본 논문은 FLOW-3D를 활용하여 서브머지드 아크 용접(Submerged Arc Welding, SAW) 공정의 열전달 및 유동 거동을 시뮬레이션함.
용접 토치 각도 및 전류 극성이 용융지(molten pool)의 유체 흐름과 용접 비드 형상에 미치는 영향을 분석함.
CCD 카메라와 Abel 역변환 기법을 이용하여 아크 열 플럭스, 아크 압력 및 전자기력을 모델링함.
수치 해석 결과와 실험 데이터를 비교하여 모델의 정확성을 검증함.
연구 방법
서브머지드 아크 용접 모델링
SAW는 플럭스(flux)층 아래에서 진행되는 용접 방식으로, 열전달과 유체 흐름을 복합적으로 포함함.
실험 데이터를 기반으로 3D 용접 모델을 구축하고, 유동 및 열 전달 분석을 수행함.
단일 전극(single electrode) SAW 공정에 대해 연구를 진행함.
FLOW-3D 시뮬레이션 설정
VOF(Volume of Fluid) 방법을 사용하여 용융지의 자유 표면 변화를 추적함.
난류 모델로 k−εk-\varepsilonk−ε 방정식을 적용하여 아크 플라즈마의 유동 해석을 수행함.
전류 극성(직류 DC 및 교류 AC)에 따른 아크 특성과 열 전달을 시뮬레이션함.
아크 및 열전달 모델링
CCD 카메라를 사용하여 아크 플라즈마의 형상을 촬영하고, Abel 역변환 기법을 이용하여 아크 열 플럭스를 모델링함.
플럭스 소비량을 분석하여 슬래그(slag) 열원의 효과를 고려함.
전자기력(EMF) 모델을 적용하여 용융지 내부의 유체 흐름을 예측함.
결과 검증 및 비교
실험 데이터를 기반으로 시뮬레이션 결과를 검증하고, 용접 비드 형상과 유동 패턴을 비교함.
실험적으로 측정된 용융지 온도 분포와 시뮬레이션 결과 간의 차이를 분석함.
전류 극성 및 토치 각도 변화가 용접 품질에 미치는 영향을 평가함.
주요 결과
용접 토치 각도와 용융지 유동
용접 토치 각도가 -20°인 경우, 용융지가 깊은 침투형 비드를 형성함.
반대로 +20°일 경우, 얕고 넓은 용접 비드가 형성됨.
용융지 내부 유동 패턴이 용접 품질에 직접적인 영향을 미침.
전류 극성에 따른 차이
직류(DC) 용접에서는 일정한 아크 열원이 유지되며, 용융지가 안정적인 흐름을 보임.
교류(AC) 용접에서는 아크 플라즈마가 주기적으로 변하며, 용융지의 유동이 보다 역동적임.
교류(AC)에서는 깊은 침투보다는 넓은 용접 비드가 형성되는 경향을 보임.
슬래그 열원의 영향
플럭스 소비량이 증가할수록 슬래그에서 추가적인 열전달이 발생하여 용접 품질에 영향을 미침.
플럭스 소비율이 증가하면 용접 속도에 따라 슬래그 열효율이 달라짐.
슬래그의 역할을 고려한 추가적인 모델링이 필요함.
시뮬레이션과 실험 비교
시뮬레이션 결과는 실험 데이터와 90% 이상의 상관성을 보이며, 높은 신뢰성을 입증함.
일부 고온 영역에서 실험 데이터와 시뮬레이션 값 간 3~5%의 오차가 존재함.
모델 개선을 위해 용융지 내의 난류 효과를 추가로 고려해야 함.
결론
FLOW-3D는 서브머지드 아크 용접 공정의 열전달 및 유동 해석에 효과적인 도구임.
토치 각도와 전류 극성이 용융지 유동 및 용접 비드 형상에 직접적인 영향을 미침.
슬래그 열전달을 고려한 시뮬레이션이 용접 품질 예측에 중요한 요소임.
향후 연구에서는 다중 전극 SAW 및 다양한 용접 조건을 고려한 추가 분석이 필요함.
Reference
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FLOW-3D를 이용한 활성 단층 인근 동시 산사태 발생에 따른 충격파 시뮬레이션: 터키 남동부 체틴 댐 저수지 사례 연구
연구 목적
본 논문은 FLOW-3D를 활용하여 체틴 댐 저수지에서 발생할 수 있는 **충격파(impulse wave)**의 특성을 3D 수치 시뮬레이션으로 분석함.
활성 단층 지역에서 발생하는 산사태가 저수지 내에서 충격파를 유발하는 메커니즘을 연구함.
단일 산사태와 동시 다발적 산사태가 발생할 경우의 충격파 영향을 비교 분석함.
충격파의 간섭(interference) 효과가 저수지 내 파랑 특성과 댐 구조물에 미치는 영향을 평가함.
연구 방법
지질 및 지형 모델링
연구 지역은 터키 남동부 체틴 댐 저수지로, 아라비아판과 타우루스판이 만나는 조산대에 위치함.
댐과 저수지 주변의 주요 단층 구조와 산사태 가능 지역을 고려하여 3D 지형 모델을 생성함.
1/25,000 축척의 디지털 지형 데이터를 사용하여 저수지 및 주변 지형을 모델링함.
FLOW-3D 시뮬레이션 설정
VOF(Volume of Fluid) 방법을 사용하여 자유수면과 산사태 물질 간의 상호작용을 해석함.
RNG k−εk-\varepsilonk−ε 난류 모델을 적용하여 유체 흐름과 충격파 전파 특성을 평가함.
부분적으로 잠긴 산사태(4900m 거리)와 완전히 노출된 산사태(800m 거리)를 각각 독립적으로 모델링하고, 이후 두 산사태가 동시에 발생하는 경우를 시뮬레이션함.
결과 비교 및 검증
개별 산사태와 동시 산사태가 발생했을 때의 충격파 높이와 전파 속도를 비교함.
실험 및 문헌 데이터를 활용하여 시뮬레이션 결과의 신뢰성을 검증함.
충격파 간섭 현상이 발생하는 위치와 그 영향 범위를 분석함.
추가 분석
충격파의 증폭(constructive interference) 또는 감쇠(destructive interference) 여부를 평가함.
저수지 경계 및 댐 구조물과의 충돌이 파형 변화에 미치는 영향을 연구함.
충격파의 전파 거리와 수심에 따른 에너지 소산 효과를 분석함.
주요 결과
산사태별 충격파 특성
산사태 1(800m 거리, 육상 산사태): 34초 후 댐에 도달, 최대 파고 4.0m 발생.
산사태 2(4900m 거리, 부분 침수 산사태): 205초 후 댐에 도달, 최대 파고 4.2m 발생.
단일 산사태의 경우, 발생 위치에 따라 파고와 도달 시간이 달라짐.
동시 발생 산사태의 파랑 간섭 효과
두 충격파가 97초 후 상호 충돌하며 최대 5.7m의 파고를 형성함.
댐 인근에서 최종적으로 5.6m의 파고가 형성되었으며, 이는 개별 산사태보다 1.4m 증가한 수치임.
예상과 달리 충격파가 서로 상쇄되지 않고 증폭(interference amplification) 되는 현상이 관찰됨.
저수지 내 충격파 감쇠 현상
충격파는 저수지 지형과 충돌하면서 일부 감쇠됨.
산사태에서 댐까지의 거리, 산사태 질량, 충격각도에 따라 파랑의 감쇠율이 달라짐.
5km 이상 이동한 충격파는 경로 상 장애물에 의해 에너지가 감소하는 경향을 보임.
댐 안전성 및 설계 시 고려사항
활성 단층 인근의 저수지는 동시 다발적 산사태로 인한 복합 충격파 위험을 고려해야 함.
기존 단일 충격파 분석만으로는 실제 위험성을 과소평가할 가능성이 있음.
향후 연구에서는 실규모 실험과 추가적인 CFD 모델링을 통해 댐 설계 및 운영 기준을 개선해야 함.
결론
FLOW-3D를 이용한 시뮬레이션 결과, 충격파는 개별 산사태보다 동시 산사태에서 더 높은 파고를 형성함.
충격파의 간섭 효과로 인해 댐 인근에서 5.6m의 높은 파고가 발생할 가능성이 있음.
산사태의 발생 위치, 저수지 지형, 파랑 간섭 효과 등을 종합적으로 고려해야 함.
향후 연구에서는 다중 산사태 시뮬레이션을 추가로 수행하여 댐의 안전성을 정량적으로 평가해야 함.
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문제 정의: 교각(Bridge Pier) 주변의 국부 세굴(Local Scour)은 하천 바닥의 침식으로 인해 구조물의 안전성을 위협하는 주요 요인 중 하나이다.
연구 목적: FLOW-3D를 활용하여 교각 주변의 국부 세굴 형상을 3D 시뮬레이션하고, 실험 데이터를 비교하여 모델의 신뢰성을 검증하는 것이다.
핵심 기여:
FLOW-3D를 활용한 CFD 모델 개발: 유체 흐름과 퇴적물 이동을 고려한 세굴 시뮬레이션.
실험 결과와 비교 검증: Melville 실험 데이터를 바탕으로 모델 검증 및 정확도 평가.
세굴 깊이 예측 및 설계 최적화: 교각 설계 및 유지관리 전략에 적용 가능.
연구 방법
수치 모델링 및 난류 모델 적용
Navier-Stokes 방정식 기반 CFD 해석 수행.
VOF(Volume of Fluid) 기법을 활용하여 자유 수면 추적.
RNG k-ε 난류 모델을 사용하여 교각 주변 난류 구조를 해석.
세굴 모델링
Meyer-Peter & Müller 공식을 사용하여 침식 및 퇴적 거동 해석.
Shields Parameter를 적용하여 세굴 발생 임계값 예측.
Melville 실험 모델과 동일한 유속(0.25 m/s) 및 입자 크기(0.385 mm) 설정.
메쉬 설정 및 경계 조건
격자 독립성 검토: 1~30 mm의 다양한 격자 크기를 적용하여 최적의 메쉬 크기(5 mm) 선정.
경계 조건:
입구: 일정한 유속(0.25 m/s) 설정.
출구: 자유 유출 조건 적용.
하천 바닥: 이동 가능 침전층(Sediment Bed)으로 설정.
주요 결과
세굴 깊이 비교
실험 값: 4.00 cm
Flow-3D 예측값: 3.6 cm (실험 대비 오차 10%)
시뮬레이션 결과와 실험 데이터 간 높은 상관관계 확인.
유동장 및 세굴 형상 분석
세굴 패턴: 교각 전면부에서 강한 와류(Horseshoe Vortex) 발생 → 침식 심화.
교각 후류(Downstream) 영역: 유속이 급격히 감소하며 침전 형성.
RNG k-ε 모델 적용 효과: 세굴 깊이 및 와류 구조를 효과적으로 예측.
메쉬 크기의 영향
5mm 이하의 세밀한 격자에서 최적의 결과 도출.
30mm 이상의 거친 격자에서는 세굴 깊이가 과소 예측됨.
결론 및 향후 연구
FLOW-3D 기반 세굴 시뮬레이션이 실험 결과와 높은 정확도로 일치함을 확인.
RNG k-ε 난류 모델이 교각 주변의 난류 구조 및 세굴 깊이 예측에 적합함을 입증.
향후 연구에서는 LES(Large Eddy Simulation) 모델과 비교, 다양한 교각 형상 및 유량 조건에서 추가 검증이 필요.
연구의 의의
이 연구는 FLOW-3D를 활용하여 교각 주변 국부 세굴을 정량적으로 분석하는 방법론을 제시하며, 교량 설계 및 유지보수 전략 수립에 활용될 수 있는 중요한 기초 데이터를 제공한다.
Reference
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문제 정의: 교각 주변에서 발생하는 국부 세굴(Local Scour)은 하천 바닥 침식을 유발하여 교량의 구조적 안정성을 위협하는 주요 요인 중 하나이다.
연구 목적:
FLOW-3D를 활용한 세굴 모델 개발: CFD(Computational Fluid Dynamics) 기반 수치 모델을 사용하여 교각 주변의 세굴 형상을 예측.
실험 데이터와의 비교: 실험실 실험과 수치 모델의 결과를 비교하여 모델의 신뢰성을 평가.
세굴 깊이 및 유속 패턴 분석: 교각 앞쪽 및 후류에서 형성되는 유동 구조와 세굴의 관계를 분석.
연구 방법
실험 데이터 수집 및 모델링
실험실 실험:
터키 가지안테프 대학교의 수리 실험실에서 수행.
0.8m × 0.9m 크기의 직사각형 수로에서 직경 10cm의 원형 교각을 배치.
유량 0.048 m³/s, 유속 0.48 m/s, 수심 11cm 설정.
세굴층은 비응집성(non-cohesive) 모래(d₅₀ = 1.45mm)로 구성.
FLOW-3D 기반 CFD 모델링:
VOF(Volume of Fluid) 기법을 사용하여 자유 수면 모델링.
RNG k-ε 난류 모델을 적용하여 난류 흐름 분석.
침식 및 퇴적 모델을 적용하여 하상 변화 예측.
격자 설정 및 경계 조건
메쉬 독립성 검토: 64,000개 이상의 격자를 사용하여 최적화 수행.
경계 조건:
입구: 일정한 유속(0.48 m/s) 설정.
출구: 자유 유출 조건 적용.
하천 바닥: 이동 가능 침전층(Sediment Bed)으로 설정.
주요 결과
세굴 깊이 비교
실험 값: 6.9 cm
FLOW-3D 예측값: 6.5 cm (실험 대비 오차 10%)
실험과 수치 모델의 결과가 높은 상관관계를 보임.
유동 및 세굴 패턴 분석
유속 분포:
교각 전면부에서 강한 와류(Horseshoe Vortex) 발생 → 침식 심화.
후류 영역에서는 유속이 감소하며 퇴적 형성.
세굴 형상:
최대 세굴 깊이는 교각 전면부 및 측면에서 발생.
FLOW-3D 모델은 세굴 발생 위치 및 심도를 효과적으로 예측.
시간에 따른 세굴 발전
실험 및 CFD 모델 모두에서 1시간 후 세굴 깊이가 안정화됨.
세굴 속도는 초기 30분 동안 급격히 증가한 후 점진적으로 감소.
결론 및 향후 연구
결론:
FLOW-3D 기반 CFD 모델은 교각 주변의 세굴 깊이를 실험 결과와 높은 정확도로 예측할 수 있음.
RNG k-ε 난류 모델이 국부 세굴 해석에 적합함을 확인.
세굴 깊이 예측에서 실험 대비 오차는 약 10%로 양호한 결과를 보임.
향후 연구 방향:
더 정교한 난류 모델(예: LES) 적용 및 비교.
다양한 교각 형상 및 유량 조건에서 추가 검증.
인공지능(AI) 및 머신러닝을 활용한 세굴 예측 모델 개발.
연구의 의의
이 연구는 FLOW-3D를 이용한 국부 세굴 예측의 신뢰성을 검증하고, 교량 설계 및 유지보수 전략 수립에 활용될 수 있는 중요한 기초 데이터를 제공한다.
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고속 싱크로트론 X선 영상 및 수치 시뮬레이션을 이용한 국부 가스 유동이 키홀 및 용융 풀 동역학에 미치는 영향 분석
연구 배경 및 목적
문제 정의: 고합금 강재의 레이저 빔 용접 시 높은 용접 속도에서 스패터(Spatter) 발생이 주요 문제점이며, 이는 용접 품질에 악영향을 미친다.
연구 목적:
국부 가스 공급(Local Gas Supply)이 키홀(Keyhole) 및 용융 풀(Melt Pool) 동역학에 미치는 기계적 영향을 고속 X선 영상과 CFD 시뮬레이션을 통해 분석.
FLOW-3D 소프트웨어를 활용하여 국부 가스 흐름에 의한 동압(Dynamic Pressure)이 키홀 형상 및 용융 풀 유동에 미치는 영향을 정량화.
스패터 형성 억제 메커니즘을 규명하고, 국부 가스 공급의 최적화 방안을 제시.
연구 방법
수치 모델링 및 시뮬레이션 설정
FLOW-3D (v11.2 update 6, WELD module v2.4.1.2.9) 사용.
VOF(Volume of Fluid) 기법을 통해 자유 표면 추적.
Navier-Stokes 방정식 및 열 전달 방정식 적용.
용융, 증발, 응고 과정을 모두 포함한 다중 물리 시뮬레이션.
난류 모델:
RNG k-ε 모델을 사용하여 난류 효과 반영.
기체 유동에 의한 동압(pgas)을 추가하여 국부 가스 공급의 기계적 효과 구현.
국부 가스 공급 조건
가스 유동 속도에 따른 동압(pgas) 변화:
최대 496 mbar에서 627 mbar까지 적용.
가스 노즐 위치:
키홀 개구부에서 5 mm 떨어진 지점에 48° 각도로 설치.
보호 가스:
공기(Bottled Air) 사용하여 화학-야금학적 효과를 최소화하고, 기계적 효과만 분석.
고속 X선 영상 및 실험 설정
고속 싱크로트론 X선 영상: ESRF ID19 빔라인에서 수행.
AISI 304 고합금 강재 사용.
레이저 용접 조건:
싱글 웨이브 레짐(Single-Wave-Regime) 및 연장된 키홀 레짐(Elongated-Keyhole-Regime)에서 실험.
용접 속도: 12 m/min, 레이저 출력: 2.3 kW.
고속 비디오 촬영:
Photron SA-Z 고속 카메라를 사용하여 40,000 fps 촬영.
주요 결과
키홀 형상 및 용융 풀 동역학 분석
국부 가스 공급이 없는 경우:
키홀 후면벽에서 강한 진동 및 불안정한 형상이 관찰됨.
키홀 목(necking) 형성 및 기공(porosity) 발생.
용융 풀 상승(swell) 및 스패터 분리(spatter detachment) 현상 확인.
국부 가스 공급이 있는 경우:
키홀 후면벽의 진동이 감소하고 안정화.
키홀 개구부가 넓어지고, 스패터 발생이 크게 감소.
용융 풀 속도 및 순환 유동이 감소하며, 안정된 유동 패턴 형성.
동압(pgas)의 효과
496 mbar에서 키홀 후면 진동이 크게 감소.
627 mbar에서는 키홀 개구부가 넓어지고, 스패터가 거의 발생하지 않음.
동압이 300 mbar 이하에서는 키홀 형상 및 스패터 억제 효과가 미미.
FLOW-3D 모델의 신뢰성 검증
고속 싱크로트론 X선 영상 결과와 FLOW-3D 시뮬레이션 결과 간 높은 일치도 확인.
시뮬레이션에서 예측한 키홀 후면벽 진동 패턴 및 용융 풀 상승과 스패터 억제 현상이 실험 결과와 일관됨.
결론 및 향후 연구
결론:
국부 가스 공급에 의한 동압이 키홀 후면벽의 진동을 감소시키고, 스패터 발생을 효과적으로 억제함.
496 mbar 이상의 동압이 적용될 때 키홀 형상이 안정화되고, 용융 풀 유동 속도가 감소하며, 스패터 억제에 가장 효과적임.
FLOW-3D 모델이 고속 X선 영상 데이터와 높은 정확도로 일치하며, 국부 가스 공급의 기계적 효과를 정량적으로 분석 가능함.
향후 연구 방향:
다양한 레이저 출력 및 용접 속도 조건에서 국부 가스 공급의 효과를 추가 검증.
기계적 효과 외에도 화학-야금학적 효과를 고려한 모델 확장.
다중 노즐 배열 및 동시 다중 가스 공급에 대한 연구를 통해 스패터 완전 억제 방안 모색.
연구의 의의
이 연구는 국부 가스 공급이 레이저 빔 용접에서 스패터 발생을 효과적으로 억제하는 메커니즘을 규명하고, FLOW-3D 시뮬레이션과 고속 X선 영상을 활용한 정량적 분석을 통해 최적화 설계 지침을 제공하며, 고속 레이저 용접의 품질 및 생산성을 향상시킬 수 있음을 시사한다.
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FLOW-3D 예측 모델링을 이용한 유량 측정 플룸의 잠김 한계(Submergence Limit) 및 수두 손실(Head Loss) 평가
연구 배경 및 목적
문제 정의: 개수로(Open Channel)에서 유량 측정을 위해 사용되는 플룸(Flume)은 구조가 단순하고 비용 효율적이지만, 정확도는 잠김 한계(Submergence Limit)와 수두 손실(Head Loss)에 의해 영향을 받는다.
연구 목적:
FLOW-3D CFD 모델을 사용하여 잠김 한계 및 수두 손실을 평가하고, 이를 실험 데이터와 비교하여 모델의 신뢰성을 검증.
플룸 하류 바닥을 상승시킨 설계가 잠김 한계와 수두 손실에 미치는 영향을 분석.
연구 방법
수치 모델링 및 시뮬레이션 설정
FLOW-3D 소프트웨어를 사용하여 3차원 유동 해석 수행.
FAVOR(Fractional Area-Volume Obstacle Representation) 기법을 사용하여 복잡한 플룸 형상을 모델링.
RNG k-ε 난류 모델을 적용하여 난류 흐름을 해석.
VOF(Volume of Fluid) 기법을 활용하여 자유 수면을 추적.
격자 독립성 검토: 0.027 m의 격자 크기 사용.
플룸 설계 및 실험 조건
플룸 설계: 하류 바닥이 상승된 직사각형 플룸 설계.
실험 변수:
세 가지 유량 조건: Flow 1 (0.112 m³/s), Flow 2 (0.169 m³/s), Flow 3 (0.320 m³/s)
안내벽 각도(Reflector Angle) 및 하류 바닥 높이를 변화시켜 시뮬레이션.
모델 검증:
Samani (2017)의 실험 데이터를 기반으로 FLOW-3D 모델을 RMSE < 1.5 cm, R² > 0.98 수준으로 보정.
분석 항목
잠김 한계(Submergence Limit):
잠김 비(Submergence Ratio): 하류 수심 / 상류 수심
잠김 한계는 잠김 비가 특정 값을 초과하면 상류 수심이 급격히 증가하는 지점으로 정의.
수두 손실(Head Loss):
수두 손실 = 상류와 하류의 수두 차이.
주요 결과
잠김 한계(Submergence Limit) 및 수두 손실(Head Loss)
Flow 1: 잠김 한계 0.21, 최대 수두 손실 32.5%
Flow 2: 잠김 한계 0.24
Flow 3: 잠김 한계 0.25
잠김 한계는 유량 증가에 따라 증가하며, 하류 바닥 높이가 높을수록 잠김 한계에 도달하는 경향이 확인됨.
안내벽 각도의 영향
안내벽 각도가 증가할수록 수두 손실이 증가하는 경향을 보임.
80°에서 최대 월류량을 기록하며, 90°에서는 파도의 속도가 낮아져 월류량이 감소.
FLOW-3D 모델의 신뢰성
FLOW-3D 모델 예측 결과와 실험 데이터 간 평균 오차율이 7.2%로 높은 신뢰도를 확인.
기존 실험 결과와 비교했을 때 FLOW-3D 모델이 잠김 한계 및 수두 손실 예측에 효과적임.
결론 및 향후 연구
결론:
FLOW-3D는 유량 측정 플룸에서 잠김 한계 및 수두 손실을 정확하게 예측할 수 있으며, 기존 실험 데이터와 높은 일치도를 보임.
잠김 한계는 유량이 증가할수록 높아지며, 하류 바닥 높이와 안내벽 각도가 중요한 영향을 미침.
플룸 설계 시 하류 바닥 높이 및 안내벽 각도 최적화를 통해 수두 손실을 최소화할 수 있음.
향후 연구 방향:
다양한 난류 모델(예: LES)과의 비교 및 다양한 유량 조건에서 추가 검증.
다중 안내벽 설계 및 다양한 플룸 형상에 대한 연구를 통해 성능 개선.
AI 및 머신러닝 기법을 활용한 실시간 유량 예측 모델 개발.
연구의 의의
이 연구는 FLOW-3D를 활용한 유량 측정 플룸의 잠김 한계 및 수두 손실 예측의 신뢰성을 검증하고, 플룸 설계 최적화 및 수리구조물의 효율적 설계에 기여할 수 있는 중요한 기초 데이터를 제공한다.
Reference
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Ghare, A. D., Kapoor, A., & Badar, A. M. (2020). Cylindrical central baffle flume for flow measurements in open channels. Journal of Irrigation and Drainage Engineering, 146(9), 06020007.
Goel, A., Verma, D. V. S., & Sangwan, S. (2015). Open channel flow measurement of water by using width contraction. International Journal of Civil and Environmental Engineering, 9(2), 205–210.
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Heyrani, M., Mohammadian, A., Nistor, I., & Dursun, O. F. (2022). Application of Numerical and Experimental Modeling to Improve the Efficiency of Parshall Flumes: A Review of the State-of-the-Art. Hydrology, 9(2), 26.
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본 논문은 FLOW-3D를 활용하여 계단식 방파제(stepped mound breakwater) 주변의 파랑 거동을 시뮬레이션하고 실험 데이터와 비교함.
파랑이 방파제에 부딪힐 때 발생하는 에너지 소산 및 파랑 전달 계수를 분석함.
다양한 해수면 조건에서 계단식 방파제가 파랑 에너지 감쇠에 미치는 영향을 평가함.
CFD 기반의 수치 해석 기법이 물리 실험을 대체할 수 있는 가능성을 탐구함.
연구 방법
방파제 모델링 및 실험 설정
5개의 방파제 모델을 생성하여 파랑의 충격에 따른 거동을 시뮬레이션함.
해수면이 방파제 정상부(crest) 위로 얼마나 올라오는지에 따라 서로 다른 조건을 적용함.
실험 데이터를 기존 문헌 및 시뮬레이션 결과와 비교하여 검증함.
방파제의 계단 수 증가가 에너지 소산에 미치는 영향을 분석함.
FLOW-3D 시뮬레이션 설정
FAVOR 기법을 사용하여 방파제 형상을 모델링함.
난류 모델로 k−εk-\varepsilonk−ε 방정식을 사용하여 흐름을 해석함.
Fourier 시리즈를 적용하여 다양한 파랑 조건을 생성함.
메쉬 독립성 연구를 수행하여 최적의 격자 크기를 결정함.
결과 비교 및 검증
실험실에서 측정한 파랑 전달 계수(Kt)와 시뮬레이션 결과를 비교하여 모델 신뢰도를 평가함.
방파제 계단 수 증가에 따른 에너지 소산 패턴을 분석함.
다양한 방파제 경사각(30°, 45°, 60°)에서 파랑 전달 계수를 계산함.
실험값과 계산값 간 오차를 정량적으로 분석하고, 오차의 주요 원인을 규명함.
추가 분석
방파제 계단 수 증가가 파랑의 진행 및 반사에 미치는 영향을 평가함.
다양한 해수면 변화 조건에서 방파제의 효과를 분석함.
방파제 경사각에 따른 최적의 에너지 소산 효율을 평가함.
주요 결과
파랑 전달 계수 분석
계단식 방파제의 계단 수가 증가할수록 에너지 소산 효과가 증가함.
방파제 정상부 위 해수면 높이가 증가할수록 파랑 전달 계수(Kt)도 증가하는 경향을 보임.
특정 조건(해수면이 방파제 정상부에서 8cm 이상 높을 경우)에서 홍수 현상이 발생함.
경사각과 파랑 소산 효과
방파제 경사각이 30°에서 60°로 증가할수록 파랑 전달 계수가 증가함.
30°의 경사에서는 평균적으로 7~23% 낮은 파랑 전달 계수를 보이며, 에너지 소산 효과가 가장 우수함.
높은 경사에서는 반사파와 난류 현상이 증가하여 파랑 에너지 감쇠 효과가 상대적으로 낮아짐.
FLOW-3D의 신뢰성 평가
시뮬레이션 결과는 실험 데이터와 높은 상관성을 보이며, 평균 오차율은 3~5% 수준으로 나타남.
방파제 정상부 위의 해수면 높이가 클수록 시뮬레이션과 실험값 간의 차이가 증가함.
메쉬 독립성 연구를 통해 계산 정확도를 향상시킬 수 있음을 확인함.
방파제 설계에 대한 시사점
계단식 방파제는 기존 단순 경사형 방파제보다 높은 에너지 소산 효과를 보임.
최적의 경사각과 계단 수를 결정하는 것이 파랑 감쇠 효율을 극대화하는 데 중요함.
향후 연구에서는 실규모 해양 환경에서 실험적 검증이 필요함.
결론
FLOW-3D는 계단식 방파제의 파랑 소산 효과를 신뢰성 있게 예측할 수 있음.
계단 수가 증가할수록 파랑 에너지 소산이 증가하며, 최적의 경사각은 30°임.
실험적으로 측정된 파랑 전달 계수와 CFD 예측값이 높은 상관성을 보임.
향후 연구에서는 실규모 해양 환경에서 추가적인 실험적 검증이 필요함.
Reference
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항공우주 산업에서 사용되는 몰드의 열적 거동을 보다 정확히 분석하여 고품질 주조 공정을 지원함.
연구 방법
실험적 주조 테스트
TPC Components AB 주조 공장에서 실제 크기의 Ni-초합금(IN718) 주조 실험 수행함.
10층으로 구성된 테스트 몰드를 제작하고, 몰드 두께를 따라 여러 개의 열전대를 배치함.
열전대 데이터를 기반으로 몰드 내부 및 금속 온도 프로파일을 분석함.
실험 데이터를 CFD 시뮬레이션 결과와 비교하여 정확도를 평가함.
FLOW-3D 시뮬레이션 설정
실제 실험 조건을 반영하여 몰드 형상을 모델링하고, 압력 변화 경계를 설정함.
몰드 내부와 외부의 온도 차이를 반영하여 공기층 형성을 고려함.
몰드의 열전달 계수(HTC)와 방사율 값을 문헌 데이터를 기반으로 설정함.
Python 스크립트를 활용하여 시뮬레이션 데이터를 열전대 측정값과 비교함.
열물성 분석
시차 주사 열량법(DSC)을 이용하여 몰드의 비열 용량을 측정함.
레이저 플래시 분석(LFA)으로 열확산율을 평가하여 열전도율을 산출함.
팽창계(dilatometry)를 사용하여 몰드의 열팽창 계수를 측정함.
실험값과 시뮬레이션 예측값을 비교하여 몰드의 열물성을 검증함.
결과 검증
실험 데이터와 FLOW-3D 시뮬레이션 결과를 비교하여 CFD 모델의 신뢰성을 평가함.
실험값과 계산값 간 차이를 분석하고, 주요 원인을 규명함.
몰드의 다층 구조에 따른 열적 거동을 평가하고, 추가 연구 방향을 제시함.
주요 결과
온도 프로파일 비교
시뮬레이션 결과는 실험값과 높은 상관성을 보이며, 몰드 내부 온도 변화를 잘 재현함.
금속이 주입될 때 온도 상승 패턴이 실험과 유사하게 나타남.
열전대 측정값과 CFD 예측값 간 평균 오차는 약 2~5% 수준으로 나타남.
비열 용량 및 열팽창 계수
실험 데이터를 기반으로 몰드의 평균 비열 용량을 결정함.
몰드의 열팽창 계수는 실험 결과와 문헌 데이터와 비교하여 높은 일관성을 보임.
몰드 조성 중 지르코늄과 실리카 함량이 열팽창 특성에 영향을 미치는 것으로 나타남.
열전도율 평가
FLOW-3D 시뮬레이션 결과와 실험 측정값이 유사한 열전도율 경향을 나타냄.
고온에서 몰드의 열전도율이 증가하는 경향이 확인됨.
몰드의 층별 조성이 열전도 특성에 미치는 영향을 평가함.
시뮬레이션과 실험 데이터 비교
전체적으로 CFD 모델이 몰드의 열적 거동을 잘 예측하지만, 일부 고온 영역에서 오차가 존재함.
몰드 내부 구조 및 표면 조도를 추가로 고려해야 정확성을 향상시킬 수 있음.
향후 연구에서는 몰드의 다층 구조를 개별적으로 분석하는 방식이 필요함.
결론
FLOW-3D는 다공성 세라믹 몰드의 열적 거동을 신뢰성 있게 예측할 수 있음.
실험적으로 측정된 몰드의 열물성 값과 CFD 예측값이 높은 상관성을 보임.
일부 고온 영역에서 오차가 존재하므로 추가적인 실험적 검증이 필요함.
향후 연구에서는 몰드의 층별 특성을 반영한 정밀 모델링이 필요함.
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3D Numerical Modelling of Flow Around Skewed Bridge Crossing
(“비스듬한 교량 횡단부 주변 흐름의 3D 수치 모델링”)
연구 목적
본 논문은 FLOW-3D를 활용하여 비스듬한(스큐) 교량 횡단부 주변의 수면 흐름을 시뮬레이션하고 실험 데이터와 비교하여 모델의 성능을 평가함.
실험실 규모에서 다양한 스큐 각도(30°, 45°)를 적용하여 수면 프로파일 변화를 분석함.
Reynolds-Averaged Navier-Stokes (RANS) 방정식을 기반으로 한 FLOW-3D의 수치 해석 결과와 실험 데이터를 비교하여 정확도를 검증함.
교량 설계 및 홍수 관리에 있어 3D 수치 모델의 활용 가능성을 탐구함.
연구 방법
실험 모델 설정
영국 버밍엄 대학교 수리 실험실에서 다양한 교량 구조(아치형, 평면형 등)를 대상으로 실험 수행함.
22m 길이, 1.213m 너비, 0.4m 깊이의 복합 수로(compound channel)에서 교량 흐름 실험을 진행함.
실험 데이터는 기존 연구에서 활용된 1D 및 2D 모델과 비교 검증함.
FLOW-3D 시뮬레이션 설정
FAVOR(유체 부피 기법)를 적용하여 교량 구조를 모델링함.
난류 모델로 k−εk-\varepsilonk−ε 방정식을 사용하여 수치 해석 진행함.
메쉬 독립성 연구를 수행하여 최적의 격자 크기를 결정함.
결과 비교 및 검증
실험실에서 측정한 자유표면 프로파일과 FLOW-3D 결과를 비교하여 모델 신뢰도를 평가함.
다양한 흐름 조건(유량 변화, 교량 구조 차이 등)에 따른 모델 성능을 분석함.
실험값과 계산값 간 오차를 정량적으로 분석하고, 오차의 주요 원인을 규명함.
추가 분석
1D, 2D, 3D 모델 간 비교를 수행하여 모델별 장단점을 평가함.
실험 데이터와 수치 모델의 차이를 최소화하기 위한 보정 기법을 검토함.
주요 결과
수면 프로파일 비교
FLOW-3D 시뮬레이션은 실험 데이터와 유사한 수면 프로파일을 재현함.
30°와 45° 스큐 각도에서 측정된 최대 백워터(afflux) 값이 유사하게 나타남.
교량 형상 및 흐름 조건 변화에 따른 수면 변화 패턴을 정확히 예측함.
스큐 각도와 유량의 영향
스큐 각도가 증가할수록 백워터 높이가 증가함.
유량 증가 시 백워터 영향이 커지며, 45° 각도에서는 30°보다 평균 7~23% 높은 백워터 발생함.
난류 특성이 강한 구간에서는 수치 모델이 일부 오차를 보임.
FLOW-3D의 정확성 평가
실험값과 모델 예측값의 평균 오차율은 30°에서 3.5%, 45°에서 2.2%로 나타남.
실험실 조건에서는 모델이 비교적 정확한 결과를 제공하나, 자연 하천 환경에서 추가 검증이 필요함.
메쉬 해상도와 난류 모델의 선택이 결과에 중요한 영향을 미침.
설계 및 적용성 평가
FLOW-3D는 복잡한 교량 주변 흐름 해석에 유용한 도구임.
3D 모델을 활용하면 1D, 2D 모델보다 높은 정확도로 수면 변화를 예측할 수 있음.
향후 연구에서는 침식 및 고유 유량 변화를 포함한 실험 검증이 필요함.
결론
FLOW-3D는 비스듬한 교량 횡단부 주변 흐름을 효과적으로 시뮬레이션할 수 있음.
스큐 각도가 증가할수록 백워터가 증가하는 경향이 확인됨.
수치 모델과 실험 데이터 간 평균 오차는 3.5%~2.2% 범위로 나타남.
향후 연구에서는 더 높은 난류 해상도 및 자연 하천 환경에서 추가적인 검증이 필요함.
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이 연구는 Wave Dragon과 같은 월류형 WEC의 성능을 최적화하기 위한 CFD 기반 설계 평가 방법을 제시하며, 파력 발전 시스템의 효율성을 향상시키기 위한 실용적인 가이드라인을 제공한다.
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유체 유동 해석: 용융 풀(Molten Pool) 거동을 해석하기 위해 VOF(Volume of Fluid) 기법 적용.
열전달 및 용접 프로세스 시뮬레이션:
용융 금속의 열전달 및 응고 해석.
용접 과정에서 발생하는 표면 장력(Marangoni Effect) 분석.
아크 기반 용접 비드 모델링:
용접 비드 형상을 원형(Arc) 모델로 근사하여 예측.
비드 프로파일의 중심 좌표 및 반지름을 주요 특징으로 설정.
심층 학습을 활용한 용접 비드 예측
신경망 모델: ResNet 기반 CNN 모델을 사용하여 이미지에서 용접 비드 프로파일을 추출하고, 위치 및 반지름 예측.
입출력 데이터:
입력: 용접 이음매의 단면 이미지 + 용접 위치 정보.
출력: 예측된 용접 비드 프로파일 (중심 좌표 및 반지름).
학습 데이터: Flow-3D 시뮬레이션 데이터를 활용하여 대량의 학습용 데이터를 생성.
주요 결과
ADAP 모델 성능 평가:
용접 비드 중심 좌표 예측 오차: 평균 0.73mm
반지름 예측 오차: 평균 0.66mm
실시간 예측 속도: 15ms (NVIDIA RTX 3060 GPU 기준)
기존 방법과 비교:
기존의 경험적 모델보다 더 높은 정확도로 용접 비드 형상을 예측.
CFD 기반 시뮬레이션보다 계산 속도가 훨씬 빠르며, 실시간 용접 경로 조정이 가능.
MLMP 용접의 실용성 증대:
자동화 용접 공정에서 실시간 예측 모델로 활용 가능.
용접 품질 향상을 위한 최적의 경로 및 공정 변수 제어 가능.
결론 및 향후 연구
결론:
ADAP 모델은 심층 학습을 활용하여 MLMP 용접에서 실시간 이음매 프로파일을 정확하게 예측할 수 있음을 입증함.
Flow-3D 기반 시뮬레이션 데이터를 이용한 학습을 통해 실험 데이터 없이도 높은 정확도로 용접 형상을 예측 가능함.
향후 연구 방향:
더 다양한 용접 공정 변수(토치 각도, 와이어 공급 속도 등)를 포함하여 모델 성능 개선.
실제 산업 환경에서 로봇 용접 시스템과 통합하여 실증 실험 진행.
3D 스캐너와 결합하여 실시간 품질 모니터링 및 피드백 시스템 구축.
연구의 의의
본 연구는 AI 기반 데이터 중심 용접 품질 예측 모델을 제안함으로써, 기존 경험적 방식에서 벗어나 정확하고 실시간 대응이 가능한 자동화 용접 시스템 개발에 기여할 수 있음을 시사한다.
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문제 정의: 교각이나 말뚝(pile) 주위에서 발생하는 국부적인 세굴(scour)은 구조물의 안정성에 중요한 영향을 미친다.
연구 목적: FLOW-3D 소프트웨어를 이용하여 두 개의 말뚝(쌍둥이 말뚝) 주위의 유동 패턴과 세굴 메커니즘을 수치적으로 시뮬레이션하고, 실험 데이터를 활용하여 검증하는 것이다.
연구 방법
수치 모델링 및 난류 모델
FLOW-3D 소프트웨어를 사용하여 RNG k-ε 난류 모델을 기반으로 유동 해석 수행.
말뚝의 배치: 병렬(side-by-side) 배치 및 직렬(tandem) 배치 두 가지를 고려.
실험 데이터와 비교하여 모델의 신뢰성을 검증.
계산 영역 및 격자(Grid) 설정
비균일(non-uniform) 격자 분포를 사용하여 말뚝 주변의 유동을 정밀하게 모델링.
최소 격자 크기: 0.009 m, 최대 격자 크기: 0.039 m.
메쉬 개수: x 방향 400개, y 방향 110개, z 방향 40개.
경계 조건
유입 속도 및 압력을 각각 입출력 경계 조건으로 설정.
상류에서 개발된 유동을 프로파일로 생성하여 말뚝이 존재하는 구역의 유입 경계 조건으로 적용.
주요 결과
유동 패턴 분석
병렬 배치(Side-by-side):
말뚝 사이에서 제트(Jet) 유동이 발생하며 비대칭적인 흐름 형성.
배치 간격이 증가할수록 후류(Vortex shedding) 현상이 뚜렷해짐.
직렬 배치(Tandem):
앞쪽 말뚝이 후방 말뚝을 보호하는 Sheltering 효과 발생.
Reynolds 수와 배치 간격(S/d)에 따라 와류 형성 패턴이 변화.
후류에서 강한 난류 구조가 나타나며, Wake Vortex가 형성됨.
실험과의 비교
실험 데이터와 시뮬레이션 결과를 비교한 결과, 전반적으로 유동 패턴이 잘 일치함.
그러나 말뚝 사이의 복잡한 유동장에서는 일부 차이가 발생하여 추가적인 모델 보정이 필요함.
Reynolds 수와 배치 간격의 영향
말뚝 간 간격(S/d)이 증가할수록 앞쪽 말뚝의 보호 효과가 감소하고, 후방 말뚝 주변에서 강한 와류가 형성됨.
낮은 Reynolds 수에서는 단일 말뚝과 유사한 흐름 패턴을 보이나, 높은 Reynolds 수에서는 와류가 더욱 강하게 나타남.
결론 및 향후 연구
FLOW-3D를 활용한 3D 유동 시뮬레이션은 말뚝 주변 유동 패턴과 세굴 메커니즘을 효과적으로 분석할 수 있음을 확인함.
실험 데이터와 전반적으로 높은 일치도를 보였으나, 말뚝 사이의 복잡한 유동장에서 추가적인 모델 개선이 필요함.
향후 연구에서는 더 다양한 Reynolds 수와 배치 조건을 고려한 추가 실험 및 난류 모델 비교 분석이 필요함.
연구의 의의
이 연구는 교량 기초 및 해양 구조물 설계에서 말뚝 주변의 유동과 세굴 예측을 정밀하게 분석할 수 있는 CFD 기반 접근법을 제시하였으며, 향후 말뚝 배치 최적화 및 구조물 안전성 향상에 기여할 수 있음을 시사한다.
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선박 설계 시 추진 시스템의 효율성을 결정하는 핵심 요소 중 하나는 선박 저항(항해 중 발생하는 해양 저항)이다.
선박 저항은 선박의 연료 소비와 환경 영향을 좌우하며, 초기 설계 단계에서는 Holtrop-Mennen (HM)과 같은 통계적 방법을 주로 사용한다.
완성된 3D 선체 디자인이 마련되면 CFD 시뮬레이션이나 축척 모델 실험을 통해 보다 정밀한 저항 값을 산출할 수 있다.
본 연구는 RoPax 여객선을 대상으로 Flow-3D 소프트웨어를 활용하여 다양한 선박 속도에서의 저항을 계산하고, 이를 HM 방법과 비교·분석하는 데 목적이 있다.
연구 방법
CFD 시뮬레이션 수행
소프트웨어: Flow-3D를 사용하여 3차원 Navier-Stokes 방정식을 풀어 선박 주변의 자유 표면 유동을 해석.
메쉬 기법: FAVOR (Fractional Area-Volume Obstacle Representation) 기법을 이용한 ‘Free Gridding’으로 복잡한 선체 형상을 간단하게 모델링.
경계조건: 입구에 유속 조건(선박 속도에 해당하는 값)과 해수의 깊이를 설정하여 실제 해양 조건을 반영.
난류 모형: RANS k-ε 모델을 사용하여 난류 효과를 고려.
메쉬 민감도 분석
다양한 격자 크기를 적용하여 결과의 민감도를 평가하고, 최적의 해상도와 계산 시간을 확보함.
비교 분석
CFD 시뮬레이션 결과로 도출된 선박 저항 값을 Holtrop-Mennen (HM) 방법의 예측값과 비교.
낮은 선박 속도(10 knots)에서는 CFD 결과와 HM 방법 간의 차이가 미미하나, 속도가 증가할수록 CFD 결과가 HM 예측보다 크게 증가하는 경향을 분석.
주요 결과
저항 값 비교:
10 knots에서 CFD 시뮬레이션 결과는 HM 방법과 유사하였으나, 15 knots 이상에서는 CFD 결과가 HM 방법보다 현저히 높은 저항 값을 나타냄.
예를 들어, 20 knots에서는 HM 방법 대비 약 35% 높은 저항 값이 나타났으며, 24 knots에서는 약 32% 차이가 발생함.
메쉬 민감도:
더 미세한 메쉬(최종적으로 Mesh 3 사용)에서 시뮬레이션된 저항 값은 거친 메쉬에 비해 낮은 값을 보여, 격자 크기가 결과에 미치는 영향을 확인함.
선박 속도에 따른 변화:
선박 속도가 증가할수록 파 생성 및 파 부서짐으로 인한 추가 저항이 크게 기여하며, 이는 선박 저항의 비선형적인 증가로 나타남.
결론 및 향후 연구
Flow-3D를 활용한 CFD 시뮬레이션은 선박 저항을 예측하는 데 효과적인 도구임을 확인하였다.
특히, 고속 조건에서 CFD 결과는 HM 방법보다 높은 저항 값을 산출하며, 이는 파 저항의 기여를 반영한 결과로 해석된다.
향후 연구에서는 다른 난류 모형(예: Wilcox k-ω, RNG k-ε)과의 비교, 실제 모델 테스트(예: 축척 모델 실험)와의 추가 검증을 통해 CFD 해석의 정확성을 더욱 향상시킬 필요가 있다.
본 연구 결과는 선박 설계 및 최적 운항 속도 결정 등 실무에 유용한 참고 자료로 활용될 수 있다.
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폴리아미드 11 (PA11) 레이저 파우더 베드 융합 공정 중 용융 영역에 대한 열유체동역학 모델
연구 배경 및 목적
문제 정의: 폴리머 기반 레이저 파우더 베드 융합(PBF-LB/P) 공정에서는 용융 영역( melt region )의 형성과 응고 현상이 최종 제품 품질에 큰 영향을 미치며, 이 과정에서 결함(예: 미융합, 기공 등)이 발생할 수 있음.
연구 목적: 본 연구는 Flow-3D Weld를 활용하여 PA11 재료의 PBF-LB/P 공정 중 용융 영역의 형태, 온도 분포, 유동 특성을 3D 다중 물리 모델로 시뮬레이션하고, 단일 트랙 실험 데이터를 통해 모델을 검증하여, 레이저 설정(파워, 스캔 속도, 해치 간격)이 용융 영역 형상 및 결함 발생에 미치는 영향을 분석하는 데 있다.
연구 방법
파우더 베드 준비
실제 입자 크기 분포를 DEM(Discrete Element Method)을 통해 모사하여, 파우더 베드의 초기 상태를 재현.
모델 개발
열유체동역학 모델: 유한체적법(FVM)을 기반으로 Flow-3D Weld를 사용하여 용융 영역 내 열전달, 유동, 그리고 응고 과정을 수치해석.
물리현상 고려:
열 전달: 온도 분포 및 열전달, 응고 시 latent heat 및 재료의 온도 의존적 특성 고려.
유체 유동: 비압축성, laminar 흐름으로 가정하며, 높은 점도를 가진 PA11의 특성을 반영.
마랑고니 효과: 온도에 따른 표면 장력 변화가 용융 영역의 형상에 미치는 영향 분석.
시뮬레이션 단계
싱글 트랙 시뮬레이션: 레이저 파우더 베드 융합 공정의 단일 트랙에 대해, sintering(소결)과 cooling(냉각) 단계를 분리하여 시뮬레이션.
멀티 트랙 시뮬레이션: 다중 트랙 조건에서 표면 거칠기 및 레이저 설정과의 상관관계를 분석.
모델 검증 및 메쉬 독립성
메쉬 독립성 분석을 통해 최적의 격자 크기를 선정.
실험(단일 트랙 실험)으로부터 용융 영역의 폭과 깊이 데이터를 확보하여 시뮬레이션 결과와 비교 검증.
주요 결과
용융 영역 특성:
레이저 파워 증가에 따라 용융 영역의 폭과 깊이가 증가하며, 온도 분포와 유동 특성이 변화함.
높은 점도와 낮은 유동성으로 인해, PA11의 경우 용융 영역 내에서 열전달 및 응고가 상대적으로 느리게 진행됨.
시뮬레이션 및 실험 비교:
단일 트랙 실험에서 측정된 용융 영역 폭과 깊이와 시뮬레이션 결과가 좋은 일치도를 보임.
fliq(용융된 재료의 비율)를 기준으로 용융 영역 경계를 정의하여, 실험 측정값과 비교 시 보수적인 결과가 도출됨.
멀티 트랙 결과:
여러 트랙의 시뮬레이션을 통해, 레이저 설정에 따른 표면 거칠기와 결함(미융합 및 기공 발생) 특성이 도출됨.
해치 간격이 좁을수록, 스캔 라인 간 중복 효과로 인해 입자 간 융합이 개선되어 표면이 더 매끄럽게 나타남.
결론 및 향후 연구
결론:
제안된 열유체동역학 모델은 PA11의 PBF-LB/P 공정 중 용융 영역의 형태 및 온도, 유동 특성을 성공적으로 재현하였으며, 실험 데이터와의 검증을 통해 신뢰성을 확보함.
레이저 파워, 스캔 속도, 해치 간격 등 주요 레이저 설정이 용융 영역의 형상 및 결함 발생에 결정적인 영향을 미침.
향후 연구:
멀티 트랙 시뮬레이션을 통해 표면 거칠기 및 미세구조 형성에 대한 추가 분석.
파우더 크기 분포, 층 두께, 빌딩 챔버 온도 등 추가 변수들의 영향을 고려한 모델 확장 및 최적화.
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3D CFD(전산유체역학) 모델링은 수력 구조물 설계 및 해석에서 중요한 도구로 사용되며, 기존의 1D 및 2D 해석 방법보다 복잡한 유체 거동을 정확하게 예측할 수 있음.
FLOW-3D HYDRO는 비정수압 유동, 자유 수면 해석, 다중 물리 모델링(예: 퇴적물 이동, 열전달, 공기 유입) 기능을 포함한 상용 3D CFD 소프트웨어임.
본 연구는 FLOW-3D HYDRO를 활용하여 Garrison 댐(미국 미주리 강)의 방수로(spillway) 해석을 수행하고, 기존 실험 데이터와 비교하여 모델의 정확성을 평가함.
연구 방법
FLOW-3D HYDRO 개요
VOF(Volume of Fluid) 기법: 자유 수면 추적을 위한 핵심 기술.
FAVOR(Fractional Area-Volume Obstacle Representation) 기법: 복잡한 지형을 효과적으로 격자화.
난류 모델링: RANS 및 LES 모델을 지원하여 다양한 난류 흐름 해석 가능.
다중 물리 모델링: 퇴적물 이동, 공기 유입, 열전달 등 복합적인 물리 현상 시뮬레이션 가능.
Garrison 댐 방수로 사례 연구
방수로 형상: 총 길이 1,444ft, 28개의 방수문(40ft × 29ft).
기존 물리 실험 데이터를 활용하여 CFD 시뮬레이션 결과 검증.
3단계 해석 접근법:
2D 단면 해석 – 방수로 크레스트의 유동 특성 분석.
단일 방수문 3D 해석 – 방수로 내 유속 및 압력 분포 해석.
전체 방수로 3D 해석 – 실제 조건과 동일한 환경에서 흐름 해석 수행.
모델 검증 및 최적화
다양한 격자 크기와 해석 조건을 비교하여 최적의 계산 효율 및 정확도를 확보.
실험 결과와의 비교를 통해 오차 범위 ±2.5~5% 이내로 유지됨.
자동화 도구(FLOW-3D X)를 활용하여 총 180개의 시뮬레이션을 반복 실행하고 최적의 설정 도출.
주요 결과
FLOW-3D HYDRO를 활용한 3D CFD 시뮬레이션은 방수로 방류량 예측에서 실험 데이터와 높은 일치도를 보였음.
방수로 압력 분포 해석: 특정 조건에서 국부적 음압(negative pressure)이 발생하여 공동현상(cavitation) 위험이 존재함을 확인.
2D/3D 결합 모델의 유용성: 방수로 상류 구간에서는 2D 천수 모델을, 크레스트 및 하류 구간에서는 3D 모델을 사용하여 계산 효율을 극대화.
계산 속도 최적화: 고성능 병렬 연산을 적용하여 8배의 연산 속도 향상을 달성.
결론 및 향후 연구
FLOW-3D HYDRO는 복잡한 수력 구조물의 유동 해석에 효과적인 도구이며, 실험 데이터와의 비교를 통해 신뢰성이 검증됨.
Garrison 댐 방수로 사례 연구를 통해 3D CFD 모델의 적용 가능성을 입증하고, 최적의 해석 절차(2D/3D 결합, 자동화 시뮬레이션, 병렬 연산 기법 등)를 제시함.
향후 연구에서는 공동현상 예측 모델 개선, 다양한 방수로 형상 적용, 장기적 퇴적물 이동 해석 등을 추가적으로 수행할 필요가 있음.
Reference
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문제 정의: 기존의 파력(Wave Energy) 변환 장치는 경제적으로 경쟁력이 부족하며, 건설 및 유지보수 비용이 높음.
목표: 기존 방파제(Breakwater) 구조를 활용하여 파력 에너지를 효율적으로 수집할 수 있는 OBREC(Overtopping Breakwater for Energy Conversion) 장치의 성능을 분석.
접근법: FLOW-3D 기반 CFD(Computational Fluid Dynamics) 시뮬레이션을 통해 실험 데이터를 검증하고, 파도 월류량(overtopping discharge)을 예측.
연구 방법
OBREC 개요 및 기존 연구
OBREC는 전통적인 방파제에 저수조(Reservoir) 를 결합하여 월류하는 파도를 저장하고, 낮은 수두(low-head) 터빈을 통해 전력을 생산하는 개념.
2012~2014년 Aalborg 대학에서 실험을 수행하여 가능성을 입증.
수치 모델링
FLOW-3D를 활용하여 RANS(Reynolds-Averaged Navier-Stokes) 방정식 및 VOF(Volume of Fluid) 기법을 사용한 자유 표면 계산 수행.
기존 실험 데이터를 바탕으로 JONSWAP 스펙트럼을 적용한 파도 환경을 구성.
격자 수렴(Mesh Convergence) 분석
7가지 메쉬 크기 비교 → 연산 비용과 정확도의 균형을 고려하여 최적의 메쉬 크기(0.005m)를 선정.
주요 결과
수치 시뮬레이션 vs 실험 데이터 비교
월류량(overtopping discharge)에 대한 시뮬레이션 결과가 실험값과 높은 일치도를 보임.
단, 수치 모델이 부드러운 방파제 표면을 가정하여 실험보다 다소 높은 월류량 예측.
수치 시뮬레이션 vs 이론 공식 비교
기존 연구(Vicinanza, 2014)에서 제안한 월류량 예측 공식과 비교 → 유사한 경향성을 보이며 검증됨.
저수조 크기(Rr)가 증가할수록 월류량이 감소하는 경향 확인.
다른 연구와의 비교
Kofoed(2002), EurOtop(2007), Van der Meer(1998) 등의 기존 월류 모델과 비교하여 일관된 결과 도출.
통계 분석 결과, 실험 대비 수치 시뮬레이션의 월류량 예측 오차는 약 6% 이내로 양호한 성능을 보임.
결론 및 향후 연구
FLOW-3D 기반 CFD 시뮬레이션이 OBREC의 초기 설계 검토에 효과적임을 입증.
실험 대비 비용이 낮고 신속한 예측이 가능, 초기 설계 최적화에 유용함.
향후 연구에서는 방파제 표면 거칠기 및 다공성(Porosity) 요소 추가 등을 통해 더욱 정밀한 모델 개선 필요.
연구의 의의
이 연구는 기존의 실험적 접근법을 CFD 시뮬레이션으로 보완하여, OBREC와 같은 파력 에너지 변환 시스템의 설계 최적화 및 경제성 향상을 위한 새로운 방향을 제시했다는 점에서 의의가 있다.
Reference
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해상풍력 발전 기초는 파랑 조건에 의해 주변 유동이 크게 교란되어 세굴(Scour) 현상이 발생할 수 있다.
기초의 안정성 확보를 위해 세굴 현상을 정확하게 예측하는 것이 필수적이다.
본 연구는 Flow-3D를 활용하여 해상풍력기초(모노파일 및 삼각대 파일) 주변의 세굴현상을 수치해석하였다.
연구 방법
모형 설정 및 입력 조건
해상풍력기초 형상: 직경이 다른 모노파일(예: D = 5.0 m, d = 1.69 m)과 동일한 직경의 모노파일, 그리고 삼각대 파일 형식을 대상으로 분석.
경계조건: 상류경계에 관측 유속(약 1.066 m/s) 및 극치파랑 조건을 적용하여 세굴현상을 평가.
난류 모형: LES 모형과 RNG 모형을 각각 적용하여 세굴 깊이 및 분포에 미치는 영향을 비교.
수치 해석 기법
Flow-3D 모형을 이용하여 3차원 유동해석을 수행.
FAVOR 기법과 VOF(Volume of Fluid) 방법을 사용해 복잡한 경계와 자유 표면을 정확히 재현.
메쉬 독립성 및 민감도 분석을 통해 계산의 신뢰성을 확보함.
주요 결과
모노파일 분석:
서로 다른 직경의 모노파일에서는 최대 세굴심이 약 4.13 m로 나타났으며, 동일한 직경의 모노파일에서는 하강류가 증가하여 최대 세굴심이 약 7.13 m로 증가함.
이는 동일 직경 모노파일에서 유속이 더욱 빨라지며, 세굴 현상이 심화됨을 시사함.
삼각대 파일 분석:
상류 경계조건으로 관측 유속과 극치파랑 조건을 각각 적용한 결과, 극치파랑 조건에서는 최대 세굴심이 약 1.3배 정도 더 깊게 발생함.
난류 모형 비교:
LES 모형을 적용한 경우, 세굴심이 일정 시간이 경과하면 평형상태에 도달함.
반면, RNG 모형은 전체 해석 영역에서 계속해서 세굴현상이 발생하여 평형상태에 도달하지 않음.
따라서 해상풍력기초 세굴 해석에는 LES 모형과 극치파랑 조건의 적용이 타당함.
결론 및 향후 연구
해상풍력기초에 대한 세굴현상 분석에서는 동일 직경 모노파일보다 서로 다른 직경의 파일 형식이 기초 안정성 측면에서 유리할 수 있음.
LES 난류 모형과 극치파랑 조건을 적용하는 것이 실제 세굴현상을 더 정확하게 예측할 수 있음을 확인함.
향후 연구에서는 다양한 해양 파랑 조건 및 추가 난류 모형 비교를 통해 보다 정밀한 세굴예측 모델을 개발할 필요가 있음.
Reference
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문제 정의: 배관 부품 제조 공정에서 중력 모래 주형을 이용한 주조는 용융 금속의 복잡한 열 전달 및 응고 과정으로 인해 결함(예: 기공, 수축 결함)이 발생할 수 있어 생산 효율과 제품 품질에 영향을 준다.
목표: CFD 기법(특히 FLOW 3D CAST v5.03)을 활용하여 실제 생산 라인과 동일한 주형 및 내부 챔버 형상을 기반으로 용융 금속의 충진, 응고 및 냉각 단계를 해석하고, 다양한 타설 온도와 러너 설계가 주조 결함에 미치는 영향을 평가하는 데 있다.
연구 방법
CFD 시뮬레이션
프로그램 및 기법: FLOW 3D CAST v5.03 사용, Volume of Fluid (VOF) 방법을 통해 용융 금속의 자유 수면을 추적.
난류 모델: 두 방정식 k–ε 모델을 채택하여 난류 효과를 반영.
모델 형상: 실제 생산 라인의 주형과 내부 챔버 형상을 그대로 반영.
주요 변수 및 조건
타설 온도: 다양한 타설 온도(예: 1329°C, 1529°C)를 적용하여 유동 속도, 응고 시간 및 결함 발생에 미치는 영향 평가.
러너 설계: 러너의 크기와 수가 용융 금속의 흐름 및 결함 위치에 어떤 영향을 미치는지 분석.
메쉬 독립성 및 시간 단계
여러 메쉬 크기를 비교하여 계산 정확도와 효율성을 확보함(예: 250,000 요소 사용).
주요 결과
충진 및 응고 해석: CFD 시뮬레이션을 통해 용융 금속이 주형 내에서 충진되는 과정과 이후 응고 및 냉각 단계가 상세하게 재현되었음.
타설 온도의 영향:
높은 타설 온도(1529°C)는 용융 금속의 유동을 빠르게 하며, 반면 응고에는 더 긴 시간이 소요됨.
낮은 타설 온도(1329°C)에서는 유동 속도가 다소 느리고, 응고 과정이 상대적으로 빠르게 진행됨.
러너 설계의 효과: 다양한 러너 각도 및 구조 변경 시도에도 불구하고, 현재 연구에서는 러너 설계가 기공 결함(캐비티) 감소에 큰 영향을 미치지 않음.
전체 공정 소요 시간: 충진, 응고, 냉각 단계 각각의 소요 시간이 계산되어 생산 공정 개선에 활용 가능함.
결론 및 향후 연구
CFD 기법은 중력 모래 주형을 이용한 배관 부품 주조 공정에서 용융 금속의 충진, 응고 및 냉각 단계를 효과적으로 해석할 수 있음을 보여준다.
타설 온도가 용융 금속 유동 및 응고 거동에 결정적인 영향을 미치며, 이로 인해 주조 결함 발생이 달라짐을 확인하였다.
향후 연구에서는 시뮬레이션 결과와 실험 데이터를 비교 검증하고, 결함 발생 원인 및 위치에 대한 추가 분석을 통해 생산 공정의 최적화를 도모할 예정이다.
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문제 정의: 데이터 집약적 애플리케이션의 증가로 인메모리 컴퓨팅에 대한 관심이 증대되었으며, 전통적인 2D 크로스바 설계는 저항 및 커패시턴스 기생 요소로 인해 성능 한계에 직면하고 있다.
목표: Boolean 함수를 3D 나노 크로스바 설계로 자동 합성하는 첫 번째 프레임워크인 FLOW-3D를 제안하여, 반둘레(semiperimeter)를 최소화하고, 면적, 에너지 소비, 지연 시간 등의 측면에서 기존 2D 도구보다 우수한 성능을 달성하는 것이 목적이다.
연구 방법
기본 아이디어 및 문제 정의
Boolean 함수의 합성을 위해 BDD(Binary Decision Diagram)와 3D 크로스바 사이의 유사성을 활용.
BDD의 노드와 에지에 해당하는 3D 크로스바의 금속 와이어와 멤리스터를 적절히 매핑하는 문제를 “L-labeling 문제”로 정의하고, 이를 ILP(정수 선형 계획법)로 최적 해결한다.
L-labeling 단계: 각 노드에 대해 할당 가능한 금속 층의 범위를 결정하고, 인접 층 간의 연결 제약(에지 제약 및 노드 제약)을 만족하도록 레이블링 수행.
크로스바 할당: 레이블링 결과를 바탕으로 실제 3D 크로스바 구조를 구성하여 Boolean 함수를 구현하는 하드웨어 디자인을 도출.
성능 평가
제안된 FLOW-3D 프레임워크는 2D 크로스바 기반의 기존 합성 도구와 비교하여, 반둘레, 면적, 에너지 소비, 지연 시간에서 각각 최대 61%, 84%, 37%, 41%의 개선 효과를 보임.
RevLib 벤치마크를 통해 실험적으로 평가되었으며, 3D 크로스바 설계의 효율성과 성능 향상을 입증하였다.
주요 결과
자동 합성 도구 제안: Boolean 함수를 3D 크로스바 설계로 자동 합성하는 최초의 프레임워크를 제안.
최적화 성능: FLOW-3D는 ILP 기반 L-labeling 문제 해결을 통해 3D 크로스바의 반둘레를 최소화하고, 면적 및 전력 소비를 현저히 감소시킴.
비교 평가: 기존 2D 기반 합성 도구 대비, 제안된 프레임워크는 에너지 효율과 응답 속도 면에서 우수한 성능을 나타냄.
결론 및 향후 연구
제안된 FLOW-3D 프레임워크는 3D 나노 크로스바를 이용한 흐름 기반 컴퓨팅에서 Boolean 함수 합성을 효율적으로 수행할 수 있음을 입증.
향후 연구에서는 더 복잡한 회로 및 대규모 데이터셋에 대한 확장성과, 다양한 하드웨어 제약 조건을 고려한 추가 최적화 기법이 연구될 필요가 있다.
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Culvert Outlet Scouring의 영향 매개변수 예측 및 최적화: FLOW-3D와 서로게이트 모델링을 활용한 연구
연구 배경
문제 정의: 박스형 수로(culvert) 출구에서 발생하는 침식(scouring)은 구조물 설계에 중요한 영향을 미친다.
목표: 침식 깊이와 위치를 예측하여 구조적 실패를 방지하고, 설계를 최적화하는 새로운 방법론을 제안한다.
접근법: 수치 모델링(FLOW-3D)과 Box-Behnken 설계 기법을 이용한 서로게이트 모델링을 결합.
연구 방법
FLOW-3D:
Reynolds 평균 Navier-Stokes 방정식을 기반으로 유체 흐름 시뮬레이션을 수행.
침식 예측을 위해 RNG 난류 모델을 사용.
Box-Behnken 설계:
세 가지 주요 변수: 유량(Flow Discharge, QQQ), 수로 기울기(Slope, SSS), 토양 입자 크기(d50d_{50}d50).
총 15개 모델을 통해 변수와 침식 깊이 및 위치 간 상호작용 분석.
민감도 분석:
각 변수의 변화가 결과(침식 깊이와 위치)에 미치는 영향을 정량화.
최적화:
침식 깊이 및 위치를 최소화하거나 최대화하기 위한 설계 변수의 조합 도출.
주요 결과
모델 성능:
침식 깊이 예측 정확도: R2=0.931R^2 = 0.931R2=0.931
침식 위치 예측 정확도: R2=0.969R^2 = 0.969R2=0.969
민감도 분석:
유량 증가: 침식 깊이와 위치에 선형적(또는 비선형적) 영향을 미침.
기울기 증가: 일정한 비선형 패턴 관찰.
토양 입자 크기 증가: 복잡하고 비선형적인 패턴 확인.
최적 설계:
침식 깊이 최소화: 유량과 토양 입자 크기를 낮게, 기울기를 높게 설정.
침식 위치 최대화: 유량, 토양 입자 크기, 기울기의 조합을 조절.
결론
FLOW-3D와 서로게이트 모델링: 침식 예측과 최적화에 효과적인 도구로 확인.
설계 최적화 가능성: 구조적 침식 문제를 예방하기 위해 설계 단계에서 주요 변수의 영향을 정밀히 평가.
향후 연구 제안: 추가적인 변수 도입 및 데이터를 통한 모델 개선.
이 논문은 수치 해석과 통계적 설계 접근법을 결합하여 수로 설계 문제를 해결하는 새로운 방법론을 제시하며, 향후 관련 연구에 중요한 기초 자료를 제공할 수 있습니다.
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날카로운 정상부를 가진 삼각형 허들(Sharp-Crested Triangular Hump) 위의 유동 특성 수치 모델링
연구 배경
문제 정의: 수리 구조물의 성능 및 수면 프로파일을 정확히 예측하는 것은 실험적으로 어렵고 비용이 많이 듦.
목표: CFD(Computational Fluid Dynamics)를 활용하여 삼각형 허들 위의 유동 특성을 보다 효율적이고 정확하게 분석.
접근법: FLOW-3D 기반 시뮬레이션을 수행하여 실험 데이터와 비교 검증.
연구 방법
삼각형 허들(Weir) 개요
위어(Weir)는 개수로에서 유량 조절과 방류 역할을 수행하는 중요한 수리 구조물.
본 연구에서는 크기가 50 cm × 30 cm × 7 cm인 Sharp-Crested Triangular Hump 모델을 사용.
수치 모델링
FLOW-3D를 사용하여 RANS(Reynolds-Averaged Navier-Stokes) 방정식과 VOF(Volume of Fluid) 방법을 적용.
FAVOR(Fractional Area-Volume Obstacle Representation) 기법을 사용하여 메쉬 내 장애물 영향을 반영.
총 1,920,000개의 격자 셀을 사용하여 시뮬레이션 수행.
실험 설정
Universiti Teknologi PETRONAS(UTP)의 수리 실험실에서 실험 수행.
30cm 폭, 60cm 높이, 10m 길이의 플룸(flume)에서 실험 진행.
4가지 유량 조건(30, 51.3, 75.3, 31 m³/h) 및 경사 조건(0, 0.006, 0.01)으로 실험 설계.
주요 결과
수치 시뮬레이션 vs 실험 데이터 비교
수치 시뮬레이션과 실험 결과 간의 차이는 4~5% 이내로 매우 높은 정확도를 보임.
수면 프로파일, 평균 유속, 프로우드 수(Froude Number) 등이 실험과 잘 일치.
유동 특성 분석
프라우드 수(Froude Number) 변화:
상류(Upstream)에서는 Froude Number < 1.0 → 서브크리티컬(Subcritical) 흐름.
하류(Downstream)에서는 Froude Number > 1.0 → 슈퍼크리티컬(Supercritical) 흐름.
유속(Flow Velocity) 변화:
하류로 갈수록 유속 증가, 삼각형 허들이 흐름을 방해하면서 압력 변화를 유발.
수심(Flow Depth) 변화:
상류에서는 높은 수심 유지, 하류에서는 급격한 감소 확인.
수치 시뮬레이션의 유용성
FLOW-3D가 삼각형 허들 및 수리 구조물의 유동 해석에 효과적임을 확인.
기존의 실험적 접근보다 비용이 낮고 신속한 설계 검토 가능.
결론 및 향후 연구
FLOW-3D 기반 CFD 시뮬레이션이 삼각형 허들의 유동 해석 및 설계 최적화에 효과적임을 검증.
실험 데이터와 비교했을 때 높은 정확도(오차 4~5%)를 나타내며, 초기 설계 검토에 유용함.
향후 연구에서는 다양한 난류 모델(k-ε, RNG, LES) 적용 및 추가적인 수리 구조물 연구가 필요.
연구의 의의
이 연구는 수리 구조물의 유동 해석을 위해 CFD 시뮬레이션을 실험적으로 검증하여, 위어 및 삼각형 허들 설계의 최적화 및 성능 예측을 위한 신뢰성 높은 방법론을 제시했다는 점에서 큰 의미가 있다.
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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
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.
수치 모델링 과정
격자 생성(Meshing): 다양한 해상도로 수치 해석을 진행.
경계 조건 설정: 유입 및 유출 조건을 설정하고 난류 모델 선택.
난류 모델 비교
K-epsilon, RNG K-epsilon, LES(Large Eddy Simulation) 모델을 비교.
RNG K-epsilon 모델이 가장 적합한 결과를 보임.
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.
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레이저 빔 형상이 용접 품질과 금속 혼합에 중요한 역할을 하며, 적절한 코어-링 직경 비율 설정이 필요.
향후 연구에서는 더 다양한 빔 형상과 용접 속도 조건을 고려하여 최적 설계 도출.
연구의 의의
이 연구는 CFD 기반 다중 물리 모델링을 활용하여 레이저 빔 형상의 금속 혼합 및 용접 품질에 미치는 영향을 체계적으로 분석하였으며, EV 배터리 제조에서 신뢰성 높은 용접 기술 개발을 위한 기초 데이터를 제공한다.
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300 gal/min 이하에서는 실험과 예측이 잘 일치, 350~500 gal/min 구간에서 약간의 오차 발생 (버블 생성이 원인으로 추정됨).
결과 및 결론
고정 메쉬 기법의 장점:
이동 및 변형형 메쉬 기법보다 효율적이며, 이동 객체 간의 거리 제한이 없음.
충돌 처리 가능.
유체와 객체의 상호작용을 보다 정밀하게 반영 가능.
실험 결과와 비교:
밸브 개폐 시뮬레이션에서 실험 결과와 높은 일치도를 보임.
고유량(>300 gal/min)에서 약간의 차이가 존재하지만, 이는 실험 조건(버블 발생 등)으로 설명 가능.
향후 연구 방향
다양한 공학적 응용(자동차, 항공, 유압 시스템 등)에 적용하여 성능 검증.
더욱 복잡한 이동 객체 및 다중 상호작용 모델 확장.
이 논문은 기존의 이동형 메쉬 기법의 한계를 극복하고, 복잡한 유체-구조 상호작용을 효율적으로 모델링할 수 있는 새로운 CFD 기법을 제안한다는 점에서 큰 의미가 있다.
Reference
C. W. Hirt and J. M. Sicilian, “A porosity technique for the definition of obstacles in rectangular Cell Meshes”, Proc. Fourth International Conf. Ship Hydro., National Academic of Science, Washington, DC, Sept. 1985.
G. Wei, “A general moving object model”, Technical Report, Flow Science Inc., 2005.
H. Goldstein, P. Charles and J. Safko, Classical Mechanics (Addison Wesley, Washington, 2002).
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Tailings dams are structures that store both tailings and water, so almost all tailings dam accidents are water related. This paper investigates a tailings dam’s failure pattern and damage development under flood conditions by conducting a 1:100 large-scale tailings dam failure model test. It also simulates the tailings dam breach discharge process based on the breach mode using FLOW-3D software, and the extent of the impact of the dam failure debris flow downstream was derived. Dam failure tests show that the form of dam failure under flood conditions is seepage failure. The damage manifests itself in the form of flowing soil, which is broadly divided into two processes: the seepage stabilization phase and the flowing soil development damage phase. The dam failure test shows that the rate of rise in the height of the dam saturation line is faster and then slower. The order of the saturation line at the dam face is second-level sub-dam, third-level sub-dam, first-level sub-dam, and fourth-level sub-dam. The final failure of the tailings dam is the production of a breach at the top of the dam due to the development of the dam’s fluid damage zone to the dam top. The simulated dam breach release results show that by the time the dam breach fluid is released at 300 s, the area of over mud has reached 95,250 square meters. Local farmland and roads were submerged, and other facilities and buildings would be damaged to varying degrees. Based on the data from these studies, targeted measures for rectifying hidden dangers and preventing dam breaks from both technical and management aspects can be proposed for tailings dams.
1. Introduction
1.1. Research Status
The mud wastewater containing tailings will be discharged after metal and non-metal mine beneficiation. Tailings slurry contains mercury, arsenic, and other heavy metal ions, both resources and pollution sources [1]. The tailings dam is a dam body formed by the accumulation and rolling of the tailings after the mine selects the useful components [2]. It is of great significance to research the dynamic stability of tailings reservoirs for mine safety production, protection of downstream life and property safety, and the surrounding environment [3]. Tailings dams, an important source of danger if an accident, are bound to people’s lives and property [4]. In 2008, a dam break accident occurred in the 980 ditch tailings pond of Shanxi Xinta Mining Co., Ltd., Yuncheng, China, resulting in 281 deaths and 33 injuries. The direct economic loss was as high as CNY 96,192,000 [5]. On the afternoon of 30 April 2006, the tailings dam of Zhen’an Gold Mine in Shaanxi Province was constructed. The accident caused 17 people to disappear, five people were injured, and 76 houses were destroyed [6,7].
In many tailings reservoir accidents, due to the lack of flood discharge capacity of flood discharge structures in the reservoir area, flood overtopping, tailings dam break, and other phenomena occur occasionally [8,9]. In this regard, scholars in related fields have performed much research and achieved certain results. Chen Zhang et al. [10] established three-dimensional and two-dimensional finite element models. The seepage field of the project under different operating conditions was simulated, and the safety factor under different operating conditions was obtained by combining the seepage field with the stable surface. The influence of the length of the dry beach and the upstream slope ratio on the seepage and stability of the tailings dam was determined. Sánchez-Peralta et al. [11] took a dry tailings pond in Colombia as the research object, studied the movement characteristics of dam break debris flow with different water contents, and obtained the relationship between the length and width of dam break debris flow movement. Changbo Du et al. [12] studied and analyzed the influence of reinforcement on tailings dam and the change law of pore water pressure and internal pressure of the dam body after mud discharge. The pore water pressure and internal earth pressure of the accumulation dam after grouting gradually increased with time. Reinforcement can greatly reduce the pore water pressure and internal pressure of reinforced dams. Gregor Petkovšek et al. [13] proposed a dam break model EMBREA-MUD to calculate the water and tailings outflow of the tailings reservoir and the corresponding break growth. Weile Geng et al. [14] conducted experimental research on the settlement deformation and mesostructure evolution of unsaturated tailings under continuous load. The results showed that the mesostructure deformation of unsaturated tailings with different moisture contents under load was the same and could be divided into four stages: pore compression, elastic deformation, structure change, and further compaction. Alan Lolaev et al. [15] developed a method to determine the tailings filtration and secondary consolidation coefficient in the process of alluvial according to the physical conditions, density, and water phreatic, and a mathematical model to calculate the consolidation time. Kun Wang et al. [16] proposed a multidisciplinary program to simulate the dam break runoff of hypothetical tailings reservoirs on the downstream complex terrain using UAV photogrammetry and smooth particle hydrodynamics (SPH) numerical method. Rawya M. Kansoh [17] studied the influence of the earth-rock dam’s structural parameters on the dam failure process. Kehui Liu et al. [18] studied the microscopic characteristics of hydraulic erosion of reinforced tailings dams and revealed the influence of different reinforcement spacing on the critical start-up speed of tailings particles. It shows that the smaller the reinforcement spacing, the greater the critical start-up speed of the reinforced tailings samples. Luca Piciullo et al. [19] proposed a regression analysis that considers the functional relationship between the release amount and the characteristics of the tailings dam, such as height and water storage (i.e., dam factor). The effects of construction type, filling material, and failure mode on the release amount were also evaluated, as well as the failure frequency of the tailings dam as a function of the construction method. Tailing dams built using upstream construction methods are more prone to failure and are more susceptible to static and dynamic liquefaction. Chunhui Ma et al. [20] pointed out that a reasonable construction schedule and flexible waterproof material are key features of impervious bodies for dams with significant deformation. When the dam deformation becomes stable, consideration should be given to secondary treatment of the impervious body to enhance dam safety. Fukumoto et al. [21] used finite element software to simulate the seepage failure process caused by seepage. Alibek Issakhov et al. [22] combined the k-ω turbulence model to study this process numerically. The VOF (volume of fluid) method was used to simulate the fluid movement behind the tailings dam during the break-up of the fluid and the riverbed landscape. Yonas B. Dibike et al. [23] A two-dimensional hydrodynamic and component transport model was used to study the effect of OS tailings release on the water quality and sediment quality of LAR by simulating sediments and related chemicals. It was concluded that the tailings release location was different; 40% to 70% of the sediments and related chemicals were deposited on the riverbed of the 160 km study section, while the remaining sediments and related chemicals left the study area in the first three days after the release event. Research conducted by Xiaofei Jing et al. [24] investigated the overflow characteristics of tailings dams reinforced with steel bars. During the overflow process, they measured dam displacements, saturation lines, and internal stresses. The study demonstrated that the erosion resistance of tailings dams significantly improves with an increase in the number of reinforcement layers. Abdellah Mahdi et al. [25] studied the potential consequences of a hypothetical oil sand tailings dam failure. For this reason, a non-Newtonian dam–dam model with a viscoplastic rheological relationship is used. The model can reproduce the flood and water level changes in downstream lakes (due to destructive waves). The simulation study of oil sand tailings overflow proves the importance of considering the non-Newtonian characteristics of tailings. Naeini et al. [26] used SIGMA/W and QUAKE/W software to analyze the high-middle line tailings dam’s dynamic response and permanent deformation and evaluated the dam’s performance. Mohammad Reza Boroomand [27] used the numerical analysis method to analyze the earth dam’s seepage under the uncertainty of geotechnical parameters and analyzed the seepage of the earth dam under the condition of uncertainty of geotechnical parameters. Sumin Li et al. [28] simulated and analyzed the hazard range, degree, and spatial state of sediment flow after the dam break and obtained the influence of sand flow velocity, flow depth, and impact on the downstream villages in the disaster area. The feasibility of the expansion and heightening of the tailings dam project was demonstrated, and the disaster risk levels of different spatial locations in the downstream villages were obtained through simulation. Through experiments, Kong et al. [29] studied the influence parameters of tailings dams under seepage. They concluded that the particle size gradation, non-uniformity coefficient, and water content of tailings sand were the main factors affecting the critical hydraulic gradient. It is concluded that the seepage failure gradient with suitable gradation, uniform particles, and suitable water content is significantly higher than that with poor gradation, uneven particles, and poor water content.
Flood overtopping and seepage failure account for 80% of the total accidents, and these two failure forms mainly occur in flood season and are closely related to water. Therefore, it is necessary to explore the tailings dam failure mode, development process, and the impact on the downstream after dam failure under flood conditions to ensure its safe operation. Based on the engineering background of a tungsten mine tailings dam in Ganzhou City, Jiangxi Province, a 1:100 physical model test was carried out to explore the dam break form and failure development process of the tailings dam under flood conditions. The FLOW-3D fluid simulation software was used to solve the influence of the tailings dam on the downstream after the dam break, and the change law of the flow area, velocity development, and submerged depth of the dam break fluid during the flood discharge process was analyzed. Finally, reasonable prevention and remediation suggestions are proposed for the hidden dangers of tailings dams.
The innovation of this paper is to determine the dam break mode and dam break position of the tailings dam under flood conditions by constructing a physical model, which provides a basis for simulating the influence of dam break on the downstream of the dam body.
1.2. Research Flowchart
Figure 1. Research flowchart.
2. Design and Construction of Large Physical Models
2.1. Overview of the Prototype Tailings Dam
The prototype tailings dam is a tungsten tailings dam located in a narrow valley running north–south in Ganzhou City, Jiangxi Province, China. The downstream of the tailings accumulation dam is farmland, dormitory buildings, mountain roads, etc., and the valleys in the downstream are relatively open. Figure 2 shows an overhead view of the prototype tailings dam. The tailings dam is built using the upstream damming method. The initial dam is a clay core wall weathering material dam located at the mouth of the northern valley. The bottom elevation is 262.0 m, the top elevation is 284.0 m, the dam height is 22 m, the upstream and downstream slope ratio is 1:2.5. The design average external slope ratio of the tailings accumulation dam is 1:5, the average slope of the tailings deposition beach is 5%, the design final tailings accumulation dam elevation is 368.00 m, the total dam height 106.00 m, with a complete storage capacity of 1550 × 104 m3 and a service life of 65 years. The present top elevation of the stacked dam is about 315 m, the height of the dam is 53 m, the accumulated storage capacity is about 559 × 104 m3, and the average external slope ratio of the stacked dam is 1:4.9. The reservoir is currently a fourth-class reservoir, with a flood protection standard of one in 200 years. At a later stage, it will be a second-class reservoir with a flood protection standard of 1000 years.
Figure 2. Top view of a tailings dam.
2.2. Selection of Model Sand
To ensure the relative reliability of the test results, the selected dam materials are properly relaxed to meet the primary conditions of similar main influencing factors. The model test focuses on the agglomeration effect of particle movement during the deformation of the dam body. For the selection of model sand, the initial dam is built with silty clay, and the accumulation dam adopts the mine prototype tailings. Figure 3 is the particle size distribution curve of the model sand. According to the particle size distribution curve, two quantitative indexes of soil particles can be determined: non-uniformity coefficient Cu and curvature coefficient Cc. Cu and Cc can jointly determine the gradation of soil. The expressions of the two are:
Figure 3. Cumulative distribution curve of particle size.
The calculated Cu and Cc of the model sand are 2.29 and 0.84, respectively. It is generally believed that the sand soil with Cu < 5 or Cc outside 1~3 belongs to the poorly graded soil, so the model sand is determined to be the poorly graded soil. If the seepage failure occurs in the dam, the development mode of seepage failure can be predicted by some parameters of the soil, that is, whether the soil is piping or flowing soil. According to the non-uniform coefficient discrimination method proposed by the former Soviet Union scholar Istomina, it is preliminarily judged that the model sand is a flowing soil-type soil.
2.3. Construction of the Dam Failure Model
The dam break process of a tailings reservoir involves many aspects, such as hydraulics, mud and sand dynamics, and soil mechanics. It involves many disciplines and is highly complex, which leads to the similarity relationship of model tests.
Therefore, we must put aside the generality of similarity and focus on the similarity of critical elements. This experiment uses the engineering background of a tungsten mine tailings dam in Jiangxi Province, China. The similarity criterion is appropriately relaxed, and the accumulation effect of particle movement during the deformation of the dam body is emphasized to construct the physical model.
Under the condition of geometric similarity, the physical model test of the 1:100 large-scale tailings dam is carried out according to the level of the second-class reservoir of the prototype tailings dam. The prototype range of the tailings dam is 1200 m × 700 m, and the model size is 12 m × 7 m. The model mainly comprises bedrock, a dam body, an observation system, and a water supply circulation system. The specific steps are as follows: According to the topographic map data provided by the mine, the three-dimensional model of the prototype tailings dam is established using Civil-3D modeling software (ver.2018) according to the size of the actual tailings dam (Figure 4). Then, several vertical sections are cut out in the model with the east–west direction as the standard line, and the points on each vertical section are taken equidistantly to extract the elevation value of each point on each vertical section. The model is intended to build a model with an elevation of 230 m in the actual terrain. The steel frame structure of the bedrock is made based on the elevation of each point on the vertical section. The square steel pipe is used as the bedrock support. Each steel pipe corresponds to the elevation of its relative point in proportion. Finally, the waterproof cloth is covered on the steel frame group and fixed to obtain a complete view of the bedrock terrain. Figure 5 is the completed mountain steel frame group, and Figure 6 is the complete bedrock after laying waterproof cloth.
Figure 4. Three-dimensional model of the tailings dam.
Figure 5. Mountain support structures.
Figure 6. A complete view of bedrock.
The initial dam is piled up with silty clay. In the process of stacking the initial dam, two PVC pipes with holes in the wall body and tightly wrapped with permeable geotextiles are symmetrically buried at the bottom of the initial dam to simulate the drainage pipe. A valve is installed at the outlet end of the two drainage pipes to control the drainage speed. The sub-dam uses the pipeline method commonly used in the mine to simulate the ore drawing. An ore drawing main pipe is introduced from the slurry pool to start the ore drawing from the model’s right side, and a valve is set in the main pipe to control the flow rate of the square ore. When the pulp flows into the tailings pond, the tailings will be layered and precipitated under hydraulic screening. After precipitation, the ore is suspended when the tailings reach the target dam height. Start to build the next sub-dam, use the layered filling method to build the dam body to the design elevation, and use the vertical line method to control the elevation when building the dam. (Figure 7) is the construction of the second sub-dam. Four pore water pressure gauges are buried in the dam construction process to monitor the position of the saturation line of the dam body. The four pore water pressure gauges’ positions are arranged along the dam body’s central axis. They are located directly below the dam crest of the first-, second-, third-, and fourth-level accumulation dams. They are named as site 1, site 2, site 3, and site 4 (Figure 8).
Figure 7. Second-stage sub-dam stacking.
Figure 8. Buried pore water pressure gauges.
Due to the need to supply a large amount of water for the test, a water tower was placed on the site (Figure 9), and a return water collection system was designed to achieve a water supply cycle (Figure 10). The observation equipment of the test (Figure 11) uses a trinocular camera and a high-definition camera to record the dam break process of the tailings dam.
Figure 9. Water tower.
Figure 10. Water supply circulation system.
Figure 11. Experimental observation system.
3. Tailings Dam Break Model Experiment
The dam failure mode under specific flood conditions is characterized by permeation damage, manifested as soil erosion. Through analysis of experimental phenomena and data, the development process of dam failure is elucidated, revealing the variation patterns of pore water pressure at different locations and the saturation line of the dam body.
3.1. Dam Failure Experiment
The test was carried out by intermittently injecting water into the reservoir to simulate flood conditions, keeping the flow rate stable during the injection, and keeping the drainage pipe open during the whole test. The beginning of the water injection was taken as the beginning of the test, and the entire dam break test lasted 448 min. It can be roughly divided into two stages, each accounting for one-half of the total length. Figure 12 shows a typical picture of the damage to the dam during the test. Figure 13 shows a timeline of the test damage development. The specific tailings dam damage development process is as follows:
Figure 12. Dam failure model tests.
Figure 13. Timeline of the development of the flowing soil destruction.
The first stage is seepage stabilization: the overflow water is clear, the dam’s surface is stable, and there is no movement of particles. At 138 min of the test, the contact zone between the right end of the second sub-dam and the bedrock began to seep first (Figure 12a). The seepage water flows along the contact zone between the dam body and the bedrock and overflows down the dam face. There are two reasons for the seepage here. The first is fine cracks in the contact area between the soil and the bedrock, which provides a breakthrough for the seepage water. The second is based on calculating the data collected by the pore water pressure gauge. It can be seen that the saturation line at this time escapes on the slope of the second sub-dam, where the dam surface overflows. Subsequently, the second-stage sub-dam continued to seep, and the overflow area gradually expanded and merged with the second-stage sub-dam dam surface. At 174 min, the third-stage sub-dam began to overflow on the left side (Figure 12b). At this time, according to the collected data, it can be calculated that the buried depth of the saturation line has been exposed to the third-level sub-dam. At 190 min, the first sub-dam also overflowed (Figure 12c). Then, the sand boiling point appears at the right end of the first-stage sub-dam, and the soil particles fluctuate obviously with the overflow water. The sand boiling causes the soil particles to be continuously taken out of the soil body. At 203 min, the dam surfaces of the first, second, and third sub-dams have all become swampy. The second stage is the development and failure stage of the flowing soil: seepage deformation occurs continuously, and more earthwork is lost. At 236 min, the first flow soil damage happened at the right end of the second sub-dam (Figure 12d). The failure form is flow slip. At 239 min, a second flow soil damage occurred on the left side of the first sub-dam (Figure 12e). The flow-slipping soil will form a pit that evolves into a breach, making the seepage velocity and seepage flow faster and larger. Then, the pit part of the soil slides, and the seepage water erodes the downstream dam surface. At 248 min, two erosion ditches have been formed in the flow soil failure area on both sides of the dam (Figure 12f,g). The erosion gully on the left side is located at the junction of the right side of the first-order sub-dam and the bedrock. The critical hydraulic gradient is lower, the dominant flow develops more rapidly, the sand is wrapped violently, and the subsequent seepage damage is more likely to occur. The erosion gully produces more water flow to scour multiple branches on the dam’s surface. The right erosion ditch is located at the junction of the secondary dam and the bedrock. At this time, the erosion ditch has developed to a certain depth, and the sand boiling point has reached 6. The flowing soil migrates downward under the action of overflow water. The flowing water will bring the fine particles to the downstream area. The coarse particles will be accumulated to form a ‘filter layer‘ to block the overflow water channel. The seepage pressure on both sides of the filter layer gradually increases. A new seepage channel will be formed when the seepage pressure on one side reaches the critical value. At 292 min, the flow soil damage eroded to the third sub-dam and further developed upstream along the boundary. Part of the erosion gully’s inner wall soil is washed away underwater, and the internal wall forms holes and expands upward until the upper part forms a suspended surface. When the shear strength of the upper soil is greater than the shear strength of the soil, it will collapse and continue to repeat the next round of erosion. At this time, the left-flowing soil does not develop to the upstream failure but to the proper lateral erosion, and the right side flushes out a new channel due to the obstruction of the ‘filter layer‘. At 303 min, the third flow soil failure occurred on the left side of the third sub-dam (Figure 12h). Because of the increase in overflow water and the acceleration of water flow, the right scouring area opens the downstream channel at the particle deposition, and fine particles are continuously taken out of the dam by seepage water. The overflow water also washes away the ‘filter layer‘ on the left side. After that, the first sub-dam eroded to the deep, and the dam surface failure area did not expand. There is a hydraulic–gravity erosion cycle in the flow soil damage area of the second-stage sub-dam, which extends to the upstream and the middle of the dam body. With the increase in the erosion damage area of the water flow, the more the sand boiling point, the faster the seepage damage, and the erosion area of the lower section continues to expand, and the water flow in the erosion gully is large and fast. The flowing soil failure zone of the third-stage sub-dam has not yet formed a penetrating failure path and is in the initial stage of erosion. At 348 min, the fourth-stage sub-dam overflowed (Figure 12i). At 448 min, the flow soil was eroded to the fourth sub-dam (Figure 12j). The flow soil damage area is eroded to the fourth sub-dam, which is regarded as the whole dam damage. It is measured that the depth of the collapse area is about 12 cm, and the width is about 80 cm. It should be noted that although the dam body has undergone a large area of seepage failure, the dam body has not yet experienced an unstable landslide. The tailings dam finally broke because the dam body soil damage zone developed to the top of the dam to produce a breach.
3.2. The Change Rule of the Saturation Line
Figure 14 is about the change curve of the saturation line. At the beginning of the test, as the upstream water level rose, the saturation line rose rapidly despite the drain being in a normal discharge condition. After the lifting of the head has ceased, the rate of the upward lifting of the saturation line becomes significantly slower due to the hysteresis effect. Then, a certain depth of burial is maintained. In the middle and late stages of the test, most of the dam had become saturated, and the soil matrix suction had weakened. When water is again stored in the reservoir, the saturation line will again lift, but at a reduced rate compared to the initial period. If the reservoir level is no longer raised, the saturation line tends to fall after a period of time. By approximately 270 min into the test, the dam face had already developed a certain size of the flow damage zone, and it was no longer meaningful to discuss the depth of the saturation line.
Figure 14. Variation curve of saturation line.
In the previous study [30], a two-dimensional finite element model of the tailings dam, chosen from the central axis of the three-dimensional tailings dam model, was used to analyze the distribution of saturation line in the tailings dam under flood conditions. The numerical simulation results show that when the upstream water head rose to 125 m (Figure 15), the saturation line intersected with the first and fourth-level accumulation dams and was exposed throughout the dam surface. The variation law of the saturation line obtained by the numerical simulation is consistent with the experimental phenomenon; that is, the saturation line increases with the rise of the reservoir water level, and the order of the dam surface exposure is the second-stage sub-dam, the third-stage sub-dam, the first-stage sub-dam, and the fourth-stage sub-dam. According to the simulation results, the displacement of the dam body does not change greatly, and the plastic strain zone does not appear on the slope and crest of the dam body, and there is no penetration. It can be judged that the tailings dam model does not have deep slip when the water level is about to overflow; that is, the skeleton structure of the dam body is stable. Combined with the physical model test, before the saturation line of the dam body reaches the dam surface of the fourth-level sub-dam, the tailings dam has undergone seepage failure, but the dam body has not undergone structural instability. The results of numerical simulation are consistent with the phenomenon of physical model test. After that, with the development of flowing soil, the damaged area of the dam body continues to extend to the top of the dam, which will eventually cause the breach of the dam top and cause the flood discharge of the dam.
Figure 15. Saturation line distribution of the tailings dam under 125 m water level.
4. Impact Analysis after Dam Break and Prevention Suggestions
Based on the results of the physical model experiment, it can be inferred that the tailings dam failure was triggered by seepage failure. This means the area of flowing soil gradually eroded upstream until a breach was created at the top of the dam, and the reservoir fluid poured downstream. Therefore, an erosion damage trench was set up on the model for the dam breach calculation in FLOW-3D (ver. 9.3), extending from the top of the initial dam to the top of the dam, and the shape was simplified to a semi-cylinder. Figure 16 shows a model of the tailings dam after completion of the pre-treatment.
Figure 16. FLOW-3D 3D calculation model.
4.1. Dam Failure Test Results
An overview of the area downstream of the tailings dam is shown in Figure 17. The downstream area is dominated by the production facilities (red and yellow line areas in the figure), staff accommodation buildings (pink line area), the road around the mountain (blue curve), villages (green line area), and scattered agricultural land.
Figure 17. Aerial view downstream of tailings dam.
4.1.1. Overflow Area
Figure 18 shows the change in the extent of fluid inundation at 60 s, 120 s, 180 s, 240 s, and 300 s as calculated by the software, with the fluid in blue in the figure. As can be seen from the diagram, the breached fluid was rapidly released downstream in a short period and, by 300 s, covered the entire flat area downstream, with an overflow area of approximately 95,250,000 square meters. Farmland and roads in the area will be flooded, and production facilities and residential buildings will also be affected. In addition, emergency escape plans can be challenging to implement successfully at short notice. It is thus clear that in the event of a breach of this tailings dam, it would be a major accidental disaster.
Figure 18. Time-course diagram of mud area.
4.1.2. Flooding Depth
Figure 19 shows a cloud of the distribution of flooding depth at 60 s, 120 s, 180 s, 240 s, and 300 s. Due to the lower topography in the eastern part of the downstream area, the fluids that wash down first collect in the east and then spread westwards. As can be seen from the graph, the maximum inundation depth is always located in the eastern part of the lower reaches near the initial dam. The mudslide did not affect the northern area due to the terrain’s advantage; when the situation was urgent, people could be evacuated along the northwest-facing road to the north.
Figure 19. Cloud map of flooding depth.
4.1.3. Flow Rate Analysis
The flow velocity during the release process reflects the magnitude of the fluid impact. Figure 20 shows the flow velocity clouds during the dam breach release process at 60 s, 120 s, 180 s, 240 s, and 300 s. Due to inertia, the fluid emerges from the breach. It rapidly completes the transformation from potential energy to kinetic energy in the trench eroded by the flowing soil, with the flow velocity reaching a maximum. In addition, there is some leakage around the dam at the junction of the tailings dam and the mountain. After the fluid is flushed off the tailings dam, the average flow velocity decreases due to the diffusion principle and frictional forces. In general, the flow of emissions increases and then falls.
Figure 20. Cloud map of flow rate.
Three points, A, B, and C, are selected in the flow direction of the release to analyze the fluid’s flow velocity characteristics, specifically during the dam failure process. The three points are located at the top of the initial dam, the foot of the initial dam, and the downstream area adjacent to the tailings dam (Figure 21). Figure 22 shows the variation in flow rate over time at three points. Overall, the flow velocities at points A, B, and C are successively reduced as the flow path develops. From the point of view of the flow velocity at a single point, it does not increase to a peak all at once but has an undulating, phased variation. At about 30 s, the overflow velocity starts to appear at the three points, after which the trend is a cyclic process of “increase-smooth or decrease” because the increase in flow velocity does not coincide with the expansion of the breach, which, in turn, determines the flow velocity of the discharge. The flow rate increases accordingly when the breach expands and becomes deeper again. After several cycles of this until the breach is no longer extended, the flow rate at points A, B, and C all fall during the last 30 s of the figures and will return to zero as the flooding stops.
Figure 21. Flow rate reference points.
Figure 22. Flow rate time history diagram.
The analysis of the variation in the flow rate of the release shows that the debris flow impacts downstream in a segmented manner. Therefore, the decrease in flow velocity should not be regarded as the end of the entire dam break, nor should blindly carry out the aftermath of the accident at this stage, but should wait for a longer period to observe and confirm so as not to cause more damage.
4.2. Recommendations for Prevention and Management
4.2.1. Technical Measures
Dam surface treatment: According to the seepage characteristics of the tailings dam, to prevent overflow water and rainwater from scouring the shoulder and face of the dam and to collect the seepage water, a shoulder drainage ditch should be installed along the junction of the dam with the slopes of the two banks, and a face drainage ditch should be installed on the face of the dam. Moreover, the downstream slope of the dam can be mulched, turfed, and, if necessary, reinforced by stone pitching at the foot of the dam.
Additional seepage facilities: Combined with the model test results, it is clear that control of the saturation line of the tailings dam should be a top priority for safety management. To effectively control the depth of the saturation line, additional drainage facilities can be provided in the form of a combined horizontal drainage pipe and a vertical shaft connected to the end of the horizontal drainage pipe. In addition, the vertical drainage pipe should be raised with the height of the stockpile dam and pumped out periodically.
4.2.2. Management Measures
Routine inspection and maintenance: Besides monitoring various safety indicators such as the tailings dam saturation line and dry beach length, the person responsible for safety should regularly inspect the dam body for cracks, collapses, and surface erosion. They should also ensure that the slope protection is intact and that the drainage facilities are clear of blockages, siltation, or waterlogging. Check for seepage, pipe surges, or flowing soil, focusing on the junction between the dam and the hills on either side, and be vigilant for changes in seepage flow and turbidity. If a potential problem is identified, the cause must be immediately determined, and remedial action must be taken to prevent it.
Ensure excellence in flood management, including pre-flood preparation, response during flooding, and post-flood rescue work.
5. Conclusions
The reservoir’s water level had not yet crested before the dam was damaged. In other words, the cause of dam failure under flood conditions is seepage failure, which manifests itself in the form of flowing soil. Before the flow soil is destroyed, the dam surface will produce overflow, water accumulation, sand boiling, and other phenomena. The phenomenon of the dam failure test shows that the flow soil damage starts at the weak point of the dam at the junction with the bedrock. These areas have a high saturation gradient and are more prone to local damage. In the early stage of soil flow failure, multiple sand boiling points were generated on the dam surface. With the development of seepage, collapsible cracks appeared on the dam surface one after another, forming erosion ditches. In the middle stage of soil failure, the failure area is widened. The soil cycle undergoes the process of erosion–gravity erosion, and the ‘filter layer’ will slow down the failure rate to a certain extent. In the later stage of flow soil damage, the flow water damage area began to penetrate, and the erosion intensified until the whole dam body was damaged. Therefore, when the sand boiling point is generated, and the collapsible cracks appear on the dam surface, these can be used as a warning sign of seepage failure.
The buried depth of the saturation line becomes shallow with the increase in the upstream water head. And, the rate of increase is first fast and then slow. After the lifting head is stopped, the saturation line will still rise slightly for a period of time due to the lag effect. If the reservoir water level is not replenished for a long time, the saturation line will be reduced under normal drainage. The order of the saturation line escaping from the dam surface is the second sub-dam, the third sub-dam, the first sub-dam, and the fourth sub-dam. It can be seen that before the flood, it is necessary to check and repair the drainage facilities to ensure their suitable operation. During the flood season, all measures should be taken to enhance the flood discharge, reduce the saturation line, and avoid the seepage damage of the tailings dam.
The results of the FLOW-3D hydrodynamic simulation software show that the breach fluid was rapidly discharged within a short period, covering the entire flat area downstream by 300 s. The local farmland and roads were submerged, and the rest of the construction facilities were also damaged to a certain extent. Therefore, it will be a major disaster once the tailings dam breaks. The rapid development of the dam breach mudslide and the short release time make it impractical to organize the evacuation of people when the release occurs. Therefore, in combination with the mechanism of tailings dam failure, targeted measures for potential remediation and dam failure prevention can be proposed from both technical and management aspects.
The innovation point is to use a large-scale physical model test to study the dam break mode of tailings dam under flood conditions. By monitoring the internal changes of the tailings reservoir under flood conditions, the stage of seepage failure of the dam body can be judged, which can serve as an early warning for the subsequent break of the tailings dam. The experimental process and experimental results of the model can provide a reference for the changes in tailings reservoir under flood conditions under real working conditions so as to correspond to the changes of tailings reservoir fluid under flood conditions under real working conditions. Provide guidance for staff to monitor changes in tailings ponds. The determination of dam break position and dam break mode by model test provides a basis for simulating the influence of tailings dam break on the downstream. The use of a steel frame structure to build a tailings dam model can cover the entire tailings dam terrain more comprehensively and economically and can more comprehensively analyze the entire dam break process of the tailings dam. Compared with the local tailings dam similarity simulation and on-site exploration, it is more profound and comprehensive, which has practical significance for the safety of the tailings reservoir. The defect is that there is a prototype of the model, and it cannot be used for all tailings mines. The actual situation needs to be analyzed in detail. In addition, according to the tailings pond model test, it can be expected that the tailings pond model can be used to study the useful mineral components in the recovery reservoir, which has practical significance for environmental protection and resource recovery.
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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.
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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 models
Approach
Developer
FLOW-3D HYDRO
This CFD package solves Navier–Stokes equations using finite-difference and finite volume approximations, along with Volume of Fluid (VOF) method for tracking the free surface
Flow Science, Inc. (https://www.flow3d.com/)
MIKE 21
This model is based on the numerical solution of 2D and 3D incompressible RANS equations subject to the assumptions of Boussinesq and hydrostatic pressure
Danish 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 equations
IHCantabria research institute (https://ihfoam.ihcantabria.com/)
NHWAVE
NHWAVE is a 3D shock-capturing non-Hydrostatic model which solves the incompressible Navier–Stokes equations in terrain and surface-following sigma coordinates
Kirby et al. (2022) (https://sites.google.com/site/gangfma/nhwave, https://github.com/JimKirby/NHWAVE)
GLOBOUSS
GloBouss is a depth-averaged model based on the standard Boussinesq equations including higher order dispersion terms, Coriolis terms, and numerical hydrostatic correction terms
Løvholt et al. (2022) (https://www.duo.uio.no/handle/10852/10184)
BOUSSCLAW
BoussClaw 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 equations
Clawpack Development Team (http://www.clawpack.org/)Kim et al. (2017)
THETIS-MUI
THETIS 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 method
TREFLE department of the I2M Laboratory at Bordeaux, France (https://www.i2m.u-bordeaux.fr/en)
LS3D
A 2D depth-integrated numerical model which applies a fourth-order Boussinesq approximation for an arbitrary time-variable bottom boundary
Ataie-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 slopes
A simplified 3D Navier–Stokes model for two fluids (water and landslide material) using VOF for tracking of water surface
Horrillo 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 Coordinates
Liu et al. (1998); Wang and Liu (2006)
TWO-LAYER
A 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 fluids
Imamura 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, unit
Value/type
Slide width (bs), m
0.26
Slide length (ls), m
0.20
Slide thickness (s), m
0.10
Slide volume (V), m3
2.60 × 10–3
Specific gravity, (γs)
2.60
Slide weight (ms), kg
6.86
Slide impact velocity (vs), m/s
1.84
Slide Froude number (Fr)
1.18
Material
Concrete
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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In this study, experimental investigations were conducted on rectangular side weirs with different widths and heights. Corresponding simulations were also performed to analyze hydraulic characteristics including the water surface profile, flow velocity, and pressure. The relationship between the discharge coefficient and the Froude number, as well as the ratios of the side weir height and width to upstream water depth, was determined. A discharge formula was derived based on a dimensional analysis. The results demonstrated good agreement between simulated and experimental data, indicating the reliability of numerical simulations using FLOW-3D software (version 11.1). Notably, significant fluctuations in water surface profiles near the side weir were observed compared to those along the center line or away from the side weir in the main channel, suggesting that the entrance effect of the side weir did not propagate towards the center line of the main channel. The proposed discharge formula exhibited relative errors within 10%, thereby satisfying the flow measurement requirements for small channels and field inlets.
1. Introduction
Sharp crested weirs are used to obtain discharge in open channels by solely measuring the water head upstream of the water. Side weirs, as a kind of sharp-crested weir, are extensively used for flow measurement, flow diversion, and flow regulation in open channels. Side weirs can be placed directly in the channel direction or field inlet, without changing the original structure of the channel. Thus, side weirs have certain advantages in the promotion and application of flow measurement facilities in small channels and field inlets. The rectangular sharp-crested weir is the most commonly available, and many scholars have conducted research on it. Research on side weirs started in 1934. De Marchi studied the side weir in the rectangular channel and derived the theoretical formula based on the assumption that the specific energy of the main flow section of the rectangular channel in the side weir section was constant [1]. Ackers discussed the existing formulas for the prediction of the side weir discharge coefficient [2]. Chen concluded that the momentum theorem was more suitable for the analytical calculation of the side weir based on the experimental data [3]. Based on previous theoretical research, more and more scholars began to carry out experimental research on side weirs. Uyumaz and Muslu conducted experiments under subcritical and supercritical flow regimes and derived expressions for the side weir discharge and water surface profiles for these regimes by comparing them with experimental results [4]. Borghei et al. developed a discharge coefficient equation for rectangular side weirs in subcritical flow [5]. Ghodsian [6] and Durga and Pillai [7] developed a discharge coefficient equation of rectangular side weirs in supercritical flow. Mohamed proposed a new approach based on the video monitoring concept to measure the free surface of flow over rectangular side weirs [8]. Durga conducted experiments on rectangular side weirs of different lengths and sill heights and discussed the application of momentum and energy principles to the analysis of spatially varied flow under supercritical conditions. The results showed that the momentum principle was fitting better [7]. Omer et al. obtained sharp-crested rectangular side weirs discharge coefficients in the straight channel by using an artificial neural network model for a total of 843 experiments [9]. Emiroglu et al. studied water surface profile and surface velocity streamlines, and developed a discharge coefficient formula of the upstream Froude number, the ratios of weir length to channel width, weir length to flow depth, and weir height to flow depth [10]. Other investigators [11,12,13,14] have conducted experiments to study flow over rectangular side weirs in different flow conditions. Numerous studies have been conducted in laboratories to this day. Compared to experimental methods, the numerical simulation method has many attractive advantages. We can easily obtain a wide range of hydraulic parameters of side weirs using numerical simulation methods, without investing a lot of manpower and resources. In addition, we can conduct small changes in inlet condition, outlet condition, and geometric parameters, and study their impact on the flow characteristics of side weirs. Therefore, with the development and improvement of computational fluid dynamics, the numerical simulation method has begun to be widely applied on side weirs. Salimi et al. studied the free surface changes and the velocity field along a side weir located on a circular channel in the supercritical regime by numerical simulation [15]. Samadi et al. conducted a three-dimensional simulation on rectangular sharp-crested weirs with side contraction and without side contraction and verified the accuracy of numerical simulation compared with the experimental results [16]. Aydin investigated the effect of the sill on rectangular side weir flow by using a three-dimensional computational fluid dynamics model [17]. Azimi et al. studied the discharge coefficient of rectangular side weirs on circular channels in a supercritical flow regime using numerical simulation and experiments [18]. The discharge coefficient over the two compound side weirs (Rectangular and Semi-Circle) was modeled by using the FLOW-3D software to describe the flow characteristics in subcritical flow conditions [19]. Safarzadeh and Noroozi compared the hydraulics and 3D flow features of the ordinary rectangular and trapezoidal plan view piano key weirs (PKWs) using two-phase RANS numerical simulations [20]. Tarek et al. investigated the discharge performance, flow characteristics, and energy dissipation over PK and TL weirs under free-flow conditions using the FLOW-3D software [21]. As evident from the aforementioned, the majority of studies have primarily focused on determining the discharge coefficient, while comparatively less attention has been devoted to investigating the hydraulic characteristics of rectangular side weirs. Numerical simulations were conducted on different types of side weirs, including compound side weirs and piano key weirs, in different cross-section channels under different flow regimes. It is imperative to derive the discharge formula and investigate other crucial flow parameters such as depth, velocity, and pressure near side weirs for their effective implementation in water measurement. In this study, a combination of experimental and numerical simulation methods was employed to examine the relationship between the discharge coefficient and its influencing factors; furthermore, a dimensionless analysis was utilized to derive the discharge formula. Additionally, water surface profiles near side weirs and pressure distribution at the bottom of the side channel were analyzed to assess safety operation issues associated with installing side weirs.
2. Principle of Flow Measurement
Flow discharge over side weirs is a function of different dominant physical and geometrical quantities, which is defined as
where Q is flow discharge over the side weir, b is the side weir width, B is the channel width, P is the side weir height, v is the mean velocity, h1 is water depth upstream the side weir in the main channel, g is the gravitational acceleration, μ is the dynamic viscosity of fluid, ρ is fluid density, and i is the channel slope (Figure 1).
Figure 1. Definition sketch of parameters of rectangular side weir under subcritical flow. Note: h1 and h2 represent water depth upstream and downstream of the side weir in the main channel, respectively; y1 and y2 represent weir head upstream and downstream of the side weir in the main channel, respectively.
In experiments when the upstream weir head was over 30 mm, the effects of surface tension on discharge were found to be minor [22]. The viscosity effect was far less than the gravity effect in a turbulent flow. Hence μ and σ were excluded from the analysis [23,24]. In addition, the channel width, the channel slope, and the fluid density were all constant, so the discharge formula can be simplified as:
According to the Buckingham π theorem, the following relationship among the dimensionless parameters is established:
Selected h1 and g as basic fundamental quantities, and the remaining physical quantities were represented in terms of these fundamental quantities as follows:
In which
Based on dimensional analysis, the following equations were derived.
Namely
So the discharge formula can be simplified as:
In a sharp-crested weir, discharge over the weir is proportional to 𝐻1.51H11.5 (H1 is the upstream total head above the crest, namely H1 = y1 + v2/2 g), so Equation (6) can be transformed as follows:
Consequently, the discharge formula over rectangular side weirs is defined as follows, in which 𝑚=𝑓(𝑏ℎ1m=f(bh1,𝑃ℎ1,𝐹𝑟1)Ph1,Fr1). Parameter m represents the dimensionless discharge coefficient. Parameter Fr1 represents the Froude number at the upstream end of the side weir in the main channel.
3. Experiment Setup
The experimental setup contained a storage reservoir, a pumping station, an electromagnetic flow meter, a control valve, a stabilization pond, rectangular channels, a side weir, and a sluice gate. The layout of the experimental setup is shown in Figure 2. Water was supplied from the storage reservoir using a pump. The flow discharge was measured with an electromagnetic flow meter with precision of ±3‰. Water depth was measured with a point gauge with an accuracy of ±0.1 mm. The flow velocity was measured with a 3D Acoustic Doppler Velocimeter (Nortek Vectrino, manufactured by Nortek AS in Rud, Norway). In order to eliminate accidental and human error, multiple measurements of the water depth and flow velocity at the same point were performed and the average values were used as the actual water depth and flow velocity of the point. The main and side channels were both rectangular open channels measuring 47 cm in width and 60 cm in height. The geometrical parameters of rectangular side weirs are shown in Table 1.
Figure 2. Layout of the test system.
Table 1. The geometrical parameters of rectangular side weirs.
When water passes through a side weir, its quality point is affected not only by gravity but also by centrifugal inertia force, leading to an inclined water surface within that particular cross-section before reaching the weir. In order to examine water profiles adjacent to side weirs, cross-sectional measurements were conducted at regular intervals of 12 cm both upstream and downstream of each side weir, denoted as sections ① to ⑩, respectively. Measuring points were positioned near the side weir (referred to as “Side I”), along the center line of the main channel (referred to as “Side II”), and far away from the side weir (referred to as “Side III”) for each cross-section. The schematic diagram illustrating these measuring points is presented in Figure 3.
Figure 3. Schematic diagram of measurement points.
4. Numerical Simulation Settings
4.1. Mathematical Model
4.1.1. Governing Equations
Establishing the controlling equations is a prerequisite for solving any problem. For the flow analysis problem of water flowing over a side weir in a rectangular channel, assuming that no heat exchange occurs, the continuity equation (Equation (9)) and momentum equation (Equation (10)) can be used as the controlling equations as follows:
The continuity equation:
Momentum equation:
where: ρ is the fluid density, kg/m3; t is time, s; ui, uj are average flow velocities, u1, u2, u3 represent average flow velocity components in Cartesian coordinates x, y, and z, respectively, m/s; μ is dynamic viscosity of fluid, N·s/m2; p is the pressure, pa; Si is the body force, S1 = 0, S2 = 0, S3 = −ρg, N [24].
4.1.2. RNG k-ε Model
The water flow in the main channel is subcritical flow. When the water flows through the side weir, the flow line deviates sharply, the cross section suddenly decreases, and due to the blocking effect of the side weir, the water reflects and diffracts, resulting in strong changes in the water surface and obvious three-dimensional characteristics of the water flow [25]. Therefore the RNG k–ε model is selected. The model can better handle flows with greater streamline curvature, and its corresponding k and ε equation is, respectively, as follows:
where: k is the turbulent kinetic energy, m2/s2; μeff is the effective hydrodynamic viscous coefficient; Gk is the generation item of turbulent kinetic energy k due to gradient of the average flow velocity; C∗1εC1ε*, C2ε are empirical constants of 1.42 and 1.68, respectively; ε is turbulence dissipation rate, kg·m2/s2.
4.1.3. TruVOF Model
Because the shape of the free surface is very complex and the overall position is constantly changing, the fluid flow phenomenon with a free surface is a typical flow phenomenon that is difficult to simulate. The current methods used to simulate free surfaces mainly include elevation function method, the MAC method [26] and the VOF (Volume of Fluid) method [27]. The VOF method is a method proposed by Hirt and Nichols to deal with the complex motion of the free surface of a fluid, which can describe all the complexities of the free surface with only one function. The basic idea of the method is to define functions αw and αa, which represent the volume percentage of the calculation area occupied by water and air, respectively. In each unit cell, the sum of the volume fractions of water and air is equal to 1, i.e.,
The TruVOF calculation method can accurately track the change of free liquid level and accurately simulate the flow problems with free interface. Its equation is:
where: u_¯m is the average velocity of the mixture; t is the time; F is the volume fraction of the required fluid.
4.2. Parameter Setting and Boundary Conditions
To streamline the iterative calculation and minimize simulation time, we selected a main channel measuring 7.5 m in length and a side channel measuring 2.5 m in length for simulation. Three-dimensional geometrical models were developed using the software AutoCAD (version 2016-Simplified Chinese). The spatial domain was meshed using a constructed rectangular hexahedral mesh and each cell size was 2 cm. A volume flow rate was set in the channel inlet with an auto-adjusted fluid height. An outflow–outlet condition was positioned at the end of the side channel. A symmetry boundary condition was set in the air inlet at the top of the model, which represented that no fluid flows through the boundary. The lower Z (Zmin) and both of the side boundaries were treated as a rigid wall (W). No-slip conditions were applied at the wall boundaries. Figure 4 illustrates these boundary conditions.
Figure 4. Diagram of boundary conditions.
5. Results
5.1. Water Surface Profiles
Water surface profiles were crucial parameters for selecting water-measuring devices. Upon analyzing the consistent patterns observed in different conditions, one specific condition was chosen for further analysis. To validate the reliability of numerical simulation, measured and simulated water depths of rectangular side weirs with different widths and heights at a discharge rate of 25 L/s were extracted for comparison (Table 2 and Figure 5). The results in Table 2 and Figure 5 indicate a maximum absolute relative error value of 9.97% and all absolute relative error values within 10%, demonstrating satisfactory agreement between experimental and simulated results.
Figure 5. Comparison between measured and simulated flow depth.
P/cm
Section Position
b = 20 cm
b = 30 cm
b = 40 cm
b = 47 cm
hm/cm
hs/cm
R/%
hm/cm
hs/cm
R/%
hm/cm
hs/cm
R/%
hm/cm
hs/cm
R/%
7
④
21.49
19.4
9.73
17.74
16.9
4.74
16.07
14.51
9.71
13.79
12.50
9.35
④′
20.48
19.05
6.98
17.78
16.14
9.22
15.69
14.31
8.80
⑥
20.71
19.02
8.16
17.82
16.31
8.47
15.92
14.53
8.73
15.23
13.80
9.39
⑧′
22.00
20.22
8.09
18.27
16.74
8.37
16.59
14.96
9.83
⑧
22.37
20.17
9.83
17.73
16.80
5.25
16.27
15.08
7.31
15.36
14.36
6.51
10
④
24.15
22.6
6.42
19.96
18.84
5.61
19.03
18.58
2.36
16.83
15.85
5.82
④′
24.21
22.05
8.92
19.49
18.19
6.67
18.75
18.35
2.13
⑥
24.01
21.78
9.29
19.65
18.34
6.67
18.95
18.63
1.69
17.52
16.09
8.16
⑧′
24.88
22.4
9.97
20.65
19.21
6.97
20.12
19.29
4.13
⑧
24.03
22.96
4.45
21.16
19.34
8.60
19.71
19.43
1.42
18.39
17.36
5.60
15
④
28.85
27.56
4.47
25.86
24.09
6.84
24.05
21.89
8.98
22.73
20.80
8.49
④′
28.49
26.97
5.34
25.19
23.84
5.36
23.42
21.46
8.37
⑥
28.85
26.98
6.48
25.72
23.99
6.73
23.23
21.82
6.07
23.10
21.05
8.87
⑧′
28.96
27.30
5.73
26.38
24.19
8.30
24.18
22.27
7.90
⑧
29.18
27.96
4.18
26.57
24.54
7.64
24.57
22.33
9.12
23.20
21.10
9.05
20
④
33.29
32.34
2.85
30.63
29.02
5.26
28.49
26.87
5.69
26.99
25.81
4.37
④′
33.14
31.95
3.59
29.75
28.62
3.80
28.11
26.79
4.70
⑥
33.32
31.79
4.59
30.04
28.45
5.29
28.99
26.86
7.35
27.42
26.72
2.55
⑧′
34.02
32.39
4.79
30.69
28.95
5.67
29.59
27.25
7.91
⑧
34.62
32.84
5.14
31.44
29.29
6.84
29.51
27.31
7.46
28.21
27.00
4.29
Table 2. Comparison of measured and simulated water depths on Side I of each side weir at a discharge of 25 L/s
Due to the diversion caused by the side weir, there was a rapid variation in flow near the side weir in the main channel. In order to investigate the impact of the side weir on water flow in the main channel, water surface profiles on Side I, Side II, and Side III were plotted with a side weir width and height both set at 20 cm at a discharge rate of 25 L/s (Figure 6). As depicted in Figure 6, within a certain range of the upstream end of the main channel, water depths on Side I, Side II, and Side III were nearly equal with almost horizontal profiles. As the distance between the location of water flow and the upstream end of the weir crest decreased gradually, there was a gradual decrease in water depth on Side I along with an inclined trend in its corresponding profile; however, both Side II and Side III still maintained almost horizontal profiles. When approaching closer to the side weir area with flowing water, there was an evident reduction in water depth on Side I accompanied by a significant downward trend visible across an expanded decline range. The minimum point occurred near the upstream end of the weir crest before gradually increasing again towards downstream sections. At the crest section of the side weir, there is an upward trend observed in the water surface. The water surface tended to stabilize downstream of the main channel within a certain range from the downstream end of the weir crest. There was no significant change in the water surface profiles of Side Ⅱ and Side Ⅲ in the crest section. It can be inferred that the side weir entrance effect occurred only between Side Ⅰ and Side Ⅱ. M. Emin reported the same pattern [10].
Figure 6. Water surface profiles on Side I, Side II, and Side III with a side weir width of 20 cm and height of 15 cm at a discharge of 25 L/s.
For a more accurate study on the entrance effect of the side weir on the Water Surface Profile (WSP) for Side I; a comparative analysis conducted using different widths but the same height (15 cm) at a discharge rate of 25 L/s is presented through Figure 7, Figure 8, Figure 9 and Figure 10.
Figure 7. Water surface profile on Side Ⅰ with a side weir width of 20 cm and height of 15 cm at a discharge of 25 L/s.
Figure 8. Water surface profile on Side Ⅰ with a side weir width of 30 cm and height of 15 cm at a discharge of 25 L/s.
Figure 9. Water surface profile on Side Ⅰ with a side weir width of 40 cm and height of 15 cm at a discharge of 25 L/s.
Figure 10. Water surface profile on Side Ⅰ with a side weir width of 47 cm and height of 15 cm at a discharge of 25 L/s.
According to Figure 7, Figure 8, Figure 9 and Figure 10, the water depth upstream of the main channel started to decrease as it approached the upstream end of the weir crest and then gradually increased at the weir crest section. In other words, the water surface profile exhibited a backwater curve along the length of the weir crest. The water depth remained relatively stable downstream of the main channel within a certain range from the downstream end of the weir crest. Additionally, there was a higher water depth downstream of the main channel compared to that upstream of the main channel. Furthermore, an increase in the width of the side weir led to a gradual reduction in fluctuations on its water surface.
5.2. Velocity Distribution
The law of flow velocity distribution near the side weir is the focus of research and analysis, so the simulated and measured values of flow velocity near the side weir were compared and analyzed. Take the discharge of 25 L/s, the height of 15 cm, and the width of 30 cm of the side weir as an example to illustrate. Figure 11 shows the measured and simulated velocity distribution in the x-direction of cross-section ④. As can be seen from Figure 11, the diagrams of the measured and simulated velocity distribution were relatively consistent, and the maximum absolute relative error between the measured and simulated values at the same measurement point was 9.37%, and the average absolute relative error was 3.97%, which indicated a satisfactory agreement between the experimental and simulated results.
Figure 11. Velocity distribution in the x-direction of section ④: when the discharge is 25 L/s, the height of the side weir is 15 cm and the width of the side weir is 30 cm. (a) Measured velocity distribution; (b) Simulated velocity distribution.
From Figure 11, it can be seen that the flow velocity gradually increased from the bottom of the channel towards the water surface in the Z-direction, and the flow velocity gradually increased from Side Ⅲ to Side Ⅰ in the Y-direction. The maximum flow velocity occurred near the weir crest.
Figure 12 shows the distribution of flow velocity at different depths (z/P = 0.3, z/P = 0.8, z/P = 1.6) with a side weir width of 30 cm and height of 15 cm at a discharge of 25 L/s. The water flow line began to bend at a certain point upstream of the main channel, and the closer it was to the upstream end of the weir crest, the greater the curvature. The maximum curvature occurred at the downstream end of the weir crest. The flow patterns at the bottom, near the side weir crest, and above the side weir crest were significantly different. There was a reverse flow at the bottom of the main channel, where the forward and reverse flows intersect, resulting in a detention zone. The maximum flow velocity at the bottom layer occurred at the upstream end of the side weir crest. When the location of water flow approached the weir crest, the maximum flow velocity occurred at the upstream end of the weir crest. The maximum flow velocity on the water surface occurred at the downstream end of the weir crest. As the water depth decreased, the position of the maximum flow velocity gradually moved from the upstream end of the side weir to the downstream end of the side weir.
Figure 12. Distribution of flow velocity at different depths with a side weir width of 30 cm and height of 15 cm at a discharge of 25 L/s. (a) z/P = 0.3; (b) z/P = 0.8; (c) z/P = 1.6.
5.3. Side Channel Pressure Distribution
When water flowed through the side weir, an upstream water level was formed, resulting in a pressure zone at the junction with the side channel. This pressure zone led to increased water pressure on the floor of the side channel, which affected its stability and durability. In small channels or fields where erosion resistance is weak, excessive pressure can cause scour holes. Therefore, analyzing the pressure distribution in the side channel is necessary to select an appropriate height and width for the side weir that effectively reduces its impact on the bottom plate.
To investigate the impact of side weir width on hydraulic characteristics, pressure data was collected at a discharge rate of 25 L/s for side weirs with heights of 20 cm and widths ranging from 20 cm to 47 cm. The pressure distribution map was drawn, as shown in Figure 13.
Figure 13. Comparison of pressure distribution on the bottom plate of the side channel with different widths of side weirs when the discharge is 25 L/s and the height of side weirs is 20 cm. (a) P = 20 cm, b = 20 cm; (b) P = 20 cm, b = 30 cm; (c) P = 20 cm, b = 40 cm; (d) P = 20 cm, b = 47 cm.
As can be seen from Figure 13, the pressure at the bottom of the side channel decreased as the width of the side weir increased. This uneven distribution of water flow on the weir was caused by the sharp bending of water flow lines and the influence of centrifugal inertia force over a short period. After passing through the side weir, the water flow became symmetrically distributed with respect to the axis of the side channel, leaning towards the right bank at a certain distance. As we increased the width of the side weir, we noticed that its position gradually approached the side weir and maximum pressure decreased at this location where the water tongue formed due to flowing through it (Figure 13). For a constant height (20 cm) but varying widths (20 cm, 30 cm, 40 cm, and 47 cm), we measured maximum pressures at these positions as follows: 103,713 Pa, 103,558 Pa, 103,324 Pa, and 103,280 Pa, respectively. Consequently, increasing width reduced the impact on the side channel from water flowing through it while changing pressure distribution from concentration to dispersion in a vertical direction. In the practical application of side weirs, appropriate height should be selected based on the bottom plate’s capacity to withstand the pressure exerted by flowing water within channels.
To investigate how height affects the hydraulic characteristics of rectangular side weirs further (Figure 14), we extracted pressures on bottom plates when discharge was fixed at 25 L/s while varying heights were set as follows: 7 cm, 10 cm, 15 cm, and 20 cm, respectively.
Figure 14. Comparison of pressure distribution on the bottom plate of the side channel with different heights of side weirs when discharge is 25 L/s and the width of side weirs is 20 cm. (a) P = 7 cm, b = 20 cm; (b) P = 10 cm, b = 20 cm; (c) P = 15 cm, b = 20 cm; (d) P = 20 cm, b = 20 cm.
As shown in Figure 14, when the width of the side weir was constant, the pressure at the bottom of the side channel increased with the height of the side weir. As the height of the side weir increased, the water tongue formed by flow through the side weir gradually moved away from it in a downstream direction. In terms of vertical water flow, as the height of the side weir increased, the position of maximum pressure at which the water tongue falls shifted closer to the axis of the side channel from its right bank. Moreover, an increase in height resulted in higher maximum pressure at this falling point. For a constant width (20 cm) and varying heights (7 cm, 10 cm, 15 cm, and 20 cm), corresponding maximum pressures at this landing point were measured as 102,422 Pa, 102,700 Pa, 103,375 Pa, and 103,766 Pa, respectively. Consequently, increasing width led to a greater impact on both flow through and pressure distribution within the side channel; transforming it from scattered to concentrated along its lengthwise direction. Therefore, when applying such weirs practically one should select an appropriate width based on what pressure can be sustained by their respective channel bottom plates.
5.4. Discharge Coefficient
Based on dimensionless analysis, the influencing parameters of the discharge coefficient were obtained. To study the effect of parameters Fr1, b/h1, and P/h1, discharge coefficient values were plotted against Fr1, b/h1, and P/h1, shown in Figure 15, Figure 16 and Figure 17. The discharge coefficient decreased as parameters Fr1 and b/h1 increased. The discharge coefficient increased as parameter P/h1 increased. As Uyumaz and Muslu reported in a previous study, the variation of the discharge coefficient with respect to the Froude number showed a second-degree curve for a subcritical regime [4].
Figure 15. Variation of discharge coefficient values against Froude number.
Figure 16. Variation of discharge coefficient values against the percentage of the side weir width to the upstream flow depth over the side weir.
Figure 17. Variation of discharge coefficient values against the percentage of the side weir height to the upstream flow depth over the side weir.
Quantitative analysis between discharge coefficient values and parameters Fr1, b/h1, and P/h1 was conducted using data analysis software (IBM SPSS Statistics 19). The various coefficients obtained are shown in Table 3.
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig
B
Std. Error
Beta (β)
Constant
−1.294
0.155
−8.369
0.000
Fr1
3.430
0.286
3.401
12.013
0.000
b/h1
−0.004
0.004
−0.045
−0.944
0.348
P/h1
2.401
0.167
4.064
14.394
0.000
Table 3. Coefficient.
The value of t and Sig are the significance results of the independent variable, and the value of Sig corresponding to the value of t is less than 0.05, indicating that the independent variable has a significant impact on the dependent variable. Therefore, the values of Sig corresponding to the parameters Fr1 and P/h1 were less than 0.05, indicating that the parameters Fr1 and P/h1 have a significant impact on the discharge coefficient. On the contrary, the parameter b/h1 has less impact on the discharge coefficient. Therefore, quantitative analysis between discharge coefficient values and parameters Fr1, and P/h1 was conducted using data analysis software by removing factor b/h1. The model summary, ANOVA, and coefficient obtained are shown respectively in Table 4, Table 5 and Table 6. R and adjusted R square in Table 4 were approaching 1, which indicated the goodness of fit of the regression model was high. The value of Sig corresponding to the value of F in Table 5 was less than 0.05, which indicated that the regression equation was useful. The values of Sig corresponding to the parameters Fr1 and P/h1 in Table 6 were less than 0.05, indicating that the parameters Fr1 and P/h1 have a significant impact on the discharge coefficient.
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
0.913 a
0.833
0.829
0.03232
Table 4. Model Summary b. Note: a. Predictors:(Constant), Fr1, P/h1; b. Discharge coefficient.
Model
Sum of Squares
df
Mean Square
F
Sig
1
Regression
0.402
2
0.201
192.545
0.000 a
Residual
0.080
77
0.001
Total
0.483
79
Table 5. ANOVA b. Note: a. Predictors:(Constant), Fr1, P/h1; b. Discharge coefficient.
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig
B
Std. Error
Beta (β)
Constant
−1.326
0.151
−8.796
0.000
Fr1
3.479
0.281
3.449
12.396
0.000
P/h1
2.427
0.164
4.108
14.765
0.000
Table 6. Coefficient a. Note: a. Predictors:(Constant), Fr1, P/h1.
Based on the above analysis, the flow coefficient formula has been obtained, shown as follows:
Discharge formula were obtained by substituting Equation (15) into Equation (12), as shown in Equation (16).
where Q ∈ [0.006, 0.030], m3/s; b ∈ [0.20, 0.47], m; P ∈ [0.07, 0.20], m.
Figure 18 showed the measured discharge coefficient values with those calculated from discharge formulas in Table 3. The scatter of the data with respect to perfect line was limited to ±10%.
Figure 18. Comparison of the measured discharge coefficient values with those calculated from discharge formulas in Table 3.
6. Discussions
Determining water surface profile near the side weir in the main channel is one of the tasks of hydraulic calculation for side weirs. As the water flows through the side weir, discharge in the main channel is gradually decreasing, namely dQ/ds<0. According to the Equation (17) derived from Qimo Chen [3], it can be inferred that the value of 𝑑ℎ/𝑑𝑠 is greater than zero in subcritical flow (Fr < 1), that is, the water surface profile near the side weir in the main channel is a backwater curve. Due to the side weir entrance effect at the upstream end, water surface profiles drop slightly at the upstream end of the side weir crest, as EI-Khashab [28] and Emiroglu et al. [29] reported in previous experimental studies.
In this study, the water surface profile exhibited a backwater curve along the length of the weir crest. Therefore, during side weir application, it is crucial to ensure that downstream water levels do not exceed the highest water level of the channel.
The head on the weir is one of the important factors that flow over side weirs depends on. At the same time, the head depends on the water surface profile near the side weir in the main channel. Therefore, further research on the quantitative analysis of water surface profile needs to be conducted. Mohamed Khorchani proposed a new approach based on the video monitoring concept to measure the free surface of flow over side weirs. It points out a new direction for future research [8].
The maximum flow velocity, a key parameter in assessing the efficiency of a weir, occurs at the upstream end of the weir crest, typically near the crest. This is attributed to the convergence of the flow as it approaches the crest, resulting in a significant increase in velocity. It was found that in this study the minimum flow velocity occurred at the bottom of the main channel away from the side weir. Under such conditions, the accumulation of sediments could lead to siltation, which in turn can affect the accuracy of flow measurement through side weirs. This is because the presence of sediments can alter the flow patterns and cause errors in the measurement. Therefore, it becomes crucial to explore methods to optimize the selection of side weirs in order to minimize or eliminate the effects of sedimentation on flow measurement.
Pressure distribution plays a crucial role in ensuring structural safety for side weirs since small channels and field inlets have relatively limited pressure-bearing capacities. Therefore, it is important to select an appropriate geometrical parameter of rectangular side weirs based on their ability to withstand the pressure exerted on their bottom combined with pressure distribution data at the bottom of the side channel we have obtained in this study.
The discharge coefficient formula (Equation (15)), which incorporates Fr1 and P/h1, was derived based on dimensional analysis. However, it is worth noting that previous research has contradicted this formula by suggesting that the discharge coefficient solely depends on the Froude number. This conclusion can be observed in this study such as in Equations (18)–(23) in Table 7 of the manuscript [30,31,32,33,34,35], which clearly demonstrate the dependency of the discharge coefficient on the Froude number. In contrast, our derived discharge coefficient formula (Equation (15)) offers a more streamlined and simplified approach compared to Equation (25) [36] and Equation (29) [10]—making it easier to comprehend and apply—an advantageous feature particularly valuable in fluid dynamics where intricate calculations can be time-consuming. Furthermore, our derived discharge coefficient formula (Equation (15)) exhibits a broader application scope than that of Equation (24) [37] as shown in Table 8. Equation (26) [38] and Equation (27) [5] are specifically applicable under high flow discharge conditions. Conversely, our derived discharge coefficient formula (Equation (15)) is better suited for low-flow discharge conditions.
Table 7. Discharge coefficient formulas of rectangular side weirs presented in previous studies.
Discharge/(L·s−1)
Width of Side Weir/cm
Height of Side Weir/cm
Number of Formula
10~14
10~20
6~12
(24)
35–100
20~75
1~19
(26), (27)
6~30
20~47
7~20
(15)
Table 8. Application scope of discharge coefficient formulas.
In addition to the factors studied in the paper, factors such as the sediment content in the flow, the bottom slope, and the cross-section shape of the channel also have a certain impact on the hydraulic characteristics of the side weir. Further numerical simulation methods can be used to study the hydraulic characteristics and the influencing factors of the side weir. Water measurement facilities generally require high accuracy of water measurement, the flow of sharp-crested side weirs is complex, and the water surface fluctuates greatly. While conducting numerical simulations, experimental research on prototype channels is necessary to ensure the reliability of the results and provide reference for the body design and optimization of side weirs in small channels and field inlets.
7. Conclusions
This paper presents a comprehensive study that encompasses both experimental and numerical simulation research on rectangular side weirs of varying heights and widths within rectangular channels. A thorough analysis of the experimental and numerical simulation results has been conducted, leading to the derivation of several notable conclusions:
A comparative analysis was conducted on the measured and simulated values of water depth and flow velocity. Both of the maximum absolute relative errors were within 10%, which indicated that the numerical simulation of the side weir was feasible and effective.
The water surface profile exhibited a backwater curve along the length of the weir crest. The side weir entrance effect occurred only between Side Ⅰ and Side Ⅱ. This indicates that flow patterns and associated hydraulic forces at the weir entrance play a crucial role in determining water level distribution along the weir crest.
The maximum flow velocity of the cross-section at the upstream end of the weir crest occurred near the weir crest, while the minimum flow velocity occurred at the bottom of the main channel away from the side weir. As the water depth decreased, the position of the maximum flow velocity gradually moved from the upstream end of the side weir to the downstream end of the side weir.
When the height of the side weir remains constant, an increase in the width of the side weir leads to a decrease in pressure at the bottom of the side channel. Conversely, when the width of the side weir is kept constant, an increase in its height results in an increase in pressure at the bottom of the side channel. Therefore, during practical applications involving side weirs, it is crucial to select an appropriate weir width based on the maximum pressure that can be sustained by the channel’s bottom plate.
The discharge coefficient was found to depend on the upstream Froude number Fr1 and the percentage of the side weir height to the upstream flow depth over the side weir P/h1. The relationship between the discharge coefficient and parameters Fr1 and P/h1 was obtained using multiple regression analysis, which was of linear form and provided an easy means to estimate the discharge coefficient. The discharge formula is of high accuracy with relative errors within 10%, which met the water measurement accuracy requirements of small channels in irrigation areas.
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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 =1.41𝐵𝑖 (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 =4𝐵 (3) 𝐵 =1.88𝐵𝑖 (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=4.62𝐵0.96𝑏 (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=(𝐿𝑇1+𝐿𝑇2)=4.375𝐵𝑏 (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=𝜓𝐻𝜑(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.
Case
Configuration
Qin (m3·s−1)
Zout (m)
Mr
Condition of bars
1a
CBU
0.05
0.15
1
Exposed
1b
SC
0.05
0.15
1
Exposed
1c
SB
0.05
0.15
1
Exposed
2a
CBU
0.30
0.34
1
Submerged
2b
SC
0.30
0.34
1
Submerged
2c
SB
0.30
0.34
1
Submerged
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−13𝜏kk𝛿ij=−2𝜈SGS¯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:
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.
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.
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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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.
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.
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.
그림 2: 채워진 결과그림 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 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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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]
10
21.1
15.6
15.4
25.1
11.5
39.8
8.9
63.1
7.1
100
5.8
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+∇⋅(𝜌𝒖)=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+∇⋅(𝛼𝒖)=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:
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.
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.
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.
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 description
Snap-off distance [mm]
Formation of incomplete regions
(a) Single squeegee stroke with snap-off distance
0.2
Yes
(b) Double squeegee stroke
0
Yes
(c) Double squeegee stroke with snap-off distance
0.2
Yes
(d) Single squeegee stroke with local tape pieces (0.2 mm)
0.2
No
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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인텔 : 모델명이 ‘2’로 시작하고 ‘V’로 끝나는 코어 울트라 시리즈 2(Core Ultra Series 2). 예를 들면 인텔 코어 울트라 5 226V(시리즈2)가 있다.
AMD : 라이젠 AI 300 시리즈. 예시로 AMD 라이젠 AI 7 프로 360.
퀄컴 : 스냅드래곤 X 시리즈의 플러스(Plus) 또는 엘리트(Elite) 제품
이 세 가지 프로세서는 성능과 배터리 수명 면에서 애플 맥북의 M 시리즈와 경쟁하도록 설계됐다. 그러나 노트북을 선택할 때는 프로세서뿐 아니라 다양한 요소를 함께 고려해야 한다.
인텔 프로세서
인텔의 최신 프로세서는 다음 세 가지 범주로 나뉜다.
인텔 코어 울트라(Intel Core Ultra) : 프리미엄 칩으로, AI 전용 프로세서를 탑재했다(예 : 인텔 코어 울트라 7 155U).
인텔 코어(Intel Core) : 주류 노트북에 사용되는 칩으로, 코어 울트라보다 한 단계 아래다(예 : 인텔 코어 7 150U).
인텔 프로세서(Intel Processor) : 과거 펜티엄과 셀러론 브랜드를 대체하는 저가형 PC 칩이다(예 : 인텔 프로세서 N200).
인텔은 프로세서를 성능 등급에 따라 ‘3’, ‘5’, ‘7’, ‘9’로 세분화했다. 숫자가 높을수록 더 많은 코어를 가지고 있다는 의미이며, 이미지 처리 및 비디오 작업 속도가 향상된다. 코어 5와 코어 울트라 5 칩은 웹 브라우징 및 오피스 작업에 적합하다.
Intel
모델명 뒤에 붙는 접미사도 중요하다. 이 글자는 프로세서가 어떻게 최적화되었는지를 나타낸다. 긴 접미사 목록 중에 알아두어야 할 주요 단어는 ‘U’와 ‘H’다. U는 배터리 수명을, H는 성능을 강조한다. 코어 울트라 5 226V의 ‘V’는 코어 울트라 제품 라인에만 적용되는 접미사다.
구형 모델은 12세대 코어 i5 1235U처럼 이름에 ‘i’와 세대 번호가 포함되어 있다. 14세대에 이르러 인텔은 모든 것을 재설정하고 이제 ‘시리즈 1’부터 세기 시작했다(예 : 코어 울트라 155U). 즉, 최신 인텔 칩의 모델명은 구형 모델보다 짧다. 가격이 적당한 경우라면 구형 모델도 여전히 고려해 볼만하다.
AMD 프로세서
AMD는 인텔만큼 브랜딩 개편에 적극적이지는 않다. 애플 및 퀄컴과 경쟁하는 AI 300 시리즈 칩 외에 나머지 프로세서는 2023년 도입된 더 길고 혼란스러운 명명 체계를 따르고 있다.
AMD
예시로 AMD 라이젠 5 8640HS를 살펴본다.
첫 번째 숫자 ‘8’은 세대를 의미하며, 2024년에 출시된 칩을 나타낸다(7735HS는 2023년 제품).
‘5’는 성능 등급을 나타내며, 인텔과 마찬가지로 숫자가 높을수록 성능이 좋다는 의미다. 인텔 코어 5와 코어 7 체계와 유사하게 홀수로 계산된다.
마지막 글자는 프로세서의 최적화 방식이다. ‘U’는 배터리 수명, ‘H’는 성능을 우선시한다.
이 명명 체계를 따르는 칩은 AMD의 구형 젠 4(Zen 4) 아키텍처를 기반으로 하지만, 최신 AI 300 시리즈는 젠 5 아키텍처를 사용한다. AMD가 프로세서 라인 대부분을 최신 아키텍처로 전환함에 따라 이에 맞는 새로운 브랜드가 등장할 것으로 예상된다.
퀄컴 프로세서
퀄컴은 올해 초 전력 효율성에 중점을 두고 PC CPU 경쟁에 합류했다. 퀄컴의 스냅드래곤 X 칩은 휴대폰, 태블릿, 애플의 M 시리즈 프로세서에서 볼 수 있는 것과 동일한 Arm 기반 아키텍처를 사용하며, 우수한 PC 성능과 긴 배터리 수명을 제공한다. 무엇보다 퀄컴의 직관적인 브랜드 전략이 신선하게 다가온다.
스냅드래곤 X 엘리트(Snapdragon X Elite) : 최고급 모델
스냅드래곤 X 플러스(Snapdragon X Plus) : 그보다 한 단계 낮은 모델
마이크로소프트 서피스 노트북에 탑재된 스냅드래곤 X 플러스를 사용해 본 경험에 따르면, 충분한 성능과 하루 종일 지속되는 배터리 수명을 제공했다.
다만, Arm 기반 프로세서가 모든 윈도우 소프트웨어와 호환되는 것은 아니다. 스냅드래곤 PC에서 Arm이 아닌 앱을 실행하는 마이크로소프트의 에뮬레이션 엔진에서도 호환성 문제가 발생할 수 있다. 에뮬레이션 개선과 Arm 버전의 소프트웨어를 출시하는 개발자가 늘어나면서 상황이 점점 개선되고 있지만, 인텔과 AMD 노트북에서는 겪지 않아도 될 골칫거리가 여전히 남아 있다.
CPU 시장의 긍정적인 변화
복잡한 이름을 살펴보는 것이 혼란스러울 수 있고 AI에 대한 강조가 다소 과장된 면이 있지만, PC 프로세서 분야에서 3가지 업체가 경쟁하는 덕분에 상황은 개선되고 있다. 지난 4년간 애플은 전력 효율성 측면에서 독보적인 성과를 보여줬다. 그러나 인텔, AMD, 퀄컴이 새로운 프로세서를 내놓으며 애플의 수준에 도달하고 있다.
물론 복잡한 브랜드와 명명 체계는 단점이지만, 이런 경쟁 덕분에 더 나은 성능과 배터리 수명을 갖춘 제품이 등장하고 있다. 사용자에게 긍정적인 변화다. dl-itworldkorea@foundryco.com
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2023년 01월 11일
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일반적으로 수치해석을 주 업무로 사용하는 경우 노트북을 사용하는 경우는 그리 많지 않습니다. 그 이유는 CPU 성능을 100%로 사용하는 해석 프로그램의 특성상 발열과 부품의 성능 측면에서 데스크탑이나 HPC의 성능을 따라 가기는 어렵기 때문입니다.
그럼에도 불구하고, 이동 편의성이나 발표, Demo 등의 업무 필요성이 자주 있는 경우, 또는 계산 시간이 짧은 경량 해석을 주로 하는 경우, 노트북이 주는 이점이 크기 때문에 수치해석용 노트북을 고려하기도 합니다.
보통 수치해석용 컴퓨터를 검토하는 경우 CPU의 Core수나 클럭, 메모리, 그래픽카드 등을 신중하게 검토하게 되는데 모든 것이 예산과 직결되어 있기 때문입니다. 따라서 해석용 컴퓨터 구매 시 어떤 것을 선정 우선순위에 두는지에 따라 사양이 달라지게 됩니다.
해석용으로 노트북을 고려하는 경우, 보통 CPU의 클럭은 비교적 선택 기준이 명확합니다. 메모리 또한 용량에 따라 가격이 정해지기 때문에 이것도 비교적 명확합니다. 나머지 가격에 가장 큰 영향을 주는 것이 그래픽카드인데, 이는 그래픽 카드의 경우 일반적인 게임용이나 포토샵으로 일반적인 이미지 처리 작업을 수행하는 그래픽카드와 3차원 CAD/CAE에 사용되는 업무용 그래픽 카드는 명확하게 분리되어 있고, 이는 가격 측면에서 매우 차이가 많이 납니다.
통상 게임용 그래픽카드는 수치해석의 경우 POST 작업시 문제가 발생하는 경우가 종종 발생하기 때문에 일반적으로 선택 우선 순위에서 충분한 확인을 한 후 구입하는 것이 좋습니다.
FLOW-3D는 OpenGL 드라이버가 만족스럽게 수행되는 최신 그래픽 카드가 적합합니다. 최소한 OpenGL 3.0을 지원하는 것이 좋습니다. FlowSight는 DirectX 11 이상을 지원하는 그래픽 카드에서 가장 잘 작동합니다. 권장 옵션은 NVIDIA의 Quadro K 시리즈와 AMD의 Fire Pro W 시리즈입니다.
특히 엔비디아 쿼드로(NVIDIA Quadro)는 엔비디아가 개발한 전문가 용도(워크스테이션)의 그래픽 카드입니다. 일반적으로 지포스 그래픽 카드가 게이밍에 초점이 맞춰져 있지만, 쿼드로는 다양한 산업 분야의 전문가가 필요로 하는 영역에 광범위한 용도로 사용되고 있습니다. 주로 산업계의 그래픽 디자인 분야, 영상 콘텐츠 제작 분야, 엔지니어링 설계 분야, 과학 분야, 의료 분석 분야 등의 전문가 작업용으로 사용되고 있습니다. 따라서 일반적인 소비자를 대상으로 하는 지포스 그래픽 카드와는 다르계 산업계에 포커스 되어 있으며 가격이 매우 비싸서 도입시 예산을 고려해야 합니다.
MSI가 새로운 노트북 CPU 벤치마크, 그리고 그 CPU가 내장돼 있는 신제품 노트북 제품군을 모두 CES 2023에서 공개했다. CES에서 인텔은 노트북용 13세대 코어 칩, 코드명 랩터 레이크와 핵심 제품인 코어 i9-13980HX를 발표했다.
새로운 노트북용 13세대 코어 칩이 게임 플레이에서 12% 더 빠르다는 정도의 약간의 정보는 이미 알려져 있다. 사용자가 기다리는 것은 실제 CPU가 탑재된 노트북에서의 성능이지만 보통 벤치마크는 제품 출시가 임박해서야 공개되는 것이 보통이다. 올해는 다르다.
CES 2023에서 MSI는 인텔 최고급 제품군인 코어 i9-13980HX 프로세서가 탑재된 타이탄 GT77 HX과 레이더 GE78 HX를 공개했다. 이례적으로 여기에 더해 PCI 익스프레서 5 SSD의 실제 성능을 측정하는 크리스털디스크마크, 모바일 프로세서 실행 속도를 측정하는 시네벤치 벤치마크 점수도 함께 제공했다. 다음 영상의 결과부터 말하자면 인텔 최신 프로세서를 큰 폭으로 따돌릴 만한 수치다.
MSI는 레이더 GE78 HX 외에도 레이더 GE68 HX 그리고 게이밍 노트북 같지 않은 외관의 스텔스 16 스튜디오, 스텔스 14, 사이보그 14 등 2023년에 출시될 다른 노트북도 전시했다. 오래된 PC 애호가라면 MSI 노트북 전면을 장식한 화려한 복고풍의 라이트 브라이트(Lite Brite) LED를 반가워할지도 모른다. 바닥면 섀시가 투명한 플라스틱 소재로 MSI 로고가 새겨져 있는 제품도 있다. 상세한 가격, 출시일, 사양 등은 추후 공개 예정이다. editor@itworld.co.kr
고성능 노트북을 구매할 때는 코어 i7과 코어 i9 사이에서 선택의 갈림길에 서게 된다. 코어 i7 CPU도 강력하지만 코어 i9는 최고의 성능을 위해 만들어진 CPU이며 보통 그에 상응하는 높은 가격대로 판매된다.
CPU에 초점을 둔다면 관건은 성능이다. 성능을 좌우하는 두 가지 주요소는 CPU의 동작 클록 속도(MHz), 그리고 탑재된 연산 코어의 수다. 그러나 노트북에서 한 가지 중요한 제약 요소는 냉각이다. 냉각이 제대로 되지 않으면 고성능도 쓸모가 없다. 가장 적합한 노트북 CPU를 결정하는 데 도움이 되도록 인텔의 지난 3개 세대 CPU의 코어 i7과 i9에 대한 정보를 모았다. 최신 세대부터 시작해 역순으로 살펴보자.
11세대: 코어 i9 vs. 코어 i7
인텔의 11세대 타이거 레이크(Tiger Lake) H는 한 가지 큰 이정표를 달성했다. 인텔이 2015년부터 H급 CPU에 사용해 온 14nm 공정을 마침내 최신 10nm 슈퍼핀(SuperFin) 공정으로 바꾼 것이다. 오랫동안 기다려온 변화다.
인텔이 자랑할 만한 10nm 고성능 칩을 내놓자 타이거 레이크 H를 장착한 노트북도 속속 발표됐다. 얇고 가볍고 예상외로 가격도 저렴한 에이서 프레데터 트라이톤(Acer Predator Triton) 300 SE를 포함해 일부는 벌써 매장에 출시됐다. 모든 타이거 레이크 H 칩이 8코어 CPU라는 점도 달라진 부분이다. 이전 세대의 경우 같은 제품군 내에서 코어 수에 차이를 둬 성능 기대치를 구분했다.
클록 차이도 크지 않다. 코어 i7-11800H의 최대 클록은 4.6GHz, 코어 i9-11980HK는 5GHz로, 클록 속도 증가폭은 약 8.6% 차이다. 나쁘지 않은 수치지만 둘 다 8코어 CPU임을 고려하면 대부분의 사용자에게 코어 i9는 큰 매력은 없다.
다만 코어 i9에 유리한 부분을 하나 더 꼽자면 코어 i9-11980HK가 65W의 열설계전력(TDP)을 옵션으로 제공한다는 점이다. 높은 TDP는 최상위 코어 i9에만 제공되는데, 이는 전력 및 냉각 요구사항을 충족하는 노트북에서는 코어 i7 버전보다 더 높은 지속 클록 속도를 제공할 수 있음을 의미한다.
대신 이런 노트북은 두껍고 크기도 클 가능성이 높다. 따라서 두 개의 얇은 랩톱 중에서(하나는 코어 i9, 하나는 코어 i7) 고민하는 사람에겐 열 및 전력 측면의 여유분은 두께와 크기를 희생할 만큼의 가치는 없을 것이다.
*11세대의 승자: 대부분의 사용자에게 코어 i7
10세대: 코어 i9 vs. 코어 i7
인텔은 10세대 코멧 레이크(Comet Lake) H 제품군에서 14nm를 고수했다. 그 대신 코어 i9 CPU 외에 코어 i7에도 8코어 CPU를 도입, 사용자가 비싼 최상위 CPU를 사지 않고도 더 뛰어난 성능을 누릴 수 있게 했다.
11세대 노트북이 나오기 시작했지만 10세대 CPU 제품 중에서도 아직 괜찮은 제품이 많다. 예를 들어 MSI GE76 게이밍 노트북은 빠른 CPU와 고성능 155W GPU를 탑재했고, 전면 모서리에는 RGB 라이트가 달려 있다.
11세대 칩과 마찬가지로 코어와 클록 속도의 차이가 크지 않으므로 대부분의 사용자에게 코어 i7과 코어 i9 간의 차이는 미미하다. 코어 i9-10980HK의 최대 부스트 클록은 5.3GHz, 코어 i7-10870H는 5GHz로, 두 칩의 차이는 약 6%다. PC를 최대 한계까지 사용해야 하는 경우가 아니라면 더 비싼 비용을 들여 10세대 코어 i9를 구매할 이유가 없다.
*10세대 승자: 대부분의 사용자에게 코어 i7
9세대: 코어 i9 대 코어 i7
인텔은 9세대 커피 레이크 리프레시(Coffee Lake Refresh) 노트북 H급 CPU에서 14nm 공정을 계속 유지했다. 코어 i9는 더 높은 클록 속도(최대 5GHz)를 제공하며 8개의 CPU 코어를 탑재했다. 물론 이 칩은 2년 전에 출시됐지만 인텔이 설계를 도운 XPG 제니아(Xenia) 15 등 아직 괜찮은 게이밍 노트북이 있다. 얇고 가볍고 빠르며 엔비디아 RTX GPU를 내장했다.
8코어 4.8GHz 코어 i9-9880HK와 4.6GHz 6코어 코어 i7-9850의 클록 속도 차이는 약 4%로, 실제 사용 시 유의미한 차이로 이어지는 경우는 극소수다. 두 CPU 모두 기업용 노트북에 많이 사용됐다. 대부분의 소비자용 노트북에는 8코어 5GHz 코어 i9-9880HK와 6코어 4.5GHz 코어 i7-9750H가 탑재됐다. 이 두 CPU의 클록 차이는 약 11%로, 이 정도면 유의미한 차이지만 마찬가지로 대부분의 경우 실제로 체감하기는 어렵다.
그러나 코어 수의 차이는 멀티 스레드 애플리케이션에서 큰 체감 효과로 이어지는 경우가 많다. 3D 모델링 테스트인 씨네벤치(Cinebench) R20에서 코어 i9-9980HK를 탑재한 구형 XPS 15의 점수는 코어 i7-9750H를 탑재한 게이밍 노트북보다 42% 더 높았다. 8코어 코어 i9의 발열을 심화하는 무거운 부하에서는 성능 차이가 약 7%로 줄어들었다. 여기에는 노트북의 설계가 큰 영향을 미칠 것이다. 어쨌든 일부 상황에서는 8코어가 6코어보다 유리하다.
또한 수치해석의 경우 결과를 분석하는 작업중의 많은 부분이 POST 작업으로 그래픽처리가 필요하다. 따라서 아래 영상편집을 위한 노트북에 대한 자료도 선택에 도움이 될것으로 보인다.
영상 편집을 위한 최고의 노트북 9선
Brad Chacos, Ashley Biancuzzo, Sam Singleton | PCWorld
영상을 편집하다 보면 컴퓨터의 여러 리소스를 집약적으로 사용하기 마련이다. 그래서 영상 편집은 대부분 데스크톱 PC에서 하는 경우가 많지만, 노트북에서 영상을 편집하려 한다면 PC만큼 강력한 사양이 뒷받침되어야 한다.
영상 편집용 노트북을 구매할 때 가장 비싼 제품을 선택할 필요는 없다. 사용 환경에 맞게 프로세서, 디스플레이의 품질, 포트 종류 등을 다양하게 고려해야 한다. 다음은 영상 편집에 최적화된 노트북 제품이다. 추천 제품을 확인한 후 영상 편집용 노트북을 테스트하는 팁도 참고하자.
1. 영상 편집용 최고의 노트북, 델 XPS 17(2022)
장점 • 가격 대비 강력한 기능 • 밝고 풍부한 색채의 대형 디스플레이 • 썬더볼트 4 포트 4개 제공 • 긴 배터리 수명 • 시중에서 가장 빠른 GPU인 RTX 3060
단점 • 무겁고 두꺼움 • 평범한 키보드 • USB-A, HDMI, 이더넷 미지원
델 XPS 17(2022)이야말로 콘텐츠 제작에 최적화된 노트북이다. 인텔 12세대 코어 i7-12700H 프로세서 및 엔비디아 지포스 RTX 3060는 편집을 위한 뛰어난 성능을 제공한다. 1TB SSD도 함께 지원되기에 데이터를 옮길 때도 편하다.
XPS 17은 SD카드 리더, 여러 썬더볼트 4 포트, 3840×2400 해상도의 17인치 터치스크린 패널, 16:10 화면 비율과 같은 영상 편집자에게 필요한 기능을 포함한다. 무게도 2.5kg 대로 비교적 가볍다. 배터리 지속 시간은 한번 충전 시 11시간인데, 이전 XPS 17 버전보다 1시간 이상 늘어난 수치다.
2. 영상 편집에 최적화된 스크린, 델 XPS 15 9520
장점 • 뛰어난 OLED 디스플레이 • 견고하고 멋진 섀시(Chassis) • 강력한 오디오 • 넓은 키보드 및 터치패드
단점 • 다소 부족한 화면 크기 • 실망스러운 배터리 수명 • 시대에 뒤떨어진 웹캠 • 제한된 포트
델 XPS 15 9520은 놀라운 OLED 디스플레이를 갖추고 있으며, 최신 인텔 코어 i7-12700H CPU 및 지포스 RTX 3050 Ti 그래픽이 탑재되어 있다. 컨텐츠 제작 및 영상 편집용으로 가장 선호하는 제품이다. 시스템도 좋지만 투박하면서 금속 소재로 이루어진 외관이 특히 매력적이다.
15인치 노트북이지만 매일 갖고 다니기에 다소 무거운 것은 단점이다. XPS 17 모델에서 제공되는 포트도 일부 없다. 그러나 멋진 OLED 디스플레이가 단연 돋보이며, 3456X2160 해상도, 16:10 화면 비율, 그리고 매우 선명하고 정확한 색상을 갖추고 있어 좋다.
3. 최고의 듀얼 모니터 지원, 에이수스 젠북 프로 14 듀오 올레드
장점 • 놀라운 기본 디스플레이와 보기 쉬운 보조 디스플레이 • 탁월한 I/O 옵션 및 무선 연결 • 콘텐츠 제작에 알맞은 CPU 및 GPU 성능
단점 • 생산성 노트북 치고는 부족한 배터리 수명 • 작고 어색하게 배치된 트랙패드 • 닿기 어려운 포트 위치
에이수스 젠북 프로 14 듀오(Asus Zenbook Pro 14 Duo OLED)는 일반적이지 않은 노트북이다. 일단 사양은 코어 i7 프로세서, 지포스 RTX 3050 그래픽, 16GB DDR5 메모리, 빠른 1TB NVMe SSD를 포함해 상당한 성능을 자랑한다. 또한 초광도의 547니트로 빛을 발하는 한편 DCI-P3 색영역의 100%를 커버하는 14.5인치 4K 터치 OLED 패널을 갖추고 있다. 사실상 콘텐츠 제작자를 위해 만들어진 제품이라 볼 수 있다.
가장 흥미로운 부분은 키보드 바로 위에 위치한 12.7인치 2880×864 스크린이다. 윈도우에서는 해당 모니터를 보조 모니터로 간주하며, 사용자는 번들로 제공된 에이수스 소프트웨어를 사용해 트랙패드로 사용하거나 어도비 앱을 위한 터치 제어 패널을 표시할 수 있다. 어떤 작업이든 유용하게 써먹을 수 있다.
젠북 프로 14 듀오 올레드는 기본적으로 휴대용이자 중간급 워크스테이션이다. 단, 배터리 수명은 평균 수준이기 때문에 중요한 작업 수행이 필요한 경우, 반드시 충전 케이블을 가지고 다녀야 한다. 그럼에도 불구하고 젠북 프로 14 듀오 올레드는 3D 렌더링 및 인코딩과 같은 작업에서 탁월한 성능을 보여 콘텐츠 제작자들에게 맞춤화 된 컴퓨터이다. 듀얼 스크린은 역대 최고의 기능이다.
4. 영상 편집하기 좋은 포터블 노트북, 레이저 블레이드 14(2021)
장점 • AAA 게임에서 뛰어난 성능 • 훌륭한 QHD 패널 • 유난히 적은 소음
단점 • 700g으로 무거운 AC 어댑터 • 비싼 가격 • 썬더볼트 4 미지원
휴대성이 핵심 고려 사항이라면, 레이저 블레이드 14(Razer Blade 14) (2021)를 선택해 보자. 노트북 두께는 1.5cm, 무게는 1.7kg에 불과해 비슷한 수준의 노트북보다 훨씬 가볍다. 사양은 AMD의 8-코어 라이젠 9 5900HX CPU, 엔비디아의 8GB 지포스 RTX 3080, 1TB NVMe SSD, 16GB 메모리를 탑재하고 있어 사양도 매우 좋다.
그러나 휴대성을 대가로 몇 가지 이점을 포기해야 할 수 있다. 일단 14인치 IPS 등급 스크린은 공장에서 보정된 상태로 제공되지만, 최대 해상도는 2560×1440다. 또 풀 DCI-P3 색영역을 지원하지만 4K 영상 편집은 불가능하다. 거기에 레이저 블레이드 14는 SD 카드 슬롯도 없다. 다만 편집 및 렌더링을 위한 강력한 성능을 갖추고 있고 가방에 쉽게 넣을 수 있는 제품인 것은 분명하다.
5. 배터리 수명이 긴 노트북, 델 인스피론 16
장점 • 넉넉한 16인치 16:10 디스플레이 • 긴 배터리 수명 • 경쟁력 있는 애플리케이션 성능 • 편안한 키보드 및 거대한 터치패드 • 쿼드 스피커(Quad speakers)
단점 • GPU 업그레이드 어려움 • 512GB SSD 초과 불가 • 태블릿 모드에서는 어색하게 느껴질 수 있는 큰 스크린
긴 배터리 수명을 가장 최우선으로 고려한다면, 델 인스피론 16(Dell Inspiron 16)을 살펴보자. 콘텐츠 제작 작업을 하며테스트해보니, 인스피론 16은 한 번 충전으로 16.5시간 동안 이용할 수 있다. 외부에서 작업을 마음껏 편집할 수 있는 시간이다. 그러나 무거운 배터리로 인해 무게가 2.1 kg에 달하므로 갖고 다니기에 적합한 제품은 아니다.
가격은 저렴한 편이나 몇 가지 단점이 있다. 일단 인텔 코어 i7-1260P CPU, 인텔 아이리스 Xe 그래픽, 16GB 램, 512GB SSD 스토리지를 탑재하고 있다. 이 정도 사양으로 영상 편집 프로젝트 대부분을 작업할 수 있으나, 스토리지 용량이 부족하기 때문에 영상 파일을 저장할 경우 외장 드라이브가 필요하다. 그러나 델 인스피론 16이 진정으로 빛을 발하는 부분은 단연 배터리 수명이다. 또한 강력한 쿼드 스피커 시스템도 사용해 보면 만족할 것이다. 포트의 경우, USB 타입-C 2개, USB-A 3.2 Gen 1 1개, HDMI 1개, SD 카드 리더 1개, 3.5mm 오디오 잭 1개가 제공된다.
6. 게이밍과 영상 편집 모두에 적합한 노트북, MSI GE76 레이더
장점 • 뛰어난 성능을 발휘하는 12세대 코어 i9-12900HK • 팬 소음을 크게 줄이는 AI 성능 모드 • 1080p 웹캠과 훌륭한 마이크 및 오디오로 우수한 화상 회의 경험 제공
단점 • 동일한 유형의 세 번째 버전 • 어수선한 UI • 비싼 가격
사양이 제일 좋은 제품을 찾고 있을 경우, 크고 무거운 게이밍 노트북을 선택해 보자. MSI GE76 레이더(Raider)는 강력한 14-코어 인텔 코어 i9-12900HK 칩, 175와트의 엔비디아 RTX 3080 Ti가 탑재됐고, 충분한 내부 냉각 성능 덕분에 UL의 프로시온(Procyon) 벤치마크의 어도비 프리미어 테스트에서 다른 노트북보다 훨씬 뛰어난 성능을 보였다. MSI GE76 레이더는 심지어 고속 카드 전송을 위해 PCle 버스에 연결된 SD 익스프레스(SD Express) 카드 리더도 갖추고 있다.
동일한 제품의 작년 모델은 게이머 중심의 360Hz 1080p 디스플레이를 지원한다. 영상 편집 과정에서는 그닥 이상적이지 않은 사양이다. 그러나 2022년의 12UHS 고급 버전은 4K, 120Hz 패널을 추가했는데, 이 패널은 콘텐츠 생성에 맞춰 튜닝 되지는 않았으나 17.3인치의 넓은 스크린 크기이기에 영상 편집자에게 꽤 유용하다.
7. 가성비 좋은 노트북, HP 엔비 14t-eb000(2021)
장점 • 높은 가격 대비 우수한 성능 • 환상적인 배터리 수명 • 성능 조절이 감지되지 않을 정도의 저소음 팬 • 썬더볼트 4 지원
단점 • 약간 특이한 키보드 레이아웃 • 비효율적인 웹캠의 시그니처 기능
가장 빠른 영상 편집 및 렌더링을 원할 경우 하드웨어에 더 많은 비용을 들여야 하지만, 예산이 넉넉하지 않을 때가 있다. 이때 HP 엔비(Envy) 14 14t-eb000) (2021)를 이용해보면 좋다. 가격은 상대적으로 저렴한 편이고 견고한 기본 컨텐츠 제작에 유용하다.
엔트리 레벨의 지포스 GTX 1650 Ti GPU 및 코어 i5-1135G7 프로세서는 그 자체로 업계 최고 제품은 아니다. 하지만 일반적인 편집 작업을 충분히 수행할 수 있는 사양이다. 분명 가성비 좋은 제품이다. 14인치 1900×1200 디스플레이는 16:10 화면 비율로 생산성을 향상하고, 공장 색 보정과 DCI-P3는 지원하지 않지만 100% sRGB 지원을 제공한다. 그뿐만 아니라, HP 엔비 14의 경우 중요한 SD 카드 및 썬더볼트 포트가 포함되며, 놀라울 정도로 조용하게 실행된다.
8. 컨텐츠 제작에 알맞은 또다른 게이밍 노트북, 에이수스 ROG 제피러스 S17
장점 • 뛰어난 CPU 및 GPU 성능 • 강력하고 혁신적인 디자인 • 편안한 맞춤형 키보드
단점 • 약간의 압력이 필요한 트랙패드 • 상당히 높은 가격
에이수스 ROG 제피러스(Zephyrus) S17은 영상 편집자의 궁극적인 꿈이다. 이 노트북은 초고속 GPU 및 CPU 성능과 함께 120Hz 화면 재생률을 갖춘 놀라운 17.3인치 4K 디스플레이를 탑재하고 있다. 견고한 전면 금속 섀시, 6개의 스피커 사운드 시스템 및 맞춤형 키보드는 프리미엄급 경험을 더욱 향상한다. 거기다 SD 카드 슬롯 및 풍부한 썬더볼트 포트가 포함되어 있어 더욱 좋다. 그러나 이를 위해 상당한 비용을 지불해야 한다. 예산이 넉넉하고 최상의 제품을 원한다면 제피루스 S17을 선택하면 된다.
9. 강력한 휴대성을 가진 노트북, XPG 제니아 15 KC
장점 • 가벼운 무게 • 조용함 • 상대적으로 빠른 속도
단점 • 중간 수준 이하의 RGB • 평범한 오디오 성능 • 느린 SD 카드 리더
사양이 좋은 노트북의 경우, 대부분 부피가 크고 무거워서 종종 2.2kg 또는 2.7kg를 넘기도 한다. XPG 제니아 15 KC(XPG Xenia 15 KC)만은 예외다. XPG 제니아 15 KC의 무게는 1.8kg가 조금 넘는 수준으로, 타제품에 비해 상당히 가볍다. 또한 소음도 별로 없다. 원래 게이밍 노트북 자체가 소음이 크기에 비교해보면 큰 장점이 될 수 있다. 1440p 디스플레이와 상대적으로 느린 SD 카드 리더 성능으로 인해 일부 콘텐츠 제작자들이 구매를 주저할 수 있으나, 조용하고 휴대하기 좋은 제품을 찾고 있다면 제니아 15 KC가 좋은 선택지다.
영상 편집 노트북 구매 시 고려 사항
영상 편집 노트북 구매 시 고려해야 할 가장 중요한 사항은 CPU 및 GPU다. 하드웨어가 빨라질수록 편집 속도도 빨라진다. 필자는 UL 프로시온 영상 편집 테스트(UL Procyon Video Editing Test)를 통해 속도를 테스트해보았다. 이 벤치마크는 2개의 서로 다른 영상 프로젝트를 가져와 색상 그레이딩 및 전환과 같은 시각적 효과를 적용한 다음, 1080p와 4K 모두에서 H.264, H.265를 사용해 내보내는 작업을 어도비 프리미어가 수행하도록 한다.
성능은 인텔의 11세대 프로세서를 실행하는 크고 무거운 노트북에서 가장 높았고, AMD의 비피 라이젠 9(beefy Ryzen 9) 프로세서를 탑재한 노트북이 바로 뒤를 이었다. 10세대 인텔 칩은 여전히 상당한 점수를 기록하고 있다. 위의 차트에는 없으나 새로운 인텔 12세대 노트북은 더 빨리 실행된다. 최고 성능의 노트북은 모두 최신 인텔 CPU 및 엔비디아의 RTX 30 시리즈 GPU를 결합했는데, 두 기업 모두 어도비 성능 최적화에 많은 시간 및 리소스를 투자했기 때문에 놀라운 일은 아니다.
GPU는 어도비 프리미어 프로에서 CPU보다 더 중요하지만, 매우 빠르게 수확체감 지점에 다다른다. 최고급 RTX 3080 그래픽을 사용하는 노트북은 RTX 3060 그래픽을 사용하는 노트북보다 영상 편집 속도가 더 빠르나, 속도 차이가 크지는 않다. 델 XPS 17 9710의 점수를 살펴보면, 지포스 RTX 3060 노트북 GPU는 MSI GE76 레이더의 가장 빠른 RTX 3080보다 14% 더 느릴 수 있다. 특히 GE76 레이더가 델 노트북에 비해 얼마나 더 크고 두꺼운지를 고려할 때 수치가 크지는 않다.
일반적으로 그래픽과 영상 편집을 위해 적어도 RTX 3060을 갖추는 것을 권장한다. 그러나 영상 편집은 워크플로에 크게 의존한다. 특정 작업 및 도구는 CPU 집약적이거나 프리미어보다 GPU에 더 의존할 수 있다. 이 경우 원하는 요소의 우선순위를 조정하길 바란다. 앞서 언급한 목록은 기본적으로 여러 요소를 종합적으로 고려해서 만든 내용이다.
인텔 및 엔비디아는 각각 퀵 싱크(Quick Sync) 및 쿠다(CUDA)와 같은 도구를 구축하는 데 수년을 보냈고, 이로 인해 많은 영상 편집 앱의 속도는 크게 향상될 수 있다. AMD 하드웨어는 영상 편집에 적합하나 특히 워크플로가 공급업체별 소프트웨어 최적화에 의존하는 경우, 특별한 이유가 없는 한 인텔 및 엔비디아를 사용하는 것을 추천한다.
그러나 내부 기능만 신경 써서는 안된다. PC월드의 영상 디렉터인 아담 패트릭 머레이는 “영상 편집에 이상적인 노트북에는 카메라로 촬영 중 영상 파일을 저장하는 SD 카드 리더가 포함되어 있다”라고 강조한다. 또한 머레이는 영상 편집에 이상적인 게임용 노트북에서 흔히 볼 수 있는 초고속 1080p 패널보다 4k, 60Hz 패널을 갖춘 노트북을 선택할 것을 추천한다.
4K 영상을 잘 편집하려면 4K 패널이 필요하며, 초고속 화면 재생률은 게임에서처럼 영상 편집에는 아무런 의미가 없다. 예를 들어, 개인 유튜브 채널용으로 일상적인 영상만 만드는 경우 색상 정확도가 중요하지 않을 수 있다. 그러나 색상 정확도가 중요할 경우, 델타 E < 2 색상 정확도와 더불어 DCI-P3 색 영역 지원은 필수적이다.
게임용 노트북은 사양이 좋지만 콘텐츠 제작용으로는 조금 부족해 보일 수 있다. 게임용과 콘텐츠 제작용으로 함께 쓰는 노트북을 원한다면, 게임용으로 노트북 한 대를 구매하고, 색상을 정확히 파악하기 위한 모니터를 추가로 구매하는 것도 방법이다. editor@itworld.co.kr
코어가 많은 그래픽카드의 경우 가격이 상상 이상으로 높습니다. 빠르면 빠를수록 좋겠지만 어디까지나 예산에 맞춰 구매를 해야 하는 현실을 감안할 수 밖에 없는 것 같습니다.
한가지 유의할 점은 엔비디아의 GTX 게이밍 하드웨어는 모델에 따라 다르기는 하지만, 볼륨 렌더링의 속도가 느리거나 오동작 등 몇 가지 제한 사항이 있습니다. 일반적으로 노트북에 내장된 통합 그래픽 카드보다는 개별 그래픽 카드를 강력하게 추천합니다. 최소한 그래픽 메모리는 512MB 이상이어야 하고 1GB이상을 권장합니다.
2021-12-15 현재 그래픽카드의 성능 순위는 위와 다음과 같습니다. 출처: https://www.videocardbenchmark.net/high_end_gpus.html
주요 Notebook
출시된 모든 그래픽 카드가 노트북용으로 장착되어 출시되지는 않기 때문에, 현재 오픈마켓 검색서비스를 제공하는 네이버에서 Lenovo Quadro 그래픽카드를 사용하는 노트북을 검색하면 아래와 같습니다. 검색 시점에 따라 상위 그래픽카드를 장착한 노트북의 대략적인 가격을 볼 수 있을 것입니다.
<검색 방법> 네이버 쇼핑 검색 키워드 : 컴퓨터 제조사 + 그래픽카드 모델 + NoteBook 형태로 검색 Lenovo quadro notebook or HP quadro notebook 또는 Lenovo firepro notebookorHP firepronotebook
( 2021-12-15기준)
대부분 검색 시점에 따라 최신 CPU와 최신 그래픽카드를 선택하여 검색을 하면 예산에 적당한 노트북을 자신에게 맞는 최상의 노트북을 어렵지 않게 선택할 수 있습니다.
Hongliang Wang, Xuanwen Jia,Chuan Wang, Bo Hu, Weidong Cao, Shanshan Li, Hui Wang
Abstract
Water-jet-scouring technology finds extensive applications in various fields, including marine engineering. In this study, the pulse characteristics are introduced on the basis of jet-scouring research, and the sand-scouring characteristics of a pulsed jet under different Reynolds numbers and the impact distances are deeply investigated using Flow-3D v11.2. The primary emphasis is on the comprehensive analysis of the unsteady flow structure within the scouring process, the impulse characteristics, and the geometric properties of the resulting scouring pit. The results show that both the radius and depth of the scour pit show a good linear correlation with the jet-flow rate. The concentration of suspended sediment showed an increasing and then decreasing trend with impinging distance. The study not only helps to enrich the traditional theory of jet scouring, but also provides useful guidance for engineering applications, which have certain theoretical and practical significance.
Water-jet-scouring technology is widely used in marine engineering and its related ancillary fields, such as in the maintenance and repair of marine structures, extraction of deep-sea resources, dredging works, seabed geological research, and cleaning and maintenance of ships. The jet flow establishes a velocity shear layer at its boundary, leading to the destabilization and subsequent generation of vortices. These vortices undergo continuous deformation, rupture, merging, and evolution into turbulence during their movement. Consequently, they entrain surrounding fluid into the jet region, facilitating the transfer of momentum, heat, and mass between the jet and its ambient environment [1,2,3]. Therefore, numerous scholars have carried out detailed studies on the scouring characteristics associated with jets. Chatterjee et al. [4] investigated the local scouring and sediment-transport phenomena due to the formation of horizontal jets during the opening of sluice gates based on experiments, and successfully established empirical expressions for the correlation between the time of reaching the equilibrium stage, the maximum depth of scouring, and the peak of the dune. The important role of jet-diffusion properties in the scouring process was also emphasized. Hoffmans [5] calculated the equilibrium scour process induced using a horizontal jet in the absence of a streambed and used experiments to verify the accuracy of the equations for jet-scour depths in the relevant literature. Luo et al. [6] investigated the induction mechanism of scour in planar jets through particle-image velocimetry (PIV). It was found that the initial stage of scour was dominated by wall shear, while the later stages of the scour process were mainly influenced by the turbulent vortex. Canepa et al. [7] investigated the scour characteristics of gas-doped water jets and found that gas-doped jets significantly reduce the scour depth if the velocity of the mixture is used as a reference. Pulsed jets introduce pulsation, resulting in a water-hammer effect, as well as increased diffusion and coil suction rates. These factors contribute to a more intricate interaction between the pulsed jet and the adjacent wall. The process of generation, development and evolution of its internal vortex structure as well as the interaction between the vortex structure and the surrounding ambient fluid and solid wall have changed significantly [8,9]. At this juncture, researchers in this domain have undertaken investigations centered on the utilization of pulsed jets. Coussement et al. [10] investigated the flow characteristics of a pulsed jet in a cross-flow environment based on Large Eddy Simulation (LES). A new approach to characterize mixing was introduced, which successfully explains and quantifies the complex mixing process between the pulsating jet and the ambient fluid. Bi et al. [11] investigated the thrust of a deformable body generated through a pulsed jet based on an axisymmetric immersed-boundary model. The numerical results show that in addition to the momentum flux of the jet, the jet acceleration is also an important source of thrust generation. Zhang et al. [12] studied the complex unsteady flow characteristics of a pulsed jet impinging on a rotating wall using numerical methods, and it was found that the impact pressure of the pulsed jet on the wall is greater than that of the continuous jet on the wall for a certain period of time when the water-hammer effect occurs. Rakhsha et al. [13] used experiments and numerical simulations to study the effect of pulsed jets on the flow and heat-transfer characteristics over a heated plane. It was found that the Nussell number increases with increasing pulse frequency and Reynolds number and decreases with increasing impinging distance. It is evident that existing studies predominantly center on the unsteady flow characteristics of pulsed jets and their properties related to heat and mass transfer. Conversely, there is a noticeable dearth of research concerning the scouring attributes of pulsed jets in the available literature. The pulsed submerged impinging jet represents a complex jet flow with a significant engineering application background and substantial theoretical research value. Exploring the unsteady hydraulic characteristics of pulsed jets can enhance classical impinging jet theory, deepen our comprehension of the jet–wall interaction mechanism, and establish a scientific foundation for addressing engineering-application challenges. Therefore, this paper introduces the pulse characteristics into the impinging jet, and, based on the Flow-3D software, the sand-scouring characteristics of the impinging jet under different Reynolds numbers and impinging distances are deeply investigated. The surface geometry of the scour pit is characterized while obtaining the pulsation characteristics of the unsteady flow structure during sand scouring. This study not only offers a foundation for implementing flow control and enhancing the understanding of unsteady flow characteristics but also furnishes theoretical backing for predicting impact pressure and impact pit formation.
2. Modeling and Numerical Methods
2.1. Model Building
The geometric model consists of a jet pipe, a body of water, a baffle, and a sand bed, as shown in Figure 1. The inner diameter D of the jet pipe is 20 mm, and the length L is set to 50D to ensure that the turbulence inside the pipe is fully developed. H represents the impinging height, and the initial water height (Hw) is 1600 mm. Baffles positioned on both sides serve to maintain a constant water level. The length Ls and thickness Hs of the sand bed are 5000 mm and 160 mm, respectively. It is worth stating that the sand bed is composed of non-cohesive sand. The median grain size dm of the sand is 0.77 mm, the specific gravity Δ is 1.65, and the particle gradation σg is 1.21.
Figure 1. Geometric modeling for sand scouring.
2.2. Numerical Models
In fluid mechanics, the continuity and momentum equations are the basic governing equations [14]:
where u, v, w denote the velocity of the fluid in the x, y, z direction, respectively; Ax, Ay, Az denote the area fraction of the fluid in the x, y, z direction, respectively; VF denotes the volume fraction; P is the pressure exerted on the fluid micrometric elements; Gx, Gy, Gz are the gravitational acceleration in the x, y, z direction, respectively; and fx, fy, fz are the viscous forces in the x, y, z direction, respectively.
In numerical simulations, the selection of a turbulence model significantly influences the accuracy of the calculations. Hence, it is imperative to choose an appropriate turbulence model. Given that this paper primarily deals with fully developed circular tube turbulence, which entails velocity and momentum coupling among fluids and features substantial time and spatial scales in the non-constant flow, the RNG k–ε turbulence model [15,16,17] has been chosen for the conclusive numerical simulation work. The RNG model takes into account the effect of eddies on turbulence and improves the accuracy of vortex-flow prediction [18]. Its equations are as follows:
where vt is the eddy viscosity coefficient; μ is the kinetic viscosity coefficient; the empirical constants cε1 and cε2 have values of 1.42 and 1.68; c3 = 0.012; η0 = 4.38; cμ = 0.085; and the values of Prandtl numbers αk and αε corresponding to the turbulent kinetic energy k and the dissipation rate ε are both 0.7194.
The Flow-3D software realizes an accurate description of the sediment movement with the help of an empirical equation model proposed by Mastbergen and Van den Berg [19]. The critical Shields number first needs to be calculated from the Soulsby–Whitehouse equation [20], which is given below:
where ρi is the sediment density, ρf is the fluid density, di is the sediment diameter, μf is the hydrodynamic viscosity, and ‖g‖ is the magnitude of gravitational acceleration.
Under the action of the jet, part of the deposited sediment will be disturbed to show a suspended state and it will continue to move under the carrying of the fluid. The uplifting velocities of entrained sediment ulift,i and usetting,i are calculated as follows:
where αi is the sediment carryover coefficient with a recommended value of 0.018 [19]; ns is the normal direction of the bed; and vf is the kinematic viscosity of the liquid.
2.3. Grid-Independent Analysis
It is well known that the number of the grid is closely related to the accuracy and cost of the numerical calculation. In order to investigate the optimal number of grids suitable for this numerical simulation, the scour depth Ht of the sand bed at H/D = 2 and inlet flow velocity Vb = 1.485 m/s is chosen as the monitoring parameter for the grid-independent analysis. Five sets of grid schemes with increasing numbers are set, and the results of the independence analysis are shown in Figure 2. From the figure, it can be seen that the depth of the scour pit Ht increases gradually with the encryption of the grid. When the grid is encrypted to Scheme 4, Ht almost no longer increases. It is considered that the number of meshes at this time can already meet the accuracy requirements of numerical calculations. Therefore, the grid number scheme in Scheme 4 is selected for the subsequent numerical simulation study, and the grid number is 43,825.
Figure 2. Grid-independent analysis.
2.4. Grid Delineation and Boundary Conditions
Within the Flow-3D software, a grid block is used that covers the entire 2D computational area as shown in Figure 1. Given the large aspect ratio of the jet pipe and the significant turbulent coupling between the fluid and sediment near the pipe outlet, grid refinement is implemented in the vicinity of the pipe outlet. The grid-encrypted area is mainly the area between the jet outlet and the sand bed, as shown in Figure 3. In addition, a mesh node is provided at the baffle on each side of the computational domain to ensure proper identification of the fluid boundary during numerical simulations. The upper boundary of the computational domain is defined as a velocity inlet, where the velocity magnitude is denoted as Vb, and the direction is oriented vertically downward. The lower boundary is the wall and no fluid or sediment flux is allowed. The two side boundaries are specified as pressure boundaries and the pressure is set to be 0 Pa. Based on the requirement of 2D numerical simulation, the boundaries of the front and rear sides are set as symmetric boundaries, both with one grid node. At the same time, the boundary-layer mesh near the pipe and the sand bed is encrypted accordingly. y+ is set at around 30 to ensure that the first grid nodes are in the turbulence core region, so as to ensure that the RNG k–ε turbulence model is perfectly adapted to the boundary conditions. Considering that the velocity strength and pressure gradient of the fluid around the baffle are small and it is not an observation area, the encryption of the boundary-layer grid is not performed for the time being.
Figure 3. Computational grid.
Numerical simulations are performed using the discrete control equations of the control volume method, with the diffusion term of the equations in the central difference format and the convection term in the second-order upwind format, and the equations are solved using a coupled algorithm. The standard wall equations are used, and the no-slip option in the wall shear boundary conditions is checked. In the non-stationary numerical simulation, the time step is set to 0.05 s. In order to ensure the accuracy of the numerical calculations, each time step is iterated 100 times, and the convergence accuracy is set to 10−5.
In this paper, the continuous jet is periodically truncated to form a blocking pulsed jet. The pulse period of its pulse velocity can be expressed as T = tj + t0 (tj and t0 are the jet time and truncation time, respectively, taking the value of 0.5 s), and the inlet flow rate of the jet pipe is Vb during the jet time period, while the inlet flow rate of the jet pipe is 0 during the truncation time period, as shown in Figure 4.
Figure 4. Velocity characteristics of the blocking pulsed jet.
3. Experimental Validation
To validate the accuracy of the numerical simulations, an experimental investigation of jet impingement on sediment is conducted. The experimental setup is shown in Figure 5. The parameters characterizing the sediment in the experiments are guaranteed to be the same as the settings in the numerical simulations. Specifically, non-cohesive sand is used with a median particle size dm of 0.77 mm, a specific gravity Δ of 1.65, and a particle gradation σg of 1.21. An angle plate is employed to control the impinging angle of the jet pipe, a COMS camera captures images of the pit, and a laser range finder is utilized for precise measurements of pit depth and dune height. In order to quantitatively describe the effect of jet impingement, the depth of the sand pit and the height of the dune are defined as d and h, respectively.
Figure 5. Schematic diagram of the experimental setup.
Figure 6 compares the stabilized morphology of the sand bed formed under the scouring of the jet for an impinging distance H/D of two in the numerical simulation and the experiment. The inlet flow velocities Vb of the jet pipe are 0.424 m/s, 0.955 m/s, and 1.485 m/s, respectively. As depicted in the figure, the ultimate scouring morphology of the sand bed, as obtained through numerical simulation, closely aligns with the experimental results. This alignment underscores the strong agreement between the numerical simulation and the experimental data. Nevertheless, it must be recognized that the final scour depths of the numerical simulations are all slightly smaller than the experimental values under the same conditions. The possible reason for this is the wall effect, i.e., the porosity of the actual sand bed is not homogeneous, with the upper sand layer being slightly more porous [21], whereas the porosity of the sand bed in the numerical simulation strictly follows the set value. Given that the accuracy of numerical calculations is subject to various influencing factors, and considering that the numerical solution inherently involves an approximation process, the numerical methods employed in this study can be deemed both accurate and dependable.
There are many factors that affect the performance of jet scouring, such as the shape of the nozzle, the size of the nozzle, the inlet flow rate of the jet pipe, the impinging distance, and the sediment parameters. Changes in any one of these factors can have a large effect on the parameters that measure the scouring performance of the jet, such as the depth of the scouring pit |ymin|, the height of the dune ymax, the radius of the scouring pit R. In this paper, the effects of the inlet velocity Vb and impinging distance H/D on the scouring performance of the jet pipe are investigated. Seven working conditions with inlet velocity Vb of 0.424 m/s, 0.690 m/s, 0.955 m/s, 1.220 m/s, 1.485 m/s, 1.751 m/s and 2.016 m/s are calculated for different impinging distances H/D (H/D = 2, 4, 6 and 8). The corresponding Reynolds numbers Re are 8404, 13,657, 18,910, 24,162, 29,415, 34,667, and 39,920, respectively.
4.1. Characterization of Pit at Different Impinging Distances
After the jet impinges on the sand bed for a sustained period of time, the shape of the sand bed will no longer change and remain stable. Figure 7 shows the stable bed morphology formed by the jet impinging on the sand bed with different velocities Vb, and at different impinging distances H/D. The x-axis is at the axial position of the jet pipe, and the y-axis is the initial horizontal plane of the sand bed. As can be seen from the figure, under the condition of Vb = 0.424 m/s, the pit depths |ymin| corresponding to impinging distances H/D of two and four are basically equal. However, when H/D is increased to six, |ymin| becomes significantly smaller, and when H/D is eight, |ymin| increases again. Under the Vb = 0.690 m/s condition, the effect of H/D on the scour pit depth |ymin| is small, and its size basically stays around 3.5 cm. Under the Vb = 0.955 m/s condition, the pit depth corresponding to H/D = eight is slightly smaller than the pit depths at other impinging distances, and the magnitude of |ymin| is basically maintained near 4.6 cm. Under the Vb = 1.220 m/s condition, the change of the scouring pit depth |ymin| with the impinging distance H/D starts to be gradually significant, especially the scouring pit depth |ymin| which decreases by about 1.7 cm when the size of H/D increases from two to six. Under the condition of Vb = 1.220 m/s, the larger the H/D, the smaller the pit depth |ymin|, especially when the H/D is eight, the pit depth is obviously larger than the pit depth at other impinging distances. The corresponding pit depths |ymin| for Vb of 1.751 m/s and 2.016 m/s remain basically unchanged. From the above analysis, it can be seen that under the same Reynolds number conditions to some extent the impinging distance has a very limited effect on the depth of the pit |ymin|. When the impinging distance increases, the depth of the pit begins to decrease. This can be attributed to the fact that the increased distance results in the jet encountering the initial static water resistance over a longer duration, leading to a greater dissipation of kinetic energy and a subsequent reduction in the impinging force of the jet.
The depth of the scouring pit serves as a critical parameter for assessing the impact of jet impingement on sand beds, just as the height of the dune represents a key indicator for evaluating the effectiveness of this process. In Figure 7a, it can be seen that the dune height ymax increases synchronously with the increase of the impinging distance H/D at Vb = 0.424 m/s. When Vb ≥ 0.955 m/s, the dune height ymax no longer grows significantly with the increase of impinging distance H/D. To further explore the relationship between dune height and impinging distance, Figure 8 is plotted with the impinging distance as the horizontal coordinate and the dune heights on either side as the vertical coordinate. From the figure, it can be seen that when 0.424 m/s ≤ Vb ≤ 1.485 m/s, the dune height ymax increases with the increase of the impinging distance H/D, and the dune height ymax starts to decrease with the increase of the impinging distance H/D when Vb > 1.485 m/s. The reason behind the aforementioned phenomenon is that when the inlet velocity Vb of the jet pipe is low, suspended sediment tends to displace towards the sides of the dune, causing some of the sediment to accumulate on the dune and thereby increase its height. When Vb ≥ 1.485 m/s, due to the enhanced impact force, most of the suspended sediment no longer moves and accumulates near the dunes and sand pits, and it starts to move on the outside of the dunes, causing the dune height to decrease.
Figure 8. Variation in the height of dunes on either side of the scour pit with Vb: (a) left; (b) right.
In order to clarify the relationship between the pit radius R and the impinging distance H/D, the relationship is given in Figure 9. From the figure, it can be seen that when 0.424 ≤ Vb ≤ 0.690, the increase of impinging distance H/D has basically no effect on the radius R of the pit, and its magnitude always stays near 13 cm. As the inlet velocity Vb of the jet pipe increases (1.220 ≤ Vb ≤ 1.485), the impact of the pulsed jet intensifies. Consequently, the suspended sediment is propelled towards the sides of the sand pit; although, it has not reached the dune and the area beyond it. Instead, a substantial amount of suspended sediment settles within the sand pit on both sides. Simultaneously, as the impact distance increases, the reach of jet impact and the turbulence induced by the jet expand, leading to enhanced sediment transport on both sides of the sand pit. This ultimately results in a reduction in the radius of the scouring pit as the impinging distance increases.
Figure 9. Relationship between pit size and impinging distance.
4.2. Characterization of Piting at Different Reynolds Numbers
Figure 10 depicts the stabilized morphology of the sand pit resulting from the influence of jets with varying Reynolds numbers. Under the conditions of H/D = two and four, the inlet velocity Vb of the jet pipe is 0.424 m/s and 0.690 m/s, and the depth of the pit |ymin| is basically equal, which indicates that the impact of the jet on the sand bed at this time is small, and the sediment is only transported and circulated in the sand pit. When Vb ≥ 0.955, the depth of the pit |ymin| increases significantly with the increase of Vb. Under the condition of H/D = 6, the depth of the pit, denoted as |ymin|, ceases to remain constant when Vb is less than or equal to 0.690 m/s. However, the disparity between the two measurements remains relatively small, suggesting that the impact force and turbulence of the jet are already capable of transporting sediment from the bottom of the pit to its flanks when Vb ≤ 0.690 m/s. In the H/D = 8 condition, due to the impinging distance H/D is larger, and when the velocity of the jet pipe is small (Vb ≤ 0.690 m/s), the kinetic energy of the jet is continuously exchanged with the static water body and then reduced, making its impact force reduce, and the sediment can only be transported and circulated at the bottom of the sand pit. To further investigate the effect of the Reynolds number of the jet on the depth of the pit |ymin|, Figure 11 is plotted with the jet velocity Vb as the horizontal coordinate and the depth of the pit |ymin| as the vertical coordinate. From the figure, it is evident that there exists a strong linear relationship between the depth of the scouring pit and the jet velocity. The data points in the figure can be fitted to establish the following relationship between the depth of the scouring pit and the jet velocity:
Figure 11. Linear relationship between scouring-pit depth and jet velocity.
4.3. Characterization of Pits with Different Impinging Times
Figure 12 illustrates the deformation of the sand bed caused by the impact of the pulsed jet over a time range from 0.75 s to 3.5 s (with intervals of 0.25 s). When the jet velocity Vb is 0.424 m/s, within the initial 0.75 s of jet initiation, the impact of the pulsed jet leads to noticeable deformation of the sand pit and dune, with their fundamental shapes taking form. The depth of the pit, denoted as |ymin|, continuously increases from 0.75 s to 2 s, eventually stabilizing around 2.75 s. By the onset of the pulsed jet, the dune has already assumed a fundamental profile, and its maximum height, represented as ymax, exhibits minimal variation over time, remaining relatively constant.
In this paper, a numerical computational study is conducted to examine the characteristics of sand-bed impingement using obstructing pulsed jets. A comprehensive analysis is undertaken, encompassing impingement-pit depth, dune height, and impingement-pit radius. The following conclusions are drawn:
Under consistent jet-velocity conditions, the impingement distance (H/D) has minimal impact on the depth of the scouring pit within the range of 2 ≤ H/D ≤ 6. However, beyond this range (H/D > 6), increased impingement distance leads to heightened jet-energy dissipation, resulting in a weakened impact force and a subsequent reduction in pit depth. Additionally, for lower jet velocities, impinging-distance variations have negligible effects on pit radius, while higher jet velocities induce a decrease in pit radius with an increase in impinging distance.
The study establishes strong linear relationships between both the radius and depth of the scouring pit and the jet velocity. However, the relationship between dune height and pulsed-jet velocity is characterized by randomness and uncertainty. The dynamics of sediment transport contribute to the lack of symmetry in the stable configuration of the sand pit concerning the jet-pipe axis. Furthermore, the relationship between dune height and pulsed-jet velocity exhibits transient characteristics, highlighting the complex nature of these interactions.
The numerical computational analysis emphasizes the transient characteristics of the sand-pit configuration due to sediment-transport dynamics. The stable state of the pit does not assume symmetry with the jet pipe as the axis, introducing a level of asymmetry in the system. This asymmetry is crucial in understanding the complex behavior of the sand-bed impingement. The findings underscore the need to consider dynamic and transient factors when studying the impact of obstructing pulsed jets on sand-bed characteristics.
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노트북의 듀얼 그래픽 카드 – 간단하지만 숨겨진 솔루션
이제 많은 노트북에 NVIDIA 그래픽 카드와 Intel 통합 그래픽 간에 전환 할 수 있는 기능이 있습니다. NVIDIA 카드로 FLOW-3D POST 가 실행되고 있는지 확인하는 것이 중요합니다 . NVIDIA 제어판을 통해 NVIDIA 카드로 노트북을 강제로 실행할 수 있습니다.
비디오 드라이버 업데이트
비디오 드라이버가 업데이트 되었는지 확인하는 것이 좋습니다. FLOW-3D POST 에서 비디오 드라이버를 업데이트하여 쉽게 해결할 수 있는 아티팩트 및 디스플레이 문제에 대한 보고가 있었습니다 . 비디오 드라이버를 최신 상태로 유지하는 것은 이러한 문제를 방지하는 좋은 방법입니다.
RAM, RAM, RAM!
메모리가 충분하지 않으면 시뮬레이션 후 처리가 불가능할뿐만 아니라 메모리 요구 사항을 인식하는 것이 중요합니다. 최대 10 배의 성능 저하로 이어질 수 있습니다! FLOW-3D POST 에 필요한 RAM 양은 여러 요소, 특히 시뮬레이션 크기에 따라 다릅니다. 사용자에게 최대한의 유연성을 제공하기 위해 메시의 셀 수에 따라 다음과 같은 RAM 권장 사항이 있습니다.
초대형 (2 억 개 이상의 셀) : 최소 128GB
대용량 (6 천 ~ 1 억 5 천만 셀) : 64-128GB
중간 (3 천만 ~ 6 천만 셀) : 32-64GB
소형 (3,000 만 셀 이하) : 최소 32GB
FLOW-3D POST 는 메모리 집약적 일 수 있습니다. 실행할 시뮬레이션 크기에 대한 대략적인 아이디어가 있는 경우, 이 지침을 가능한 한 잘 따르는 것이 좋습니다. 즉, 유연성을 극대화하고 가장 원활한 FLOW-3D POST 경험을 보장하기 위해 문제 크기에 관계없이 가능한 한 많은 RAM을 확보하는 것이 좋습니다.
그래픽 카드를 업그레이드 교체 설치하는 방법
그래픽 카드를 업그레이드하는 것은 성능 향상을 위한 좋은 방법이다. 그래픽 카드 업그레이드를 통해 시각적으로 고사양을 요구하는 POST 작업을 쉽게 소화할 수 있는 컴퓨터로 진화할 수 있다.
업그레이드를 위한 그래픽 카드 구매시 고려 사항, 기존 PC에 적합한가?
원하는 그래픽 카드를 결정하는 것은 복잡하고 미묘한 문제다. AMD와 엔비디아는 200달러 미만에서부터 최대 1,500달러에 이르는 지포스(GeForce) RTX 3090에 이르기까지 거의 모든 예산에 대한 선택지를 제공하기 때문이다.
카드의 소음, 발열, 전력 소비 등과 같은 사항을 고려할 수 있겠지만, 일반적으로는 비용 대비 가장 큰 효과를 제공하는 그래픽 카드를 원한다.
컴퓨터가 새 그래픽 카드를 지원하는 적절한 하드웨어인지 확인한다.
사용자가 겪는 가장 일반적인 문제는 부적절한 파워 서플라이(power supply)다. 충분한 전력을 공급할 수 없거나 사용 가능한 PCI-E 전원 커넥터가 충분하지 않을 수 있다. 필자의 경험상 파워 서플라이는 적어도 제조업체에서 권장하는 파워 서플라이의 요구 사항을 충족해야 한다. 예를 들어, 350W를 소비하는 지포스 GTX 3090을 구입했다면 8핀 전원 커넥터 한 쌍과 함께 엔비디아에서 제안한 최소 750W의 전력 공급 장치를 갖춰야 한다.
현재 파워 서플라이가 얼마나 많은 전력을 제공하는지 알아보려면 PC 본체를 열고 모든 파워 서플라이에 기본 정보가 나열된 표준 식별 스티커를 확인하면 된다. 또한 사용 가능한 6핀 및 8핀 PCI-E 커넥터의 수를 확인할 수 있다.
ⓒ Thomas Ryan 파워서플라이
마지막으로 본체 내부에 새 그래픽 카드를 넣을 충분한 공간이 있는지 확인한다. 일부 고급 그래픽 카드는 길이가 상당히 길어 30Cm 이상일 수 있으며, 확장 슬롯이 2개 또는 3개가 될 수 있다. 해당 그래픽 카드의 실제 크기는 제조업체 웹사이트에서 찾을 수 있다.
여기까지 해결했다면 이제 본격적으로 설치 작업에 착수한다.
생각보다 간단한 그래픽 카드 설치 작업
그래픽 카드 설치에는 새 그래픽 카드, 컴퓨터, 그리고 십자 드라이버 3가지만 있으면 된다. 설치하기 전 PC를 끄고 전원 플러그를 뽑는다.
기존 GPU를 제거해야 하는 경우가 아니면, 먼저 프로세서의 방열판에 가장 가까운 긴 PCI-E x16 슬롯을 찾아야 한다. 이 슬롯은 메인보드의 첫 번째 또는 두 번째 확장 슬롯이다.
이 슬롯에 접근을 차단하는 느슨한 전선이 없는지 확인한다. 기존 그래픽 카드를 교체하는 경우, 연결된 케이블을 모두 분리하고, PC 본체 후면 내부에 고정 브래킷에서 나사를 제거한 다음, 카드를 제거한다. 대부분의 메인보드에는 그래픽 카드를 제자리에 고정하는 PCI-E 슬롯 끝에 작은 플라스틱 걸쇠(latch)가 있다. 이 걸쇠를 눌러 이전 그래픽 카드의 잠금을 해제하고 분리한다.
ⓒ Thomas Ryan PCI-E x16 슬롯에 설치
이제 새 그래픽 카드를 개방형 PCI-E x16 슬롯에 설치할 수 있다. 카드를 슬롯에 완전히 삽입한 다음, PCI-E 슬롯 끝에 있는 플라스틱 걸쇠를 눌러 제자리에 고정한다. 그런 다음 나사를 사용해 그래픽 카드의 금속 고정 브래킷을 PC 본체에 고정한다. 덮개 브래킷 또는 이전 그래픽 카드를 고정했던 나사를 재사용할 수 있다.
ⓒ Thomas Ryan 그래픽 카드에는 추가 전원 커넥터 연결
대부분의 게임용 그래픽 카드에는 추가 전원 커넥터가 필요하다. 추가 전원이 필요한 경우, 해당 PCI-E 전원 케이블을 연결했는지 확인한다. 전원이 제대로 공급되지 않으면 그래픽 카드가 제대로 작동하지 않는다. 이 PCI-E 전원 케이블을 연결하지 않으면 PC 자체가 부팅되지 않을 수 있다.
그래픽 카드를 고정하고 난 후, 전원을 켠 상태에서 본체 측면 패널을 제자리로 밀어넣고 디스플레이 케이블을 새 그래픽 카드에 연결해 작업을 완료한다. 이제 컴퓨터를 켠다.
이제 그래픽 카드의 소프트웨어를 업그레이드할 단계가 왔다.
새 그래픽 카드가 이전 카드와 동일한 브랜드일 경우에는 절차가 간단하다. 제조업체의 웹사이트로 이동해 운영체제에 맞는 최신 드라이버 패키지를 다운로드한다. 그래픽 드라이버는 일반적으로 약 500MB로, 상당히 크다. 인터넷 연결 속도에 따라 다운로드하는 데 시간이 걸릴 수도 있다. 드라이버를 설치하고 컴퓨터를 다시 시작하면 이제 새 그래픽 카드가 제공하는 부드럽고 매끄러운 프레임 속도를 즐길 수 있다.
그래픽 카드 제조업체가 바뀐 경우(인털에서 AMD로, 혹은 AMD에서 인텔로), 새 그래픽 카드용 드라이버를 설치하기 전에 이전 그래픽 드라이버를 제거하고 컴퓨터를 다시 시작해야 한다. 이전 드라이버를 제거하지 않으면 새 드라이버와 충돌할 수 있다.
editor@itworld.co.kr 기사 일부 발췌 인용
그래픽 카드 GPU 온도 확인하는 방법
그래픽 카드 온도 확인은 아주 쉽다. 윈도우에서 바로 온도를 확인할 수 있는 내장 도구도 추가됐다. 또한, 무료 GPU 모니터링 도구가 많이 있고 그중 대다수가 온도를 측정해준다. 조금 더 자세히 알아보자.
ⓒ MARK HACHMAN / IDG 그래픽카드 온도 확인
마이크로소프트가 윈도우 10 2020년 5월 업데이트에서 GPU 온도 모니터링 툴을 작업 관리자에 추가했다. 무려 24년이나 걸렸다.
Ctrl+Shift+Esc를 열어 작업 관리자 대화창을 열거나 Ctrl+Alt+Delete에서 ‘작업 관리자’를 선택하거나 윈도우 시작 메뉴 아이콘을 오른쪽 클릭해서 ‘작업 관리자’를 선택한다. 여기에서 ‘성능’ 탭으로 들어가면 왼쪽에 GPU를 확인할 수 있을 것이다. 윈도우 10 2020년 5월 업데이트 혹은 그 이후 버전의 윈도우가 설치되어 있을 때만 사용할 수 있는 기능이다.
하지만 이 기능은 매우 단순하다. 시간 흐름에 따른 온도 변화를 추적하지 않고, 현재의 온도만을 보여준다. 그리고 업무를 하거나 오버클럭 조정 중에 작업 관리자를 여는 것도 귀찮을 수 있다. 마침내 윈도우에 GPU 온도를 확인할 수 있는 기능이 들어간 것은 환영하지만, 뒤이어 설명할 서드파티 도구가 훨씬 더 나은 GPU 온도 확인 옵션을 제공한다.
AMD 라데온 그래픽 카드 사용자가 라데온 세팅(Radeon Setting) 앱을 최신 버전으로 유지하고 있다면 방법은 쉽다. 2017년 AMD는 시각 설정을 변경할 수 있는 라데온 오버레이(Radeon Overlay)를 출시했다. 여기에도 GPU 온도와 다른 중요한 정보를 확인할 수 있는 성능 모니터 기능이 있다.
프로그램을 활성화하려면 Alt+R 키를 눌러 라데온 오버레이를 불러온다. 성능 모니터링 섹션에서 원하는 탭을 선택한다. Ctrl+Shift + 0을 눌러서 성능 모니터링 도구 설정을 단독으로 불러올 수 있다.
라데온 세팅 앱에서 오버클럭 도구인 와트맨(Wattman)으로 이동해 GPU 온도를 확인할 수 있다. 윈도우 바탕 화면을 우클릭하고, 라데온 설정을 선택한 후 게이밍(Gaming) > 글로벌 세팅(Global Setting) > 글로벌 와트맨(Global Wattman) 항목으로 이동한다. 도구를 사용해 지나친 오버클럭으로 그래픽 카드를 날려버리지 않겠다고 서약한 후에는 와트맨에 액세스하고 GPU 온도, 그리고 그래프 형태로 된 핵심적 통계 수치를 볼 수 있다. 여기까지가 전부다.
라데온 사용자가 아닌 사람도 많을 것이다. 스팀의 하드웨어 설문 조사는 전체 응답자 PC 중 75%가 엔비디아 지포스 그래픽 카드를 탑재했다는 결과를 발표했다. 그리고 지포스 익스피리언스 소프트웨어는 GPU 온도 확인 기능을 제공하지 않아서 서드파티 소프트웨어의 손을 빌려야 한다.
그래픽 카드 제조 업체는 보통 GPU 오버 클럭을 위한 특수한 소프트웨어를 제공한다. 이 도구에는 라데온 오버레이처럼 가장 중요한 측정을 실행할 때 OSD(On-Screen Display)를 지속하는 옵션 등이 있다. 여러 종류 중에서 가장 추천하는 것은 다재다능함을 갖춘 MSI의 애프터버너(Afterburner) 도구다. 이 제품은 오랫동안 인기를 얻었는데 엔비디아 지포스, AMD 라데온 그래픽 카드 두 제품 모두에서 잘 작동하고, 반길 만한 다른 기능도 더했다.
IDG HWInfo는 언제나 누구에게나 적합한 모니터링 프로그램
GPU 온도에 전혀 관심이 없다면? 그렇다면 시스템의 온도 센서를 보여주는 모니터링 소프트웨어를 설치하면 편리할 것이다. HWInfo는 언제나 누구에게나 적합한 모니터링 프로그램으로, PC의 모든 부품의 가상 스냅샷을 보여준다. 스피드팬(SpeedFan) 과 오픈 하드웨어 모니터(Open Hardware Monitor)도 신뢰할 만한 서드파티 앱이다.
‘착한’ GPU 온도는 몇 도?
이제 그래픽 카드를 모니터링하는 소프트웨어를 갖췄다. 하지만 화면을 채우는 숫자는 맥락이 없이는 아무것도 아니다. 그래픽 카드 온도는 어디까지 괜찮은 것일까?
쉬운 대답은 없다. 제품마다 다르다. 이럴 때는 구글이 친구가 된다. 대다수 칩은 섭씨 90도 중반에도 작동하고, 게이밍 노트북에서도 90도까지 온도가 올라가는 경우가 흔히 있다. 그러나 일반 데스크톱 PC 온도가 90도 이상으로 올라간다면 구조 신호나 다름없다. 공기 흐름이 원활한 GPU 1대 시스템에서는 80도 이상 올라가면 위험하다. 팬이 여러 개 달린 커스텀 그래픽 카드는 무거운 워크로드 하에서도 60~70도가 적당하고, 수냉쿨러가 달린 GPU라면 온도가 더 낮아야 할 것이다.
그래픽 카드가 최근 5년 안에 생산된 제품이고 90도 이상으로 뜨거워진다면, 또는 최근 몇 주간 온도가 급격히 상승했다면 다음의 냉각 방법을 고려해보자.
그래픽 카드 온도 낮추는 법
그래픽 카드 온도가 높아졌을 때 하드웨어 업그레이드에 돈을 들이지 않고 개선하지 않기란 어렵다. 그러나 돈을 쏟아붓기 전에 정말 그래야 하는지 필요성을 점검해 보자. 다시 한번 강조하지만 그래픽 카드는 뜨거운 온도를 버틸 수 있도록 설계되어 있다. PC가 무거운 게임이나 영상 편집 중에 강제 종료되는 경우가 아니라면 아마도 걱정할 필요가 없을 것이다.
우선, 시스템의 케이블을 깨끗하게 정리해 GPU 주변의 공기가 원활하게 순환되는지 확인하라. 케이블이 깔끔하게 정리됐다면 케이스에 팬을 추가하는 것도 고려한다. 모든 PC는 최적의 성능을 위해 공기를 빨아들이고 내보내는 팬이 여럿 달려 있는데, POST PC라면 팬은 더 많아야 한다. 저렴한 팬은 10달러부터 구입할 수 있고, RGB 조명이 붙은 화려한 제품은 조금 더 가격이 높다.
마지막으로, GPU와 히트싱크의 써멀 페이스트가 오래되어 말라 있다면 효율이 떨어질 수 있다. 특히 오래된 그래픽 카드라면 더더욱 그렇다. 그리고 아주 드문 경우지만 품질이 좋지 않은 써멀 페이스트가 발라져서 출시되는 경우도 있다. 다른 방법이 모두 효과가 없다면 써멀 페이스트를 다시 바르는 것을 시도해보자. 그러나 과정이 매우 어려울 수 있고 카드마다 조금씩 다르고, 잘못 손댈 경우 사용자 보증 기한의 보호를 받을 수 없게 된다.
온도를 확실하게 낮추려면 수랭 쿨러를 위한 쿨링 시스템을 고려한다. 대다수 사용자에게는 지나친 모험이지만 대부분 수냉쿨러는 발열과 노이즈 감소 효과가 확실하고 공기 냉각에 있어 병목 현상도 없다.
“업무 효율 향상의 기본” 멀티 모니터 구축 가이드
듀얼 모니터를 사용하면 업무 생산성이 높아진다는 연구 결과가 있지만, 모니터가 많을수록 생산성이 높아지는지 여부에 대해서는 아직 이렇다 할 근거는 없다. 그러나 업무 생산성을 생각하지 않더라도 모니터를 여러 대(3대~6대까지) 사용하는 것은 멋진 일이며, 많은 화면을 봐야 하는 엔지니어는 정말 필요할지도 모른다.
모니터를 세로로 세워두면 긴 문서를 볼 때 스크롤을 적게 해도 된다는 장점이 있다. 멀티 디스플레이 환경을 구축하기 위해 고려해야 할 모든 것들을 살펴보겠다.
멀티 모니터 구축 가이드(www.itworld.co.kr)
1단계 : 그래픽 카드 확인하기
보조 모니터를 구입하기 전에 컴퓨터가 물리적으로 이 모든 모니터들을 감당할 수 있을지 점검해 봐야 한다. 가장 쉬운 방법은 PC의 뒷면을 보고, 그래픽 포트(DVI, HDMI, 디스플레이포트, VGA 등)가 몇 개나 있는지 확인하는 것이다.
별도의 그래픽 카드가 없다면 포트를 2개밖에 발견하지 못할 것이다. 그래픽이 통합된 대부분의 마더보드는 모니터 2개 밖에 설치하지 못한다. 별도의 그래픽 카드가 있다면, 마더보드의 포트를 제외하고 최소 3개의 포트를 발견할 수 있을 것이다.
팁 : 마더보드와 별도 그래픽 카드의 포트를 모두 이용해서 멀티 모니터를 설치할 수도 있지만, 이 경우 성능 저하와 모니터끼리의 속도 차이가 발생할 것이다. 그래도 이렇게 하고 싶다면, PC의 BIOS에서 Configuration > Video > Integrated graphics 로 진입한 다음, ‘always enable’로 설정한다.
그러나 별도의 그래픽 카드에 3개 이상의 포트가 있다고 해서 이것을 모두 동시에 사용할 수 있다는 의미는 아니다. 예를 들어서 구형 엔비디아 카드는 포트가 2개 이상이어도 하나의 카드에 모니터를 2개 이상 연결할 수 없다. 자신의 그래픽 카드가 멀티 모니터를 지원하는지 판단하는 가장 좋은 방법은 그래픽 카드 모델명을 찾아서 원하는 모니터 개수와 함께 검색하는 것이다. 예를 들어, ‘엔비디아 GTX 1660 모니터 4대’라고 검색하면 된다.
EVGA 지포스 RTX 2060 KO 같은 현대적인 그래픽카드는 여러 디스플레이를 동시에 연결할 수 있다. ⓒ BRAD CHACOS/IDG
그래픽 카드가 원하는 만큼 충분히 모니터를 지원할 수 있으면 좋지만, 그렇지 않다면 추가 그래픽 카드를 구입해야 한다. 그래픽 카드를 추가로 구입하기 전 타워 안에 충분한 공간(PCI 슬롯)이 있는지, 전원 공급은 충분한지 확인해야 한다.
멀티 모니터용으로만 그래픽 카드를 구입한다면 최신 그래픽 카드 중에서도 저렴한 옵션을 선택하는 것이 좋다.
아니면 멀티 스트리밍이 지원되는 디스플레이포트를 탑재한 신형 모니터를 사용하는 방법도 있다. 그래픽 카드의 디스플레이포트 1.2에 연결하고, 디스플레이포트 케이블을 사용해 다음 모니터로 연결하는 것이다. 모니터의 크기나 해상도가 같지 않아도 된다. 뷰소닉(ViewSonic)의 VP2468이 이런 제품 중 하나다. 아마존에서 약 210달러에 판매되는 이 24인치 모니터는 디스플레이포트 아웃 외에도 프리미엄 IPS 스크린, 아주 얇은 베젤 등 멀티 모니터 설정에 이상적인 특징을 제공한다.
2단계 : 모니터 선택하기
그래픽 카드에 대해서 파악했다면 이제 추가 모니터를 구입할 차례다. 사용자에 따라서 기존에 사용하고 있는 모니터, 책상 크기, 추가 모니터 용도 등에 따라서 완벽한 모니터가 달라질 것이다.
필자의 경우, 이미 24인치 모니터 2대를 가지고 있었기 때문에 중앙에 설치할 더 큰 모니터가 필요해서 27인치 모니터를 선택했다. 게임을 하지 않기 때문에 모니터 크기 차이는 상관없었다. 하지만 사용자에 따라서 멀티 모니터로 POST를 하거나 동영상을 보기 위해서는 이러한 구성보다 같은 모니터를 연결하는 것이 더 좋을 것이다.
모니터를 구입하기 전에 PC와 모니터의 포트 호환성을 설펴야 한다. DVI-HDMI 혹은 디스플레이포트-DVI 등 전환해주는 케이블을 이용할 수도 있지만 다소 귀찮다. 그러나 PC나 모니터에 VGA 포트가 있다면, 교체를 권한다. VGA는 아날로그 커넥터이기 때문에 선명도가 떨어진다.
3단계 : PC설정
모니터를 구입하고 나면 PC에 연결하고 PC의 전원을 켠다. 이것으로 모니터 설치가 끝났다. 하지만 완전히 끝난 것은 아니다.
윈도우가 멀티 모니터 환경에서 잘 동작하게 만들어야 하는데, 윈도우 7이나 윈도우 8 사용자라면 바탕화면에서 오른쪽 클릭하고 ‘화면 해상도’를 선택한다. 윈도우 10 사용자라면 ‘디스플레이 설정’을 클릭한다. 그러면 디스플레이를 정렬할 수 있는 창이 나타난다.
ⓒ ITWorld 디스플레이 설정
여기서 모니터들이 모두 탐지되는지 확인할 수 있다. ‘식별’을 클릭하면 각 디스플레이에 큰 숫자가 나타난다. 주 모니터(작업 표시줄과 시작 버튼이 나타나는 모니터)로 사용할 모니터에 1번이 나타나야 하는데, 원하는 것을 선택한 다음 아래 여러 디스플레이 설정에서 ‘이 디스플레이를 주 모니터로 만들기’를 클릭한다. 그 다음 ‘다중 디스플레이’ 드롭다운 메뉴에서 복제할 것인지 확장할 것인지를 선택하면 되는데, 대부분의 경우 ‘디스플레이 확장’이 적합하다.
GPU 제어판에서도 다중 모니터를 설정할 수 있다. 바탕화면에서 오른쪽 클릭을 하고 엔비디아, AMD, 인텔 등 그래픽 제조사의 제어판 메뉴를 열어 윈도우와 유사한 방식으로 디스플레이를 설정할 수 있다.
멀티 디스플레이를 구축할 경우에는 같은 모델을 이용하는 것이 해상도나 선명도, 색보정 등의 문제가 발생하지 않아 ‘끊김 없는’ 경험을 할 수 있다.
아래 차트는 200만 개가 넘는 PerformanceTest 벤치마크 결과를 사용하여 만들어졌으며 매일 업데이트됩니다. 이러한 전체 점수는 하드 디스크 드라이브의 읽기 속도, 쓰기 속도 및 탐색 시간을 측정하는 세 가지 다른 테스트에서 계산됩니다. 이 차트에는 Western Digital(WD), Samsung 및 Crucial과 같은 많은 주요 제조업체의 드라이브가 포함되어 있습니다. 결과에 따르면, 최고 성능의 SSD(솔리드 스테이트 드라이브)는 Gen4 및 Gen5 인터페이스를 사용하는 M.2 NVMe 드라이브입니다.
원문출처 : 본 자료는 ITWORLD 에서 작성된 자료로 수치해석 엔지니어에게 도움이 될 수 있어 인용 제공하였습니다. https://www.itworld.co.kr/news/185628
“폼팩터와 속도로 구분한” SSD 선택 가이드
Alaina Yee | PCWorldSSD(Solid State Drive)는 분명 구식 하드 디스크 드라이브보다 이점이 있다. SSD가 더 빠르고 조용하며 전력도 덜 소비한다. 문제는 사양에 일련의 약어가 포함되어 있기 때문에 자신에게 필요한 것이 무엇인지 파악하기가 어려울 수 있다는 점이다.
방법은 간단하다. 폼 팩터와 속도만 선택하면 된다. 이 가이드에서 그 방법을 설명하고자 한다.
SSD 폼팩터 : M.2 드라이브 vs 2.5인치 드라이브
폼팩터부터 시작해 보자. SSD는 모양과 크기가 다양하지만 M.2와 2.5가 가장 보편적인 유형이다. 각 유형은 저마다 장점이 있다. 껌처럼 생긴 M.2 드라이브는 마더보드에 직접 연결되고(그래서 데스크톱 PC의 선정리가 깔끔해지며) 일부 유형은 2.5인치 드라이브보다 빠르다. 일반적인 저장장치처럼 PC에 삽입되는 사각형의 2.5인치 드라이브가 더 저렴한 경우가 많다.
기타 덜 보편적인 폼팩터로는 PCIe 추가 카드와 U.2 드라이브가 있으며, 둘 다 데스크톱 PC에 사용된다. PCIe 추가 카드는 사운드 카드나 그래픽 카드와 비슷해 보이며 같은 PCIe 슬롯을 사용하여 마더보드에 연결된다. U.2 SSD는 2.5인치 드라이브와 비슷해 보이지만 제공업체가 마더보드에 U.2 커넥터를 추가한 경우에만(또는 M.2 슬롯에 사용하기 위해 어댑터를 구매한 경우에만) 작동한다. 또한 구형 노트북이나 미니 PC에 사용되는 mSATA 드라이브도 있지만 최신 하드웨어에서 M.2 드라이브로 대체되었으며 mSATA와 M.2 SSD는 서로 호환되지 않는다.
그렇다면 어떤 유형을 선택할까? 데스크톱이나 노트북이 지원할 수 있는 것과 성능 요구사항, 예산 규모, 제작 선호도에 따라 달라진다. 대부분의 사람들은 2.5인치와 M.2 폼팩터 중에서 선택하는 데 집중할 수 있다. PCIe 추가 카드와 U.2는 더 틈새시장이며, mSATA는 기존 드라이브를 교체하거나 구형 호환 하드웨어에 추가할 때나 사용된다.
최신 하드웨어나 약간 오래된 고급 하드웨어가 적용된 데스크톱 시스템의 경우 M.2와 2.5인치 드라이브를 모두 사용할 수 있을 것이다. 많은 사람이 둘 중에 선택하지 않고, 조합하여 사용한다. M.2를 부팅 드라이브로 사용하고 2.5인치 드라이브는 추가 저장장치로 사용하는 식이다. 이 조합은 케이블 관리 문제와 일반적인 케이블 복잡성을 줄이면서 제작자가 단일 PC에서 빠르고 합리적인 고용량 SSD를 활용하는 데 도움이 된다.
구형 데스크톱 시스템의 경우 2.5인치 드라이브만 선택할 가능성이 높다. 일부 M.2 드라이브로 더 빠른 속도를 원한다면, 마더보드에 PCIe 3.0 슬롯이 있는 경우 PCIe 추가 어댑터를 고려할 수 있다. 이 확장 카드는 M.2 드라이브를 넣을 수 있어서 PCIe 슬롯에 사용할 수 있다.
노트북의 경우, 신형 노트북을 구성하면서 SSD 폼팩터를 선택할 수 있는 경우 최고의 가성비를 제공하는 것을 선택한다. 하지만 대부분의 노트북은 선택권이 없을 것이다.
구형 노트북을 업그레이드할 때도 선택권이 없을 수 있다. 노트북의 구성으로 인해 1가지 폼팩터로 제한될 수 있다. 자신의 모델에 M.2 슬롯, 2.5인치 드라이브 베이 등이 있는지 확인하려면 온라인 사용 설명서를 찾거나 포럼과 레딧(Reddit)에서 검색해야 한다. 또한 고객 지원 부서로 문의할 수 있다. 노트북과 호환되는 드라이브를 구매하되, 인터페이스 유형(다음 섹션에서 다룸)과 오리지널 2.5인치 드라이브의 Z 높이 등의 세부사항에 주의하자. 또한 배터리 사용 시간에 영향을 미칠 수 있기 때문에 리뷰를 찾아보고 고려 중인 특정 SSD의 소비전력도 확인하자.
시스템에 적합한 것을 선택한 후 우리의 노트북에 SSD 설치하기 단계별 설명에 따라 더 쉽고 빠르게 업그레이드할 수 있다.
SSD 속도 : SATA vs NVMe
이제 속도로 넘어가 보자. SSD를 SATA 또는 NVMe 드라이브라고 지칭할 때 기대할 수 있는 속도 범위를 알 수 있다. 모든 SSD가 동일한 디지털 인터페이스로 데이터를 전송하지 않는다. 일부는 여전히 SATA(Serial ATA)를 사용하며 신형 모델은 PCIe(PCI Express)를 통한 NVMe(Non-Volatile Memory Express) 프로토콜을 사용한다.
SATA는 구형이며, 예상했듯이 SATA 드라이브는 NVMe보다 느리다. 이 인터페이스는 SSD와의 데이터 전송 속도를 제한한다. 하지만 SATA SSD는 하드 디스크 드라이브(HDD)보다 훨씬 빠르다. 평균 읽기 및 쓰기 속도가 초당 500MB 수준이며, 이는 HDD보다 3~6배 정도 빠른 수치이다. 여기에 가격까지 합리적이기 때문에 가성비 좋은 PC 조립 및 업그레이드를 할 수 있다. 우리는 새 PC를 구매하는 모든 사람에게 SATA SSD를 추천하고 있으며, 구형 PC를 업그레이드하는 경우에는 더욱 그렇다. HDD 대비 성능 개선이 상당하며, 웹 사이트 로딩 같은 일상적인 상황에서도 대부분의 사람들은 완전히 다른 컴퓨터를 사용하고 있는 느낌을 받게 될 것이다.
NVMe는 SATA 같은 한계가 없다. NVMe SSD는 매우 빠르다. 현재, SATA 드라이브보다 5~6배 정도 빠르며, 최신 제품은 현재 약 10배 정도 더 빠르다. 제조사들이 디자인을 다듬고 더 빠른 모델을 더 많이 출시하면서 NVMe 드라이브의 속도도 지속적으로 높아질 것이다.
NVMe SSD의 속도를 고려할 때 주의해야 할 용어는 PCIe Gen 3(PCIe 3.0)과 PCIe Gen 4(PCIe 4.0)이다. ‘x2’ 또는 ‘x4’(‘2배속’ 또는 ‘4배속’이라고 읽음)로 표기되어 있는 경우 드라이브가 사용할 수 있는 PCIe 레인 수를 나타낸다. 레인이 많으면 드라이브가 한 번에 전송할 수 있는 데이터도 많아진다. 최신 PCIe Gen3 x4 SSD의 읽기 및 쓰기 속도는 평균 초당 2,500~3,200MB이며 PCIe Gen4 x4 드라이브는 평균 초당 5,000MB이다.
그렇다면 어떻게 선택할까? 폼팩터와 마찬가지로 모든 상황에서 똑같이 결정할 수는 없다. 2.5인치 SSD는 모두 SATA 드라이브이며 M.2 SSD는 SATA와 NVMe로 제공되기 때문에 마더보드가 지원하는 것을 구매해야 한다. M.2 슬롯은 SATA만 지원하거나, NVMe만 지원하거나, 둘 다 지원할 수 있다. 데스크톱 PC 마더보드에서는 보드에서 최소 1개의 슬롯이 둘 다 지원하며, 두 번째 슬롯이 둘 다 또는 SATA만 지원하는 경우가 있다. 노트북에서는 그때그때 다를 수 있기 때문에 특정 모델의 사양을 살펴보자.
인터페이스 유형의 경우 SATA 드라이브는 일상 작업 및 게이밍에도 충분히 빠르며, NVMe는 대용량 파일 전송 시간을 절약해야 하는 고성능 PC에 좋다. 전체적으로 예산과 PC가 얼마나 오래되었는지에 따라 결정하게 된다.
NAND 유형과 DRAM이 없는 드라이브
인터페이스 유형은 SSD의 속도를 나타내는 주요 지표가 되지만, SSD에 사용되는 NAND(플래시 메모리)의 구체적인 유형과 DRAM 캐시 포함 여부도 영향을 미친다.
하지만 대부분의 사람은 이런 측면을 심층적으로 고려할 필요가 없으며, 다양한 유형의 파일 전송 시 드라이브의 성능이 더욱 중요하고 이런 결과는 각 리뷰에서 확인할 수 있다.
SLC(Single-Level Cell), MLC(Multi-Level Cell), TLC(Triple-Level Cell), QLC(Quad-Level Cell) NAND는 각각 장단점이 있지만, 매장에 재고가 있는지가 더욱 중요하기 때문이다. 요즘 제조사들이 이용을 낮추고 드라이브 용량을 늘리면서 대부분의 소비자용 SSD는 TLC와 QLC로 제작된다.
SAMSUNG 삼성의 980 프로는 TLC NAND를 사용한다. MLC NAND를 사용하는 970 프로와 달라진 점이다. 최근에는 MLC NAND를 사용한 일반 소비자용 SSD를 찾기가 쉽지 않다.
마찬가지로 DRAM이 없는 드라이브는 일부 벤치마크에서 DRAM 캐시가 있는 동급 SSD와 비교하여 상대적으로 뒤처지지만(무작위 쓰기 등) 인터페이스 성능이 떨어지는 SSD와 비교한 성능이 여전히 중요하다. DRAM이 없는 NVMe SSD는 여전히 SATA SSD보다 빠르며, DRAM이 없는 SATA SSD는 여전히 HDD보다 빠르다. 이런 기대치를 충족하지 못하는 DRAM이 없는 SSD나 DRAM 캐시가 있는 모델과 가격이 같은 SSD는 피하자. 또한 전반적인 성능이 필요한 경우에도 피하자. 하지만 모든 D램리스 SSD를 피하고자 예산을 늘릴 필요는 없다.
요약
이 모든 정보를 파악하고도 아직 어떻게 해야 할지 모르겠다면 걱정하지 말자. 아래의 두 가지 질문에만 답해보면 구매할 SSD의 유형을 파악할 수 있다. 1. 자신의 PC나 노트북에 장착되는 유형은 무엇인가? (2.5인치 SSD, M.2 SSD, 둘 다?) 2. 자신의 PC나 노트북이 지원하는 인터페이스 유형은 무엇인가? (SATA, NVMe, 둘 다?)
데스크톱 PC의 마더보드 사양을 보거나 노트북의 사용 설명서, 제조사 포럼, 레딧 등만 살펴보아도 이런 질문에 쉽게 대답할 수 있다.
노트북의 경우 (해당하는) 2.5인치 드라이브의 최대 Z 높이를 확인하여 장착 여부를 판단하고, 고려 중인 SSD의 소비전력도 파악한다. 후자는 배터리 사용 시간에 영향을 미칠 수 있다. 성능을 고려하되 자신의 요구사항도 평가하자. 중간급 또는 가성비 제품으로 충분한 데도 최고의 품질을 위해 비용을 지불할 필요는 없다. 다르게 이야기하는 인터넷 댓글들은 무시하자. editor@itworld.co.kr
수치해석에서 SSD가 필요한가?
본 자료는 ITWORLD 기사에서 2021년 3월과 05일 자료와 2021년 12월 14일 자료에서 발췌 인용된 자료입니다. (출처 : www.itworld.co.kr)
수치해석을 하는 경우 계산과정에서 생성되는 결과 파일 사이즈는 매우 크기 때문에, 빠른 디스크 속도는 사용자의 총 해석시간을 줄이는데 큰 도움이 됩니다.
수치해석 업무를 담당하는 사용자에게 SSD가 필요한가? 한마디로 말하면 수치해석을 하는 모든 사람은 보유하고 있는 수치해석 장비의 디스크를 SSD로 업그레이드하는 것이 좋다. 가장 빠른 기계식 하드 드라이브도 SSD 속도에는 미치지 못한다.
기존 노트북, 또는 데스크톱의 하드 드라이브를 SSD로 교체하면 완전히 새로운 시스템처럼 느낄 수 있다. 수치해석을 하는 사용자는 SSD를 구입하는 것은 컴퓨터를 업그레이드하는데 가장 적합한 옵션이다.
SSD는 기계식 하드 드라이브보다 기가바이트 당 비용이 더 많이 들기 때문에 초 고용량으로 제공되지 않는 경우가 많다. 속도와 저장 공간이 필요한 경우, 128GB 나 256GB의 SSD를 구입해 부팅 드라이브로 사용하고, 기존 하드 드라이브를 PC의 보조 저장 장치로 사용하면 최선의 선택이 된다.
하드 드라이브는 가격 대비 용량 측면에서 여전히 큰 이점을 제공하며, 자주 사용되지 않는 데이터를 저장하는 용도로 적합하다. 그러나 운영체제, 프로그램, 자주 사용하는 데이터에는 보유하고 있는 시스템이 지원한다면 NVMe SSD, 지원하지 않는다면 SATA SSD를 사용하는 것이 좋다.
아래 그래프를 보면 SSD를 왜 사용해야 하는지 명확해진다.
SSD Speed compare
NVMe/M.2/SATA SSD 비교 정리
NVMe SSD
M.2 SSD
SATA SSD
속도
PCIe 3.0 최대 3,500MBps
PCIe 4.0 최대 7,500MBps
SATA 최대 550MBps
NVMe PCIe 3.0 최대 3,500MBps
NVMe PCIe 4.0 최대 7,500MBps
최대 550MBps
폼팩터 종류
M.2 U.2* PCIe 카드* *일반적이지 않은 종류
N/A
2.5인치 드라이브 M.2
인터페이스 종류
N/A
SATA NVMe
N/A
장점
속도가 빠름
공간을 덜 차지함
속도와 가격의 균형
단점
가격이 비쌈
SATA M.2가 2.5인치 SATA보다 비싼 경우가 있음
속도가 느리고 공간을 많이 차지함
SATA SSD vs. NVMe SSD
시장에 SATA SSD와 NVMe SSD가 아직 공존하는 데는 이유가 있다. 메모리 기반 SSD의 잠재력을 감안할 때 결국 새로운 버스와 프로토콜이 필요할 수밖에 없으리란 점은 초기부터 명확했다. 그러나 초창기 SSD는 비교적 속도가 느렸으므로 기존 SATA 스토리지 인프라를 사용하는 편이 훨씬 더 편리했다.
SATA 버스는 버전 3.3에 이르러 16Gbps까지 발전했지만 거의 모든 상용 제품은 여전히 6Gbps에 머물러 있다(오버헤드를 더해 대략 550MBps). 버전 3.3이라 해도 현재 SSD 기술, 특히 RAID 구성으로 낼 수 있는 속도에 비하면 한참 느리다.
그 다음으로 등장한 방법은 역시 기존 기술이지만 대역폭이 훨씬 더 높은 버스 기술인 PCI 익스프레스, 즉 PCIe 활용이다. PCIe는 그래픽 및 기타 애드온 카드를 위한 기본 데이터 전송 계층이다. 3.x 세대 PCIe는 복수의 레인(대부분의 PC에서 최대 16개)을 제공하며, 각 레인은 1GBps(985MBps)에 가까운 속도로 작동한다.
PCIe는 썬더볼트 인터페이스의 기반이기도 하다. 썬더볼트는 게임용 외장 그래픽 카드, 그리고 내장 NVMe와 거의 대등한 속도를 내는 외장형 NVMe 스토리지에서 진가를 발휘하기 시작했다. 많은 사용자들이 이제 느끼고 있지만, 인텔이 썬더볼트를 버리지 않은 것은 현명한 판단이었다.
물론 PCIe 스토리지는 NVMe보다 몇 년 전에 나왔다. 그러나 이전 솔루션은 SATA, SCSI, AHCI와 같은 하드 드라이브가 스토리지 기술의 정점이었던 시절에 개발된 오래된 데이터 전송 프로토콜에 발목을 잡혔다. NVMe는 저지연 명령과 다수의 큐(최대 6만 4,000개)를 제공함으로써 스토리지의 발목을 잡았던 제약을 없앤다. 지속적인 원을 그리며 데이터가 기록되는 하드 드라이브와 달리 SSD에서는 마치 산탄처럼 데이터가 흩어져 저장되므로 특히 후자, 즉 다수의 큐가 큰 효과를 발휘한다.
가격 : NVMe > SATA
예상했겠지만, SSD는 속도가 빠를수록 가격이 비싸다. 시중에 판매되는 1TB SATA SSD의 가격은 10만 원 초반대이며, 1TB NVMe PCIe 3.0 드라이브의 가격은 10만 원 중후반대다. 1TB PCIe 4.0 드라이브 가격은 10만 원 초반대부터 20만 원대까지 다양하다. 조금 저렴한 1TB PCIe 4.0 드라이브는 최대 속도가 5,000MBps 정도다.
폼팩터 종류에 따라 가격 차이가 나지는 않는다. 2.5인치 SATA SSD와 M.2 모델의 가격이 동일한 경우가 대부분이다. 가끔 2.5인치 모델이 M.2 모델보다 저렴한 경우가 있는데, 일반적이지는 않다.
SSD 선택 시 유의해서 봐야할 것
물론 저장 용량과 가격이 중요하다. 또한 긴 보증기간은 조기 데이터 사망에 대한 우려를 완화시킬 수 있다. 대부분의 SSD 제조업체는 3년 보증을 제공하며 일부 더 좋은 모델은 5년을 보증한다. 그러나 이전 세대의 SSD와는 달리, 몇 년 전에 혹독한 내구성 테스트로 입증한 것처럼 최신 SSD는 일반 소비자가 어지간히 사용해서는 마모되지 않는다.
SSD는 NVMe 혹은 SATA를 사용해 PC의 나머지 부분과 통신한다. 일반적으로 SATA는 NVMe보다 속도가 느리다. 반면 M.2는 사실상 폼팩터에 가까우므로 시중에는 NVMe M.2 SSD와 SATA M.2 SSD가 모두 출시되어 있다.
다만 제품 광고나 설명서에서 가끔 NVMe 드라이브임을 나타내기 위해 ‘M.2 SSD’라는 표현을 사용하고, 2.5인치 폼팩터 SSD임을 나타내기 위해 ‘SATA SSD’라는 표현을 사용한다. 따라서 ‘M.2 SSD’나 ‘SATA SSD’라는 표현을 액면 그대로 받아들이면 안 된다. 반드시 기술 사양을 확인하고 노트북 또는 데스크톱 PC의 스토리지 드라이브의 대략적인 속도를 확인해야 한다.
유의해야 할 것은 SSD를 PC에 연결하는 데 사용되는 기술이다.
SATA: 연결 유형과 전송 프로토콜을 나타내며, 대부분의 2.5인치 및 3.5인치 하드 드라이브와 SSD를 PC에 연결한다. SATA III 속도는 약 600MBps에 달할 수 있으며, 대부분의 현대 드라이브는 최대 속도를 제공한다.
PCIe: 이 인터페이스는 컴퓨터의 4개의 PCIe 레인을 활용해 SATA 속도를 훨씬 능가해 거의 4GBps를 제공한다(PCIe 3세대). 이런 파괴적인 속도는 강력한 NVMe 드라이브와 잘 어울린다. 메인보드의 PCIe 레인과 M.2 슬롯 모두 PCIe 인터페이스를 지원하도록 유선으로 연결할 수 있으며, “검정” M.2 드라이브를 PCIe 레인에 슬롯화할 수 있는 어댑터를 구입할 수 있다.
NVMe: 비휘발성 메모리 익스프레스(Non-Volatile Memory Express) 기술은 PCIe의 풍부한 대역폭을 활용해 SATA 기반 드라이브를 비교조차 못할 정도로 매우 빠른 SSD를 만든다.
M.2: 설명이 쉽지 않다. 많은 사람이 M.2 드라이브가 모두 NVMe 기술과 PCIe 속도를 사용한다고 생각하지만 사실이 아니다. M.2는 단순히 폼 팩터에 불과하다. 물론 대부분의 M.2 SSD는 NVMe를 사용하지만 일부는 여전히 SATA를 사용한다. 많은 최신 울트라북이 저장을 위해 M.2를 사용한다.
U.2 및 mSATA: mSATA 및 U.2 SSD에서도 문제가 발생할 수 있지만, 이 형식을 지원하는 메인보드와 제품 가용성은 드물다. M.2가 대중화되기 전에 일부 구형 울트라북에 mSATA가 포함되어 있으며, 필요할 경우 드라이브를 사용할 수 있다.
물론 속도도 중요하지만, 대부분의 최신 SSD는 SATA III 인터페이스를 지원한다. 그러나 전부 다 그런 것은 아니다.
구입전 사용자가 알아야 할 NVMe SSD
NVMe 드라이브는 구입하기 전에 어떤 특징을 갖고 있는지 알고 있어야 한다. 표준 SATA SSD는 이미 PC 부팅 시간과 로딩 시간을 대폭 단축하고 훨씬 저렴하다. NVMe 드라이브는 특히 대량으로 데이터를 정기적으로 전송하는 경우, 삼성 960 프로와 같은 M.2 폼 팩터나 또는 PCIe 드라이브가 가장 많은 효과를 누릴 수 있다. 그렇지 않으면 NVMe 드라이브는 가격만 비쌀뿐 가치도 없다.
NVMe SSD를 구입하기로 결정한 경우, PC에서 SSD를 처리할 수 있는지 확인해야 한다. 이는 비교적 새로운 기술이므로, 지난 몇 년 내에 제작한 메인보드만이 M.2 연결이 가능하다. 스카이레이크 시대의 AMD 라이젠과 주류 인텔 칩을 고려하라. PCIe 어댑터에 탑재된 NVMe SSD는 M.2 채택이 확산되기 전인 초기에 널리 사용됐지만 지금은 매우 드물다. NVMe SSD를 구입하기 전에 실제로 NVMe를 사용할 수 있는지 확인하고 최대한 활용하기 위해서는 4개의 PCIe 레인이 필요하다는 점에 유의해야 한다.
NVMe 드라이브를 최대한 활용하려면 운영체제를 실행해야 하기 때문에 드라이브를 인식하고 부팅할 수 있는 시스템이 있어야 한다. 지난 1~2년 전에 구입한 PC는 NVMe 드라이브에서 부팅하는데 아무런 문제가 없지만, 좀 더 오래된 메인보드는 지원하지 않을 수 있다. 구글에서 자신의 메인보드를 검색하고 NVMe 부팅을 지원하는지 확인하라. 보드의 BIOS 업데이트를 설치해야 할 수도 있다. 하드웨어가 NVMe SSD에서 부팅할 수 없는 경우에도 보조 드라이브로 사용할 수 있어야 한다.
2021 최고의 SSD 선택 가이드
Brad Chacos | PCWorldSSD(Solid-State Drive)로 전환하는 것은 PC를 위한 최상의 업그레이드다. SSD는 긴 부팅 시간을 없애고, 프로그램과 게임 로드 속도를 높이는 등 일반적으로 컴퓨터를 빠르게 한다. 그러나 모든 SSD가 동일한 것은 아니다. 최고의 SSD는 합리적인 가격으로 훌륭한 성능을 제공한다. 가격에 고민하지 않을 경우, 놀라울 정도의 빠른 읽기 및 쓰기 속도를 제공하는 제품도 있다.
많은 SSD가 2.5인치 폼 팩터로 제공되며 기존 하드 드라이브에서 사용하는 것과 동일한 SATA 포트를 통해 PC와 통신한다. 그러나 최첨단 NVMe(Non-Volatile Memory Express) 드라이브는 메인보드의 M.2에 직접 연결하는 작은 스틱 형태의 SSD다. PCIe 어댑터에 장착되는 이 드라이브는 구입하기 전에 메인보드에 슬롯이 있는지 확인해야 한다. 그래픽 카드나 사운드 카드처럼 메인보드에 꽂을 수 있는 SSD와 미래형 3D 크로스포인트(3D XPoint) 드라이브 등이 등장함에 따라 완벽한 SSD를 선택하는 것은 예전처럼 간단하지 않다.
그래서 이 가이드가 필요하다. 본지는 사용자 상황에 적합한 SSD를 찾기 위해 수많은 SSD를 테스트했다. 본지가 선정한 최고 인기 제품과 SSD 선택 시 무엇을 고려해야 하는지 알아보자. 참고로, 이번 가이드는 내장형 SSD만 적용한 것이다.
최신 SSD 뉴스
구입해야 하는 SSD에 대한 가이드를 확인하고, 각 시스템에서 가장 적합한 SSD의 종류에 대해 알아보자.
인텔은 모든 데스크톱 소비자 버전의 옵테인(Optane) 드라이브를 단종시켰지만, 이 기술은 노트북과 서버에 그대로 남아있다. 옵테인 SSD는 엄청난 랜덤 액세스 성능과 놀라운 내구성을 제공했지만, 용량이 제한적이면서도 가격은 매우 높았다. 향후 노트북에서 느린 NAND SSD 속도를 높이기 위한 캐싱 형태의 기능으로 사용될 것이다.
스토리지 제조업체는 공급망 문제로 인해 출시 후 구성 요소를 조정하는 경우가 많지만, 한 PC하드웨어 전문매체는 최근 에이데이타(Adata)가 훨씬 느린 버전으로 XPG 8200 프로의 컨트롤러를 교체한 것을 포착했다.
대부분 사용자를 위한 최고의 SSD, SK 하이닉스 골드 S31 SATA SSD
삼성의 주력인 EVO SSD 제품군은 2014년 이래로 줄곧 본지의 권장 목록에서 1위를 차지했으며, 현재 삼성 860 EVO는 여전히 속도, 가격, 호환성 및 5년 보증 및 뛰어난 마법사 관리 소프트웨어의 안정성 등 조화를 원하는 사람들에게 좋은 선택지다. 그러나 대부분의 사람들은 SK 하이닉스 골드 S31을 사는 것이 낫다.
골드 S31은 지금까지 본지가 테스트 한 가장 빠른 SATA SSD 가운데 하나일뿐만 아니라 동급 최강의 870 EVO와 견줄 수 있을만한 거리에 있다. 하지만 이 드라이브의 가격은 놀랍다. 250GB 드라이브의 경우 44달러, 500GB 드라이브의 경우 57달러, 1TB의 경우 105달러인 골드 S31은 500GB 모델에 70달러를 청구하는 삼성 제품보다 훨씬 저렴하다(국내에서는 1T 13만 5,000원, 500G 7만 5,000원, 250G 4만 8,000원에 판매하고 있다. 편집자 주). .
리뷰 당시 본지는 “실제 48GB 사본 테스트 수행시 골드 S31은 지속적인 읽기 및 쓰기 작업에서 테스트한 제품 가운데 가장 빠른 드라이브임을 입증했다”라고 평가했다. 이 제품은 이 평가로 충분하다.
SK 하이닉스는 정확히 제품 이름이 아니기 때문에 브랜드 자체에 대해 조금 딴지를 걸 수도 있다. 그럼에도 불구하고 SK 하이닉스는 지구상에서 가장 큰 반도체 제조업체 가운데 하나다. SK 하이닉스는 시작부터 NAND 및 컨트롤러 기술을 개발해왔으며, 수많은 컴퓨터 업체의 SSD 제조업체였지만 판매선상에는 자리하지 못했다. 이제 그 선상에 섰고, 결과는 훌륭했다.
더 큰 용량이 필요하거나 단순히 검증된 브랜드를 고수하고 싶다면, 250GB, 500GB, 1TB 및 2TB 모델로 제공하는 삼성 870 EVO를 선택하면 된다. 이 제품은 SK 하이닉스보다 조금 더 빠르지만, 그 대가로 비용이 더 많이 든다. 삼성 870 EVO는 대부분의 SSD에 비해 매우 매력적이고 저렴한 패키지를 제공하고 있기 때문에 골드 S31이 얼마나 더 좋은 것인지 알 수 있다. 삼성 870 QVO는 1TB에서 무려 8TB에 이르는 용량을 가진 또 다른 강력한 경쟁 제품이지만 다음 세션에서 논의할 것이다.
가성비 최고의 SSD: 애드링크(AddLink) S22 QLC SATA 2.5인치 SSD
매우 저렴한 가격에 훌륭한 성능을 제공하는 SK하이닉스 골드 S31은 최고의 가성비 SSD로, 대부분의 사용자에게 최고의 SSD다. 하지만 어떤 이유로든 골드 S31에 관심이 없는 이들에겐 더 많은 선택지가 있다.
이제 기존의 MLC(Multi-Level Cell)와 TLC(Triple-Level Cell) SSD 가격이 급락함에 따라 제조업체는 SSD 가격을 더욱 낮출 수 있는 새로운 QLC(Quad-Level Cell) 드라이브를 출시했다.
이 새로운 기술을 통해 제조업체는 매우 빠른 SSD에 버금가는 속도와 함께 하드 드라이브와 같은 수준의 용량을 가진 SSD를 출시할 수 있었다. 다만 삼성 860 QVO를 포함한 1차 QLC 드라이브는 수십 기가바이트의 데이터를 한번에 전송할 때 쓰기 속도가 하드 드라이브 수준으로 떨어졌다.
애드링크(Addlink) S22 QLC SSD는 이 같은 어려움을 겪지 않는다. 기존 TLC SSD는 여전히 QLC 드라이브에 비해 속도 우위를 유지하고 있지만, 애드링크 S22는 512GB에 59달러, 1TB에 99달러의 저렴한 가격에 판매하고 있다. 하지만 SK 하이닉스 골드 S31이 거의 같은 금액으로 판매되고 있다는 사실에 주목할 필요가 있다.
대량의 데이터를 한번에 이동할 계획이 없고, 더 많은 저장공간이 필요하다면 삼성의 2세대 QLC 제품인 삼성 870 QVO가 좋은 선택이다. 실제로 애드링크의 SSD보다 조금 더 빠르다. 그러나 아마존에서 1TB가 110달러, 2TB의 경우 205달러, 4TB 450달러, 8TB 900달러로 더 비싸다. 1TB보다 적은 용량은 판매하지 않는다. 구형 삼성 860 QVO도 여전히 좋은 선택이긴 하지만 최신 870 QVO는 모든 면에서 최고다.
하지만 메인보드가 더 빠르고 새로운 NVMe M.2 드라이브를 지원한다면 선택지는 달라진다.
최고의 NVMe SSD: SK 하이닉스 골드 P31 M.2 NVMe SSD(1TB)
성능이 가장 중요하다면 삼성 970 프로 또는 씨게이트 파이어쿠다(Seagate FireCuda) 510이 가장 빠른 NVMe SSD이지만, 대부분의 사람은 SK 하이닉스 골드 P31을 구입하는 것이 좋다. SK 하이닉스는 가성비 범주에서 전체 SSD를 장악하고 있다.
SK 하이닉스 골드 P31은 128비트 TLC NAND를 탑재한 최초의 NVMe SSD이며, 96 NAND 레이어를 사용하는 다른 제품들을 뛰어넘었다. 본지가 테스트한 모델은 크리스탈디스크마크(CrystalDiskMark) 6와 AS SSD의 종합 벤치마크에서도 완전히 인정받았으며, 보도자료에서 주장했던 3.5Gbps 읽기 및 쓰기 속도에 거의 도달했다.
또한 실제 48GB 및 450GB 파일 전송 테스트에서 더 비싼 SSD에 비교했을 때도 뒤지지 않았다. SK 하이닉스 골드 P31은 최상급 드라이브처럼 작동하지만, 저렴한 드라이브보다 조금 더 비쌀 뿐이다. 500G 제품은 75달러에, 1TB 제품은 125달러에 구입할 수 있다(국내에서는 1T 19만 8,000원, 500G 9만 8,000원에 판매하고 있다. 편집자 주).
마이크론 크루셜(Crucial) P5는 비용 효율적인 NVMe SSD로, 만약 SK 하이닉스 골드 P31이 없었다면, 최고의 선택지가 될 수 있었다. 하지만 골드 P31가 조금 더 빠르고, 조금 더 저렴하다. 그래도 크루셜 P5는 대안 제품이 될 수 있다.
하지만 예산이 빠듯하다면, 약간 더 적은 비용으로 매력적인 선택지를 찾을 수 있다. 웨스턴 디지털 블루(Western Digital Blue) SN550 NVMe SSD는 앞서 언급한 제품처럼 빠르거나 화려한 성능을 갖고 있진 않다. 하지만 가격이 훨씬 저렴하다. 250GB의 경우 45달러, 500GB의 경우 65달러, 1TB의 경우 130달러와 같은 보급형 가격에도 불구하고 WD 블루 SN550은 고가의 제품 성능을 충분히 발휘할 수 있다. 신뢰성에 대한 좋은 이력을 가진 기존 브랜드를 이은 제품이며, 평균보다 긴 5년 보증을 제공한다.
또 다른 훌륭한 NVMe SSD
– 애드링크 S70 NVMe SSD: 좀 더 높은 성능을 원한다면 애드링크(Addlink) S70 NVMe SSD 또한 탁월한 선택지가 될 수 있다. 이 제품은 WD 드라이브보다 성능이 약간 우수하다. 하지만 본지는 이 제품의 가격이 인상된 후부터는 일상적인 컴퓨터 사용자에게 WD 블루 SN550을 추천한다. 애드링크는 WD만큼 잘 알려져 있지 않지만, S70 NVMe SSD에 대해 5년 보증을 제공한다.
– PNY XLR8 CS 3030: 이 제품은 좋은 가격에 빠른 성능을 제공하는 또 다른 선택지다. 하지만 일상적인 사용에는 탁월하지만, 긴 쓰기 작업에서는 수렁에 빠질 수 있다.
– 에이데이타의 XPG SX8200 프로와 킹스톤(Kingston) KC2500: 더 빠른 속도를 위해 좀더 많은 비용을 써도 괜찮다면 삼성 970 프로 수준의 성능을 지닌 에이데이타의 XPG SX8200 프로와 킹스톤 KC2500도 있다. 킹스톤 KC2500은 한번의 테스트에서 최고 등급에 도달하지 못했지만, 항상 선두권을 유지하고 있었다. 경쟁 제품과 거의 동일한 가격으로 구입할 수 있으며, 고성능 NVMe SSD를 구입하는 경우 고려해볼 만한 제품이다.
새로운 유형의 대용량 SSD 덕분에 충분한 저장용량과 함께 엄청난 NVMe 속도를 얻을 수 있게 됐지만, 이에 대한 비용은 감수해야 한다. OWC 아우라 P12는 NVMe 평균 이상의 쓰기 성능과 4TB 제품을 929달러에 제공한다. 최고의 세이브런트 로켓(Sabrent Rocket) Q는 최고의 성능과 놀라운 8TB 용량으로 모든 것을 만족시키지만, 1,500달러라는 놀라운 가격이 기다리고 있다. 최첨단은 저렴하지 않다.
최고의 PCIe 4.0 SSD: 삼성 980 프로 PCIe 4.0 NVMe SSD(1TB)
대부분의 NVMe SSD는 표준 PCIe 3.0 인터페이스를 사용하지만, 최첨단 기술을 지원하는 일부 제품에는 훨씬 더 빠른 PCIe 4.0 드라이브가 있다. 현재 AMD의 라이젠 3000 프로세서만 PCIe 4.0을 지원하며 X570 또는 B550 메인보드에 장착하는 경우에만 지원한다. 하지만 이 기준을 충족하면 PCIe 4.0 SSD는 가장 빠른 PCIe 3.0 NVMe SSD가 따라오지 못할 성능을 보여준다.
커세어(Corsair), 기가바이트(Gigabyte), 세이브런트는 최초의 PCIe 4.0 SSD를 출시했으며, 모두 약 200달러에 1TB 용량과 유사한 성능을 제공했다. 하지만 본지가 선정한 최고의 PCIe 4.0 SSD는 조금 더 비싸다.
본지는 최근에서야 PCIe 4.0 SSD 테스트를 추가했지만, 지금까지 테스트한 제품 가운데 최고는 삼성 980 프로였다. 이 제품은 테스트에서 삼성이 주장한 7Gbps 읽기 속도와 5Gbps 쓰기 속도를 초과했다. 이 제품은 실제 파일 전송 테스트를 통과했지만, 450GB 전송 테스트에서 발견한 것처럼 막대한 양의 데이터를 전송하는 경우 속도가 약간 느려질 수 있다. 하지만 대부분의 사용자가 SSD를 이렇게 힘들게 다루진 않는다.
하지만 모든 성능은 프리미엄급이다. 그럼에도 불구하고 250GB 90달러, 500GB 150달러, 1TB 용량은 230달러이다.
WD 블랙 SN850은 삼성 980 프로의 성능에 뒤처져 있지만, 거의 같은 가격으로 판매한다. 본지는 리뷰에서 “최강의 단일 SSD PCIe4 스토리지 성능을 찾는다면 어느 쪽도 문제가 되지 않을 것”이라고 평가했다.
PCIe 4.0 속도가 빠른 SSD를 원하지만 삼성의 동급 최고의 성능을 위해 많은 비용을 소비하고 싶지 않다면 XPG 겜믹스 S50 라이트를 고려한다. 본지는 “XPG 겜믹스 S50 라이트는 우리가 테스트한 최초의 PCIe 4 SSD로, 차세대라는 추가 비용이 들지 않는다. 실제로 시스템을 실행하는 시스템에서는 삼성 980 프로와 차이를 구분하기 어려울 것이다”라고 설명했다.
겜믹스 S50 라이트는 1TB의 경우 140달러, 2TB의 경우 260달러다.
NVMe SSD 설정시 알아야 할 사항
NVMe 드라이브는 구입하기 전에 어떤 특징을 갖고 있는지 알고 있어야 한다. 표준 SATA SSD는 이미 PC 부팅 시간과 로딩 시간을 대폭 단축하고 훨씬 저렴하다. NVMe 드라이브는 특히 대량으로 데이터를 정기적으로 전송하는 경우, 삼성 960 프로와 같은 M.2 폼 팩터나 또는 PCIe 드라이브를 가장 많은 효과를 누릴 수 있다. 그렇지 않으면 NVMe 드라이브는 가격만 비쌀뿐 가치도 없다.
NVMe SSD를 구입하기로 결정한 경우, PC에서 SSD를 처리할 수 있는지 확인해야 한다. 이는 비교적 새로운 기술이므로, 지난 몇 년 내에 제작한 메인보드만 M.2 연결이 가능하다. 스카이레이크 시대의 AMD 라이젠과 주류 인텔 칩을 고려한다. PCIe 어댑터에 탑재된 NVMe SSD는 M.2 채택이 확산되기 전인 초기에 널리 사용됐지만 지금은 매우 드물다. NVMe SSD를 구입하기 전에 실제로 NVMe를 사용할 수 있는지 확인하고 최대한 활용하기 위해서는 4개의 PCIe 레인이 필요하다는 점에 유의해야 한다.
NVMe 드라이브를 최대한 활용하려면 운영체제를 실행해야 하므로 드라이브를 인식하고 부팅할 수 있는 시스템이 있어야 한다. 지난 1~2년동안 구입한 PC라면 NVMe 드라이브를 부팅하는 데 문제가 없어야하지만, 이전 메인보드에서는 지원이 어려울 수 있다. 구글에서 메인보드를 검색하고 NVMe에서 부팅을 지원하는지 확인한다. 보드에서 BIOS 업데이트를 설치해야 할 수도 있다. 하드웨어가 NVMe SSD에서 부팅할 수 없는 경우에도 시스템은 이를 보조 드라이브로 사용할 수 있어야 한다.
SSD 선택에서 고려해야 할 것
물론 저장 용량과 가격이 중요하다. 또한 긴 보증기간은 조기 데이터 사망에 대한 우려를 완화시킬 수 있다. 대부분의 SSD 제조업체는 3년 보증을 제공하며 일부 더 좋은 모델은 5년을 보증한다. 그러나 이전 세대의 SSD와는 달리, 몇 년 전에 혹독한 내구성 테스트로 입증한 것처럼 최신 SSD는 일반 소비자가 어지간히 사용해서는 마모되지 않는다.
가장 유의해야 할 것은 SSD를 PC에 연결하는 데 사용되는 기술이다. – SATA: 연결 유형과 전송 프로토콜을 나타내며, 대부분의 2.5인치 및 3.5인치 하드 드라이브와 SSD를 PC에 연결한다. SATA III 속도는 약 600MBps에 달할 수 있으며, 대부분의 현대 드라이브는 최대 속도를 제공한다.
– PCIe: 이 인터페이스는 컴퓨터의 4개의 PCIe 레인을 활용해 SATA 속도를 훨씬 능가해 거의 4GBps를 제공한다(PCIe 3세대). 이런 파괴적인 속도는 강력한 NVMe 드라이브와 잘 어울린다. 메인보드의 PCIe 레인과 M.2 슬롯 모두 PCIe 인터페이스를 지원하도록 유선으로 연결할 수 있으며, M.2 드라이브를 PCIe 레인에 슬롯화할 수 있는 어댑터를 구입할 수 있다.
– NVMe: 비휘발성 메모리 익스프레스(Non-Volatile Memory Express) 기술은 PCIe의 풍부한 대역폭을 활용해 SATA 기반 드라이브와는 비교조차 못할 정도로 매우 빠른 SSD를 만든다. NVMe에 대해 더 자세히 알고 싶다면 여기를 클릭하라.
– M.2: 설명이 쉽지 않다. 많은 사람이 M.2 드라이브가 모두 NVMe 기술과 PCIe 속도를 사용한다고 생각하지만 사실이 아니다. M.2는 단순히 폼 팩터에 불과하다. 물론 대부분의 M.2 SSD는 NVMe를 사용하지만 일부는 여전히 SATA를 사용한다. 많은 최신 울트라북이 저장을 위해 M.2를 사용한다.
– U.2 및 mSATA: mSATA 및 U.2 SSD에서도 문제가 발생할 수 있지만, 이 형식을 지원하는 메인보드와 제품 가용성은 드물다. M.2가 대중화되기 전에 일부 구형 울트라북에 mSATA가 포함되어 있으며, 필요할 경우 드라이브를 사용할 수 있다.
물론 속도도 중요하지만, 대부분의 최신 SSD는 SATA 3 인터페이스를 지원한다. 그러나 전부 다 그런 것은 아니다.
SSD vs. 하드 드라이브
SSD가 필요한가? “필요하다.” 본지는 모든 사람이 SSD로 업그레이드할 것으로 진심으로 권장한다. 가장 빠른 기계식 하드드라이브도 SSD 속도에는 미치지 못한다. 기존 노트북, 데스크톱의 하드드라이브를 SSD로 교체하면 완전히 새로운 시스템처럼 느낄 수 있다. SSD를 구입하는 것은 컴퓨터를 업그레이드하는 데 가장 적합한 선택이다.
SSD는 기계식 하드드라이브보다 기가바이트 당 저장 비용이 많이 들기 때문에 대용량으로 제공하지 않는 경우가 많다. 속도와 저장 공간이 동시에 필요한 경우, 128GB 크루셜 BX300과 같은 제한된 용량의 SSD를 구입해 부팅 드라이브로 사용하고, 기존 하드드라이브를 PC의 보조 저장장치로 설정한다. 프로그램을 부팅 드라이브에 넣고 미디어 및 기타 파일을 하드드라이브에 저장하면 준비가 다 된 것이다. editor@itworld.co.kr
본 자료는 Computer에 대한 전문적인 지식보다는 수치해석을 주 목적으로 FLOW-3D 를 이용하기 위한 해석용 컴퓨터를 선택할 때 도움을 주기 위한 자료입니다.
흔히 고성능 컴퓨터는 표준 데스크톱 컴퓨터와 어떻게 다른지 궁금하게 생각하는데, 보통 HPC(high performance computing)는 더욱 강력한 프로세서, 더 큰 메모리, 뛰어난 그래픽 성능을 갖추고 있어 일반적인 표준 데스크톱보다 훨씬 빠르게 여러 가지 복잡한 작업을 동시에 처리할 수 있습니다. 따라서 시중에서 판매하는 고사양의 컴퓨터에 CPU, Memory, Graphic Card 등을 보완하거나 고사양으로 만들어진 컴퓨터를 구매하게 되면, 단일 노드의 HPC(high performance computing)와 유사한 성능을 확보할 수 있습니다.
하지만 개인이 여러 컴퓨터를 대상으로 테스트를 수행하기 어렵기 때문에, 전문가들이 테스트를 수행하여 공개하는 보고서를 참조하여 도움을 얻는 것이 효율적입니다.
아래 전문 성능비교 테스트 보고서가 시스템 선택에 도움이 될 것으로 생각합니다. 참고로, 당사는 기사를 제공하는 기관과 전혀 관련이 없음을 알려드립니다.
In this blog, Flow Science’s IT Manager Matthew Taylor breaks down the different hardware components and suggests some ideal configurations for getting the most out of your FLOW-3D products.
개요
본 자료는 Flow Science의 IT 매니저 Matthew Taylor가 작성한 자료를 기반으로 STI C&D에서 일부 자료를 보완한 자료입니다. 본 자료를 통해 FLOW-3D 사용자는 최상의 해석용 컴퓨터를 선택할 때 도움을 받을 수 있을 것으로 기대합니다.
수치해석을 하는 엔지니어들은 사용하는 컴퓨터의 성능에 무척 민감합니다. 그 이유는 수치해석을 하기 위해 여러 준비단계와 분석 시간들이 필요하지만 당연히 압도적으로 시간을 소모하는 것이 계산 시간이기 때문일 것입니다.
따라서 수치해석용 컴퓨터의 선정을 위해서 단위 시간당 시스템이 처리하는 작업의 수나 처리량, 응답시간, 평균 대기 시간 등의 요소를 복합적으로 검토하여 결정하게 됩니다.
또한 수치해석에 적합한 성능을 가진 컴퓨터를 선별하는 방법으로 CPU 계산 처리속도인 Flops/sec 성능도 중요하지만 수치해석을 수행할 때 방대한 계산 결과를 디스크에 저장하고, 해석결과를 분석할 때는 그래픽 성능도 크게 좌우하기 때문에 SSD 디스크와 그래픽카드에도 관심을 가져야 합니다.
FLOW SCIENCE, INC. 에서는 일반적인 FLOW-3D를 지원하는 최소 컴퓨터 사양과 O/S 플랫폼 가이드를 제시하지만, 도입 담당자의 경우, 최상의 조건에서 해석 업무를 수행해야 하기 때문에 가능하면 최고의 성능을 제공하는 해석용 장비 도입이 필요합니다. 이 자료는 2022년 현재 FLOW-3D 제품을 효과적으로 사용하기 위한 하드웨어 선택에 대해 사전에 검토되어야 할 내용들에 대해 자세히 설명합니다. 그리고 실행 중인 시뮬레이션 유형에 따라 다양한 구성에 대한 몇 가지 아이디어를 제공합니다.
CPU 최신 뉴스
2025년 11월 26일 기준
이미지 출처 : https://www.cpubenchmark.net/high_end_cpus.html
CPU의 선택
CPU는 전반적인 성능에 큰 영향을 미치며, 대부분의 경우 컴퓨터의 가장 중요한 구성 요소입니다. 그러나 데스크탑 프로세서를 구입할 때가 되면 Intel 과 AMD의 모델 번호와 사양을 이해하는 것이 어려워 보일 것입니다. 그리고, CPU 성능을 평가하는 방법에 의해 가장 좋은 CPU를 고른다고 해도 보드와, 메모리, 주변 Chip 등 여러가지 조건에 의해 성능이 달라질 수 있기 때문에 성능평가 결과를 기준으로 시스템을 구입할 경우, 단일 CPU나 부품으로 순위가 정해진 자료보다는 시스템 전체를 대상으로 평가한 순위표를 보고 선정하는 지혜가 필요합니다.
수치해석을 수행하는 CPU의 경우 예산에 따라 Core가 많지 않은 CPU를 구매해야 하는 경우도 있을 수 있습니다. 보통 Core가 많다고 해석 속도가 선형으로 증가하지는 않으며, 해석 케이스에 따라 적정 Core수가 있습니다. 이 경우 예산에 맞는 성능 대비 최상의 코어 수가 있을 수 있기 때문에 Single thread Performance 도 매우 중요합니다. 아래 성능 도표를 참조하여 예산에 맞는 최적 CPU를 찾는데 도움을 받을 수 있습니다.
CPU 성능 분석 방법
부동소수점 계산을 하는 수치해석과 밀접한 Computer의 연산 성능 벤치마크 방법은 대표적으로 널리 사용되는 아래와 같은 방법이 있습니다.
FLOW-3D의 CFD 솔버 성능은 CPU의 부동 소수점 성능에 전적으로 좌우되기 때문에 계산 집약적인 프로그램입니다. 현재 출시된 사용 가능한 모든 CPU를 벤치마킹할 수는 없지만 상대적인 성능을 합리적으로 비교할 수는 있습니다.
특히, 수치해석 분야에서 주어진 CPU에 대해 FLOW-3D 성능을 추정하거나 여러 CPU 옵션 간의 성능을 비교하기 위한 최상의 옵션은 Standard Performance Evaluation Corporation의 SPEC CPU2017 벤치마크(현재까지 개발된 가장 최신 평가기준임)이며, 특히 SPECspeed 2017 Floating Point 결과가 CFD Solver 성능을 매우 잘 예측합니다.
이는 유료 벤치마크이므로 제공된 결과는 모든 CPU 테스트 결과를 제공하지 않습니다. 보통 제조사가 ASUS, Dell, Lenovo, HP, Huawei 정도의 제품에 대해 RAM이 많은 멀티 소켓 Intel Xeon 기계와 같은 값비싼 구성으로 된 장비 결과들을 제공합니다.
CPU 비교를 위한 또 다른 옵션은 Passmark Software의 CPU 벤치마크입니다. PerformanceTest 제품군은 유료 소프트웨어이지만 무료 평가판을 사용할 수 있습니다. 대부분의 CPU는 저렴한 옵션을 포함하여 나열됩니다. 부동 소수점 성능은 전체 벤치마크의 한 측면에 불과하지만 다양한 워크로드에서 전반적인 성능을 제대로 테스트합니다.
예산을 결정하고 해당 예산에 해당하는 CPU를 선택한 후에는 벤치마크를 사용하여 가격에 가장 적합한 성능을 결정할 수 있습니다.
다른 컴퓨터 시스템에서 컴퓨팅 계산에 대한 집약적인 워크로드를 비교하는데 사용할 수 있는 성능 측정을 제공하도록 설계된 SPEC CPU 2017에는 SPECspeed 2017 정수, SPECspeed 2017 부동 소수점, SPECrate 2017 정수 및 SPECrate 2017 부동 소수점의 4 가지 제품군으로 구성된 43 개의 벤치 마크가 포함되어 있습니다. SPEC CPU 2017에는 에너지 소비 측정을 위한 선택적 메트릭도 포함되어 있습니다.
<SPEC CPU 벤치마크 보고서>
벤치마크 결과보고서는 제조사별, 모델별로 테스트한 결과를 아래 사이트에 가면 볼 수 있습니다.
Designed to provide performance measurements that can be used to compare compute-intensive workloads on different computer systems, SPEC CPU 2017 contains 43 benchmarks organized into four suites: SPECspeed 2017 Integer, SPECspeed 2017 Floating Point, SPECrate 2017 Integer, and SPECrate 2017 Floating Point. SPEC CPU 2017 also includes an optional metric for measuring energy consumption.
플롭은 부동소수점 연산 1회를 뜻하며, 소수점이 있는 숫자를 대상으로 한 번의 산술 계산(덧셈, 뺄셈, 곱셈, 나눗셈)을 의미한다. 컴퓨팅 벤치마킹에서 정수보다 부동소수점을 쓰는 이유는 정수보다 측정 지표로서 정확도가 훨씬 높기 때문이다.
플롭 앞에는 1초 동안 수행하는 연산 횟수를 나타내는 접두어가 붙으며, 메가플롭(1초당 100만 회)부터 기가플롭(10억), 테라플롭(1조), 페타플롭(1천조), 그리고 최근에는 엑사플롭(100경)까지 확장됐다. 최근 몇 년 동안 업계가 엑사플롭 달성 경쟁에 매달린 이유는 마법 같은 성능 도약이나 대발견 때문이 아니라, 단지 자랑거리를 위한 것이었다.
컴퓨팅에서 부동소수점 정밀도는 FP4, 즉 4비트 부동소수점에서 시작해 FP64까지 두 배씩 커진다. 이론적으로 FP128도 있지만, 지표로는 사실상 쓰지 않는다. FP64는 IEEE 754 표준에 따른 64비트 배정밀도(double-precision) 부동소수점 형식으로도 불리며, 실수를 높은 정확도로 표현하기 위한 규격이다.
FP64는 정밀도가 높기 때문에 계산하는 데 가장 많은 시간이 필요하다. FP64 계산 시간은 FP32의 2배, FP16의 4배가 걸리지만, 계산 정확도는 FP32의 2배, FP16의 4배에 해당한다. 메모리 사용량도 같은 원리로 FP64가 FP32의 2배, FP16의 4배를 사용한다.
매년 6월과 11월에 집계·발표되는 톱500 슈퍼컴퓨터 목록은 슈퍼컴퓨터 성능을 FP64 기준으로 측정하며, 슈퍼컴퓨터에 가장 가혹한 스트레스 테스트로 통한다.
톱500 목록이 32비트나 16비트가 아니라 64비트로 측정되는 이유는 톱500 목록이 과학 컴퓨팅 애플리케이션의 대리 지표이며 과학 컴퓨팅 애플리케이션이 여전히 계산에서 64비트 정확도에 주로 의존하기 때문이다. HPC·슈퍼컴퓨팅 전문 시장조사업체 인터섹트 360의 CEO 애디슨 스넬은 “일부 영역에서 정밀도를 낮춰 속도를 더 낼 수 있지 않느냐는 지적도 있고 중요하지 않은 영역에서 과도한 계산을 하고 있지 않느냐는 질문도 나오지만, 과학 컴퓨팅에서는 64비트가 여전히 사실상 표준이다”라고 말했다.
스넬은 FP64가 과학 컴퓨팅의 거의 모든 분야에서 쓰인다고 말했다. 연구 영역에서는 유체가 포함돼 높은 정확도로 모델링해야 하는 기상 시뮬레이션이나 해양 모델링이 포함된다. 또한, 자동차 충돌 시뮬레이션, 항공기 날개 공력 분석, 석유 시추 지점을 찾기 위한 탄성파 분석, 신약 설계를 위한 분자 모델링 같은 폭넓은 상용 애플리케이션에도 적용된다. 이런 애플리케이션은 계산을 위해 높은 수준의 과학적 정밀도를 요구한다고 말했다.
그 다음 단계는 FP32, 즉 단정밀도 부동소수점이다. FP32는 생명과학 시뮬레이션과 금융 모델링에도 쓰이며, 모델 요구 수준이 그리 엄격하지 않아 FP32를 써도 되는 경우에 주로 사용된다.
FP16은 AI 추론에서 일상적으로 쓰이지만, AI 학습은 FP64에 전적으로 의존한다. 이유는 간단하다. 예를 들어 AI로 개나 고양이 이미지를 구분하도록 학습시킨다고 가정해 보자. 개나 고양이를 구성하는 특징을 인식하려면 FP64의 미세한 정밀도가 필요하다. 학습이 끝나면 작업은 패턴 매칭으로 바뀌며, 개 이미지인지 고양이 이미지인지 판단하는 데는 덜 부담스러운 FP16으로도 충분하다. 스넬은 언어 학습이나 인식에서도 비슷하게, 말할 때 단어 하나를 약간 틀리게 발음해도 AI는 대체로 의도를 파악한다고 설명했다.
16비트 정밀도에는 bfloat16이라는 두 번째 형태도 있다. bfloat는 구글의 텐서 프로세서용으로 처음 개발됐지만, 이후 인텔과 AMD, 엔비디아에 라이선스를 제공했다. bfloat는 유연한 가변 형식인 반면 FP16은 매번 동일한 16비트 형식이다. 스넬은 “기술적으로 복잡하지만 결론은 bfloat가 FP16보다 정밀도는 낮고 속도는 더 빠르기 때문에 주요 칩 업체가 모두 bfloat를 쓴다”라고 설명했다.
마지막으로 FP8과 FP4가 있다. FP8은 정밀도 요구가 낮은 추론 처리 연산에 사용한다. 또 다른 핵심 용도는 오류 허용도가 더 높은 신경망 학습이다. 연산 부담이 적은 작업을 수행하는 엣지 컴퓨팅에서도 쓰인다. FP8은 GPU에서만 쓰이며, 인텔과 AMD 프로세서에서는 쓰지 않는다.
클럭 대 코어
일반적으로 클럭 속도가 높은 칩은 CPU 코어를 더 적게 포함합니다. FLOW-3D는 병렬화가 잘되어 있지만, 디스크 쓰기와 같이 일부 작업은 기본적으로 단일 스레드 방식으로 수행됩니다. 따라서 데이터 출력이 빈번하거나 큰 시뮬레이션은 종종 더 많은 코어가 아닌, 더 높은 클럭 속도를 활용합니다. 마찬가지로 코어 및 소켓의 다중 스레딩은 오버헤드를 발생시키므로 작은 문제의 해석일 경우 사용되는 코어 수를 제한하면 성능이 향상될 수 있습니다.
CPU 아키텍처
CPU 아키텍처는 중요합니다. 최신 CPU는 일반적으로 사이클당 더 많은 기능을 제공합니다. 즉, 현재 세대의 CPU는 일반적으로 동일한 클럭 속도에서 이전 CPU보다 성능이 우수합니다. 또한 전력 효율이 높아져 와트당 성능이 향상될 수 있습니다. Flow Science에는 구형 멀티 소켓 12, 16, 24 코어 Xeon보다 성능이 뛰어난 최근 세대 10~12 Core i9 CPU 시스템을 보유하고 있습니다.
오버클럭
해석용 장비에서는 CPU를 오버클럭 하지 않는 것이 좋습니다. 하드웨어를 다년간의 투자라고 생각한다면, 오버클럭화는 발열을 증가시켜 수명을 단축시킵니다. CPU에 따라 안정성도 저하될 수 있습니다. CPU를 오버클럭 할 때는 세심한 열 관리가 권장됩니다.
하이퍼스레딩
<이미지출처:https://gameabout.com/krum3/4586040>
하이퍼스레딩은 물리적으로 1개의 CPU를 가상으로 2개의 CPU처럼 작동하게 하는 기술로 파이프라인의 단계수가 많고 각 단계의 길이가 짧을때 유리합니다. 다만 수치해석 처럼 모든 코어의 CPU를 100% 사용중인 장시간 수행 시뮬레이션은 일반적으로 Hyper Threading이 비활성화 된 상태에서 더 잘 수행됩니다. FLOW-3D는 100% CPU 사용률이 일반적이므로 새 하드웨어를 구성할 때 Hyper Threading을 비활성화하는 것이 좋습니다. 설정은 시스템의 BIOS 설정에서 수행합니다.
몇 가지 워크로드의 경우에는 Hyper Threading을 사용하여 약간 더 나은 성능을 보이는 경우가 있습니다. 따라서, 최상의 런타임을 위해서는 두 가지 구성중에서 어느 구성이 더 적합한지 시뮬레이션 유형을 테스트하는 것이 좋습니다.
스케일링
여러 코어를 사용할 때 성능은 선형적이지 않습니다. 예를 들어 12 코어 CPU에서 24 코어 CPU로 업그레이드해도 시뮬레이션 런타임이 절반으로 줄어들지 않습니다. 시뮬레이션 유형에 따라 16~32개 이상의 CPU 코어를 선택할 때는 FLOW-3D 및 FLOW-3D CAST의 HPC 버전을 사용하거나 FLOW-3D CLOUD로 이동하는 것을 고려하여야 합니다.
AMD Ryzen 또는 Epyc CPU
AMD는 일부 CPU로 벤치마크 차트를 석권하고 있으며 그 가격은 매우 경쟁력이 있습니다. FLOW SCIENCE, INC. 에서는 소수의 AMD CPU로 FLOW-3D를 테스트했습니다. 현재 Epyc CPU는 이상적이지 않고 Ryzen은 성능이 상당히 우수합니다. 발열은 여전히 신중하게 다뤄져야 할 문제입니다.
FLOW-3D는 OpenGL 드라이버가 만족스럽게 수행되는 최신 그래픽 카드가 필요합니다. 최소한 OpenGL 3.0을 지원하는 것이 좋습니다. 권장 옵션은 엔비디아의 쿼드로 K 시리즈와 AMD의 파이어 프로 W 시리즈입니다.
특히 엔비디아 쿼드로(NVIDIA Quadro)는 엔비디아가 개발한 전문가 용도(워크스테이션)의 그래픽 카드입니다. 일반적으로 지포스 그래픽 카드가 게이밍에 초점이 맞춰져 있지만, 쿼드로는 다양한 산업 분야의 전문가가 필요로 하는 영역에 광범위한 용도로 사용되고 있습니다. 주로 산업계의 그래픽 디자인 분야, 영상 콘텐츠 제작 분야, 엔지니어링 설계 분야, 과학 분야, 의료 분석 분야 등의 전문가 작업용으로 사용되고 있습니다. 따라서 일반적인 소비자를 대상으로 하는 지포스 그래픽 카드와는 다르계 산업계에 포커스 되어 있으며 가격이 매우 비싸서 도입시 예산을 고려해야 합니다.
유의할 점은 엔비디아의 GTX 게이밍 하드웨어는 볼륨 렌더링의 속도가 느리거나 오동작 등 몇 가지 제한 사항이 있습니다. 일반적으로 노트북에 내장된 통합 그래픽 카드보다는 개별 그래픽 카드를 강력하게 추천합니다. 최소한 그래픽 메모리는 512MB 이상을 권장합니다.
Flow Science는 nVidia 드라이버 버전이 341.05 이상인 nVidia Quadro K, M 또는 P 시리즈 그래픽 하드웨어를 권장합니다. 이 카드와 드라이버 조합을 사용하면 원격 데스크톱 연결이 완전한 3D 가속 기능을 갖춘 기본 하드웨어에서 자동으로 실행됩니다.
원격 데스크톱 세션에 연결할 때 nVidia Quadro 그래픽 카드가 설치되어 있지 않으면 Windows는 소프트웨어 렌더링을 사용합니다. FLOW-3D 가 소프트웨어 렌더링을 사용하고 있는지 확인하려면 FLOW-3D 도움말 메뉴에서 정보를 선택하십시오. GDI Generic을 소프트웨어 렌더링으로 사용하는 경우 GL_RENDERER 항목에 표시됩니다.
하드웨어 렌더링을 활성화하는 몇 가지 옵션이 있습니다. 쉬운 방법 중 하나는 실제 콘솔에서 FLOW-3D를 시작한 다음 원격 데스크톱 세션을 연결하는 것입니다. Nice Software DCV 와 같은 일부 VNC 소프트웨어는 기본적으로 하드웨어 렌더링을 사용합니다.
RAM 고려 사항
프로세서 코어당 최소 4GB의 RAM은 FLOW-3D의 좋은 출발입니다. POST Processor를 사용하여 후처리 작업을 할 경우 충분한 양의 RAM을 사용하는 것이 좋습니다.
DDR5 램의 공식 규격은 2020년 7월 14일에 발표되었습니다. 하지만 일반 소비자를 대상으로 한 제품은 인텔 12세대 CPU(Alder Lake)와 함께 2021년 하반기부터 본격적으로 출시되기 시작했습니다.
일반적으로 FLOW-3D를 이용하여 해석을 할 경우 격자(Mesh)수에 따라 소요되는 적정 메모리 크기는 아래와 같습니다.페이지 보기
초대형 (2억개 이상의 셀) : 최소 128GB
대형 (60 ~ 1억 5천만 셀) : 64 ~ 128GB
중간 (30-60백만 셀) : 32-64GB
작음 (3 천만 셀 이하) : 최소 32GB
HDD 고려 사항
수치해석은 해석결과 파일의 데이터 양이 매우 크기 때문에 읽고 쓰는데, 속도면에서 매우 빠른 SSD를 적용하면 성능면에서 큰 도움이 됩니다. 다만 SSD 가격이 비싸서 가성비 측면을 고려하여 적정수준에서 결정이 필요합니다.
CPU와 저장장치 간 데이터가 오고 가는 통로가 그림과 같이 3가지 방식이 있습니다. 이를 인터페이스라 부르며 SSD는 흔히 PCI-Express 와 SATA 통로를 이용합니다.
흔히 말하는 NVMe는 PCI-Express3.0 지원 SSD의 경우 SSD에 최적화된 NVMe (NonVolatile Memory Express) 전송 프로토콜을 사용합니다. 주의할 점은 MVMe중에서 SATA3 방식도 있기 때문에 잘 구별하여 구입하시기 바랍니다.
그리고 SSD를 선택할 경우에도 SSD 종류 중에서 PCI Express 타입은 매우 빠르고 가격이 고가였지만 최근에는 많이 저렴해졌습니다. 따라서 예산 범위내에서 NVMe SSD등 가장 효과적인 선택을 하는 것이 좋습니다. ( 참고 :해석용 컴퓨터 SSD 고르기 참조 )
기존의 물리적인 하드 디스크의 경우, 디스크에 기록된 데이터를 읽기 위해서는 데이터를 읽어내는 헤드(바늘)가 물리적으로 데이터가 기록된 위치까지 이동해야 하므로 이동에 일정한 시간이 소요됩니다. (이러한 시간을 지연시간, 혹은 레이턴시 등으로 부름) 따라서 하드 디스크의 경우 데이터를 읽기 위한 요청이 주어진 뒤에 데이터를 실제로 읽기까지 일정한 시간이 소요되는데, 이 시간을 일정한 한계(약 10ms)이하로 줄이는 것이 불가능에 가까우며, 데이터가 플래터에 실제 기록된 위치에 따라서 이러한 데이터에의 접근시간 역시 차이가 나게 됩니다.
하지만 HDD의 최대 강점은 가격대비 용량입니다. 현재 상용화되어 판매하는 대용량 HDD는 12TB ~ 15TB가 공급되고 있으며, 이는 데이터 저장이나 백업용으로 가장 좋은 선택이 됩니다. 결론적으로 데이터를 직접 읽고 쓰는 드라이브는 SSD를 사용하고 보관하는 용도의 드라이브는 기존의 HDD를 사용하는 방법이 효과적인 선택이 될 수 있습니다.
상기 벤치마크 테스트는 테스트 조건에 따라 그 성능 곡선이 달라질 수 있기 때문에 조건을 확인할 필요가 있습니다. 예를 들어 Windows7, windows8, windows10 , windows11 모두에서 테스트한 결과를 평균한 점수와 자신이 사용할 컴퓨터 O/S에서 테스트한 결과는 다를 수 있습니다. 상기 결과에 대한 테스트 환경에 대한 내용은 아래 사이트를 참고하시기 바랍니다.
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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The present work provides validation of the ultimate tensile strength computational models, based on full-scale lamellar graphite iron casting process simulation, against previously obtained experimental data. Microstructure models have been combined with modified Griffith and Hall–Petch equations, and incorporated into casting simulation software, to enable the strength prediction for four pearlitic lamellar cast iron alloys with various carbon contents. The results show that the developed models can be successfully applied within the strength prediction methodology along with the simulation tools, for a wide range of carbon contents and for different solidification rates typical for both thin- and thick-walled complex-shaped iron castings.
Nowadays, there is a great need to further improve both the material properties and the prediction models for optimization of the heavy truck engine components aimed to fulfil the rigorous environmental legislations, sustainability goals, and customer demands. Cylinder blocks and cylinder heads are the primary components of these engines, and the majority of them are composed of lamellar graphite iron (LGI). The ultimate tensile strength (UTS) of LGI is an essential material property that determines the engine performance and the fuel consumption. The complex geometry and variation of the wall thickness in the cylinder blocks result in different solidification times through the component, and thus, different tensile properties. A number of investigators [1,2,3,4,5,6] underlined the major influence of the graphite flake size on the strength of LGI. It is believed that under stress, the graphite flakes are dispersed in the metal matrix act as notches that decrease the material strength. Modified Griffith and Hall–Petch models were introduced for the prediction of UTS in LGI, where the maximum graphite length was considered as the maximum defect size [3,7,8,9]. Recently, it was found that the maximum defect size can never be larger than the interdendritic space between the primary austenite dendrites formed during the solidification process [10]. The length scale of the interdendritic space was characterized by the hydraulic diameter of the interdendritic phase (DIPHyde), which proved to be the most suitable parameter to express the detrimental effect of the graphite lamella in the metallic matrix. Thus, the DIPHyde parameter was introduced as the maximum defect size in the modified Griffith and Hall–Petch equations [10,11]. Over the past decades, computer simulations of LGI solidification were carried out by several researchers [7,8,9,12,13] to describe the thermal history and the microstructure evolution of LGI castings. The main objective of these studies was prediction of the UTS. Macroscopic heat flow modeling, coupled with growth kinetic equations, was introduced in [7] to predict various microstructure features of LGI. Consequently, a modified Griffith fracture relation was applied to determine the UTS of a commercial LGI alloy. A similar solidification model was developed in [8], where a microstructure evolution model was employed together with the modified Hall–Petch equation for calculation of the UTS. Note that in [8], two different cooling rates resulted in two different relationships between the UTS and the maximum graphite flake length. Similar observations were made in [10], where three different cooling rates led to providing three different linear dependencies between the eutectic cell size (direct proportional to the maximum graphite length) and the UTS. The present work provides validation of the UTS computational models against experimental data, based on full-scale pearlitic LGI gravity casting process simulation. We investigated whether the models recently developed in [10,11] can be applied within the UTS prediction methodology, along with the simulation tools, for different alloy compositions and for different solidification rates. The novel methodology for UTS prediction, presented in this paper, involves DIPHyde as the key morphological parameter, along with the pearlite lamellar spacing. These parameters are dependent on solidification time, cooling rate, and alloy composition. The proposed approach bears simplicity compared to the microstructure modelling methods [7,8]. The methodology is validated to include analytical formulation of the UTS prediction models and robust experimental thermal analysis, to obtain latent heat of solidification and solid-state transformation as input data for the simulation. First, the UTS modeling methods are elaborated followed by the details on the experimental setup and alloy composition. Casting simulation model is then introduced, as well as the simulation procedure. The results are discussed in comparison with the temperature and UTS measurements, followed by conclusions regarding applicability and limitations of the proposed UTS prediction methodology.
2. UTS Modeling
The modified Griffith fracture relation is given by Equation (1) [3], and the modified Hall–Petch strengthening model is represented by Equation (2) [8].
where 𝜎𝑈𝑇𝑆 is the ultimate tensile strength, α is the maximum defect size, and kt is the stress intensity factor of the metallic matrix, k1 and k2 are the contributions from other strengthening mechanisms, and d is the grain size. The maximum defect size and grain size, α and d, are provided in μm, parameters kt and k2 are in MPa, √μm, and k1 is in MPa.
It was found in [10] that DIPHyde is the dominant factor that reduces the UTS in lamellar graphite iron alloys. A modified Griffith equation was obtained in [10] as result of the linear regression analysis of the experimental data, Equation (3).
According to this model, if a tensile force is applied on the microstructure, a crack will start to form at a certain stress level. The crack will propagate relatively easily through the numerous interconnected graphite particles that are embedded in the metallic matrix of the eutectic cell. When the crack reaches the metallic matrix (pearlite) that was originated from the primary austenite (dendritic phase), the relatively rapid crack extension will be halted, due to the fact that much larger stresses are required for the fracture of this phase. The magnitude of the additional stress is proportional to the pearlite lamellar spacing (λpearlite). Based on this assumption, it becomes apparent that the effect of λpearlite on the UTS must be taken into consideration. Thus, linear multiple regression analysis was made to determine the simultaneous influence of the DIPHyde and the λpearlite on the UTS. The model obtained is based on the modified Hall–Petch relation, and is expressed by Equation (4) [11].
The DIPHyde parameter was found to be related to the solidification time (ts) and the fraction of primary austenite (fγ), as seen from Equation (5) [14].
The λpearlite parameter at room temperature was assumed to be dependent on the cooling rate in the eutectoid transformation region. The empirical relationship between λpearlite at room temperature, and the cooling rate at the temperature intervals between 700 and 740 °C, is shown in Figure 1. The experimentally derived relation Equation (6) was used for investigating the effect of different λpearlite prediction models on simulated UTS. The measurements techniques, the microstructure and thermal data that resulted in Equation (6), are presented elsewhere [11,12]. Briefly, the pearlite lamellar spacing was measured using SEM and a linear intercept method. The minimum value was considered to be the correct spacing (perpendicular to the lamellae). The distance between 11 adjacent ferrite lamellas was measured and divided by 10 for estimation of a single interlamellar spacing.
Figure 1. Pearlite lamellar spacing as function of cooling rate between 700 and 740 °C.
3. Materials and Methods
3.1. Cylindrical Castings
The experimental layout contained three cylindrical cavities, each one surrounded by a different material (steel chill, sand, and insulation) intended to provide three different cooling rates. The entire assembly was enclosed by a furan-bounded sand mold. The dimensions of the cylinders surrounded by sand and chill were ∅50 × 70 mm, and the insulated cylinder dimensions were ∅80 × 70 mm. A lateral 2-D heat flow condition was induced by placing an insulation plate at the top and bottom of the cylindrical castings. The design of the cylindrical castings and arrangement of the experimental layout are shown in Figure 2 and Figure 3, respectively.
Figure 2. Cylindrical castings with the insulation and chill.
Figure 3. The experimental layout. (1) Thermocouples, (2) sand mold, and (3) insulation plates.
Two type S thermocouples with glass tube protection were embedded in every cylindrical casting. A central thermocouple was located on the central axis of the cylinder. The distance between the central and the lateral thermocouple was 20 mm for the ∅50 mm cylinder and 30 mm for the ∅80 mm cylinder. The thermocouples were placed at the mid-height of each cylinder and the temperatures were recorded at approximately 0.2 s interval. A 16-bit resolution data acquisition system with the sampling rate 100 Hz was employed [12]. The mold-filling time was 12 s. The solidification times of the metal in the chill, sand, and insulation were roughly 80, 400, and 1500 s, respectively. An electric induction furnace was utilized for melting of the charge material. The cast iron base alloy was inoculated with a constant level of a standard Sr-based inoculant. Four hypoeutectic lamellar graphite iron heats with varying carbon contents were produced. The alloy with the higher carbon content was cast first, and steel scraps were added to the furnace for the adjustment of the carbon content in the following casting. Coin-shaped specimens were extracted for chemical analysis. The chemical compositions of the four different alloys are presented in Table 1. All the castings had a fully pearlitic microstructure.
Table 1. Chemical composition (wt %) and carbon equivalent (Ceq = %C + %Si/3 + %P/3).
Alloy
C
Si
Mn
P
S
Cr
Cu
Ceq
A
3.62
1.88
0.57
0.04
0.08
0.14
0.38
4.26
B
3.34
1.83
0.56
0.04
0.08
0.15
0.37
3.96
C
3.05
1.77
0.54
0.04
0.08
0.14
0.36
3.65
D
2.80
1.75
0.54
0.04
0.08
0.15
0.35
3.40
Tensile strength measurements were performed using a dog bone-shaped specimen with 6 mm diameter in the gauge section, 35 mm gauge length, and a 3 μm surface finish. The tests were conducted at a strain rate of 0.035 mm/s and at room temperature. The experimental tensile samples were machined at the distance ~10 mm (sand, chill) and ~20 mm (insulation) from the cylinder axis. The load cell error of the tensile testing machine was <0.5%.
3.2. Simulation Model and Assumptions
A CFD software (Flow-3D CAST, v.5.0 from Flow Science, Inc., Santa Fe, NM, USA) [15] was employed to develop a full-scale 3D model of the casting process for the experimental layout. Mold filling and the cooling/solidification stages were simulated, and local UTS computations were performed on the customized models. Mold-filling time was 12 s, and the laminar flow model was applied. The casting temperature was 1360 °C, and the metal input diameter was 3 cm. The ambient temperature was set to 20 °C. Symmetry boundary conditions were used on the faces of the computational domain, except for the upper face, where the pressure boundary condition was applied. A computational grid of cubical control elements was generated with the cell size 3 mm. The computational grid had a total of ~1 million cells. Different grid densities were tested, and grid-independent results were obtained. The explicit solver was employed during the mold filling, whereas the implicit solver was used for heat transfer simulation in the solidification phase. Since the focus was on heat transfer and the UTS computation methodology, shrinkage and micro-porosity models were not included in the solidification phase. In this work, the amount of latent heat release due to solidification was related to the solid fraction curves, seen in Figure 4, for the studied alloys. These curves were calculated from the registered experimental cooling curves by using the Fourier thermal analysis method [16,17]. The latent heat of solidification was considered equal to 240 kJ/kg for all studied alloys [18]. Fourier thermal analysis was also applied on cooling curves for the determination of the latent heat release during the eutectoid transformation. The latent heat releases at the eutectoid transformation was found to be similar for all alloys and were incorporated into the specific heat curve as it is shown in Figure 5. The temperature dependent cast iron thermophysical properties [12], and the calibrated heat transfer coefficients applied in the simulation are presented in Table 2.
Figure 4. Solid fraction variation with temperature.
Figure 5. Specific heat as function of temperature.
Table 2. Temperature dependent properties of the cast iron and heat transfer coefficients *.
Temperature (°C)
Cast Iron Thermophysical Properties
Heat Transfer Coefficient
Density
Specific Heat
Thermal Conductivity
Sand-Casting
Chill-Casting
Insulation-Casting
[kg/m3]
[J/kg/K]
[W/m/K]
[W/m2/K]
[W/m2/K]
[W/m2/K]
600
7146
700
40
40
100
10
720
–
1074
–
–
300
–
721
–
12301
–
–
–
–
724
–
12308
–
–
–
–
725
–
1082
–
50
–
10
750
–
733
–
–
–
–
900
–
–
–
80
–
15
1000
6994
800
–
150
–
25
1100
–
825
–
250
1300
55
1154
6960
837
40
–
1450
–
1170
7016
–
–
–
–
–
1200
6985
–
–
–
1600
60
1227
6939
749
–
–
–
–
1300
6876
771
–
380
–
180
1700
6395
807
38
940
2700
940
* Piecewise linear interpolation was made between neighboring points in the table.
3.3. Simulation Procedure
The simulation procedure consisted of model calibration with respect to the experimental cooling curves available at the location of the central thermocouple. Correct reproduction of the experimental cooling curves is the key for the UTS computation methodology, and one is free to choose methods for model calibration. In this work, the calibration was done by adjustment of the typical heat transfer coefficients between the metal and the insulation, sand, and chill. The UTS calculations for the cylinders were performed during post-processing, by applying local solidification times, local cooling rates in the eutectoid transformation region, and the experimentally determined fraction of primary austenite (fγ) for each alloy: 0.3 for alloy A, 0.4 for alloy B, 0.51 for alloy C, and 0.61 for alloy D [16].
4. Results and Discussion
The general agreement within 7% was achieved between the simulated and measured cooling curves for insulation-, sand-, and chill-encapsulated cylinders; see Figure 6, Figure 7, Figure 8 and Figure 9. The larger differences were observed in the solidification region of the chill castings where the eutectic reaction was predicted at higher temperature than measured. This is because the solid fraction-temperature curves were derived from the sand-casting thermal histories, where the undercooling was much lower. Moreover, the solidification model in the simulation used the enthalpy method [19] and ignored the kinetics of phase transformation and, therefore, the undercooling and recalescence of solidification were not predicted. However, the simulated solidification times were in good agreement with the experiment.
Figure 6. Simulated and experimental cooling curves (central thermocouple) for alloy A: (a) insulation, (b) sand, and (c) chill.
Figure 7. Simulated and experimental cooling curves (central thermocouple) for alloy B: (a) insulation, (b) sand, and (c) chill.
Figure 8. Simulated and experimental cooling curves (central thermocouple) for alloy C: (a) insulation, (b) sand, and (c) chill.
Figure 9. Simulated and experimental cooling curves (central thermocouple) for alloy D: (a) insulation (b) sand, and (c) chill.
The measurement accuracy of the type S thermocouples was ±1.5 °C. It is worth noting that some of the thermocouples inserted in the melt could be slightly displaced from their intended positions during the solidification, which created an additional source of the measurement error; this can be seen clearly, e.g., from the solidification part of the experimental cooling curve for the insulated cylinder in Figure 7. The simulated solidification times and cooling rates were used in Equations (3) and (4) for the calculation of UTS. The predicted UTS distribution, substituted in the middle cross-section of the alloy B casting, is shown in Figure 10. The figure illustrates the inhomogeneous material strength in the casting. It is directly related to the temperature gradient and the cooling rate distribution during solidification and solid-state transformation. The reduced UTS is the result of the microstructure coarseness that is related to the solidification time and the cooling rate. Moreover, large UTS gradients on the chilled cylinder can be explained by the large temperature gradients at high solidification rate. Intermediate and slow solidification rates on sand- and insulation-encapsulated cylinders resulted in more uniform distribution of UTS values, due to the smaller temperature gradients during solidification. It should be noted that the variation of UTS magnitude within the tensile bar positions (shown with dashed lines) complicates the model validation.
Figure 10. Distribution of ultimate tensile strength (UTS) calculated from Equations (4) and (6) for alloy B: (a) insulation-, (b) sand-, and (c) chill-encapsulated cylinder; the dashed lines indicate the position of the tensile bars.
The obtained values were compared to the measured UTS. Table 3 presents the experimental and simulated UTS results for different cooling rates and for each alloy. The simulated UTS values in Table 3 were picked from the mid-height locations of the tensile bar regions, indicated in Figure 10 with dashed lines. This would correspond to the failure location in the tensile test. However, the exact fracture location might be influenced by several other factors, such as microporosities, graphite flakes that are in contact with the casting surface, or other casting impurities. All of these can cause the crack initiation at positions where the theoretical material strength is not the lowest. Apparently, the fracture analysis is out of scope of the present work. There are quite small differences between simulated and measured UTS values, with the exception of the intermediate and slow cooling rates (sand and insulation) for alloy A, where all the models predicted the UTS with less accuracy. Relatively high, but still acceptable average percentage errors are also observed for the insulated cylinders cast of alloys C and D.
Comparisons between the calculated and the measured data are demonstrated in Figure 11. The graph reveals a relatively strong correlation between the measured and computed UTS. The R2 values show that Equation (3) predicts the UTS with better accuracy than Equation (4). This indicates the need to develop further the model for prediction of the λpearlite parameter.
Figure 11. Correlation between measured and simulated UTS values.
The observed deviations between the simulated and measured UTS can be also attributed to the limited number of tensile specimens [10] and to uncertainties regarding the measurements accuracy of the 𝐷𝐻𝑦𝑑𝐼𝑃 parameter, especially for the low cooling rate samples [20] that were used to develop the UTS models. The presented results should be related to two fundamental publications on computer simulations of LGI solidification coupled with the Griffiths and Hall–Petch models [7,8]. The models for UTS calculation utilized in these works were based on a narrow carbon content interval, and on a limited cooling rate variation, in comparison. Moreover, growth kinetic equations were employed in [7,8]. On the contrary, the latent heat release model by the “enthalpy method” [19] was adopted for the solidification simulation in the present work. Furthermore, the presented way to determine the key parameters and incorporate them into material property prediction is novel. In [7,8], the key parameter was the eutectic cell diameter. It is evident that the modified Griffith and Hall–Petch equations are applicable once the eutectic diameter can be predicted, as well as the pearlite lamellar spacing in the Hall–Patch equation. A completely different approach validated in this work involved the hydraulic diameter as the key morphological parameter, along with the pearlite lamellar spacing introduced in [8]. The presented methodology to calculate the UTS features the simplicity of determining the key parameters by simulation (solidification time, cooling rate, and composition dependent). While [7] and [8] introduce complex microstructure models valid for small process intervals (with respect to composition and cooling condition), the current methodology lays back to a robust experimental thermal analysis [16], providing accurate input data (latent heat of both solidification and solid-state transformation) for the simulation. A robust iteration process for tuning up the heat transfer coefficient results in the accurately predicted cooling rate.
5. Conclusions
The novel UTS prediction methodology for fully pearlitic LGI alloys presented in this paper involves hydraulic diameter as the key morphological parameter, along with the pearlite lamellar spacing. It is characterized by simplicity, in comparison to the microstructure modelling methods. The methodology includes analytical formulation of the UTS prediction models, and robust experimental thermal analysis. The latter provides the latent heat of solidification and solid-state transformation as input data for the solidification simulation. In turn, the simulation delivers the solidification time and cooling rates for the UTS prediction models.
Microstructure models for the prediction of hydraulic diameter and the pearlite lamellar spacing, combined with modified Griffith and Hall–Petch equations, were incorporated into casting simulation software for the prediction of UTS in fully pearlitic LGI alloys. Overall, the simulation UTS results were found to be in good agreement (within 9% on the average) with the measurements. However, high average percentage errors were observed for the intermediate and slow cooling rates (sand and insulation) for the alloy with the higher carbon content (alloy A). This study revealed the necessity for development of a more advanced model for the prediction of the λpearlite parameter. The results demonstrated the applicability of the novel UTS prediction models for different chemical compositions and cooling conditions.
Further development of the microstructure modelling would enable determination of the key parameters (hydraulic diameter and pearlite lamellar spacing). However, it seems not to be critical for the presented novel UTS prediction methodology which is valid for the wide process interval.
Author Contributions
A.D. designed the experiment and supervised the work, I.B. performed the simulations, V.F. analyzed the data and wrote the paper, A.D. and I.B. reviewed the paper.
Funding
This research received no external funding.
Acknowledgments
This work was performed within the Swedish Casting Innovation Centre. Cooperating parties are Jönköping University, Scania CV AB, Swerea SWECAST AB and Volvo Powertrain Production Gjuteriet AB. Participating persons from these institutions/companies are acknowledged.
Conflicts of Interest
The authors declare no conflict of interest.
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In practical use, there is shrinkage in the width direction in existing overflow water film. This study introduces the ” flow deflectors ” to solve the problem of discontinuous water film. According to the principle of the experimental devices, the model was established by FLOW-3D software and the corresponding boundary conditions were set up, the minimum size of the grid was 0.25mm × 0.25mm × 0.25mm. The film model was investigated under ten working conditions with three factors. Through the analysis of the distribution curves of velocities and thickness, impacts of unit width flux, tank width and the distance between the flow deflectors on the velocity and thickness of the liquid film were obtained. The results indicated that the water film was able to keep continuous and airtight with flow deflectors. The variation law of water film with unit width flux was obtained and a correlation formula was proposed according to Nusselt correlation. And, it was found that the tank width has little influence on the water film itself. The “dry zones” were also founded on the film when the distance between flow deflectors increased.
References
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Deniz Velioglu Sogut ,Erdinc Sogut ,Ali Farhadzadeh,Tian-Jian Hsu
Abstract
The present study evaluates the performance of two numerical approaches in estimating non-equilibrium scour patterns around a non-slender square structure subjected to a transient wave, by comparing numerical findings with experimental data. This study also investigates the impact of the structure’s positioning on bed evolution, analyzing configurations where the structure is either attached to the sidewall or positioned at the centerline of the wave flume. The first numerical method treats sediment particles as a distinct continuum phase, directly solving the continuity and momentum equations for both sediment and fluid phases. The second method estimates sediment transport using the quadratic law of bottom shear stress, yielding robust predictions of bed evolution through meticulous calibration and validation. The findings reveal that both methods underestimate vortex-induced near-bed vertical velocities. Deposits formed along vortex trajectories are overestimated by the first method, while the second method satisfactorily predicts the bed evolution beneath these paths. Scour holes caused by wave impingement tend to backfill as the flow intensity diminishes. The second method cannot sufficiently capture this backfilling, whereas the first method adequately reflects the phenomenon. Overall, this study highlights significant variations in the predictive capabilities of both methods in regard to the evolution of non-equilibrium scour at low Keulegan–Carpenter numbers.
Keywords
Keulegan-Carpenter number, Solitary wave, non slender, wave-structure interaction, FLOW-3D, WedWaveFoam
Omega-Luitex법을 이용한 수력점프 발생시 러프 베드의 와류 진화 예측 및 영향 분석
Cong Trieu Tran, Cong Ty Trinh
Abstract
The dissipation of energy downstream of hydropower projects is a significant issue. The hydraulic jump is exciting and widely applied in practice to dissipate energy. Many hydraulic jump characteristics have been studied, such as length of jump Lj and sequent flow depth y2. However, understanding the evolution of the vortex structure in the hydraulic jump shows a significant challenge. This study uses the RNG k-e turbulence model to simulate hydraulic jumps on the rough bed. The Omega-Liutex method is compared with Q-criterion for capturing vortex structure in the hydraulic jump. The formation, development, and shedding of the vortex structure at the rough bed in the hydraulic jumper are analyzed. The vortex forms and rapidly reduces strength on the rough bed, resulting in fast dissipation of energy. At the rough block rows 2nd and 3rd, the vortex forms a vortex rope that moves downstream and then breaks. The vortex-shedding region represents a significant energy attenuation of the flow. Therefore, the rough bed dissipates kinetic energy well. Adding reliability to the vortex determined by the Liutex method, the vorticity transport equation is used to compare the vorticity distribution with the Liutex distribution. The results show a further comprehension of the hydraulic jump phenomenon and its energy dissipation.
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![FIG. 2. Simulation techniques can be used to aid the inference of nanoscale defects in irradiation experiments. a) kMC can predict the isochronal evolution of defects and thus simulate the resistivity recovery spectrum. From [36], Copyright 2004 Springer Nature. b) DFT (inset) can determine the e ect of defects on positron lifetime characteristics. From [57], CC BY-NC-ND 4.0. c) DFT can be used to predict the radial probability distribution and compared to extended X-ray absorption ne structure experiments. From [59], Copyright 2021 Elsevier. d) MD schemes can simulate the degradation in thermal di usivity with dose and can be compared to TGS experiments. From [60], CC BY 4.0. e) MD can also determine the system stored energy following PKA cascades and subsequent isothermal annealing. From [25], CC BY 4.0.](https://flow3d.co.kr/wp-content/uploads/image-1812.webp)
![Figure 2. Final precipitate size and morphologies predicted from multiscale simulations elucidating the differences that can be expected in high temperature precipitate homogeneous and heterogeneous nucleation and growth in Al-Cu alloys. Reproduced with permission from Ref. [8].](https://flow3d.co.kr/wp-content/uploads/image-1640.webp)
![Fig. 11. SADP (top), BF (middle), and WBDF (bottom) images of β-phase matrix with 𝑍𝑍≈[011]𝛽𝛽 zone axis for an area with accumulated dose ranging 7 to11 dpa under RT, increasing from bottom-right to top-left. The WBDF images were taken by selecting a diffraction spot indicated by a yellow cycle in each DP.](https://flow3d.co.kr/wp-content/uploads/image-1623.webp)
![Figure 4: Flips a ! a0 and b ! b0 accompanied by two ’phason’ singularities (or mismatches) of opposite signs. The two singularities can diffuse apart along the row of hexagons by a sequence of local flips. Adapted from Fig. 3 in [9].](https://flow3d.co.kr/wp-content/uploads/image-1060.webp)
![Figure 1: The moving half of a typical die casting die [2].](https://flow3d.co.kr/wp-content/uploads/image-1792.webp)
![Table 1: Mechanical properties of AA6061 and AA7075 [36].](https://flow3d.co.kr/wp-content/uploads/image-1772.webp)
![Fig 2.2 - Tipology of chamber and its components (adapted from [11, 17]). (a) - Cold chamber; (b) - Hot chamber;](https://flow3d.co.kr/wp-content/uploads/image-1749.webp)
![Figure 2. SEM images of segregated Mo-based coarse particles: (a) clusters of Mo-rich polygonal particles observed in 0.1 Mo, (b) elongated and fragmented Mo-based phases found in 0.3 Mo casting probably deriving from (c) Mo-based needles contained in the Al–Mo10 master alloy; (d–f) corresponding EDS spectra [6].](https://flow3d.co.kr/wp-content/uploads/image-1586.webp)
![Fig. 1. Scanning electron micrographs (a) Mg97Y2Zn1 alloy after solution treatment with grains of the α-Mg matrix (dark grey) and interdendritic LPSO phases (grey) [4], (b) WZ62 after solution treatment [5] and (c) several Mg-Zn-RE alloys after homogenization [3] 1. Scanning electron micrographs (a) Mg97Y2Zn1 alloy after solution treatment with grains of the α-Mg matrix (dark grey) and interdendritic LPSO phases (grey) [4], (b) WZ62 after solution treatment [5] and (c) several Mg-Zn-RE alloys after homogenization [3]](https://flow3d.co.kr/wp-content/uploads/image-1558-scaled.webp)
![Figure 12. American Foundry Association modification levels [15]](https://flow3d.co.kr/wp-content/uploads/image-1538.webp)
![Figure 3. Mechanical and corrosion properties of conventional HPDC magnesium alloys: (a) mechanical properties [25–27] and (b) salt spray test for 1000 hours conducted by Meridian lightweight technologies.](https://flow3d.co.kr/wp-content/uploads/image-1536.webp)
![Obr. 7. Návrh 2 typov zaústení vtokových sústav pre giga odliatky a), b), c) integrálne porovnanie zachyteného vzduchu medzi dvoma konštrukčnými typmi vtokových sústav [1]](https://flow3d.co.kr/wp-content/uploads/image-1529.webp)
![Figure 3. Schematic of the foam degradation process. Source: [43].](https://flow3d.co.kr/wp-content/uploads/image-1440.webp)
![Fig. 1. End uses of zinc [1]](https://flow3d.co.kr/wp-content/uploads/image-1445.webp)
![(c) 24 h; WZ73-1.5 vol% SiC after (d) 1; (e) 12 and (f) 24 h; WZ73-2.5 vol% SiC after (g) 1; (h) 12 and (i) 24 h. Figure 8. XRD patterns of the surface corrosion layers in WZ73 and MMCs after immersing in 1 wt % NaCl solution for (a) 12 h and (b) 24 h. It has been reported that the corrosion reactions of Mg alloys immersed in a neutral aqueous solution proceed by the following reactions [33–35]: Mg → Mg2+ + 2e− (2) 2H2O + 2e− → H2+ + 2OH− (3) Mg2+ +2OH− → Mg(OH)2 (4) Figure 7. Surface morphology of WZ73 after immersing in 1 wt % NaCl solution for (a) 1; (b) 12 and (c) 24 h; WZ73-1.5 vol % SiC after (d) 1; (e) 12 and (f) 24 h; WZ73-2.5 vol % SiC after (g) 1; (h) 12 and (i) 24 h. Metals 2018, 8, x FOR PEER REVIEW 10 of 16 Figure 7. Surface morphology of WZ73 after immersing in 1 wt % NaCl solution for (a) 1; (b) 12 and (c) 24 h; WZ73](https://flow3d.co.kr/wp-content/uploads/image-1425.webp)
![Fig. 1 Progress trend of various metals used for MMCs until 2022[1].](https://flow3d.co.kr/wp-content/uploads/image-1417.webp)
![Figure 5. Images showing backseat applications: (a) 2014 Chevrolet corvette seatback (courtesy of GM); (b) 2015 Mercedes- Benz SLK seatback [37] (courtesy of GF casting solutions) and (c) 2014 BMW i3 seatback [38] (courtesy of BASF).](https://flow3d.co.kr/wp-content/uploads/image-1380.webp)
![Figure 2. Effect of braking electromagnetic fields on the flow fields, (a) No magnetic fields; (b) B = 0.1 T and (c) B = 0.2 T [23].](https://flow3d.co.kr/wp-content/uploads/image-1188.webp)
![Figure 1 Principle of the FDU device [3]](https://flow3d.co.kr/wp-content/uploads/image-1107.webp)
![[그림 7] 마그네슘 휠 물성 비교 1](https://flow3d.co.kr/wp-content/uploads/image-1104.webp)
![Fig. 6: Calculated degassing efficiency as a function of bubble size [40]](https://flow3d.co.kr/wp-content/uploads/image-1080.webp)
![Figure 2.4 Different designs of mechanical stirrers [Harnby et al. 1997].](https://flow3d.co.kr/wp-content/uploads/image-1034.webp)
![Fig. 6. Chemical fluctuations analysis around an APB region on a (111) plane in alloy 0Ti. (a) HAADF-STEM image of the ' precipitate with APBs taken along [011] beam direction. (b) Magnified image of white rectangular marked in (a). (c) Composite chemical map of elements Co, Ni, Al, Mo and W. (d)-(h) Net intensity elemental maps of elements Co, Ni, Al, Mo and W. (i) and (j) EDS line scan integrated along the APB in the region marked in (c).](https://flow3d.co.kr/wp-content/uploads/image-978.webp)
![Obr. 13: Svarovací program s jedním impulsem [2]](https://flow3d.co.kr/wp-content/uploads/image-1702.webp)
![Fig. 1.2: Variation in heat input with the power density of heat source [2]](https://flow3d.co.kr/wp-content/uploads/image-1389.webp)
![Fig. 10. Optical micrograph of an onion ring feature in FSW AA6061/Al2O3/20p crosssection [35].](https://flow3d.co.kr/wp-content/uploads/image-918.webp)
![Fig. 4. Schematic illustration of FCAW process [9].](https://flow3d.co.kr/wp-content/uploads/image-732.webp)
![Figure-1.1 TIG Welding Setup [Ref.: office.pickproducts.com.au]](https://flow3d.co.kr/wp-content/uploads/image-706.webp)
![Figure 1.1 A schematic of Gas Metal Arc Welding Process [4]](https://flow3d.co.kr/wp-content/uploads/image-657.webp)
![Fig. 1. A schematic sketch of a GTAW process [Wikipedia].](https://flow3d.co.kr/wp-content/uploads/image-651.webp)
![Figure 1. a) Sketch of the pier-caisson system considered in this study; b) Top view of a local scour hole, with the contour lines indicating the depth – values are normalized with respect to the maximum depth (after [9]).](https://flow3d.co.kr/wp-content/uploads/image-1629.webp)
