modelling of wave-structure interaction is conducted using the computational fluid dynamics package Flow3D-Hydro version 1.1 (Flow Science 2022). Flow3D-Hydro solves the transient Navier–Stokes equations of conservation of mass and momentum using a finite difference method and on Eulerian and Lagrangian frameworks (Flow Science 2022). The aforementioned governing equations are:

    ∇.u=0∇.u=0

    (1)

    ∂u∂t+u.∇u=−∇Pρ+υ∇2u+g∂u∂t+u.∇u=−∇Pρ+υ∇2u+g

    (2)

    where uu is the velocity vector, PP is the pressure, ρρ is the water density, υυ is the kinematic viscosity and gg is the gravitational acceleration. A Fractional Area/Volume Obstacle Representation (FAVOR) is adapted in Flow3D-Hydro, which applies solid boundaries within the Eulerian grid and calculates the fraction of areas and volume in partially blocked volume in order to compute flows on corresponding boundaries (Hirt and Nichols 1981). We validated the numerical modelling through comparing the results with Sainflou’s analytical equation for the design of vertical seawalls (Sainflou 1928; Ackhurst 2020), which is as follows:

    pd=ρgHcoshk(d+z)coshkdcosσtpd=ρgHcoshk(d+z)coshkdcosσt

    (3)

    where pdpd is the hydrodynamic pressure, ρρ is the water density, gg is the gravitational acceleration, HH is the wave height, dd is the water depth, kk is the wavenumber, zz is the difference in still water level and mean water level, σσ is the angular frequency and tt is the time. The Sainflou’s equation (Eq. 3) is used to calculate the dynamic pressure from wave action, which is combined with static pressure on the seawall.

    Using Flow3D-Hydro, a model of the Dawlish seawall was made with a computational domain which is 250.0 m in length, 15.0 m in height and 0.375 m in width (Fig. 3a). The computational domain was discretised using a single uniform grid with a mesh size of 0.125 m. The model has a wave boundary at the left side of the domain (x-min), an outflow boundary on the right side (x-max), a symmetry boundary at the bottom (z-min) and a wall boundary at the top (z-max). A wall boundary implies that water or waves are unable to pass through the boundary, whereas a symmetry boundary means that the two edges of the boundary are identical and therefore there is no flow through it. The water is considered incompressible in our model. For volume of fluid advection for the wave boundary (i.e. the left-side boundary) in our simulations, we utilised the “Split Lagrangian Method”, which guarantees the best accuracy (Flow Science, 2022).

    figure 3
    Fig. 3

    The stability of the numerical scheme is controlled and maintained through checking the Courant number (CC) as given in the following:

    C=VΔtΔxC=VΔtΔx

    (4)

    where VV is the velocity of the flow, ΔtΔt is the time step and ΔxΔx is the spatial step (i.e. grid size). For stability and convergence of the numerical simulations, the Courant number must be sufficiently below one (Courant et al. 1928). This is maintained by a careful adjustment of the ΔxΔx and ΔtΔt selections. Flow3D-Hydro applies a dynamic Courant number, meaning the program adjusts the value of time step (ΔtΔt) during the simulations to achieve a balance between accuracy of results and speed of simulation. In our simulation, the time step was in the range ΔtΔt = 0.0051—0.051 s.

    In order to achieve the most efficient mesh resolution, we varied cell size for five values of ΔxΔx = 0.1 m, 0.125 m, 0.15 m, 0.175 m and 0.20 m. Simulations were performed for all mesh sizes, and the results were compared in terms of convergence, stability and speed of simulation (Fig. 3). A linear wave with an amplitude of 1.5 m and a period of 6 s was used for these optimisation simulations. We considered wave time histories at two gauges A and B and recorded the waves from simulations using different mesh sizes (Fig. 3). Although the results are close (Fig. 3), some limited deviations are observed for larger mesh sizes of 0.20 m and 0.175 m. We therefore selected mesh size of 0.125 m as the optimum, giving an extra safety margin as a conservative solution.

    The pressure from the incident waves on the vertical wall is validated in our model by comparing them with the analytical equation of Sainflou (1928), Eq. (3), which is one of the most common set of equations for design of coastal structures (Fig. 4). The model was tested by running a linear wave of period 6 s and wave amplitude of 1.5 m against the wall, with a still water level of 4.5 m. It can be seen that the model results are very close to those from analytical equations of Sainflou (1928), indicating that our numerical model is accurately modelling the wave-structure interaction (Fig. 4).

    figure 4
    Fig. 4

    Eyewitness account analysis

    Contemporary reporting of the 4th and 5th February 2014 storms by the main national news outlets in the UK highlights the extreme nature of the events and the significant damage and disruption they were likely to have on the communities of the south-west of England. In interviews, this was reinforced by Network Rail engineers who, even at this early stage, were forecasting remedial engineering works to last for at least 6 weeks. One week later, following subsequent storms the cascading nature of the events was obvious. Multiple breaches of the seawall had taken place with up to 35 separate landslide events and significant damage to parapet walls along the coastal route also were reported. Residents of the area reported extreme effects of the storm, one likening it to an earthquake and reporting water ingress through doors windows and even through vertical chimneys (Table 1). This suggests extreme wave overtopping volumes and large wave impact forces. One resident described the structural effects as: “the house was jumping up and down on its footings”.

    Disaster management plans were quickly and effectively put into action by the local council, police service and National Rail. A major incident was declared, and decisions regarding evacuation of the residents under threat were taken around 2100 h on the night of 4th February when reports of initial damage to the seawall were received (Table 1). Local hotels were asked to provide short-term refuge to residents while local leisure facilities were prepared to accept residents later that evening. Initial repair work to the railway line was hampered by successive high spring tides and storms in the following days although significant progress was still made when weather conditions permitted (Table 1).

    Sea level observations and spectral analysis

    The results of surge and wave analyses are presented in Figs. 5 and 6. A surge height of up to 0.8 m was recorded in the examined tide gauge stations (Fig. 5b-d). Two main episodes of high surge heights are identified: the first surge started on 3rd February 2014 at 03:00 (UTC) and lasted until 4th of February 2014 at 00:00; the second event occurred in the period 4th February 2014 15:00 to 5th February 2014 at 17:00 (Fig. 5b-d). These data imply surge durations of 21 h and 26 h for the first and the second events, respectively. Based on the surge data in Fig. 5, we note that the storm event of early February 2014 and the associated surges was a relatively powerful one, which impacted at least 230 km of the south coast of England, from Land’s End to Weymouth, with large surge heights.

    figure 5
    Fig. 5
    figure 6
    Fig. 6

    Based on wave buoy records, the maximum recorded amplitudes are at least 20.5 m in Dawlish and West Bay, 1.9 m in Tor Bay and 4.9 m in Chesil (Fig. 6a-b). The buoys at Tor Bay and Chesil recorded dual peak period bands of 4–8 and 8–12 s, whereas at Dawlish and West Bay registered triple peak period bands at 4–8, 8–12 and 20–25 s (Fig. 6c, d). It is important to note that the long-period waves at 20–25 s occur with short durations (approximately 2 min) while the waves at the other two bands of 4–8 and 8–12 s appear to be present at all times during the storm event.

    The wave component at the period band of 4–8 s can be most likely attributed to normal coastal waves while the one at 8–12 s, which is longer, is most likely the swell component of the storm. Regarding the third component of the waves with long period of 20 -25 s, which occurs with short durations of 2 min, there are two hypotheses; it is either the result of a local (port and harbour) and regional (the Lyme Bay) oscillations (eg. Rabinovich 1997; Heidarzadeh and Satake 2014; Wang et al. 1992), or due to an abnormally long swell. To test the first hypothesis, we consider various water bodies such as Lyme Bay (approximate dimensions of 70 km × 20 km with an average water depth of 30 m; Fig. 6), several local bays (approximate dimensions of 3.6 km × 0.6 km with an average water depth of 6 m) and harbours (approximate dimensions of 0.5 km × 0.5 km with an average water depth of 4 m). Their water depths are based on the online Marine navigation website.Footnote8 According to Rabinovich (2010), the oscillation modes of a semi-enclosed rectangle basin are given by the following equation:

    Tmn=2gd−−√[(m2L)2+(nW)2]−1/2Tmn=2gd[(m2L)2+(nW)2]−1/2

    (5)

    where TmnTmn is the oscillation period, gg is the gravitational acceleration, dd is the water depth, LL is the length of the basin, WW is the width of the basin, m=1,2,3,…m=1,2,3,… and n=0,1,2,3,…n=0,1,2,3,…; mm and nn are the counters of the different modes. Applying Eq. (5) to the aforementioned water bodies results in oscillation modes of at least 5 min, which is far longer than the observed period of 20–25 s. Therefore, we rule out the first hypothesis and infer that the long period of 20–25 s is most likely a long swell wave coming from distant sources. As discussed by Rabinovich (1997) and Wang et al. (2022), comparison between sea level spectra before and after the incident is a useful method to distinguish the spectrum of the weather event. A visual inspection of Fig. 6 reveals that the forcing at the period band of 20–25 s is non-existent before the incident.

    Numerical simulations of wave loading and overtopping

    Based on the results of sea level data analyses in the previous section (Fig. 6), we use a dual peak wave spectrum with peak periods of 10.0 s and 25.0 s for numerical simulations because such a wave would be comprised of the most energetic signals of the storm. For variations of water depth (2.0–4.0 m), coastal wave amplitude (0.5–1.5 m) (Fig. 7) and storm surge height (0.5–0.8 m) (Fig. 5), we developed 20 scenarios (Scn) which we used in numerical simulations (Table 2). Data during the incident indicated that water depth was up to the crest level of the seawall (approximately 4 m water depth); therefore, we varied water depth from 2 to 4 m in our simulation scenarios. Regarding wave amplitudes, we referred to the variations at a nearby tide gauge station (West Bay) which showed wave amplitude up to 1.2 m (Fig. 7). Therefore, wave amplitude was varied from 0.5 m to 1.5 m by considering a factor a safety of 25% for the maximum wave amplitude. As for the storm surge component, time series of storm surges calculated at three coastal stations adjacent to Dawlish showed that it was in the range of 0.5 m to 0.8 m (Fig. 5). These 20 scenarios would help to study uncertainties associated with wave amplitudes and pressures. Figure 8 shows snapshots of wave propagation and impacts on the seawall at different times.

    figure 7
    Fig. 7

    Table 2 The 20 scenarios considered for numerical simulations in this study

    Full size table

    figure 8
    Fig. 8

    Results of wave amplitude simulations

    Large wave amplitudes can induce significant wave forcing on the structure and cause overtopping of the seawall, which could eventually cascade to other hazards such as erosion of the backfill and scour (Adams and Heidarzadeh, 2021). The first 10 scenarios of our modelling efforts are for the same incident wave amplitudes of 0.5 m, which occur at different water depths (2.0–4.0 m) and storm surge heights (0.5–0.8 m) (Table 2 and Fig. 9). This is because we aim at studying the impacts of effective water depth (deff—the sum of mean sea level and surge height) on the time histories of wave amplitudes as the storm evolves. As seen in Fig. 9a, by decreasing effective water depth, wave amplitude increases. For example, for Scn-1 with effective depth of 4.5 m, the maximum amplitude of the first wave is 1.6 m, whereas it is 2.9 m for Scn-2 with effective depth of 3.5 m. However, due to intensive reflections and interferences of the waves in front of the vertical seawall, such a relationship is barely seen for the second and the third wave peaks. It is important to note that the later peaks (second or third) produce the largest waves rather than the first wave. Extraordinary wave amplifications are seen for the Scn-2 (deff = 3.5 m) and Scn-7 (deff = 3.3 m), where the corresponding wave amplitudes are 4.5 m and 3.7 m, respectively. This may indicate that the effective water depth of deff = 3.3–3.5 m is possibly a critical water depth for this structure resulting in maximum wave amplitudes under similar storms. In the second wave impact, the combined wave height (i.e. the wave amplitude plus the effective water depth), which is ultimately an indicator of wave overtopping, shows that the largest wave heights are generated by Scn-2, 7 and 8 (Fig. 9a) with effective water depths of 3.5 m, 3.3 m and 3.8 m and combined heights of 8.0 m, 7.0 m and 6.9 m (Fig. 9b). Since the height of seawall is 5.4 m, the combined wave heights for Scn-2, 7 and 8 are greater than the crest height of the seawall by 2.6 m, 1.6 m and 1.5 m, respectively, which indicates wave overtopping.

    figure 9
    Fig. 9

    For scenarios 11–20 (Fig. 10), with incident wave amplitudes of 1.5 m (Table 2), the largest wave amplitudes are produced by Scn-17 (deff = 3.3 m), Scn-13 (deff = 2.5 m) and Scn-12 (deff = 3.5 m), which are 5.6 m, 5.1 m and 4.5 m. The maximum combined wave heights belong to Scn-11 (deff = 4.5 m) and Scn-17 (deff = 3.3 m), with combined wave heights of 9.0 m and 8.9 m (Fig. 10b), which are greater than the crest height of the seawall by 4.6 m and 3.5 m, respectively.

    figure 10
    Fig. 10

    Our simulations for all 20 scenarios reveal that the first wave is not always the largest and wave interactions, reflections and interferences play major roles in amplifying the waves in front of the seawall. This is primarily because the wall is fully vertical and therefore has a reflection coefficient of close to one (i.e. full reflection). Simulations show that the combined wave height is up to 4.6 m higher than the crest height of the wall, implying that severe overtopping would be expected.

    Results of wave loading calculations

    The pressure calculations for scenarios 1–10 are given in Fig. 11 and those of scenarios 11–20 in Fig. 12. The total pressure distribution in Figs. 11, 12 mostly follows a triangular shape with maximum pressure at the seafloor as expected from the Sainflou (1928) design equations. These pressure plots comprise both static (due to mean sea level in front of the wall) and dynamic (combined effects of surge and wave) pressures. For incident wave amplitudes of 0.5 m (Fig. 11), the maximum wave pressure varies in the range of 35–63 kPa. At the sea surface, it is in the range of 4–20 kPa (Fig. 11). For some scenarios (Scn-2 and 7), the pressure distribution deviates from a triangular shape and shows larger pressures at the top, which is attributed to the wave impacts and partial breaking at the sea surface. This adds an additional triangle-shaped pressure distribution at the sea surface elevation consistent with the design procedure developed by Goda (2000) for braking waves. The maximum force on the seawall due to scenarios 1–10, which is calculated by integrating the maximum pressure distribution over the wave-facing surface of the seawall, is in the range of 92–190 KN (Table 2).

    figure 11
    Fig. 11
    figure 12
    Fig. 12

    For scenarios 11–20, with incident wave amplitude of 1.5 m, wave pressures of 45–78 kPa and 7–120 kPa, for  the bottom and top of the wall, respectively, were observed (Fig. 12). Most of the plots show a triangular pressure distribution, except for Scn-11 and 15. A significant increase in wave impact pressure is seen for Scn-15 at the top of the structure, where a maximum pressure of approximately 120 kPa is produced while other scenarios give a pressure of 7–32 kPa for the sea surface. In other words, the pressure from Scn-15 is approximately four times larger than the other scenarios. Such a significant increase of the pressure at the top is most likely attributed to the breaking wave impact loads as detailed by Goda (2000) and Cuomo et al. (2010). The wave simulation snapshots in Fig. 8 show that the wave breaks before reaching the wall. The maximum force due to scenarios 11–20 is 120–286 KN.

    The breaking wave impacts peaking at 286 KN in our simulations suggest destabilisation of the upper masonry blocks, probably by grout malfunction. This significant impact force initiated the failure of the seawall which in turn caused extensive ballast erosion. Wave impact damage was proposed by Adams and Heidarzadeh (2021) as one of the primary mechanisms in the 2014 Dawlish disaster. In the multi-hazard risk model proposed by these authors, damage mechanism III (failure pathway 5 in Adams and Heidarzadeh, 2021) was characterised by wave impact force causing damage to the masonry elements, leading to failure of the upper sections of the seawall and loss of infill material. As blocks were removed, access to the track bed was increased for inbound waves allowing infill material from behind the seawall to be fluidised and subsequently removed by backwash. The loss of infill material critically compromised the stability of the seawall and directly led to structural failure. In parallel, significant wave overtopping (discussed in the next section) led to ballast washout and cascaded, in combination with masonry damage, to catastrophic failure of the wall and suspension of the rails in mid-air (Fig. 1b), leaving the railway inoperable for two months.

    Wave Overtopping

    The two most important factors contributing to the 2014 Dawlish railway catastrophe were wave impact forces and overtopping. Figure 13 gives the instantaneous overtopping rates for different scenarios, which experienced overtopping. It can be seen that the overtopping rates range from 0.5 m3/s/m to 16.1 m3/s/m (Fig. 13). Time histories of the wave overtopping rates show that the phenomenon occurs intermittently, and each time lasts 1.0–7.0 s. It is clear that the longer the overtopping time, the larger the volume of the water poured on the structure. The largest wave overtopping rates of 16.1 m3/s/m and 14.4 m3/s/m belong to Scn-20 and 11, respectively. These are the two scenarios that also give the largest combined wave heights (Fig. 10b).

    figure 13
    Fig. 13

    The cumulative overtopping curves (Figs. 14, 15) show the total water volume overtopped the structure during the entire simulation time. This is an important hazard factor as it determines the level of soil saturation, water pore pressure in the soil and soil erosion (Van der Meer et al. 2018). The maximum volume belongs to Scn-20, which is 65.0 m3/m (m-cubed of water per metre length of the wall). The overtopping volumes are 42.7 m3/m for Scn-11 and 28.8 m3/m for Scn-19. The overtopping volume is in the range of 0.7–65.0 m3/m for all scenarios.

    figure 14
    Fig. 14
    figure 15
    Fig. 15

    For comparison, we compare our modelling results with those estimated using empirical equations. For the case of the Dawlish seawall, we apply the equation proposed by Van Der Meer et al. (2018) to estimate wave overtopping rates, based on a set of decision criteria which are the influence of foreshore, vertical wall, possible breaking waves and low freeboard:

    qgH3m−−−−√=0.0155(Hmhs)12e(−2.2RcHm)qgHm3=0.0155(Hmhs)12e(−2.2RcHm)

    (6)

    where qq is the mean overtopping rate per metre length of the seawall (m3/s/m), gg is the acceleration due to gravity, HmHm is the incident wave height at the toe of the structure, RcRc is the wall crest height above mean sea level, hshs is the deep-water significant wave height and e(x)e(x) is the exponential function. It is noted that Eq. (6) is valid for 0.1<RcHm<1.350.1<RcHm<1.35. For the case of the Dawlish seawall and considering the scenarios with larger incident wave amplitude of 1.5 m (hshs= 1.5 m), the incident wave height at the toe of the structure is HmHm = 2.2—5.6 m, and the wall crest height above mean sea level is RcRc = 0.6–2.9 m. As a result, Eq. (6) gives mean overtopping rates up to approximately 2.9 m3/s/m. A visual inspection of simulated overtopping rates in Fig. 13 for Scn 11–20 shows that the mean value of the simulated overtopping rates (Fig. 13) is close to estimates using Eq. (6).

    Discussion and conclusions

    We applied a combination of eyewitness account analysis, sea level data analysis and numerical modelling in combination with our engineering judgement to explain the damage to the Dawlish railway seawall in February 2014. Main findings are:

    • Eyewitness data analysis showed that the extreme nature of the event was well forecasted in the hours prior to the storm impact; however, the magnitude of the risks to the structures was not well understood. Multiple hazards were activated simultaneously, and the effects cascaded to amplify the damage. Disaster management was effective, exemplified by the establishment of an emergency rendezvous point and temporary evacuation centre during the storm, indicating a high level of hazard awareness and preparedness.
    • Based on sea level data analysis, we identified triple peak period bands at 4–8, 8–12 and 20–25 s in the sea level data. Storm surge heights and wave oscillations were up to 0.8 m and 1.5 m, respectively.
    • Based on the numerical simulations of 20 scenarios with different water depths, incident wave amplitudes, surge heights and peak periods, we found that the wave oscillations at the foot of the seawall result in multiple wave interactions and interferences. Consequently, large wave amplitudes, up to 4.6 m higher than the height of the seawall, were generated and overtopped the wall. Extreme impulsive wave impact forces of up to 286 KN were generated by the waves interacting with the seawall.
    • We measured maximum wave overtopping rates of 0.5–16.1 m3/s/m for our scenarios. The cumulative overtopping water volumes per metre length of the wall were 0.7–65.0 m3/m.
    • Analysis of all the evidence combined with our engineering judgement suggests that the most likely initiating cause of the failure was impulsive wave impact forces destabilising one or more grouted joints between adjacent masonry blocks in the wall. Maximum observed pressures of 286 KN in our simulations are four times greater in magnitude than background pressures leading to block removal and initiating failure. Therefore, the sequence of cascading events was :1) impulsive wave impact force causing damage to masonry, 2) failure of the upper sections of the seawall, 3) loss of infill resulting in a reduction of structural strength in the landward direction, 4) ballast washout as wave overtopping and inbound wave activity increased and 5) progressive structural failure following successive tides.

    From a risk mitigation point of view, the stability of the seawall in the face of future energetic cyclonic storm events and sea level rise will become a critical factor in protecting the rail network. Mitigation efforts will involve significant infrastructure investment to strengthen the civil engineering assets combined with improved hazard warning systems consisting of meteorological forecasting and real-time wave observations and instrumentation. These efforts must take into account the amenity value of coastal railway infrastructure to local communities and the significant number of tourists who visit every year. In this regard, public awareness and active engagement in the planning and execution of the project will be crucial in order to secure local stakeholder support for the significant infrastructure project that will be required for future resilience.

    Notes

    1. https://www.networkrail.co.uk/..
    2. https://www.flow3d.com/products/flow-3d-hydro/.
    3. https://www.devonmuseums.net/Dawlish-Museum/Devon-Museums/.
    4. https://ntslf.org/.
    5. https://www.datawell.nl/Products/Buoys/DirectionalWaveriderMkIII.aspx.
    6. https://www.bodc.ac.uk/.
    7. https://coastalmonitoring.org/cco/.
    8. https://webapp.navionics.com/#boating@8&key=iactHlwfP.

    References

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    Acknowledgements

    We are grateful to Brunel University London for administering the scholarship awarded to KA. The Flow3D-Hydro used in this research for numerical modelling is licenced to Brunel University London through an academic programme contract. We sincerely thank Prof Harsh Gupta (Editor-in-Chief) and two anonymous reviewers for their constructive review comments.

    Funding

    This project was funded by the UK Engineering and Physical Sciences Research Council (EPSRC) through a PhD scholarship to Keith Adams.

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    Authors and Affiliations

    1. Department of Civil and Environmental Engineering, Brunel University London, Uxbridge, UB8 3PH, UKKeith Adams
    2. Department of Architecture and Civil Engineering, University of Bath, Bath, BA2 7AY, UKMohammad Heidarzadeh

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    Correspondence to Keith Adams.

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    Adams, K., Heidarzadeh, M. Extratropical cyclone damage to the seawall in Dawlish, UK: eyewitness accounts, sea level analysis and numerical modelling. Nat Hazards (2022). https://doi.org/10.1007/s11069-022-05692-2

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    • Received17 May 2022
    • Accepted17 October 2022
    • Published14 November 2022
    • DOIhttps://doi.org/10.1007/s11069-022-05692-2

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    Keywords

    • Storm surge
    • Cyclone
    • Railway
    • Climate change
    • Infrastructure
    • Resilience
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    TianLiabJ.M.T.DaviesaXiangzhenZhuc
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    cBrunel Centre for Advanced Solidification Technology, Brunel University London, Kingston Ln, London, Uxbridge UB8 3PH, United Kingdom

    Abstract

    An entrainment defect (also known as a double oxide film defect or bifilm) acts a void containing an entrapped gas when submerged into a light-alloy melt, thus reducing the quality and reproducibility of the final castings. Previous publications, carried out with Al-alloy castings, reported that this trapped gas could be subsequently consumed by the reaction with the surrounding melt, thus reducing the void volume and negative effect of entrainment defects. Compared with Al-alloys, the entrapped gas within Mg-alloy might be more efficiently consumed due to the relatively high reactivity of magnesium. However, research into the entrainment defects within Mg alloys has been significantly limited. In the present work, AZ91 alloy castings were produced under different carrier gas atmospheres (i.e., SF6/CO2, SF6/air). The evolution processes of the entrainment defects contained in AZ91 alloy were suggested according to the microstructure inspections and thermodynamic calculations. The defects formed in the different atmospheres have a similar sandwich-like structure, but their oxide films contained different combinations of compounds. The use of carrier gases, which were associated with different entrained-gas consumption rates, affected the reproducibility of AZ91 castings.

    연행 결함(이중 산화막 결함 또는 이중막이라고도 함)은 경합금 용융물에 잠길 때 갇힌 가스를 포함하는 공극으로 작용하여 최종 주물의 품질과 재현성을 저하시킵니다. Al-합금 주물을 사용하여 수행된 이전 간행물에서는 이 갇힌 가스가 주변 용융물과의 반응에 의해 후속적으로 소모되어 공극 부피와 연행 결함의 부정적인 영향을 줄일 수 있다고 보고했습니다. Al-합금에 비해 마그네슘의 상대적으로 높은 반응성으로 인해 Mg-합금 내에 포집된 가스가 더 효율적으로 소모될 수 있습니다. 그러나 Mg 합금 내 연행 결함에 대한 연구는 상당히 제한적이었습니다. 현재 작업에서 AZ91 합금 주물은 다양한 캐리어 가스 분위기(즉, SF6/CO2, SF6/공기)에서 생산되었습니다. AZ91 합금에 포함된 연행 결함의 진화 과정은 미세 조직 검사 및 열역학 계산에 따라 제안되었습니다. 서로 다른 분위기에서 형성된 결함은 유사한 샌드위치 구조를 갖지만 산화막에는 서로 다른 화합물 조합이 포함되어 있습니다. 다른 동반 가스 소비율과 관련된 운반 가스의 사용은 AZ91 주물의 재현성에 영향을 미쳤습니다.

    Keywords

    Magnesium alloy, Casting, Oxide film, Bifilm, Entrainment defect, Reproducibility

    1. Introduction

    As the lightest structural metal available on Earth, magnesium became one of the most attractive light metals over the last few decades. The magnesium industry has consequently experienced a rapid development in the last 20 years [1,2], indicating a large growth in demand for Mg alloys all over the world. Nowadays, the use of Mg alloys can be found in the fields of automobiles, aerospace, electronics and etc.[3,4]. It has been predicted that the global consumption of Mg metals will further increase in the future, especially in the automotive industry, as the energy efficiency requirement of both traditional and electric vehicles further push manufactures lightweight their design [3,5,6].

    The sustained growth in demand for Mg alloys motivated a wide interest in the improvement of the quality and mechanical properties of Mg-alloy castings. During a Mg-alloy casting process, surface turbulence of the melt can lead to the entrapment of a doubled-over surface film containing a small quantity of the surrounding atmosphere, thus forming an entrainment defect (also known as a double oxide film defect or bifilm) [7], [8], [9], [10]. The random size, quantity, orientation, and placement of entrainment defects are widely accepted to be significant factors linked to the variation of casting properties [7]. In addition, Peng et al. [11] found that entrained oxides films in AZ91 alloy melt acted as filters to Al8Mn5 particles, trapping them as they settle. Mackie et al. [12] further suggested that entrained oxide films can act to trawl the intermetallic particles, causing them to cluster and form extremely large defects. The clustering of intermetallic compounds made the entrainment defects more detrimental for the casting properties.

    Most of the previous studies regarding entrainment defects were carried out on Al-alloys [7,[13], [14], [15], [16], [17], [18], and a few potential methods have been suggested for diminishing their negative effect on the quality of Al-alloy castings. Nyahumwa et al.,[16] shows that the void volume within entrainment defects could be reduced by a hot isostatic pressing (HIP) process. Campbell [7] suggested the entrained gas within the defects could be consumed due to reaction with the surrounding melt, which was further verified by Raiszedeh and Griffiths [19].The effect of the entrained gas consumption on the mechanical properties of Al-alloy castings has been investigated by [8,9], suggesting that the consumption of the entrained gas promoted the improvement of the casting reproducibility.

    Compared with the investigation concerning the defects within Al-alloys, research into the entrainment defects within Mg-alloys has been significantly limited. The existence of entrainment defects has been demonstrated in Mg-alloy castings [20,21], but their behaviour, evolution, as well as entrained gas consumption are still not clear.

    In a Mg-alloy casting process, the melt is usually protected by a cover gas to avoid magnesium ignition. The cavities of sand or investment moulds are accordingly required to be flushed with the cover gas prior to the melt pouring [22]. Therefore, the entrained gas within Mg-alloy castings should contain the cover gas used in the casting process, rather than air only, which may complicate the structure and evolution of the corresponding entrainment defects.

    SF6 is a typical cover gas widely used for Mg-alloy casting processes [23], [24], [25]. Although this cover gas has been restricted to use in European Mg-alloy foundries, a commercial report has pointed out that this cover is still popular in global Mg-alloy industry, especially in the countries which dominated the global Mg-alloy production, such as China, Brazil, India, etc. [26]. In addition, a survey in academic publications also showed that this cover gas was widely used in recent Mg-alloy studies [27]. The protective mechanism of SF6 cover gas (i.e., the reaction between liquid Mg-alloy and SF6 cover gas) has been investigated by several previous researchers, but the formation process of the surface oxide film is still not clearly understood, and even some published results are conflicting with each other. In early 1970s, Fruehling [28] found that the surface film formed under SF6 was MgO mainly with traces of fluorides, and suggested that SF6 was absorbed in the Mg-alloy surface film. Couling [29] further noticed that the absorbed SF6 reacted with the Mg-alloy melt to form MgF2. In last 20 years, different structures of the Mg-alloy surface films have been reported, as detailed below.(1)

    Single-layered film. Cashion [30,31] used X-ray Photoelectron Spectroscopy (XPS) and Auger Spectroscopy (AES) to identify the surface film as MgO and MgF2. He also found that composition of the film was constant throughout the thickness and the whole experimental holding time. The film observed by Cashion had a single-layered structure created from a holding time from 10 min to 100 min.(2)

    Double-layered film. Aarstad et. al [32] reported a doubled-layered surface oxide film in 2003. They observed several well-distributed MgF2 particles attached to the preliminary MgO film and grew until they covered 25–50% of the total surface area. The inward diffusion of F through the outer MgO film was the driving force for the evolution process. This double-layered structure was also supported by Xiong’s group [25,33] and Shih et al. [34].(3)

    Triple-layered film. The triple-layered film and its evolution process were reported in 2002 by Pettersen [35]. Pettersen found that the initial surface film was a MgO phase and then gradually evolved to the stable MgF2 phase by the inward diffusion of F. In the final stage, the film has a triple-layered structure with a thin O-rich interlayer between the thick top and bottom MgF2 layers.(4)

    Oxide film consisted of discrete particles. Wang et al [36] stirred the Mg-alloy surface film into the melt under a SF6 cover gas, and then inspect the entrained surface film after the solidification. They found that the entrained surface films were not continues as the protective surface films reported by other researchers but composed of discrete particles. The young oxide film was composed of MgO nano-sized oxide particles, while the old oxide films consist of coarse particles (about 1  µm in average size) on one side that contained fluorides and nitrides.

    The oxide films of a Mg-alloy melt surface or an entrained gas are both formed due to the reaction between liquid Mg-alloy and the cover gas, thus the above-mentioned research regarding the Mg-alloy surface film gives valuable insights into the evolution of entrainment defects. The protective mechanism of SF6 cover gas (i.e., formation of a Mg-alloy surface film) therefore indicated a potential complicated evolution process of the corresponding entrainment defects.

    However, it should be noted that the formation of a surface film on a Mg-alloy melt is in a different situation to the consumption of an entrained gas that is submerged into the melt. For example, a sufficient amount of cover gas was supported during the surface film formation in the studies previously mentioned, which suppressed the depletion of the cover gas. In contrast, the amount of entrained gas within a Mg-alloy melt is finite, and the entrained gas may become fully depleted. Mirak [37] introduced 3.5%SF6/air bubbles into a pure Mg-alloy melt solidifying in a specially designed permanent mould. It was found that the gas bubbles were entirely consumed, and the corresponding oxide film was a mixture of MgO and MgF2. However, the nucleation sites (such as the MgF2 spots observed by Aarstad [32] and Xiong [25,33]) were not observed. Mirak also speculated that the MgF2 formed prior to MgO in the oxide film based on the composition analysis, which was opposite to the surface film formation process reported in previous literatures (i.e., MgO formed prior to MgF2). Mirak’s work indicated that the oxide-film formation of an entrained gas may be quite different from that of surface films, but he did not reveal the structure and evolution of the oxide films.

    In addition, the use of carrier gas in the cover gases also influenced the reaction between the cover gas and the liquid Mg-alloy. SF6/air required a higher content of SF6 than did a SF6/CO2 carrier gas [38], to avoid the ignition of molten magnesium, revealing different gas-consumption rates. Liang et.al [39] suggested that carbon was formed in the surface film when CO2 was used as a carrier gas, which was different from the films formed in SF6/air. An investigation into Mg combustion [40] reported a detection of Mg2C3 in the Mg-alloy sample after burning in CO2, which not only supported Liang’s results, but also indicated a potential formation of Mg carbides in double oxide film defects.

    The work reported here is an investigation into the behaviour and evolution of entrainment defects formed in AZ91 Mg-alloy castings, protected by different cover gases (i.e., SF6/air and SF6/CO2). These carrier gases have different protectability for liquid Mg alloy, which may be therefore associated with different consumption rates and evolution processes of the corresponding entrained gases. The effect of the entrained-gas consumption on the reproducibility of AZ91 castings was also studied.

    2. Experiment

    2.1. Melting and casting

    Three kilograms AZ91 alloy was melted in a mild steel crucible at 700 ± 5 °C. The composition of the AZ91 alloy has been shown in Table 1. Prior to heating, all oxide scale on the ingot surface was removed by machining. The cover gases used were 0.5%SF6/air or 0.5%SF6/CO2 (vol.%) at a flow rate of 6 L/min for different castings. The melt was degassed by argon with a flow rate of 0.3 L/min for 15 min [41,42], and then poured into sand moulds. Prior to pouring, the sand mould cavity was flushed with the cover gas for 20 min [22]. The residual melt (around 1 kg) was solidified in the crucible.

    Table 1. Composition (wt.%) of the AZ91 alloy used in this study.

    AlZnMnSiFeNiMg
    9.40.610.150.020.0050.0017Residual

    Fig. 1(a) shows the dimensions of the casting with runners. A top-filling system was deliberately used to generate entrainment defects in the final castings. Green and Campbell [7,43] suggested that a top-filling system caused more entrainment events (i.e., bifilms) during a casting process, compared with a bottom-filling system. A melt flow simulation (Flow-3D software) of this mould, using Reilly’s model [44] regarding the entrainment events, also predicted that a large amount of bifilms would be contained in the final casting (denoted by the black particles in Fig. 1b).

    Fig. 1. (a) Dimensions of the casting with runners (unit: mm), (b) a melt flow simulation using Flow-3D software together with Reilly's model[44], predicted that a large amount of bifilms (denoted by the black particles) would be contained in the final casting. (c) A solidification simulation using Pro-cast software showed that no shrinkage defect was contained in the final casting.

    Shrinkage defects also affect the mechanical properties and reproducibility of castings. Since this study focused on the effect of bifilms on the casting quality, the mould has been deliberately designed to avoid generating shrinkage defects. A solidification simulation using ProCAST software showed that no shrinkage defect would be contained in the final casting, as shown in Fig. 1c. The casting soundness has also been confirmed using a real time X-ray prior to the test bar machining.

    The sand moulds were made from resin-bonded silica sand, containing 1wt. % PEPSET 5230 resin and 1wt. % PEPSET 5112 catalyst. The sand also contained 2 wt.% Na2SiF6 to act as an inhibitor [45]. The pouring temperature was 700 ± 5 °C. After the solidification, a section of the runner bars was sent to the Sci-Lab Analytical Ltd for a H-content analysis (LECO analysis), and all the H-content measurements were carried out on the 5th day after the casting process. Each of the castings was machined into 40 test bars for a tensile strength test, using a Zwick 1484 tensile test machine with a clip extensometer. The fracture surfaces of the broken test bars were examined using Scanning Electron Microscope (SEM, Philips JEOL7000) with an accelerating voltage of 5–15 kV. The fractured test bars, residual Mg-alloy solidified in the crucible, and the casting runners were then sectioned, polished and also inspected using the same SEM. The cross-section of the oxide film found on the test-bar fracture surface was exposed by the Focused Ion Beam milling technique (FIB), using a CFEI Quanta 3D FEG FIB-SEM. The oxide film required to be analysed was coated with a platinum layer. Then, a gallium ion beam, accelerated to 30 kV, milled the material substrate surrounding the platinum coated area to expose the cross section of the oxide film. EDS analysis of the oxide film’s cross section was carried out using the FIB equipment at accelerating voltage of 30 kV.

    2.2. Oxidation cell

    As previously mentioned, several past researchers investigated the protective film formed on a Mg-alloy melt surface [38,39,[46], [47], [48], [49], [50], [51], [52]. During these experiments, the amount of cover gas used was sufficient, thus suppressing the depletion of fluorides in the cover gas. The experiment described in this section used a sealed oxidation cell, which limited the supply of cover gas, to study the evolution of the oxide films of entrainment defects. The cover gas contained in the oxidation cell was regarded as large-size “entrained bubble”.

    As shown in Fig. 2, the main body of the oxidation cell was a closed-end mild steel tube which had an inner length of 400 mm, and an inner diameter of 32 mm. A water-cooled copper tube was wrapped around the upper section of the cell. When the tube was heated, the cooling system created a temperature difference between the upper and lower sections, causing the interior gas to convect within the tube. The temperature was monitored by a type-K thermocouple located at the top of the crucible. Nie et al. [53] suggested that the SF6 cover gas would react with the steel wall of the holding furnace when they investigated the surface film of a Mg-alloy melt. To avoid this reaction, the interior surface of the steel oxidation cell (shown in Fig. 2) and the upper half section of the thermocouple were coated with boron nitride (the Mg-alloy was not in contact with boron nitride).

    Fig. 2. Schematic of the oxidation cell used to study the evolution of the oxide films of the entrainment defects (unit mm).

    During the experiment, a block of solid AZ91 alloy was placed in a magnesia crucible located at the bottom of the oxidation cell. The cell was heated to 100 °C in an electric resistance furnace under a gas flow rate of 1 L/min. The cell was held at this temperature for 20 min, to replace the original trapped atmosphere (i.e. air). Then, the oxidation cell was further heated to 700 °C, melting the AZ91 sample. The gas inlet and exit valves were then closed, creating a sealed environment for oxidation under a limited supply of cover gas. The oxidation cell was then held at 700 ± 10 °C for periods of time from 5 min to 30 min in 5-min intervals. At the end of each holding time, the cell was quenched in water. After cooling to room temperature, the oxidised sample was sectioned, polished, and subsequently examined by SEM.

    3. Results

    3.1. Structure and composition of the entrainment defects formed in SF6/air

    The structure and composition of the entrainment defect formed in the AZ91 castings under a cover gas of 0.5%SF6/air was observed by SEM and EDS. The results indicate that there exist two types of entrainment defects which are sketched in Fig. 3: (1) Type A defect whose oxide film has a traditional single-layered structure and (2) Type B defect, whose oxide film has two layers. The details of these defects were introduced in the following. Here it should be noticed that, as the entrainment defects are also known as biofilms or double oxide film, the oxide films of Type B defect were referred to as “multi-layered oxide film” or “multi-layered structure” in the present work to avoid a confusing description such as “the double-layered oxide film of a double oxide film defect”.

    Fig. 3. Schematic of the different types of entrainment defects found in AZ91 castings. (a) Type A defect with a single-layered oxide film and (b) Type B defect with two-layered oxide film.

    Fig. 4(a-b) shows a Type A defect having a compact single-layered oxide film with about 0.4 µm thickness. Oxygen, fluorine, magnesium and aluminium were detected in this film (Fig. 4c). It is speculated that oxide film is the mixture of fluoride and oxide of magnesium and aluminium. The detection of fluorine revealed that an entrained cover gas was contained in the formation of this defect. That is to say that the pores shown in Fig. 4(a) were not shrinkage defects or hydrogen porosity, but entrainment defects. The detection of aluminium was different with Xiong and Wang’s previous study [47,48], which showed that no aluminium was contained in their surface film of an AZ91 melt protected by a SF6 cover gas. Sulphur could not be clearly recognized in the element map, but there was a S-peak in the corresponding ESD spectrum.

    Fig. 4. (a) A Type A entrainment defect formed in SF6/air and having a single-layered oxide film, (b) the oxide film of this defect, (c) SEM-EDS element maps (using Philips JEOL7000) corresponding to the area highlighted in (b).

    Fig. 5(a-b) shows a Type B entrainment defect having a multi-layered oxide film. The compact outer layers of the oxide films were enriched with fluorine and oxygen (Fig. 5c), while their relatively porous inner layers were only enriched with oxygen (i.e., poor in fluorine) and partly grew together, thus forming a sandwich-like structure. Therefore, it is speculated that the outer layer is the mixture of fluoride and oxide, while the inner layer is mainly oxide. Sulphur could only be recognized in the EDX spectrum and could not be clearly identified in the element map, which might be due to the small S-content in the cover gas (i.e., 0.5% volume content of SF6 in the cover gas). In this oxide film, aluminium was contained in the outer layer of this oxide film but could not be clearly detected in the inner layer. Moreover, the distribution of Al seems to be uneven. It can be found that, in the right side of the defect, aluminium exists in the film but its concentration can not be identified to be higher than the matrix. However, there is a small area with much higher aluminium concentration in the left side of the defect. Such an uneven distribution of aluminium was also observed in other defects (shown in the following), and it is the result of the formation of some oxide particles in or under the film.

    Fig. 5. (a) A Type B entrainment defect formed in SF6/air and having a multi-layered oxide film, (b) the oxide films of this defect have grown together, (c) SEM-EDS element maps (using Philips JEOL7000) corresponding to the area shown in (b).

    Figs. 4 and 5 show cross sectional observations of the entrainment defects formed in the AZ91 alloy sample cast under a cover gas of SF6/air. It is not sufficient to characterize the entrainment defects only by the figures observed from the two-dimensional section. To have a further understanding, the surface of the entrainment defects (i.e. the oxide film) was further studied by observing the fracture surface of the test bars.

    Fig. 6(a) shows fracture surfaces of an AZ91 alloy tensile test bar produced in SF6/air. Symmetrical dark regions can be seen on both sides of the fracture surfaces. Fig. 6(b) shows boundaries between the dark and bright regions. The bright region consisted of jagged and broken features, while the surface of the dark region was relatively smooth and flat. In addition, the EDS results (Fig. 6c-d and Table 2) show that fluorine, oxygen, sulphur, and nitrogen were only detected in the dark regions, indicating that the dark regions were surface protective films entrained into the melt. Therefore, it could be suggested that the dark regions were an entrainment defect with consideration of their symmetrical nature. Similar defects on fracture surfaces of Al-alloy castings have been previously reported [7]. Nitrides were only found in the oxide films on the test-bar fracture surfaces but never detected in the cross-sectional samples shown in Figs. 4 and 5. An underlying reason is that the nitrides contained in these samples may have hydrolysed during the sample polishing process [54].

    Fig. 6. (a) A pair of the fracture surfaces of a AZ91 alloy tensile test bar produced under a cover gas of SF6/air. The dimension of the fracture surface is 5 mm × 6 mm, (b) a section of the boundary between the dark and bright regions shown in (a), (c-d) EDS spectrum of the (c) bright regions and (d) dark regions, (e) schematic of an entrainment defect contained in a test bar.

    Table 2. EDS results (wt.%) corresponding to the regions shown in Fig. 6 (cover gas: SF6/air).

    Empty CellCOMgFAlZnSN
    Dark region in Fig. 6(b)3.481.3279.130.4713.630.570.080.73
    Bright region in Fig. 6(b)3.58–84.48–11.250.68––

    In conjunction with the cross-sectional observation of the defects shown in Figs. 4 and 5, the structure of an entrainment defect contained in a tensile test bar was sketched as shown in Fig. 6(e). The defect contained an entrained gas enclosed by its oxide film, creating a void section inside the test bar. When the tensile force applied on the defect during the fracture process, the crack was initiated at the void section and propagated along the entrainment defect, since cracks would be propagated along the weakest path [55]. Therefore, when the test bar was finally fractured, the oxide films of entrainment defect appeared on both fracture surfaces of the test bar, as shown in Fig. 6(a).

    3.2. Structure and composition of the entrainment defects formed in SF6/CO2

    Similar to the entrainment defect formed in SF6/air, the defects formed under a cover gas of 0.5%SF6/CO2 also had two types of oxide films (i.e., single-layered and multi-layered types). Fig. 7(a) shows an example of the entrainment defects containing a multi-layered oxide film. A magnified observation to the defect (Fig. 7b) shows that the inner layers of the oxide films had grown together, presenting a sandwich-like structure, which was similar to the defects formed in an atmosphere of SF6/air (Fig. 5b). An EDS spectrum (Fig. 7c) revealed that the joint area (inner layer) of this sandwich-like structure mainly contained magnesium oxides. Peaks of fluorine, sulphur, and aluminium were recognized in this EDS spectrum, but their amount was relatively small. In contrast, the outer layers of the oxide films were compact and composed of a mixture of fluorides and oxides (Fig. 7d-e).

    Fig. 7. (a) An example of entrainment defects formed in SF6/CO2 and having a multi-layered oxide film, (b) magnified observation of the defect, showing the inner layer of the oxide films has grown together, (c) EDS spectrum of the point denoted in (b), (d) outer layer of the oxide film, (e) SEM-EDS element maps (using Philips JEOL7000) corresponding to the area shown in (d).

    Fig. 8(a) shows an entrainment defect on the fracture surfaces of an AZ91 alloy tensile test bar, which was produced in an atmosphere of 0.5%SF6/CO2. The corresponding EDS results (Table 3) showed that oxide film contained fluorides and oxides. Sulphur and nitrogen were not detected. Besides, a magnified observation (Fig. 8b) indicated spots on the oxide film surface. The diameter of the spots ranged from hundreds of nanometres to a few micron meters.

    Fig. 8. (a) A pair of the fracture surfaces of a AZ91 alloy tensile test bar, produced in an atmosphere of SF6/CO2. The dimension of the fracture surface is 5 mm × 6 mm, (b) surface appearance of the oxide films on the fracture surfaces, showing spots on the film surface.

    To further reveal the structure and composition of the oxide film clearly, the cross-section of the oxide film on a test-bar fracture surface was onsite exposed using the FIB technique (Fig. 9). As shown in Fig. 9a, a continuous oxide film was found between the platinum coating layer and the Mg-Al alloy substrate. Fig. 9 (b-c) shows a magnified observation to oxide films, indicating a multi-layered structure (denoted by the red box in Fig. 9c). The bottom layer was enriched with fluorine and oxygen and should be the mixture of fluoride and oxide, which was similar to the “outer layer” shown in Figs. 5 and 7, while the only-oxygen-enriched top layer was similar to the “inner layer” shown in Figs. 5 and 7.

    Fig. 9. (a) A cross-sectional observation of the oxide film on the fracture surface of the AZ91 casting produced in SF6/CO2, exposed by FIB, (b) a magnified observation of area highlighted in (a), and (c) SEM-EDS elements map of the area shown in (b), obtained by CFEI Quanta 3D FEG FIB-SEM.

    Except the continuous film, some individual particles were also observed in or below the continuous film, as shown in Fig. 9. An Al-enriched particle was detected in the left side of the oxide film shown in Fig. 9b and might be speculated to be spinel Mg2AlO4 because it also contains abundant magnesium and oxygen elements. The existing of such Mg2AlO4 particles is responsible for the high concentration of aluminium in small areas of the observed film and the uneven distribution of aluminium, as shown in Fig. 5(c). Here it should be emphasized that, although the other part of the bottom layer of the continuous oxide film contains less aluminium than this Al-enriched particle, the Fig. 9c indicated that the amount of aluminium in this bottom layer was still non-negligible, especially when comparing with the outer layer of the film. Below the right side of the oxide film shown in Fig. 9b, a particle was detected and speculated to be MgO because it is rich in Mg and O. According to Wang’s result [56], lots of discrete MgO particles can be formed on the surface of the Mg melt by the oxidation of Mg melt and Mg vapor. The MgO particles observed in our present work may be formed due to the same reasons. While, due to the differences in experimental conditions, less Mg melt can be vapored or react with O2, thus only a few of MgO particles formed in our work. An enrichment of carbon was also found in the film, revealing that CO2 was able to react with the melt, thus forming carbon or carbides. This carbon concentration was consistent with the relatively high carbon content of the oxide film shown in Table 3 (i.e., the dark region). In the area next to the oxide film.

    Table 3. EDS results (wt.%) corresponding to the regions shown in Fig. 8 (cover gas: SF6/ CO2).

    Empty CellCOMgFAlZnSN
    Dark region in Fig. 8(a)7.253.6469.823.827.030.86––
    Bright region in Fig. 8(a)2.100.4482.83–13.261.36––

    This cross-sectional observation of the oxide film on a test bar fracture surface (Fig. 9) further verified the schematic of the entrainment defect shown in Fig. 6(e). The entrainment defects formed in different atmospheres of SF6/CO2 and SF6/air had similar structures, but their compositions were different.

    3.3. Evolution of the oxide films in the oxidation cell

    The results in Section 3.1 and 3.2 have shown the structures and compositions of entrainment defects formed in AZ91 castings under cover gases of SF6/air and SF6/CO2. Different stages of the oxidation reaction may lead to the different structures and compositions of entrainment defects. Although Campbell has conjectured that an entrained gas may react with the surrounding melt, it is rarely reported that the reaction occurring between the Mg-alloy melt and entrapped cover gas. Previous researchers normally focus on the reaction between a Mg-alloy melt and the cover gas in an open environment [38,39,[46], [47], [48], [49], [50], [51], [52], which was different from the situation of a cover gas trapped into the melt. To further understand the formation of the entrainment defect in an AZ91 alloy, the evolution process of oxide films of the entrainment defect was further studied using an oxidation cell.

    Fig. 10 (a and d) shows a surface film held for 5 min in the oxidation cell, protected by 0.5%SF6/air. There was only one single layer consisting of fluoride and oxide (MgF2 and MgO). In this surface film. Sulphur was detected in the EDS spectrum, but its amount was too small to be recognized in the element map. The structure and composition of this oxide film was similar to the single-layered films of entrainment defects shown in Fig. 4.

    Fig. 10. Oxide films formed in the oxidation cell under a cover gas of 0.5%SF6/air and held at 700 °C for (a) 5 min; (b) 10 min; (c) 30 min, and (d-f) the SEM-EDS element maps (using Philips JEOL7000) corresponding to the oxide film shown in (a-c) respectively, (d) 5 min; (e) 10 min; (f) 30 min. The red points in (c and f) are the location references, denoting the boundary of the F-enriched layer in different element maps.

    After a holding time of 10 min, a thin (O, S)-enriched top layer (around 700 nm) appeared upon the preliminary F-enriched film, forming a multi-layered structure, as shown in Fig. 10(b and e). The thickness of the (O, S)-enriched top layer increased with increased holding time. As shown in Fig. 10(c and f), the oxide film held for 30 min also had a multi-layered structure, but the thickness of its (O, S)-enriched top layer (around 2.5 µm) was higher than the that of the 10-min oxide film. The multi-layered oxide films shown in Fig. 10(b-c) presented a similar appearance to the films of the sandwich-like defect shown in Fig. 5.

    The different structures of the oxide films shown in Fig. 10 indicated that fluorides in the cover gas would be preferentially consumed due to the reaction with the AZ91 alloy melt. After the depletion of fluorides, the residual cover gas reacted further with the liquid AZ91 alloy, forming the top (O, S)-enriched layer in the oxide film. Therefore, the different structures and compositions of entrainment defects shown in Figs. 4 and 5 may be due to an ongoing oxidation reaction between melt and entrapped cover gas.

    This multi-layered structure has not been reported in previous publications concerning the protective surface film formed on a Mg-alloy melt [38,[46], [47], [48], [49], [50], [51]. This may be due to the fact that previous researchers carried out their experiments with an un-limited amount of cover gas, creating a situation where the fluorides in the cover gas were not able to become depleted. Therefore, the oxide film of an entrainment defect had behaviour traits similar to the oxide films shown in Fig. 10, but different from the oxide films formed on the Mg-alloy melt surface reported in [38,[46], [47], [48], [49], [50], [51].

    Similar with the oxide films held in SF6/air, the oxide films formed in SF6/CO2 also had different structures with different holding times in the oxidation cell. Fig. 11(a) shows an oxide film, held on an AZ91 melt surface under a cover gas of 0.5%SF6/CO2 for 5 min. This film had a single-layered structure consisting of MgF2. The existence of MgO could not be confirmed in this film. After the holding time of 30 min, the film had a multi-layered structure; the inner layer was of a compact and uniform appearance and composed of MgF2, while the outer layer is the mixture of MgF2 and MgO. Sulphur was not detected in this film, which was different from the surface film formed in 0.5%SF6/air. Therefore, fluorides in the cover gas of 0.5%SF6/CO2 were also preferentially consumed at an early stage of the film growth process. Compared with the film formed in SF6/air, the MgO in film formed in SF6/CO2 appeared later and sulphide did not appear within 30 min. It may mean that the formation and evolution of film in SF6/air is faster than SF6/CO2. CO2 may have subsequently reacted with the melt to form MgO, while sulphur-containing compounds accumulated in the cover gas and reacted to form sulphide in very late stage (may after 30 min in oxidation cell).

    Fig. 11. Oxide films formed in the oxidation cell under a cover gas of 0.5%SF6/CO2, and their SEM-EDS element maps (using Philips JEOL7000). They were held at 700 °C for (a) 5 min; (b) 30 min. The red points in (b) are the location references, denoting the boundary between the top and bottom layers in the oxide film.

    4. Discussion

    4.1. Evolution of entrainment defects formed in SF6/air

    HSC software from Outokumpu HSC Chemistry for Windows (http://www.hsc-chemistry.net/) was used to carry out thermodynamic calculations needed to explore the reactions which might occur between the trapped gases and liquid AZ91 alloy. The solutions to the calculations suggest which products are most likely to form in the reaction process between a small amount of cover gas (i.e., the amount within a trapped bubble) and the AZ91-alloy melt.

    In the trials, the pressure was set to 1 atm, and the temperature set to 700 °C. The amount of the cover gas was assumed to be 7 × 10−7 kg, with a volume of approximately 0.57 cm3 (3.14 × 10−8 kmol) for 0.5%SF6/air, and 0.35 cm3 (3.12 × 10−8 kmol) for 0.5%SF6/CO2. The amount of the AZ91 alloy melt in contact with the trapped gas was assumed to be sufficient to complete all reactions. The decomposition products of SF6 were SF5, SF4, SF3, SF2, F2, S(g), S2(g) and F(g) [57], [58], [59], [60].

    Fig. 12 shows the equilibrium diagram of the thermodynamic calculation of the reaction between the AZ91 alloy and 0.5%SF6/air. In the diagram, the reactants and products with less than 10−15 kmol have not been shown, as this was 5 orders of magnitude less than the amount of SF6 present (≈ 1.57 × 10−10 kmol) and therefore would not affect the observed process in a practical way.

    Fig. 12. An equilibrium diagram for the reaction between 7e-7 kg 0.5%SF6/air and a sufficient amount of AZ91 alloy. The X axis is the amount of AZ91 alloy melt having reacted with the entrained gas, and the vertical Y-axis is the amount of the reactants and products.

    This reaction process could be divided into 3 stages.

    Stage 1: The formation of fluorides. the AZ91 melt preferentially reacted with SF6 and its decomposition products, producing MgF2, AlF3, and ZnF2. However, the amount of ZnF2 may have been too small to be detected practically (1.25 × 10−12 kmol of ZnF2 compared with 3 × 10−10 kmol of MgF2), which may be the reason why Zn was not detected in any the oxide films shown in Sections 3.1–3.3. Meanwhile, sulphur accumulated in the residual gas as SO2.

    Stage 2: The formation of oxides. After the liquid AZ91 alloy had depleted all the available fluorides in the entrapped gas, the amount of AlF3 and ZnF2 quickly reduced due to a reaction with Mg. O2(g) and SO2 reacted with the AZ91 melt, forming MgO, Al2O3, MgAl2O4, ZnO, ZnSO4 and MgSO4. However, the amount of ZnO and ZnSO4 would have been too small to be found practically by EDS (e.g. 9.5 × 10−12 kmol of ZnO,1.38 × 10−14 kmol of ZnSO4, in contrast to 4.68 × 10−10 kmol of MgF2, when the amount of AZ91 on the X-axis is 2.5 × 10−9 kmol). In the experimental cases, the concentration of F in the cover gas is very low, whole the concentration f O is much higher. Therefore, the stage 1 and 2, i.e, the formation of fluoride and oxide may happen simultaneously at the beginning of the reaction, resulting in the formation of a singer-layered mixture of fluoride and oxide, as shown in Figs. 4 and 10(a). While an inner layer consisted of oxides but fluorides could form after the complete depletion of F element in the cover gas.

    Stages 1- 2 theoretically verified the formation process of the multi-layered structure shown in Fig. 10.

    The amount of MgAl2O4 and Al2O3 in the oxide film was of a sufficient amount to be detected, which was consistent with the oxide films shown in Fig. 4. However, the existence of aluminium could not be recognized in the oxide films grown in the oxidation cell, as shown in Fig. 10. This absence of Al may be due to the following reactions between the surface film and AZ91 alloy melt:(1)

    Al2O3 + 3Mg + = 3MgO + 2Al, △G(700 °C) = -119.82 kJ/mol(2)

    Mg + MgAl2O4 = MgO + Al, △G(700 °C) =-106.34 kJ/molwhich could not be simulated by the HSC software since the thermodynamic calculation was carried out under an assumption that the reactants were in full contact with each other. However, in a practical process, the AZ91 melt and the cover gas would not be able to be in contact with each other completely, due to the existence of the protective surface film.

    Stage 3: The formation of Sulphide and nitride. After a holding time of 30 min, the gas-phase fluorides and oxides in the oxidation cell had become depleted, allowing the melt reaction with the residual gas, forming an additional sulphur-enriched layer upon the initial F-enriched or (F, O)-enriched surface film, thus resulting in the observed multi-layered structure shown in Fig. 10 (b and c). Besides, nitrogen reacted with the AZ91 melt until all reactions were completed. The oxide film shown in Fig. 6 may correspond to this reaction stage due to its nitride content. However, the results shows that the nitrides were not detected in the polished samples shown in Figs. 4 and 5, but only found on the test bar fracture surfaces. The nitrides may have hydrolysed during the sample preparation process, as follows [54]:(3)

    Mg3N2 + 6H2O =3Mg(OH)2 + 2NH3↑(4)

    AlN+ 3H2O =Al(OH)3 + NH3↑

    In addition, Schmidt et al. [61] found that Mg3N2 and AlN could react to form ternary nitrides (Mg3AlnNn+2, n= 1, 2, 3…). HSC software did not contain the database of ternary nitrides, and it could not be added into the calculation. The oxide films in this stage may also contain ternary nitrides.

    4.2. Evolution of entrainment defects formed in SF6/CO2

    Fig. 13 shows the results of the thermodynamic calculation between AZ91 alloy and 0.5%SF6/CO2. This reaction processes can also be divided into three stages.

    Fig. 13. An equilibrium diagram for the reaction between 7e-7 kg 0.5%SF6/CO2 and a sufficient amount of AZ91 alloy. The X axis denotes the amount of Mg alloy melt having reacted with the entrained gas, and the vertical Y-axis denotes the amounts of the reactants and products.

    Stage 1: The formation of fluorides. SF6 and its decomposition products were consumed by the AZ91 melt, forming MgF2, AlF3, and ZnF2. As in the reaction of AZ91 in 0.5%SF6/air, the amount of ZnF2 was too small to be detected practically (1.51 × 10−13 kmol of ZnF2 compared with 2.67 × 10−10 kmol of MgF2). Sulphur accumulated in the residual trapped gas as S2(g) and a portion of the S2(g) reacted with CO2, to form SO2 and CO. The products in this reaction stage were consistent with the film shown in Fig. 11(a), which had a single layer structure that contained fluorides only.

    Stage 2: The formation of oxides. AlF3 and ZnF2 reacted with the Mg in the AZ91 melt, forming MgF2, Al and Zn. The SO2 began to be consumed, producing oxides in the surface film and S2(g) in the cover gas. Meanwhile, the CO2 directly reacted with the AZ91 melt, forming CO, MgO, ZnO, and Al2O3. The oxide films shown in Figs. 9 and 11(b) may correspond to this reaction stage due to their oxygen-enriched layer and multi-layered structure.

    The CO in the cover gas could further react with the AZ91 melt, producing C. This carbon may further react with Mg to form Mg carbides, when the temperature reduced (during solidification period) [62]. This may be the reason for the high carbon content in the oxide film shown in Figs. 8–9. Liang et al. [39] also reported carbon-detection in an AZ91 alloy surface film protected by SO2/CO2. The produced Al2O3 may be further combined with MgO, forming MgAl2O4 [63]. As discussed in Section 4.1, the alumina and spinel can react with Mg, causing an absence of aluminium in the surface films, as shown in Fig. 11.

    Stage 3: The formation of Sulphide. the AZ91 melt began to consume S2(g) in the residual entrapped gas, forming ZnS and MgS. These reactions did not occur until the last stage of the reaction process, which could be the reason why the S-content in the defect shown Fig. 7(c) was small.

    In summary, thermodynamic calculations indicate that the AZ91 melt will react with the cover gas to form fluorides firstly, then oxides and sulphides in the last. The oxide film in the different reaction stages would have different structures and compositions.

    4.3. Effect of the carrier gases on consumption of the entrained gas and the reproducibility of AZ91 castings

    The evolution processes of entrainment defects, formed in SF6/air and SF6/CO2, have been suggested in Sections 4.1 and 4.2. The theoretical calculations were verified with respect to the corresponding oxide films found in practical samples. The atmosphere within an entrainment defect could be efficiently consumed due to the reaction with liquid Mg-alloy, in a scenario dissimilar to the Al-alloy system (i.e., nitrogen in an entrained air bubble would not efficiently react with Al-alloy melt [64,65], however, nitrogen would be more readily consumed in liquid Mg alloys, commonly referred to as “nitrogen burning” [66]).

    The reaction between the entrained gas and the surrounding liquid Mg-alloy converted the entrained gas into solid compounds (e.g. MgO) within the oxide film, thus reducing the void volume of the entrainment defect and hence probably causing a collapse of the defect (e.g., if an entrained gas of air was depleted by the surrounding liquid Mg-alloy, under an assumption that the melt temperature is 700 °C and the depth of liquid Mg-alloy is 10 cm, the total volume of the final solid products would be 0.044% of the initial volume taken by the entrapped air).

    The relationship between the void volume reduction of entrainment defects and the corresponding casting properties has been widely studied in Al-alloy castings. Nyahumwa and Campbell [16] reported that the Hot Isostatic Pressing (HIP) process caused the entrainment defects in Al-alloy castings to collapse and their oxide surfaces forced into contact. The fatigue lives of their castings were improved after HIP. Nyahumwa and Campbell [16] also suggested a potential bonding of the double oxide films that were in contact with each other, but there was no direct evidence to support this. This binding phenomenon was further investigated by Aryafar et.al.[8], who re-melted two Al-alloy bars with oxide skins in a steel tube and then carried out a tensile strength test on the solidified sample. They found that the oxide skins of the Al-alloy bars strongly bonded with each other and became even stronger with an extension of the melt holding time, indicating a potential “healing” phenomenon due to the consumption of the entrained gas within the double oxide film structure. In addition, Raidszadeh and Griffiths [9,19] successfully reduced the negative effect of entrainment defects on the reproducibility of Al-alloy castings, by extending the melt holding time before solidification, which allowed the entrained gas to have a longer time to react with the surrounding melt.

    With consideration of the previous work mentioned, the consumption of the entrained gas in Mg-alloy castings may diminish the negative effect of entrainment defects in the following two ways.

    (1) Bonding phenomenon of the double oxide films. The sandwich-like structure shown in Fig. 5 and 7 indicated a potential bonding of the double oxide film structure. However, more evidence is required to quantify the increase in strength due to the bonding of the oxide films.

    (2) Void volume reduction of entrainment defects. The positive effect of void-volume reduction on the quality of castings has been widely demonstrated by the HIP process [67]. As the evolution processes discussed in Section 4.1–4.2, the oxide films of entrainment defects can grow together due to an ongoing reaction between the entrained gas and surrounding AZ91 alloy melt. The volume of the final solid products was significant small compared with the entrained gas (i.e., 0.044% as previously mentioned).

    Therefore, the consumption rate of the entrained gas (i.e., the growth rate of oxide films) may be a critical parameter for improving the quality of AZ91 alloy castings. The oxide film growth rate in the oxidization cell was accordingly further investigated.

    Fig. 14 shows a comparison of the surface film growth rates in different cover gases (i.e., 0.5%SF6/air and 0.5%SF6/CO2). 15 random points on each sample were selected for film thickness measurements. The 95% confidence interval (95%CI) was computed under an assumption that the variation of the film thickness followed a Gaussian distribution. It can be seen that all the surface films formed in 0.5%SF6/air grew faster than those formed in 0.5%SF6/CO2. The different growth rates suggested that the entrained-gas consumption rate of 0.5%SF6/air was higher than that of 0.5%SF6/CO2, which was more beneficial for the consumption of the entrained gas.

    Fig. 14. A comparison of the AZ91 alloy oxide film growth rates in 0.5%SF6/air and 0.5%SF6/CO2

    It should be noted that, in the oxidation cell, the contact area of liquid AZ91 alloy and cover gas (i.e. the size of the crucible) was relatively small with consideration of the large volume of melt and gas. Consequently, the holding time for the oxide film growth within the oxidation cell was comparatively long (i.e., 5–30 min). However, the entrainment defects contained in a real casting are comparatively very small (i.e., a few microns size as shown in Figs. 3–6, and [7]), and the entrained gas is fully enclosed by the surrounding melt, creating a relatively large contact area. Hence the reaction time for cover gas and the AZ91 alloy melt may be comparatively short. In addition, the solidification time of real Mg-alloy sand castings can be a few minutes (e.g. Guo [68] reported that a Mg-alloy sand casting with 60 mm diameter required 4 min to be solidified). Therefore, it can be expected that an entrained gas trapped during an Mg-alloy melt pouring process will be readily consumed by the surrounding melt, especially for sand castings and large-size castings, where solidification times are long.

    Therefore, the different cover gases (0.5%SF6/air and 0.5%SF6/CO2) associated with different consumption rates of the entrained gases may affect the reproducibility of the final castings. To verify this assumption, the AZ91 castings produced in 0.5%SF6/air and 0.5%SF6/CO2 were machined into test bars for mechanical evaluation. A Weibull analysis was carried out using both linear least square (LLS) method and non-linear least square (non-LLS) method [69].

    Fig. 15(a-b) shows a traditional 2-p linearized Weibull plot of the UTS and elongation of the AZ91 alloy castings, obtained by the LLS method. The estimator used is P= (i-0.5)/N, which was suggested to cause the lowest bias among all the popular estimators [69,70]. The casting produced in SF6/air has an UTS Weibull moduli of 16.9, and an elongation Weibull moduli of 5.0. In contrast, the UTS and elongation Weibull modulus of the casting produced in SF6/CO2 are 7.7 and 2.7 respectively, suggesting that the reproducibility of the casting protected by SF6/CO2 were much lower than that produced in SF6/air.

    Fig. 15. The Weibull modulus of AZ91 castings produced in different atmospheres, estimated by (a-b) the linear least square method, (c-d) the non-linear least square method, where SSR is the sum of residual squares.

    In addition, the author’s previous publication [69] demonstrated a shortcoming of the linearized Weibull plots, which may cause a higher bias and incorrect R2 interruption of the Weibull estimation. A Non-LLS Weibull estimation was therefore carried out, as shown in Fig. 15 (c-d). The UTS Weibull modulus of the SF6/air casting was 20.8, while the casting produced under SF6/CO2 had a lower UTS Weibull modulus of 11.4, showing a clear difference in their reproducibility. In addition, the SF6/air elongation (El%) dataset also had a Weibull modulus (shape = 5.8) higher than the elongation dataset of SF6/CO2 (shape = 3.1). Therefore, both the LLS and Non-LLS estimations suggested that the SF6/air casting has a higher reproducibility than the SF6/CO2 casting. It supports the method that the use of air instead of CO2 contributes to a quicker consumption of the entrained gas, which may reduce the void volume within the defects. Therefore, the use of 0.5%SF6/air instead of 0.5%SF6/CO2 (which increased the consumption rate of the entrained gas) improved the reproducibility of the AZ91 castings.

    However, it should be noted that not all the Mg-alloy foundries followed the casting process used in present work. The Mg-alloy melt in present work was degassed, thus reducing the effect of hydrogen on the consumption of the entrained gas (i.e., hydrogen could diffuse into the entrained gas, potentially suppressing the depletion of the entrained gas [7,71,72]). In contrast, in Mg-alloy foundries, the Mg-alloy melt is not normally degassed, since it was widely believed that there is not a ‘gas problem’ when casting magnesium and hence no significant change in tensile properties [73]. Although studies have shown the negative effect of hydrogen on the mechanical properties of Mg-alloy castings [41,42,73], a degassing process is still not very popular in Mg-alloy foundries.

    Moreover, in present work, the sand mould cavity was flushed with the SF6 cover gas prior to pouring [22]. However, not all the Mg-alloy foundries flushed the mould cavity in this way. For example, the Stone Foundry Ltd (UK) used sulphur powder instead of the cover-gas flushing. The entrained gas within their castings may be SO2/air, rather than the protective gas.

    Therefore, although the results in present work have shown that using air instead of CO2 improved the reproducibility of the final casting, it still requires further investigations to confirm the effect of carrier gases with respect to different industrial Mg-alloy casting processes.

    7. Conclusion

    Entrainment defects formed in an AZ91 alloy were observed. Their oxide films had two types of structure: single-layered and multi-layered. The multi-layered oxide film can grow together forming a sandwich-like structure in the final casting.2.

    Both the experimental results and the theoretical thermodynamic calculations demonstrated that fluorides in the trapped gas were depleted prior to the consumption of sulphur. A three-stage evolution process of the double oxide film defects has been suggested. The oxide films contained different combinations of compounds, depending on the evolution stage. The defects formed in SF6/air had a similar structure to those formed in SF6/CO2, but the compositions of their oxide films were different. The oxide-film formation and evolution process of the entrainment defects were different from that of the Mg-alloy surface films previous reported (i.e., MgO formed prior to MgF2).3.

    The growth rate of the oxide film was demonstrated to be greater under SF6/air than SF6/CO2, contributing to a quicker consumption of the damaging entrapped gas. The reproducibility of an AZ91 alloy casting improved when using SF6/air instead of SF6/CO2.

    Acknowledgements

    The authors acknowledge funding from the EPSRC LiME grant EP/H026177/1, and the help from Dr W.D. Griffiths and Mr. Adrian Carden (University of Birmingham). The casting work was carried out in University of Birmingham.

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    원문보기
    Fig. 1. Schematic figure showing the PREP with additional gas flowing on the end face of electrode.

    플라즈마 회전 전극 공정 중 분말 형성에 대한 공정 매개변수 및 냉각 가스의 영향

    Effects of process parameters and cooling gas on powder formation during the plasma rotating electrode process

    Yujie Cuia Yufan Zhaoa1 Haruko Numatab Kenta Yamanakaa Huakang Biana Kenta Aoyagia AkihikoChibaa
    aInstitute for Materials Research, Tohoku University, Sendai 980-8577, JapanbDepartment of Materials Processing, Graduate School of Engineering, Tohoku University, Sendai 980-8577, Japan

    Highlights

    •The limitation of increasing the rotational speed in decreasing powder size was clarified.

    •Cooling and disturbance effects varied with the gas flowing rate.

    •Inclined angle of the residual electrode end face affected powder formation.

    •Additional cooling gas flowing could be applied to control powder size.

    Abstract

    The plasma rotating electrode process (PREP) is rapidly becoming an important powder fabrication method in additive manufacturing. However, the low production rate of fine PREP powder limits the development of PREP. Herein, we investigated different factors affecting powder formation during PREP by combining experimental methods and numerical simulations. The limitation of increasing the rotation electrode speed in decreasing powder size is attributed to the increased probability of adjacent droplets recombining and the decreased tendency of granulation. The effects of additional Ar/He gas flowing on the rotational electrode on powder formation is determined through the cooling effect, the disturbance effect, and the inclined effect of the residual electrode end face simultaneously. A smaller-sized powder was obtained in the He atmosphere owing to the larger inclined angle of the residual electrode end face compared to the Ar atmosphere. Our research highlights the route for the fabrication of smaller-sized powders using PREP.

    플라즈마 회전 전극 공정(PREP)은 적층 제조 에서 중요한 분말 제조 방법으로 빠르게 자리잡고 있습니다. 그러나 미세한 PREP 분말의 낮은 생산율은 PREP의 개발을 제한합니다. 여기에서 우리는 실험 방법과 수치 시뮬레이션을 결합하여 PREP 동안 분말 형성에 영향을 미치는 다양한 요인을 조사했습니다. 분말 크기 감소에서 회전 전극 속도 증가의 한계는 인접한 액적 재결합 확률 증가 및 과립화 경향 감소에 기인합니다.. 회전 전극에 흐르는 추가 Ar/He 가스가 분말 형성에 미치는 영향은 냉각 효과, 외란 효과 및 잔류 전극 단면의 경사 효과를 통해 동시에 결정됩니다. He 분위기에서는 Ar 분위기에 비해 잔류 전극 단면의 경사각이 크기 때문에 더 작은 크기의 분말이 얻어졌다. 우리의 연구는 PREP를 사용하여 더 작은 크기의 분말을 제조하는 경로를 강조합니다.

    Keywords

    Plasma rotating electrode process

    Ti-6Al-4 V alloy, Rotating speed, Numerical simulation, Gas flowing, Powder size

    Introduction

    With the development of additive manufacturing, there has been a significant increase in high-quality powder production demand [1,2]. The initial powder characteristics are closely related to the uniform powder spreading [3,4], packing density [5], and layer thickness observed during additive manufacturing [6], thus determining the mechanical properties of the additive manufactured parts [7,8]. Gas atomization (GA) [9–11], centrifugal atomization (CA) [12–15], and the plasma rotating electrode process (PREP) are three important powder fabrication methods.

    Currently, GA is the dominant powder fabrication method used in additive manufacturing [16] for the fabrication of a wide range of alloys [11]. GA produces powders by impinging a liquid metal stream to droplets through a high-speed gas flow of nitrogen, argon, or helium. With relatively low energy consumption and a high fraction of fine powders, GA has become the most popular powder manufacturing technology for AM.

    The entrapped gas pores are generally formed in the powder after solidification during GA, in which the molten metal is impacted by a high-speed atomization gas jet. In addition, satellites are formed in GA powder when fine particles adhere to partially molten particles.

    The gas pores of GA powder result in porosity generation in the additive manufactured parts, which in turn deteriorates its mechanical properties because pores can become crack initiation sites [17]. In CA, a molten metal stream is poured directly onto an atomizer disc spinning at a high rotational speed. A thin film is formed on the surface of the disc, which breaks into small droplets due to the centrifugal force. Metal powder is obtained when these droplets solidify.

    Compared with GA powder, CA powder exhibits higher sphericity, lower impurity content, fewer satellites, and narrower particle size distribution [12]. However, very high speed is required to obtain fine powder by CA. In PREP, the molten metal, melted using the plasma arc, is ejected from the rotating rod through centrifugal force. Compared with GA powder, PREP-produced powders also have higher sphericity and fewer pores and satellites [18].

    For instance, PREP-fabricated Ti6Al-4 V alloy powder with a powder size below 150 μm exhibits lower porosity than gas-atomized powder [19], which decreases the porosity of additive manufactured parts. Furthermore, the process window during electron beam melting was broadened using PREP powder compared to GA powder in Inconel 718 alloy [20] owing to the higher sphericity of the PREP powder.

    In summary, PREP powder exhibits many advantages and is highly recommended for powder-based additive manufacturing and direct energy deposition-type additive manufacturing. However, the low production rate of fine PREP powder limits the widespread application of PREP powder in additive manufacturing.

    Although increasing the rotating speed is an effective method to decrease the powder size [21,22], the reduction in powder size becomes smaller with the increased rotating speed [23]. The occurrence of limiting effects has not been fully clarified yet.

    Moreover, the powder size can be decreased by increasing the rotating electrode diameter [24]. However, these methods are quite demanding for the PREP equipment. For instance, it is costly to revise the PREP equipment to meet the demand of further increasing the rotating speed or electrode diameter.

    Accordingly, more feasible methods should be developed to further decrease the PREP powder size. Another factor that influences powder formation is the melting rate [25]. It has been reported that increasing the melting rate decreases the powder size of Inconel 718 alloy [26].

    In contrast, the powder size of SUS316 alloy was decreased by decreasing the plasma current within certain ranges. This was ascribed to the formation of larger-sized droplets from fluid strips with increased thickness and spatial density at higher plasma currents [27]. The powder size of NiTi alloy also decreases at lower melting rates [28]. Consequently, altering the melting rate, varied with the plasma current, is expected to regulate the PREP powder size.

    Furthermore, gas flowing has a significant influence on powder formation [27,29–31]. On one hand, the disturbance effect of gas flowing promotes fluid granulation, which in turn contributes to the formation of smaller-sized powder [27]. On the other hand, the cooling effect of gas flowing facilitates the formation of large-sized powder due to increased viscosity and surface tension. However, there is a lack of systematic research on the effect of different gas flowing on powder formation during PREP.

    Herein, the authors systematically studied the effects of rotating speed, electrode diameter, plasma current, and gas flowing on the formation of Ti-6Al-4 V alloy powder during PREP as additive manufactured Ti-6Al-4 V alloy exhibits great application potential [32]. Numerical simulations were conducted to explain why increasing the rotating speed is not effective in decreasing powder size when the rotation speed reaches a certain level. In addition, the different factors incited by the Ar/He gas flowing on powder formation were clarified.

    Fig. 1. Schematic figure showing the PREP with additional gas flowing on the end face of electrode.
    Fig. 1. Schematic figure showing the PREP with additional gas flowing on the end face of electrode.

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    원문보기
    Figure 2. Schematic diagram for pilot-scale cooling-water circulation system (a) along with a real picture of the system (b).

    Application of Computational Fluid Dynamics in Chlorine-Dynamics Modeling of In-Situ Chlorination Systems for Cooling Systems

    Jongchan Yi 1, Jonghun Lee 1, Mohd Amiruddin Fikri 2,3, Byoung-In Sang 4 and Hyunook Kim 1,*

    Abstract

    염소화는 상대적인 효율성과 저렴한 비용으로 인해 발전소 냉각 시스템에서 생물학적 오염을 제어하는​​데 선호되는 방법입니다. 해안 지역에 발전소가 있는 경우 바닷물을 사용하여 현장에서 염소를 전기화학적으로 생성할 수 있습니다. 이를 현장 전기염소화라고 합니다. 이 접근 방식은 유해한 염소화 부산물이 적고 염소를 저장할 필요가 없다는 점을 포함하여 몇 가지 장점이 있습니다. 그럼에도 불구하고, 이 전기화학적 공정은 실제로는 아직 초기 단계에 있습니다. 이 연구에서는 파일럿 규모 냉각 시스템에서 염소 붕괴를 시뮬레이션하기 위해 병렬 1차 동역학을 적용했습니다. 붕괴가 취수관을 따라 발생하기 때문에 동역학은 전산유체역학(CFD) 코드에 통합되었으며, 이후에 파이프의 염소 거동을 시뮬레이션하는데 적용되었습니다. 실험과 시뮬레이션 데이터는 강한 난류가 형성되는 조건하에서도 파이프 벽을 따라 염소 농도가 점진적인 것으로 나타났습니다. 염소가 중간보다 파이프 표면을 따라 훨씬 더 집중적으로 남아 있다는 사실은 전기 염소화를 기반으로 하는 시스템의 전체 염소 요구량을 감소시킬 수 있었습니다. 현장 전기 염소화 방식의 냉각 시스템은 직접 주입 방식에 필요한 염소 사용량의 1/3만 소비했습니다. 따라서 현장 전기염소화는 해안 지역의 발전소에서 바이오파울링 제어를 위한 비용 효율적이고 환경 친화적인 접근 방식으로 사용될 수 있다고 결론지었습니다.

    Chlorination is the preferred method to control biofouling in a power plant cooling system due to its comparative effectiveness and low cost. If a power plant is located in a coastal area, chlorine can be electrochemically generated in-situ using seawater, which is called in-situ electrochlorination; this approach has several advantages including fewer harmful chlorination byproducts and no need for chlorine storage. Nonetheless, this electrochemical process is still in its infancy in practice. In this study, a parallel first-order kinetics was applied to simulate chlorine decay in a pilot-scale cooling system. Since the decay occurs along the water-intake pipe, the kinetics was incorporated into computational fluid dynamics (CFD) codes, which were subsequently applied to simulate chlorine behavior in the pipe. The experiment and the simulation data indicated that chlorine concentrations along the pipe wall were incremental, even under the condition where a strong turbulent flow was formed. The fact that chlorine remained much more concentrated along the pipe surface than in the middle allowed for the reduction of the overall chlorine demand of the system based on the electro-chlorination. The cooling system, with an in-situ electro-chlorination, consumed only 1/3 of the chlorine dose demanded by the direct injection method. Therefore, it was concluded that in-situ electro-chlorination could serve as a cost-effective and environmentally friendly approach for biofouling control at power plants on coastal areas.

    Keywords

    computational fluid dynamics; power plant; cooling system; electro-chlorination; insitu chlorination

    Figure 1. Electrodes and batch experiment set-up. (a) Two cylindrical electrodes used in this study. (b) Batch experiment set-up for kinetic tests.
    Figure 1. Electrodes and batch experiment set-up. (a) Two cylindrical electrodes used in this study. (b) Batch experiment set-up for kinetic tests.
    Figure 2. Schematic diagram for pilot-scale cooling-water circulation system (a) along with a real picture of the system (b).
    Figure 2. Schematic diagram for pilot-scale cooling-water circulation system (a) along with a real picture of the system (b).
    Figure 3. Free chlorine decay curves in seawater with different TOC and initial chlorine concentration. Each line represents the predicted concentration of chlorine under a given condition. (a) Artificial seawater solution with 1 mg L−1 of TOC; (b) artificial seawater solution with 2 mg L−1 of TOC; (c) artificial seawater solution with 3 mg L−1 of TOC; (d) West Sea water (1.3 mg L−1 of TOC).
    Figure 3. Free chlorine decay curves in seawater with different TOC and initial chlorine concentration. Each line represents the predicted concentration of chlorine under a given condition. (a) Artificial seawater solution with 1 mg L−1 of TOC; (b) artificial seawater solution with 2 mg L−1 of TOC; (c) artificial seawater solution with 3 mg L−1 of TOC; (d) West Sea water (1.3 mg L−1 of TOC).
    Figure 4. Correlation between model and experimental data in the chlorine kinetics using seawater.
    Figure 4. Correlation between model and experimental data in the chlorine kinetics using seawater.
    Figure 5. Free chlorine concentrations in West Sea water under different current conditions in an insitu electro-chlorination system.
    Figure 5. Free chlorine concentrations in West Sea water under different current conditions in an insitu electro-chlorination system.
    Figure 6. Free chlorine distribution along the sampling ports under different flow rates. Each dot represents experimental data, and each point on the black line is the expected chlorine concentration obtained from computational fluid dynamics (CFD) simulation with a parallel first-order decay model. The red-dotted line is the desirable concentration at the given flow rate: (a) 600 L min−1 of flow rate, (b) 700 L min−1 of flow rate, (c) 800 L min−1 of flow rate, (d) 900 L min−1 of flow rate.
    Figure 6. Free chlorine distribution along the sampling ports under different flow rates. Each dot represents experimental data, and each point on the black line is the expected chlorine concentration obtained from computational fluid dynamics (CFD) simulation with a parallel first-order decay model. The red-dotted line is the desirable concentration at the given flow rate: (a) 600 L min−1 of flow rate, (b) 700 L min−1 of flow rate, (c) 800 L min−1 of flow rate, (d) 900 L min−1 of flow rate.
    Figure 7. Fluid contour images from CFD simulation of the electro-chlorination experiment. Inlet flow rate is 800 L min−1. Outlet pressure was set to 10.8 kPa. (a) Chlorine concentration; (b) expanded view of electrode side in image (a); (c) velocity magnitude; (d) pressure.
    Figure 7. Fluid contour images from CFD simulation of the electro-chlorination experiment. Inlet flow rate is 800 L min−1. Outlet pressure was set to 10.8 kPa. (a) Chlorine concentration; (b) expanded view of electrode side in image (a); (c) velocity magnitude; (d) pressure.
    Figure 8. Chlorine concentration contour in the simulation of full-scale in-situ electro-chlorination with different cathode positions. The pipe diameter is 2 m and the flow rate is 14 m3 s−1. The figure shows 10 m of the pipeline. (a) The simulation result when the cathode is placed on the surface of the pipe wall. (b) The simulation result when the cathode is placed on the inside of the pipe with 100 mm of distance from the pipe wall.
    Figure 8. Chlorine concentration contour in the simulation of full-scale in-situ electro-chlorination with different cathode positions. The pipe diameter is 2 m and the flow rate is 14 m3 s−1. The figure shows 10 m of the pipeline. (a) The simulation result when the cathode is placed on the surface of the pipe wall. (b) The simulation result when the cathode is placed on the inside of the pipe with 100 mm of distance from the pipe wall.
    Figure 9. Comparison of in-situ electro-chlorination and direct chlorine injection in full-scale applications. (a) Estimated chlorine concentrations along the pipe surface. (b) Relative chlorine demands.
    Figure 9. Comparison of in-situ electro-chlorination and direct chlorine injection in full-scale applications. (a) Estimated chlorine concentrations along the pipe surface. (b) Relative chlorine demands.

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    PDF 원문 보기
    Fig. 5. The predicted shapes of initial breach (a) Rectangular (b) V-notch. Fig. 6. Dam breaching stages.

    Investigating the peak outflow through a spatial embankment dam breach

    공간적 제방댐 붕괴를 통한 최대 유출량 조사

    Mahmoud T.GhonimMagdy H.MowafyMohamed N.SalemAshrafJatwaryFaculty of Engineering, Zagazig University, Zagazig 44519, Egypt

    Abstract

    Investigating the breach outflow hydrograph is an essential task to conduct mitigation plans and flood warnings. In the present study, the spatial dam breach is simulated by using a three-dimensional computational fluid dynamics model, FLOW-3D. The model parameters were adjusted by making a comparison with a previous experimental model. The different parameters (initial breach shape, dimensions, location, and dam slopes) are studied to investigate their effects on dam breaching. The results indicate that these parameters have a significant impact. The maximum erosion rate and peak outflow for the rectangular shape are higher than those for the V-notch by 8.85% and 5%, respectively. Increasing breach width or decreasing depth by 5% leads to increasing maximum erosion rate by 11% and 15%, respectively. Increasing the downstream slope angle by 4° leads to an increase in both peak outflow and maximum erosion rate by 2.0% and 6.0%, respectively.

    유출 유출 수문곡선을 조사하는 것은 완화 계획 및 홍수 경보를 수행하는 데 필수적인 작업입니다. 본 연구에서는 3차원 전산유체역학 모델인 FLOW-3D를 사용하여 공간 댐 붕괴를 시뮬레이션합니다. 이전 실험 모델과 비교하여 모델 매개변수를 조정했습니다.

    다양한 매개변수(초기 붕괴 형태, 치수, 위치 및 댐 경사)가 댐 붕괴에 미치는 영향을 조사하기 위해 연구됩니다. 결과는 이러한 매개변수가 상당한 영향을 미친다는 것을 나타냅니다. 직사각형 형태의 최대 침식율과 최대 유출량은 V-notch보다 각각 8.85%, 5% 높게 나타났습니다.

    위반 폭을 늘리거나 깊이를 5% 줄이면 최대 침식률이 각각 11% 및 15% 증가합니다. 하류 경사각을 4° 증가시키면 최대 유출량과 최대 침식률이 각각 2.0% 및 6.0% 증가합니다.

    Keywords

    Spatial dam breach; FLOW-3D; Overtopping erosion; Computational fluid dynamics (CFD)

    1. Introduction

    There are many purposes for dam construction, such as protection from flood disasters, water storage, and power generation. Embankment failures may have a catastrophic impact on lives and infrastructure in the downstream regions. One of the most common causes of embankment dam failure is overtopping. Once the overtopping of the dam begins, the breach formation will start in the dam body then end with the dam failure. This failure occurs within a very short time, which threatens to be very dangerous. Therefore, understanding and modeling the embankment breaching processes is essential for conducting mitigation plans, flood warnings, and forecasting flood damage.

    The analysis of the dam breaching process is implemented by different techniques: comparative methods, empirical models with dimensional and dimensionless solutions, physical-based models, and parametric models. These models were described in detail [1]. Parametric modeling is commonly used to simulate breach growth as a time-dependent linear process and calculate outflow discharge from the breach using hydraulics principles [2]. Alhasan et al. [3] presented a simple one-dimensional mathematical model and a computer code to simulate the dam breaching process. These models were validated by small dams breaching during the floods in 2002 in the Czech Republic. Fread [4] developed an erosion model (BREACH) based on hydraulics principles, sediment transport, and soil mechanics to estimate breach size, time of formation, and outflow discharge. Říha et al. [5] investigated the dam break process for a cascade of small dams using a simple parametric model for piping and overtopping erosion, as well as a 2D shallow-water flow model for the flood in downstream areas. Goodarzi et al. [6] implemented mathematical and statistical methods to assess the effect of inflows and wind speeds on the dam’s overtopping failure.

    Dam breaching studies can be divided into two main modes of erosion. The first mode is called “planar dam breach” where the flow overtops the whole dam width. While the second mode is called “spatial dam breach” where the flow overtops through the initial pilot channel (i.e., a channel created in the dam body). Therefore, the erosion will be in both vertical and horizontal directions [7].

    The erosion process through the embankment dams occurs due to the shear stress applied by water flows. The dam breaching evolution can be divided into three stages [8], [9], but Y. Yang et al. [10] divided the breach development into five stages: Stage I, the seepage erosion; Stage II, the initial breach formation; Stage III, the head erosion; Stage IV, the breach expansion; and Stage V, the re-equilibrium of the river channel through the breach. Many experimental tests have been carried out on non-cohesive embankment dams with an initial breach to examine the effect of upstream inflow discharges on the longitudinal profile evolution and the time to inflection point [11].

    Zhang et al. [12] studied the effect of changing downstream slope angle, sediment grain size, and dam crest length on erosion rates. They noticed that increasing dam crest length and decreasing downstream slope angle lead to decreasing sediment transport rate. While the increase in sediment grain size leads to an increased sediment transport rate at the initial stages. Höeg et al. [13] presented a series of field tests to investigate the stability of embankment dams made of various materials. Overtopping and piping were among the failure tests carried out for the dams composed of homogeneous rock-fill, clay, or gravel with a height of up to 6.0 m. Hakimzadeh et al. [14] constructed 40 homogeneous cohesive and non-cohesive embankment dams to study the effect of changing sediment diameter and dam height on the breaching process. They also used genetic programming (GP) to estimate the breach outflow. Refaiy et al. [15] studied different scenarios for the downstream drain geometry, such as length, height, and angle, to minimize the effect of piping phenomena and therefore increase dam safety.

    Zhu et al. [16] examined the effect of headcut erosion on dam breach growth, especially in the case of cohesive dams. They found that the breach growth in non-cohesive embankments is slower than cohesive embankments due to the little effect of headcut. Schmocker and Hager [7] proposed a relationship for estimating peak outflow from the dam breach process.(1)QpQin-1=1.7exp-20hc23d5013H0

    where: Qp = peak outflow discharge.

    Qin = inflow discharge.

    hc = critical flow depth.

    d50 = mean sediment diameter.

    Ho = initial dam height.

    Yu et al. [17] carried out an experimental study for homogeneous non-cohesive embankment dams in a 180° bending rectangular flume to determine the effect of overtopping flows on breaching formation. They found that the main factors influencing breach formation are water level, river discharge, and embankment material diameter.

    Wu et al. [18] carried out a series of experiments to investigate the effect of breaching geometry on both non-cohesive and cohesive embankment dams in a U-bend flume due to overtopping flows. In the case of non-cohesive embankments, the non-symmetrical lateral expansion was noticed during the breach formation. This expansion was described by a coefficient ranging from 2.7 to 3.3.

    The numerical models of the dam breach can be categorized according to different parameters, such as flow dimensions (1D, 2D, or 3D), flow governing equations, and solution methods. The 1D models are mainly used to predict the outflow hydrograph from the dam breach. Saberi et al. [19] applied the 1D Saint-Venant equation, which is solved by the finite difference method to investigate the outflow hydrograph during dam overtopping failure. Because of the ability to study dam profile evolution and breach formation, 2D models are more applicable than 1D models. Guan et al. [20] and Wu et al. [21] employed both 2D shallow water equations (SWEs) and sediment erosion equations, which are solved by the finite volume method to study the effect of the dam’s geometry parameters on outflow hydrograph and dam profile evolution. Wang et al. [22] also proposed a second-order hybrid-type of total variation diminishing (TVD) finite-difference to estimate the breach outflow by solving the 2D (SWEs). The accuracy of (SWEs) for both vertical flow contraction and surface roughness has been assessed [23]. They noted that the accuracy of (SWEs) is acceptable for milder slopes, but in the case of steeper slopes, modelers should be more careful. Generally, the accuracy of 2D models is still low, especially with velocity distribution over the flow depth, lateral momentum exchange, density-driven flows, and bottom friction [24]. Therefore, 3D models are preferred. Larocque et al. [25] and Yang et al. [26] started to use three-dimensional (3D) models that depend on the Reynolds-averaged Navier-Stokes (RANS) equations.

    Previous experimental studies concluded that there is no clear relationship between the peak outflow from the dam breach and the initial breach characteristics. Some of these studies depend on the sharp-crested weir fixed at the end of the flume to determine the peak outflow from the breach, which leads to a decrease in the accuracy of outflow calculations at the microscale. The main goals of this study are to carry out a numerical simulation for a spatial dam breach due to overtopping flows by using (FLOW-3D) software to find an empirical equation for the peak outflow discharge from the breach and determine the worst-case that leads to accelerating the dam breaching process.

    2. Numerical simulation

    The current study for spatial dam breach is simulated by using (FLOW-3D) software [27], which is a powerful computational fluid dynamics (CFD) program.

    2.1. Geometric presentations

    A stereolithographic (STL) file is prepared for each change in the initial breach geometry and dimensions. The CAD program is useful for creating solid objects and converting them to STL format, as shown in Fig. 1.

    2.2. Governing equations

    The governing equations for water flow are three-dimensional Reynolds Averaged Navier-Stokes equations (RANS).

    The continuity equation:(2)∂ui∂xi=0

    The momentum equation:(3)∂ui∂t+1VFuj∂ui∂xj=1ρ∂∂xj-pδij+ν∂ui∂xj+∂uj∂xi-ρu`iu`j¯

    where u is time-averaged velocity,ν is kinematic viscosity, VF is fractional volume open to flow, p is averaged pressure and -u`iu`j¯ are components of Reynold’s stress. The Volume of Fluid (VOF) technique is used to simulate the free surface profile. Hirt et al. [28] presented the VOF algorithm, which employs the function (F) to express the occupancy of each grid cell with fluid. The value of (F) varies from zero to unity. Zero value refers to no fluid in the grid cell, while the unity value refers to the grid cell being fully occupied with fluid. The free surface is formed in the grid cells having (F) values between zero and unity.(4)∂F∂t+1VF∂∂xFAxu+∂∂yFAyv+∂∂zFAzw=0

    where (u, v, w) are the velocity components in (x, y, z) coordinates, respectively, and (Ax, Ay, Az) are the area fractions.

    2.3. Boundary and initial conditions

    To improve the accuracy of the results, the boundary conditions should be carefully determined. In this study, two mesh blocks are used to minimize the time consumed in the simulation. The boundary conditions for mesh block 1 are as follows: The inlet and sides boundaries are defined as a wall boundary condition (wall boundary condition is usually used for bound fluid by solid regions. In the case of viscous flows, no-slip means that the tangential velocity is equal to the wall velocity and the normal velocity is zero), the outlet is defined as a symmetry boundary condition (symmetry boundary condition is usually used to reduce computational effort during CFD simulation. This condition allows the flow to be transferred from one mesh block to another. No inputs are required for this boundary condition except that its location should be defined accurately), the bottom boundary is defined as a uniform flow rate boundary condition, and the top boundary is defined as a specific pressure boundary condition with assigned atmospheric pressure. The boundary conditions for mesh block 2 are as follows: The inlet is defined as a symmetry boundary condition, the outlet is defined as a free flow boundary condition, the bottom and sides boundaries are defined as a wall boundary condition, and the top boundary is defined as a specific pressure boundary condition with assigned atmospheric pressure as shown in Fig. 2. The initial conditions required to be set for the fluid (i.e., water) inside of the domain include configuration, temperature, velocities, and pressure distribution. The configuration of water depends on the dimensions and shape of the dam reservoir. While the other conditions have been assigned as follows: temperature is normal water temperature (25 °c) and pressure distribution is hydrostatic with no initial velocity.

    2.4. Numerical method

    FLOW-3D uses the finite volume method (FVM) to solve the governing equation (Reynolds-averaged Navier-Stokes) over the computational domain. A finite-volume method is an Eulerian approach for representing and evaluating partial differential equations in algebraic equations form [29]. At discrete points on the mesh geometry, values are determined. Finite volume expresses a small volume surrounding each node point on a mesh. In this method, the divergence theorem is used to convert volume integrals with a divergence term to surface integrals. After that, these terms are evaluated as fluxes at each finite volume’s surfaces.

    2.5. Turbulent models

    Turbulence is the chaotic, unstable motion of fluids that occurs when there are insufficient stabilizing viscous forces. In FLOW-3D, there are six turbulence models available: the Prandtl mixing length model, the one-equation turbulent energy model, the two-equation (k – ε) model, the Renormalization-Group (RNG) model, the two-equation (k – ω) models, and a large eddy simulation (LES) model. For simulating flow motion, the RNG model is adopted to simulate the motion behavior better than the k – ε and k – ω.

    models [30]. The RNG model consists of two main equations for the turbulent kinetic energy KT and its dissipation.εT(5)∂kT∂t+1VFuAx∂kT∂x+vAy∂kT∂y+wAz∂kT∂z=PT+GT+DiffKT-εT(6)∂εT∂t+1VFuAx∂εT∂x+vAy∂εT∂y+wAz∂εT∂z=C1.εTKTPT+c3.GT+Diffε-c2εT2kT

    where KT is the turbulent kinetic energy, PT is the turbulent kinetic energy production, GT is the buoyancy turbulence energy, εT is the turbulent energy dissipation rate, DiffKT and Diffε are terms of diffusion, c1, c2 and c3 are dimensionless parameters, in which c1 and c3 have a constant value of 1.42 and 0.2, respectively, c2 is computed from the turbulent kinetic energy (KT) and turbulent production (PT) terms.

    2.6. Sediment scour model

    The sediment scour model available in FLOW-3D can calculate all the sediment transport processes including Entrainment transport, Bedload transport, Suspended transport, and Deposition. The erosion process starts once the water flows remove the grains from the packed bed and carry them into suspension. It happens when the applied shear stress by water flows exceeds critical shear stress. This process is represented by entrainment transport in the numerical model. After entrained, the grains carried by water flow are represented by suspended load transport. After that, some suspended grains resort to settling because of the combined effect of gravity, buoyancy, and friction. This process is described through a deposition. Finally, the grains sliding motions are represented by bedload transport in the model. For the entrainment process, the shear stress applied by the fluid motion on the packed bed surface is calculated using the standard wall function as shown in Eq.7.(7)ks,i=Cs,i∗d50

    where ks,i is the Nikuradse roughness and Cs,i is a user-defined coefficient. The critical bed shear stress is defined by a dimensionless parameter called the critical shields number as expressed in Eq.8.(8)θcr,i=τcr,i‖g‖diρi-ρf

    where θcr,i is the critical shields number, τcr,i is the critical bed shear stress, g is the absolute value of gravity acceleration, di is the diameter of the sediment grain, ρi is the density of the sediment species (i) and ρf is the density of the fluid. The value of the critical shields number is determined according to the Soulsby-Whitehouse equation.(9)θcr,i=0.31+1.2d∗,i+0.0551-exp-0.02d∗,i

    where d∗,i is the dimensionless diameter of the sediment, given by Eq.10.(10)d∗,i=diρfρi-ρf‖g‖μf213

    where μf is the fluid dynamic viscosity. For the sloping bed interface, the value of the critical shields number is modified according to Eq.11.(11)θ`cr,i=θcr,icosψsinβ+cos2βtan2φi-sin2ψsin2βtanφi

    where θ`cr,i is the modified critical shields number, φi is the angle of repose for the sediment, β is the angle of bed slope and ψ is the angle between the flow and the upslope direction. The effects of the rolling, hopping, and sliding motions of grains along the packed bed surface are taken by the bedload transport process. The volumetric bedload transport rate (qb,i) per width of the bed is expressed in Eq.12.(12)qb,i=Φi‖g‖ρi-ρfρfdi312

    where Φi is the dimensionless bedload transport rate is calculated by using Meyer Peter and Müller equation.(13)Φi=βMPM,iθi-θ`cr,i1.5cb,i

    where βMPM,i is the Meyer Peter and Müller user-defined coefficient and cb,i is the volume fraction of species i in the bed material. The suspended load transport is calculated as shown in Eq.14.(14)∂Cs,i∂t+∇∙Cs,ius,i=∇∙∇DCs,i

    where Cs,i is the suspended sediment mass concentration, D is the diffusivity, and us,i is the grain velocity of species i. Entrainment and deposition are two opposing processes that take place at the same time. The lifting and settling velocities for both entrainment and deposition processes are calculated according to Eq.15 and Eq.16, respectively.(15)ulifting,i=αid∗,i0.3θi-θ`cr,igdiρiρf-1(16)usettling,i=υfdi10.362+1.049d∗,i3-10.36

    where αi is the entrainment coefficient of species i and υf is the kinematic viscosity of the fluid.

    2.7. Grid type

    Using simple rectangular orthogonal elements in planes and hexahedral in volumes in the (FLOW-3D) program makes the mesh generation process easier, decreases the required memory, and improves numerical accuracy. Two mesh blocks were used in a joined form with a size ratio of 2:1. The first mesh block is coarser, which contains the reservoir water, and the second mesh block is finer, which contains the dam. For achieving accuracy and efficiency in results, the mesh size is determined by using a grid convergence test. The optimum uniform cell size for the first mesh block is 0.012 m and for the second mesh block is 0.006 m.

    2.8. Time step

    The maximum time step size is determined by using a Courant number, which controls the distance that the flow will travel during the simulation time step. In this study, the Courant number was taken equal to 0.25 to prevent the flow from traveling through more than one cell in the time step. Based on the Courant number, a maximum time step value of 0.00075 s was determined.

    2.9. Numerical model validation

    The numerical model accuracy was achieved by comparing the numerical model results with previous experimental results. The experimental study of Schmocker and Hager [7] was based on 31 tests with changes in six parameters (d50, Ho, Bo, Lk, XD, and Qin). All experimental tests were conducted in a straight open glass-sided flume. The horizontal flume has a rectangular cross-section with a width of 0.4 m and a height of 0.7 m. The flume was provided with a flow straightener and an intake with a length of 0.66 m. All tested dams were inserted at various distances (XD) from the intake. Test No.1 from this experimental program was chosen to validate the numerical model. The different parameters used in test No.1 are as follows:

    (1) uniform sediment with a mean diameter (d50 = 0.31 mm), (2) Ho = 0.2 m, (3) Bo = 0.2 m, (4) Lk = 0.1 m,

    (5) XD = 1.0 m, (6) Qin = 6.0 lit/s, (7) Su and Sd = 2:1, (8) mass density (ρs = 2650 kg/m3) (9) Homogenous and non-cohesive embankment dam. As shown in Fig. 2, the simulation is contained within a rectangular grid with dimensions: 3.56 m in the x-direction (where 0.66 m is used as inlet, 0.9 m as dam base width, and 1.0 m as outlet), in y-direction 0.2 m (dam length), and in the z-direction 0.3 m, which represents the dam height (0.2 m) with a free distance (0.1 m) above the dam. There are two main reasons that this experimental program is preferred for the validation process. The first reason is that this program deals with homogenous, non-cohesive soil, which is available in FLOW-3D. The second reason is that this program deals with small-scale models which saves time for numerical simulation. Finally, some important assumptions were considered during the validation process. The flow is assumed to be incompressible, viscous, turbulent, and three-dimensional.

    By comparing dam profiles at different time instants for the experimental test with the current numerical model, it appears that the numerical model gives good agreement as shown in Fig. 3 and Fig. 4, with an average error percentage of 9% between the experimental results and the numerical model.

    3. Analysis and discussions

    The current model is used to study the effects of different parameters such as (initial breach shapes, dimensions, locations, upstream and downstream dam slopes) on the peak outflow discharge, QP, time of peak outflow, tP, and rate of erosion, E.

    This study consists of a group of scenarios. The first scenario is changing the shapes of the initial breach according to Singh [1], the most predicted shapes are rectangular and V-notch as shown in Fig. 5. The second scenario is changing the initial breach dimensions (i.e., width and depth). While the third scenario is changing the location of the initial breach. Eventually, the last scenario is changing the upstream and downstream dam slopes.

    All scenarios of this study were carried out under the same conditions such as inflow discharge value (Qin=1.0lit/s), dimensions of the tested dam, where dam height (Ho=0.20m), crest width.

    (Lk=0.1m), dam length (Bo=0.20m), and homogenous & non-cohesive soil with a mean diameter (d50=0.31mm).

    3.1. Dam breaching process evolution

    The dam breaching process is a very complex process due to the quick changes in hydrodynamic conditions during dam failure. The dam breaching process starts once water flows reach the downstream face of the dam. During the initial stage of dam breaching, the erosion process is relatively quiet due to low velocities of flow. As water flows continuously, erosion rates increase, especially in two main zones: the crest and the downstream face. As soon as the dam crest is totally eroded, the water levels in the dam reservoir decrease rapidly, accompanied by excessive erosion in the dam body. The erosion process continues until the water levels in the dam reservoir equal the remaining height of the dam.

    According to Zhou et al. [11], the breaching process consists of three main stages. The first stage starts with beginning overtopping flow, then ends when the erosion point directed upstream and reached the inflection point at the inflection time (ti). The second stage starts from the end of the stage1 until the occurrence of peak outflow discharge at the peak outflow time (tP). The third stage starts from the end of the stage2 until the value of outflow discharge becomes the same as the value of inflow discharge at the final time (tf). The outflow discharge from the dam breach increases rapidly during stage1 and stage2 because of the large dam storage capacity (i.e., the dam reservoir is totally full of water) and excessive erosion. While at stage3, the outflow values start to decrease slowly because most of the dam’s storage capacity was run out. The end of stage3 indicates that the dam storage capacity was totally run out, so the outflow equalized with the inflow discharge as shown in Fig. 6 and Fig. 7.

    3.2. The effect of initial breach shape

    To identify the effect of the initial breach shape on the evolution of the dam breaching process. Three tests were carried out with different cross-section areas for each shape. The initial breach is created at the center of the dam crest. Each test had an ID to make the process of arranging data easier. The rectangular shape had an ID (Rec5h & 5b), which means that its depth and width are equal to 5% of the dam height, and the V-notch shape had an ID (V-noch5h & 1:1) which means that its depth is equal to 5% of the dam height and its side slope is equal to 1:1. The comparison between rectangular and V-notch shapes is done by calculating the ratio between maximum dam height at different times (ZMax) to the initial dam height (Ho), rate of erosion, and hydrograph of outflow discharge for each test. The rectangular shape achieves maximum erosion rate and minimum inflection time, in addition to a rapid decrease in the dam reservoir levels. Therefore, the dam breaching is faster in the case of a rectangular shape than in a V-notch shape, which has the same cross-section area as shown in Fig. 8.

    Also, by comparing the hydrograph for each test, the peak outflow discharge value in the case of a rectangular shape is higher than the V-notch shape by 5% and the time of peak outflow for the rectangular shape is shorter than the V-notch shape by 9% as shown in Fig. 9.

    3.3. The effect of initial breach dimensions

    The results of the comparison between the different initial breach shapes indicate that the worst initial breach shape is rectangular, so the second scenario from this study concentrated on studying the effect of a change in the initial rectangular breach dimensions. Groups of tests were carried out with different depths and widths for the rectangular initial breach. The first group had a depth of 5% from the dam height and with three different widths of 5,10, and 15% from the dam height, the second group had a depth of 10% with three different widths of 5,10, and 15%, the third group had a depth of 15% with three different widths of 5,10, and 15% and the final group had a width of 15% with three different heights of 5, 10, and 15% for a rectangular breach shape. The comparison was made as in the previous section to determine the worst case that leads to the quick dam failure as shown in Fig. 10.

    The results show that the (Rec 5 h&15b) test achieves a maximum erosion rate for a shorter period of time and a minimum ratio for (Zmax / Ho) as shown in Fig. 10, which leads to accelerating the dam failure process. The dam breaching process is faster with the minimum initial breach depth and maximum initial breach width. In the case of a minimum initial breach depth, the retained head of water in the dam reservoir is high and the crest width at the bottom of the initial breach (L`K) is small, so the erosion point reaches the inflection point rapidly. While in the case of the maximum initial breach width, the erosion perimeter is large.

    3.4. The effect of initial breach location

    The results of the comparison between the different initial rectangular breach dimensions indicate that the worst initial breach dimension is (Rec 5 h&15b), so the third scenario from this study concentrated on studying the effect of a change in the initial breach location. Three locations were checked to determine the worst case for the dam failure process. The first location is at the center of the dam crest, which was named “Center”, the second location is at mid-distance between the dam center and dam edge, which was named “Mid”, and the third location is at the dam edge, which was named “Edge” as shown in Fig. 11. According to this scenario, the results indicate that the time of peak outflow discharge (tP) is the same in the three cases, but the maximum value of the peak outflow discharge occurs at the center location. The difference in the peak outflow values between the three cases is relatively small as shown in Fig. 12.

    The rates of erosion were also studied for the three cases. The results show that the maximum erosion rate occurs at the center location as shown in Fig. 13. By making a comparison between the three cases for the dam storage volume. The results show that the center location had the minimum values for the dam storage volume, which means that a large amount of water has passed to the downstream area as shown in Fig. 14. According to these results, the center location leads to increased erosion rate and accelerated dam failure process compared with the two other cases. Because the erosion occurs on both sides, but in the case of edge location, the erosion occurs on one side.

    3.5. The effect of upstream and downstream dam slopes

    The results of the comparison between the different initial rectangular breach locations indicate that the worst initial breach location is the center location, so the fourth scenario from this study concentrated on studying the effect of a change in the upstream (Su) and downstream (Sd) dam slopes. Three slopes were checked individually for both upstream and downstream slopes to determine the worst case for the dam failure process. The first slope value is (2H:1V), the second slope value is (2.5H:1V), and the third slope value is (3H:1V). According to this scenario, the results show that the decreasing downstream slope angle leads to increasing time of peak outflow discharge (tP) and decreasing value of peak outflow discharge. The difference in the peak outflow values between the three cases for the downstream slope is 2%, as shown in Fig. 15, but changing the upstream slope has a negligible impact on the peak outflow discharge and its time as shown in Fig. 16.

    The rates of erosion were also studied in the three cases for both upstream and downstream slopes. The results show that the maximum erosion rate increases by 6.0% with an increasing downstream slope angle by 4°, as shown in Fig. 17. The results also indicate that the erosion rates aren’t affected by increasing or decreasing the upstream slope angle, as shown in Fig. 18. According to these results, increasing the downstream slope angle leads to increased erosion rate and accelerated dam failure process compared with the upstream slope angle. Because of increasing shear stress applied by water flows in case of increasing downstream slope.

    According to all previous scenarios, the dimensionless peak outflow discharge QPQin is presented for a fixed dam height (Ho) and inflow discharge (Qin). Fig. 19 illustrates the relationship between QP∗=QPQin and.

    Lr=ho2/3∗bo2/3Ho. The deduced relationship achieves R2=0.96.(17)QP∗=2.2807exp-2.804∗Lr

    4. Conclusions

    A spatial dam breaching process was simulated by using FLOW-3D Software. The validation process was performed by making a comparison between the simulated results of dam profiles and the dam profiles obtained by Schmocker and Hager [7] in their experimental study. And also, the peak outflow value recorded an error percentage of 12% between the numerical model and the experimental study. This model was used to study the effect of initial breach shape, dimensions, location, and dam slopes on peak outflow discharge, time of peak outflow, and the erosion process. By using the parameters obtained from the validation process, the results of this study can be summarized in eight points as follows.1.

    The rectangular initial breach shape leads to an accelerating dam failure process compared with the V-notch.2.

    The value of peak outflow discharge in the case of a rectangular initial breach is higher than the V-notch shape by 5%.3.

    The time of peak outflow discharge for a rectangular initial breach is shorter than the V-notch shape by 9%.4.

    The minimum depth and maximum width for the initial breach achieve maximum erosion rates (increasing breach width, b0, or decreasing breach depth, h0, by 5% from the dam height leads to an increase in the maximum rate of erosion by 11% and 15%, respectively), so the dam failure is rapid.5.

    The center location of the initial breach leads to an accelerating dam failure compared with the edge location.6.

    The initial breach location has a negligible effect on the peak outflow discharge value and its time.7.

    Increasing the downstream slope angle by 4° leads to an increase in both peak outflow discharge and maximum rate of erosion by 2.0% and 6.0%, respectively.8.

    The upstream slope has a negligible effect on the dam breaching process.

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    PDF 전체 원문 보기
    Figure 3 Simulation PTC pipes enhanced with copper foam and nanoparticles in FLOW-3D software.

    다공성 미디어 및 나노유체에 의해 강화된 수집기로 태양광 CCHP 시스템의 최적화

    Optimization of Solar CCHP Systems with Collector Enhanced by Porous Media and Nanofluid

    Navid Tonekaboni,1Mahdi Feizbahr,2 Nima Tonekaboni,1Guang-Jun Jiang,3,4 and Hong-Xia Chen3,4

    Abstract

    태양열 집열기의 낮은 효율은 CCHP(Solar Combined Cooling, Heating, and Power) 사이클의 문제점 중 하나로 언급될 수 있습니다. 태양계를 개선하기 위해 나노유체와 다공성 매체가 태양열 집열기에 사용됩니다.

    다공성 매질과 나노입자를 사용하는 장점 중 하나는 동일한 조건에서 더 많은 에너지를 흡수할 수 있다는 것입니다. 이 연구에서는 평균 일사량이 1b인 따뜻하고 건조한 지역의 600 m2 건물의 전기, 냉방 및 난방을 생성하기 위해 다공성 매질과 나노유체를 사용하여 태양열 냉난방 복합 발전(SCCHP) 시스템을 최적화했습니다.

    본 논문에서는 침전물이 형성되지 않는 lb = 820 w/m2(이란) 정도까지 다공성 물질에서 나노유체의 최적량을 계산하였다. 이 연구에서 태양열 집열기는 구리 다공성 매체(95% 다공성)와 CuO 및 Al2O3 나노 유체로 향상되었습니다.

    나노유체의 0.1%-0.6%가 작동 유체로 물에 추가되었습니다. 나노유체의 0.5%가 태양열 집열기 및 SCCHP 시스템에서 가장 높은 에너지 및 엑서지 효율 향상으로 이어지는 것으로 밝혀졌습니다.

    본 연구에서 포물선형 집열기(PTC)의 최대 에너지 및 엑서지 효율은 각각 74.19% 및 32.6%입니다. 그림 1은 태양 CCHP의 주기를 정확하게 설명하기 위한 그래픽 초록으로 언급될 수 있습니다.

    The low efficiency of solar collectors can be mentioned as one of the problems in solar combined cooling, heating, and power (CCHP) cycles. For improving solar systems, nanofluid and porous media are used in solar collectors. One of the advantages of using porous media and nanoparticles is to absorb more energy under the same conditions. In this research, a solar combined cooling, heating, and power (SCCHP) system has been optimized by porous media and nanofluid for generating electricity, cooling, and heating of a 600 m2 building in a warm and dry region with average solar radiation of Ib = 820 w/m2 in Iran. In this paper, the optimal amount of nanofluid in porous materials has been calculated to the extent that no sediment is formed. In this study, solar collectors were enhanced with copper porous media (95% porosity) and CuO and Al2O3 nanofluids. 0.1%–0.6% of the nanofluids were added to water as working fluids; it is found that 0.5% of the nanofluids lead to the highest energy and exergy efficiency enhancement in solar collectors and SCCHP systems. Maximum energy and exergy efficiency of parabolic thermal collector (PTC) riches in this study are 74.19% and 32.6%, respectively. Figure 1 can be mentioned as a graphical abstract for accurately describing the cycle of solar CCHP.

    1. Introduction

    Due to the increase in energy consumption, the use of clean energy is one of the important goals of human societies. In the last four decades, the use of cogeneration cycles has increased significantly due to high efficiency. Among clean energy, the use of solar energy has become more popular due to its greater availability [1]. Low efficiency of energy production, transmission, and distribution system makes a new system to generate simultaneously electricity, heating, and cooling as an essential solution to be widely used. The low efficiency of the electricity generation, transmission, and distribution system makes the CCHP system a basic solution to eliminate waste of energy. CCHP system consists of a prime mover (PM), a power generator, a heat recovery system (produce extra heating/cooling/power), and thermal energy storage (TES) [2]. Solar combined cooling, heating, and power (SCCHP) has been started three decades ago. SCCHP is a system that receives its propulsive force from solar energy; in this cycle, solar collectors play the role of propulsive for generating power in this system [3].

    Increasing the rate of energy consumption in the whole world because of the low efficiency of energy production, transmission, and distribution system causes a new cogeneration system to generate electricity, heating, and cooling energy as an essential solution to be widely used. Building energy utilization fundamentally includes power required for lighting, home electrical appliances, warming and cooling of building inside, and boiling water. Domestic usage contributes to an average of 35% of the world’s total energy consumption [4].

    Due to the availability of solar energy in all areas, solar collectors can be used to obtain the propulsive power required for the CCHP cycle. Solar energy is the main source of energy in renewable applications. For selecting a suitable area to use solar collectors, annual sunshine hours, the number of sunny days, minus temperature and frosty days, and the windy status of the region are essentially considered [5]. Iran, with an average of more than 300 sunny days, is one of the suitable countries to use solar energy. Due to the fact that most of the solar radiation is in the southern regions of Iran, also the concentration of cities is low in these areas, and transmission lines are far apart, one of the best options is to use CCHP cycles based on solar collectors [6]. One of the major problems of solar collectors is their low efficiency [7]. Low efficiency increases the area of collectors, which increases the initial cost of solar systems and of course increases the initial payback period. To increase the efficiency of solar collectors and improve their performance, porous materials and nanofluids are used to increase their workability.

    There are two ways to increase the efficiency of solar collectors and mechanical and fluid improvement. In the first method, using porous materials or helical filaments inside the collector pipes causes turbulence of the flow and increases heat transfer. In the second method, using nanofluids or salt and other materials increases the heat transfer of water. The use of porous materials has grown up immensely over the past twenty years. Porous materials, especially copper porous foam, are widely used in solar collectors. Due to the high contact surface area, porous media are appropriate candidates for solar collectors [8]. A number of researchers investigated Solar System performance in accordance with energy and exergy analyses. Zhai et al. [9] reviewed the performance of a small solar-powered system in which the energy efficiency was 44.7% and the electrical efficiency was 16.9%.

    Abbasi et al. [10] proposed an innovative multiobjective optimization to optimize the design of a cogeneration system. Results showed the CCHP system based on an internal diesel combustion engine was the applicable alternative at all regions with different climates. The diesel engine can supply the electrical requirement of 31.0% and heating demand of 3.8% for building.

    Jiang et al. [11] combined the experiment and simulation together to analyze the performance of a cogeneration system. Moreover, some research focused on CCHP systems using solar energy. It integrated sustainable and renewable technologies in the CCHP, like PV, Stirling engine, and parabolic trough collector (PTC) [2, 12–15].

    Wang et al. [16] optimized a cogeneration solar cooling system with a Rankine cycle and ejector to reach the maximum total system efficiency of 55.9%. Jing et al. analyzed a big-scale building with the SCCHP system and auxiliary heaters to produced electrical, cooling, and heating power. The maximum energy efficiency reported in their work is 46.6% [17]. Various optimization methods have been used to improve the cogeneration system, minimum system size, and performance, such as genetic algorithm [18, 19].

    Hirasawa et al. [20] investigated the effect of using porous media to reduce thermal waste in solar systems. They used the high-porosity metal foam on top of the flat plate solar collector and observed that thermal waste decreased by 7% due to natural heat transfer. Many researchers study the efficiency improvement of the solar collector by changing the collector’s shapes or working fluids. However, the most effective method is the use of nanofluids in the solar collector as working fluid [21]. In the experimental study done by Jouybari et al. [22], the efficiency enhancement up to 8.1% was achieved by adding nanofluid in a flat plate collector. In this research, by adding porous materials to the solar collector, collector efficiency increased up to 92% in a low flow regime. Subramani et al. [23] analyzed the thermal performance of the parabolic solar collector with Al2O3 nanofluid. They conducted their experiments with Reynolds number range 2401 to 7202 and mass flow rate 0.0083 to 0.05 kg/s. The maximum efficiency improvement in this experiment was 56% at 0.05 kg/s mass flow rate.

    Shojaeizadeh et al. [24] investigated the analysis of the second law of thermodynamic on the flat plate solar collector using Al2O3/water nanofluid. Their research showed that energy efficiency rose up to 1.9% and the exergy efficiency increased by a maximum of 0.72% compared to pure water. Tiwari et al. [25] researched on the thermal performance of solar flat plate collectors for working fluid water with different nanofluids. The result showed that using 1.5% (optimum) particle volume fraction of Al2O3 nanofluid as an absorbing medium causes the thermal efficiency to enhance up to 31.64%.

    The effect of porous media and nanofluids on solar collectors has already been investigated in the literature but the SCCHP system with a collector embedded by both porous media and nanofluid for enhancing the ratio of nanoparticle in nanofluid for preventing sedimentation was not discussed. In this research, the amount of energy and exergy of the solar CCHP cycles with parabolic solar collectors in both base and improved modes with a porous material (copper foam with 95% porosity) and nanofluid with different ratios of nanoparticles was calculated. In the first step, it is planned to design a CCHP system based on the required load, and, in the next step, it will analyze the energy and exergy of the system in a basic and optimize mode. In the optimize mode, enhanced solar collectors with porous material and nanofluid in different ratios (0.1%–0.7%) were used to optimize the ratio of nanofluids to prevent sedimentation.

    2. Cycle Description

    CCHP is one of the methods to enhance energy efficiency and reduce energy loss and costs. The SCCHP system used a solar collector as a prime mover of the cogeneration system and assisted the boiler to generate vapor for the turbine. Hot water flows from the expander to the absorption chiller in summer or to the radiator or fan coil in winter. Finally, before the hot water wants to flow back to the storage tank, it flows inside a heat exchanger for generating domestic hot water [26].

    For designing of solar cogeneration system and its analysis, it is necessary to calculate the electrical, heating (heating load is the load required for the production of warm water and space heating), and cooling load required for the case study considered in a residential building with an area of 600 m2 in the warm region of Iran (Zahedan). In Table 1, the average of the required loads is shown for the different months of a year (average of electrical, heating, and cooling load calculated with CARRIER software).Table 1 The average amount of electric charges, heating load, and cooling load used in the different months of the year in the city of Zahedan for a residential building with 600 m2.

    According to Table 1, the maximum magnitude of heating, cooling, and electrical loads is used to calculate the cogeneration system. The maximum electric load is 96 kW, the maximum amount of heating load is 62 kW, and the maximum cooling load is 118 kW. Since the calculated loads are average, all loads increased up to 10% for the confidence coefficient. With the obtained values, the solar collector area and other cogeneration system components are calculated. The cogeneration cycle is capable of producing 105 kW electric power, 140 kW cooling capacity, and 100 kW heating power.

    2.1. System Analysis Equations

    An analysis is done by considering the following assumptions:(1)The system operates under steady-state conditions(2)The system is designed for the warm region of Iran (Zahedan) with average solar radiation Ib = 820 w/m2(3)The pressure drops in heat exchangers, separators, storage tanks, and pipes are ignored(4)The pressure drop is negligible in all processes and no expectable chemical reactions occurred in the processes(5)Potential, kinetic, and chemical exergy are not considered due to their insignificance(6)Pumps have been discontinued due to insignificance throughout the process(7)All components are assumed adiabatic

    Schematic shape of the cogeneration cycle is shown in Figure 1 and all data are given in Table 2.

    Figure 1 Schematic shape of the cogeneration cycle.Table 2 Temperature and humidity of different points of system.

    Based on the first law of thermodynamic, energy analysis is based on the following steps.

    First of all, the estimated solar radiation energy on collector has been calculated:where α is the heat transfer enhancement coefficient based on porous materials added to the collector’s pipes. The coefficient α is increased by the porosity percentage, the type of porous material (in this case, copper with a porosity percentage of 95), and the flow of fluid to the collector equation.

    Collector efficiency is going to be calculated by the following equation [9]:

    Total energy received by the collector is given by [9]

    Also, the auxiliary boiler heat load is [2]

    Energy consumed from vapor to expander is calculated by [2]

    The power output form by the screw expander [9]:

    The efficiency of the expander is 80% in this case [11].

    In this step, cooling and heating loads were calculated and then, the required heating load to reach sanitary hot water will be calculated as follows:

    First step: calculating the cooling load with the following equation [9]:

    Second step: calculating heating loads [9]:

    Then, calculating the required loud for sanitary hot water will be [9]

    According to the above-mentioned equations, efficiency is [9]

    In the third step, calculated exergy analysis as follows.

    First, the received exergy collector from the sun is calculated [9]:

    In the previous equation, f is the constant of air dilution.

    The received exergy from the collector is [9]

    In the case of using natural gas in an auxiliary heater, the gas exergy is calculated from the following equation [12]:

    Delivering exergy from vapor to expander is calculated with the following equation [9]:

    In the fourth step, the exergy in cooling and heating is calculated by the following equation:

    Cooling exergy in summer is calculated [9]:

    Heating exergy in winter is calculated [9]:

    In the last step based on thermodynamic second law, exergy efficiency has been calculated from the following equation and the above-mentioned calculated loads [9]:

    3. Porous Media

    The porous medium that filled the test section is copper foam with a porosity of 95%. The foams are determined in Figure 2 and also detailed thermophysical parameters and dimensions are shown in Table 3.

    Figure 2 Copper foam with a porosity of 95%.Table 3 Thermophysical parameters and dimensions of copper foam.

    In solar collectors, copper porous materials are suitable for use at low temperatures and have an easier and faster manufacturing process than ceramic porous materials. Due to the high coefficient conductivity of copper, the use of copper metallic foam to increase heat transfer is certainly more efficient in solar collectors.

    Porous media and nanofluid in solar collector’s pipes were simulated in FLOW-3D software using the finite-difference method [27]. Nanoparticles Al2O3 and CUO are mostly used in solar collector enhancement. In this research, different concentrations of nanofluid are added to the parabolic solar collectors with porous materials (copper foam with porosity of 95%) to achieve maximum heat transfer in the porous materials before sedimentation. After analyzing PTC pipes with the nanofluid flow in FLOW-3D software, for energy and exergy efficiency analysis, Carrier software results were used as EES software input. Simulation PTC with porous media inside collector pipe and nanofluids sedimentation is shown in Figure 3.

    Figure 3 Simulation PTC pipes enhanced with copper foam and nanoparticles in FLOW-3D software.

    3.1. Nano Fluid

    In this research, copper and silver nanofluids (Al2O3, CuO) have been added with percentages of 0.1%–0.7% as the working fluids. The nanoparticle properties are given in Table 4. Also, system constant parameters are presented in Table 4, which are available as default input in the EES software.Table 4 Properties of the nanoparticles [9].

    System constant parameters for input in the software are shown in Table 5.Table 5 System constant parameters.

    The thermal properties of the nanofluid can be obtained from equations (18)–(21). The basic fluid properties are indicated by the index (bf) and the properties of the nanoparticle silver with the index (np).

    The density of the mixture is shown in the following equation [28]:where ρ is density and ϕ is the nanoparticles volume fraction.

    The specific heat capacity is calculated from the following equation [29]:

    The thermal conductivity of the nanofluid is calculated from the following equation [29]:

    The parameter β is the ratio of the nanolayer thickness to the original particle radius and, usually, this parameter is taken equal to 0.1 for the calculated thermal conductivity of the nanofluids.

    The mixture viscosity is calculated as follows [30]:

    In all equations, instead of water properties, working fluids with nanofluid are used. All of the above equations and parameters are entered in the EES software for calculating the energy and exergy of solar collectors and the SCCHP cycle. All calculation repeats for both nanofluids with different concentrations of nanofluid in the solar collector’s pipe.

    4. Results and Discussion

    In the present study, relations were written according to Wang et al. [16] and the system analysis was performed to ensure the correctness of the code. The energy and exergy charts are plotted based on the main values of the paper and are shown in Figures 4 and 5. The error rate in this simulation is 1.07%.

    Figure 4 Verification charts of energy analysis results.

    Figure 5 Verification charts of exergy analysis results.

    We may also investigate the application of machine learning paradigms [31–41] and various hybrid, advanced optimization approaches that are enhanced in terms of exploration and intensification [42–55], and intelligent model studies [56–61] as well, for example, methods such as particle swarm optimizer (PSO) [60, 62], differential search (DS) [63], ant colony optimizer (ACO) [61, 64, 65], Harris hawks optimizer (HHO) [66], grey wolf optimizer (GWO) [53, 67], differential evolution (DE) [68, 69], and other fusion and boosted systems [41, 46, 48, 50, 54, 55, 70, 71].

    At the first step, the collector is modified with porous copper foam material. 14 cases have been considered for the analysis of the SCCHP system (Table 6). It should be noted that the adding of porous media causes an additional pressure drop inside the collector [9, 22–26, 30, 72]. All fourteen cases use copper foam with a porosity of 95 percent. To simulate the effect of porous materials and nanofluids, the first solar PTC pipes have been simulated in the FLOW-3D software and then porous media (copper foam with porosity of 95%) and fluid flow with nanoparticles (AL2O3 and CUO) are generated in the software. After analyzing PTC pipes in FLOW-3D software, for analyzing energy and exergy efficiency, software outputs were used as EES software input for optimization ratio of sedimentation and calculating energy and exergy analyses.Table 6 Collectors with different percentages of nanofluids and porous media.

    In this research, an enhanced solar collector with both porous media and Nanofluid is investigated. In the present study, 0.1–0.5% CuO and Al2O3 concentration were added to the collector fully filled by porous media to achieve maximum energy and exergy efficiencies of solar CCHP systems. All steps of the investigation are shown in Table 6.

    Energy and exergy analyses of parabolic solar collectors and SCCHP systems are shown in Figures 6 and 7.

    Figure 6 Energy and exergy efficiencies of the PTC with porous media and nanofluid.

    Figure 7 Energy and exergy efficiency of the SCCHP.

    Results show that the highest energy and exergy efficiencies are 74.19% and 32.6%, respectively, that is achieved in Step 12 (parabolic collectors with filled porous media and 0.5% Al2O3). In the second step, the maximum energy efficiency of SCCHP systems with fourteen steps of simulation are shown in Figure 7.

    In the second step, where 0.1, −0.6% of the nanofluids were added, it is found that 0.5% leads to the highest energy and exergy efficiency enhancement in solar collectors and SCCHP systems. Using concentrations more than 0.5% leads to sediment in the solar collector’s pipe and a decrease of porosity in the pipe [73]. According to Figure 7, maximum energy and exergy efficiencies of SCCHP are achieved in Step 12. In this step energy efficiency is 54.49% and exergy efficiency is 18.29%. In steps 13 and 14, with increasing concentration of CUO and Al2O3 nanofluid solution in porous materials, decreasing of energy and exergy efficiency of PTC and SCCHP system at the same time happened. This decrease in efficiency is due to the formation of sediment in the porous material. Calculations and simulations have shown that porous materials more than 0.5% nanofluids inside the collector pipe cause sediment and disturb the porosity of porous materials and pressure drop and reduce the coefficient of performance of the cogeneration system. Most experience showed that CUO and AL2O3 nanofluids with less than 0.6% percent solution are used in the investigation on the solar collectors at low temperatures and discharges [74]. One of the important points of this research is that the best ratio of nanofluids in the solar collector with a low temperature is 0.5% (AL2O3 and CUO); with this replacement, the cost of solar collectors and SCCHP cycle is reduced.

    5. Conclusion and Future Directions

    In the present study, ways for increasing the efficiency of solar collectors in order to enhance the efficiency of the SCCHP cycle are examined. The research is aimed at adding both porous materials and nanofluids for estimating the best ratio of nanofluid for enhanced solar collector and protecting sedimentation in porous media. By adding porous materials (copper foam with porosity of 95%) and 0.5% nanofluids together, high efficiency in solar parabolic collectors can be achieved. The novelty in this research is the addition of both nanofluids and porous materials and calculating the best ratio for preventing sedimentation and pressure drop in solar collector’s pipe. In this study, it was observed that, by adding 0.5% of AL2O3 nanofluid in working fluids, the energy efficiency of PTC rises to 74.19% and exergy efficiency is grown up to 32.6%. In SCCHP cycle, energy efficiency is 54.49% and exergy efficiency is 18.29%.

    In this research, parabolic solar collectors fully filled by porous media (copper foam with a porosity of 95) are investigated. In the next step, parabolic solar collectors in the SCCHP cycle were simultaneously filled by porous media and different percentages of Al2O3 and CuO nanofluid. At this step, values of 0.1% to 0.6% of each nanofluid were added to the working fluid, and the efficiency of the energy and exergy of the collectors and the SCCHP cycle were determined. In this case, nanofluid and the porous media were used together in the solar collector and maximum efficiency achieved. 0.5% of both nanofluids were used to achieve the biggest efficiency enhancement.

    In the present study, as expected, the highest efficiency is for the parabolic solar collector fully filled by porous material (copper foam with a porosity of 95%) and 0.5% Al2O3. Results of the present study are as follows:(1)The average enhancement of collectors’ efficiency using porous media and nanofluids is 28%.(2)Solutions with 0.1 to 0.5% of nanofluids (CuO and Al2O3) are used to prevent collectors from sediment occurrence in porous media.(3)Collector of solar cogeneration cycles that is enhanced by both porous media and nanofluid has higher efficiency, and the stability of output temperature is more as well.(4)By using 0.6% of the nanofluids in the enhanced parabolic solar collectors with copper porous materials, sedimentation occurs and makes a high-pressure drop in the solar collector’s pipe which causes decrease in energy efficiency.(5)Average enhancement of SCCHP cycle efficiency is enhanced by both porous media and nanofluid 13%.

    Nomenclature

    :Solar radiation
    a:Heat transfer augmentation coefficient
    A:Solar collector area
    Bf:Basic fluid
    :Specific heat capacity of the nanofluid
    F:Constant of air dilution
    :Thermal conductivity of the nanofluid
    :Thermal conductivity of the basic fluid
    :Viscosity of the nanofluid
    :Viscosity of the basic fluid
    :Collector efficiency
    :Collector energy receives
    :Auxiliary boiler heat
    :Expander energy
    :Gas energy
    :Screw expander work
    :Cooling load, in kilowatts
    :Heating load, in kilowatts
    :Solar radiation energy on collector, in Joule
    :Sanitary hot water load
    Np:Nanoparticle
    :Energy efficiency
    :Heat exchanger efficiency
    :Sun exergy
    :Collector exergy
    :Natural gas exergy
    :Expander exergy
    :Cooling exergy
    :Heating exergy
    :Exergy efficiency
    :Steam mass flow rate
    :Hot water mass flow rate
    :Specific heat capacity of water
    :Power output form by the screw expander
    Tam:Average ambient temperature
    :Density of the mixture.

    Greek symbols

    ρ:Density
    ϕ:Nanoparticles volume fraction
    β:Ratio of the nanolayer thickness.

    Abbreviations

    CCHP:Combined cooling, heating, and power
    EES:Engineering equation solver.

    Data Availability

    For this study, data were generated by CARRIER software for the average electrical, heating, and cooling load of a residential building with 600 m2 in the city of Zahedan, Iran.

    Conflicts of Interest

    The authors declare that they have no conflicts of interest.

    Acknowledgments

    This work was partially supported by the National Natural Science Foundation of China under Contract no. 71761030 and Natural Science Foundation of Inner Mongolia under Contract no. 2019LH07003.

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    Fig. 11. Velocity vectors along x-direction through the center of the box culvert for B0, B30, B50, and B70 respectively.

    Numerical investigation of scour characteristics downstream of blocked culverts

    막힌 암거 하류의 세굴 특성 수치 조사

    NesreenTahabMaged M.El-FekyaAtef A.El-SaiadaIsmailFathya
    aDepartment of Water and Water Structures Engineering, Faculty of Engineering, Zagazig University, Zagazig 44519, Egypt
    bLab Manager, Faculty of Engineering, Zagazig University, Zagazig 44519, Egypt

    Abstract

    횡단 구조물을 통한 막힘은 안정성을 위협하는 위험한 문제 중 하나입니다. 암거의 막힘 형상 및 하류 세굴 특성에 미치는 영향에 관한 연구는 거의 없습니다.

    이 연구의 목적은 수면과 세굴 모두에서 상자 암거를 통한 막힘의 작용을 수치적으로 논의하는 것입니다. 이를 위해 FLOW 3D v11.1.0을 사용하여 퇴적물 수송 모델을 조사했습니다.

    상자 암거를 통한 다양한 차단 비율이 연구되었습니다. FLOW 3D 모델은 실험 데이터로 보정되었습니다. 결과는 FLOW 3D 프로그램이 세굴 다운스트림 상자 암거를 정확하게 시뮬레이션할 수 있음을 나타냅니다.

    막힌 경우에 대한 속도 분포, 최대 세굴 깊이 및 수심을 플롯하고 비차단된 사례(기본 사례)와 비교했습니다.

    그 결과 암거 높이의 70% 차단율은 상류의 수심을 암거 높이의 2.3배 증가시키고 평균 유속은 기본 경우보다 3배 더 증가시키는 것으로 입증되었다. 막힘 비율의 함수로 상대 최대 세굴 깊이를 추정하는 방정식이 만들어졌습니다.

    Blockage through crossing structures is one of the dangerous problems that threaten its stability. There are few researches concerned with blockage shape in culverts and its effect on characteristics of scour downstream it.

    The study’s purpose is to discuss the action of blockage through box culvert on both water surface and scour numerically. A sediment transport model has been investigated for this purpose using FLOW 3D v11.1.0. Different ratios of blockage through box culvert have been studied. The FLOW 3D model was calibrated with experimental data.

    The results present that the FLOW 3D program was capable to simulate accurately the scour downstream box culvert. The velocity distribution, maximum scour depth and water depths for blocked cases have been plotted and compared with the non-blocked case (base case).

    The results proved that the blockage ratio 70% of culvert height makes the water depth upstream increases by 2.3 times of culvert height and mean velocity increases by 3 times more than in the base case. An equation has been created to estimate the relative maximum scour depth as a function of blockage ratio.

    1. Introduction

    Local scour is the removal of granular bed material by the action of hydrodynamic forces. As the depth of scour hole increases, the stability of the foundation of the structure may be endangered, with a consequent risk of damage and failure [1]. So the prediction and control of scour is considered to be very important for protecting the water structures from failure. Most previous studies were designed to study the different factors that impact on scour and their relationship with scour hole dimensions like fluid characteristics, flow conditions, bed properties, and culvert geometry. Many previous researches studied the effect of flow rate on scour hole by information Froude number or modified Froude number [2], [3], [4], [5], [6]. Cesar Mendoza [6] found a good correlation between the scour depth and the discharge Intensity (Qg−.5D−2.5). Breusers and Raudkiv [7] used shear velocity in the outlet-scour prediction procedure. Ali and Lim [8] used the densimetric Froude number in estimation of the scour depth [1], [8], [9], [10], [11], [12], [13], [14]. “The densimetric Froude number presents the ratio of the tractive force on sediment particle to the submerged specific weight of the sediment” [15](1)Fd=uρsρ-1gD50

    Ali and Lim [8] pointed to the consequence of tailwater depth on scour behavior [1], [2], [8], [13]. Abida and Townsend [2] indicated that the maximum depth of local scour downstream culvert was varying with the tailwater depth in three ways: first, for very shallow tailwater depths, local scouring decreases with a decrease in tailwater depth; second, when the ratio of tailwater depth to culvert height ranged between 0.2 and 0.7, the scour depth increases with decreasing tailwater depth; and third for a submerged outlet condition. The tailwater depth has only a marginal effect on the maximum depth of scour [2]. Ruff et al. [16] observed that for materials having similar mean grain sizes (d50) but different standard deviations (σ). As (σ) increased, the maximum scour hole depth decreased. Abt et al. [4] mentioned to role of soil type of maximum scour depth. It was noticed that local scour was more dangerous for uniform sands than for well-graded mixtures [1], [2], [4], [9], [17], [18]. Abt et al [3], [19] studied the culvert shape effect on scour hole. The results evidenced that the culvert shape has a limited effect on outlet scour. Under equivalent discharge conditions, it was noted that a square culvert with height equal to the diameter of a circular culvert would reduce scour [16], [20]. The scour hole dimension was also effected by the culvert slope. Abt et al. [3], [21] showed that the culvert slope is a key element in estimating the culvert flow velocity, the discharge capacity, and sediment transport capability. Abt et al. [21], [22] tested experimentally culvert drop height effect on maximum scour depth. It was observed that as the drop height was increasing, the depth of scour was also increasing. From the previous studies, it could have noticed that the most scour prediction formula downstream unblocked culvert was the function of densimetric Froude number, soil properties (d50, σ), tailwater depth and culvert opening size. Blockage is the phenomenon of plugging water structures due to the movement of water flow loaded with sediment and debris. Water structures blockage has a bad effect on water flow where it causes increasing of upstream water level that may cause flooding around the structure and increase of scour rate downstream structures [23], [24]. The blockage phenomenon through was studied experimentally and numerical [15], [25], [26], [27], [28], [29], [30], [31], [32], [33]. Jaeger and Lucke [33] studied the debris transport behavior in a natural channel in Australia. Froude number scale model of an existing culvert was used. It was noticed that through rainfall event, the mobility of debris was impressed by stream shape (depth and width). The condition of the vegetation (size and quantities) through the catchment area was the main factor in debris transport. Rigby et al. [26] reported that steep slope was increasing the ability to mobilize debris that form field data of blocked culverts and bridges during a storm in Wollongong city.

    Streftaris et al. [32] studied the probability of screen blockage by debris at trash screens through a numerical model to relate between the blockage probability and nature of the area around. Recently, many commercial computational fluid programs (CFD) such as SSIIM, Fluent, and FLOW 3D are used in the analysis of the scour process. Scour and sediment transport numerical model need to validate by using experimental data or field data [34], [35], [36], [37], [38]. Epely-Chauvin et al. [36] investigated numerically the effect of a series of parallel spur diked. The experimental data were compared by SSIIM and FLOW 3D program. It was found that the accuracy of calibrated FLOW 3D model was better than SSIIM model. Nielsen et al. [35] used the physical model and FLOW 3D model to analyze the scour process around the pile. The soil around the pile was uniform coarse stones in the physical models that were simulated by regular spheres, porous media, and a mixture of them. The calibrated porous media model can be used to determine the bed shear stress. In partially blocked culverts, there aren’t many studies that explain the blockage impact on scour dimensions. Sorourian et al. [14], [15] studied the effect of inlet partial blockage on scour characteristics downstream box culvert. It resulted that the partial blockage at the culvert inlet could be the main factor in estimating the depth of scour. So, this study is aiming to investigate the effects of blockage through a box culvert on flow and scour characteristics by different blockage ratios and compares the results with a non-blocked case. Create a dimensionless equation relates the blockage ratio of the culvert with scour characteristics downstream culvert.

    2. Experimental data

    The experimental work of the study was conducted in the Hydraulics and Water Engineering Laboratory, Faculty of Engineering, Zagazig University, Egypt. The flume had a rectangular cross-section of 66 cm width, 65.5 cm depth, and 16.2 m long. A rectangular culvert was built with 0.2 m width, 0.2 m height and 3.00 m long with θ = 25° gradually outlet and 0.8 m fixed apron. The model was located on the mid-point of the channel. The sediment part was extended for a distance 2.20 m with 0.66 m width and 0.20 m depth of coarse sand with specific weight 1.60 kg/cm3, d50 = 2.75 mm and σ (d90/d50) = 1.50. The particle size distribution was as shown in Fig. 1. The experimental model was tested for different inlet flow (Q) of 25, 30, 34, 40 l/s for different submerged ratio (S) of 1.25, 1.50, 1.75.

    3. Dimensional analysis

    A dimensional analysis has been used to reduce the number of variables which affecting on the scour pattern downstream partial blocked culvert. The main factors affecting the maximum scour depth are:(2)ds=f(b.h.L.hb.lb.Q.ud.hu.hd.D50.ρ.ρs.g.ls.dd.ld)

    Fig. 2 shows a definition sketch of the experimental model. The maximum scour depth can be written in a dimensionless form as:(3)dsh=f(B.Fd.S)where the ds/h is the relative maximum scour depth.

    4. Numerical work

    The FLOW 3D is (CFD) program used by many researchers and appeared high accuracy in solving hydrodynamic and sediment transport models in the three dimensions. Numerical simulation with FLOW 3D was performed to study the impacts of blockage ratio through box culvert on shear stress, velocity distribution and the sediment transport in terms of the hydrodynamic features (water surface, velocity and shear stress) and morphological parameters (scour depth and sizes) conditions in accurately and efficiently. The renormalization group (RNG) turbulence model was selected due to its high ability to predict the velocity profiles and turbulent kinetic energy for the flow through culvert [39]. The one-fluid incompressible mode was used to simulate the water surface. Volume of fluid (VOF) method was employed in FLOW 3D to tracks a liquid interface through arbitrary deformations and apply the correct boundary conditions at the interface [40].1.

    Governing equations

    Three-dimensional Reynolds-averaged Navier Stokes (RANS) equation was applied for incompressible viscous fluid motion. The continuity equation is as following:(4)VF∂ρ∂t+∂∂xρuAx+∂∂yρvAy+∂∂zρwAz=RDIF(5)∂u∂t+1VFuAx∂u∂x+vAy∂u∂y+ωAz∂u∂z=-1ρ∂P∂x+Gx+fx(6)∂v∂t+1VFuAx∂v∂x+vAy∂v∂y+ωAz∂v∂z=-1ρ∂P∂y+Gy+fy(7)∂ω∂t+1VFuAx∂ω∂x+vAy∂ω∂y+ωAz∂ω∂z=-1ρ∂P∂z+Gz+fz

    ρ is the fluid density,

    VF is the volume fraction,

    (x,y,z) is the Cartesian coordinates,

    (u,v,w) are the velocity components,

    (Ax,Ay,Az) are the area fractions and

    RDIF is the turbulent diffusion.

    P is the average hydrodynamic pressure,

    (Gx, Gy, Gz) are the body accelerations and

    (fx, fy, fz) are the viscous accelerations.

    The motion of sediment transport (suspended, settling, entrainment, bed load) is estimated by predicting the erosion, advection and deposition process as presented in [41].

    The critical shields parameter is (θcr) is defined as the critical shear stress τcr at which sediments begin to move on a flat and horizontal bed [41]:(8)θcr=τcrgd50(ρs-ρ)

    The Soulsby–Whitehouse [42] is used to predict the critical shields parameter as:(9)θcr=0.31+1.2d∗+0.0551-e(-0.02d∗)(10)d∗=d50g(Gs-1ν3where:

    d* is the dimensionless grain size

    Gs is specific weight (Gs = ρs/ρ)

    The entrainment coefficient (0.005) was used to scale the scour rates and fit the experimental data. The settling velocity controls the Soulsby deposition equation. The volumetric sediment transport rate per width of the bed is calculated using Van Rijn [43].2.

    Meshing and geometry of model

    After many trials, it was found that the uniform cell size with 0.03 m cell size is the closest to the experimental results and takes less time. As shown in Fig. 3. In x-direction, the total model length in this direction is 700 cm with mesh planes at −100, 0, 300, 380 and 600 cm respectively from the origin point, in y-direction, the total model length in this direction is 66 cm at distances 0, 23, 43 and 66 cm respectively from the origin point. In z-direction, the total model length in this direction is 120 cm. with mesh planes at −20, 0, 20 and 100 cm respectively.3.

    Boundary condition

    As shown in Fig. 4, the boundary conditions of the model have been defined to simulate the experimental flow conditions accurately. The upstream boundary was defined as the volume flow rate with a different flow rate. The downstream boundary was defined as specific pressure with different fluid elevation. Both of the right side, the left side, and the bottom boundary were defined as a wall. The top boundary defined as specified pressure with pressure value equals zero.

    5. Validation of experimental results and numerical results

    The experimental results investigated the flow and scour characteristics downstream culvert due to different flow conditions. The measured value of maximum scour depth is compared with the simulated depth from FLOW 3D model as shown in Fig. 5. The scour results show that the simulated results from the numerical model is quite close to the experimental results with an average error of 3.6%. The water depths in numerical model results is so close to the experimental results as shown in Fig. 6 where the experiment and numerical results are compared at different submerged ratios and flow rates. The results appear maximum error percentage in water depths upstream and downstream the culvert is about 2.37%. This indicated that the FLOW 3D is efficient for the prediction of maximum scour depth and the flow depths downstream box culvert.

    6. Computation time

    The run time was chosen according to reaching to the stability limit. Hydraulic stability was achieved after 50 s, where the scour development may still go on. For run 1, the numerical simulation was run for 1000 s as shown in Fig. 7 where it mostly reached to scour stability at 800 s. The simulation time was taken 500 s at about 95% of scour stability.

    7. Analysis and discussions

    Fig. 8 shows the study sections where sec 1 represents to upstream section, sec2 represents to inside section and sec3 represents to downstream stream section. Table 1 indicates the scour hole dimensions at different blockage case. The symbol (B) represents to blockage and the number points to blockage ratio. B0 case signifies to the non-blocked case, B30 is that blockage height is 30% to the culvert height and so on.

    Table 1. The scour results of different blockage ratio.

    Casehb cmB = hb/hQ lit/sSFdd50 mmds/h measuredls/hdd/hld/hds/h estimated
    B000351.261.692.50.581.500.275.000.46
    B3060.30351.261.682.50.481.250.274.250.40
    B50100.50351.221.742.50.451.100.244.000.37
    B70140.70351.231.732.50.431.500.165.500.33

    7.1. Scour hole geometry

    The scour hole geometry mainly depends on the properties of soil of the bed downstream the fixed apron. From Table 1, the results show that the maximum scour depth in B0 case is about 0.58 of culvert height while the maximum deposition in B0 is 0.27 culvert height. There is a symmetric scour hole as shown in Fig. 9 in B0 case. An asymmetric scour hole is created in B50 and B70 due to turbulences that causes the deviation of the jet direction from the center of the flume where appear in Fig. 11 and Fig. 19.

    7.2. Flow water surface

    Fig. 10 presents the relative free surface water (hw/h) along the x-direction at center of the box culvert. From the mention Figure, it is easy to release the effect of different blockage ratios. The upstream water level rises by increasing the blockage ratio. Increasing upstream water level may cause flooding over the banks of the waterway. In the 70% blockage case, the upstream water level rises to 2.3 times of culvert height more than the non-blocked case at the same discharge and submerged ratio. The water surface profile shows an increase in water level upstream the culvert due to a decrease in transverse velocity. Because of decreasing velocity downstream culvert, there is an increase in water level before it reaches its uniform depth.

    7.3. Velocity vectors

    Scour downstream hydraulic structures mainly affects by velocities distribution and bed shear stress. Fig. 11 shows the velocity vectors and their magnitude in xz plane at the same flow conditions. The difference in the upstream water level due to the different blockage ratios is so clear. The maximum water level is in B70 and the minimum level is in B0. The inlet mean velocity value is about 0.88 m/s in B0 increases to 2.86 m/s in B70. As the blockage ratio increases, the inlet velocity increases. The outlet velocity in B0 case makes downward jet causes scour hole just after the fixed apron in the middle of the bed while the blockage causes upward water flow that appears clearly in B70. The upward jet decreases the scour depth to 0.13 culvert height less than B0 case. After the scour hole, the velocity decreases and the flow becomes uniform.

    7.4. Velocity distribution

    Fig. 12 represents flow velocity (Vx) distribution along the vertical depth (z/hu) upstream the inlet for the different blockage ratios at the same flow conditions. From the Figure, the maximum velocity creates closed to bed in B0 while in blocked case, the maximum horizontal velocity creates at 0.30 of relative vertical depth (z/hu). Fig. 13 shows the (Vz) distribution along the vertical depth (z/hu) upstream culvert at sec 1. From the mentioned Figure, it is easy to note that the maximum vertical is in B70 which appears that as the blockage ratio increases the vertical ratio also increases. In the non-blocked case. The vertical velocity (Vz) is maximum at (z/hu) equals 0.64. At the end of the fixed apron (sec 3), the horizontal velocity (Vx) is slowly increasing to reach the maximum value closed to bed in B0 and B30 while the maximum horizontal velocity occurs near to the top surface in B50 and B70 as shown in Fig. 14. The vertical velocity component along the vertical depth (z/hd) is presented in Fig. 15. The vertical velocity (Vz) is maximum in B0 at vertical depth (z/hd) 0.3 with value 0.45 m/s downward. Figs. 16 and 17 observe velocity components (Vx, Vz) along the vertical depth just after the end of blockage length at the centerline of the culvert barrel. It could be noticed the uniform velocity distribution in B0 case with horizontal velocity (Vx) closed to 1.0 m/s and vertical velocity closed to zero. In the blocked case, the maximum horizontal velocity occurs in depth more than the blockage height.

    7.5. Bed velocity distribution

    Fig. 18 presents the x-velocity vectors at 1.5 cm above the bed for different blockage ratios from the velocity vectors distribution and magnitude, it is easy to realize the position of the scour hole and deposition region. In B0 and B30, the flow is symmetric so that the scour hole is created around the centerline of flow while in B50 and B70 cases, the flow is asymmetric and the scour hole creates in the right of flow direction in B50. The maximum scour depth is found in the left of flow direction in B70 case where the high velocity region is found.

    8. Maximum scour depth prediction

    Regression analysis is used to estimate maximum scour depth downstream box culvert for different ratios of blockage by correlating the maximum relative scour by other variables that affect on it in one formula. An equation is developed to predict maximum scour depth for blocked and non-blocked. As shown in the equation below, the relative maximum scour depth(ds/hd) is a function of densimetric Froude number (Fd), blockage ratio (B) and submerged ratio (S)(11)dsh=0.56Fd-0.20B+0.45S-1.05

    In this equation the coefficient of correlation (R2) is 0.82 with standard error equals 0·08. The developed equation is valid for Fd = [0.9 to 2.10] and submerged ratio (S) ≥ 1.00. Fig. 19 shows the comparison between relative maximum scour depths (ds/h) measured and estimated for different blockage ratios. Fig. 20 clears the comparison between residuals and ds/h estimated for the present study. From these figures, it could be noticed that there is a good agreement between the measured and estimated relative scour depth.

    9. Comparison with previous scour equations

    Many previous scour formulae have been produced for calculation the maximum scour depth downstream non-blockage culvert. These equations have been included the effect of flow regime, culvert shape, soil properties and the flow rate on maximum scour depth. Two of previous experimental studies data have been chosen to be compared with the present study results in non-blocked study data. Table 2 shows comparison of culvert shape, densmetric Froude number, median particle size and scour equations for these previous studies. By applying the present study data in these studies scour formula as shown in Fig. 21, it could be noticed that there are a good agreement between present formula results and others empirical equations results. Where that Lim [44] and Abt [4] are so closed to the present study data.

    Table 2. Comparison of some previous scour formula.

    ResearchersFdCulvert shaped50(mm)Proposed equationSubmerged ratio
    Present study0.9–2.11square2.75dsh=0.56Fd-0.20B+0.45S-1.051.25–1.75
    Lim [44]1–10Circular1.65dsh=0.45Fd0.47
    Abt [4]Fd ≥ 1Circular0.22–7.34-dsh=3.67Fd0.57∗D500.4∗σ-0.4–

    10. Conclusions

    The present study has shown that the FLOW 3D model can accurately simulate water surface and the scour hole characteristics downstream the box culvert with error percentage in water depths does not exceed 2.37%. Velocities distribution through and outlets culvert barrel helped on understanding the scour hole shape.

    The blockage through culvert had caused of increasing of water surface upstream structure where the upstream water level in B70 was 2.3 of culvert height more than non-blocked case at the same discharge that could be dangerous on the stability of roads above. The depth averaged velocity through culvert barrel increased by 3 times its value in non-blocked case.

    On the other hand, blockage through culvert had a limited effect on the maximum scour depth. The little effect of blockage on maximum scour depth could be noticed in Fig. 11. From this Figure, it could be noted that the residual part of culvert barrel after the blockage part had made turbulences. These turbulences caused the deviation of the flow resulting in the formation of asymmetric scour hole on the side of channel. This not only but in B70 the blockage height caused upward jet which made a wide far scour hole as cleared from the results in Table 1.

    An empirical equation was developed from the results to estimate the maximum scour depth relative to culvert height function of blockage ratio (B), submerged ratio (S), and densimetric Froude number (Fd). The equation results was compared with some scour formulas at the same densimetric Froude number rang where the present study results was in between the other equations results as shown in Fig. 21.

    Declaration of Competing Interest

    The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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    Peer review under responsibility of Faculty of Engineering, Alexandria University.

    Figure 1- Schematic diagram of pooled stepped spillway conducted by Felder et al. (2012A): Notes: h step height (10 cm): w pool height (3.1 cm): l horizontal step length (20 cm): lw pool weir length (1.5 cm): d' is the water depth above the crest; y' is the distance normal to the crest invert

    Study of inception point, void fraction and pressure over pooled stepped spillways using Flow-3D

    Khosro Morovati , Afshin Eghbalzadeh 
    International Journal of Numerical Methods for Heat & Fluid Flow

    ISSN: 0961-5539

    Article publication date: 3 April 2018

    Abstract

    많은 계단식 배수로 지오메트리 설계 지침이 평평한 단계를 위해 개발되었지만 통합 단계를 설계하는 것이 더 효율적으로 작동하는 배수로에 대한 적절한 대안이 될 수 있습니다.

    이 논문은 POOL의 다른 높이에서 공기 연행과 보이드 비율의 시작점을 다루는 것을 목표로 합니다. 그 후, FLOW-3D 소프트웨어를 사용하여 POOL과 경사면의 높이를 다르게 하여 폭기된 지역과 폭기되지 않은 지역에서 압력 분포를 평가했습니다.

    얻어진 수치 결과와 실험 결과의 비교는 본 연구에 사용된 모든 방류에 대해 잘 일치했습니다. POOL 높이는 시작 지점 위치에 미미한 영향을 미쳤습니다. 공극률의 값은 높은 방류에 비해 낮은 방전에서 더 많은 영향을 받았습니다.

    여수로의 마루(통기되지 않은 지역)에서는 음압이 나타나지 않았으며 각 방류에서 마루를 따라 높이가 15cm인 수영장에서 최대 압력 값이 얻어졌습니다.

    모든 사면에서 웅덩이 및 평평한 계단형 여수로의 계단층 부근에서는 음압이 형성되지 않았습니다. 그러나 평단식 여수로에 비해 평단식 여수로의 수직면 부근에서 음압이 더 많이 형성되어 평단식 슈트에서 캐비테이션 현상이 발생할 확률이 증가하였습니다.

    Study of inception point, void fraction and pressure over pooled
    stWhile many stepped spillways geometry design guidelines were developed for flat steps, designing pooled steps might be an appropriate alternative to spillways working more efficiency. This paper aims to deal with the inception point of air-entrainment and void fraction in the different height of the pools. Following that, pressure distribution was evaluated in aerated and non-aerated regions under the effect of different heights of the pools and slopes through the use of the FLOW-3D software. Comparison of obtained numerical results with experimental ones was in good agreement for all discharges used in this study. Pools height had the insignificant effect on the inception point location. The value of void fraction was more affected in lower discharges in comparison with higher ones. Negative pressure was not seen over the crest of spillway (non-aerated region), and the maximum pressure values were obtained for pools with 15 cm height along the crest in each discharge. In all slopes, negative pressure was not formed near the step bed in the pooled and flat stepped spillways. However, negative pressure was formed in more area near the vertical face in the flat stepped spillway compared with the pooled stepped spillway which increases the probability of cavitation phenomenon in the flat stepped chute.

    Design/methodology/approach

    압력, 공극률 및 시작점을 평가하기 위해 POOL된 계단식 여수로가 사용되었습니다. 또한 POOL의 다른 높이가 사용되었습니다. 이 연구의 수치 시뮬레이션은 Flow-3D 소프트웨어를 통해 수행되었습니다. 얻어진 결과는 풀이 압력, 공극률 및 시작점을 포함한 2상 유동 특성에 영향을 미칠 수 있음을 나타냅니다.

    Findings

    마루 위에는 음압이 보이지 않았습니다. 압력 값은 사용된 모든 높이와 15cm 높이에서 얻은 최대 값에 대해 다릅니다. 또한, 풀링 스텝은 플랫 케이스에 비해 음압점 감소에 더 효과적인 역할을 하였습니다. 시작 지점 위치는 특히 9 및 15cm 높이에 대해 스키밍 흐름 영역과 비교하여 낮잠 및 전환 흐름 영역에서 더 많은 영향을 받았습니다.

    Keywords

    Citation

    Morovati, K. and Eghbalzadeh, A. (2018), “Study of inception point, void fraction and pressure over pooled stepped spillways using Flow-3D”, International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 28 No. 4, pp. 982-998. https://doi.org/10.1108/HFF-03-2017-0112

    Figure 1- Schematic diagram of pooled stepped spillway conducted by Felder et al. (2012A): Notes: h step height (10 cm): w pool height (3.1 cm): l horizontal step length (20 cm): lw pool weir length (1.5 cm): d' is the water depth above the crest; y' is the distance normal to the crest invert
    Figure 1- Schematic diagram of pooled stepped spillway conducted by Felder et al. (2012A): Notes: h step height (10 cm): w pool height (3.1 cm): l horizontal step length (20 cm): lw pool weir length (1.5 cm): d’ is the water depth above the crest; y’ is the distance normal to the crest invert
    Figure 2- meshing domain and distribution of blocks
    Figure 2- meshing domain and distribution of blocks
    Figure 3- Comparison of numerical simulation with experimental data by Felder et al. (2012A); mesh convergence analysis; pooled stepped spillway (slope: 26.6 0 )
    Figure 3- Comparison of numerical simulation with experimental data by Felder et al. (2012A); mesh convergence analysis; pooled stepped spillway (slope: 26.6 0 )
    Figure 4- Comparison of numerical simulation with experimental data by Felder et al. (2012A); Flat stepped spillway (slope: 0 26 6. )
    Figure 4- Comparison of numerical simulation with experimental data by Felder et al. (2012A); Flat stepped spillway (slope: 0 26 6. )
    Figure 5-Comparison of numerical simulation with experimental data by Felder et al. (2012B); pooled and flat stepped spillways (slope: 0 9.8 )
    Figure 5-Comparison of numerical simulation with experimental data by Felder et al. (2012B); pooled and flat stepped spillways (slope: 0 9.8 )
    Figure 6- TKE distribution on steps 8, 9 and 10 for four different mesh numbers: 261252 (model 1), 288941 (model 2), 323578 (model 3) and 343154 (model 4)
    Figure 6- TKE distribution on steps 8, 9 and 10 for four different mesh numbers: 261252 (model 1), 288941 (model 2), 323578 (model 3) and 343154 (model 4)
    Figure 7- Comparison of obtained Void fraction distribution on step 10 in numerical simulation with experimental work conducted by Felder et al. (2012A); (slope 26.60 )
    Figure 7- Comparison of obtained Void fraction distribution on step 10 in numerical simulation with experimental work conducted by Felder et al. (2012A); (slope 26.60 )
    Figure 8- Results of inception point of air entrainment in different height of the pools: comparison with empirical correlations (Eqs 8-9), experimental (Felder et al. (2012A)) and numerical data
    Figure 8- Results of inception point of air entrainment in different height of the pools: comparison with empirical correlations (Eqs 8-9), experimental (Felder et al. (2012A)) and numerical data
    Figure 9- Void fraction distribution for different pool heights on steps 10; slope 26.6 0
    Figure 9- Void fraction distribution for different pool heights on steps 10; slope 26.6 0
    Figure 10- Comparison of pressure distribution between numerical simulation and experimental work conducted by Zhang and Chanson (2016); flat stepped spillway (slope: 0 45 )
    Figure 10- Comparison of pressure distribution between numerical simulation and experimental work conducted by Zhang and Chanson (2016); flat stepped spillway (slope: 0 45 )
    Figure 11- A comparison of the pressure distribution above the crest of the spillway; B comparison of the free surface profile along the crest of the spillway. Note: x' indicates the longitudinal distance from the starting point of the crest.
    Figure 11- A comparison of the pressure distribution above the crest of the spillway; B comparison of the free surface profile along the crest of the spillway. Note: x’ indicates the longitudinal distance from the starting point of the crest.
    Figure 12- pressure distribution along crest of spillway in different discharges; slope 26.6
    Figure 12- pressure distribution along crest of spillway in different discharges; slope 26.6
    Figure 13- Pressure distribution near the last step bed for different slopes and discharges: x'' indicatesthe longitudinal distance from the intersection of the horizontal and vertical faces of step 10; y" is the distance from the intersection of the horizontal and vertical faces in the vertical direction
    Figure 13- Pressure distribution near the last step bed for different slopes and discharges: x” indicatesthe longitudinal distance from the intersection of the horizontal and vertical faces of step 10; y” is the distance from the intersection of the horizontal and vertical faces in the vertical direction
    Figure 14- Pressure distribution adjacent the vertical face of step 9 for different discharges and slopes
    Figure 14- Pressure distribution adjacent the vertical face of step 9 for different discharges and slopes
    Table1- Used discharges for assessments of mesh convergence analysis and hydraulic characteristics
    Table1- Used discharges for assessments of mesh convergence analysis and hydraulic characteristics

    Conclusion

    본 연구에서는 자유표면을 모사하기 위해 VOF 방법과 k -ε (RNG) 난류 모델을 활용하여 FLOW-3D 소프트웨어를 사용하였고, 계단식 배수로의 유동을 모사하기 위한 목적으로 난류 특성을 모사하였다. 얻은 결과는 수치 모델이 시작점 위치, 보이드 비율 및 압력을 적절하게 시뮬레이션했음을 나타냅니다. 풀의 높이는 공기 유입 위치에 미미한 영향을 미치므로 얻은 결과는 이 문서에서 제시된 상관 관계와 잘 일치했습니다. 즉, 사용 가능한 상관 관계를 서로 다른 풀 높이에 사용할 수 있습니다. 공극률의 결과는 스텝 풀 근처의 나프 유동 영역에서 공극율 값이 다른 배출보다 더 큰 것으로 나타났다. 더욱이 고방출량 .0 113m3/s에서 수영장 높이를 변경해도 수영장 표면 근처의 공극률 값에는 영향을 미치지 않았습니다.

    낮잠 및 전환 체제의 압력 분포에 대한 0 및 3cm 높이의 수영장 효과는 많은 지점에서 대부분 유사했습니다. 더욱이 조사된 모든 높이에서 여수로의 마루를 따라 부압이 없었습니다. 여수로 끝단의 바닥 부근의 압력 결과는 평평하고 고인 경우 부압이 발생하지 않았음을 나타냅니다. 수직면 부근의 음압은 웅덩이에 비해 평평한 계단형 여수로의 깊이(w=0 cm)의 대부분에서 발생하였다. 또한 더 큰 사면에 대한 풀링 케이스에서 음압이 제거되었습니다. 평단식 여수로에서는 계단의 수직면에 인접한 더 넓은 지역에서 음압이 발생하였기 때문에 이 여수로에서는 고형단식여수로보다 캐비테이션 현상이 발생할 가능성이 더 큽니다.

    In this study, the FLOW-3D software was used through utilizing the VOF method and k −ε (RNG) turbulence model in order to simulate free surface, and turbulence characteristics for the purpose of simulating flow over pooled stepped spillway. The results obtained indicated that the numerical model properly simulated the inception point location, void fraction, and pressure. The height of the pools has the insignificant effect on the location of air entrainment, so that obtained results were in good agreement with the correlations presented in this paper. In other words, available correlations can be used for different pool heights. The results of void fraction showed that the void fraction values in nappe flow regime near the step pool were more than the other discharges. Furthermore in high discharge, 0.113m3/s, altering pool height had no effect on the value of void fraction near the pool surface.

    The effect of the pools with 0 and 3 cm heights over the pressure distribution in nappe and transition regimes was mostly similar in many points. Furthermore, in all examined heights there was no negative pressure along the crest of the spillway. The pressure results near the bed of the step at the end of the spillway indicated that negative pressure did not occur in the flat and pooled cases. Negative pressure near the vertical face occurred in the most part of the depth in the flat stepped spillway (w=0 cm) in comparison with the pooled case. Also, the negative pressure was eliminated in the pooled case for the larger slopes. Since negative pressure occurred in a larger area adjacent the vertical face of the steps in the flat stepped spillways, it is more likely that cavitation phenomenon occurs in this spillway rather than the pooled stepped spillways.

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    원문보기
    Fig. 1. (a) Dimensions of the casting with runners (unit: mm), (b) a melt flow simulation using Flow-3D software together with Reilly's model[44], predicted that a large amount of bifilms (denoted by the black particles) would be contained in the final casting. (c) A solidification simulation using Pro-cast software showed that no shrinkage defect was contained in the final casting.

    AZ91 합금 주물 내 연행 결함에 대한 캐리어 가스의 영향

    Effect of carrier gases on the entrainment defects within AZ91 alloy castings

    Tian Liab J.M.T.Daviesa Xiangzhen Zhuc
    aUniversity of Birmingham, Birmingham B15 2TT, United Kingdom
    bGrainger and Worrall Ltd, Bridgnorth WV15 5HP, United Kingdom
    cBrunel Centre for Advanced Solidification Technology, Brunel University London, Kingston Ln, London, Uxbridge UB8 3PH, United Kingdom

    Abstract

    An entrainment defect (also known as a double oxide film defect or bifilm) acts a void containing an entrapped gas when submerged into a light-alloy melt, thus reducing the quality and reproducibility of the final castings. Previous publications, carried out with Al-alloy castings, reported that this trapped gas could be subsequently consumed by the reaction with the surrounding melt, thus reducing the void volume and negative effect of entrainment defects. Compared with Al-alloys, the entrapped gas within Mg-alloy might be more efficiently consumed due to the relatively high reactivity of magnesium. However, research into the entrainment defects within Mg alloys has been significantly limited. In the present work, AZ91 alloy castings were produced under different carrier gas atmospheres (i.e., SF6/CO2, SF6/air). The evolution processes of the entrainment defects contained in AZ91 alloy were suggested according to the microstructure inspections and thermodynamic calculations. The defects formed in the different atmospheres have a similar sandwich-like structure, but their oxide films contained different combinations of compounds. The use of carrier gases, which were associated with different entrained-gas consumption rates, affected the reproducibility of AZ91 castings.

    Keywords

    Magnesium alloyCastingOxide film, Bifilm, Entrainment defect, Reproducibility

    연행 결함(이중 산화막 결함 또는 이중막 결함이라고도 함)은 경합금 용융물에 잠길 때 갇힌 가스를 포함하는 공극으로 작용하여 최종 주물의 품질과 재현성을 저하시킵니다. Al-합금 주조로 수행된 이전 간행물에서는 이 갇힌 가스가 주변 용융물과의 반응에 의해 후속적으로 소모되어 공극 부피와 연행 결함의 부정적인 영향을 줄일 수 있다고 보고했습니다. Al-합금에 비해 마그네슘의 상대적으로 높은 반응성으로 인해 Mg-합금 내에 포집된 가스가 더 효율적으로 소모될 수 있습니다. 그러나 Mg 합금 내 연행 결함에 대한 연구는 상당히 제한적이었습니다. 현재 작업에서 AZ91 합금 주물은 다양한 캐리어 가스 분위기(즉, SF 6 /CO2 , SF 6 / 공기). AZ91 합금에 포함된 엔트레인먼트 결함의 진화 과정은 미세조직 검사 및 열역학적 계산에 따라 제안되었습니다. 서로 다른 분위기에서 형성된 결함은 유사한 샌드위치 구조를 갖지만 산화막에는 서로 다른 화합물 조합이 포함되어 있습니다. 다른 동반 가스 소비율과 관련된 운반 가스의 사용은 AZ91 주물의 재현성에 영향을 미쳤습니다.

    키워드

    마그네슘 합금주조Oxide film, Bifilm, Entrainment 불량, 재현성

    1 . 소개

    지구상에서 가장 가벼운 구조용 금속인 마그네슘은 지난 수십 년 동안 가장 매력적인 경금속 중 하나가 되었습니다. 결과적으로 마그네슘 산업은 지난 20년 동안 급속한 발전을 경험했으며 [1 , 2] , 이는 전 세계적으로 Mg 합금에 대한 수요가 크게 증가했음을 나타냅니다. 오늘날 Mg 합금의 사용은 자동차, 항공 우주, 전자 등의 분야에서 볼 수 있습니다. [3 , 4] . Mg 금속의 전 세계 소비는 특히 자동차 산업에서 앞으로 더욱 증가할 것으로 예측되었습니다. 기존 자동차와 전기 자동차 모두의 에너지 효율성 요구 사항이 설계를 경량화하도록 더욱 밀어붙이기 때문입니다 [3 , 5, 6] .

    Mg 합금에 대한 수요의 지속적인 성장은 Mg 합금 주조의 품질 및 기계적 특성 개선에 대한 광범위한 관심을 불러일으켰습니다. Mg 합금 주조 공정 동안 용융물의 표면 난류는 소량의 주변 대기를 포함하는 이중 표면 필름의 포획으로 이어질 수 있으므로 동반 결함(이중 산화막 결함 또는 이중막 결함이라고도 함)을 형성합니다. ) [7] , [8] , [9] , [10] . 무작위 크기, 수량, 방향 및 연행 결함의 배치는 주조 특성의 변화와 관련된 중요한 요인으로 널리 받아들여지고 있습니다 [7] . 또한 Peng et al. [11]AZ91 합금 용융물에 동반된 산화물 필름이 Al 8 Mn 5 입자에 대한 필터 역할을 하여 침전될 때 가두는 것을 발견했습니다 . Mackie et al. [12]는 또한 동반된 산화막이 금속간 입자를 트롤(trawl)하는 작용을 하여 입자가 클러스터링되어 매우 큰 결함을 형성할 수 있다고 제안했습니다. 금속간 화합물의 클러스터링은 비말동반 결함을 주조 특성에 더 해롭게 만들었습니다.

    연행 결함에 관한 이전 연구의 대부분은 Al-합금에 대해 수행되었으며 [7 , [13] , [14] , [15] , [16] , [17] , [18] 몇 가지 잠재적인 방법이 제안되었습니다. 알루미늄 합금 주물의 품질에 대한 부정적인 영향을 줄이기 위해. Nyahumwa et al., [16] 은 연행 결함 내의 공극 체적이 열간 등방압 압축(HIP) 공정에 의해 감소될 수 있음을 보여줍니다. Campbell [7] 은 결함 내부의 동반된 가스가 주변 용융물과의 반응으로 인해 소모될 수 있다고 제안했으며, 이는 Raiszedeh와 Griffiths [19]에 의해 추가로 확인되었습니다 ..혼입 가스 소비가 Al-합금 주물의 기계적 특성에 미치는 영향은 [8 , 9]에 의해 조사되었으며 , 이는 혼입 가스의 소비가 주조 재현성의 개선을 촉진함을 시사합니다.

    Al-합금 내 결함에 대한 조사와 비교하여 Mg-합금 내 연행 결함에 대한 연구는 상당히 제한적입니다. 연행 결함의 존재는 Mg 합금 주물 [20 , 21] 에서 입증 되었지만 그 거동, 진화 및 연행 가스 소비는 여전히 명확하지 않습니다.

    Mg 합금 주조 공정에서 용융물은 일반적으로 마그네슘 점화를 피하기 위해 커버 가스로 보호됩니다. 따라서 모래 또는 매몰 몰드의 공동은 용융물을 붓기 전에 커버 가스로 세척해야 합니다 [22] . 따라서, Mg 합금 주물 내의 연행 가스는 공기만이 아니라 주조 공정에 사용되는 커버 가스를 포함해야 하며, 이는 구조 및 해당 연행 결함의 전개를 복잡하게 만들 수 있습니다.

    SF 6 은 Mg 합금 주조 공정에 널리 사용되는 대표적인 커버 가스입니다 [23] , [24] , [25] . 이 커버 가스는 유럽의 마그네슘 합금 주조 공장에서 사용하도록 제한되었지만 상업 보고서에 따르면 이 커버는 전 세계 마그네슘 합금 산업, 특히 다음과 같은 글로벌 마그네슘 합금 생산을 지배한 국가에서 여전히 인기가 있습니다. 중국, 브라질, 인도 등 [26] . 또한, 최근 학술지 조사에서도 이 커버가스가 최근 마그네슘 합금 연구에서 널리 사용된 것으로 나타났다 [27] . SF 6 커버 가스 의 보호 메커니즘 (즉, 액체 Mg 합금과 SF 6 사이의 반응Cover gas)에 대한 연구는 여러 선행연구자들에 의해 이루어졌으나 표면 산화막의 형성과정이 아직 명확하게 밝혀지지 않았으며, 일부 발표된 결과들도 상충되고 있다. 1970년대 초 Fruehling [28] 은 SF 6 아래에 형성된 표면 피막이 주로 미량의 불화물과 함께 MgO 임을 발견 하고 SF 6 이 Mg 합금 표면 피막에 흡수 된다고 제안했습니다 . Couling [29] 은 흡수된 SF 6 이 Mg 합금 용융물과 반응하여 MgF 2 를 형성함을 추가로 확인했습니다 . 지난 20년 동안 아래에 자세히 설명된 것처럼 Mg 합금 표면 필름의 다양한 구조가 보고되었습니다.(1)

    단층 필름 . Cashion [30 , 31] 은 X선 광전자 분광법(XPS)과 오제 분광법(AES)을 사용하여 표면 필름을 MgO 및 MgF 2 로 식별했습니다 . 그는 또한 필름의 구성이 두께와 전체 실험 유지 시간에 걸쳐 일정하다는 것을 발견했습니다. Cashion이 관찰한 필름은 10분에서 100분의 유지 시간으로 생성된 단층 구조를 가졌다.(2)

    이중층 필름 . Aarstad et. al [32] 은 2003년에 이중층 표면 산화막을 보고했습니다. 그들은 예비 MgO 막에 부착된 잘 분포된 여러 MgF 2 입자를 관찰 하고 전체 표면적의 25-50%를 덮을 때까지 성장했습니다. 외부 MgO 필름을 통한 F의 내부 확산은 진화 과정의 원동력이었습니다. 이 이중층 구조는 Xiong의 그룹 [25 , 33] 과 Shih et al. 도 지지했습니다 . [34] .(삼)

    트리플 레이어 필름 . 3층 필름과 그 진화 과정은 Pettersen [35]에 의해 2002년에 보고되었습니다 . Pettersen은 초기 표면 필름이 MgO 상이었고 F의 내부 확산에 의해 점차적으로 안정적인 MgF 2 상 으로 진화한다는 것을 발견했습니다 . 두꺼운 상부 및 하부 MgF 2 층.(4)

    산화물 필름은 개별 입자로 구성 됩니다. Wang et al [36] 은 Mg-alloy 표면 필름을 SF 6 커버 가스 하에서 용융물에 교반 한 다음 응고 후 동반된 표면 필름을 검사했습니다. 그들은 동반된 표면 필름이 다른 연구자들이 보고한 보호 표면 필름처럼 계속되지 않고 개별 입자로 구성된다는 것을 발견했습니다. 젊은 산화막은 MgO 나노 크기의 산화물 입자로 구성되어 있는 반면, 오래된 산화막은 한쪽 면에 불화물과 질화물이 포함된 거친 입자(평균 크기 약 1μm)로 구성되어 있습니다.

    Mg 합금 용융 표면의 산화막 또는 동반 가스는 모두 액체 Mg 합금과 커버 가스 사이의 반응으로 인해 형성되므로 Mg 합금 표면막에 대한 위에서 언급한 연구는 진화에 대한 귀중한 통찰력을 제공합니다. 연행 결함. 따라서 SF 6 커버 가스 의 보호 메커니즘 (즉, Mg-합금 표면 필름의 형성)은 해당 동반 결함의 잠재적인 복잡한 진화 과정을 나타냅니다.

    그러나 Mg 합금 용융물에 표면 필름을 형성하는 것은 용융물에 잠긴 동반된 가스의 소비와 다른 상황에 있다는 점에 유의해야 합니다. 예를 들어, 앞서 언급한 연구에서 표면 성막 동안 충분한 양의 커버 가스가 담지되어 커버 가스의 고갈을 억제했습니다. 대조적으로, Mg 합금 용융물 내의 동반된 가스의 양은 유한하며, 동반된 가스는 완전히 고갈될 수 있습니다. Mirak [37] 은 3.5% SF 6 /기포를 특별히 설계된 영구 금형에서 응고되는 순수한 Mg 합금 용융물에 도입했습니다. 기포가 완전히 소모되었으며, 해당 산화막은 MgO와 MgF 2 의 혼합물임을 알 수 있었다.. 그러나 Aarstad [32] 및 Xiong [25 , 33]에 의해 관찰된 MgF 2 스팟 과 같은 핵 생성 사이트 는 관찰되지 않았습니다. Mirak은 또한 조성 분석을 기반으로 산화막에서 MgO 이전에 MgF 2 가 형성 되었다고 추측했는데 , 이는 이전 문헌에서 보고된 표면 필름 형성 과정(즉, MgF 2 이전에 형성된 MgO)과 반대 입니다. Mirak의 연구는 동반된 가스의 산화막 형성이 표면막의 산화막 형성과 상당히 다를 수 있음을 나타내었지만 산화막의 구조와 진화에 대해서는 밝히지 않았습니다.

    또한 커버 가스에 캐리어 가스를 사용하는 것도 커버 가스와 액체 Mg 합금 사이의 반응에 영향을 미쳤습니다. SF 6 /air 는 용융 마그네슘의 점화를 피하기 위해 SF 6 /CO 2 운반 가스 [38] 보다 더 높은 함량의 SF 6을 필요로 하여 다른 가스 소비율을 나타냅니다. Liang et.al [39] 은 CO 2 가 캐리어 가스로 사용될 때 표면 필름에 탄소가 형성된다고 제안했는데 , 이는 SF 6 /air 에서 형성된 필름과 다릅니다 . Mg 연소 [40]에 대한 조사 에서 Mg 2 C 3 검출이 보고되었습니다.CO 2 연소 후 Mg 합금 샘플 에서 이는 Liang의 결과를 뒷받침할 뿐만 아니라 이중 산화막 결함에서 Mg 탄화물의 잠재적 형성을 나타냅니다.

    여기에 보고된 작업은 다양한 커버 가스(즉, SF 6 /air 및 SF 6 /CO 2 )로 보호되는 AZ91 Mg 합금 주물에서 형성된 연행 결함의 거동과 진화에 대한 조사 입니다. 이러한 캐리어 가스는 액체 Mg 합금에 대해 다른 보호성을 가지며, 따라서 상응하는 동반 가스의 다른 소비율 및 발생 프로세스와 관련될 수 있습니다. AZ91 주물의 재현성에 대한 동반 가스 소비의 영향도 연구되었습니다.

    2 . 실험

    2.1 . 용융 및 주조

    3kg의 AZ91 합금을 700 ± 5 °C의 연강 도가니에서 녹였습니다. AZ91 합금의 조성은 표 1 에 나타내었다 . 가열하기 전에 잉곳 표면의 모든 산화물 스케일을 기계가공으로 제거했습니다. 사용 된 커버 가스는 0.5 %이었다 SF 6 / 공기 또는 0.5 % SF 6 / CO 2 (부피. %) 다른 주물 6L / 분의 유량. 용융물은 15분 동안 0.3L/min의 유속으로 아르곤으로 가스를 제거한 다음 [41 , 42] , 모래 주형에 부었습니다. 붓기 전에 샌드 몰드 캐비티를 20분 동안 커버 가스로 플러싱했습니다 [22] . 잔류 용융물(약 1kg)이 도가니에서 응고되었습니다.

    표 1 . 본 연구에 사용된 AZ91 합금의 조성(wt%).

    알아연미네소타시철니마그네슘
    9.40.610.150.020.0050.0017잔여

    그림 1 (a)는 러너가 있는 주물의 치수를 보여줍니다. 탑 필링 시스템은 최종 주물에서 연행 결함을 생성하기 위해 의도적으로 사용되었습니다. Green과 Campbell [7 , 43] 은 탑 필링 시스템이 바텀 필링 시스템에 비해 주조 과정에서 더 많은 연행 현상(즉, 이중 필름)을 유발한다고 제안했습니다. 이 금형의 용융 흐름 시뮬레이션(Flow-3D 소프트웨어)은 연행 현상에 관한 Reilly의 모델 [44] 을 사용하여 최종 주조에 많은 양의 이중막이 포함될 것이라고 예측했습니다( 그림 1 에서 검은색 입자로 표시됨) . NS).

    그림 1

    수축 결함은 또한 주물의 기계적 특성과 재현성에 영향을 미칩니다. 이 연구는 주조 품질에 대한 이중 필름의 영향에 초점을 맞추었기 때문에 수축 결함이 발생하지 않도록 금형을 의도적으로 설계했습니다. ProCAST 소프트웨어를 사용한 응고 시뮬레이션은 그림 1c 와 같이 최종 주조에 수축 결함이 포함되지 않음을 보여주었습니다 . 캐스팅 건전함도 테스트바 가공 전 실시간 X-ray를 통해 확인했다.

    모래 주형은 1wt를 함유한 수지 결합된 규사로 만들어졌습니다. % PEPSET 5230 수지 및 1wt. % PEPSET 5112 촉매. 모래는 또한 억제제로 작용하기 위해 2중량%의 Na 2 SiF 6 을 함유했습니다 .. 주입 온도는 700 ± 5 °C였습니다. 응고 후 러너바의 단면을 Sci-Lab Analytical Ltd로 보내 H 함량 분석(LECO 분석)을 하였고, 모든 H 함량 측정은 주조 공정 후 5일째에 실시하였다. 각각의 주물은 인장 강도 시험을 위해 클립 신장계가 있는 Zwick 1484 인장 시험기를 사용하여 40개의 시험 막대로 가공되었습니다. 파손된 시험봉의 파단면을 주사전자현미경(SEM, Philips JEOL7000)을 이용하여 가속전압 5~15kV로 조사하였다. 파손된 시험 막대, 도가니에서 응고된 잔류 Mg 합금 및 주조 러너를 동일한 SEM을 사용하여 단면화하고 연마하고 검사했습니다. CFEI Quanta 3D FEG FIB-SEM을 사용하여 FIB(집속 이온 빔 밀링 기술)에 의해 테스트 막대 파괴 표면에서 발견된 산화막의 단면을 노출했습니다. 분석에 필요한 산화막은 백금층으로 코팅하였다. 그런 다음 30kV로 가속된 갈륨 이온 빔이 산화막의 단면을 노출시키기 위해 백금 코팅 영역을 둘러싼 재료 기판을 밀링했습니다. 산화막 단면의 EDS 분석은 30kV의 가속 전압에서 FIB 장비를 사용하여 수행되었습니다.

    2.2 . 산화 세포

    전술 한 바와 같이, 몇몇 최근 연구자들은 마그네슘 합금의 용탕 표면에 형성된 보호막 조사 [38 , 39 , [46] , [47] , [48] , [49] , [50] , [51] , [52 ] . 이 실험 동안 사용된 커버 가스의 양이 충분하여 커버 가스에서 불화물의 고갈을 억제했습니다. 이 섹션에서 설명하는 실험은 엔트레인먼트 결함의 산화막의 진화를 연구하기 위해 커버 가스의 공급을 제한하는 밀봉된 산화 셀을 사용했습니다. 산화 셀에 포함된 커버 가스는 큰 크기의 “동반된 기포”로 간주되었습니다.

    도 2에 도시된 바와 같이 , 산화셀의 본체는 내부 길이가 400mm, 내경이 32mm인 폐쇄형 연강관이었다. 수냉식 동관을 전지의 상부에 감았습니다. 튜브가 가열될 때 냉각 시스템은 상부와 하부 사이에 온도 차이를 만들어 내부 가스가 튜브 내에서 대류하도록 했습니다. 온도는 도가니 상단에 위치한 K형 열전대로 모니터링했습니다. Nieet al. [53] 은 Mg 합금 용융물의 표면 피막을 조사할 때 SF 6 커버 가스가 유지로의 강철 벽과 반응할 것이라고 제안했습니다 . 이 반응을 피하기 위해 강철 산화 전지의 내부 표면(그림 2 참조)) 및 열전대의 상반부는 질화붕소로 코팅되었습니다(Mg 합금은 질화붕소와 ​​접촉하지 않았습니다).

    그림 2

    실험 중에 고체 AZ91 합금 블록을 산화 셀 바닥에 위치한 마그네시아 도가니에 넣었습니다. 전지는 1L/min의 가스 유속으로 전기 저항로에서 100℃로 가열되었다. 원래의 갇힌 대기(즉, 공기)를 대체하기 위해 셀을 이 온도에서 20분 동안 유지했습니다. 그런 다음, 산화 셀을 700°C로 더 가열하여 AZ91 샘플을 녹였습니다. 그런 다음 가스 입구 및 출구 밸브가 닫혀 제한된 커버 가스 공급 하에서 산화를 위한 밀폐된 환경이 생성되었습니다. 그런 다음 산화 전지를 5분 간격으로 5분에서 30분 동안 700 ± 10°C에서 유지했습니다. 각 유지 시간이 끝날 때 세포를 물로 켄칭했습니다. 실온으로 냉각한 후 산화된 샘플을 절단하고 연마한 다음 SEM으로 검사했습니다.

    3 . 결과

    3.1 . SF 6 /air 에서 형성된 엔트레인먼트 결함의 구조 및 구성

    0.5 % SF의 커버 가스 하에서 AZ91 주물에 형성된 유입 결함의 구조 및 조성 6 / 공기는 SEM 및 EDS에 의해 관찰되었다. 결과는 그림 3에 스케치된 엔트레인먼트 결함의 두 가지 유형이 있음을 나타냅니다 . (1) 산화막이 전통적인 단층 구조를 갖는 유형 A 결함 및 (2) 산화막이 2개 층을 갖는 유형 B 결함. 이러한 결함의 세부 사항은 다음에 소개되었습니다. 여기에서 비말동반 결함은 생물막 또는 이중 산화막으로도 알려져 있기 때문에 B형 결함의 산화막은 본 연구에서 “다층 산화막” 또는 “다층 구조”로 언급되었습니다. “이중 산화막 결함의 이중층 산화막”과 같은 혼란스러운 설명을 피하기 위해.

    그림 3

    그림 4 (ab)는 약 0.4μm 두께의 조밀한 단일층 산화막을 갖는 Type A 결함을 보여줍니다. 이 필름에서 산소, 불소, 마그네슘 및 알루미늄이 검출되었습니다( 그림 4c). 산화막은 마그네슘과 알루미늄의 산화물과 불화물의 혼합물로 추측됩니다. 불소의 검출은 동반된 커버 가스가 이 결함의 형성에 포함되어 있음을 보여주었습니다. 즉, Fig. 4 (a)에 나타난 기공 은 수축결함이나 수소기공도가 아니라 연행결함이었다. 알루미늄의 검출은 Xiong과 Wang의 이전 연구 [47 , 48] 와 다르며 , SF 6으로 보호된 AZ91 용융물의 표면 필름에 알루미늄이 포함되어 있지 않음을 보여주었습니다.커버 가스. 유황은 원소 맵에서 명확하게 인식할 수 없었지만 해당 ESD 스펙트럼에서 S-피크가 있었습니다.

    그림 4

    도 5 (ab)는 다층 산화막을 갖는 Type B 엔트레인먼트 결함을 나타낸다. 산화막의 조밀한 외부 층은 불소와 산소가 풍부하지만( 그림 5c) 상대적으로 다공성인 내부 층은 산소만 풍부하고(즉, 불소가 부족) 부분적으로 함께 성장하여 샌드위치 모양을 형성합니다. 구조. 따라서 외층은 불화물과 산화물의 혼합물이며 내층은 주로 산화물로 추정된다. 황은 EDX 스펙트럼에서만 인식될 수 있었고 요소 맵에서 명확하게 식별할 수 없었습니다. 이는 커버 가스의 작은 S 함량(즉, SF 6 의 0.5% 부피 함량 때문일 수 있음)커버 가스). 이 산화막에서는 이 산화막의 외층에 알루미늄이 포함되어 있지만 내층에서는 명확하게 검출할 수 없었다. 또한 Al의 분포가 고르지 않은 것으로 보입니다. 결함의 우측에는 필름에 알루미늄이 존재하지만 그 농도는 매트릭스보다 높은 것으로 식별할 수 없음을 알 수 있다. 그러나 결함의 왼쪽에는 알루미늄 농도가 훨씬 높은 작은 영역이 있습니다. 이러한 알루미늄의 불균일한 분포는 다른 결함(아래 참조)에서도 관찰되었으며, 이는 필름 내부 또는 아래에 일부 산화물 입자가 형성된 결과입니다.

    그림 5

    무화과 도 4 및 5 는 SF 6 /air 의 커버 가스 하에 주조된 AZ91 합금 샘플에서 형성된 연행 결함의 횡단면 관찰을 나타낸다 . 2차원 단면에서 관찰된 수치만으로 연행 결함을 특성화하는 것만으로는 충분하지 않습니다. 더 많은 이해를 돕기 위해 테스트 바의 파단면을 관찰하여 엔트레인먼트 결함(즉, 산화막)의 표면을 더 연구했습니다.

    Fig. 6 (a)는 SF 6 /air 에서 생산된 AZ91 합금 인장시험봉의 파단면을 보여준다 . 파단면의 양쪽에서 대칭적인 어두운 영역을 볼 수 있습니다. 그림 6 (b)는 어두운 영역과 밝은 영역 사이의 경계를 보여줍니다. 밝은 영역은 들쭉날쭉하고 부서진 특징으로 구성되어 있는 반면, 어두운 영역의 표면은 비교적 매끄럽고 평평했습니다. 또한 EDS 결과( Fig. 6 c-d 및 Table 2) 불소, 산소, 황 및 질소는 어두운 영역에서만 검출되었으며, 이는 어두운 영역이 용융물에 동반된 표면 보호 필름임을 나타냅니다. 따라서 어두운 영역은 대칭적인 특성을 고려할 때 연행 결함이라고 제안할 수 있습니다. Al-합금 주조물의 파단면에서 유사한 결함이 이전에 보고되었습니다 [7] . 질화물은 테스트 바 파단면의 산화막에서만 발견되었지만 그림 1과 그림 4에 표시된 단면 샘플에서는 검출되지 않았습니다 . 4 및 5 . 근본적인 이유는 이러한 샘플에 포함된 질화물이 샘플 연마 과정에서 가수분해되었을 수 있기 때문입니다 [54] .

    그림 6

    표 2 . EDS 결과(wt.%)는 그림 6에 표시된 영역에 해당합니다 (커버 가스: SF 6 /공기).

    씨영형마그네슘NS알아연NSNS
    그림 6 (b)의 어두운 영역3.481.3279.130.4713.630.570.080.73
    그림 6 (b)의 밝은 영역3.58–84.48–11.250.68––

    도 1 및 도 2에 도시된 결함의 단면 관찰과 함께 . 도 4 및 도 5 를 참조하면, 인장 시험봉에 포함된 연행 결함의 구조를 도 6 (e) 와 같이 스케치하였다 . 결함에는 산화막으로 둘러싸인 동반된 가스가 포함되어 있어 테스트 바 내부에 보이드 섹션이 생성되었습니다. 파괴 과정에서 결함에 인장력이 가해지면 균열이 가장 약한 경로를 따라 전파되기 때문에 보이드 섹션에서 균열이 시작되어 연행 결함을 따라 전파됩니다 [55] . 따라서 최종적으로 시험봉이 파단되었을 때 Fig. 6 (a) 와 같이 시험봉의 양 파단면에 연행결함의 산화피막이 나타났다 .

    3.2 . SF 6 /CO 2 에 형성된 연행 결함의 구조 및 조성

    SF 6 /air 에서 형성된 엔트레인먼트 결함과 유사하게, 0.5% SF 6 /CO 2 의 커버 가스 아래에서 형성된 결함 도 두 가지 유형의 산화막(즉, 단층 및 다층 유형)을 가졌다. 도 7 (a)는 다층 산화막을 포함하는 엔트레인먼트 결함의 예를 도시한다. 결함에 대한 확대 관찰( 그림 7b )은 산화막의 내부 층이 함께 성장하여 SF 6 /air 의 분위기에서 형성된 결함과 유사한 샌드위치 같은 구조를 나타냄을 보여줍니다 ( 그림 7b). 5 나 ). EDS 스펙트럼( 그림 7c) 이 샌드위치형 구조의 접합부(내층)는 주로 산화마그네슘을 함유하고 있음을 보여주었다. 이 EDS 스펙트럼에서는 불소, 황, 알루미늄의 피크가 확인되었으나 그 양은 상대적으로 적었다. 대조적으로, 산화막의 외부 층은 조밀하고 불화물과 산화물의 혼합물로 구성되어 있습니다( 그림 7d-e).

    그림 7

    Fig. 8 (a)는 0.5%SF 6 /CO 2 분위기에서 제작된 AZ91 합금 인장시험봉의 파단면의 연행결함을 보여준다 . 상응하는 EDS 결과(표 3)는 산화막이 불화물과 산화물을 함유함을 보여주었다. 황과 질소는 검출되지 않았습니다. 게다가, 확대 관찰( 도 8b)은 산화막 표면에 반점을 나타내었다. 반점의 직경은 수백 나노미터에서 수 마이크론 미터까지 다양했습니다.

    그림 8

    산화막의 구조와 조성을 보다 명확하게 나타내기 위해 테스트 바 파단면의 산화막 단면을 FIB 기법을 사용하여 현장에서 노출시켰다( 그림 9 ). 도 9a에 도시된 바와 같이 , 백금 코팅층과 Mg-Al 합금 기재 사이에 연속적인 산화피막이 발견되었다. 그림 9 (bc)는 다층 구조( 그림 9c 에서 빨간색 상자로 표시)를 나타내는 산화막에 대한 확대 관찰을 보여줍니다 . 바닥층은 불소와 산소가 풍부하고 불소와 산화물의 혼합물이어야 합니다 . 5 와 7, 유일한 산소가 풍부한 최상층은 도 1 및 도 2에 도시 된 “내층”과 유사하였다 . 5 및 7 .

    그림 9

    연속 필름을 제외하고 도 9 에 도시된 바와 같이 연속 필름 내부 또는 하부에서도 일부 개별 입자가 관찰되었다 . 그림 9( b) 의 산화막 좌측에서 Al이 풍부한 입자가 검출되었으며, 마그네슘과 산소 원소도 풍부하게 함유하고 있어 스피넬 Mg 2 AlO 4 로 추측할 수 있다 . 이러한 Mg 2 AlO 4 입자의 존재는 Fig. 5 와 같이 관찰된 필름의 작은 영역에 높은 알루미늄 농도와 알루미늄의 불균일한 분포의 원인이 된다 .(씨). 여기서 강조되어야 할 것은 연속 산화막의 바닥층의 다른 부분이 이 Al이 풍부한 입자보다 적은 양의 알루미늄을 함유하고 있지만, 그림 9c는 이 바닥층의 알루미늄 양이 여전히 무시할 수 없는 수준임을 나타냅니다 . , 특히 필름의 외층과 비교할 때. 도 9b에 도시된 산화막의 우측 아래에서 입자가 검출되어 Mg와 O가 풍부하여 MgO인 것으로 추측되었다. Wang의 결과에 따르면 [56], Mg 용융물과 Mg 증기의 산화에 의해 Mg 용융물의 표면에 많은 이산 MgO 입자가 형성될 수 있다. 우리의 현재 연구에서 관찰된 MgO 입자는 같은 이유로 인해 형성될 수 있습니다. 실험 조건의 차이로 인해 더 적은 Mg 용융물이 기화되거나 O2와 반응할 수 있으므로 우리 작업에서 형성되는 MgO 입자는 소수에 불과합니다. 또한 필름에서 풍부한 탄소가 발견되어 CO 2 가 용융물과 반응하여 탄소 또는 탄화물을 형성할 수 있음을 보여줍니다 . 이 탄소 농도는 표 3에 나타낸 산화막의 상대적으로 높은 탄소 함량 (즉, 어두운 영역) 과 일치하였다 . 산화막 옆 영역.

    표 3 . 도 8에 도시된 영역에 상응하는 EDS 결과(wt.%) (커버 가스: SF 6 / CO 2 ).

    씨영형마그네슘NS알아연NSNS
    그림 8 (a)의 어두운 영역7.253.6469.823.827.030.86––
    그림 8 (a)의 밝은 영역2.100.4482.83–13.261.36––

    테스트 바 파단면( 도 9 ) 에서 산화막의 이 단면 관찰은 도 6 (e)에 도시된 엔트레인먼트 결함의 개략도를 추가로 확인했다 . SF 6 /CO 2 와 SF 6 /air 의 서로 다른 분위기에서 형성된 엔트레인먼트 결함 은 유사한 구조를 가졌지만 그 조성은 달랐다.

    3.3 . 산화 전지에서 산화막의 진화

    섹션 3.1 및 3.2 의 결과 는 SF 6 /air 및 SF 6 /CO 2 의 커버 가스 아래에서 AZ91 주조에서 형성된 연행 결함의 구조 및 구성을 보여줍니다 . 산화 반응의 다른 단계는 연행 결함의 다른 구조와 조성으로 이어질 수 있습니다. Campbell은 동반된 가스가 주변 용융물과 반응할 수 있다고 추측했지만 Mg 합금 용융물과 포획된 커버 가스 사이에 반응이 발생했다는 보고는 거의 없습니다. 이전 연구자들은 일반적으로 개방된 환경에서 Mg 합금 용융물과 커버 가스 사이의 반응에 초점을 맞췄습니다 [38 , 39 , [46] , [47], [48] , [49] , [50] , [51] , [52] , 이는 용융물에 갇힌 커버 가스의 상황과 다릅니다. AZ91 합금에서 엔트레인먼트 결함의 형성을 더 이해하기 위해 엔트레인먼트 결함의 산화막의 진화 과정을 산화 셀을 사용하여 추가로 연구했습니다.

    .도 10 (a 및 d) 0.5 % 방송 SF 보호 산화 셀에서 5 분 동안 유지 된 표면 막 (6) / 공기. 불화물과 산화물(MgF 2 와 MgO) 로 이루어진 단 하나의 층이 있었습니다 . 이 표면 필름에서. 황은 EDS 스펙트럼에서 검출되었지만 그 양이 너무 적어 원소 맵에서 인식되지 않았습니다. 이 산화막의 구조 및 조성은 도 4 에 나타낸 엔트레인먼트 결함의 단층막과 유사하였다 .

    그림 10

    10분의 유지 시간 후, 얇은 (O,S)가 풍부한 상부층(약 700nm)이 예비 F-농축 필름에 나타나 그림 10 (b 및 e) 에서와 같이 다층 구조를 형성했습니다 . ). (O, S)가 풍부한 최상층의 두께는 유지 시간이 증가함에 따라 증가했습니다. Fig. 10 (c, f) 에서 보는 바와 같이 30분간 유지한 산화막도 다층구조를 가지고 있으나 (O,S)가 풍부한 최상층(약 2.5μm)의 두께가 10분 산화막의 그것. 도 10 (bc) 에 도시 된 다층 산화막 은 도 5에 도시된 샌드위치형 결함의 막과 유사한 외관을 나타냈다 .

    도 10에 도시된 산화막의 상이한 구조는 커버 가스의 불화물이 AZ91 합금 용융물과의 반응으로 인해 우선적으로 소모될 것임을 나타내었다. 불화물이 고갈된 후, 잔류 커버 가스는 액체 AZ91 합금과 추가로 반응하여 산화막에 상부 (O, S)가 풍부한 층을 형성했습니다. 따라서 도 1 및 도 3에 도시된 연행 결함의 상이한 구조 및 조성 . 4 와 5 는 용융물과 갇힌 커버 가스 사이의 진행 중인 산화 반응 때문일 수 있습니다.

    이 다층 구조는 Mg 합금 용융물에 형성된 보호 표면 필름에 관한 이전 간행물 [38 , [46] , [47] , [48] , [49] , [50] , [51] 에서 보고되지 않았습니다 . . 이는 이전 연구원들이 무제한의 커버 가스로 실험을 수행했기 때문에 커버 가스의 불화물이 고갈되지 않는 상황을 만들었기 때문일 수 있습니다. 따라서 엔트레인먼트 결함의 산화피막은 도 10에 도시된 산화피막과 유사한 거동특성을 가지나 [38 ,[46] , [47] , [48] , [49] , [50] , [51] .

    SF 유지 산화막와 마찬가지로 6 / 공기, SF에 형성된 산화물 막 (6) / CO 2는 또한 세포 산화 다른 유지 시간과 다른 구조를 가지고 있었다. .도 11 (a)는 AZ91 개최 산화막, 0.5 %의 커버 가스 하에서 SF 표면 용융 도시 6 / CO 2, 5 분. 이 필름은 MgF 2 로 이루어진 단층 구조를 가졌다 . 이 영화에서는 MgO의 존재를 확인할 수 없었다. 30분의 유지 시간 후, 필름은 다층 구조를 가졌다; 내부 층은 조밀하고 균일한 외관을 가지며 MgF 2 로 구성 되고 외부 층은 MgF 2 혼합물및 MgO. 0.5%SF 6 /air 에서 형성된 표면막과 다른 이 막에서는 황이 검출되지 않았다 . 따라서, 0.5%SF 6 /CO 2 의 커버 가스 내의 불화물 도 막 성장 과정의 초기 단계에서 우선적으로 소모되었다. SF 6 /air 에서 형성된 막과 비교하여 SF 6 /CO 2 에서 형성된 막에서 MgO 는 나중에 나타났고 황화물은 30분 이내에 나타나지 않았다. 이는 SF 6 /air 에서 필름의 형성과 진화 가 SF 6 /CO 2 보다 빠르다 는 것을 의미할 수 있습니다 . CO 2 후속적으로 용융물과 반응하여 MgO를 형성하는 반면, 황 함유 화합물은 커버 가스에 축적되어 반응하여 매우 늦은 단계에서 황화물을 형성할 수 있습니다(산화 셀에서 30분 후).

    그림 11

    4 . 논의

    4.1 . SF 6 /air 에서 형성된 연행 결함의 진화

    Outokumpu HSC Chemistry for Windows( http://www.hsc-chemistry.net/ )의 HSC 소프트웨어를 사용하여 갇힌 기체와 액체 AZ91 합금 사이에서 발생할 수 있는 반응을 탐색하는 데 필요한 열역학 계산을 수행했습니다. 계산에 대한 솔루션은 소량의 커버 가스(즉, 갇힌 기포 내의 양)와 AZ91 합금 용융물 사이의 반응 과정에서 어떤 생성물이 가장 형성될 가능성이 있는지 제안합니다.

    실험에서 압력은 1기압으로, 온도는 700°C로 설정했습니다. 커버 가스의 사용량은 7 × 10으로 가정 하였다 -7  약 0.57 cm의 양으로 kg 3 (3.14 × 10 -6  0.5 % SF위한 kmol) 6 / 공기, 0.35 cm (3) (3.12 × 10 – 8  kmol) 0.5%SF 6 /CO 2 . 포획된 가스와 접촉하는 AZ91 합금 용융물의 양은 모든 반응을 완료하기에 충분한 것으로 가정되었습니다. SF 6 의 분해 생성물 은 SF 5 , SF 4 , SF 3 , SF 2 , F 2 , S(g), S 2(g) 및 F(g) [57] , [58] , [59] , [60] .

    그림 12 는 AZ91 합금과 0.5%SF 6 /air 사이의 반응에 대한 열역학적 계산의 평형 다이어그램을 보여줍니다 . 다이어그램에서 10 -15  kmol 미만의 반응물 및 생성물은 표시되지 않았습니다. 이는 존재 하는 SF 6 의 양 (≈ 1.57 × 10 -10  kmol) 보다 5배 적 으므로 영향을 미치지 않습니다. 실제적인 방법으로 과정을 관찰했습니다.

    그림 12

    이 반응 과정은 3단계로 나눌 수 있다.

    1단계 : 불화물의 형성. AZ91 용융물은 SF 6 및 그 분해 생성물과 우선적으로 반응하여 MgF 2 , AlF 3 및 ZnF 2 를 생성 합니다. 그러나 ZnF 2 의 양 이 너무 적어서 실제적으로 검출되지  않았을 수 있습니다(  MgF 2 의 3 × 10 -10 kmol에 비해 ZnF 2 1.25 × 10 -12 kmol ). 섹션 3.1 – 3.3에 표시된 모든 산화막 . 한편, 잔류 가스에 황이 SO 2 로 축적되었다 .

    2단계 : 산화물의 형성. 액체 AZ91 합금이 포획된 가스에서 사용 가능한 모든 불화물을 고갈시킨 후, Mg와의 반응으로 인해 AlF 3 및 ZnF 2 의 양이 빠르게 감소했습니다. O 2 (g) 및 SO 2 는 AZ91 용융물과 반응하여 MgO, Al 2 O 3 , MgAl 2 O 4 , ZnO, ZnSO 4 및 MgSO 4 를 형성 합니다. 그러나 ZnO 및 ZnSO 4 의 양은 EDS에 의해 실제로 발견되기에는 너무 적었을 것입니다(예: 9.5 × 10 -12  kmol의 ZnO, 1.38 × 10 -14  kmol의 ZnSO 4 , 대조적으로 4.68 × 10−10  kmol의 MgF 2 , X 축의 AZ91 양 이 2.5 × 10 -9  kmol일 때). 실험 사례에서 커버 가스의 F 농도는 매우 낮고 전체 농도 f O는 훨씬 높습니다. 따라서 1단계와 2단계, 즉 불화물과 산화물의 형성은 반응 초기에 동시에 일어나 그림 1과 2와 같이 불화물과 산화물의 가수층 혼합물이 형성될 수 있다 . 4 및 10 (a). 내부 층은 산화물로 구성되어 있지만 불화물은 커버 가스에서 F 원소가 완전히 고갈된 후에 형성될 수 있습니다.

    단계 1-2는 도 10 에 도시 된 다층 구조의 형성 과정을 이론적으로 검증하였다 .

    산화막 내의 MgAl 2 O 4 및 Al 2 O 3 의 양은 도 4에 도시된 산화막과 일치하는 검출하기에 충분한 양이었다 . 그러나, 도 10 에 도시된 바와 같이, 산화셀에서 성장된 산화막에서는 알루미늄의 존재를 인식할 수 없었다 . 이러한 Al의 부재는 표면 필름과 AZ91 합금 용융물 사이의 다음 반응으로 인한 것일 수 있습니다.(1)

    Al 2 O 3  + 3Mg + = 3MgO + 2Al, △G(700°C) = -119.82 kJ/mol(2)

    Mg + MgAl 2 O 4  = MgO + Al, △G(700°C) = -106.34 kJ/mol이는 반응물이 서로 완전히 접촉한다는 가정 하에 열역학적 계산이 수행되었기 때문에 HSC 소프트웨어로 시뮬레이션할 수 없었습니다. 그러나 실제 공정에서 AZ91 용융물과 커버 가스는 보호 표면 필름의 존재로 인해 서로 완전히 접촉할 수 없습니다.

    3단계 : 황화물과 질화물의 형성. 30분의 유지 시간 후, 산화 셀의 기상 불화물 및 산화물이 고갈되어 잔류 가스와 용융 반응을 허용하여 초기 F-농축 또는 (F, O )이 풍부한 표면 필름, 따라서 그림 10 (b 및 c)에 표시된 관찰된 다층 구조를 생성합니다 . 게다가, 질소는 모든 반응이 완료될 때까지 AZ91 용융물과 반응했습니다. 도 6 에 도시 된 산화막 은 질화물 함량으로 인해 이 반응 단계에 해당할 수 있다. 그러나, 그 결과는 도 1 및 도 5에 도시 된 연마된 샘플에서 질화물이 검출되지 않음을 보여준다. 4 와 5, 그러나 테스트 바 파단면에서만 발견됩니다. 질화물은 다음과 같이 샘플 준비 과정에서 가수분해될 수 있습니다 [54] .(삼)

    Mg 3 N 2  + 6H 2 O = 3Mg(OH) 2  + 2NH 3 ↑(4)

    AlN+ 3H 2 O = Al(OH) 3  + NH 3 ↑

    또한 Schmidt et al. [61] 은 Mg 3 N 2 와 AlN이 반응하여 3원 질화물(Mg 3 Al n N n+2, n=1, 2, 3…) 을 형성할 수 있음을 발견했습니다 . HSC 소프트웨어에는 삼원 질화물 데이터베이스가 포함되어 있지 않아 계산에 추가할 수 없습니다. 이 단계의 산화막은 또한 삼원 질화물을 포함할 수 있습니다.

    4.2 . SF 6 /CO 2 에서 형성된 연행 결함의 진화

    도 13 은 AZ91 합금과 0.5%SF 6 /CO 2 사이의 열역학적 계산 결과를 보여준다 . 이 반응 과정도 세 단계로 나눌 수 있습니다.

    그림 13

    1단계 : 불화물의 형성. SF 6 및 그 분해 생성물은 AZ91 용융물에 의해 소비되어 MgF 2 , AlF 3 및 ZnF 2 를 형성했습니다 . 0.5% SF 6 /air 에서 AZ91의 반응에서와 같이 ZnF 2 의 양 이 너무 작아서 실제적으로 감지되지  않았습니다( 2.67 x 10 -10  kmol의 MgF 2 에 비해 ZnF 2 1.51 x 10 -13 kmol ). S와 같은 잔류 가스 트랩에 축적 유황 2 (g) 및 (S)의 일부분 (2) (g)가 CO와 반응하여 2 SO 형성하는 2및 CO. 이 반응 단계의 생성물은 도 11 (a)에 도시된 필름과 일치하며 , 이는 불화물만을 함유하는 단일 층 구조를 갖는다.

    2단계 : 산화물의 형성. ALF 3 및 ZnF 2 MgF로 형성 용융 AZ91 마그네슘의 반응 2 , Al 및 Zn으로한다. SO 2 는 소모되기 시작하여 표면 필름에 산화물을 생성 하고 커버 가스에 S 2 (g)를 생성했습니다. 한편, CO 2 는 AZ91 용융물과 직접 반응하여 CO, MgO, ZnO 및 Al 2 O 3 를 형성 합니다. 도 1에 도시 된 산화막 . 9 및 11 (b)는 산소가 풍부한 층과 다층 구조로 인해 이 반응 단계에 해당할 수 있습니다.

    커버 가스의 CO는 AZ91 용융물과 추가로 반응하여 C를 생성할 수 있습니다. 이 탄소는 온도가 감소할 때(응고 기간 동안) Mg와 추가로 반응하여 Mg 탄화물을 형성할 수 있습니다 [62] . 이것은 도 4에 도시된 산화막의 탄소 함량이 높은 이유일 수 있다 . 8 – 9 . Liang et al. [39] 또한 SO 2 /CO 2 로 보호된 AZ91 합금 표면 필름에서 탄소 검출을 보고했습니다 . 생성된 Al 2 O 3 는 MgO와 더 결합하여 MgAl 2 O 4 [63]를 형성할 수 있습니다 . 섹션 4.1 에서 논의된 바와 같이, 알루미나 및 스피넬은 도 11 에 도시된 바와 같이 표면 필름에 알루미늄 부재를 야기하는 Mg와 반응할 수 있다 .

    3단계 : 황화물의 형성. AZ91은 용융물 S 소비하기 시작 2 인 ZnS와 MGS 형성 갇힌 잔류 가스 (g)를. 이러한 반응은 반응 과정의 마지막 단계까지 일어나지 않았으며, 이는 Fig. 7 (c)에 나타난 결함의 S-함량 이 적은 이유일 수 있다 .

    요약하면, 열역학적 계산은 AZ91 용융물이 커버 가스와 반응하여 먼저 불화물을 형성한 다음 마지막에 산화물과 황화물을 형성할 것임을 나타냅니다. 다른 반응 단계에서 산화막은 다른 구조와 조성을 가질 것입니다.

    4.3 . 운반 가스가 동반 가스 소비 및 AZ91 주물의 재현성에 미치는 영향

    SF 6 /air 및 SF 6 /CO 2 에서 형성된 연행 결함의 진화 과정은 4.1절 과 4.2 절 에서 제안되었습니다 . 이론적인 계산은 실제 샘플에서 발견되는 해당 산화막과 관련하여 검증되었습니다. 연행 결함 내의 대기는 Al-합금 시스템과 다른 시나리오에서 액체 Mg-합금과의 반응으로 인해 효율적으로 소모될 수 있습니다(즉, 연행된 기포의 질소가 Al-합금 용융물과 효율적으로 반응하지 않을 것입니다 [64 , 65] 그러나 일반적으로 “질소 연소”라고 하는 액체 Mg 합금에서 질소가 더 쉽게 소모될 것입니다 [66] ).

    동반된 가스와 주변 액체 Mg-합금 사이의 반응은 동반된 가스를 산화막 내에서 고체 화합물(예: MgO)로 전환하여 동반 결함의 공극 부피를 감소시켜 결함(예: 공기의 동반된 가스가 주변의 액체 Mg 합금에 의해 고갈되면 용융 온도가 700 °C이고 액체 Mg 합금의 깊이가 10 cm라고 가정할 때 최종 고체 제품의 총 부피는 0.044가 됩니다. 갇힌 공기가 취한 초기 부피의 %).

    연행 결함의 보이드 부피 감소와 해당 주조 특성 사이의 관계는 알루미늄 합금 주조에서 널리 연구되었습니다. Nyahumwa와 Campbell [16] 은 HIP(Hot Isostatic Pressing) 공정이 Al-합금 주물의 연행 결함이 붕괴되고 산화물 표면이 접촉하게 되었다고 보고했습니다. 주물의 피로 수명은 HIP 이후 개선되었습니다. Nyahumwa와 Campbell [16] 도 서로 접촉하고 있는 이중 산화막의 잠재적인 결합을 제안했지만 이를 뒷받침하는 직접적인 증거는 없었습니다. 이 결합 현상은 Aryafar et.al에 의해 추가로 조사되었습니다. [8], 그는 강철 튜브에서 산화물 스킨이 있는 두 개의 Al-합금 막대를 다시 녹인 다음 응고된 샘플에 대해 인장 강도 테스트를 수행했습니다. 그들은 Al-합금 봉의 산화물 스킨이 서로 강하게 결합되어 용융 유지 시간이 연장됨에 따라 더욱 강해짐을 발견했으며, 이는 이중 산화막 내 동반된 가스의 소비로 인한 잠재적인 “치유” 현상을 나타냅니다. 구조. 또한 Raidszadeh와 Griffiths [9 , 19] 는 연행 가스가 반응하는 데 더 긴 시간을 갖도록 함으로써 응고 전 용융 유지 시간을 연장함으로써 Al-합금 주물의 재현성에 대한 연행 결함의 부정적인 영향을 성공적으로 줄였습니다. 주변이 녹습니다.

    앞서 언급한 연구를 고려할 때, Mg 합금 주물에서 혼입 가스의 소비는 다음 두 가지 방식으로 혼입 결함의 부정적인 영향을 감소시킬 수 있습니다.

    (1) 이중 산화막의 결합 현상 . 도 5 및 도 7 에 도시 된 샌드위치형 구조 는 이중 산화막 구조의 잠재적인 결합을 나타내었다. 그러나 산화막의 결합으로 인한 강도 증가를 정량화하기 위해서는 더 많은 증거가 필요합니다.

    (2) 연행 결함의 보이드 체적 감소 . 주조품의 품질에 대한 보이드 부피 감소의 긍정적인 효과는 HIP 프로세스 [67]에 의해 널리 입증되었습니다 . 섹션 4.1 – 4.2 에서 논의된 진화 과정과 같이 , 동반된 가스와 주변 AZ91 합금 용융물 사이의 지속적인 반응으로 인해 동반 결함의 산화막이 함께 성장할 수 있습니다. 최종 고체 생성물의 부피는 동반된 기체에 비해 상당히 작았다(즉, 이전에 언급된 바와 같이 0.044%).

    따라서, 혼입 가스의 소모율(즉, 산화막의 성장 속도)은 AZ91 합금 주물의 품질을 향상시키는 중요한 매개변수가 될 수 있습니다. 이에 따라 산화 셀의 산화막 성장 속도를 추가로 조사했습니다.

    도 14 는 상이한 커버 가스(즉, 0.5%SF 6 /air 및 0.5%SF 6 /CO 2 ) 에서의 표면 필름 성장 속도의 비교를 보여준다 . 필름 두께 측정을 위해 각 샘플의 15개의 임의 지점을 선택했습니다. 95% 신뢰구간(95%CI)은 막두께의 변화가 가우시안 분포를 따른다는 가정하에 계산하였다. 0.5%SF 6 /air 에서 형성된 모든 표면막이 0.5%SF 6 /CO 2 에서 형성된 것보다 빠르게 성장함을 알 수 있다 . 다른 성장률은 0.5%SF 6 /air 의 연행 가스 소비율 이 0.5%SF 6 /CO 2 보다 더 높음 을 시사했습니다., 이는 동반된 가스의 소비에 더 유리했습니다.

    그림 14

    산화 셀에서 액체 AZ91 합금과 커버 가스의 접촉 면적(즉, 도가니의 크기)은 많은 양의 용융물과 가스를 고려할 때 상대적으로 작았다는 점에 유의해야 합니다. 결과적으로, 산화 셀 내에서 산화막 성장을 위한 유지 시간은 비교적 길었다(즉, 5-30분). 하지만, 실제 주조에 함유 된 혼입 결함은 (상대적으로 매우 적은, 즉, 수 미크론의 크기에 도시 된 바와 같이 ,도 3. – 6 및 [7]), 동반된 가스는 주변 용융물로 완전히 둘러싸여 상대적으로 큰 접촉 영역을 생성합니다. 따라서 커버 가스와 AZ91 합금 용융물의 반응 시간은 비교적 짧을 수 있습니다. 또한 실제 Mg 합금 모래 주조의 응고 시간은 몇 분일 수 있습니다(예: Guo [68] 은 직경 60mm의 Mg 합금 모래 주조가 응고되는 데 4분이 필요하다고 보고했습니다). 따라서 Mg-합금 용융주조 과정에서 포획된 동반된 가스는 특히 응고 시간이 긴 모래 주물 및 대형 주물의 경우 주변 용융물에 의해 쉽게 소모될 것으로 예상할 수 있습니다.

    따라서, 동반 가스의 다른 소비율과 관련된 다른 커버 가스(0.5%SF 6 /air 및 0.5%SF 6 /CO 2 )가 최종 주물의 재현성에 영향을 미칠 수 있습니다. 이 가정을 검증하기 위해 0.5%SF 6 /air 및 0.5%SF 6 /CO 2 에서 생산된 AZ91 주물 을 기계적 평가를 위해 테스트 막대로 가공했습니다. Weibull 분석은 선형 최소 자승(LLS) 방법과 비선형 최소 자승(비 LLS) 방법을 모두 사용하여 수행되었습니다 [69] .

    그림 15 (ab)는 LLS 방법으로 얻은 UTS 및 AZ91 합금 주물의 연신율의 전통적인 2-p 선형 Weibull 플롯을 보여줍니다. 사용된 추정기는 P= (i-0.5)/N이며, 이는 모든 인기 있는 추정기 중 가장 낮은 편향을 유발하는 것으로 제안되었습니다 [69 , 70] . SF 6 /air 에서 생산된 주물 은 UTS Weibull 계수가 16.9이고 연신율 Weibull 계수가 5.0입니다. 대조적으로, SF 6 /CO 2 에서 생산된 주물의 UTS 및 연신 Weibull 계수는 각각 7.7과 2.7로, SF 6 /CO 2 에 의해 보호된 주물의 재현성이 SF 6 /air 에서 생산된 것보다 훨씬 낮음을 시사합니다. .

    그림 15

    또한 저자의 이전 출판물 [69] 은 선형화된 Weibull 플롯의 단점을 보여주었으며, 이는 Weibull 추정 의 더 높은 편향과 잘못된 R 2 중단을 유발할 수 있습니다 . 따라서 그림 15 (cd) 와 같이 Non-LLS Weibull 추정이 수행되었습니다 . SF 6 /공기주조물 의 UTS Weibull 계수 는 20.8인 반면, SF 6 /CO 2 하에서 생산된 주조물의 UTS Weibull 계수는 11.4로 낮아 재현성에서 분명한 차이를 보였다. 또한 SF 6 /air elongation(El%) 데이터 세트는 SF 6 /CO 2 의 elongation 데이터 세트보다 더 높은 Weibull 계수(모양 = 5.8)를 가졌습니다.(모양 = 3.1). 따라서 LLS 및 Non-LLS 추정 모두 SF 6 /공기 주조가 SF 6 /CO 2 주조 보다 더 높은 재현성을 갖는다고 제안했습니다 . CO 2 대신 공기를 사용 하면 혼입된 가스의 더 빠른 소비에 기여하여 결함 내의 공극 부피를 줄일 수 있다는 방법을 지원합니다 . 따라서 0.5%SF 6 /CO 2 대신 0.5%SF 6 /air를 사용 하면(동반된 가스의 소비율이 증가함) AZ91 주물의 재현성이 향상되었습니다.

    그러나 모든 Mg 합금 주조 공장이 현재 작업에서 사용되는 주조 공정을 따랐던 것은 아니라는 점에 유의해야 합니다. Mg의 합금 용탕 본 작업은 탈기에 따라서, 동반 가스의 소비에 수소의 영향을 감소 (즉, 수소 잠재적 동반 가스의 고갈 억제, 동반 된 기체로 확산 될 수있다 [7 , 71 , 72] ). 대조적으로, 마그네슘 합금 주조 공장에서는 마그네슘을 주조할 때 ‘가스 문제’가 없고 따라서 인장 특성에 큰 변화가 없다고 널리 믿어지기 때문에 마그네슘 합금 용융물은 일반적으로 탈기되지 않습니다 [73] . 연구에 따르면 Mg 합금 주물의 기계적 특성에 대한 수소의 부정적인 영향 [41 ,42 , 73] , 탈기 공정은 마그네슘 합금 주조 공장에서 여전히 인기가 없습니다.

    또한 현재 작업에서 모래 주형 공동은 붓기 전에 SF 6 커버 가스 로 플러싱되었습니다 [22] . 그러나 모든 Mg 합금 주조 공장이 이러한 방식으로 금형 캐비티를 플러싱한 것은 아닙니다. 예를 들어, Stone Foundry Ltd(영국)는 커버 가스 플러싱 대신 유황 분말을 사용했습니다. 그들의 주물 내의 동반된 가스 는 보호 가스라기 보다는 SO 2 /공기일 수 있습니다 .

    따라서 본 연구의 결과는 CO 2 대신 공기를 사용 하는 것이 최종 주조의 재현성을 향상시키는 것으로 나타났지만 다른 산업용 Mg 합금 주조 공정과 관련하여 캐리어 가스의 영향을 확인하기 위해서는 여전히 추가 조사가 필요합니다.

    7 . 결론

    1.

    AZ91 합금에 형성된 연행 결함이 관찰되었습니다. 그들의 산화막은 단층과 다층의 두 가지 유형의 구조를 가지고 있습니다. 다층 산화막은 함께 성장하여 최종 주조에서 샌드위치 같은 구조를 형성할 수 있습니다.2.

    실험 결과와 이론적인 열역학적 계산은 모두 갇힌 가스의 불화물이 황을 소비하기 전에 고갈되었음을 보여주었습니다. 이중 산화막 결함의 3단계 진화 과정이 제안되었습니다. 산화막은 진화 단계에 따라 다양한 화합물 조합을 포함했습니다. SF 6 /air 에서 형성된 결함 은 SF 6 /CO 2 에서 형성된 것과 유사한 구조를 갖지만 산화막의 조성은 달랐다. 엔트레인먼트 결함의 산화막 형성 및 진화 과정은 이전에 보고된 Mg 합금 표면막(즉, MgF 2 이전에 형성된 MgO)의 것과 달랐다 .삼.

    산화막의 성장 속도는 SF하에 큰 것으로 입증되었다 (6) / SF보다 공기 6 / CO 2 손상 봉입 가스의 빠른 소비에 기여한다. AZ91 합금 주물의 재현성은 SF 6 /CO 2 대신 SF 6 /air를 사용할 때 향상되었습니다 .

    감사의 말

    저자는 EPSRC LiME 보조금 EP/H026177/1의 자금 지원 과 WD Griffiths 박사와 Adrian Carden(버밍엄 대학교)의 도움을 인정합니다. 주조 작업은 University of Birmingham에서 수행되었습니다.

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    Conflict resolution in the multi-stakeholder stepped spillway design under uncertainty by machine learning techniques

    기계 학습 기술에 의한 불확실성 하에서 다중 이해 관계자 계단형 배수로 설계의 충돌 해결

    Conflict resolution in the multi-stakeholder stepped spillway design under uncertainty by machine learning techniques

    Mehrdad GhorbaniMooseluaMohammad RezaNikoobParnian HashempourBakhtiaribNooshin BakhtiariRayanicAzizallahIzadyd
    aDepartment of Engineering Sciences, University of Agder, Norway
    bDepartment of Civil and Environmental Engineering, Shiraz University, Shiraz, Iran
    cSchool of Engineering, Department of Civil and Environmental Engineering, Shiraz University, Shiraz, IrandWater Research Center, Sultan Qaboos University, Muscat, Oman

    Abstract

    The optimal spillway design is of great significance since these structures can reduce erosion downstream of the dams. This study proposes a risk-based optimization framework for a stepped spillway to achieve an economical design scenario with the minimum loss in hydraulic performance. Accordingly, the stepped spillway was simulated in the FLOW-3D® model, and the validated model was repeatedly performed for various geometric states.

    The results were used to form a Multilayer Perceptron artificial neural network (MLP-ANN) surrogate model. Then, a risk-based optimization model was formed by coupling the MLP-ANN and NSGA-II. The concept of conditional value at risk (CVaR) was utilized to reduce the risk of the designed spillway malfunctions in high flood flow rates, while minimizing the construction cost and the loss in hydraulic performance.

    Lastly, given the conflicting objectives of stakeholders, the non-cooperative graph model for conflict resolution (GMCR) was applied to achieve a compromise on the Pareto optimal solutions. Applicability of the suggested approach in the Jarreh Dam, Iran, resulted in a practical design scenario, which simultaneously minimizes the loss in hydraulic performance and the project cost and satisfies the priorities of decision-makers.

    Keywords

    Stepped spillway, FLOW-3D® ,CVaR-based optimization model, GMCR-plus, NSGA-II

    최적의 배수로 설계는 이러한 구조가 댐 하류의 침식을 줄일 수 있기 때문에 매우 중요합니다. 본 연구에서는 유압 성능 손실을 최소화하면서 경제적인 설계 시나리오를 달성하기 위해 계단형 여수로에 대한 위험 기반 최적화 프레임워크를 제안합니다. 따라서 FLOW-3D® 모델에서 계단식 배수로를 시뮬레이션하고 다양한 기하학적 상태에 대해 검증된 모델을 반복적으로 수행했습니다.

    결과는 다층 퍼셉트론 인공 신경망(MLP-ANN) 대리 모델을 형성하는 데 사용되었습니다. 그런 다음 MLP-ANN과 NSGA-II를 결합하여 위험 기반 최적화 모델을 구성했습니다. 위험 조건부 값(CVaR)의 개념은 높은 홍수 유량에서 설계된 방수로 오작동의 위험을 줄이는 동시에 건설 비용과 수리 성능 손실을 최소화하기 위해 활용되었습니다.

    마지막으로 이해관계자의 상충되는 목표를 고려하여 파레토 최적해에 대한 절충안을 달성하기 위해 갈등 해결을 위한 비협조적 그래프 모델(GMCR)을 적용하였다. 이란 Jarreh 댐에서 제안된 접근 방식의 적용 가능성은 수력 성능 손실과 프로젝트 비용을 동시에 최소화하고 의사 결정자의 우선 순위를 만족시키는 실용적인 설계 시나리오로 귀결되었습니다.

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