FLOW-3D 수치해석용 컴퓨터 선택 가이드

Top 20 Fastest Desktops for 2024

Top 20 Fastest Desktops for 2024

Edit: 2024-11-28

원문 출처: https://www.pcbenchmarks.net/fastest-desktop.html

PositionScoreBL#CPU TypeCPU speed (MHz)#Phys. CPUsOSMotherboardRAMVideo cardDate uploaded
126054.32223537Intel Core i9-14900KS31881Windows 11 Pro for Workstations build 26100 (64-bit)ASUSTeK COMPUTER INC. ROG MAXIMUS Z790 APEX ENCORE49.0 GBGeForce RTX 40902024-10-19 05:20:40
225140.32102766Intel Core i9-14900KS31881Windows 11 Pro for Workstations build 26100 (64-bit)ASUSTeK COMPUTER INC. ROG MAXIMUS Z790 APEX ENCORE49.0 GBGeForce RTX 40902024-05-16 19:37:40
325130.72229143Intel Core i9-14900KS31881Windows 11 Pro for Workstations build 26100 (64-bit)ASUSTeK COMPUTER INC. ROG MAXIMUS Z790 FORMULA32.5 GBGeForce RTX 40902024-10-25 16:08:42
425022.62096097Intel Core i9-14900KF31881Windows 11 Pro for Workstations build 26100 (64-bit)ASUSTeK COMPUTER INC. ROG MAXIMUS Z790 APEX ENCORE49.0 GBGeForce RTX 40902024-05-08 01:22:49
524977.12093965Intel Core i9-14900KF31871Windows 11 Pro for Workstations build 22631 (64-bit)ASUSTeK COMPUTER INC. ROG MAXIMUS Z790 APEX ENCORE49.0 GBGeForce RTX 40902024-05-04 21:23:54
624550.71756060Intel Core i9-13900KS31881Windows 10 Home build 19045 (64-bit)Micro-Star International Co., Ltd. MAG Z790 TOMAHAWK WIFI DDR4(MS-7D91)32.5 GBGeForce RTX 40902023-02-27 01:36:21
724124.92010540Intel Core i9-14900KF31881Windows 11 Pro for Workstations build 22631 (64-bit)ASUSTeK COMPUTER INC. ROG MAXIMUS Z790 APEX ENCORE32.6 GBGeForce RTX 40902024-01-30 06:25:31
823924.41989560Intel Core i9-13900KS31881Windows 11 Pro for Workstations build 22631 (64-bit)ASUSTeK COMPUTER INC. ROG MAXIMUS Z790 APEX ENCORE32.6 GBGeForce RTX 40902024-01-06 11:51:42
923117.01986111Intel Core i9-14900K31871Windows 11 Pro for Workstations build 22631 (64-bit)ASUSTeK COMPUTER INC. ROG MAXIMUS Z790 APEX ENCORE32.6 GBGeForce RTX 40902024-01-02 23:37:24
1023035.82196479Intel Core i9-14900K31881Windows 11 Professional Edition build 26120 (64-bit)ASUSTeK COMPUTER INC. ROG MAXIMUS Z790 FORMULA32.5 GBGeForce RTX 40902024-09-16 06:54:48
1123011.32219063AMD Ryzen 9 9950X43011Windows 11 Pro for Workstations build 26100 (64-bit)ASUSTeK COMPUTER INC. ROG CROSSHAIR X870E HERO48.8 GBGeForce RTX 40902024-10-14 01:33:56
1223002.92219004AMD Ryzen 9 9950X43011Windows 11 Pro for Workstations build 26100 (64-bit)ASUSTeK COMPUTER INC. ROG CROSSHAIR X870E HERO48.8 GBGeForce RTX 40902024-10-13 22:45:27
1322696.62216075Intel Core i9-14900KS31881Windows 11 Professional Edition build 26100 (64-bit)ASUSTeK COMPUTER INC. ROG MAXIMUS Z790 APEX ENCORE49.0 GBGeForce RTX 40902024-10-10 10:13:14
1422676.21936617Intel Core i9-14900K31871Windows 11 Professional Edition build 22631 (64-bit)ASUSTeK COMPUTER INC. ROG MAXIMUS Z790 APEX ENCORE32.6 GBGeForce RTX 40902023-10-31 18:47:25
1522626.02214448AMD Ryzen 9 9950X43001Windows 11 Pro for Workstations build 26100 (64-bit)ASUSTeK COMPUTER INC. ROG CROSSHAIR X870E HERO32.4 GBGeForce RTX 40902024-10-08 12:43:52
1622561.71947982Intel Core i9-14900K31881Windows 11 Professional Edition build 22631 (64-bit)ASUSTeK COMPUTER INC. ROG MAXIMUS Z790 FORMULA32.5 GBGeForce RTX 40902023-11-16 12:20:10
1722561.52214771AMD Ryzen 9 9950X43001Windows 11 Pro for Workstations build 26100 (64-bit)ASUSTeK COMPUTER INC. ROG CROSSHAIR X870E HERO32.4 GBGeForce RTX 40902024-10-08 21:38:56
1822423.62014883Intel Core i9-14900K31881Windows 11 Professional Edition build 22635 (64-bit)ASUSTeK COMPUTER INC. ROG MAXIMUS Z790 FORMULA32.5 GBGeForce RTX 40902024-02-03 17:43:54
1922378.52079225Intel Core i9-14900K31881Windows 11 Professional Edition build 26100 (64-bit)ASUSTeK COMPUTER INC. ROG MAXIMUS Z790 FORMULA32.5 GBGeForce RTX 40902024-04-16 04:53:25
2022368.41947167Intel Core i9-14900K31871Windows 11 Professional Edition build 22631 (64-bit)ASUSTeK COMPUTER INC. ROG MAXIMUS Z790 FORMULA32.5 GBGeForce RTX 40902023-11-15 11:19:39

CPU 벤치마크

아래는 차트에 나타나는 모든 단일 및 다중 소켓 CPU 유형의 목록입니다. 열특정 프로세서 이름을 클릭하면 해당 프로세서가 나타나는 차트로 이동하여 강조 표시됩니다.

https://www.cpubenchmark.net/CPU_mega_page.html

CPU NameCoresCPU MarkThread MarkTDP (W)SocketCategory
AMD Ryzen Threadripper PRO 7995WX96153,5983,964350sTR5Desktop
AMD Ryzen Threadripper 7980X64133,9023,956350sTR5Desktop
AMD Ryzen Threadripper PRO 7985WX64133,1943,890350sTR5Desktop
[Dual CPU] AMD Ryzen Threadripper PRO 3995WX64113,6932,559280sWRX8Desktop, Server
[Dual CPU] AMD Ryzen Threadripper PRO 3975WX3298,8112,676280sWRX8Desktop, Server
AMD Ryzen Threadripper 7970X3298,6854,137350sTR5Desktop
AMD Ryzen Threadripper PRO 7975WX3295,6234,065350sTR5Desktop
AMD Ryzen Threadripper PRO 5995WX6493,1923,207280sWRX8Desktop, Server
AMD Ryzen Threadripper PRO 3995WX6483,6972,598280sWRX8Desktop, Server
AMD Ryzen Threadripper 7960X2483,6244,123350sTR5Desktop
AMD Ryzen Threadripper PRO 7965WX2480,9203,945350sTR5Desktop
AMD Ryzen Threadripper 3990X6480,6592,565280sTRX4Desktop
AMD Ryzen Threadripper PRO 5975WX3275,6543,315280sWRX8Desktop, Server
Intel Core Ultra 9 285K2468,7685,087125FCLGA1851Desktop
AMD Ryzen Threadripper PRO 5965WX2466,6803,359280sWRX8Desktop, Server
AMD Ryzen 9 9950X1666,3584,731170AM5Desktop
[Dual CPU] AMD Ryzen Threadripper PRO 3955WX1663,8852,439280sWRX8Desktop, Server
AMD Ryzen Threadripper 3970X3263,1152,665280sTRX4Desktop
AMD Ryzen 9 7950X1662,7044,275170AM5Desktop
AMD Ryzen 9 7950X3D1662,5114,149120AM5Desktop
AMD Ryzen Threadripper PRO 3975WX3262,4772,656280sWRX8Desktop, Server
Intel Core i9-14900KS2462,3744,871150FCLGA1700Desktop
Intel Core Ultra 7 265KF2061,9644,956125FCLGA1851Desktop
Intel Core i9-13900KS2461,5364,746150FCLGA1700Desktop
Intel Core i9-14900K2460,1164,735125FCLGA1700Desktop
AMD Ryzen Threadripper PRO 7955WX1659,9684,096350sTR5Desktop
Intel Core i9-14900KF2459,5634,710125FCLGA1700Desktop
Intel Core Ultra 7 265K2059,1624,784125FCLGA1851Desktop
Intel Core i9-13900K2458,9964,620125FCLGA1700Desktop
Intel Core i9-13900KF2458,3044,609125FCLGA1700Desktop
AMD Ryzen Threadripper 3960X2454,8912,682280sTRX4Desktop
AMD Ryzen 9 9900X1254,6954,684120AM5Desktop

Hardware Selection for FLOW-3D Products – FLOW-3D

부분 업데이트 / ㈜에스티아이씨앤디 솔루션사업부

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

2024년 04월 01일 기준

CPU Benchmarks
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.

PassMark - CPU Mark
High End CPUs
Updated 31st of March 2024
PassMark – CPU Mark High End CPUs Updated 31st of March 2024

<출처>https://www.cpubenchmark.net/high_end_cpus.html

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.

<참고>

SPEC의 벤치 마크https://www.spec.org/benchmarks.html#cpu )

SPEC CPU 2017 (현재까지 가장 최근에 개발된 CPU 성능측정 기준)

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.

https://www.spec.org/cgi-bin/osgresults

<보고서 샘플>

  • SPEC CPU 2017

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.

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.

<관련 기사>

https://www.techspot.com/news/78122-report-software-fix-can-double-threadripper-2990wx-performance.html

Graphics 고려 사항

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.

PassMark - G3D Mark
High End Videocards
PassMark – G3D Mark High End Videocards

출처 : https://www.videocardbenchmark.net/high_end_gpus.html

원격데스크탑 사용시 고려 사항

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.

현재 주력제품인 DDR4보다 2배 빠른 DDR5가 곧 출시된다는 소식도 있습니다.

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.

PassMark – Disk Rating High End Drives

PassMark - Disk Rating
High End Drives
PassMark – Disk Rating High End Drives

출처 : https://www.harddrivebenchmark.net/high_end_drives.html

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.

참고 : 테스트 환경

페이지 보기

Coating_image

Template-Free Scalable Fabrication of Linearly Periodic Microstructures by Controlling Ribbing Defects Phenomenon in Forward Roll Coating for Multifunctional Applications

다기능 응용을 위한 Forward Roll Coating 공정의 리브 경함 형상 제어를 통한 선형 주기적 미세구조물의 템플릿 프리 제작

Md Didarul Islam, Himendra Perera, Benjamin Black, Matthew Phillips,Muh-Jang Chen, Greyson Hodges, Allyce Jackman, Yuxuan Liu, Chang-Jin Kim,Mohammed Zikry, Saad Khan, Yong Zhu, Mark Pankow, and Jong Eun Ryu

Abstract


Periodic micro/nanoscale structures from nature have inspired the scientific community to adopt surface design for various applications, including superhydrophobic drag reduction. One primary concern of practical applications of such periodic microstructures remains the scalability of conventional microfabrication technologies. This study demonstrates a simple template-free scalable manufacturing technique to fabricate periodic microstructures by controlling the ribbing defects in the forward roll coating. Viscoelastic composite coating materials are designed for roll-coating using carbon nanotubes (CNT) and polydimethylsiloxane (PDMS), which helps achieve a controllable ribbing with a periodicity of 114–700 µm. Depending on the process parameters, the patterned microstructures transition from the linear alignment to a random structure. The periodic microstructure enables hydrophobicity as the water contact angles of the samples ranged from 128° to 158°. When towed in a static water pool, a model boat coated with the microstructure film shows 7%–8% faster speed than the boat with a flat PDMS film. The CNT addition shows both mechanical and electrical properties improvement. In a mechanical scratch test, the cohesive failure of the CNT-PDMS film occurs in ≈90% higher force than bare PDMS. Moreover, the nonconductive bare PDMS shows sheet resistance of 747.84–22.66 Ω □−1 with 0.5 to 2.5 wt% CNT inclusion.

 

Keywords


multifunctional surfaces, periodic microtrenches, ribbing instabilities,roll coating, scalable manufacturing

 

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Image_Sacrificial_Pier

Sacrificial Piles as Scour Countermeasures in River Bridges A Numerical Study using FLOW-3D

하천 교량의 파괴 대책으로서 희생파일에 대한 FLOW-3D를 이용한 수치 연구

Mohammad Nazari-Sharabian, Aliasghar Nazari-Sharabian, Moses Karakouzian, Mehrdad Karami

Abstract

Scour is defined as the erosive action of flowing water, as well as the excavating and carrying away materials from beds and banks of streams, and from the vicinity of bridge foundations, which is one of the main causes of river bridge failures. In the present study, implementing a numerical approach, and using the FLOW-3D model that works based on the finite volume method (FVM), the applicability of using sacrificial piles in different configurations in front of a bridge pier as countermeasures against scouring is investigated. In this regard, the numerical model was calibrated based on an experimental study on scouring around an unprotected circular river bridge pier. In simulations, the bridge pier and sacrificial piles were circular, and the riverbed was sandy. In all scenarios, the flow rate was constant and equal to 45 L/s. Furthermore, one to five sacrificial piles were placed in front of the pier in different locations for each scenario. Implementation of the sacrificial piles proved to be effective in substantially reducing the scour depths. The results showed that although scouring occurred in the entire area around the pier, the maximum and minimum scour depths were observed on the sides (using three sacrificial piles located upstream, at three and five times the pier diameter) and in the back (using five sacrificial piles located upstream, at four, six, and eight times the pier diameter) of the pier. Moreover, among scenarios where single piles were installed in front of the pier, installing them at a distance of five times the pier diameter was more effective in reducing scour depths. For other scenarios, in which three piles and five piles were installed, distances of six and four times the pier diameter for the three piles scenario, and four, six, and eight times the pier diameter for the five piles scenario were most effective.

 

Keywords

Scouring; River Bridges; Sacrificial Piles; Finite Volume Method (FVM); FLOW-3D.

 

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DOI: 10.28991/cej-2020-03091531

Numerical Investigation of the Local Scour for Tripod Pile Foundation

Numerical Investigation of the Local Scour for Tripod Pile Foundation

Waqed H. Hassan Zahraa Mohammad Fadhe* Rifqa F. Thiab Karrar Mahdi
Civil Engineering Department, Faculty of Engineering, University of Warith Al-Anbiyaa, Kerbala 56001, Iraq
Civil Engineering Department, Faculty of Engineering, University of Kerbala, Kerbala 56001, Iraq
Corresponding Author Email: Waqed.hammed@uowa.edu.iq

OPEN ACCESS

Abstract: 

This work investigates numerically a local scour moves in irregular waves around tripods. It is constructed and proven to use the numerical model of the seabed-tripod-fluid with an RNG k turbulence model. The present numerical model then examines the flow velocity distribution and scour characteristics. After that, the suggested computational model Flow-3D is a useful tool for analyzing and forecasting the maximum scour development and the flow field in random waves around tripods. The scour values affecting the foundations of the tripod must be studied and calculated, as this phenomenon directly and negatively affects the structure of the structure and its design life. The lower diagonal braces and the main column act as blockages, increasing the flow accelerations underneath them.  This increases the number of particles that are moved, which in turn creates strong scouring in the area. The numerical model has a good agreement with the experimental model, with a maximum percentage of error of 10% between the experimental and numerical models. In addition, Based on dimensional analysis parameters, an empirical equation has been devised to forecast scour depth with flow depth, median size ratio, Keulegan-Carpenter (Kc), Froud number flow, and wave velocity that the results obtained in this research at various flow velocities and flow depths demonstrated that the maximum scour depth rate depended on wave height with rising velocities and decreasing particle sizes (d50) and the scour depth attains its steady-current value for Vw < 0.75. As the Froude number rises, the maximum scour depth will be large.

Keywords: 

local scour, tripod foundation, Flow-3D​, waves

1. Introduction

New energy sources have been used by mankind since they become industrialized. The main energy sources have traditionally been timber, coal, oil, and gas, but advances in the science of new energies, such as nuclear energy, have emerged [1, 2]. Clean and renewable energy such as offshore wind has grown significantly during the past few decades. There are numerous different types of foundations regarding offshore wind turbines (OWTs), comprising the tripod, jacket, gravity foundation, suction anchor (or bucket), and monopile [3, 4]. When the water depth is less than 30 meters, Offshore wind farms usually employ the monopile type [4]. Engineers must deal with the wind’s scouring phenomenon turbine foundations when planning and designing wind turbines for an offshore environment [5]. Waves and currents generate scour, this is the erosion of soil near a submerged foundation and at its location [6]. To predict the regional scour depth at a bridge pier, Jalal et al. [7-10] developed an original gene expression algorithm using artificial neural networks. Three monopiles, one main column, and several diagonal braces connecting the monopiles to the main column make up the tripod foundation, which has more complicated shapes than a single pile. The design of the foundation may have an impact on scour depth and scour development since the foundation’s form affects the flow field [11, 12]. Stahlmann [4] conducted several field investigations. He discovered that the main column is where the greatest scour depth occurred. Under the main column is where the maximum scour depth occurs in all experiments. The estimated findings show that higher wave heights correspond to higher flow velocities, indicating that a deeper scour depth is correlated with finer silt granularity [13] recommends as the design value for a single pile. These findings support the assertion that a tripod may cause the seabed to scour more severely than a single pile. The geography of the scour is significantly more influenced by the KC value (Keulegan–Carpenter number)

The capability of computer hardware and software has made computational fluid dynamics (CFD) quite popular to predict the behavior of fluid flow in industrial and environmental applications has increased significantly in recent years [14].

Finding an acceptable piece of land for the turbine’s construction and designing the turbine pile precisely for the local conditions are the biggest challenges. Another concern related to working in a marine environment is the effect of sea waves and currents on turbine piles and foundations. The earth surrounding the turbine’s pile is scoured by the waves, which also render the pile unstable.

In this research, the main objective is to investigate numerically a local scour around tripods in random waves. It is constructed and proven to use the tripod numerical model. The present numerical model is then used to examine the flow velocity distribution and scour characteristics.

2. Numerical Model

To simulate the scouring process around the tripod foundation, the CFD code Flow-3D was employed. By using the fractional area/volume method, it may highlight the intricate boundaries of the solution domain (FAVOR).

This model was tested and validated utilizing data derived experimentally from Schendel et al. [15] and Sumer and Fredsøe [6]. 200 runs were performed at different values of parameters.

2.1 Momentum equations

The incompressible viscous fluid motion is described by the three RANS equations listed below [16]:

(1)

\frac{\partial u}{\partial t}+\frac{1}{{{V}_{F}}}\left( u{{A}_{x}}\frac{\partial u}{\partial x}+v{{A}_{y}}\frac{\partial u}{\partial y}+w{{A}_{z}}\frac{\partial u}{\partial z} \right)=-\frac{1}{\rho }\frac{\partial p}{\partial x}+{{G}_{x}}+fx

(2)

\frac{\partial v}{\partial t}+\frac{1}{{{V}_{F}}}\left( u{{A}_{x}}\frac{\partial v}{\partial x}+v{{A}_{y}}\frac{\partial v}{\partial y}+w{{A}_{z}}\frac{\partial v}{\partial z} \right)=-\frac{1}{\rho }\frac{\partial p}{\partial y}+{{G}_{y}}+\text{f}y

 (3)

\frac{\partial w}{\partial t}+\frac{1}{{{V}_{F}}}\left( u{{A}_{x}}\frac{\partial w}{\partial x}+v{{A}_{y}}\frac{\partial w}{\partial y}+w{{A}_{z}}\frac{\partial w}{\partial z} \right)=-\frac{1}{\rho }\frac{\partial p}{\partial z}+{{G}_{z}}+\text{fz}

where, respectively, uv, and w represent the xy, and z flow velocity components; volume fraction (VF), area fraction (AiI=xyz), water density (f), viscous force (fi), and body force (Gi) are all used in the formula.

2.2 Model of turbulence

Several turbulence models would be combined to solve the momentum equations. A two-equation model of turbulence is the RNG k-model, which has a high efficiency and accuracy in computing the near-wall flow field. Therefore, the flow field surrounding tripods was captured using the RNG k-model.

2.3 Model of sediment scour

2.3.1 Induction and deposition

Eq. (4) can be used to determine the particle entrainment lift velocity [17].

(4)

{{u}_{lift,i}}={{\alpha }_{i}}{{n}_{s}}d_{*}^{0.3}{{\left( \theta -{{\theta }_{cr}} \right)}^{1.5}}\sqrt{\frac{\parallel g\parallel {{d}_{i}}\left( {{\rho }_{i}}-{{\rho }_{f}} \right)}{{{\rho }_{f}}}}

α𝛼  is the Induction parameter, ns the normal vector is parallel to the seafloor, and for the present numerical model, ns=(0,0,1), θ𝜃cr is the essential Shields variable, g is the accelerated by gravity, di is the size of the particles, ρi is species density in beds, and d The diameter of particles without dimensions; these values can be obtained in Eq. (5).

(5)

{{d}_{*}}={{d}_{i}}{{\left( \frac{\parallel g\parallel {{\rho }_{f}}\left( {{\rho }_{i}}-{{\rho }_{f}} \right)}{\mu _{f}^{2}} \right)}^{1/3}}

μ𝜇f is this equation a dynamic viscosity of the fluid. cr was determined from an equation based on Soulsby [18].

(6)

{{\theta }_{cr}}=\frac{0.3}{1+1.2{{d}_{*}}}+0.055\left[ 1-\text{exp}\left( -0.02{{d}_{*}} \right) \right]

The equation was used to determine how quickly sand particles set Eq. (7):

(7)

{{\mathbf{u}}_{\text{nsettling},i}}=\frac{{{v}_{f}}}{{{d}_{i}}}\left[ {{\left( {{10.36}^{2}}+1.049d_{*}^{3} \right)}^{0.5}}-10.36 \right]

vf  stands for fluid kinematic viscosity.

2.3.2 Transportation for bed loads

Van Rijn [19] states that the speed of bed load conveyance was determined as:

(8)

{{~}_{\text{bedload},i}}=\frac{{{q}_{b,i}}}{{{\delta }_{i}}{{c}_{b,i}}{{f}_{b}}}

fb  is the essential particle packing percentage, qbi is the bed load transportation rate, and cb, I the percentage of sand by volume i. These variables can be found in Eq. (9), Eq. (10), fbδ𝛿i the bed load thickness.

(9)

{{q}_{b,i}}=8{{\left[ \parallel g\parallel \left( \frac{{{\rho }_{i}}-{{\rho }_{f}}}{{{\rho }_{f}}} \right)d_{i}^{3} \right]}^{\frac{1}{2}}}

(10)

{{\delta }_{i}}=0.3d_{*}^{0.7}{{\left( \frac{\theta }{{{\theta }_{cr}}}-1 \right)}^{0.5}}{{d}_{i}}

In this paper, after the calibration of numerous trials, the selection of parameters for sediment scour is crucial. Maximum packing fraction is 0.64 with a shields number of 0.05, entrainment coefficient of 0.018, the mass density of 2650, bed load coefficient of 12, and entrainment coefficient of 0.01.

3. Model Setup

To investigate the scour characteristics near tripods in random waves, the seabed-tripod-fluid numerical model was created as shown in Figure 1. The tripod basis, a seabed, and fluid and porous medium were all components of the model. The seabed was 240 meters long, 40 meters wide, and three meters high. It had a median diameter of d50 and was composed of uniformly fine sand. The 2.5-meter main column diameter D. The base of the main column was three dimensions above the original seabed. The center of the seafloor was where the tripod was, 130 meters from the offshore and 110 meters from the onshore. To prevent wave reflection, the porous media were positioned above the seabed on the onshore side.

image013.png

Figure 1. An illustration of the numerical model for the seabed-tripod-fluid

3.1 Generation of meshes

Figure 2 displays the model’s mesh for the Flow-3D software grid. The current model made use of two different mesh types: global mesh grid and nested mesh grid. A mesh grid with the following measurements was created by the global hexahedra mesh grid: 240m length, 40m width, and 32m height. Around the tripod, a finer nested mesh grid was made, with dimensions of 0 to 32m on the z-axis, 10 to 30 m on the x-axis, and 25 to 15 m on the y-axis. This improved the calculation’s precision and mesh quality.

image014.png

Figure 2. The mesh block sketch

3.2 Conditional boundaries

To increase calculation efficiency, the top side, The model’s two x-z plane sides, as well as the symmetry boundaries, were all specified. For u, v, w=0, the bottom boundary wall was picked. The offshore end of the wave boundary was put upstream. For the wave border, random waves were generated using the wave spectrum from the Joint North Sea Wave Project (JONSWAP). Boundary conditions are shown in Figure 3.

image015.png

Figure 3. Boundary conditions of the typical problem

The wave spectrum peak enhancement factor (=3.3 for this work) and can be used to express the unidirectional JONSWAP frequency spectrum.

3.3 Mesh sensitivity

Before doing additional research into scour traits and scour depth forecasting, mesh sensitivity analysis is essential. Three different mesh grid sizes were selected for this section: Mesh 1 has a 0.45 by 0.45 nested fine mesh and a 0.6 by 0.6 global mesh size. Mesh 2 has a 0.4 global mesh size and a 0.35 nested fine mesh size, while Mesh 3 has a 0.25 global mesh size and a nested fine mesh size of 0.15. Comparing the relative fine mesh size (such as Mesh 2 or Mesh 3) to the relatively coarse mesh size (such as Mesh 1), a larger scour depth was seen; this shows that a finer mesh size can more precisely represent the scouring and flow field action around a tripod. Significantly, a lower mesh size necessitates a time commitment and a more difficult computer configuration. Depending on the sensitivity of the mesh guideline utilized by Pang et al., when Mesh 2 is applied, the findings converge and the mesh size is independent [20]. In the next sections, scouring the area surrounding the tripod was calculated using Mesh 2 to ensure accuracy and reduce computation time. The working segment generates a total of 14, 800,324 cells.

3.4 Model validation

Comparisons between the predicted outcomes from the current model and to confirm that the current numerical model is accurate and suitably modified, experimental data from Sumer and Fredsøe [6] and Schendel et al. [15] were used. For the experimental results of Run 05, Run 15, and Run 22 from Sumer and Fredsøe [6], the experimental A9, A13, A17, A25, A26, and A27 results from Schendel et al. [15], and the numerical results from the current model are shown in Figure 4. The present model had d50=0.051cm, the height of the water wave(h)=10m, and wave velocity=0.854 m.s-1.

image016.png

Figure 4. Cell size effect

image017.png

Figure 5. Comparison of the present study’s maximum scour depth with that authored by Sumer and Fredsøe [6] and Schendel et al. [15]

According to Figure 5, the highest discrepancy between the numerical results and experimental data is about 10%, showing that overall, there is good agreement between them. The ability of the current numerical model to accurately depict the scour process and forecast the maximum scour depth (S) near foundations is demonstrated by this. Errors in the simulation were reduced by using the calibrated values of the parameter. Considering these results, a suggested simulated scouring utilizing a Flow-3D numerical model is confirmed as a superior way for precisely forecasting the maximum scour depth near a tripod foundation in random waves.

3.5 Dimensional analysis

The variables found in this study as having the greatest impacts, variables related to flow, fluid, bed sediment, flume shape, and duration all had an impact on local scouring depth (t). Hence, scour depth (S) can be seen as a function of these factors, shown as:

(11)

S=f\left(\rho, v, V, h, g, \rho s, d_{50}, \sigma g, V_w, D, d, T_v, t\right)

With the aid of dimensional analysis, the 14-dimensional parameters in Eq. (11) were reduced to 6 dimensionless variables using Buckingham’s -theorem. D, V, and were therefore set as repetition parameters and others as constants, allowing for the ignoring of their influence. Eq. (12) thus illustrates the relationship between the effect of the non-dimensional components on the depth of scour surrounding a tripod base.

(12)

\frac{S}{D}=f\left(\frac{h}{D}, \frac{d 50}{D}, \frac{V}{V W}, F r, K c\right)

where, SD𝑆𝐷 are scoured depth ratio, VVw𝑉𝑉𝑤 is flow wave velocity, d50D𝑑50𝐷 median size ratio, $Fr representstheFroudnumber,and𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠𝑡ℎ𝑒𝐹𝑟𝑜𝑢𝑑𝑛𝑢𝑚𝑏𝑒𝑟,𝑎𝑛𝑑Kc$ is the Keulegan-Carpenter.

4. Result and Discussion

4.1 Development of scour

Similar to how the physical model was used, this numerical model was also used. The numerical model’s boundary conditions and other crucial variables that directly influence the outcomes were applied (flow depth, median particle size (d50), and wave velocity). After the initial 0-300 s, the scour rate reduced as the scour holes grew quickly. The scour depths steadied for about 1800 seconds before reaching an asymptotic value. The findings of scour depth with time are displayed in Figure 6.

4.2 Features of scour

Early on (t=400s), the scour hole began to appear beneath the main column and then began to extend along the diagonal bracing connecting to the wall-facing pile. Gradually, the geography of the scour; of these results is similar to the experimental observations of Stahlmann [4] and Aminoroayaie Yamini et al. [1]. As the waves reached the tripod, there was an enhanced flow acceleration underneath the main column and the lower diagonal braces as a result of the obstructing effects of the structural elements. More particles are mobilized and transported due to the enhanced near-bed flow velocity, it also increases bed shear stress, turbulence, and scour at the site. In comparison to a single pile, the main column and structural components of the tripod have a significant impact on the flow velocity distribution and, consequently, the scour process and morphology. The main column and seabed are separated by a gap, therefore the flow across the gap may aid in scouring. The scour hole first emerged beneath the main column and subsequently expanded along the lower structural components, both Aminoroayaie Yamini et al. [1] and Stahlmann [4] made this claim. Around the tripod, there are several different scour morphologies and the flow velocity distribution as shown in Figures 7 and 8.

image023.png

Figure 6. Results of scour depth with time

image024.png

image025.png

image026.png

image027.png

Figure 7. The sequence results of scour depth around tripod development (reached to steady state) simulation time

image028.png

image029.png

image030.png

image031.png

Figure 8. Random waves of flow velocity distribution around a tripod

4.3 Wave velocity’s (Vw) impact on scour depth

In this study’s section, we looked at how variations in wave current velocity affected the scouring depth. Bed scour pattern modification could result from an increase or decrease in waves. As a result, the backflow area produced within the pile would become stronger, which would increase the depth of the sediment scour. The quantity of current turbulence is the primary cause of the relationship between wave height and bed scour value. The current velocity has increased the extent to which the turbulence energy has changed and increased in strength now present. It should be mentioned that in this instance, the Jon swap spectrum random waves are chosen. The scour depth attains its steady-current value for Vw<0.75, Figure 9 (a) shows that effect. When (V) represents the mean velocity=0.5 m.s-1.

image032.png

(a)

image033.png

(b)

image034.png

(c)

image035.png

(d)

Figure 9Main effects on maximum scour depth (Smax) as a function of column diameter (D)

4.4 Impact of a median particle (d50) on scour depth

In this section of the study, we looked into how variations in particle size affected how the bed profile changed. The values of various particle diameters are defined in the numerical model for each run numerical modeling, and the conditions under which changes in particle diameter have an impact on the bed scour profile are derived. Based on Figure 9 (b), the findings of the numerical modeling show that as particle diameter increases the maximum scour depth caused by wave contact decreases. When (d50) is the diameter of Sediment (d50). The Shatt Al-Arab soil near Basra, Iraq, was used to produce a variety of varied diameters.

4.5 Impact of wave height and flow depth (h) on scour depth

One of the main elements affecting the scour profile brought on by the interaction of the wave and current with the piles of the wind turbines is the height of the wave surrounding the turbine pile causing more turbulence to develop there. The velocity towards the bottom and the bed both vary as the turbulence around the pile is increased, modifying the scour profile close to the pile. According to the results of the numerical modeling, the depth of scour will increase as water depth and wave height in random waves increase as shown in Figure 9 (c).

4.6 Froude number’s (Fr) impact on scour depth

No matter what the spacing ratio, the Figure 9 shows that the Froude number rises, and the maximum scour depth often rises as well increases in Figure 9 (d). Additionally, it is crucial to keep in mind that only a small portion of the findings regarding the spacing ratios with the smallest values. Due to the velocity acceleration in the presence of a larger Froude number, the range of edge scour downstream is greater than that of upstream. Moreover, the scouring phenomena occur in the region farthest from the tripod, perhaps as a result of the turbulence brought on by the collision of the tripod’s pile. Generally, as the Froude number rises, so does the deposition height and scour depth.

4.7 Keulegan-Carpenter (KC) number

The geography of the scour is significantly more influenced by the KC value. Greater KC causes a deeper equilibrium scour because an increase in KC lengthens the horseshoe vortex’s duration and intensifies it as shown in Figure 10.

The result can be attributed to the fact that wave superposition reduced the crucial KC for the initiation of the scour, particularly under small KC conditions. The primary variable in the equation used to calculate This is the depth of the scouring hole at the bed. The following expression is used to calculate the Keulegan-Carpenter number:

Kc=Vw∗TpD𝐾𝑐=𝑉𝑤∗𝑇𝑝𝐷                          (13)

where, the wave period is Tp and the wave velocity is shown by Vw.

image037.png

Figure 10. Relationship between the relative maximum scour depth and KC

5. Conclusion

(1) The existing seabed-tripod-fluid numerical model is capable of faithfully reproducing the scour process and the flow field around tripods, suggesting that it may be used to predict the scour around tripods in random waves.

(2) Their results obtained in this research at various flow velocities and flow depths demonstrated that the maximum scour depth rate depended on wave height with rising velocities and decreasing particle sizes (d50).

(3) A diagonal brace and the main column act as blockages, increasing the flow accelerations underneath them. This raises the magnitude of the disturbance and the shear stress on the seafloor, which in turn causes a greater number of particles to be mobilized and conveyed, as a result, causes more severe scour at the location.

(4) The Froude number and the scouring process are closely related. In general, as the Froude number rises, so does the maximum scour depth and scour range. The highest maximum scour depth always coincides with the bigger Froude number with the shortest spacing ratio.

Since the issue is that there aren’t many experiments or studies that are relevant to this subject, therefore we had to rely on the monopile criteria. Therefore, to gain a deeper knowledge of the scouring effect surrounding the tripod in random waves, further numerical research exploring numerous soil, foundation, and construction elements as well as upcoming physical model tests will be beneficial.

Nomenclature

CFDComputational fluid dynamics
FAVORFractional Area/Volume Obstacle Representation
VOFVolume of Fluid
RNGRenormalized Group
OWTsOffshore wind turbines
Greek Symbols
ε, ωDissipation rate of the turbulent kinetic energy, m2s-3
Subscripts
d50Median particle size
VfVolume fraction
GTTurbulent energy of buoyancy
KTTurbulent velocity
PTKinetic energy of the turbulence
ΑiInduction parameter
nsInduction parameter
ΘΘcrThe essential Shields variable
DiDiameter of sediment
dThe diameter of particles without dimensions
µfDynamic viscosity of the fluid
qb,iThe bed load transportation rate
Cs,iSand particle’s concentration of mass
DDiameter of pile
DfDiffusivity
DDiameter of main column
FrFroud number
KcKeulegan–Carpenter number
GAcceleration of gravity g
HFlow depth
VwWave Velocity
VMean Velocity
TpWave Period
SScour depth

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[15] Schendel, A., Welzel, M., Schlurmann, T., Hsu, T.W. (2020). Scour around a monopile induced by directionally spread irregular waves in combination with oblique currents. Coastal Engineering, 161: 103751. https://doi.org/10.1016/j.coastaleng.2020.103751

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Estimating maximum initial wave amplitude of subaerial landslide tsunamis: A three-dimensional modelling approach

Estimating maximum initial wave amplitude of subaerial landslide tsunamis: A three-dimensional modelling approach

해저 산사태 쓰나미의 최대 초기 파동 진폭 추정: 3차원 모델링 접근법

Ramtin Sabeti a, Mohammad Heidarzadeh ab

aDepartment of Architecture and Civil Engineering, University of Bath, Bath BA27AY, UK
bHydroCoast Consulting Engineers Ltd, Bath, UK

https://doi.org/10.1016/j.ocemod.2024.102360

Highlights

  • •Landslide travel distance is considered for the first time in a predictive equation.
  • •Predictive equation derived from databases using 3D physical and numerical modeling.
  • •The equation was successfully tested on the 2018 Anak Krakatau tsunami event.
  • •The developed equation using three-dimensional data exhibits a 91 % fitting quality.

Abstract

Landslide tsunamis, responsible for thousands of deaths and significant damage in recent years, necessitate the allocation of sufficient time and resources for studying these extreme natural hazards. This study offers a step change in the field by conducting a large number of three-dimensional numerical experiments, validated by physical tests, to develop a predictive equation for the maximum initial amplitude of tsunamis generated by subaerial landslides. We first conducted a few 3D physical experiments in a wave basin which were then applied for the validation of a 3D numerical model based on the Flow3D-HYDRO package. Consequently, we delivered 100 simulations using the validated model by varying parameters such as landslide volume, water depth, slope angle and travel distance. This large database was subsequently employed to develop a predictive equation for the maximum initial tsunami amplitude. For the first time, we considered travel distance as an independent parameter for developing the predictive equation, which can significantly improve the predication accuracy. The predictive equation was tested for the case of the 2018 Anak Krakatau subaerial landslide tsunami and produced satisfactory results.

Keywords

Tsunami, Subaerial landslide, Physical modelling, Numerical simulation, FLOW-3D HYDRO

1. Introduction and literature review

The Anak Krakatau landslide tsunami on 22nd December 2018 was a stark reminder of the dangers posed by subaerial landslide tsunamis (Ren et al., 2020Mulia et al. 2020a; Borrero et al., 2020Heidarzadeh et al., 2020Grilli et al., 2021). The collapse of the volcano’s southwest side into the ocean triggered a tsunami that struck the Sunda Strait, leading to approximately 450 fatalities (Syamsidik et al., 2020Mulia et al., 2020b) (Fig. 1). As shown in Fig. 1, landslide tsunamis (both submarine and subaerial) have been responsible for thousands of deaths and significant damage to coastal communities worldwide. These incidents underscored the critical need for advanced research into landslide-generated waves to aid in hazard prediction and mitigation. This is further emphasized by recent events such as the 28th of November 2020 landslide tsunami in the southern coast mountains of British Columbia (Canada), where an 18 million m3 rockslide generated a massive tsunami, with over 100 m wave run-up, causing significant environmental and infrastructural damage (Geertsema et al., 2022).

Fig 1

Physical modelling and numerical simulation are crucial tools in the study of landslide-induced waves due to their ability to replicate and analyse the complex dynamics of landslide events (Kim et al., 2020). In two-dimensional (2D) modelling, the discrepancy between dimensions can lead to an artificial overestimation of wave amplification (e.g., Heller and Spinneken, 2015). This limitation is overcome with 3D modelling, which enables the scaled-down representation of landslide-generated waves while avoiding the simplifications inherent in 2D approaches (Erosi et al., 2019). Another advantage of 3D modelling in studying landslide-generated waves is its ability to accurately depict the complex dynamics of wave propagation, including lateral and radial spreading from the slide impact zone, a feature unattainable with 2D models (Heller and Spinneken, 2015).

Physical experiments in tsunami research, as presented by authors such as Romano et al. (2020), McFall and Fritz (2016), and Heller and Spinneken (2015), have supported 3D modelling works through validation and calibration of the numerical models to capture the complexities of wave generation and propagation. Numerical modelling has increasingly complemented experimental approach in tsunami research due to the latter’s time and resource-intensive nature, particularly for 3D models (Li et al., 2019; Kim et al., 2021). Various numerical approaches have been employed, from Eulerian and Lagrangian frameworks to depth-averaged and Navier–Stokes models, enhancing our understanding of tsunami dynamics (Si et al., 2018Grilli et al., 2019Heidarzadeh et al., 20172020Iorio et al., 2021Zhang et al., 2021Kirby et al., 2022Wang et al., 20212022Hu et al., 2022). The sophisticated numerical techniques, including the Particle Finite Element Method and the Immersed Boundary Method, have also shown promising results in modelling highly dynamic landslide scenarios (Mulligan et al., 2020Chen et al., 2020). Among these methods and techniques, FLOW-3D HYDRO stands out in simulating landslide-generated tsunami waves due to its sophisticated technical features such as offering Tru Volume of Fluid (VOF) method for precise free surface tracking (e.g., Sabeti and Heidarzadeh 2022a). TruVOF distinguishes itself through a split Lagrangian approach, adeptly reducing cumulative volume errors in wave simulations by dynamically updating cell volume fractions and areas with each time step. Its intelligent adaptation of time step size ensures precise capture of evolving free surfaces, offering unparalleled accuracy in modelling complex fluid interfaces and behaviour (Flow Science, 2023).

Predictive equations play a crucial role in assessing the potential hazards associated with landslide-generated tsunami waves due to their ability to provide risk assessment and warnings. These equations can offer swift and reasonable evaluations of potential tsunami impacts in the absence of detailed numerical simulations, which can be time-consuming and expensive to produce. Among multiple factors and parameters within a landslide tsunami generation, the initial maximum wave amplitude (Fig. 1) stands out due to its critical role. While it is most likely that the initial wave generated by a landslide will have the highest amplitude, it is crucial to clarify that the term “initial maximum wave amplitude” refers to the highest amplitude within the first set of impulse waves. This parameter is essential in determining the tsunami’s impact severity, with higher amplitudes signalling a greater destructive potential (Sabeti and Heidarzadeh 2022a). Additionally, it plays a significant role in tsunami modelling, aiding in the prediction of wave propagation and the assessment of potential impacts.

In this study, we initially validate the FLOW-3D HYDRO model through a series of physical experiments conducted in a 3D wave tank at University of Bath (UK). Upon confirmation of the model’s accuracy, we use it to systematically vary parameters namely landslide volume, water depth, slope angle, and travel distance, creating an extensive database. Alongside this, we perform a sensitivity analysis on these variables to discern their impacts on the initial maximum wave amplitude. The generated database was consequently applied to derive a non-dimensional predictive equation aimed at estimating the initial maximum wave amplitude in real-world landslide tsunami events.

Two innovations of this study are: (i) The predictive equation of this study is based on a large number of 3D experiments whereas most of the previous equations were based on 2D results, and (ii) For the first time, the travel distance is included in the predictive equation as an independent parameter. To evaluate the performance of our predictive equation, we applied it to a previous real-world subaerial landslide tsunami, i.e., the Anak Krakatau 2018 event. Furthermore, we compare the performance of our predictive equation with other existing equations.

2. Data and methods

The methodology applied in this research is a combination of physical and numerical modelling. Limited physical modelling was performed in a 3D wave basin at the University of Bath (UK) to provide data for calibration and validation of the numerical model. After calibration and validation, the numerical model was employed to model a large number of landslide tsunami scenarios which allowed us to develop a database for deriving a predictive equation.

2.1. Physical experiments

To validate our numerical model, we conducted a series of physical experiments including two sets in a 3D wave basin at University of Bath, measuring 2.50 m in length (WL), 2.60 m in width (WW), and 0.60 m in height (WH) (Fig. 2a). Conducting two distinct sets of experiments (Table 1), each with different setups (travel distance, location, and water depth), provided a robust framework for validation of the numerical model. For wave measurement, we employed a twin wire wave gauge from HR Wallingford (https://equipit.hrwallingford.com). In these experiments, we used a concrete prism solid block, the dimensions of which are outlined in Table 2. In our experiments, we employed a concrete prism solid block with a density of 2600 kg/m3, chosen for its similarity to the natural density of landslides, akin to those observed with the 2018 Anak Krakatau tsunami, where the landslide composition is predominantly solid rather than granular. The block’s form has also been endorsed in prior studies (Watts, 1998Najafi-Jilani and Ataie-Ashtiani, 2008) as a suitable surrogate for modelling landslide-induced waves. A key aspect of our methodology was addressing scale effects, following the guidelines proposed by Heller et al. (2008) as it is described in Table 1. To enhance the reliability and accuracy of our experimental data, we conducted each physical experiment three times which revealed all three experimental waveforms were identical. This repetition was aimed at minimizing potential errors and inconsistencies in laboratory measurements.

Fig 2

Table 1. The locations and other information of the laboratory setups for making landslide-generated waves in the physical wave basin. This table details the specific parameters for each setup, including slope range (α), slide volume (V), kinematic viscosity (ν), water depth (h), travel distance (D), surface tension coefficient of water (σ), Reynolds number (R), Weber number (W), and the precise coordinates of the wave gauges (WG).

Labα(°)V (m³)h (m)D (m)WG’s Location(ν) (m²/s)(σ) (N/m)Acceptable range for avoiding scale effects*Observed values of W and R ⁎⁎
Lab 1452.60 × 10−30.2470.070X1=1.090 m1.01 × 10−60.073R > 3.0 × 105R1 = 3.80 × 105
Y1=1.210 m
W1 = 8.19 × 105
Z1=0.050mW >5.0 × 103
Lab 2452.60 × 10−30.2460.045X2=1.030 m1.01 × 10−60.073R2 = 3.78 × 105
Y2=1.210 mW2 = 8.13 × 105
Z2=0.050 m

The acceptable ranges for avoiding scale effects are based on the study by Heller et al. (2008).⁎⁎

The Reynolds number (R) is given by g0.5h1.5/ν, with ν denoting the kinematic viscosity. The Weber number (W) is W = ρgh2/σ, where σ represents surface tension coefficient and ρ = 1000kg/m3 is the density of water. In our experiments, conducted at a water temperature of approximately 20 °C, the kinematic viscosity (ν) and the surface tension coefficient of water (σ) are 1.01 × 10−6 m²/s and 0.073 N/m, respectively (Kestin et al., 1978).

Table 2. Specifications of the solid block used in physical experiments for generating subaerial landslides in the laboratory.

Solid-block attributesProperty metricsGeometric shape
Slide width (bs)0.26 mImage, table 2
Slide length (ls)0.20 m
Slide thickness (s)0.10 m
Slide volume (V)2.60 × 10−3 m3
Specific gravity, (γs)2.60
Slide weight (ms)6.86 kg

2.2. Numerical simulations applying FLOW-3D hydro

The detailed theoretical framework encompassing the governing equations, the computational methodologies employed, and the specific techniques used for tracking the water surface in these simulations are thoroughly detailed in the study by Sabeti et al. (2024). Here, we briefly explain some of the numerical details. We defined a uniform mesh for our flow domain, carefully crafted with a fine spatial resolution of 0.005 m (i.e., grid size). The dimensions of the numerical model directly matched those of our wave basin used in the physical experiment, being 2.60 m wide, 0.60 m deep, and 2.50 m long (Fig. 2). This design ensures comprehensive coverage of the study area. The output intervals of the numerical model are set at 0.02 s. This timing is consistent with the sampling rates of wave gauges used in laboratory settings. The friction coefficient in the FLOW-3D HYDRO is designated as 0.45. This value corresponds to the Coulombic friction measurements obtained in the laboratory, ensuring that the simulation accurately reflects real-world physical interactions.

In order to simulate the landslide motion, we applied coupled motion objects in FLOW-3D-HYDRO where the dynamics are predominantly driven by gravity and surface friction. This methodology stands in contrast to other models that necessitate explicit inputs of force and torque. This approach ensures that the simulation more accurately reflects the natural movement of landslides, which is heavily reliant on gravitational force and the interaction between sliding surfaces. The stability of the numerical simulations is governed by the Courant Number criterion (Courant et al., 1928), which dictates the maximum time step (Δt) for a given mesh size (Δx) and flow speed (U). According to Courant et al. (1928), this number is required to stay below one to ensure stability of numerical simulations. In our simulations, the Courant number is always maintained below one.

In alignment with the parameters of physical experiments, we set the fluid within the mesh to water, characterized by a density of 1000 kg/m³ at a temperature of 20 °C. Furthermore, we defined the top, front, and back surfaces of the mesh as symmetry planes. The remaining surfaces are designated as wall types, incorporating no-slip conditions to accurately simulate the interaction between the fluid and the boundaries. In terms of selection of an appropriate turbulence model, we selected the k–ω model that showed a better performance than other turbulence methods (e.g., Renormalization-Group) in a previous study (Sabeti et al., 2024). The simulations are conducted using a PC Intel® Core™ i7-10510U CPU with a frequency of 1.80 GHz, and a 16 GB RAM. On this PC, completion of a 3-s simulation required approximately 12.5 h.

2.3. Validation

The FLOW-3D HYDRO numerical model was validated using the two physical experiments (Fig. 3) outlined in Table 1. The level of agreement between observations (Oi) and simulations (Si) is examined using the following equation:(1)�=|��−����|×100where ε represents the mismatch error, Oi denotes the observed laboratory values, and Si represents the simulated values from the FLOW-3D HYDRO model. The results of this validation process revealed that our model could replicate the waves generated in the physical experiments with a reasonable degree of mismatch (ε): 14 % for Lab 1 and 8 % for Lab 2 experiments, respectively (Fig. 3). These values indicate that while the model is not perfect, it provides a sufficiently close approximation of the real-world phenomena.

Fig 3

In terms of mesh efficiency, we varied the mesh size to study sensitivity of the numerical results to mesh size. First, by halving the mesh size and then by doubling it, we repeated the modelling by keeping other parameters unchanged. This analysis guided that a mesh size of ∆x = 0.005 m is the most effective for the setup of this study. The total number of computational cells applying mesh size of 0.005 m is 9.269 × 106.

2.4. The dataset

The validated numerical model was employed to conduct 100 simulations, incorporating variations in four key landslide parameters namely water depth, slope angle, slide volume, and travel distance. This methodical approach was essential for a thorough sensitivity analysis of these variables, and for the creation of a detailed database to develop a predictive equation for maximum initial tsunami amplitude. Within the model, 15 distinct slide volumes were established, ranging from 0.10 × 10−3 m3 to 6.25 × 10−3 m3 (Table 3). The slope angle varied between 35° and 55°, and water depth ranged from 0.24 m to 0.27 m. The travel distance of the landslides was varied, spanning from 0.04 m to 0.07 m. Detailed configurations of each simulation, along with the maximum initial wave amplitudes and dominant wave periods are provided in Table 4.

Table 3. Geometrical information of the 15 solid blocks used in numerical modelling for generating landslide tsunamis. Parameters are: ls, slide length; bs, slide width; s, slide thickness; γs, specific gravity; and V, slide volume.

Solid blockls (m)bs (m)s (m)V (m3)γs
Block-10.3100.2600.1556.25 × 10−32.60
Block-20.3000.2600.1505.85 × 10−32.60
Block-30.2800.2600.1405.10 × 10−32.60
Block-40.2600.2600.1304.39 × 10−32.60
Block-50.2400.2600.1203.74 × 10−32.60
Block-60.2200.2600.1103.15 × 10−32.60
Block-70.2000.2600.1002.60 × 10−32.60
Block-80.1800.2600.0902.11 × 10−32.60
Block-90.1600.2600.0801.66 × 10−32.60
Block-100.1400.2600.0701.27 × 10−32.60
Block-110.1200.2600.0600.93 × 10−32.60
Block-120.1000.2600.0500.65 × 10−32.60
Block-130.0800.2600.0400.41 × 10−32.60
Block-140.0600.2600.0300.23 × 10−32.60
Block-150.0400.2600.0200.10 × 10−32.60

Table 4. The numerical simulation for the 100 tests performed in this study for subaerial solid-block landslide-generated waves. Parameters are aM, maximum wave amplitude; α, slope angle; h, water depth; D, travel distance; and T, dominant wave period. The location of the wave gauge is X=1.030 m, Y=1.210 m, and Z=0.050 m. The properties of various solid blocks are presented in Table 3.

Test-Block Noα (°)h (m)D (m)T(s)aM (m)
1Block-7450.2460.0290.5100.0153
2Block-7450.2460.0300.5050.0154
3Block-7450.2460.0310.5050.0156
4Block-7450.2460.0320.5050.0158
5Block-7450.2460.0330.5050.0159
6Block-7450.2460.0340.5050.0160
7Block-7450.2460.0350.5050.0162
8Block-7450.2460.0360.5050.0166
9Block-7450.2460.0370.5050.0167
10Block-7450.2460.0380.5050.0172
11Block-7450.2460.0390.5050.0178
12Block-7450.2460.0400.5050.0179
13Block-7450.2460.0410.5050.0181
14Block-7450.2460.0420.5050.0183
15Block-7450.2460.0430.5050.0190
16Block-7450.2460.0440.5050.0197
17Block-7450.2460.0450.5050.0199
18Block-7450.2460.0460.5050.0201
19Block-7450.2460.0470.5050.0191
20Block-7450.2460.0480.5050.0217
21Block-7450.2460.0490.5050.0220
22Block-7450.2460.0500.5050.0226
23Block-7450.2460.0510.5050.0236
24Block-7450.2460.0520.5050.0239
25Block-7450.2460.0530.5100.0240
26Block-7450.2460.0540.5050.0241
27Block-7450.2460.0550.5050.0246
28Block-7450.2460.0560.5050.0247
29Block-7450.2460.0570.5050.0248
30Block-7450.2460.0580.5050.0249
31Block-7450.2460.0590.5050.0251
32Block-7450.2460.0600.5050.0257
33Block-1450.2460.0450.5050.0319
34Block-2450.2460.0450.5050.0294
35Block-3450.2460.0450.5050.0282
36Block-4450.2460.0450.5050.0262
37Block-5450.2460.0450.5050.0243
38Block-6450.2460.0450.5050.0223
39Block-7450.2460.0450.5050.0196
40Block-8450.2460.0450.5050.0197
41Block-9450.2460.0450.5050.0198
42Block-10450.2460.0450.5050.0184
43Block-11450.2460.0450.5050.0173
44Block-12450.2460.0450.5050.0165
45Block-13450.2460.0450.4040.0153
46Block-14450.2460.0450.4040.0124
47Block-15450.2460.0450.5050.0066
48Block-7450.2020.0450.4040.0220
49Block-7450.2040.0450.4040.0219
50Block-7450.2060.0450.4040.0218
51Block-7450.2080.0450.4040.0217
52Block-7450.2100.0450.4040.0216
53Block-7450.2120.0450.4040.0215
54Block-7450.2140.0450.5050.0214
55Block-7450.2160.0450.5050.0214
56Block-7450.2180.0450.5050.0213
57Block-7450.2200.0450.5050.0212
58Block-7450.2220.0450.5050.0211
59Block-7450.2240.0450.5050.0208
60Block-7450.2260.0450.5050.0203
61Block-7450.2280.0450.5050.0202
62Block-7450.2300.0450.5050.0201
63Block-7450.2320.0450.5050.0201
64Block-7450.2340.0450.5050.0200
65Block-7450.2360.0450.5050.0199
66Block-7450.2380.0450.4040.0196
67Block-7450.2400.0450.4040.0194
68Block-7450.2420.0450.4040.0193
69Block-7450.2440.0450.4040.0192
70Block-7450.2460.0450.5050.0190
71Block-7450.2480.0450.5050.0189
72Block-7450.2500.0450.5050.0187
73Block-7450.2520.0450.5050.0187
74Block-7450.2540.0450.5050.0186
75Block-7450.2560.0450.5050.0184
76Block-7450.2580.0450.5050.0182
77Block-7450.2590.0450.5050.0183
78Block-7450.2600.0450.5050.0191
79Block-7450.2610.0450.5050.0192
80Block-7450.2620.0450.5050.0194
81Block-7450.2630.0450.5050.0195
82Block-7450.2640.0450.5050.0195
83Block-7450.2650.0450.5050.0197
84Block-7450.2660.0450.5050.0197
85Block-7450.2670.0450.5050.0198
86Block-7450.2700.0450.5050.0199
87Block-7300.2460.0450.5050.0101
88Block-7350.2460.0450.5050.0107
89Block-7360.2460.0450.5050.0111
90Block-7370.2460.0450.5050.0116
91Block-7380.2460.0450.5050.0117
92Block-7390.2460.0450.5050.0119
93Block-7400.2460.0450.5050.0121
94Block-7410.2460.0450.5050.0127
95Block-7420.2460.0450.4040.0154
96Block-7430.2460.0450.4040.0157
97Block-7440.2460.0450.4040.0162
98Block-7450.2460.0450.5050.0197
99Block-7500.2460.0450.5050.0221
100Block-7550.2460.0450.5050.0233

In all these 100 simulations, the wave gauge was consistently positioned at coordinates X=1.09 m, Y=1.21 m, and Z=0.05 m. The dominant wave period for each simulation was determined using the Fast Fourier Transform (FFT) function in MATLAB (MathWorks, 2023). Furthermore, the classification of wave types was carried out using a wave categorization graph according to Sorensen (2010), as shown in Fig. 4a. The results indicate that the majority of the simulated waves are on the border between intermediate and deep-water waves, and they are categorized as Stokes waves (Fig. 4a). Four sample waveforms from our 100 numerical experiments are provided in Fig. 4b.

Fig 4

The dataset in Table 4 was used to derive a new predictive equation that incorporates travel distance for the first time to estimate the initial maximum tsunami amplitude. In developing this equation, a genetic algorithm optimization technique was implemented using MATLAB (MathWorks 2023). This advanced approach entailed the use of genetic algorithms (GAs), an evolutionary algorithm type inspired by natural selection processes (MathWorks, 2023). This technique is iterative, involving selection, crossover, and mutation processes to evolve solutions over several generations. The goal was to identify the optimal coefficients and powers for each landslide parameter in the predictive equation, ensuring a robust and reliable model for estimating maximum wave amplitudes. Genetic Algorithms excel at optimizing complex models by navigating through extensive combinations of coefficients and exponents. GAs effectively identify highly suitable solutions for the non-linear and complex relationships between inputs (e.g., slide volume, slope angle, travel distance, water depth) and the output (i.e., maximum initial wave amplitude, aM). MATLAB’s computational environment enhances this process, providing robust tools for GA to adapt and evolve solutions iteratively, ensuring the precision of the predictive model (Onnen et al., 1997). This approach leverages MATLAB’s capabilities to fine-tune parameters dynamically, achieving an optimal equation that accurately estimates aM. It is important to highlight that the nondimensionalized version of this dataset is employed to develop a predictive equation which enables the equation to reproduce the maximum initial wave amplitude (aM) for various subaerial landslide cases, independent of their dimensional differences (e.g., Heler and Hager 2014Heller and Spinneken 2015Sabeti and Heidarzadeh 2022b). For this nondimensionalization, we employed the water depth (h) to nondimensionalize the slide volume (V/h3) and travel distance (D/h). The slide thickness (s) was applied to nondimensionalize the water depth (h/s).

2.5. Landslide velocity

In discussing the critical role of landslide velocity for simulating landslide-generated waves, we focus on the mechanisms of landslide motion and the techniques used to record landslide velocity in our simulations (Fig. 5). Also, we examine how these methods were applied in two distinct scenarios: Lab 1 and Lab 2 (see Table 1 for their details). Regarding the process of landslide movement, a slide starts from a stationary state, gaining momentum under the influence of gravity and this acceleration continues until the landslide collides with water, leading to a significant reduction in its speed before eventually coming to a stop (Fig. 5) (e.g., Panizzo et al. 2005).

Fig 5

To measure the landslide’s velocity in our simulations, we attached a probe at the centre of the slide, which supplied a time series of the velocity data. The slide’s velocity (vs) peaks at the moment it enters the water (Fig. 5), a point referred to as the impact time (tImp). Following this initial impact, the slides continue their underwater movement, eventually coming to a complete halt (tStop). Given the results in Fig. 5, it can be seen that Lab 1, with its longer travel distance (0.070 m), exhibits a higher peak velocity of 1.89 m/s. This increase in velocity is attributed to the extended travel distance allowing more time for the slide to accelerate under gravity. Whereas Lab 2, featuring a shorter travel distance (0.045 m), records a lower peak velocity of 1.78 m/s. This difference underscores how travel distance significantly influences the dynamics of landslide motion. After reaching the peak, both profiles show a sharp decrease in velocity, marking the transition to submarine motion until the slides come to a complete stop (tStop). There are noticeable differences observable in Fig. 5 between the Lab-1 and Lab-2 simulations, including the peaks at 0.3 s . These variations might stem from the placement of the wave gauge, which differs slightly in each scenario, as well as the water depth’s minor discrepancies and, the travel distance.

2.6. Effect of air entrainment

In this section we examine whether it is required to consider air entrainment for our modelling or not as the FLOW-3D HYDRO package is capable of modelling air entrainment. The process of air entrainment in water during a landslide tsunami and its subsequent transport involve two key components: the quantification of air entrainment at the water surface, and the simulation of the air’s transport within the fluid (Hirt, 2003). FLOW-3D HYDRO employs the air entrainment model to compute the volume of air entrained at the water’s surface utilizing three approaches: a constant density model, a variable density model accounting for bulking, and a buoyancy model that adds the Drift-FLUX mechanism to variable density conditions (Flow Science, 2023). The calculation of the entrainment rate is based on the following equation:(2)�������=������[2(��−�����−2�/���)]1/2where parameters are: Vair, volume of air; Cair, entrainment rate coefficient; As, surface area of fluid; ρ, fluid density; k, turbulent kinetic energy; gn, gravity normal to surface; Lt, turbulent length scale; and σ, surface tension coefficient. The value of k is directly computed from the Reynolds-averaged Navier-Stokes (RANS) (kw) calculations in our model.

In this study, we selected the variable density + Drift-FLUX model, which effectively captures the dynamics of phase separation and automatically activates the constant density and variable density models. This method simplifies the air-water mixture, treating it as a single, homogeneous fluid within each computational cell. For the phase volume fractions f1and f2​, the velocities are expressed in terms of the mixture and relative velocities, denoted as u and ur, respectively, as follows:(3)��1��+�.(�1�)=��1��+�.(�1�)−�.(�1�2��)=0(4)��2��+�.(�2�)=��2��+�.(�2�)−�.(�1�2��)=0

The outcomes from this simulation are displayed in Fig. 6, which indicates that the influence of air entrainment on the generated wave amplitude is approximately 2 %. A value of 0.02 for the entrained air volume fraction means that, in the simulated fluid, approximately 2 % of the volume is composed of entrained air. In other words, for every unit volume of the fluid-air mixture at that location, 2 % is air and the remaining 98 % is water. The configuration of Test-17 (Table 4) was employed for this simulation. While the effect of air entrainment is anticipated to be more significant in models of granular landslide-generated waves (Fritz, 2002), in our simulations we opted not to incorporate this module due to its negligible impact on the results.

Fig 6

3. Results

In this section, we begin by presenting a sequence of our 3D simulations capturing different time steps to illustrate the generation process of landslide-generated waves. Subsequently, we derive a new predictive equation to estimate the maximum initial wave amplitude of landslide-generated waves and assess its performance.

3.1. Wave generation and propagation

To demonstrate the wave generation process in our simulation, we reference Test-17 from Table 4, where we employed Block-7 (Tables 34). In this configuration, the slope angle was set to 45°, with a water depth of 0.246 m and a travel distance at 0.045 m (Fig. 7). At 0.220 s, the initial impact of the moving slide on the water is depicted, marking the onset of the wave generation process (Fig. 7a). Disturbances are localized to the immediate area of impact, with the rest of the water surface remaining undisturbed. At this time, a maximum water particle velocity of 1.0 m/s – 1.2 m/s is seen around the impact zone (Fig. 7d). Moving to 0.320 s, the development of the wave becomes apparent as energy transfer from the landslide to the water creates outwardly radiating waves with maximum water particle velocity of up to around 1.6 m/s – 1.8 m/s (Fig. 7b, e). By the time 0.670 s, the wave has fully developed and is propagating away from the impact point exhibiting maximum water particle velocity of up to 2.0 m/s – 2.1 m/s. Concentric wave fronts are visible, moving outwards in all directions, with a colour gradient signifying the highest wave amplitude near the point of landslide entry, diminishing with distance (Fig. 7c, f).

Fig 7

3.2. Influence of landslide parameters on tsunami amplitude

In this section, we investigate the effects of various landslide parameters namely slide volume (V), water depth (h), slipe angle (α) and travel distance (D) on the maximum initial wave amplitude (aM). Fig. 8 presents the outcome of these analyses. According to Fig. 8, the slide volume, slope angle, and travel distance exhibit a direct relationship with the wave amplitude, meaning that as these parameters increase, so does the amplitude. Conversely, water depth is inversely related to the maximum initial wave amplitude, suggesting that the deeper the water depth, the smaller the maximum wave amplitude will be (Fig. 8b).

Fig 8

Fig. 8a highlights the pronounced impact of slide volume on the aM, demonstrating a direct correlation between the two variables. For instance, in the range of slide volumes we modelled (Fig. 8a), The smallest slide volume tested, measuring 0.10 × 10−3 m3, generated a low initial wave amplitude (aM= 0.0066 m) (Table 4). In contrast, the largest volume tested, 6.25 × 10−3 m3, resulted in a significantly higher initial wave amplitude (aM= 0.0319 m) (Table 4). The extremities of these results emphasize the slide volume’s paramount impact on wave amplitude, further elucidated by their positions as the smallest and largest aM values across all conducted tests (Table 4). This is corroborated by findings from the literature (e.g., Murty, 2003), which align with the observed trend in our simulations.

The slope angle’s influence on aM was smooth. A steady increase of wave amplitude was observed as the slope angle increased (Fig. 8c). In examining travel distance, an anomaly was identified. At a travel distance of 0.047 m, there was an unexpected dip in aM, which deviates from the general increasing trend associated with longer travel distances. This singular instance could potentially be attributed to a numerical error. Beyond this point, the expected pattern of increasing aM with longer travel distances resumes, suggesting that the anomaly at 0.047 m is an outlier in an otherwise consistent trend, and thus this single data point was overlooked while deriving the predictive equation. Regarding the inverse relationship between water depth and wave amplitude, our result (Fig. 8b) is consistent with previous reports by Fritz et al. (2003), (2004), and Watts et al. (2005).

The insights from Fig. 8 informed the architecture of the predictive equation in the next Section, with slide volume, travel distance, and slope angle being multiplicatively linked to wave amplitude underscoring their direct correlations with wave amplitude. Conversely, water depth is incorporated as a divisor, representing its inverse relationship with wave amplitude. This structure encapsulates the dynamics between the landslide parameters and their influence on the maximum initial wave amplitude as discussed in more detail in the next Section.

3.3. Predictive equation

Building on our sensitivity analysis of landslide parameters, as detailed in Section 3.2, and utilizing our nondimensional dataset, we have derived a new predictive equation as follows:(5)��/ℎ=0.015(tan�)0.10(�ℎ3)0.90(�ℎ)0.10(ℎ�)−0.11where, V is sliding volume, h is water depth, α is slope angle, and s is landslide thickness. It is important to note that this equation is valid only for subaerial solid-block landslide tsunamis as all our experiments were for this type of waves. The performance of this equation in predicting simulation data is demonstrated by the satisfactory alignment of data points around a 45° line, indicating its accuracy and reliability with regard to the experimental dataset (Fig. 9). The quality of fit between the dataset and Eq. (5) is 91 % indicating that Eq. (5) represents the dataset very well. Table 5 presents Eq. (5) alongside four other similar equations previously published. Two significant distinctions between our Eq. (5) and these others are: (i) Eq. (5) is derived from 3D experiments, whereas the other four equations are based on 2D experiments. (ii) Unlike the other equations, our Eq. (5) incorporates travel distance as an independent parameter.

Fig 9

Table 5. Performance comparison among our newly-developed equation and existing equations for estimating the maximum initial amplitude (aM) of the 2018 Anak Krakatau subaerial landslide tsunami. Parameters: aM, initial maximum wave amplitude; h, water depth; vs, landslide velocity; V, slide volume; bs, slide width; ls, slide length; s, slide thickness; α, slope angle; and ����, volume of the final immersed landslide. We considered ����= V as the slide volume.

EventPredictive equationsAuthor (year)Observed aM (m) ⁎⁎Calculated aM (m)Error, ε (%) ⁎⁎⁎⁎
2018 Anak Krakatau tsunami (Subaerial landslide) *��/ℎ=1.32���ℎNoda (1970)1341340
��/ℎ=0.667(0.5(���ℎ)2)0.334(���)0.754(���)0.506(�ℎ)1.631Bolin et al. (2014) ⁎⁎⁎13459424334
��/ℎ=0.25(������ℎ2)0.8Robbe-Saule et al. (2021)1343177
��/ℎ=0.4545(tan�)0.062(�ℎ3)0.296(ℎ�)−0.235Sabeti and Heidarzadeh (2022b)1341266
��/ℎ=0.015(tan�)0.10(�ℎ3)0.911(�ℎ)0.10(ℎ�)−0.11This study1341302.9

Geometrical and kinematic parameters of the 2018 Anak Krakatau subaerial landslide based on Heidarzadeh et al. (2020)Grilli et al. (2019) and Grilli et al. (2021)V=2.11 × 107 m3h= 50 m; s= 114 m; α= 45°; ls=1250 m; bs= 2700 m; vs=44.9 m/s; D= 2500 m; aM= 100 m −150 m.⁎⁎

aM= An average value of aM = 134 m is considered in this study.⁎⁎⁎

The equation of Bolin et al. (2014) is based on the reformatted one reported by Lindstrøm (2016).⁎⁎⁎⁎

Error is calculated using Eq. (1), where the calculated aM is assumed as the simulated value.

Additionally, we evaluated the performance of this equation using the real-world data from the 2018 Anak Krakatau subaerial landslide tsunami. Based on previous studies (Heidarzadeh et al., 2020Grilli et al., 20192021), we were able to provide a list of parameters for the subaerial landslide and associated tsunami for the 2018 Anak Krakatau event (see footnote of Table 5). We note that the data of the 2018 Anak Krakatau event was not used while deriving Eq. (5). The results indicate that Eq. (5) predicts the initial amplitude of the 2018 Anak Krakatau tsunami as being 130 m indicating an error of 2.9 % compared to the reported average amplitude of 134 m for this event. This performance indicates an improvement compared to the previous equation reported by Sabeti and Heidarzadeh (2022a) (Table 5). In contrast, the equations from Robbe-Saule et al. (2021) and Bolin et al. (2014) demonstrate higher discrepancies of 4200 % and 77 %, respectively (Table 5). Although Noda’s (1970) equation reproduces the tsunami amplitude of 134 m accurately (Table 5), it is crucial to consider its limitations, notably not accounting for parameters such as slope angle and travel distance.

It is essential to recognize that both travel distance and slope angle significantly affect wave amplitude. In our model, captured in Eq. (5), we integrate the slope angle (α) through the tangent function, i.e., tan α. This choice diverges from traditional physical interpretations that often employ the cosine or sine function (e.g., Heller and Hager, 2014Watts et al., 2003). We opted for the tangent function because it more effectively reflects the direct impact of slope steepness on wave generation, yielding superior estimations compared to conventional methods.

The significance of this study lies in its application of both physical and numerical 3D experiments and the derivation of a predictive equation based on 3D results. Prior research, e.g. Heller et al. (2016), has reported notable discrepancies between 2D and 3D wave amplitudes, highlighting the important role of 3D experiments. It is worth noting that the suitability of applying an equation derived from either 2D or 3D data depends on the specific geometry and characteristics inherent in the problem being addressed. For instance, in the case of a long, narrow dam reservoir, an equation derived from 2D data would likely be more suitable. In such contexts, the primary dynamics of interest such as flow patterns and potential wave propagation are predominantly two-dimensional, occurring along the length and depth of the reservoir. This simplification to 2D for narrow dam reservoirs allows for more accurate modelling of these dynamics.

This study specifically investigates waves initiated by landslides, focusing on those characterized as solid blocks instead of granular flows, with slope angles confined to a range of 25° to 60°. We acknowledge the additional complexities encountered in real-world scenarios, such as dynamic density and velocity of landslides, which could affect the estimations. The developed equation in this study is specifically designed to predict the maximum initial amplitude of tsunamis for the aforementioned specified ranges and types of landslides.

4. Conclusions

Both physical and numerical experiments were undertaken in a 3D wave basin to study solid-block landslide-generated waves and to formulate a predictive equation for their maximum initial wave amplitude. At the beginning, two physical experiments were performed to validate and calibrate a 3D numerical model, which was subsequently utilized to generate 100 experiments by varying different landslide parameters. The generated database was then used to derive a predictive equation for the maximum initial wave amplitude of landslide tsunamis. The main features and outcomes are:

  • •The predictive equation of this study is exclusively derived from 3D data and exhibits a fitting quality of 91 % when applied to the database.
  • •For the first time, landslide travel distance was considered in the predictive equation. This inclusion provides more accuracy and flexibility for applying the equation.
  • •To further evaluate the performance of the predictive equation, it was applied to a real-world subaerial landslide tsunami (i.e., the 2018 Anak Krakatau event) and delivered satisfactory performance.

CRediT authorship contribution statement

Ramtin Sabeti: Conceptualization, Methodology, Validation, Software, Visualization, Writing – review & editing. Mohammad Heidarzadeh: Methodology, Data curation, Software, Writing – review & editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Funding

RS is supported by the Leverhulme Trust Grant No. RPG-2022-306. MH is funded by open funding of State Key Lab of Hydraulics and Mountain River Engineering, Sichuan University, grant number SKHL2101. We acknowledge University of Bath Institutional Open Access Fund. MH is also funded by the Great Britain Sasakawa Foundation grant no. 6217 (awarded in 2023).

Acknowledgements

Authors are sincerely grateful to the laboratory technician team, particularly Mr William Bazeley, at the Faculty of Engineering, University of Bath for their support during the laboratory physical modelling of this research. We appreciate the valuable insights provided by Mr. Brian Fox (Senior CFD Engineer at Flow Science, Inc.) regarding air entrainment modelling in FLOW-3D HYDRO. We acknowledge University of Bath Institutional Open Access Fund.

Data availability

  • All data used in this study are given in the body of the article.

References

Numerical Investigation of the Local Scour for Tripod Pile Foundation.

Numerical Investigation of the Local Scour for Tripod Pile Foundation.

Hassan, Waqed H.; Fadhe, Zahraa Mohammad; Thiab, Rifqa F.; Mahdi, Karrar

초록

This work investigates numerically a local scour moves in irregular waves around tripods. It is constructed and proven to use the numerical model of the seabed-tripodfluid with an RNG k turbulence model. The present numerical model then examines the flow velocity distribution and scour characteristics. After that, the suggested computational model Flow-3D is a useful tool for analyzing and forecasting the maximum scour development and the flow field in random waves around tripods. The scour values affecting the foundations of the tripod must be studied and calculated, as this phenomenon directly and negatively affects the structure of the structure and its design life. The lower diagonal braces and the main column act as blockages, increasing the flow accelerations underneath them. This increases the number of particles that are moved, which in turn creates strong scouring in the area. The numerical model has a good agreement with the experimental model, with a maximum percentage of error of 10% between the experimental and numerical models. In addition, Based on dimensional analysis parameters, an empirical equation has been devised to forecast scour depth with flow depth, median size ratio, Keulegan-Carpenter (Kc), Froud number flow, and wave velocity that the results obtained in this research at various flow velocities and flow depths demonstrated that the maximum scour depth rate depended on wave height with rising velocities and decreasing particle sizes (d50) and the scour depth attains its steady-current value for Vw < 0.75. As the Froude number rises, the maximum scour depth will be large.

주제어

BUILDING foundationsSURFACE waves (Seismic waves)FLOW velocityRANDOM fieldsDIMENSIONAL analysisFROUDE numberOCEAN waves

키워드

출판물

Mathematical Modelling of Engineering Problems, 2024, Vol 11, Issue 4, p903

ISSN 2369-0739

저자 소속기관

  • 1 Civil Engineering Department, Faculty of Engineering, University of Warith Al-Anbiyaa, Kerbala 56001, Iraq
  • 2 Civil Engineering Department, Faculty of Engineering, University of Kerbala, Kerbala 56001, Iraq
  • 3 Department of Radiological Techniques, College of Health and Medical Techniques, Al-Zahraa University for Women, Karbala 56100, Iraq
  • 4 Soil Physics and Land Management Group, Wageningen University & Research, Wageningen 6708 PB, Netherlands
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Schematic diagram of HP-LPBF melting process.

Modeling and numerical studies of high-precision laser powder bed fusion

Yi Wei ;Genyu Chen;Nengru Tao;Wei Zhou
https://doi.org/10.1063/5.0191504

In order to comprehensively reveal the evolutionary dynamics of the molten pool and the state of motion of the fluid during the high-precision laser powder bed fusion (HP-LPBF) process, this study aims to deeply investigate the specific manifestations of the multiphase flow, solidification phenomena, and heat transfer during the process by means of numerical simulation methods. Numerical simulation models of SS316L single-layer HP-LPBF formation with single and double tracks were constructed using the discrete element method and the computational fluid dynamics method. The effects of various factors such as Marangoni convection, surface tension, vapor recoil, gravity, thermal convection, thermal radiation, and evaporative heat dissipation on the heat and mass transfer in the molten pool have been paid attention to during the model construction process. The results show that the molten pool exhibits a “comet” shape, in which the temperature gradient at the front end of the pool is significantly larger than that at the tail end, with the highest temperature gradient up to 1.69 × 108 K/s. It is also found that the depth of the second track is larger than that of the first one, and the process parameter window has been determined preliminarily. In addition, the application of HP-LPBF technology helps to reduce the surface roughness and minimize the forming size.

Topics

Heat transferNonequilibrium thermodynamicsSolidification processComputer simulationDiscrete element methodLasersMass transferFluid mechanicsComputational fluid dynamicsMultiphase flows

I. INTRODUCTION

Laser powder bed fusion (LPBF) has become a research hotspot in the field of additive manufacturing of metals due to its advantages of high-dimensional accuracy, good surface quality, high density, and high material utilization.1,2 With the rapid development of electronics, medical, automotive, biotechnology, energy, communication, and optics, the demand for microfabrication technology is increasing day by day.3 High-precision laser powder bed fusion (HP-LPBF) is one of the key manufacturing technologies for tiny parts in the fields of electronics, medical, automotive, biotechnology, energy, communication, and optics because of its process characteristics such as small focal spot diameter, small powder particle size, and thin powder layup layer thickness.4–13 Compared with LPBF, HP-LPBF has the significant advantages of smaller focal spot diameter, smaller powder particle size, and thinner layer thickness. These advantages make HP-LPBF perform better in producing micro-fine parts, high surface quality, and parts with excellent mechanical properties.

HP-LPBF is in the exploratory stage, and researchers have already done some exploratory studies on the focal spot diameter, the amount of defocusing, and the powder particle size. In order to explore the influence of changing the laser focal spot diameter on the LPBF process characteristics of the law, Wildman et al.14 studied five groups of different focal spot diameter LPBF forming 316L stainless steel (SS316L) processing effect, the smallest focal spot diameter of 26 μm, and the results confirm that changing the focal spot diameter can be achieved to achieve the energy control, so as to control the quality of forming. Subsequently, Mclouth et al.15 proposed the laser out-of-focus amount (focal spot diameter) parameter, which characterizes the distance between the forming plane and the laser focal plane. The laser energy density was controlled by varying the defocusing amount while keeping the laser parameters constant. Sample preparation at different focal positions was investigated, and their microstructures were characterized. The results show that the samples at the focal plane have finer microstructure than those away from the focal plane, which is the effect of higher power density and smaller focal spot diameter. In order to explore the influence of changing the powder particle size on the characteristics of the LPBF process, Qian et al.16 carried out single-track scanning simulations on powder beds with average powder particle sizes of 70 and 40 μm, respectively, and the results showed that the melt tracks sizes were close to each other under the same process parameters for the two particle-size distributions and that the molten pool of powder beds with small particles was more elongated and the edges of the melt tracks were relatively flat. In order to explore the superiority of HP-LPBF technology, Xu et al.17 conducted a comparative analysis of HP-LPBF and conventional LPBF of SS316L. The results showed that the average surface roughness of the top surface after forming by HP-LPBF could reach 3.40 μm. Once again, it was verified that HP-LPBF had higher forming quality than conventional LPBF. On this basis, Wei et al.6 comparatively analyzed the effects of different laser focal spot diameters on different powder particle sizes formed by LPBF. The results showed that the smaller the laser focal spot diameter, the fewer the defects on the top and side surfaces. The above research results confirm that reducing the laser focal spot diameter can obtain higher energy density and thus better forming quality.

LPBF involves a variety of complex systems and mechanisms, and the final quality of the part is influenced by a large number of process parameters.18–24 Some research results have shown that there are more than 50 factors affecting the quality of the specimen. The influencing factors are mainly categorized into three main groups: (1) laser parameters, (2) powder parameters, and (3) equipment parameters, which interact with each other to determine the final specimen quality. With the continuous development of technologies such as computational materials science and computational fluid dynamics (CFD), the method of studying the influence of different factors on the forming quality of LPBF forming process has been shifted from time-consuming and laborious experimental characterization to the use of numerical simulation methods. As a result, more and more researchers are adopting this approach for their studies. Currently, numerical simulation studies on LPBF are mainly focused on the exploration of molten pool, temperature distribution, and residual stresses.

  1. Finite element simulation based on continuum mechanics and free surface fluid flow modeling based on fluid dynamics are two common approaches to study the behavior of LPBF molten pool.25–28 Finite element simulation focuses on the temperature and thermal stress fields, treats the powder bed as a continuum, and determines the molten pool size by plotting the elemental temperature above the melting point. In contrast, fluid dynamics modeling can simulate the 2D or 3D morphology of the metal powder pile and obtain the powder size and distribution by certain algorithms.29 The flow in the molten pool is mainly affected by recoil pressure and the Marangoni effect. By simulating the molten pool formation, it is possible to predict defects, molten pool shape, and flow characteristics, as well as the effect of process parameters on the molten pool geometry.30–34 In addition, other researchers have been conducted to optimize the laser processing parameters through different simulation methods and experimental data.35–46 Crystal growth during solidification is studied to further understand the effect of laser parameters on dendritic morphology and solute segregation.47–54 A multi-scale system has been developed to describe the fused deposition process during 3D printing, which is combined with the conductive heat transfer model and the dendritic solidification model.55,56
  2. Relevant scholars have adopted various different methods for simulation, such as sequential coupling theory,57 Lagrangian and Eulerian thermal models,58 birth–death element method,25 and finite element method,59 in order to reveal the physical phenomena of the laser melting process and optimize the process parameters. Luo et al.60 compared the LPBF temperature field and molten pool under double ellipsoidal and Gaussian heat sources by ANSYS APDL and found that the diffusion of the laser energy in the powder significantly affects the molten pool size and the temperature field.
  3. The thermal stresses obtained from the simulation correlate with the actual cracks,61 and local preheating can effectively reduce the residual stresses.62 A three-dimensional thermodynamic finite element model investigated the temperature and stress variations during laser-assisted fabrication and found that powder-to-solid conversion increases the temperature gradient, stresses, and warpage.63 Other scholars have predicted residual stresses and part deflection for LPBF specimens and investigated the effects of deposition pattern, heat, laser power, and scanning strategy on residual stresses, noting that high-temperature gradients lead to higher residual stresses.64–67 

In short, the process of LPBF forming SS316L is extremely complex and usually involves drastic multi-scale physicochemical changes that will only take place on a very small scale. Existing literature employs DEM-based mesoscopic-scale numerical simulations to investigate the effects of process parameters on the molten pool dynamics of LPBF-formed SS316L. However, a few studies have been reported on the key mechanisms of heating and solidification, spatter, and convective behavior of the molten pool of HP-LPBF-formed SS316L with small laser focal spot diameters. In this paper, the geometrical properties of coarse and fine powder particles under three-dimensional conditions were first calculated using DEM. Then, numerical simulation models for single-track and double-track cases in the single-layer HP-LPBF forming SS316L process were developed at mesoscopic scale using the CFD method. The flow genesis of the melt in the single-track and double-track molten pools is discussed, and their 3D morphology and dimensional characteristics are discussed. In addition, the effects of laser process parameters, powder particle size, and laser focal spot diameter on the temperature field, characterization information, and defects in the molten pool are discussed.

II. MODELING

A. 3D powder bed modeling

HP-LPBF is an advanced processing technique for preparing target parts layer by layer stacking, the process of which involves repetitive spreading and melting of powders. In this process, both the powder spreading and the morphology of the powder bed are closely related to the results of the subsequent melting process, while the melted surface also affects the uniform distribution of the next layer of powder. For this reason, this chapter focuses on the modeling of the physical action during the powder spreading process and the theory of DEM to establish the numerical model of the powder bed, so as to lay a solid foundation for the accuracy of volume of fluid (VOF) and CFD.

1. DEM

DEM is a numerical technique for calculating the interaction of a large number of particles, which calculates the forces and motions of the spheres by considering each powder sphere as an independent unit. The motion of the powder particles follows the laws of classical Newtonian mechanics, including translational and rotational,38,68–70 which are expressed as follows:����¨=���+∑��ij,

(1)����¨=∑�(�ij×�ij),

(2)

where �� is the mass of unit particle i in kg, ��¨ is the advective acceleration in m/s2, And g is the gravitational acceleration in m/s2. �ij is the force in contact with the neighboring particle � in N. �� is the rotational inertia of the unit particle � in kg · m2. ��¨ is the unit particle � angular acceleration in rad/s2. �ij is the vector pointing from unit particle � to the contact point of neighboring particle �⁠.

Equations (1) and (2) can be used to calculate the velocity and angular velocity variations of powder particles to determine their positions and velocities. A three-dimensional powder bed model of SS316L was developed using DEM. The powder particles are assumed to be perfect spheres, and the substrate and walls are assumed to be rigid. To describe the contact between the powder particles and between the particles and the substrate, a non-slip Hertz–Mindlin nonlinear spring-damping model71 was used with the following expression:�hz=��������+��[(�����ij−�eff����)−(�����+�eff����)],

(3)

where �hz is the force calculated using the Hertzian in M. �� and �� are the radius of unit particles � and � in m, respectively. �� is the overlap size of the two powder particles in m. ��⁠, �� are the elastic constants in the normal and tangential directions, respectively. �ij is the unit vector connecting the centerlines of the two powder particles. �eff is the effective mass of the two powder particles in kg. �� and �� are the viscoelastic damping constants in the normal and tangential directions, respectively. �� and �� are the components of the relative velocities of the two powder particles. ��� is the displacement vector between two spherical particles. The schematic diagram of overlapping powder particles is shown in Fig. 1.

FIG. 1.

VIEW LARGEDOWNLOAD SLIDE

Schematic diagram of overlapping powder particles.

Because the particle size of the powder used for HP-LPBF is much smaller than 100 μm, the effect of van der Waals forces must be considered. Therefore, the cohesive force �jkr of the Hertz–Mindlin model was used instead of van der Waals forces,72 with the following expression:�jkr=−4��0�*�1.5+4�*3�*�3,

(4)1�*=(1−��2)��+(1−��2)��,

(5)1�*=1��+1��,

(6)

where �* is the equivalent Young’s modulus in GPa; �* is the equivalent particle radius in m; �0 is the surface energy of the powder particles in J/m2; α is the contact radius in m; �� and �� are the Young’s modulus of the unit particles � and �⁠, respectively, in GPa; and �� and �� are the Poisson’s ratio of the unit particles � and �⁠, respectively.

2. Model building

Figure 2 shows a 3D powder bed model generated using DEM with a coarse powder geometry of 1000 × 400 × 30 μm3. The powder layer thickness is 30 μm, and the powder bed porosity is 40%. The average particle size of this spherical powder is 31.7 μm and is normally distributed in the range of 15–53 μm. The geometry of the fine powder was 1000 × 400 × 20 μm3, with a layer thickness of 20 μm, and the powder bed porosity of 40%. The average particle size of this spherical powder is 11.5 μm and is normally distributed in the range of 5–25 μm. After the 3D powder bed model is generated, it needs to be imported into the CFD simulation software for calculation, and the imported geometric model is shown in Fig. 3. This geometric model is mainly composed of three parts: protective gas, powder bed, and substrate. Under the premise of ensuring the accuracy of the calculation, the mesh size is set to 3 μm, and the total number of coarse powder meshes is 1 704 940. The total number of fine powder meshes is 3 982 250.

FIG. 2.

VIEW LARGEDOWNLOAD SLIDE

Three-dimensional powder bed model: (a) coarse powder, (b) fine powder.

FIG. 3.

VIEW LARGEDOWNLOAD SLIDE

Geometric modeling of the powder bed computational domain: (a) coarse powder, (b) fine powder.

B. Modeling of fluid mechanics simulation

In order to solve the flow, melting, and solidification problems involved in HP-LPBF molten pool, the study must follow the three governing equations of conservation of mass, conservation of energy, and conservation of momentum.73 The VOF method, which is the most widely used in fluid dynamics, is used to solve the molten pool dynamics model.

1. VOF

VOF is a method for tracking the free interface between the gas and liquid phases on the molten pool surface. The core idea of the method is to define a volume fraction function F within each grid, indicating the proportion of the grid space occupied by the material, 0 ≤ F ≤ 1 in Fig. 4. Specifically, when F = 0, the grid is empty and belongs to the gas-phase region; when F = 1, the grid is completely filled with material and belongs to the liquid-phase region; and when 0 < F < 1, the grid contains free surfaces and belongs to the mixed region. The direction normal to the free surface is the direction of the fastest change in the volume fraction F (the direction of the gradient of the volume fraction), and the direction of the gradient of the volume fraction can be calculated from the values of the volume fractions in the neighboring grids.74 The equations controlling the VOF are expressed as follows:𝛻����+�⋅(��→)=0,

(7)

where t is the time in s and �→ is the liquid velocity in m/s.

FIG. 4.

VIEW LARGEDOWNLOAD SLIDE

Schematic diagram of VOF.

The material parameters of the mixing zone are altered due to the inclusion of both the gas and liquid phases. Therefore, in order to represent the density of the mixing zone, the average density �¯ is used, which is expressed as follows:72�¯=(1−�1)�gas+�1�metal,

(8)

where �1 is the proportion of liquid phase, �gas is the density of protective gas in kg/m3, and �metal is the density of metal in kg/m3.

2. Control equations and boundary conditions

Figure 5 is a schematic diagram of the HP-LPBF melting process. First, the laser light strikes a localized area of the material and rapidly heats up the area. Next, the energy absorbed in the region is diffused through a variety of pathways (heat conduction, heat convection, and surface radiation), and this process triggers complex phase transition phenomena (melting, evaporation, and solidification). In metals undergoing melting, the driving forces include surface tension and the Marangoni effect, recoil due to evaporation, and buoyancy due to gravity and uneven density. The above physical phenomena interact with each other and do not occur independently.

FIG. 5.

VIEW LARGEDOWNLOAD SLIDE

Schematic diagram of HP-LPBF melting process.

  1. Laser heat sourceThe Gaussian surface heat source model is used as the laser heat source model with the following expression:�=2�0����2exp(−2�12��2),(9)where � is the heat flow density in W/m2, �0 is the absorption rate of SS316L, �� is the radius of the laser focal spot in m, and �1 is the radial distance from the center of the laser focal spot in m. The laser focal spot can be used for a wide range of applications.
  2. Energy absorptionThe formula for calculating the laser absorption �0 of SS316L is as follows:�0=0.365(�0[1+�0(�−20)]/�)0.5,(10)where �0 is the direct current resistivity of SS316L at 20 °C in Ω m, �0 is the resistance temperature coefficient in ppm/°C, � is the temperature in °C, and � is the laser wavelength in m.
  3. Heat transferThe basic principle of heat transfer is conservation of energy, which is expressed as follows:𝛻𝛻𝛻�(��)��+�·(��→�)=�·(�0����)+��,(11)where � is the density of liquid phase SS316L in kg/m3, �� is the specific heat capacity of SS316L in J/(kg K), 𝛻� is the gradient operator, t is the time in s, T is the temperature in K, 𝛻�� is the temperature gradient, �→ is the velocity vector, �0 is the coefficient of thermal conduction of SS316L in W/(m K), and  �� is the thermal energy dissipation term in the molten pool.
  4. Molten pool flowThe following three conditions need to be satisfied for the molten pool to flow:
    • Conservation of mass with the following expression:𝛻�·(��→)=0.(12)
    • Conservation of momentum (Navier–Stokes equation) with the following expression:𝛻𝛻𝛻𝛻���→��+�(�→·�)�→=�·[−pI+�(��→+(��→)�)]+�,(13)where � is the pressure in Pa exerted on the liquid phase SS316L microelement, � is the unit matrix, � is the fluid viscosity in N s/m2, and � is the volumetric force (gravity, atmospheric pressure, surface tension, vapor recoil, and the Marangoni effect).
    • Conservation of energy, see Eq. (11)
  5. Surface tension and the Marangoni effectThe effect of temperature on the surface tension coefficient is considered and set as a linear relationship with the following expression:�=�0−��dT(�−��),(14)where � is the surface tension of the molten pool at temperature T in N/m, �� is the melting temperature of SS316L in K, �0 is the surface tension of the molten pool at temperature �� in Pa, and σdσ/ dT is the surface tension temperature coefficient in N/(m K).In general, surface tension decreases with increasing temperature. A temperature gradient causes a gradient in surface tension that drives the liquid to flow, known as the Marangoni effect.
  6. Metal vapor recoilAt higher input energy densities, the maximum temperature of the molten pool surface reaches the evaporation temperature of the material, and a gasification recoil pressure occurs vertically downward toward the molten pool surface, which will be the dominant driving force for the molten pool flow.75 The expression is as follows:��=0.54�� exp ���−���0���,(15)where �� is the gasification recoil pressure in Pa, �� is the ambient pressure in kPa, �� is the latent heat of evaporation in J/kg, �0 is the gas constant in J/(mol K), T is the surface temperature of the molten pool in K, and Te is the evaporation temperature in K.
  7. Solid–liquid–gas phase transitionWhen the laser hits the powder layer, the powder goes through three stages: heating, melting, and solidification. During the solidification phase, mutual transformations between solid, liquid, and gaseous states occur. At this point, the latent heat of phase transition absorbed or released during the phase transition needs to be considered.68 The phase transition is represented based on the relationship between energy and temperature with the following expression:�=�����,(�<��),�(��)+�−����−����,(��<�<��)�(��)+(�−��)����,(��<�),,(16)where �� and �� are solid and liquid phase density, respectively, of SS316L in kg/m3. �� and �� unit volume of solid and liquid phase-specific heat capacity, respectively, of SS316L in J/(kg K). �� and ��⁠, respectively, are the solidification temperature and melting temperature of SS316L in K. �� is the latent heat of the phase transition of SS316L melting in J/kg.

3. Assumptions

The CFD model was computed using the commercial software package FLOW-3D.76 In order to simplify the calculation and solution process while ensuring the accuracy of the results, the model makes the following assumptions:

  1. It is assumed that the effects of thermal stress and material solid-phase thermal expansion on the calculation results are negligible.
  2. The molten pool flow is assumed to be a Newtonian incompressible laminar flow, while the effects of liquid thermal expansion and density on the results are neglected.
  3. It is assumed that the surface tension can be simplified to an equivalent pressure acting on the free surface of the molten pool, and the effect of chemical composition on the results is negligible.
  4. Neglecting the effect of the gas flow field on the molten pool.
  5. The mass loss due to evaporation of the liquid metal is not considered.
  6. The influence of the plasma effect of the molten metal on the calculation results is neglected.

It is worth noting that the formulation of assumptions requires a trade-off between accuracy and computational efficiency. In the above models, some physical phenomena that have a small effect or high difficulty on the calculation results are simplified or ignored. Such simplifications make numerical simulations more efficient and computationally tractable, while still yielding accurate results.

4. Initial conditions

The preheating temperature of the substrate was set to 393 K, at which time all materials were in the solid state and the flow rate was zero.

5. Material parameters

The material used is SS316L and the relevant parameters required for numerical simulations are shown in Table I.46,77,78

TABLE I.

SS316L-related parameters.

PropertySymbolValue
Density of solid metal (kg/m3�metal 7980 
Solid phase line temperature (K) �� 1658 
Liquid phase line temperature (K) �� 1723 
Vaporization temperature (K) �� 3090 
Latent heat of melting (⁠ J/kg⁠) �� 2.60×105 
Latent heat of evaporation (⁠ J/kg⁠) �� 7.45×106 
Surface tension of liquid phase (N /m⁠) � 1.60 
Liquid metal viscosity (kg/m s) �� 6×10−3 
Gaseous metal viscosity (kg/m s) �gas 1.85×10−5 
Temperature coefficient of surface tension (N/m K) ��/�T 0.80×10−3 
Molar mass (⁠ kg/mol⁠) 0.05 593 
Emissivity � 0.26 
Laser absorption �0 0.35 
Ambient pressure (kPa) �� 101 325 
Ambient temperature (K) �0 300 
Stefan–Boltzmann constant (W/m2 K4� 5.67×10−8 
Thermal conductivity of metals (⁠ W/m K⁠) � 24.55 
Density of protective gas (kg/m3�gas 1.25 
Coefficient of thermal expansion (/K) �� 16×10−6 
Generalized gas constant (⁠ J/mol K⁠) 8.314 

III. RESULTS AND DISCUSSION

With the objective of studying in depth the evolutionary patterns of single-track and double-track molten pool development, detailed observations were made for certain specific locations in the model, as shown in Fig. 6. In this figure, P1 and P2 represent the longitudinal tangents to the centers of the two melt tracks in the XZ plane, while L1 is the transverse profile in the YZ plane. The scanning direction is positive and negative along the X axis. Points A and B are the locations of the centers of the molten pool of the first and second melt tracks, respectively (x = 1.995 × 10−4, y = 5 × 10−7, and z = −4.85 × 10−5).

FIG. 6.

VIEW LARGEDOWNLOAD SLIDE

Schematic diagram of observation position.

A. Single-track simulation

A series of single-track molten pool simulation experiments were carried out in order to investigate the influence law of laser power as well as scanning speed on the HP-LPBF process. Figure 7 demonstrates the evolution of the 3D morphology and temperature field of the single-track molten pool in the time period of 50–500 μs under a laser power of 100 W and a scanning speed of 800 mm/s. The powder bed is in the natural cooling state. When t = 50 μs, the powder is heated by the laser heat and rapidly melts and settles to form the initial molten pool. This process is accompanied by partial melting of the substrate and solidification together with the melted powder. The molten pool rapidly expands with increasing width, depth, length, and temperature, as shown in Fig. 7(a). When t = 150 μs, the molten pool expands more obviously, and the temperature starts to transfer to the surrounding area, forming a heat-affected zone. At this point, the width of the molten pool tends to stabilize, and the temperature in the center of the molten pool has reached its peak and remains largely stable. However, the phenomenon of molten pool spatter was also observed in this process, as shown in Fig. 7(b). As time advances, when t = 300 μs, solidification begins to occur at the tail of the molten pool, and tiny ripples are produced on the solidified surface. This is due to the fact that the melt flows toward the region with large temperature gradient under the influence of Marangoni convection and solidifies together with the melt at the end of the bath. At this point, the temperature gradient at the front of the bath is significantly larger than at the end. While the width of the molten pool was gradually reduced, the shape of the molten pool was gradually changed to a “comet” shape. In addition, a slight depression was observed at the top of the bath because the peak temperature at the surface of the bath reached the evaporation temperature, which resulted in a recoil pressure perpendicular to the surface of the bath downward, creating a depressed region. As the laser focal spot moves and is paired with the Marangoni convection of the melt, these recessed areas will be filled in as shown in Fig. 7(c). It has been shown that the depressed regions are the result of the coupled effect of Marangoni convection, recoil pressure, and surface tension.79 By t = 500 μs, the width and height of the molten pool stabilize and show a “comet” shape in Fig. 7(d).

FIG. 7.

VIEW LARGEDOWNLOAD SLIDE

Single-track molten pool process: (a) t = 50  ��⁠, (b) t = 150  ��⁠, (c) t = 300  ��⁠, (d) t = 500  ��⁠.

Figure 8 depicts the velocity vector diagram of the P1 profile in a single-track molten pool, the length of the arrows represents the magnitude of the velocity, and the maximum velocity is about 2.36 m/s. When t = 50 μs, the molten pool takes shape, and the velocities at the two ends of the pool are the largest. The variation of the velocities at the front end is especially more significant in Fig. 8(a). As the time advances to t = 150 μs, the molten pool expands rapidly, in which the velocity at the tail increases and changes more significantly, while the velocity at the front is relatively small. At this stage, the melt moves backward from the center of the molten pool, which in turn expands the molten pool area. The melt at the back end of the molten pool center flows backward along the edge of the molten pool surface and then converges along the edge of the molten pool to the bottom center, rising to form a closed loop. Similarly, a similar closed loop is formed at the front end of the center of the bath, but with a shorter path. However, a large portion of the melt in the center of the closed loop formed at the front end of the bath is in a nearly stationary state. The main cause of this melt flow phenomenon is the effect of temperature gradient and surface tension (the Marangoni effect), as shown in Figs. 8(b) and 8(e). This dynamic behavior of the melt tends to form an “elliptical” pool. At t = 300 μs, the tendency of the above two melt flows to close the loop is more prominent and faster in Fig. 8(c). When t = 500 μs, the velocity vector of the molten pool shows a stable trend, and the closed loop of melt flow also remains stable. With the gradual laser focal spot movement, the melt is gradually solidified at its tail, and finally, a continuous and stable single track is formed in Fig. 8(d).

FIG. 8.

VIEW LARGEDOWNLOAD SLIDE

Vector plot of single-track molten pool velocity in XZ longitudinal section: (a) t = 50  ��⁠, (b) t = 150  ��⁠, (c) t = 300  ��⁠, (d) t = 500  ��⁠, (e) molten pool flow.

In order to explore in depth the transient evolution of the molten pool, the evolution of the single-track temperature field and the melt flow was monitored in the YZ cross section. Figure 9(a) shows the state of the powder bed at the initial moment. When t = 250 μs, the laser focal spot acts on the powder bed and the powder starts to melt and gradually collects in the molten pool. At this time, the substrate will also start to melt, and the melt flow mainly moves in the downward and outward directions and the velocity is maximum at the edges in Fig. 9(b). When t = 300 μs, the width and depth of the molten pool increase due to the recoil pressure. At this time, the melt flows more slowly at the center, but the direction of motion is still downward in Fig. 9(c). When t = 350 μs, the width and depth of the molten pool further increase, at which time the intensity of the melt flow reaches its peak and the direction of motion remains the same in Fig. 9(d). When t = 400 μs, the melt starts to move upward, and the surrounding powder or molten material gradually fills up, causing the surface of the molten pool to begin to flatten. At this time, the maximum velocity of the melt is at the center of the bath, while the velocity at the edge is close to zero, and the edge of the melt starts to solidify in Fig. 9(e). When t = 450 μs, the melt continues to move upward, forming a convex surface of the melt track. However, the melt movement slows down, as shown in Fig. 9(f). When t = 500 μs, the melt further moves upward and its speed gradually becomes smaller. At the same time, the melt solidifies further, as shown in Fig. 9(g). When t = 550 μs, the melt track is basically formed into a single track with a similar “mountain” shape. At this stage, the velocity is close to zero only at the center of the molten pool, and the flow behavior of the melt is poor in Fig. 9(h). At t = 600 μs, the melt stops moving and solidification is rapidly completed. Up to this point, a single track is formed in Fig. 9(i). During the laser action on the powder bed, the substrate melts and combines with the molten state powder. The powder-to-powder fusion is like the convergence of water droplets, which are rapidly fused by surface tension. However, the fusion between the molten state powder and the substrate occurs driven by surface tension, and the molten powder around the molten pool is pulled toward the substrate (a wetting effect occurs), which ultimately results in the formation of a monolithic whole.38,80,81

FIG. 9.

VIEW LARGEDOWNLOAD SLIDE

Evolution of single-track molten pool temperature and melt flow in the YZ cross section: (a) t = 0  ��⁠, (b) t = 250  ��⁠, (c) t = 300  ��⁠, (d) t = 350  ��⁠, (e) t = 400  ��⁠, (f) t = 450  ��⁠, (g) t = 500  ��⁠, (h) t = 550  ��⁠, (i) t = 600  ��⁠.

The wetting ability between the liquid metal and the solid substrate in the molten pool directly affects the degree of balling of the melt,82,83 and the wetting ability can be measured by the contact angle of a single track in Fig. 10. A smaller value of contact angle represents better wettability. The contact angle α can be calculated by�=�1−�22,

(17)

where �1 and �2 are the contact angles of the left and right regions, respectively.

FIG. 10.

VIEW LARGEDOWNLOAD SLIDE

Schematic of contact angle.

Relevant studies have confirmed that the wettability is better at a contact angle α around or below 40°.84 After measurement, a single-track contact angle α of about 33° was obtained under this process parameter, which further confirms the good wettability.

B. Double-track simulation

In order to deeply investigate the influence of hatch spacing on the characteristics of the HP-LPBF process, a series of double-track molten pool simulation experiments were systematically carried out. Figure 11 shows in detail the dynamic changes of the 3D morphology and temperature field of the double-track molten pool in the time period of 2050–2500 μs under the conditions of laser power of 100 W, scanning speed of 800 mm/s, and hatch spacing of 0.06 mm. By comparing the study with Fig. 7, it is observed that the basic characteristics of the 3D morphology and temperature field of the second track are similar to those of the first track. However, there are subtle differences between them. The first track exhibits a basically symmetric shape, but the second track morphology shows a slight deviation influenced by the difference in thermal diffusion rate between the solidified metal and the powder. Otherwise, the other characteristic information is almost the same as that of the first track. Figure 12 shows the velocity vector plot of the P2 profile in the double-track molten pool, with a maximum velocity of about 2.63 m/s. The melt dynamics at both ends of the pool are more stable at t = 2050 μs, where the maximum rate of the second track is only 1/3 of that of the first one. Other than that, the rest of the information is almost no significant difference from the characteristic information of the first track. Figure 13 demonstrates a detailed observation of the double-track temperature field and melts flow in the YZ cross section, and a comparative study with Fig. 9 reveals that the width of the second track is slightly wider. In addition, after the melt direction shifts from bottom to top, the first track undergoes four time periods (50 μs) to reach full solidification, while the second track takes five time periods. This is due to the presence of significant heat buildup in the powder bed after the forming of the first track, resulting in a longer dynamic time of the melt and an increased molten pool lifetime. In conclusion, the level of specimen forming can be significantly optimized by adjusting the laser power and hatch spacing.

FIG. 11.

VIEW LARGEDOWNLOAD SLIDE

Double-track molten pool process: (a) t = 2050  ��⁠, (b) t = 2150  ��⁠, (c) t = 2300  ��⁠, (d) t = 2500  ��⁠.

FIG. 12.

VIEW LARGEDOWNLOAD SLIDE

Vector plot of double-track molten pool velocity in XZ longitudinal section: (a) t = 2050  ��⁠, (b) t = 2150  ��⁠, (c) t = 2300  ��⁠, (d) t = 2500  ��⁠.

FIG. 13.

VIEW LARGEDOWNLOAD SLIDE

Evolution of double-track molten pool temperature and melt flow in the YZ cross section: (a) t = 2250  ��⁠, (b) t = 2300  ��⁠, (c) t = 2350  ��⁠, (d) t = 2400  ��⁠, (e) t = 2450  ��⁠, (f) t = 2500  ��⁠, (g) t = 2550  ��⁠, (h) t = 2600  ��⁠, (i) t = 2650  ��⁠.

In order to quantitatively detect the molten pool dimensions as well as the remolten region dimensions, the molten pool characterization information in Fig. 14 is constructed by drawing the boundary on the YZ cross section based on the isothermal surface of the liquid phase line. It can be observed that the heights of the first track and second track are basically the same, but the depth of the second track increases relative to the first track. The molten pool width is mainly positively correlated with the laser power as well as the scanning speed (the laser line energy density �⁠). However, the remelted zone width is negatively correlated with the hatch spacing (the overlapping ratio). Overall, the forming quality of the specimens can be directly influenced by adjusting the laser power, scanning speed, and hatch spacing.

FIG. 14.

VIEW LARGEDOWNLOAD SLIDE

Double-track molten pool characterization information on YZ cross section.

In order to study the variation rule of the temperature in the center of the molten pool with time, Fig. 15 demonstrates the temperature variation curves with time for two reference points, A and B. Among them, the red dotted line indicates the liquid phase line temperature of SS316L. From the figure, it can be seen that the maximum temperature at the center of the molten pool in the first track is lower than that in the second track, which is mainly due to the heat accumulation generated after passing through the first track. The maximum temperature gradient was calculated to be 1.69 × 108 K/s. When the laser scanned the first track, the temperature in the center of the molten pool of the second track increased slightly. Similarly, when the laser scanned the second track, a similar situation existed in the first track. Since the temperature gradient in the second track is larger than that in the first track, the residence time of the liquid phase in the molten pool of the first track is longer than that of the second track.

FIG. 15.

VIEW LARGEDOWNLOAD SLIDE

Temperature profiles as a function of time for two reference points A and B.

C. Simulation analysis of molten pool under different process parameters

In order to deeply investigate the effects of various process parameters on the mesoscopic-scale temperature field, molten pool characteristic information and defects of HP-LPBF, numerical simulation experiments on mesoscopic-scale laser power, scanning speed, and hatch spacing of double-track molten pools were carried out.

1. Laser power

Figure 16 shows the effects of different laser power on the morphology and temperature field of the double-track molten pool at a scanning speed of 800 mm/s and a hatch spacing of 0.06 mm. When P = 50 W, a smaller molten pool is formed due to the lower heat generated by the Gaussian light source per unit time. This leads to a smaller track width, which results in adjacent track not lapping properly and the presence of a large number of unmelted powder particles, resulting in an increase in the number of defects, such as pores in the specimen. The surface of the track is relatively flat, and the depth is small. In addition, the temperature gradient before and after the molten pool was large, and the depression location appeared at the biased front end in Fig. 16(a). When P = 100 W, the surface of the track is flat and smooth with excellent lap. Due to the Marangoni effect, the velocity field of the molten pool is in the form of “vortex,” and the melt has good fluidity, and the maximum velocity reaches 2.15 m/s in Fig. 16(b). When P = 200 W, the heat generated by the Gaussian light source per unit time is too large, resulting in the melt rapidly reaching the evaporation temperature, generating a huge recoil pressure, forming a large molten pool, and the surface of the track is obviously raised. The melt movement is intense, especially the closed loop at the center end of the molten pool. At this time, the depth and width of the molten pool are large, leading to the expansion of the remolten region and the increased chance of the appearance of porosity defects in Fig. 16(c). The results show that at low laser power, the surface tension in the molten pool is dominant. At high laser power, recoil pressure is its main role.

FIG. 16.

VIEW LARGEDOWNLOAD SLIDE

Simulation results of double-track molten pool under different laser powers: (a) P = 50 W, (b) P = 100 W, (c) P = 200 W.

Table II shows the effect of different laser powers on the characteristic information of the double-track molten pool at a scanning speed of 800 mm/s and a hatch spacing of 0.06 mm. The negative overlapping ratio in the table indicates that the melt tracks are not lapped, and 26/29 indicates the melt depth of the first track/second track. It can be seen that with the increase in laser power, the melt depth, melt width, melt height, and remelted zone show a gradual increase. At the same time, the overlapping ratio also increases. Especially in the process of laser power from 50 to 200 W, the melting depth and melting width increased the most, which increased nearly 2 and 1.5 times, respectively. Meanwhile, the overlapping ratio also increases with the increase in laser power, which indicates that the melting and fusion of materials are better at high laser power. On the other hand, the dimensions of the molten pool did not change uniformly with the change of laser power. Specifically, the depth-to-width ratio of the molten pool increased from about 0.30 to 0.39 during the increase from 50 to 120 W, which further indicates that the effective heat transfer in the vertical direction is greater than that in the horizontal direction with the increase in laser power. This dimensional response to laser power is mainly affected by the recoil pressure and also by the difference in the densification degree between the powder layer and the metal substrate. In addition, according to the experimental results, the contact angle shows a tendency to increase and then decrease during the process of laser power increase, and always stays within the range of less than 33°. Therefore, in practical applications, it is necessary to select the appropriate laser power according to the specific needs in order to achieve the best processing results.

TABLE II.

Double-track molten pool characterization information at different laser powers.

Laser power (W)Depth (μm)Width (μm)Height (μm)Remolten region (μm)Overlapping ratio (%)Contact angle (°)
50 16 54 11 −10 23 
100 26/29 74 14 18 23.33 33 
200 37/45 116 21 52 93.33 28 

2. Scanning speed

Figure 17 demonstrates the effect of different scanning speeds on the morphology and temperature field of the double-track molten pool at a laser power of 100 W and a hatch spacing of 0.06 mm. With the gradual increase in scanning speed, the surface morphology of the molten pool evolves from circular to elliptical. When � = 200 mm/s, the slow scanning speed causes the material to absorb too much heat, which is very easy to trigger the overburning phenomenon. At this point, the molten pool is larger and the surface morphology is uneven. This situation is consistent with the previously discussed scenario with high laser power in Fig. 17(a). However, when � = 1600 mm/s, the scanning speed is too fast, resulting in the material not being able to absorb sufficient heat, which triggers the powder particles that fail to melt completely to have a direct effect on the bonding of the melt to the substrate. At this time, the molten pool volume is relatively small and the neighboring melt track cannot lap properly. This result is consistent with the previously discussed case of low laser power in Fig. 17(b). Overall, the ratio of the laser power to the scanning speed (the line energy density �⁠) has a direct effect on the temperature field and surface morphology of the molten pool.

FIG. 17.

VIEW LARGEDOWNLOAD SLIDE

Simulation results of double-track molten pool under different scanning speed: (a)  � = 200 mm/s, (b)  � = 1600 mm/s.

Table III shows the effects of different scanning speed on the characteristic information of the double-track molten pool under the condition of laser power of 100 W and hatch spacing of 0.06 mm. It can be seen that the scanning speed has a significant effect on the melt depth, melt width, melt height, remolten region, and overlapping ratio. With the increase in scanning speed, the melt depth, melt width, melt height, remelted zone, and overlapping ratio show a gradual decreasing trend. Among them, the melt depth and melt width decreased faster, while the melt height and remolten region decreased relatively slowly. In addition, when the scanning speed was increased from 200 to 800 mm/s, the decreasing speeds of melt depth and melt width were significantly accelerated, while the decreasing speeds of overlapping ratio were relatively slow. When the scanning speed was further increased to 1600 mm/s, the decreasing speeds of melt depth and melt width were further accelerated, and the un-lapped condition of the melt channel also appeared. In addition, the contact angle increases and then decreases with the scanning speed, and both are lower than 33°. Therefore, when selecting the scanning speed, it is necessary to make reasonable trade-offs according to the specific situation, and take into account the factors of melt depth, melt width, melt height, remolten region, and overlapping ratio, in order to achieve the best processing results.

TABLE III.

Double-track molten pool characterization information at different scanning speeds.

Scanning speed (mm/s)Depth (μm)Width (μm)Height (μm)Remolten region (μm)Overlapping ratio (%)Contact angle (°)
200 55/68 182 19/32 124 203.33 22 
1600 13 50 11 −16.67 31 

3. Hatch spacing

Figure 18 shows the effect of different hatch spacing on the morphology and temperature field of the double-track molten pool under the condition of laser power of 100 W and scanning speed of 800 mm/s. The surface morphology and temperature field of the first track and second track are basically the same, but slightly different. The first track shows a basically symmetric morphology along the scanning direction, while the second track shows a slight offset due to the difference in the heat transfer rate between the solidified material and the powder particles. When the hatch spacing is too small, the overlapping ratio increases and the probability of defects caused by remelting phenomenon grows. When the hatch spacing is too large, the neighboring melt track cannot overlap properly, and the powder particles are not completely melted, leading to an increase in the number of holes. In conclusion, the ratio of the line energy density � to the hatch spacing (the volume energy density E) has a significant effect on the temperature field and surface morphology of the molten pool.

FIG. 18.

VIEW LARGEDOWNLOAD SLIDE

Simulation results of double-track molten pool under different hatch spacings: (a) H = 0.03 mm, (b) H = 0.12 mm.

Table IV shows the effects of different hatch spacing on the characteristic information of the double-track molten pool under the condition of laser power of 100 W and scanning speed of 800 mm/s. It can be seen that the hatch spacing has little effect on the melt depth, melt width, and melt height, but has some effect on the remolten region. With the gradual expansion of hatch spacing, the remolten region shows a gradual decrease. At the same time, the overlapping ratio also decreased with the increase in hatch spacing. In addition, it is observed that the contact angle shows a tendency to increase and then remain stable when the hatch spacing increases, which has a more limited effect on it. Therefore, trade-offs and decisions need to be made on a case-by-case basis when selecting the hatch spacing.

TABLE IV.

Double-track molten pool characterization information at different hatch spacings.

Hatch spacing (mm)Depth (μm)Width (μm)Height (μm)Remolten region (μm)Overlapping ratio (%)Contact angle (°)
0.03 25/27 82 14 59 173.33 30 
0.12 26 78 14 −35 33 

In summary, the laser power, scanning speed, and hatch spacing have a significant effect on the formation of the molten pool, and the correct selection of these three process parameters is crucial to ensure the forming quality. In addition, the melt depth of the second track is slightly larger than that of the first track at higher line energy density � and volume energy density E. This is mainly due to the fact that a large amount of heat accumulation is generated after the first track, forming a larger molten pool volume, which leads to an increase in the melt depth.

D. Simulation analysis of molten pool with powder particle size and laser focal spot diameter

Figure 19 demonstrates the effect of different powder particle sizes and laser focal spot diameters on the morphology and temperature field of the double-track molten pool under a laser power of 100 W, a scanning speed of 800 mm/s, and a hatch spacing of 0.06 mm. In the process of melting coarse powder with small laser focal spot diameter, the laser energy cannot completely melt the larger powder particles, resulting in their partial melting and further generating excessive pore defects. The larger powder particles tend to generate zigzag molten pool edges, which cause an increase in the roughness of the melt track surface. In addition, the molten pool is also prone to generate the present spatter phenomenon, which can directly affect the quality of forming. The volume of the formed molten pool is relatively small, while the melt depth, melt width, and melt height are all smaller relative to the fine powder in Fig. 19(a). In the process of melting fine powders with a large laser focal spot diameter, the laser energy is able to melt the fine powder particles sufficiently, even to the point of overmelting. This results in a large number of fine spatters being generated at the edge of the molten pool, which causes porosity defects in the melt track in Fig. 19(b). In addition, the maximum velocity of the molten pool is larger for large powder particle sizes compared to small powder particle sizes, which indicates that the temperature gradient in the molten pool is larger for large powder particle sizes and the melt motion is more intense. However, the size of the laser focal spot diameter has a relatively small effect on the melt motion. However, a larger focal spot diameter induces a larger melt volume with greater depth, width, and height. In conclusion, a small powder size helps to reduce the surface roughness of the specimen, and a small laser spot diameter reduces the minimum forming size of a single track.

FIG. 19.

VIEW LARGEDOWNLOAD SLIDE

Simulation results of double-track molten pool with different powder particle size and laser focal spot diameter: (a) focal spot = 25 μm, coarse powder, (b) focal spot = 80 μm, fine powder.

Table V shows the maximum temperature gradient at the reference point for different powder sizes and laser focal spot diameters. As can be seen from the table, the maximum temperature gradient is lower than that of HP-LPBF for both coarse powders with a small laser spot diameter and fine powders with a large spot diameter, a phenomenon that leads to an increase in the heat transfer rate of HP-LPBF, which in turn leads to a corresponding increase in the cooling rate and, ultimately, to the formation of finer microstructures.

TABLE V.

Maximum temperature gradient at the reference point for different powder particle sizes and laser focal spot diameters.

Laser power (W)Scanning speed (mm/s)Hatch spacing (mm)Average powder size (μm)Laser focal spot diameter (μm)Maximum temperature gradient (×107 K/s)
100 800 0.06 31.7 25 7.89 
11.5 80 7.11 

IV. CONCLUSIONS

In this study, the geometrical characteristics of 3D coarse and fine powder particles were first calculated using DEM and then numerical simulations of single track and double track in the process of forming SS316L from monolayer HP-LPBF at mesoscopic scale were developed using CFD method. The effects of Marangoni convection, surface tension, recoil pressure, gravity, thermal convection, thermal radiation, and evaporative heat dissipation on the heat and mass transfer in the molten pool were considered in this model. The effects of laser power, scanning speed, and hatch spacing on the dynamics of the single-track and double-track molten pools, as well as on other characteristic information, were investigated. The effects of the powder particle size on the molten pool were investigated comparatively with the laser focal spot diameter. The main conclusions are as follows:

  1. The results show that the temperature gradient at the front of the molten pool is significantly larger than that at the tail, and the molten pool exhibits a “comet” morphology. At the top of the molten pool, there is a slightly concave region, which is the result of the coupling of Marangoni convection, recoil pressure, and surface tension. The melt flow forms two closed loops, which are mainly influenced by temperature gradients and surface tension. This special dynamic behavior of the melt tends to form an “elliptical” molten pool and an almost “mountain” shape in single-track forming.
  2. The basic characteristics of the three-dimensional morphology and temperature field of the second track are similar to those of the first track, but there are subtle differences. The first track exhibits a basically symmetrical shape; however, due to the difference in thermal diffusion rates between the solidified metal and the powder, a slight asymmetry in the molten pool morphology of the second track occurs. After forming through the first track, there is a significant heat buildup in the powder bed, resulting in a longer dynamic time of the melt, which increases the life of the molten pool. The heights of the first track and second track remained essentially the same, but the depth of the second track was greater relative to the first track. In addition, the maximum temperature gradient was 1.69 × 108 K/s during HP-LPBF forming.
  3. At low laser power, the surface tension in the molten pool plays a dominant role. At high laser power, recoil pressure becomes the main influencing factor. With the increase of laser power, the effective heat transfer in the vertical direction is superior to that in the horizontal direction. With the gradual increase of scanning speed, the surface morphology of the molten pool evolves from circular to elliptical. In addition, the scanning speed has a significant effect on the melt depth, melt width, melt height, remolten region, and overlapping ratio. Too large or too small hatch spacing will lead to remelting or non-lap phenomenon, which in turn causes the formation of defects.
  4. When using a small laser focal spot diameter, it is difficult to completely melt large powder particle sizes, resulting in partial melting and excessive porosity generation. At the same time, large powder particles produce curved edges of the molten pool, resulting in increased surface roughness of the melt track. In addition, spatter occurs, which directly affects the forming quality. At small focal spot diameters, the molten pool volume is relatively small, and the melt depth, the melt width, and the melt height are correspondingly small. Taken together, the small powder particle size helps to reduce surface roughness, while the small spot diameter reduces the forming size.

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Lab-on-a-Chip 시스템의 혈류 역학에 대한 검토: 엔지니어링 관점

Review on Blood Flow Dynamics in Lab-on-a-Chip Systems: An Engineering Perspective

  • Bin-Jie Lai
  • Li-Tao Zhu
  • Zhe Chen*
  • Bo Ouyang*
  • , and 
  • Zheng-Hong Luo*

Abstract

다양한 수송 메커니즘 하에서, “LOC(lab-on-a-chip)” 시스템에서 유동 전단 속도 조건과 밀접한 관련이 있는 혈류 역학은 다양한 수송 현상을 초래하는 것으로 밝혀졌습니다.

본 연구는 적혈구의 동적 혈액 점도 및 탄성 거동과 같은 점탄성 특성의 역할을 통해 LOC 시스템의 혈류 패턴을 조사합니다. 모세관 및 전기삼투압의 주요 매개변수를 통해 LOC 시스템의 혈액 수송 현상에 대한 연구는 실험적, 이론적 및 수많은 수치적 접근 방식을 통해 제공됩니다.

전기 삼투압 점탄성 흐름에 의해 유발되는 교란은 특히 향후 연구 기회를 위해 혈액 및 기타 점탄성 유체를 취급하는 LOC 장치의 혼합 및 분리 기능 향상에 논의되고 적용됩니다. 또한, 본 연구는 보다 정확하고 단순화된 혈류 모델에 대한 요구와 전기역학 효과 하에서 점탄성 유체 흐름에 대한 수치 연구에 대한 강조와 같은 LOC 시스템 하에서 혈류 역학의 수치 모델링의 문제를 식별합니다.

전기역학 현상을 연구하는 동안 제타 전위 조건에 대한 보다 실용적인 가정도 강조됩니다. 본 연구는 모세관 및 전기삼투압에 의해 구동되는 미세유체 시스템의 혈류 역학에 대한 포괄적이고 학제적인 관점을 제공하는 것을 목표로 한다.

KEYWORDS: 

1. Introduction

1.1. Microfluidic Flow in Lab-on-a-Chip (LOC) Systems

Over the past several decades, the ability to control and utilize fluid flow patterns at microscales has gained considerable interest across a myriad of scientific and engineering disciplines, leading to growing interest in scientific research of microfluidics. 

(1) Microfluidics, an interdisciplinary field that straddles physics, engineering, and biotechnology, is dedicated to the behavior, precise control, and manipulation of fluids geometrically constrained to a small, typically submillimeter, scale. 

(2) The engineering community has increasingly focused on microfluidics, exploring different driving forces to enhance working fluid transport, with the aim of accurately and efficiently describing, controlling, designing, and applying microfluidic flow principles and transport phenomena, particularly for miniaturized applications. 

(3) This attention has chiefly been fueled by the potential to revolutionize diagnostic and therapeutic techniques in the biomedical and pharmaceutical sectorsUnder various driving forces in microfluidic flows, intriguing transport phenomena have bolstered confidence in sustainable and efficient applications in fields such as pharmaceutical, biochemical, and environmental science. The “lab-on-a-chip” (LOC) system harnesses microfluidic flow to enable fluid processing and the execution of laboratory tasks on a chip-sized scale. LOC systems have played a vital role in the miniaturization of laboratory operations such as mixing, chemical reaction, separation, flow control, and detection on small devices, where a wide variety of fluids is adapted. Biological fluid flow like blood and other viscoelastic fluids are notably studied among the many working fluids commonly utilized by LOC systems, owing to the optimization in small fluid sample volumed, rapid response times, precise control, and easy manipulation of flow patterns offered by the system under various driving forces. 

(4)The driving forces in blood flow can be categorized as passive or active transport mechanisms and, in some cases, both. Under various transport mechanisms, the unique design of microchannels enables different functionalities in driving, mixing, separating, and diagnosing blood and drug delivery in the blood. 

(5) Understanding and manipulating these driving forces are crucial for optimizing the performance of a LOC system. Such knowledge presents the opportunity to achieve higher efficiency and reliability in addressing cellular level challenges in medical diagnostics, forensic studies, cancer detection, and other fundamental research areas, for applications of point-of-care (POC) devices. 

(6)

1.2. Engineering Approach of Microfluidic Transport Phenomena in LOC Systems

Different transport mechanisms exhibit unique properties at submillimeter length scales in microfluidic devices, leading to significant transport phenomena that differ from those of macroscale flows. An in-depth understanding of these unique transport phenomena under microfluidic systems is often required in fluidic mechanics to fully harness the potential functionality of a LOC system to obtain systematically designed and precisely controlled transport of microfluids under their respective driving force. Fluid mechanics is considered a vital component in chemical engineering, enabling the analysis of fluid behaviors in various unit designs, ranging from large-scale reactors to separation units. Transport phenomena in fluid mechanics provide a conceptual framework for analytically and descriptively explaining why and how experimental results and physiological phenomena occur. The Navier–Stokes (N–S) equation, along with other governing equations, is often adapted to accurately describe fluid dynamics by accounting for pressure, surface properties, velocity, and temperature variations over space and time. In addition, limiting factors and nonidealities for these governing equations should be considered to impose corrections for empirical consistency before physical models are assembled for more accurate controls and efficiency. Microfluidic flow systems often deviate from ideal conditions, requiring adjustments to the standard governing equations. These deviations could arise from factors such as viscous effects, surface interactions, and non-Newtonian fluid properties from different microfluid types and geometrical layouts of microchannels. Addressing these nonidealities supports the refining of theoretical models and prediction accuracy for microfluidic flow behaviors.

The analytical calculation of coupled nonlinear governing equations, which describes the material and energy balances of systems under ideal conditions, often requires considerable computational efforts. However, advancements in computation capabilities, cost reduction, and improved accuracy have made numerical simulations using different numerical and modeling methods a powerful tool for effectively solving these complex coupled equations and modeling various transport phenomena. Computational fluid dynamics (CFD) is a numerical technique used to investigate the spatial and temporal distribution of various flow parameters. It serves as a critical approach to provide insights and reasoning for decision-making regarding the optimal designs involving fluid dynamics, even prior to complex physical model prototyping and experimental procedures. The integration of experimental data, theoretical analysis, and reliable numerical simulations from CFD enables systematic variation of analytical parameters through quantitative analysis, where adjustment to delivery of blood flow and other working fluids in LOC systems can be achieved.

Numerical methods such as the Finite-Difference Method (FDM), Finite-Element-Method (FEM), and Finite-Volume Method (FVM) are heavily employed in CFD and offer diverse approaches to achieve discretization of Eulerian flow equations through filling a mesh of the flow domain. A more in-depth review of numerical methods in CFD and its application for blood flow simulation is provided in Section 2.2.2.

1.3. Scope of the Review

In this Review, we explore and characterize the blood flow phenomena within the LOC systems, utilizing both physiological and engineering modeling approaches. Similar approaches will be taken to discuss capillary-driven flow and electric-osmotic flow (EOF) under electrokinetic phenomena as a passive and active transport scheme, respectively, for blood transport in LOC systems. Such an analysis aims to bridge the gap between physical (experimental) and engineering (analytical) perspectives in studying and manipulating blood flow delivery by different driving forces in LOC systems. Moreover, the Review hopes to benefit the interests of not only blood flow control in LOC devices but also the transport of viscoelastic fluids, which are less studied in the literature compared to that of Newtonian fluids, in LOC systems.

Section 2 examines the complex interplay between viscoelastic properties of blood and blood flow patterns under shear flow in LOC systems, while engineering numerical modeling approaches for blood flow are presented for assistance. Sections 3 and 4 look into the theoretical principles, numerical governing equations, and modeling methodologies for capillary driven flow and EOF in LOC systems as well as their impact on blood flow dynamics through the quantification of key parameters of the two driving forces. Section 5 concludes the characterized blood flow transport processes in LOC systems under these two forces. Additionally, prospective areas of research in improving the functionality of LOC devices employing blood and other viscoelastic fluids and potentially justifying mechanisms underlying microfluidic flow patterns outside of LOC systems are presented. Finally, the challenges encountered in the numerical studies of blood flow under LOC systems are acknowledged, paving the way for further research.

2. Blood Flow Phenomena

ARTICLE SECTIONS

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2.1. Physiological Blood Flow Behavior

Blood, an essential physiological fluid in the human body, serves the vital role of transporting oxygen and nutrients throughout the body. Additionally, blood is responsible for suspending various blood cells including erythrocytes (red blood cells or RBCs), leukocytes (white blood cells), and thrombocytes (blood platelets) in a plasma medium.Among the cells mentioned above, red blood cells (RBCs) comprise approximately 40–45% of the volume of healthy blood. 

(7) An RBC possesses an inherent elastic property with a biconcave shape of an average diameter of 8 μm and a thickness of 2 μm. This biconcave shape maximizes the surface-to-volume ratio, allowing RBCs to endure significant distortion while maintaining their functionality. 

(8,9) Additionally, the biconcave shape optimizes gas exchange, facilitating efficient uptake of oxygen due to the increased surface area. The inherent elasticity of RBCs allows them to undergo substantial distortion from their original biconcave shape and exhibits high flexibility, particularly in narrow channels.RBC deformability enables the cell to deform from a biconcave shape to a parachute-like configuration, despite minor differences in RBC shape dynamics under shear flow between initial cell locations. As shown in Figure 1(a), RBCs initiating with different resting shapes and orientations displaying display a similar deformation pattern 

(10) in terms of its shape. Shear flow induces an inward bending of the cell at the rear position of the rim to the final bending position, 

(11) resulting in an alignment toward the same position of the flow direction.

Figure 1. Images of varying deformation of RBCs and different dynamic blood flow behaviors. (a) The deforming shape behavior of RBCs at four different initiating positions under the same experimental conditions of a flow from left to right, (10) (b) RBC aggregation, (13) (c) CFL region. (18) Reproduced with permission from ref (10). Copyright 2011 Elsevier. Reproduced with permission from ref (13). Copyright 2022 The Authors, under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/. Reproduced with permission from ref (18). Copyright 2019 Elsevier.

The flexible property of RBCs enables them to navigate through narrow capillaries and traverse a complex network of blood vessels. The deformability of RBCs depends on various factors, including the channel geometry, RBC concentration, and the elastic properties of the RBC membrane. 

(12) Both flexibility and deformability are vital in the process of oxygen exchange among blood and tissues throughout the body, allowing cells to flow in vessels even smaller than the original cell size prior to deforming.As RBCs serve as major components in blood, their collective dynamics also hugely affect blood rheology. RBCs exhibit an aggregation phenomenon due to cell to cell interactions, such as adhesion forces, among populated cells, inducing unique blood flow patterns and rheological behaviors in microfluidic systems. For blood flow in large vessels between a diameter of 1 and 3 cm, where shear rates are not high, a constant viscosity and Newtonian behavior for blood can be assumed. However, under low shear rate conditions (0.1 s

–1) in smaller vessels such as the arteries and venules, which are within a diameter of 0.2 mm to 1 cm, blood exhibits non-Newtonian properties, such as shear-thinning viscosity and viscoelasticity due to RBC aggregation and deformability. The nonlinear viscoelastic property of blood gives rise to a complex relationship between viscosity and shear rate, primarily influenced by the highly elastic behavior of RBCs. A wide range of research on the transient behavior of the RBC shape and aggregation characteristics under varied flow circumstances has been conducted, aiming to obtain a better understanding of the interaction between blood flow shear forces from confined flows.

For a better understanding of the unique blood flow structures and rheological behaviors in microfluidic systems, some blood flow patterns are introduced in the following section.

2.1.1. RBC Aggregation

RBC aggregation is a vital phenomenon to be considered when designing LOC devices due to its impact on the viscosity of the bulk flow. Under conditions of low shear rate, such as in stagnant or low flow rate regions, RBCs tend to aggregate, forming structures known as rouleaux, resembling stacks of coins as shown in Figure 1(b). 

(13) The aggregation of RBCs increases the viscosity at the aggregated region, 

(14) hence slowing down the overall blood flow. However, when exposed to high shear rates, RBC aggregates disaggregate. As shear rates continue to increase, RBCs tend to deform, elongating and aligning themselves with the direction of the flow. 

(15) Such a dynamic shift in behavior from the cells in response to the shear rate forms the basis of the viscoelastic properties observed in whole blood. In essence, the viscosity of the blood varies according to the shear rate conditions, which are related to the velocity gradient of the system. It is significant to take the intricate relationship between shear rate conditions and the change of blood viscosity due to RBC aggregation into account since various flow driving conditions may induce varied effects on the degree of aggregation.

2.1.2. Fåhræus-Lindqvist Effect

The Fåhræus–Lindqvist (FL) effect describes the gradual decrease in the apparent viscosity of blood as the channel diameter decreases. 

(16) This effect is attributed to the migration of RBCs toward the central region in the microchannel, where the flow rate is higher, due to the presence of higher pressure and asymmetric distribution of shear forces. This migration of RBCs, typically observed at blood vessels less than 0.3 mm, toward the higher flow rate region contributes to the change in blood viscosity, which becomes dependent on the channel size. Simultaneously, the increase of the RBC concentration in the central region of the microchannel results in the formation of a less viscous region close to the microchannel wall. This region called the Cell-Free Layer (CFL), is primarily composed of plasma. 

(17) The combination of the FL effect and the following CFL formation provides a unique phenomenon that is often utilized in passive and active plasma separation mechanisms, involving branched and constriction channels for various applications in plasma separation using microfluidic systems.

2.1.3. Cell-Free Layer Formation

In microfluidic blood flow, RBCs form aggregates at the microchannel core and result in a region that is mostly devoid of RBCs near the microchannel walls, as shown in Figure 1(c). 

(18) The region is known as the cell-free layer (CFL). The CFL region is often known to possess a lower viscosity compared to other regions within the blood flow due to the lower viscosity value of plasma when compared to that of the aggregated RBCs. Therefore, a thicker CFL region composed of plasma correlates to a reduced apparent whole blood viscosity. 

(19) A thicker CFL region is often established following the RBC aggregation at the microchannel core under conditions of decreasing the tube diameter. Apart from the dependence on the RBC concentration in the microchannel core, the CFL thickness is also affected by the volume concentration of RBCs, or hematocrit, in whole blood, as well as the deformability of RBCs. Given the influence CFL thickness has on blood flow rheological parameters such as blood flow rate, which is strongly dependent on whole blood viscosity, investigating CFL thickness under shear flow is crucial for LOC systems accounting for blood flow.

2.1.4. Plasma Skimming in Bifurcation Networks

The uneven arrangement of RBCs in bifurcating microchannels, commonly termed skimming bifurcation, arises from the axial migration of RBCs within flowing streams. This uneven distribution contributes to variations in viscosity across differing sizes of bifurcating channels but offers a stabilizing effect. Notably, higher flow rates in microchannels are associated with increased hematocrit levels, resulting in higher viscosity compared with those with lower flow rates. Parametric investigations on bifurcation angle, 

(20) thickness of the CFL, 

(21) and RBC dynamics, including aggregation and deformation, 

(22) may alter the varying viscosity of blood and its flow behavior within microchannels.

2.2. Modeling on Blood Flow Dynamics

2.2.1. Blood Properties and Mathematical Models of Blood Rheology

Under different shear rate conditions in blood flow, the elastic characteristics and dynamic changes of the RBC induce a complex velocity and stress relationship, resulting in the incompatibility of blood flow characterization through standard presumptions of constant viscosity used for Newtonian fluid flow. Blood flow is categorized as a viscoelastic non-Newtonian fluid flow where constitutive equations governing this type of flow take into consideration the nonlinear viscometric properties of blood. To mathematically characterize the evolving blood viscosity and the relationship between the elasticity of RBC and the shear blood flow, respectively, across space and time of the system, a stress tensor (τ) defined by constitutive models is often coupled in the Navier–Stokes equation to account for the collective impact of the constant dynamic viscosity (η) and the elasticity from RBCs on blood flow.The dynamic viscosity of blood is heavily dependent on the shear stress applied to the cell and various parameters from the blood such as hematocrit value, plasma viscosity, mechanical properties of the RBC membrane, and red blood cell aggregation rate. The apparent blood viscosity is considered convenient for the characterization of the relationship between the evolving blood viscosity and shear rate, which can be defined by Casson’s law, as shown in eq 1.

𝜇=𝜏0𝛾˙+2𝜂𝜏0𝛾˙⎯⎯⎯⎯⎯⎯⎯√+𝜂�=�0�˙+2��0�˙+�

(1)where τ

0 is the yield stress–stress required to initiate blood flow motion, η is the Casson rheological constant, and γ̇ is the shear rate. The value of Casson’s law parameters under blood with normal hematocrit level can be defined as τ

0 = 0.0056 Pa and η = 0.0035 Pa·s. 

(23) With the known property of blood and Casson’s law parameters, an approximation can be made to the dynamic viscosity under various flow condition domains. The Power Law model is often employed to characterize the dynamic viscosity in relation to the shear rate, since precise solutions exist for specific geometries and flow circumstances, acting as a fundamental standard for definition. The Carreau and Carreau–Yasuda models can be advantageous over the Power Law model due to their ability to evaluate the dynamic viscosity at low to zero shear rate conditions. However, none of the above-mentioned models consider the memory or other elastic behavior of blood and its RBCs. Some other commonly used mathematical models and their constants for the non-Newtonian viscosity property characterization of blood are listed in Table 1 below. 

(24−26)Table 1. Comparison of Various Non-Newtonian Models for Blood Viscosity 

(24−26)

ModelNon-Newtonian ViscosityParameters
Power Law(2)n = 0.61, k = 0.42
Carreau(3)μ0 = 0.056 Pa·s, μ = 0.00345 Pa·s, λ = 3.1736 s, m = 2.406, a = 0.254
Walburn–Schneck(4)C1 = 0.000797 Pa·s, C2 = 0.0608 Pa·s, C3 = 0.00499, C4 = 14.585 g–1, TPMA = 25 g/L
Carreau–Yasuda(5)μ0 = 0.056 Pa·s, μ = 0.00345 Pa·s, λ = 1.902 s, n = 0.22, a = 1.25
Quemada(6)μp = 0.0012 Pa·s, k = 2.07, k0 = 4.33, γ̇c = 1.88 s–1

The blood rheology is commonly known to be influenced by two key physiological factors, namely, the hematocrit value (H

t) and the fibrinogen concentration (c

f), with an average value of 42% and 0.252 gd·L

–1, respectively. Particularly in low shear conditions, the presence of varying fibrinogen concentrations affects the tendency for aggregation and rouleaux formation, while the occurrence of aggregation is contingent upon specific levels of hematocrit. 

(27) The study from Apostolidis et al. 

(28) modifies the Casson model through emphasizing its reliance on hematocrit and fibrinogen concentration parameter values, owing to the extensive knowledge of the two physiological blood parameters.The viscoelastic response of blood is heavily dependent on the elasticity of the RBC, which is defined by the relationship between the deformation and stress relaxation from RBCs under a specific location of shear flow as a function of the velocity field. The stress tensor is usually characterized by constitutive equations such as the Upper-Convected Maxwell Model 

(29) and the Oldroyd-B model 

(30) to track the molecule effects under shear from different driving forces. The prominent non-Newtonian features, such as shear thinning and yield stress, have played a vital role in the characterization of blood rheology, particularly with respect to the evaluation of yield stress under low shear conditions. The nature of stress measurement in blood, typically on the order of 1 mPa, is challenging due to its low magnitude. The occurrence of the CFL complicates the measurement further due to the significant decrease in apparent viscosity near the wall over time and a consequential disparity in viscosity compared to the bulk region.In addition to shear thinning viscosity and yield stress, the formation of aggregation (rouleaux) from RBCs under low shear rates also contributes to the viscoelasticity under transient flow 

(31) and thixotropy 

(32) of whole blood. Given the difficulty in evaluating viscoelastic behavior of blood under low strain magnitudes and limitations in generalized Newtonian models, the utilization of viscoelastic models is advocated to encompass elasticity and delineate non-shear components within the stress tensor. Extending from the Oldroyd-B model, Anand et al. 

(33) developed a viscoelastic model framework for adapting elasticity within blood samples and predicting non-shear stress components. However, to also address the thixotropic effects, the model developed by Horner et al. 

(34) serves as a more comprehensive approach than the viscoelastic model from Anand et al. Thixotropy 

(32) typically occurs from the structural change of the rouleaux, where low shear rate conditions induce rouleaux formation. Correspondingly, elasticity increases, while elasticity is more representative of the isolated RBCs, under high shear rate conditions. The model of Horner et al. 

(34) considers the contribution of rouleaux to shear stress, taking into account factors such as the characteristic time for Brownian aggregation, shear-induced aggregation, and shear-induced breakage. Subsequent advancements in the model from Horner et al. often revolve around refining the three aforementioned key terms for a more substantial characterization of rouleaux dynamics. Notably, this has led to the recently developed mHAWB model 

(35) and other model iterations to enhance the accuracy of elastic and viscoelastic contributions to blood rheology, including the recently improved model suggested by Armstrong et al. 

(36)

2.2.2. Numerical Methods (FDM, FEM, FVM)

Numerical simulation has become increasingly more significant in analyzing the geometry, boundary layers of flow, and nonlinearity of hyperbolic viscoelastic flow constitutive equations. CFD is a powerful and efficient tool utilizing numerical methods to solve the governing hydrodynamic equations, such as the Navier–Stokes (N–S) equation, continuity equation, and energy conservation equation, for qualitative evaluation of fluid motion dynamics under different parameters. CFD overcomes the challenge of analytically solving nonlinear forms of differential equations by employing numerical methods such as the Finite-Difference Method (FDM), Finite-Element Method (FEM), and Finite-Volume Method (FVM) to discretize and solve the partial differential equations (PDEs), allowing for qualitative reproduction of transport phenomena and experimental observations. Different numerical methods are chosen to cope with various transport systems for optimization of the accuracy of the result and control of error during the discretization process.FDM is a straightforward approach to discretizing PDEs, replacing the continuum representation of equations with a set of finite-difference equations, which is typically applied to structured grids for efficient implementation in CFD programs. 

(37) However, FDM is often limited to simple geometries such as rectangular or block-shaped geometries and struggles with curved boundaries. In contrast, FEM divides the fluid domain into small finite grids or elements, approximating PDEs through a local description of physics. 

(38) All elements contribute to a large, sparse matrix solver. However, FEM may not always provide accurate results for systems involving significant deformation and aggregation of particles like RBCs due to large distortion of grids. 

(39) FVM evaluates PDEs following the conservation laws and discretizes the selected flow domain into small but finite size control volumes, with each grid at the center of a finite volume. 

(40) The divergence theorem allows the conversion of volume integrals of PDEs with divergence terms into surface integrals of surface fluxes across cell boundaries. Due to its conservation property, FVM offers efficient outcomes when dealing with PDEs that embody mass, momentum, and energy conservation principles. Furthermore, widely accessible software packages like the OpenFOAM toolbox 

(41) include a viscoelastic solver, making it an attractive option for viscoelastic fluid flow modeling. 

(42)

2.2.3. Modeling Methods of Blood Flow Dynamics

The complexity in the blood flow simulation arises from deformability and aggregation that RBCs exhibit during their interaction with neighboring cells under different shear rate conditions induced by blood flow. Numerical models coupled with simulation programs have been applied as a groundbreaking method to predict such unique rheological behavior exhibited by RBCs and whole blood. The conventional approach of a single-phase flow simulation is often applied to blood flow simulations within large vessels possessing a moderate shear rate. However, such a method assumes the properties of plasma, RBCs and other cellular components to be evenly distributed as average density and viscosity in blood, resulting in the inability to simulate the mechanical dynamics, such as RBC aggregation under high-shear flow field, inherent in RBCs. To accurately describe the asymmetric distribution of RBC and blood flow, multiphase flow simulation, where numerical simulations of blood flows are often modeled as two immiscible phases, RBCs and blood plasma, is proposed. A common assumption is that RBCs exhibit non-Newtonian behavior while the plasma is treated as a continuous Newtonian phase.Numerous multiphase numerical models have been proposed to simulate the influence of RBCs on blood flow dynamics by different assumptions. In large-scale simulations (above the millimeter range), continuum-based methods are wildly used due to their lower computational demands. 

(43) Eulerian multiphase flow simulations offer the solution of a set of conservation equations for each separate phase and couple the phases through common pressure and interphase exchange coefficients. Xu et al. 

(44) utilized the combined finite-discrete element method (FDEM) to replicate the dynamic behavior and distortion of RBCs subjected to fluidic forces, utilizing the Johnson–Kendall–Roberts model 

(45) to define the adhesive forces of cell-to-cell interactions. The iterative direct-forcing immersed boundary method (IBM) is commonly employed in simulations of the fluid–cell interface of blood. This method effectively captures the intricacies of the thin and flexible RBC membranes within various external flow fields. 

(46) The study by Xu et al. 

(44) also adopts this approach to bridge the fluid dynamics and RBC deformation through IBM. Yoon and You utilized the Maxwell model to define the viscosity of the RBC membrane. 

(47) It was discovered that the Maxwell model could represent the stress relaxation and unloading processes of the cell. Furthermore, the reduced flexibility of an RBC under particular situations such as infection is specified, which was unattainable by the Kelvin–Voigt model 

(48) when compared to the Maxwell model in the literature. The Yeoh hyperplastic material model was also adapted to predict the nonlinear elasticity property of RBCs with FEM employed to discretize the RBC membrane using shell-type elements. Gracka et al. 

(49) developed a numerical CFD model with a finite-volume parallel solver for multiphase blood flow simulation, where an updated Maxwell viscoelasticity model and a Discrete Phase Model are adopted. In the study, the adapted IBM, based on unstructured grids, simulates the flow behavior and shape change of the RBCs through fluid-structure coupling. It was found that the hybrid Euler–Lagrange (E–L) approach 

(50) for the development of the multiphase model offered better results in the simulated CFL region in the microchannels.To study the dynamics of individual behaviors of RBCs and the consequent non-Newtonian blood flow, cell-shape-resolved computational models are often adapted. The use of the boundary integral method has become prevalent in minimizing computational expenses, particularly in the exclusive determination of fluid velocity on the surfaces of RBCs, incorporating the option of employing IBM or particle-based techniques. The cell-shaped-resolved method has enabled an examination of cell to cell interactions within complex ambient or pulsatile flow conditions 

(51) surrounding RBC membranes. Recently, Rydquist et al. 

(52) have looked to integrate statistical information from macroscale simulations to obtain a comprehensive overview of RBC behavior within the immediate proximity of the flow through introduction of respective models characterizing membrane shape definition, tension, bending stresses of RBC membranes.At a macroscopic scale, continuum models have conventionally been adapted for assessing blood flow dynamics through the application of elasticity theory and fluid dynamics. However, particle-based methods are known for their simplicity and adaptability in modeling complex multiscale fluid structures. Meshless methods, such as the boundary element method (BEM), smoothed particle hydrodynamics (SPH), and dissipative particle dynamics (DPD), are often used in particle-based characterization of RBCs and the surrounding fluid. By representing the fluid as discrete particles, meshless methods provide insights into the status and movement of the multiphase fluid. These methods allow for the investigation of cellular structures and microscopic interactions that affect blood rheology. Non-confronting mesh methods like IBM can also be used to couple a fluid solver such as FEM, FVM, or the Lattice Boltzmann Method (LBM) through membrane representation of RBCs. In comparison to conventional CFD methods, LBM has been viewed as a favorable numerical approach for solving the N–S equations and the simulation of multiphase flows. LBM exhibits the notable advantage of being amenable to high-performance parallel computing environments due to its inherently local dynamics. In contrast to DPD and SPH where RBC membranes are modeled as physically interconnected particles, LBM employs the IBM to account for the deformation dynamics of RBCs 

(53,54) under shear flows in complex channel geometries. 

(54,55) However, it is essential to acknowledge that the utilization of LBM in simulating RBC flows often entails a significant computational overhead, being a primary challenge in this context. Krüger et al. 

(56) proposed utilizing LBM as a fluid solver, IBM to couple the fluid and FEM to compute the response of membranes to deformation under immersed fluids. This approach decouples the fluid and membranes but necessitates significant computational effort due to the requirements of both meshes and particles.Despite the accuracy of current blood flow models, simulating complex conditions remains challenging because of the high computational load and cost. Balachandran Nair et al. 

(57) suggested a reduced order model of RBC under the framework of DEM, where the RBC is represented by overlapping constituent rigid spheres. The Morse potential force is adapted to account for the RBC aggregation exhibited by cell to cell interactions among RBCs at different distances. Based upon the IBM, the reduced-order RBC model is adapted to simulate blood flow transport for validation under both single and multiple RBCs with a resolved CFD-DEM solver. 

(58) In the resolved CFD-DEM model, particle sizes are larger than the grid size for a more accurate computation of the surrounding flow field. A continuous forcing approach is taken to describe the momentum source of the governing equation prior to discretization, which is different from a Direct Forcing Method (DFM). 

(59) As no body-conforming moving mesh is required, the continuous forcing approach offers lower complexity and reduced cost when compared to the DFM. Piquet et al. 

(60) highlighted the high complexity of the DFM due to its reliance on calculating an additional immersed boundary flux for the velocity field to ensure its divergence-free condition.The fluid–structure interaction (FSI) method has been advocated to connect the dynamic interplay of RBC membranes and fluid plasma within blood flow such as the coupling of continuum–particle interactions. However, such methodology is generally adapted for anatomical configurations such as arteries 

(61,62) and capillaries, 

(63) where both the structural components and the fluid domain undergo substantial deformation due to the moving boundaries. Due to the scope of the Review being blood flow simulation within microchannels of LOC devices without deformable boundaries, the Review of the FSI method will not be further carried out.In general, three numerical methods are broadly used: mesh-based, particle-based, and hybrid mesh–particle techniques, based on the spatial scale and the fundamental numerical approach, mesh-based methods tend to neglect the effects of individual particles, assuming a continuum and being efficient in terms of time and cost. However, the particle-based approach highlights more of the microscopic and mesoscopic level, where the influence of individual RBCs is considered. A review from Freund et al. 

(64) addressed the three numerical methodologies and their respective modeling approaches of RBC dynamics. Given the complex mechanics and the diverse levels of study concerning numerical simulations of blood and cellular flow, a broad spectrum of numerical methods for blood has been subjected to extensive review. 

(64−70) Ye at al. 

(65) offered an extensive review of the application of the DPD, SPH, and LBM for numerical simulations of RBC, while Rathnayaka et al. 

(67) conducted a review of the particle-based numerical modeling for liquid marbles through drawing parallels to the transport of RBCs in microchannels. A comparative analysis between conventional CFD methods and particle-based approaches for cellular and blood flow dynamic simulation can be found under the review by Arabghahestani et al. 

(66) Literature by Li et al. 

(68) and Beris et al. 

(69) offer an overview of both continuum-based models at micro/macroscales and multiscale particle-based models encompassing various length and temporal dimensions. Furthermore, these reviews deliberate upon the potential of coupling continuum-particle methods for blood plasma and RBC modeling. Arciero et al. 

(70) investigated various modeling approaches encompassing cellular interactions, such as cell to cell or plasma interactions and the individual cellular phases. A concise overview of the reviews is provided in Table 2 for reference.

Table 2. List of Reviews for Numerical Approaches Employed in Blood Flow Simulation

ReferenceNumerical methods
Li et al. (2013) (68)Continuum-based modeling (BIM), particle-based modeling (LBM, LB-FE, SPH, DPD)
Freund (2014) (64)RBC dynamic modeling (continuum-based modeling, complementary discrete microstructure modeling), blood flow dynamic modeling (FDM, IBM, LBM, particle-mesh methods, coupled boundary integral and mesh-based methods, DPD)
Ye et al. (2016) (65)DPD, SPH, LBM, coupled IBM-Smoothed DPD
Arciero et al. (2017) (70)LBM, IBM, DPD, conventional CFD Methods (FDM, FVM, FEM)
Arabghahestani et al. (2019) (66)Particle-based methods (LBM, DPD, direct simulation Monte Carlo, molecular dynamics), SPH, conventional CFD methods (FDM, FVM, FEM)
Beris et al. (2021) (69)DPD, smoothed DPD, IBM, LBM, BIM
Rathnayaka (2022) (67)SPH, CG, LBM

3. Capillary Driven Blood Flow in LOC Systems

ARTICLE SECTIONS

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3.1. Capillary Driven Flow Phenomena

Capillary driven (CD) flow is a pivotal mechanism in passive microfluidic flow systems 

(9) such as the blood circulation system and LOC systems. 

(71) CD flow is essentially the movement of a liquid to flow against drag forces, where the capillary effect exerts a force on the liquid at the borders, causing a liquid–air meniscus to flow despite gravity or other drag forces. A capillary pressure drops across the liquid–air interface with surface tension in the capillary radius and contact angle. The capillary effect depends heavily on the interaction between the different properties of surface materials. Different values of contact angles can be manipulated and obtained under varying levels of surface wettability treatments to manipulate the surface properties, resulting in different CD blood delivery rates for medical diagnostic device microchannels. CD flow techniques are appealing for many LOC devices, because they require no external energy. However, due to the passive property of liquid propulsion by capillary forces and the long-term instability of surface treatments on channel walls, the adaptability of CD flow in geometrically complex LOC devices may be limited.

3.2. Theoretical and Numerical Modeling of Capillary Driven Blood Flow

3.2.1. Theoretical Basis and Assumptions of Microfluidic Flow

The study of transport phenomena regarding either blood flow driven by capillary forces or externally applied forces under microfluid systems all demands a comprehensive recognition of the significant differences in flow dynamics between microscale and macroscale. The fundamental assumptions and principles behind fluid transport at the microscale are discussed in this section. Such a comprehension will lay the groundwork for the following analysis of the theoretical basis of capillary forces and their role in blood transport in LOC systems.

At the macroscale, fluid dynamics are often strongly influenced by gravity due to considerable fluid mass. However, the high surface to volume ratio at the microscale shifts the balance toward surface forces (e.g., surface tension and viscous forces), much larger than the inertial force. This difference gives rise to transport phenomena unique to microscale fluid transport, such as the prevalence of laminar flow due to a very low Reynolds number (generally lower than 1). Moreover, the fluid in a microfluidic system is often assumed to be incompressible due to the small flow velocity, indicating constant fluid density in both space and time.Microfluidic flow behaviors are governed by the fundamental principles of mass and momentum conservation, which are encapsulated in the continuity equation and the Navier–Stokes (N–S) equation. The continuity equation describes the conservation of mass, while the N–S equation captures the spatial and temporal variations in velocity, pressure, and other physical parameters. Under the assumption of the negligible influence of gravity in microfluidic systems, the continuity equation and the Eulerian representation of the incompressible N–S equation can be expressed as follows:

∇·𝐮⇀=0∇·�⇀=0

(7)

−∇𝑝+𝜇∇2𝐮⇀+∇·𝝉⇀−𝐅⇀=0−∇�+�∇2�⇀+∇·�⇀−�⇀=0

(8)Here, p is the pressure, u is the fluid viscosity, 

𝝉⇀�⇀ represents the stress tensor, and F is the body force exerted by external forces if present.

3.2.2. Theoretical Basis and Modeling of Capillary Force in LOC Systems

The capillary force is often the major driving force to manipulate and transport blood without an externally applied force in LOC systems. Forces induced by the capillary effect impact the free surface of fluids and are represented not directly in the Navier–Stokes equations but through the pressure boundary conditions of the pressure term p. For hydrophilic surfaces, the liquid generally induces a contact angle between 0° and 30°, encouraging the spread and attraction of fluid under a positive cos θ condition. For this condition, the pressure drop becomes positive and generates a spontaneous flow forward. A hydrophobic solid surface repels the fluid, inducing minimal contact. Generally, hydrophobic solids exhibit a contact angle larger than 90°, inducing a negative value of cos θ. Such a value will result in a negative pressure drop and a flow in the opposite direction. The induced contact angle is often utilized to measure the wall exposure of various surface treatments on channel walls where different wettability gradients and surface tension effects for CD flows are established. Contact angles between different interfaces are obtainable through standard values or experimental methods for reference. 

(72)For the characterization of the induced force by the capillary effect, the Young–Laplace (Y–L) equation 

(73) is widely employed. In the equation, the capillary is considered a pressure boundary condition between the two interphases. Through the Y–L equation, the capillary pressure force can be determined, and subsequently, the continuity and momentum balance equations can be solved to obtain the blood filling rate. Kim et al. 

(74) studied the effects of concentration and exposure time of a nonionic surfactant, Silwet L-77, on the performance of a polydimethylsiloxane (PDMS) microchannel in terms of plasma and blood self-separation. The study characterized the capillary pressure force by incorporating the Y–L equation and further evaluated the effects of the changing contact angle due to different levels of applied channel wall surface treatments. The expression of the Y–L equation utilized by Kim et al. 

(74) is as follows:

𝑃=−𝜎(cos𝜃b+cos𝜃tℎ+cos𝜃l+cos𝜃r𝑤)�=−�(cos⁡�b+cos⁡�tℎ+cos⁡�l+cos⁡�r�)

(9)where σ is the surface tension of the liquid and θ

bθ

tθ

l, and θ

r are the contact angle values between the liquid and the bottom, top, left, and right walls, respectively. A numerical simulation through Coventor software is performed to evaluate the dynamic changes in the filling rate within the microchannel. The simulation results for the blood filling rate in the microchannel are expressed at a specific time stamp, shown in Figure 2. The results portray an increasing instantaneous filling rate of blood in the microchannel following the decrease in contact angle induced by a higher concentration of the nonionic surfactant treated to the microchannel wall.

Figure 2. Numerical simulation of filling rate of capillary driven blood flow under various contact angle conditions at a specific timestamp. (74) Reproduced with permission from ref (74). Copyright 2010 Elsevier.

When in contact with hydrophilic or hydrophobic surfaces, blood forms a meniscus with a contact angle due to surface tension. The Lucas–Washburn (L–W) equation 

(75) is one of the pioneering theoretical definitions for the position of the meniscus over time. In addition, the L–W equation provides the possibility for research to obtain the velocity of the blood formed meniscus through the derivation of the meniscus position. The L–W equation 

(75) can be shown below:

𝐿(𝑡)=𝑅𝜎cos(𝜃)𝑡2𝜇⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√�(�)=��⁡cos(�)�2�

(10)Here L(t) represents the distance of the liquid driven by the capillary forces. However, the generalized L–W equation solely assumes the constant physical properties from a Newtonian fluid rather than considering the non-Newtonian fluid behavior of blood. Cito et al. 

(76) constructed an enhanced version of the L–W equation incorporating the power law to consider the RBC aggregation and the FL effect. The non-Newtonian fluid apparent viscosity under the Power Law model is defined as

𝜇=𝑘·(𝛾˙)𝑛−1�=�·(�˙)�−1

(11)where γ̇ is the strain rate tensor defined as 

𝛾˙=12𝛾˙𝑖𝑗𝛾˙𝑗𝑖⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√�˙=12�˙���˙��. The stress tensor term τ is computed as τ = μγ̇

ij. The updated L–W equation by Cito 

(76) is expressed as

𝐿(𝑡)=𝑅[(𝑛+13𝑛+1)(𝜎cos(𝜃)𝑅𝑘)1/𝑛𝑡]𝑛/𝑛+1�(�)=�[(�+13�+1)(�⁡cos(�)��)1/��]�/�+1

(12)where k is the flow consistency index and n is the power law index, respectively. The power law index, from the Power Law model, characterizes the extent of the non-Newtonian behavior of blood. Both the consistency and power law index rely on blood properties such as hematocrit, the appearance of the FL effect, the formation of RBC aggregates, etc. The updated L–W equation computes the location and velocity of blood flow caused by capillary forces at specified time points within the LOC devices, taking into account the effects of blood flow characteristics such as RBC aggregation and the FL effect on dynamic blood viscosity.Apart from the blood flow behaviors triggered by inherent blood properties, unique flow conditions driven by capillary forces that are portrayed under different microchannel geometries also hold crucial implications for CD blood delivery. Berthier et al. 

(77) studied the spontaneous Concus–Finn condition, the condition to initiate the spontaneous capillary flow within a V-groove microchannel, as shown in Figure 3(a) both experimentally and numerically. Through experimental studies, the spontaneous Concus–Finn filament development of capillary driven blood flow is observed, as shown in Figure 3(b), while the dynamic development of blood flow is numerically simulated through CFD simulation.

Figure 3. (a) Sketch of the cross-section of Berthier’s V-groove microchannel, (b) experimental view of blood in the V-groove microchannel, (78) (c) illustration of the dynamic change of the extension of filament from FLOW 3D under capillary flow at three increasing time intervals. (78) Reproduced with permission from ref (78). Copyright 2014 Elsevier.

Berthier et al. 

(77) characterized the contact angle needed for the initiation of the capillary driving force at a zero-inlet pressure, through the half-angle (α) of the V-groove geometry layout, and its relation to the Concus–Finn filament as shown below:

𝜃<𝜋2−𝛼sin𝛼1+2(ℎ2/𝑤)sin𝛼<cos𝜃{�<�2−�sin⁡�1+2(ℎ2/�)⁡sin⁡�<cos⁡�

(13)Three possible regimes were concluded based on the contact angle value for the initiation of flow and development of Concus–Finn filament:

𝜃>𝜃1𝜃1>𝜃>𝜃0𝜃0no SCFSCF without a Concus−Finn filamentSCF without a Concus−Finn filament{�>�1no SCF�1>�>�0SCF without a Concus−Finn filament�0SCF without a Concus−Finn filament

(14)Under Newton’s Law, the force balance with low Reynolds and Capillary numbers results in the neglect of inertial terms. The force balance between the capillary forces and the viscous force induced by the channel wall is proposed to derive the analytical fluid velocity. This relation between the two forces offers insights into the average flow velocity and the penetration distance function dependent on time. The apparent blood viscosity is defined by Berthier et al. 

(78) through Casson’s law, 

(23) given in eq 1. The research used the FLOW-3D program from Flow Science Inc. software, which solves transient, free-surface problems using the FDM in multiple dimensions. The Volume of Fluid (VOF) method 

(79) is utilized to locate and track the dynamic extension of filament throughout the advancing interface within the channel ahead of the main flow at three progressing time stamps, as depicted in Figure 3(c).

4. Electro-osmotic Flow (EOF) in LOC Systems

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The utilization of external forces, such as electric fields, has significantly broadened the possibility of manipulating microfluidic flow in LOC systems. 

(80) Externally applied electric field forces induce a fluid flow from the movement of ions in fluid terms as the “electro-osmotic flow” (EOF).Unique transport phenomena, such as enhanced flow velocity and flow instability, induced by non-Newtonian fluids, particularly viscoelastic fluids, under EOF, have sparked considerable interest in microfluidic devices with simple or complicated geometries within channels. 

(81) However, compared to the study of Newtonian fluids and even other electro-osmotic viscoelastic fluid flows, the literature focusing on the theoretical and numerical modeling of electro-osmotic blood flow is limited due to the complexity of blood properties. Consequently, to obtain a more comprehensive understanding of the complex blood flow behavior under EOF, theoretical and numerical studies of the transport phenomena in the EOF section will be based on the studies of different viscoelastic fluids under EOF rather than that of blood specifically. Despite this limitation, we believe these studies offer valuable insights that can help understand the complex behavior of blood flow under EOF.

4.1. EOF Phenomena

Electro-osmotic flow occurs at the interface between the microchannel wall and bulk phase solution. When in contact with the bulk phase, solution ions are absorbed or dissociated at the solid–liquid interface, resulting in the formation of a charge layer, as shown in Figure 4. This charged channel surface wall interacts with both negative and positive ions in the bulk sample, causing repulsion and attraction forces to create a thin layer of immobilized counterions, known as the Stern layer. The induced electric potential from the wall gradually decreases with an increase in the distance from the wall. The Stern layer potential, commonly termed the zeta potential, controls the intensity of the electrostatic interactions between mobile counterions and, consequently, the drag force from the applied electric field. Next to the Stern layer is the diffuse mobile layer, mainly composed of a mobile counterion. These two layers constitute the “electrical double layer” (EDL), the thickness of which is directly proportional to the ionic strength (concentration) of the bulk fluid. The relationship between the two parameters is characterized by a Debye length (λ

D), expressed as

𝜆𝐷=𝜖𝑘B𝑇2(𝑍𝑒)2𝑐0⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√��=��B�2(��)2�0

(15)where ϵ is the permittivity of the electrolyte solution, k

B is the Boltzmann constant, T is the electron temperature, Z is the integer valence number, e is the elementary charge, and c

0 is the ionic density.

Figure 4. Schematic diagram of an electro-osmotic flow in a microchannel with negative surface charge. (82) Reproduced with permission from ref (82). Copyright 2012 Woodhead Publishing.

When an electric field is applied perpendicular to the EDL, viscous drag is generated due to the movement of excess ions in the EDL. Electro-osmotic forces can be attributed to the externally applied electric potential (ϕ) and the zeta potential, the system wall induced potential by charged walls (ψ). As illustrated in Figure 4, the majority of ions in the bulk phase have a uniform velocity profile, except for a shear rate condition confined within an extremely thin Stern layer. Therefore, EOF displays a unique characteristic of a “near flat” or plug flow velocity profile, different from the parabolic flow typically induced by pressure-driven microfluidic flow (Hagen–Poiseuille flow). The plug-shaped velocity profile of the EOF possesses a high shear rate above the Stern layer.Overall, the EOF velocity magnitude is typically proportional to the Debye Length (λ

D), zeta potential, and magnitude of the externally applied electric field, while a more viscous liquid reduces the EOF velocity.

4.2. Modeling on Electro-osmotic Viscoelastic Fluid Flow

4.2.1. Theoretical Basis of EOF Mechanisms

The EOF of an incompressible viscoelastic fluid is commonly governed by the continuity and incompressible N–S equations, as shown in eqs 7 and 8, where the stress tensor and the electrostatic force term are coupled. The electro-osmotic body force term F, representing the body force exerted by the externally applied electric force, is defined as 

𝐹⇀=𝑝𝐸𝐸⇀�⇀=���⇀, where ρ

E and 

𝐸⇀�⇀ are the net electric charge density and the applied external electric field, respectively.Numerous models are established to theoretically study the externally applied electric potential and the system wall induced potential by charged walls. The following Laplace equation, expressed as eq 16, is generally adapted and solved to calculate the externally applied potential (ϕ).

∇2𝜙=0∇2�=0

(16)Ion diffusion under applied electric fields, together with mass transport resulting from convection and diffusion, transports ionic solutions in bulk flow under electrokinetic processes. The Nernst–Planck equation can describe these transport methods, including convection, diffusion, and electro-diffusion. Therefore, the Nernst–Planck equation is used to determine the distribution of the ions within the electrolyte. The electric potential induced by the charged channel walls follows the Poisson–Nernst–Plank (PNP) equation, which can be written as eq 17.

∇·[𝐷𝑖∇𝑛𝑖−𝑢⇀𝑛𝑖+𝑛𝑖𝐷𝑖𝑧𝑖𝑒𝑘𝑏𝑇∇(𝜙+𝜓)]=0∇·[��∇��−�⇀��+����������∇(�+�)]=0

(17)where D

in

i, and z

i are the diffusion coefficient, ionic concentration, and ionic valence of the ionic species I, respectively. However, due to the high nonlinearity and numerical stiffness introduced by different lengths and time scales from the PNP equations, the Poisson–Boltzmann (PB) model is often considered the major simplified method of the PNP equation to characterize the potential distribution of the EDL region in microchannels. In the PB model, it is assumed that the ionic species in the fluid follow the Boltzmann distribution. This model is typically valid for steady-state problems where charge transport can be considered negligible, the EDLs do not overlap with each other, and the intrinsic potentials are low. It provides a simplified representation of the potential distribution in the EDL region. The PB equation governing the EDL electric potential distribution is described as

∇2𝜓=(2𝑒𝑧𝑛0𝜀𝜀0)sinh(𝑧𝑒𝜓𝑘b𝑇)∇2�=(2���0��0)⁡sinh(����b�)

(18)where n

0 is the ion bulk concentration, z is the ionic valence, and ε

0 is the electric permittivity in the vacuum. Under low electric potential conditions, an even further simplified model to illustrate the EOF phenomena is the Debye–Hückel (DH) model. The DH model is derived by obtaining a charge density term by expanding the exponential term of the Boltzmann equation in a Taylor series.

4.2.2. EOF Modeling for Viscoelastic Fluids

Many studies through numerical modeling were performed to obtain a deeper understanding of the effect exhibited by externally applied electric fields on viscoelastic flow in microchannels under various geometrical designs. Bello et al. 

(83) found that methylcellulose solution, a non-Newtonian polymer solution, resulted in stronger electro-osmotic mobility in experiments when compared to the predictions by the Helmholtz–Smoluchowski equation, which is commonly used to define the velocity of EOF of a Newtonian fluid. Being one of the pioneers to identify the discrepancies between the EOF of Newtonian and non-Newtonian fluids, Bello et al. attributed such discrepancies to the presence of a very high shear rate in the EDL, resulting in a change in the orientation of the polymer molecules. Park and Lee 

(84) utilized the FVM to solve the PB equation for the characterization of the electric field induced force. In the study, the concept of fractional calculus for the Oldroyd-B model was adapted to illustrate the elastic and memory effects of viscoelastic fluids in a straight microchannel They observed that fluid elasticity and increased ratio of viscoelastic fluid contribution to overall fluid viscosity had a significant impact on the volumetric flow rate and sensitivity of velocity to electric field strength compared to Newtonian fluids. Afonso et al. 

(85) derived an analytical expression for EOF of viscoelastic fluid between parallel plates using the DH model to account for a zeta potential condition below 25 mV. The study established the understanding of the electro-osmotic viscoelastic fluid flow under low zeta potential conditions. Apart from the electrokinetic forces, pressure forces can also be coupled with EOF to generate a unique fluid flow behavior within the microchannel. Sousa et al. 

(86) analytically studied the flow of a standard viscoelastic solution by combining the pressure gradient force with an externally applied electric force. It was found that, at a near wall skimming layer and the outer layer away from the wall, macromolecules migrating away from surface walls in viscoelastic fluids are observed. In the study, the Phan-Thien Tanner (PTT) constitutive model is utilized to characterize the viscoelastic properties of the solution. The approach is found to be valid when the EDL is much thinner than the skimming layer under an enhanced flow rate. Zhao and Yang 

(87) solved the PB equation and Carreau model for the characterization of the EOF mechanism and non-Newtonian fluid respectively through the FEM. The numerical results depict that, different from the EOF of Newtonian fluids, non-Newtonian fluids led to an increase of electro-osmotic mobility for shear thinning fluids but the opposite for shear thickening fluids.Like other fluid transport driving forces, EOF within unique geometrical layouts also portrays unique transport phenomena. Pimenta and Alves 

(88) utilized the FVM to perform numerical simulations of the EOF of viscoelastic fluids considering the PB equation and the Oldroyd-B model, in a cross-slot and flow-focusing microdevices. It was found that electroelastic instabilities are formed due to the development of large stresses inside the EDL with streamlined curvature at geometry corners. Bezerra et al. 

(89) used the FDM to numerically analyze the vortex formation and flow instability from an electro-osmotic non-Newtonian fluid flow in a microchannel with a nozzle geometry and parallel wall geometry setting. The PNP equation is utilized to characterize the charge motion in the EOF and the PTT model for non-Newtonian flow characterization. A constriction geometry is commonly utilized in blood flow adapted in LOC systems due to the change in blood flow behavior under narrow dimensions in a microchannel. Ji et al. 

(90) recently studied the EOF of viscoelastic fluid in a constriction microchannel connected by two relatively big reservoirs on both ends (as seen in Figure 5) filled with the polyacrylamide polymer solution, a viscoelastic fluid, and an incompressible monovalent binary electrolyte solution KCl.

Figure 5. Schematic diagram of a negatively charged constriction microchannel connected to two reservoirs at both ends. An electro-osmotic flow is induced in the system by the induced potential difference between the anode and cathode. (90) Reproduced with permission from ref (90). Copyright 2021 The Authors, under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/.

In studying the EOF of viscoelastic fluids, the Oldroyd-B model is often utilized to characterize the polymeric stress tensor and the deformation rate of the fluid. The Oldroyd-B model is expressed as follows:

𝜏=𝜂p𝜆(𝐜−𝐈)�=�p�(�−�)

(19)where η

p, λ, c, and I represent the polymer dynamic viscosity, polymer relaxation time, symmetric conformation tensor of the polymer molecules, and the identity matrix, respectively.A log-conformation tensor approach is taken to prevent convergence difficulty induced by the viscoelastic properties. The conformation tensor (c) in the polymeric stress tensor term is redefined by a new tensor (Θ) based on the natural logarithm of the c. The new tensor is defined as

Θ=ln(𝐜)=𝐑ln(𝚲)𝐑Θ=ln(�)=�⁡ln(�)�

(20)in which Λ is the diagonal matrix and R is the orthogonal matrix.Under the new conformation tensor, the induced EOF of a viscoelastic fluid is governed by the continuity and N–S equations adapting the Oldroyd-B model, which is expressed as

∂𝚯∂𝑡+𝐮·∇𝚯=𝛀Θ−ΘΩ+2𝐁+1𝜆(eΘ−𝐈)∂�∂�+�·∇�=�Θ−ΘΩ+2�+1�(eΘ−�)

(21)where Ω and B represent the anti-symmetric matrix and the symmetric traceless matrix of the decomposition of the velocity gradient tensor ∇u, respectively. The conformation tensor can be recovered by c = exp(Θ). The PB model and Laplace equation are utilized to characterize the charged channel wall induced potential and the externally applied potential.The governing equations are numerically solved through the FVM by RheoTool, 

(42) an open-source viscoelastic EOF solver on the OpenFOAM platform. A SIMPLEC (Semi-Implicit Method for Pressure Linked Equations-Consistent) algorithm was applied to solve the velocity-pressure coupling. The pressure field and velocity field were computed by the PCG (Preconditioned Conjugate Gradient) solver and the PBiCG (Preconditioned Biconjugate Gradient) solver, respectively.Ranging magnitudes of an applied electric field or fluid concentration induce both different streamlines and velocity magnitudes at various locations and times of the microchannel. In the study performed by Ji et al., 

(90) notable fluctuation of streamlines and vortex formation is formed at the upper stream entrance of the constriction as shown in Figure 6(a) and (b), respectively, due to the increase of electrokinetic effect, which is seen as a result of the increase in polymeric stress (τ

xx). 

(90) The contraction geometry enhances the EOF velocity within the constriction channel under high E

app condition (600 V/cm). Such phenomena can be attributed to the dependence of electro-osmotic viscoelastic fluid flow on the system wall surface and bulk fluid properties. 

(91)

Figure 6. Schematic diagram of vortex formation and streamlines of EOF depicting flow instability at (a) 1.71 s and (b) 1.75 s. Spatial distribution of the elastic normal stress at (c) high Eapp condition. Streamline of an electro-osmotic flow under Eapp of 600 V/cm (90) for (d) non-Newtonian and (e) Newtonian fluid through a constriction geometry. Reproduced with permission from ref (90). Copyright 2021 The Authors, under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/.

As elastic normal stress exceeds the local shear stress, flow instability and vortex formation occur. The induced elastic stress under EOF not only enhances the instability of the flow but often generates an irregular secondary flow leading to strong disturbance. 

(92) It is also vital to consider the effect of the constriction layout of microchannels on the alteration of the field strength within the system. The contraction geometry enhances a larger electric field strength compared with other locations of the channel outside the constriction region, resulting in a higher velocity gradient and stronger extension on the polymer within the viscoelastic solution. Following the high shear flow condition, a higher magnitude of stretch for polymer molecules in viscoelastic fluids exhibits larger elastic stresses and enhancement of vortex formation at the region. 

(93)As shown in Figure 6(c), significant elastic normal stress occurs at the inlet of the constriction microchannel. Such occurrence of a polymeric flow can be attributed to the dominating elongational flow, giving rise to high deformation of the polymers within the viscoelastic fluid flow, resulting in higher elastic stress from the polymers. Such phenomena at the entrance result in the difference in velocity streamline as circled in Figure 6(d) compared to that of the Newtonian fluid at the constriction entrance in Figure 6(e). 

(90) The difference between the Newtonian and polymer solution at the exit, as circled in Figure 6(d) and (e), can be attributed to the extrudate swell effect of polymers 

(94) within the viscoelastic fluid flow. The extrudate swell effect illustrates that, as polymers emerge from the constriction exit, they tend to contract in the flow direction and grow in the normal direction, resulting in an extrudate diameter greater than the channel size. The deformation of polymers within the polymeric flow at both the entrance and exit of the contraction channel facilitates the change in shear stress conditions of the flow, leading to the alteration in streamlines of flows for each region.

4.3. EOF Applications in LOC Systems

4.3.1. Mixing in LOC Systems

Rather than relying on the micromixing controlled by molecular diffusion under low Reynolds number conditions, active mixers actively leverage convective instability and vortex formation induced by electro-osmotic flows from alternating current (AC) or direct current (DC) electric fields. Such adaptation is recognized as significant breakthroughs for promotion of fluid mixing in chemical and biological applications such as drug delivery, medical diagnostics, chemical synthesis, and so on. 

(95)Many researchers proposed novel designs of electro-osmosis micromixers coupled with numerical simulations in conjunction with experimental findings to increase their understanding of the role of flow instability and vortex formation in the mixing process under electrokinetic phenomena. Matsubara and Narumi 

(96) numerically modeled the mixing process in a microchannel with four electrodes on each side of the microchannel wall, which generated a disruption through unstable electro-osmotic vortices. It was found that particle mixing was sensitive to both the convection effect induced by the main and secondary vortex within the micromixer and the change in oscillation frequency caused by the supplied AC voltage when the Reynolds number was varied. Qaderi et al. 

(97) adapted the PNP equation to numerically study the effect of the geometry and zeta potential configuration of the microchannel on the mixing process with a combined electro-osmotic pressure driven flow. It was reported that the application of heterogeneous zeta potential configuration enhances the mixing efficiency by around 23% while the height of the hurdles increases the mixing efficiency at most 48.1%. Cho et al. 

(98) utilized the PB model and Laplace equation to numerically simulate the electro-osmotic non-Newtonian fluid mixing process within a wavy and block layout of microchannel walls. The Power Law model is adapted to describe the fluid rheological characteristic. It was found that shear-thinning fluids possess a higher volumetric flow rate, which could result in poorer mixing efficiency compared to that of Newtonian fluids. Numerous studies have revealed that flow instability and vortex generation, in particular secondary vortices produced by barriers or greater magnitudes of heterogeneous zeta potential distribution, enhance mixing by increasing bulk flow velocity and reducing flow distance.To better understand the mechanism of disturbance formed in the system due to externally applied forces, known as electrokinetic instability, literature often utilize the Rayleigh (Ra) number, 

(1) as described below:

𝑅𝑎𝑣=𝑢ev𝑢eo=(𝛾−1𝛾+1)2𝑊𝛿2𝐸el2𝐻2𝜁𝛿Ra�=�ev�eo=(�−1�+1)2��2�el2�2��

(22)where γ is the conductivity ratio of the two streams and can be written as 

𝛾=𝜎el,H𝜎el,L�=�el,H�el,L. The Ra number characterizes the ratio between electroviscous and electro-osmotic flow. A high Ra

v value often results in good mixing. It is evident that fluid properties such as the conductivity (σ) of the two streams play a key role in the formation of disturbances to enhance mixing in microsystems. At the same time, electrokinetic parameters like the zeta potential (ζ) in the Ra number is critical in the characterization of electro-osmotic velocity and a slip boundary condition at the microchannel wall.To understand the mixing result along the channel, the concentration field can be defined and simulated under the assumption of steady state conditions and constant diffusion coefficient for each of the working fluid within the system through the convection–diffusion equation as below:

∂𝑐𝒊∂𝑡+∇⇀(𝑐𝑖𝑢⇀−𝐷𝑖∇⇀𝑐𝒊)=0∂��∂�+∇⇀(���⇀−��∇⇀��)=0

(23)where c

i is the species concentration of species i and D

i is the diffusion coefficient of the corresponding species.The standard deviation of concentration (σ

sd) can be adapted to evaluate the mixing quality of the system. 

(97) The standard deviation for concentration at a specific portion of the channel may be calculated using the equation below:

𝜎sd=∫10(𝐶∗(𝑦∗)−𝐶m)2d𝑦∗∫10d𝑦∗⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯�sd=∫01(�*(�*)−�m)2d�*∫01d�*

(24)where C*(y*) and C

m are the non-dimensional concentration profile and the mean concentration at the portion, respectively. C* is the non-dimensional concentration and can be calculated as 

𝐶∗=𝐶𝐶ref�*=��ref, where C

ref is the reference concentration defined as the bulk solution concentration. The mean concentration profile can be calculated as 

𝐶m=∫10(𝐶∗(𝑦∗)d𝑦∗∫10d𝑦∗�m=∫01(�*(�*)d�*∫01d�*. With the standard deviation of concentration, the mixing efficiency 

(97) can then be calculated as below:

𝜀𝑥=1−𝜎sd𝜎sd,0��=1−�sd�sd,0

(25)where σ

sd,0 is the standard derivation of the case of no mixing. The value of the mixing efficiency is typically utilized in conjunction with the simulated flow field and concentration field to explore the effect of geometrical and electrokinetic parameters on the optimization of the mixing results.

5. Summary

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5.1. Conclusion

Viscoelastic fluids such as blood flow in LOC systems are an essential topic to proceed with diagnostic analysis and research through microdevices in the biomedical and pharmaceutical industries. The complex blood flow behavior is tightly controlled by the viscoelastic characteristics of blood such as the dynamic viscosity and the elastic property of RBCs under various shear rate conditions. Furthermore, the flow behaviors under varied driving forces promote an array of microfluidic transport phenomena that are critical to the management of blood flow and other adapted viscoelastic fluids in LOC systems. This review addressed the blood flow phenomena, the complicated interplay between shear rate and blood flow behaviors, and their numerical modeling under LOC systems through the lens of the viscoelasticity characteristic. Furthermore, a theoretical understanding of capillary forces and externally applied electric forces leads to an in-depth investigation of the relationship between blood flow patterns and the key parameters of the two driving forces, the latter of which is introduced through the lens of viscoelastic fluids, coupling numerical modeling to improve the knowledge of blood flow manipulation in LOC systems. The flow disturbances triggered by the EOF of viscoelastic fluids and their impact on blood flow patterns have been deeply investigated due to their important role and applications in LOC devices. Continuous advancements of various numerical modeling methods with experimental findings through more efficient and less computationally heavy methods have served as an encouraging sign of establishing more accurate illustrations of the mechanisms for multiphase blood and other viscoelastic fluid flow transport phenomena driven by various forces. Such progress is fundamental for the manipulation of unique transport phenomena, such as the generated disturbances, to optimize functionalities offered by microdevices in LOC systems.

The following section will provide further insights into the employment of studied blood transport phenomena to improve the functionality of micro devices adapting LOC technology. A discussion of the novel roles that external driving forces play in microfluidic flow behaviors is also provided. Limitations in the computational modeling of blood flow and electrokinetic phenomena in LOC systems will also be emphasized, which may provide valuable insights for future research endeavors. These discussions aim to provide guidance and opportunities for new paths in the ongoing development of LOC devices that adapt blood flow.

5.2. Future Directions

5.2.1. Electro-osmosis Mixing in LOC Systems

Despite substantial research, mixing results through flow instability and vortex formation phenomena induced by electro-osmotic mixing still deviate from the effective mixing results offered by chaotic mixing results such as those seen in turbulent flows. However, recent discoveries of a mixing phenomenon that is generally observed under turbulent flows are found within electro-osmosis micromixers under low Reynolds number conditions. Zhao 

(99) experimentally discovered a rapid mixing process in an AC applied micromixer, where the power spectrum of concentration under an applied voltage of 20 V

p-p induces a −5/3 slope within a frequency range. This value of the slope is considered as the O–C spectrum in macroflows, which is often visible under relatively high Re conditions, such as the Taylor microscale Reynolds number Re > 500 in turbulent flows. 

(100) However, the Re value in the studied system is less than 1 at the specific location and applied voltage. A secondary flow is also suggested to occur close to microchannel walls, being attributed to the increase of convective instability within the system.Despite the experimental phenomenon proposed by Zhao et al., 

(99) the range of effects induced by vital parameters of an EOF mixing system on the enhanced mixing results and mechanisms of disturbance generated by the turbulent-like flow instability is not further characterized. Such a gap in knowledge may hinder the adaptability and commercialization of the discovery of micromixers. One of the parameters for further evaluation is the conductivity gradient of the fluid flow. A relatively strong conductivity gradient (5000:1) was adopted in the system due to the conductive properties of the two fluids. The high conductivity gradients may contribute to the relatively large Rayleigh number and differences in EDL layer thickness, resulting in an unusual disturbance in laminar flow conditions and enhanced mixing results. However, high conductivity gradients are not always achievable by the working fluids due to diverse fluid properties. The reliance on turbulent-like phenomena and rapid mixing results in a large conductivity gradient should be established to prevent the limited application of fluids for the mixing system. In addition, the proposed system utilizes distinct zeta potential distributions at the top and bottom walls due to their difference in material choices, which may be attributed to the flow instability phenomena. Further studies should be made on varying zeta potential magnitude and distribution to evaluate their effect on the slip boundary conditions of the flow and the large shear rate condition close to the channel wall of EOF. Such a study can potentially offer an optimized condition in zeta potential magnitude through material choices and geometrical layout of the zeta potential for better mixing results and manipulation of mixing fluid dynamics. The two vital parameters mentioned above can be varied with the aid of numerical simulation to understand the effect of parameters on the interaction between electro-osmotic forces and electroviscous forces. At the same time, the relationship of developed streamlines of the simulated velocity and concentration field, following their relationship with the mixing results, under the impact of these key parameters can foster more insight into the range of impact that the two parameters have on the proposed phenomena and the microfluidic dynamic principles of disturbances.

In addition, many of the current investigations of electrokinetic mixers commonly emphasize the fluid dynamics of mixing for Newtonian fluids, while the utilization of biofluids, primarily viscoelastic fluids such as blood, and their distinctive response under shear forces in these novel mixing processes of LOC systems are significantly less studied. To develop more compatible microdevice designs and efficient mixing outcomes for the biomedical industry, it is necessary to fill the knowledge gaps in the literature on electro-osmotic mixing for biofluids, where properties of elasticity, dynamic viscosity, and intricate relationship with shear flow from the fluid are further considered.

5.2.2. Electro-osmosis Separation in LOC Systems

Particle separation in LOC devices, particularly in biological research and diagnostics, is another area where disturbances may play a significant role in optimization. 

(101) Plasma analysis in LOC systems under precise control of blood flow phenomena and blood/plasma separation procedures can detect vital information about infectious diseases from particular antibodies and foreign nucleic acids for medical treatments, diagnostics, and research, 

(102) offering more efficient results and simple operating procedures compared to that of the traditional centrifugation method for blood and plasma separation. However, the adaptability of LOC devices for blood and plasma separation is often hindered by microchannel clogging, where flow velocity and plasma yield from LOC devices is reduced due to occasional RBC migration and aggregation at the filtration entrance of microdevices. 

(103)It is important to note that the EOF induces flow instability close to microchannel walls, which may provide further solutions to clogging for the separation process of the LOC systems. Mohammadi et al. 

(104) offered an anti-clogging effect of RBCs at the blood and plasma separating device filtration entry, adjacent to the surface wall, through RBC disaggregation under high shear rate conditions generated by a forward and reverse EOF direction.

Further theoretical and numerical research can be conducted to characterize the effect of high shear rate conditions near microchannel walls toward the detachment of binding blood cells on surfaces and the reversibility of aggregation. Through numerical modeling with varying electrokinetic parameters to induce different degrees of disturbances or shear conditions at channel walls, it may be possible to optimize and better understand the process of disrupting the forces that bind cells to surface walls and aggregated cells at filtration pores. RBCs that migrate close to microchannel walls are often attracted by the adhesion force between the RBC and the solid surface originating from the van der Waals forces. Following RBC migration and attachment by adhesive forces adjacent to the microchannel walls as shown in Figure 7, the increase in viscosity at the region causes a lower shear condition and encourages RBC aggregation (cell–cell interaction), which clogs filtering pores or microchannels and reduces flow velocity at filtration region. Both the impact that shear forces and disturbances may induce on cell binding forces with surface walls and other cells leading to aggregation may suggest further characterization. Kinetic parameters such as activation energy and the rate-determining step for cell binding composition attachment and detachment should be considered for modeling the dynamics of RBCs and blood flows under external forces in LOC separation devices.

Figure 7. Schematic representations of clogging at a microchannel pore following the sequence of RBC migration, cell attachment to channel walls, and aggregation. (105) Reproduced with permission from ref (105). Copyright 2018 The Authors under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/.

5.2.3. Relationship between External Forces and Microfluidic Systems

In blood flow, a thicker CFL suggests a lower blood viscosity, suggesting a complex relationship between shear stress and shear rate, affecting the blood viscosity and blood flow. Despite some experimental and numerical studies on electro-osmotic non-Newtonian fluid flow, limited literature has performed an in-depth investigation of the role that applied electric forces and other external forces could play in the process of CFL formation. Additional studies on how shear rates from external forces affect CFL formation and microfluidic flow dynamics can shed light on the mechanism of the contribution induced by external driving forces to the development of a separate phase of layer, similar to CFL, close to the microchannel walls and distinct from the surrounding fluid within the system, then influencing microfluidic flow dynamics.One of the mechanisms of phenomena to be explored is the formation of the Exclusion Zone (EZ) region following a “Self-Induced Flow” (SIF) phenomenon discovered by Li and Pollack, 

(106) as shown in Figure 8(a) and (b), respectively. A spontaneous sustained axial flow is observed when hydrophilic materials are immersed in water, resulting in the buildup of a negative layer of charges, defined as the EZ, after water molecules absorb infrared radiation (IR) energy and break down into H and OH

+.

Figure 8. Schematic representations of (a) the Exclusion Zone region and (b) the Self Induced Flow through visualization of microsphere movement within a microchannel. (106) Reproduced with permission from ref (106). Copyright 2020 The Authors under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/.

Despite the finding of such a phenomenon, the specific mechanism and role of IR energy have yet to be defined for the process of EZ development. To further develop an understanding of the role of IR energy in such phenomena, a feasible study may be seen through the lens of the relationships between external forces and microfluidic flow. In the phenomena, the increase of SIF velocity under a rise of IR radiation resonant characteristics is shown in the participation of the external electric field near the microchannel walls under electro-osmotic viscoelastic fluid flow systems. The buildup of negative charges at the hydrophilic surfaces in EZ is analogous to the mechanism of electrical double layer formation. Indeed, research has initiated the exploration of the core mechanisms for EZ formation through the lens of the electrokinetic phenomena. 

(107) Such a similarity of the role of IR energy and the transport phenomena of SIF with electrokinetic phenomena paves the way for the definition of the unknown SIF phenomena and EZ formation. Furthermore, Li and Pollack 

(106) suggest whether CFL formation might contribute to a SIF of blood using solely IR radiation, a commonly available source of energy in nature, as an external driving force. The proposition may be proven feasible with the presence of the CFL region next to the negatively charged hydrophilic endothelial glycocalyx layer, coating the luminal side of blood vessels. 

(108) Further research can dive into the resonating characteristics between the formation of the CFL region next to the hydrophilic endothelial glycocalyx layer and that of the EZ formation close to hydrophilic microchannel walls. Indeed, an increase in IR energy is known to rapidly accelerate EZ formation and SIF velocity, depicting similarity to the increase in the magnitude of electric field forces and greater shear rates at microchannel walls affecting CFL formation and EOF velocity. Such correlation depicts a future direction in whether SIF blood flow can be observed and characterized theoretically further through the lens of the relationship between blood flow and shear forces exhibited by external energy.

The intricate link between the CFL and external forces, more specifically the externally applied electric field, can receive further attention to provide a more complete framework for the mechanisms between IR radiation and EZ formation. Such characterization may also contribute to a greater comprehension of the role IR can play in CFL formation next to the endothelial glycocalyx layer as well as its role as a driving force to propel blood flow, similar to the SIF, but without the commonly assumed pressure force from heart contraction as a source of driving force.

5.3. Challenges

Although there have been significant improvements in blood flow modeling under LOC systems over the past decade, there are still notable constraints that may require special attention for numerical simulation applications to benefit the adaptability of the designs and functionalities of LOC devices. Several points that require special attention are mentioned below:

1.The majority of CFD models operate under the relationship between the viscoelasticity of blood and the shear rate conditions of flow. The relative effect exhibited by the presence of highly populated RBCs in whole blood and their forces amongst the cells themselves under complex flows often remains unclearly defined. Furthermore, the full range of cell populations in whole blood requires a much more computational load for numerical modeling. Therefore, a vital goal for future research is to evaluate a reduced modeling method where the impact of cell–cell interaction on the viscoelastic property of blood is considered.
2.Current computational methods on hemodynamics rely on continuum models based upon non-Newtonian rheology at the macroscale rather than at molecular and cellular levels. Careful considerations should be made for the development of a constructive framework for the physical and temporal scales of micro/nanoscale systems to evaluate the intricate relationship between fluid driving forces, dynamic viscosity, and elasticity.
3.Viscoelastic fluids under the impact of externally applied electric forces often deviate from the assumptions of no-slip boundary conditions due to the unique flow conditions induced by externally applied forces. Furthermore, the mechanism of vortex formation and viscoelastic flow instability at laminar flow conditions should be better defined through the lens of the microfluidic flow phenomenon to optimize the prediction of viscoelastic flow across different geometrical layouts. Mathematical models and numerical methods are needed to better predict such disturbance caused by external forces and the viscoelasticity of fluids at such a small scale.
4.Under practical situations, zeta potential distribution at channel walls frequently deviates from the common assumption of a constant distribution because of manufacturing faults or inherent surface charges prior to the introduction of electrokinetic influence. These discrepancies frequently lead to inconsistent surface potential distribution, such as excess positive ions at relatively more negatively charged walls. Accordingly, unpredicted vortex formation and flow instability may occur. Therefore, careful consideration should be given to these discrepancies and how they could trigger the transport process and unexpected results of a microdevice.

Author Information

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  • Corresponding Authors
    • Zhe Chen – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Email: zaccooky@sjtu.edu.cn
    • Bo Ouyang – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Email: bouy93@sjtu.edu.cn
    • Zheng-Hong Luo – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Orcidhttps://orcid.org/0000-0001-9011-6020; Email: luozh@sjtu.edu.cn
  • Authors
    • Bin-Jie Lai – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Orcidhttps://orcid.org/0009-0002-8133-5381
    • Li-Tao Zhu – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Orcidhttps://orcid.org/0000-0001-6514-8864
  • NotesThe authors declare no competing financial interest.

Acknowledgments

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This work was supported by the National Natural Science Foundation of China (No. 22238005) and the Postdoctoral Research Foundation of China (No. GZC20231576).

Vocabulary

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Microfluidicsthe field of technological and scientific study that investigates fluid flow in channels with dimensions between 1 and 1000 μm
Lab-on-a-Chip Technologythe field of research and technological development aimed at integrating the micro/nanofluidic characteristics to conduct laboratory processes on handheld devices
Computational Fluid Dynamics (CFD)the method utilizing computational abilities to predict physical fluid flow behaviors mathematically through solving the governing equations of corresponding fluid flows
Shear Ratethe rate of change in velocity where one layer of fluid moves past the adjacent layer
Viscoelasticitythe property holding both elasticity and viscosity characteristics relying on the magnitude of applied shear stress and time-dependent strain
Electro-osmosisthe flow of fluid under an applied electric field when charged solid surface is in contact with the bulk fluid
Vortexthe rotating motion of a fluid revolving an axis line

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Figure 4. Rectangular stepped spillway with (a) three baffle arrangement (b) five baffle arrangement

Prediction of Energy Dissipation over Stepped Spillwaywith Baffles Using Machine Learning Techniques

Saurabh Pujari*
, Vijay Kaushik, S. Anbu Kumar
Department of Civil Engineering, Delhi Technological University, India
Received February 23, 2023; Revised April 25, 2023; Accepted June 11, 2023
Cite This Paper in the Following Citation Styles
(a): [1] Saurabh Pujari, Vijay Kaushik, S. Anbu Kumar , “Prediction of Energy Dissipation over Stepped Spillway with
Baffles Using Machine Learning Techniques,” Civil Engineering and Architecture, Vol. 11, No. 5, pp. 2377 – 2391, 2023.
DOI: 10.13189/cea.2023.110510.
(b): Saurabh Pujari, Vijay Kaushik, S. Anbu Kumar (2023). Prediction of Energy Dissipation over Stepped Spillway with
Baffles Using Machine Learning Techniques. Civil Engineering and Architecture, 11(5), 2377 – 2391. DOI:
10.13189/cea.2023.110510.
Copyright©2023 by authors, all rights reserved. Authors agree that this article remains permanently open access under
the terms of the Creative Commons Attribution License 4.0 International License

Abstract

In river engineering, the stepped spillway of a dam is an important component that may be used in various ways. It is necessary to conduct research dealing with flood control in order to investigate the method, in which energy is lost along the tiered spillways. In the past, several research projects on stepped spillways without baffles have been carried out utilizing a range of research approaches. In the present study, machine learning techniques such as Support Vector Machine (SVM) and Regression Tree (RT) are used to analyze the energy dissipation on rectangular stepped spillways that make use of baffles in a variety of configurations and at a range of channel slopes. The results of many experiments indicate that the amount of energy that is lost increases with the number of baffles that are present in flat channels with slopes and rises. In order to evaluate the efficiency and usefulness of the suggested model, the statistical indices that were developed for the experimental research are used to validate the models that were created for the study. The findings indicate that the suggested SVM model properly predicted the amount of energy that was dissipated when contrasted with RT and the method that had been developed in the past. This study verifies the use of machine learning techniques in this industry, and it is unique in that it anticipates energy dissipation along stepped spillways utilizing baffle designs. In addition, this work validates the use of machine learning methods in this field.

Keywords

Rectangular Stepped Spillways, Baffle Arrangements, Channel Slope, Support Vector Machine (SVM), Regression Tree (RT)

Introduction

To regulate water flows downstream of a dam, a spillway structure is employed, with stepped spillways preventing water from overflowing and causing damage to the dam. These spillways consist of a channel with built-in steps or drops. Flow patterns observed include nappe flow, transition flow, and skimming flow [1]. Numerous scholars have looked at the energy dissipation in stepped spillways [2-4]. Boes and Hager [5] looked at the benefits of stepped spillways, such as their simplicity of construction, less danger of cavitation, and smaller stilling basins at downstream dam toes owing to considerable energy loss along the chute. Hazzab and Chafic [7] conducted an experimental study on energy dissipation in stepped spillways and reported on flow configurations. Additionally, the Manksvill dam spillway was examined using a 1:25 scale physical wooden model [6]. For moderately inclined stepped channels, Stefan and Chanson [8] explored air-water flow measurements. Daniel [9] discussed how the existence of steps and step heights affect stepped spillways’ ability to dissipate energy. A comparison of the smooth invert chute flow with the self aerated stepped spillway. The energy dissipation in stepped spillways was investigated using various methods. Katourany [10] compared experimental findings to conventional USBR outcomes to examine the effects of different baffle widths, spacing between baffle rows, and step heights of baffled aprons. Salmasi et al. [11] assessed the energy dissipation of through-flow and over-flow in gabion stepped spillways, discovering that gabion spillways with pervious surfaces dissipated energy more efficiently than those with concrete walls. Other forms of stepped spillways, such as inclined steps and steps with end sills, were also quantitatively studied for energy dissipation [12]. Saedi and Asareh [13] examined how the number of drop stairs affected energy dissipation in stepped drops and suggested using stepped drops to increase energy dissipation by providing flow path roughness. Al-Husseini [14] found that decreasing the number of steps and downstream slopes led to an increase in flow energy dissipation, and that the use of cascade spillways reduced energy dissipation compared to the original step spillway. MARS and ANN methods were used to estimate energy dissipation in flow across stepped spillways under skimming flow conditions, with both models proving reliable [15]. Frederic et al. [16] evaluated the energy dissipation effectiveness and stability of the Mekin Dam spillway by confirming that flow did not result in transitional flow and by calculating safety factors at various intervals. A numerical model was developed to validate a physical model examining the impact of geometrical parameters on the dissipation rate in flows through stepped spillways [17]. The regulation of the rates of dissipation is studied using a particular kind of fuzzy inference system (FIS). The findings are compared with a predefined numerical database to determine the predicted energy dissipation under various circumstances. The findings show that the suggested FIS may be a useful tool for the operational management of dissipator structures while taking various geometric characteristics into account. Nasralla [18] studied the four phases of the spillway and conducted eighteen runs to enhance energy dissipation through the contraction-stepped spillway. The study considered alternative baffle placements, heights, and widths. The results showed that downstream baffles on the stepped spillway of the stilling basin improve energy dissipation. Using the Flow 3D software, Ikinciogullari [19] quantitatively analyzed the energy dissipation capabilities of trapezoidal stepped spillways using four distinct models and three different discharges. The findings showed that trapezoidal stepped spillways are up to 30% more efficient in dissipating energy than traditional stepped spillways. In previous works, only a few machine learning algorithms were used to forecast energy dissipation across a rectangular stepped spillway without baffles. Therefore, this study used machine learning approaches such as Support Vector Machine (SVM) and Regression Tree (RT) to predict energy dissipation across a rectangular stepped spillway with varied rectangular-shaped baffle configurations at different channel slopes. The study compared these models using statistical analysis to assess their efficiency in predicting energy dissipation over rectangular stepped spillways with baffles. 2. Materials and Methods 2.1. Experimental Setup The experiments were carried out at the Hydraulics laboratory of Delhi Technological University. The tests were performed in a rectangular tilting flume of 8m long, 0.30m wide and 0.40m deep which has a facility to make it horizontal and sloping as well (shown in Figure 1). The flume consists of an inlet section, an outlet section, and a collecting tank at the downstream end which is used to measure the discharge. Figure 2 depicts the model of a rectangular stepped spillway prepared using an acrylic sheet having a width of 0.30m, a height of 0.20m and a base length of 0.40m. A total of four steps were designed with a step height of 0.05m, the step length is 0.10m and rectangular-shaped baffles of length 0.10m and height of 0.05m were arranged in different manner. Figure 3 represents the different baffle arrangements used in the experimental work. At first, the experiment was conducted for no baffle condition. Thereafter the experiment was conducted for the first arrangement of three baffles, in which two baffles were placed at a distance of 0.10m from the toe of the spillway and a distance of 0.10m was maintained between the first two baffles and the third baffle was placed between the first two baffles at a distance of 0.20m from the toe of the spillway (figure 4a). After that, the experiment was conducted for the third arrangement of baffles which consists of five baffles, two more baffles were introduced at a distance of 0.30m from the toe of the spillway and a distance of 0.10m was maintained between them (figure 4b). The baffles used in the experiment were rectangular shaped which had a height of 0.05m and length of 0.10m. The experiments were conducted for five different discharges 2 l/s, 4 l/s, 6 l/s, 8 l/s and 10 l/s. For the purpose of determining the head values both upstream and downstream of the spillway model, a point gauge with a precision of 0.1mm was used. In order to determine the average velocities of the upstream and downstream portions, respectively, a pitot static tube was used in conjunction with a digital manometer.

Figure 1. Rectangular tilting flume
Figure 2. Dimensions of classical stepped spillway
Figure 3. Arrangements of baffles in classical stepped spillway
Figure 4. Rectangular stepped spillway with (a) three baffle arrangement (b) five baffle arrangement
Predicting solid-state phase transformations during metal additive manufacturing: A case study on electron-beam powder bed fusion of Inconel-738

Predicting solid-state phase transformations during metal additive manufacturing: A case study on electron-beam powder bed fusion of Inconel-738

금속 적층 제조 중 고체 상 변형 예측: Inconel-738의 전자빔 분말층 융합에 대한 사례 연구

Nana Kwabena Adomako a, Nima Haghdadi a, James F.L. Dingle bc, Ernst Kozeschnik d, Xiaozhou Liao bc, Simon P. Ringer bc, Sophie Primig a

Abstract

Metal additive manufacturing (AM) has now become the perhaps most desirable technique for producing complex shaped engineering parts. However, to truly take advantage of its capabilities, advanced control of AM microstructures and properties is required, and this is often enabled via modeling. The current work presents a computational modeling approach to studying the solid-state phase transformation kinetics and the microstructural evolution during AM. Our approach combines thermal and thermo-kinetic modelling. A semi-analytical heat transfer model is employed to simulate the thermal history throughout AM builds. Thermal profiles of individual layers are then used as input for the MatCalc thermo-kinetic software. The microstructural evolution (e.g., fractions, morphology, and composition of individual phases) for any region of interest throughout the build is predicted by MatCalc. The simulation is applied to an IN738 part produced by electron beam powder bed fusion to provide insights into how γ′ precipitates evolve during thermal cycling. Our simulations show qualitative agreement with our experimental results in predicting the size distribution of γ′ along the build height, its multimodal size character, as well as the volume fraction of MC carbides. Our findings indicate that our method is suitable for a range of AM processes and alloys, to predict and engineer their microstructures and properties.

Graphical Abstract

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Keywords

Additive manufacturing, Simulation, Thermal cycles, γ′ phase, IN738

1. Introduction

Additive manufacturing (AM) is an advanced manufacturing method that enables engineering parts with intricate shapes to be fabricated with high efficiency and minimal materials waste. AM involves building up 3D components layer-by-layer from feedstocks such as powder [1]. Various alloys, including steel, Ti, Al, and Ni-based superalloys, have been produced using different AM techniques. These techniques include directed energy deposition (DED), electron- and laser powder bed fusion (E-PBF and L-PBF), and have found applications in a variety of industries such as aerospace and power generation [2][3][4]. Despite the growing interest, certain challenges limit broader applications of AM fabricated components in these industries and others. One of such limitations is obtaining a suitable and reproducible microstructure that offers the desired mechanical properties consistently. In fact, the AM as-built microstructure is highly complex and considerably distinctive from its conventionally processed counterparts owing to the complicated thermal cycles arising from the deposition of several layers upon each other [5][6].

Several studies have reported that the solid-state phases and solidification microstructure of AM processed alloys such as CMSX-4, CoCr [7][8], Ti-6Al-4V [9][10][11]IN738 [6]304L stainless steel [12], and IN718 [13][14] exhibit considerable variations along the build direction. For instance, references [9][10] have reported that there is a variation in the distribution of α and β phases along the build direction in Ti-alloys. Similarly, the microstructure of an L-PBF fabricated martensitic steel exhibits variations in the fraction of martensite [15]. Furthermore, some of the present authors and others [6][16][17][18][19][20] have recently reviewed and reported that there is a difference in the morphology and fraction of nanoscale precipitates as a function of build height in Ni-based superalloys. These non-uniformities in the as-built microstructure result in an undesired heterogeneity in mechanical and other important properties such as corrosion and oxidation [19][21][22][23]. To obtain the desired microstructure and properties, additional processing treatments are utilized, but this incurs extra costs and may lead to precipitation of detrimental phases and grain coarsening. Therefore, a through-process understanding of the microstructure evolution under repeated heating and cooling is now needed to further advance 3D printed microstructure and property control.

It is now commonly understood that the microstructure evolution during printing is complex, and most AM studies concentrate on the microstructure and mechanical properties of the final build only. Post-printing studies of microstructure characteristics at room temperature miss crucial information on how they evolve. In-situ measurements and modelling approaches are required to better understand the complex microstructural evolution under repeated heating and cooling. Most in-situ measurements in AM focus on monitoring the microstructural changes, such as phase transformations and melt pool dynamics during fabrication using X-ray scattering and high-speed X-ray imaging [24][25][26][27]. For example, Zhao et al. [25] measured the rate of solidification and described the α/β phase transformation during L-PBF of Ti-6Al-4V in-situ. Also, Wahlmann et al. [21] recently used an L-PBF machine coupled with X-ray scattering to investigate the changes in CMSX-4 phase during successive melting processes. Although these techniques provide significant understanding of the basic principles of AM, they are not widely accessible. This is due to the great cost of the instrument, competitive application process, and complexities in terms of the experimental set-up, data collection, and analysis [26][28].

Computational modeling techniques are promising and more widely accessible tools that enable advanced understanding, prediction, and engineering of microstructures and properties during AM. So far, the majority of computational studies have concentrated on physics based process models for metal AM, with the goal of predicting the temperature profile, heat transfer, powder dynamics, and defect formation (e.g., porosity) [29][30]. In recent times, there have been efforts in modeling of the AM microstructure evolution using approaches such as phase-field [31], Monte Carlo (MC) [32], and cellular automata (CA) [33], coupled with finite element simulations for temperature profiles. However, these techniques are often restricted to simulating the evolution of solidification microstructures (e.g., grain and dendrite structure) and defects (e.g., porosity). For example, Zinovieva et al. [33] predicted the grain structure of L-PBF Ti-6Al-4V using finite difference and cellular automata methods. However, studies on the computational modelling of the solid-state phase transformations, which largely determine the resulting properties, remain limited. This can be attributed to the multi-component and multi-phase nature of most engineering alloys in AM, along with the complex transformation kinetics during thermal cycling. This kind of research involves predictions of the thermal cycle in AM builds, and connecting it to essential thermodynamic and kinetic data as inputs for the model. Based on the information provided, the thermokinetic model predicts the history of solid-state phase microstructure evolution during deposition as output. For example, a multi-phase, multi-component mean-field model has been developed to simulate the intermetallic precipitation kinetics in IN718 [34] and IN625 [35] during AM. Also, Basoalto et al. [36] employed a computational framework to examine the contrasting distributions of process-induced microvoids and precipitates in two Ni-based superalloys, namely IN718 and CM247LC. Furthermore, McNamara et al. [37] established a computational model based on the Johnson-Mehl-Avrami model for non-isothermal conditions to predict solid-state phase transformation kinetics in L-PBF IN718 and DED Ti-6Al-4V. These models successfully predicted the size and volume fraction of individual phases and captured the repeated nucleation and dissolution of precipitates that occur during AM.

In the current study, we propose a modeling approach with appreciably short computational time to investigate the detailed microstructural evolution during metal AM. This may include obtaining more detailed information on the morphologies of phases, such as size distribution, phase fraction, dissolution and nucleation kinetics, as well as chemistry during thermal cycling and final cooling to room temperature. We utilize the combination of the MatCalc thermo-kinetic simulator and a semi-analytical heat conduction model. MatCalc is a software suite for simulation of phase transformations, microstructure evolution and certain mechanical properties in engineering alloys. It has successfully been employed to simulate solid-state phase transformations in Ni-based superalloys [38][39], steels [40], and Al alloys [41] during complex thermo-mechanical processes. MatCalc uses the classical nucleation theory as well as the so-called Svoboda-Fischer-Fratzl-Kozeschnik (SFFK) growth model as the basis for simulating precipitation kinetics [42]. Although MatCalc was originally developed for conventional thermo-mechanical processes, we will show that it is also applicable for AM if the detailed time-temperature profile of the AM build is known. The semi-analytical heat transfer code developed by Stump and Plotkowski [43] is used to simulate these profile throughout the AM build.

1.1. Application to IN738

Inconel-738 (IN738) is a precipitation hardening Ni-based superalloy mainly employed in high-temperature components, e.g. in gas turbines and aero-engines owing to its exceptional mechanical properties at temperatures up to 980 °C, coupled with high resistance to oxidation and corrosion [44]. Its superior high-temperature strength (∼1090 MPa tensile strength) is provided by the L12 ordered Ni3(Al,Ti) γ′ phase that precipitates in a face-centered cubic (FCC) γ matrix [45][46]. Despite offering great properties, IN738, like most superalloys with high γ′ fractions, is challenging to process owing to its propensity to hot cracking [47][48]. Further, machining of such alloys is challenging because of their high strength and work-hardening rates. It is therefore difficult to fabricate complex INC738 parts using traditional manufacturing techniques like casting, welding, and forging.

The emergence of AM has now made it possible to fabricate such parts from IN738 and other superalloys. Some of the current authors’ recent research successfully applied E-PBF to fabricate defect-free IN738 containing γ′ throughout the build [16][17]. The precipitated γ′ were heterogeneously distributed. In particular, Haghdadi et al. [16] studied the origin of the multimodal size distribution of γ′, while Lim et al. [17] investigated the gradient in γ′ character with build height and its correlation to mechanical properties. Based on these results, the present study aims to extend the understanding of the complex and site-specific microstructural evolution in E-PBF IN738 by using a computational modelling approach. New experimental evidence (e.g., micrographs not published previously) is presented here to support the computational results.

2. Materials and Methods

2.1. Materials preparation

IN738 Ni-based superalloy (59.61Ni-8.48Co-7.00Al-17.47Cr-3.96Ti-1.01Mo-0.81W-0.56Ta-0.49Nb-0.47C-0.09Zr-0.05B, at%) gas-atomized powder was used as feedstock. The powders, with average size of 60 ± 7 µm, were manufactured by Praxair and distributed by Astro Alloys Inc. An Arcam Q10 machine by GE Additive with an acceleration voltage of 60 kV was used to fabricate a 15 × 15 × 25 mm3 block (XYZ, Z: build direction) on a 316 stainless steel substrate. The block was 3D-printed using a ‘random’ spot melt pattern. The random spot melt pattern involves randomly selecting points in any given layer, with an equal chance of each point being melted. Each spot melt experienced a dwell time of 0.3 ms, and the layer thickness was 50 µm. Some of the current authors have previously characterized the microstructure of the very same and similar builds in more detail [16][17]. A preheat temperature of ∼1000 °C was set and kept during printing to reduce temperature gradients and, in turn, thermal stresses [49][50][51]. Following printing, the build was separated from the substrate through electrical discharge machining. It should be noted that this sample was simultaneously printed with the one used in [17] during the same build process and on the same build plate, under identical conditions.

2.2. Microstructural characterization

The printed sample was longitudinally cut in the direction of the build using a Struers Accutom-50, ground, and then polished to 0.25 µm suspension via standard techniques. The polished x-z surface was electropolished and etched using Struers A2 solution (perchloric acid in ethanol). Specimens for image analysis were polished using a 0.06 µm colloidal silica. Microstructure analyses were carried out across the height of the build using optical microscopy (OM) and scanning electron microscopy (SEM) with focus on the microstructure evolution (γ′ precipitates) in individual layers. The position of each layer being analyzed was determined by multiplying the layer number by the layer thickness (50 µm). It should be noted that the position of the first layer starts where the thermal profile is tracked (in this case, 2 mm from the bottom). SEM images were acquired using a JEOL 7001 field emission microscope. The brightness and contrast settings, acceleration voltage of 15 kV, working distance of 10 mm, and other SEM imaging parameters were all held constant for analysis of the entire build. The ImageJ software was used for automated image analysis to determine the phase fraction and size of γ′ precipitates and carbides. A 2-pixel radius Gaussian blur, following a greyscale thresholding and watershed segmentation was used [52]. Primary γ′ sizes (>50 nm), were measured using equivalent spherical diameters. The phase fractions were considered equal to the measured area fraction. Secondary γ′ particles (<50 nm) were not considered here. The γ′ size in the following refers to the diameter of a precipitate.

2.3. Hardness testing

A Struers DuraScan tester was utilized for Vickers hardness mapping on a polished x-z surface, from top to bottom under a maximum load of 100 mN and 10 s dwell time. 30 micro-indentations were performed per row. According to the ASTM standard [53], the indentations were sufficiently distant (∼500 µm) to assure that strain-hardened areas did not interfere with one another.

2.4. Computational simulation of E-PBF IN738 build

2.4.1. Thermal profile modeling

The thermal history was generated using the semi-analytical heat transfer code (also known as the 3DThesis code) developed by Stump and Plotkowski [43]. This code is an open-source C++ program which provides a way to quickly simulate the conductive heat transfer found in welding and AM. The key use case for the code is the simulation of larger domains than is practicable with Computational Fluid Dynamics/Finite Element Analysis programs like FLOW-3D AM. Although simulating conductive heat transfer will not be an appropriate simplification for some investigations (for example the modelling of keyholding or pore formation), the 3DThesis code does provide fast estimates of temperature, thermal gradient, and solidification rate which can be useful for elucidating microstructure formation across entire layers of an AM build. The mathematics involved in the code is as follows:

In transient thermal conduction during welding and AM, with uniform and constant thermophysical properties and without considering fluid convection and latent heat effects, energy conservation can be expressed as:(1)��∂�∂�=�∇2�+�̇where � is density, � specific heat, � temperature, � time, � thermal conductivity, and �̇ a volumetric heat source. By assuming a semi-infinite domain, Eq. 1 can be analytically solved. The solution for temperature at a given time (t) using a volumetric Gaussian heat source is presented as:(2)��,�,�,�−�0=33�����32∫0�1������exp−3�′�′2��+�′�′2��+�′�′2����′(3)and��=12��−�′+��2for�=�,�,�(4)and�′�′=�−���′Where � is the vector �,�,� and �� is the location of the heat source.

The numerical integration scheme used is an adaptive Gaussian quadrature method based on the following nondimensionalization:(5)�=��xy2�,�′=��xy2�′,�=��xy,�=��xy,�=��xy,�=���xy

A more detailed explanation of the mathematics can be found in reference [43].

The main source of the thermal cycling present within a powder-bed fusion process is the fusion of subsequent layers. Therefore, regions near the top of a build are expected to undergo fewer thermal cycles than those closer to the bottom. For this purpose, data from the single scan’s thermal influence on multiple layers was spliced to represent the thermal cycles experienced at a single location caused by multiple subsequent layers being fused.

The cross-sectional area simulated by this model was kept constant at 1 × 1 mm2, and the depth was dependent on the build location modelled with MatCalc. For a build location 2 mm from the bottom, the maximum number of layers to simulate is 460. Fig. 1a shows a stitched overview OM image of the entire build indicating the region where this thermal cycle is simulated and tracked. To increase similarity with the conditions of the physical build, each thermal history was constructed from the results of two simulations generated with different versions of a random scan path. The parameters used for these thermal simulations can be found in Table 1. It should be noted that the main purpose of the thermal profile modelling was to demonstrate how the conditions at different locations of the build change relative to each other. Accurately predicting the absolute temperature during the build would require validation via a temperature sensor measurement during the build process which is beyond the scope of the study. Nonetheless, to establish the viability of the heat source as a suitable approximation for this study, an additional sensitivity analysis was conducted. This analysis focused on the influence of energy input on γ′ precipitation behavior, the central aim of this paper. This was achieved by employing varying beam absorption energies (0.76, 0.82 – the values utilized in the simulation, and 0.9). The direct impact of beam absorption efficiency on energy input into the material was investigated. Specifically, the initial 20 layers of the build were simulated and subsequently compared to experimental data derived from SEM. While phase fractions were found to be consistent across all conditions, disparities emerged in the mean size of γ′ precipitates. An absorption efficiency of 0.76 yielded a mean size of approximately 70 nm. Conversely, absorption efficiencies of 0.82 and 0.9 exhibited remarkably similar mean sizes of around 130 nm, aligning closely with the outcomes of the experiments.

Fig. 1

Table 1. A list of parameters used in thermal simulation of E-PBF.

ParameterValue
Spatial resolution5 µm
Time step0.5 s
Beam diameter200 µm
Beam penetration depth1 µm
Beam power1200 W
Beam absorption efficiency0.82
Thermal conductivity25.37 W/(m⋅K)
Chamber temperature1000 °C
Specific heat711.756 J/(kg⋅K)
Density8110 kg/m3

2.4.2. Thermo-kinetic simulation

The numerical analyses of the evolution of precipitates was performed using MatCalc version 6.04 (rel 0.011). The thermodynamic (‘mc_ni.tdb’, version 2.034) and diffusion (‘mc_ni.ddb’, version 2.007) databases were used. MatCalc’s basic principles are elaborated as follows:

The nucleation kinetics of precipitates are computed using a computational technique based on a classical nucleation theory [54] that has been modified for systems with multiple components [42][55]. Accordingly, the transient nucleation rate (�), which expresses the rate at which nuclei are formed per unit volume and time, is calculated as:(6)�=�0��*∙�xp−�*�∙�∙exp−��where �0 denotes the number of active nucleation sites, �* the rate of atomic attachment, � the Boltzmann constant, � the temperature, �* the critical energy for nucleus formation, τ the incubation time, and t the time. � (Zeldovich factor) takes into consideration that thermal excitation destabilizes the nucleus as opposed to its inactive state [54]. Z is defined as follows:(7)�=−12�kT∂2∆�∂�2�*12where ∆� is the overall change in free energy due to the formation of a nucleus and n is the nucleus’ number of atoms. ∆�’s derivative is evaluated at n* (critical nucleus size). �* accounts for the long-range diffusion of atoms required for nucleation, provided that the matrix’ and precipitates’ composition differ. Svoboda et al. [42] developed an appropriate multi-component equation for �*, which is given by:(8)�*=4��*2�4�∑�=1��ki−�0�2�0��0�−1where �* denotes the critical radius for nucleation, � represents atomic distance, and � is the molar volume. �ki and �0� represent the concentration of elements in the precipitate and matrix, respectively. The parameter �0� denotes the rate of diffusion of the ith element within the matrix. The expression for the incubation time � is expressed as [54]:(9)�=12�*�2

and �*, which represents the critical energy for nucleation:(10)�*=16�3�3∆�vol2where � is the interfacial energy, and ∆Gvol the change in the volume free energy. The critical nucleus’ composition is similar to the γ′ phase’s equilibrium composition at the same temperature. � is computed based on the precipitate and matrix compositions, using a generalized nearest neighbor broken bond model, with the assumption of interfaces being planar, sharp, and coherent [56][57][58].

In Eq. 7, it is worth noting that �* represents the fundamental variable in the nucleation theory. It contains �3/∆�vol2 and is in the exponent of the nucleation rate. Therefore, even small variations in γ and/or ∆�vol can result in notable changes in �, especially if �* is in the order of �∙�. This is demonstrated in [38] for UDIMET 720 Li during continuous cooling, where these quantities change steadily during precipitation due to their dependence on matrix’ and precipitate’s temperature and composition. In the current work, these changes will be even more significant as the system is exposed to multiple cycles of rapid cooling and heating.

Once nucleated, the growth of a precipitate is assessed using the radius and composition evolution equations developed by Svoboda et al. [42] with a mean-field method that employs the thermodynamic extremal principle. The expression for the total Gibbs free energy of a thermodynamic system G, which consists of n components and m precipitates, is given as follows:(11)�=∑���0��0�+∑�=1�4���33��+∑�=1��ki�ki+∑�=1�4���2��.

The chemical potential of component � in the matrix is denoted as �0�(�=1,…,�), while the chemical potential of component � in the precipitate is represented by �ki(�=1,…,�,�=1,…,�). These chemical potentials are defined as functions of the concentrations �ki(�=1,…,�,�=1,…,�). The interface energy density is denoted as �, and �� incorporates the effects of elastic energy and plastic work resulting from the volume change of each precipitate.

Eq. (12) establishes that the total free energy of the system in its current state relies on the independent state variables: the sizes (radii) of the precipitates �� and the concentrations of each component �ki. The remaining variables can be determined by applying the law of mass conservation to each component �. This can be represented by the equation:(12)��=�0�+∑�=1�4���33�ki,

Furthermore, the global mass conservation can be expressed by equation:(13)�=∑�=1���When a thermodynamic system transitions to a more stable state, the energy difference between the initial and final stages is dissipated. This model considers three distinct forms of dissipation effects [42]. These include dissipations caused by the movement of interfaces, diffusion within the precipitate and diffusion within the matrix.

Consequently, �̇� (growth rate) and �̇ki (chemical composition’s rate of change) of the precipitate with index � are derived from the linear system of equation system:(14)�ij��=��where �� symbolizes the rates �̇� and �̇ki [42]. Index i contains variables for precipitate radius, chemical composition, and stoichiometric boundary conditions suggested by the precipitate’s crystal structure. Eq. (10) is computed separately for every precipitate �. For a more detailed description of the formulae for the coefficients �ij and �� employed in this work please refer to [59].

The MatCalc software was used to perform the numerical time integration of �̇� and �̇ki of precipitates based on the classical numerical method by Kampmann and Wagner [60]. Detailed information on this method can be found in [61]. Using this computational method, calculations for E-PBF thermal cycles (cyclic heating and cooling) were computed and compared to experimental data. The simulation took approximately 2–4 hrs to complete on a standard laptop.

3. Results

3.1. Microstructure

Fig. 1 displays a stitched overview image and selected SEM micrographs of various γ′ morphologies and carbides after observations of the X-Z surface of the build from the top to 2 mm above the bottom. Fig. 2 depicts a graph that charts the average size and phase fraction of the primary γ′, as it changes with distance from the top to the bottom of the build. The SEM micrographs show widespread primary γ′ precipitation throughout the entire build, with the size increasing in the top to bottom direction. Particularly, at the topmost height, representing the 460th layer (Z = 22.95 mm), as seen in Fig. 1b, the average size of γ′ is 110 ± 4 nm, exhibiting spherical shapes. This is representative of the microstructure after it solidifies and cools to room temperature, without experiencing additional thermal cycles. The γ′ size slightly increases to 147 ± 6 nm below this layer and remains constant until 0.4 mm (∼453rd layer) from the top. At this position, the microstructure still closely resembles that of the 460th layer. After the 453rd layer, the γ′ size grows rapidly to ∼503 ± 19 nm until reaching the 437th layer (1.2 mm from top). The γ′ particles here have a cuboidal shape, and a small fraction is coarser than 600 nm. γ′ continue to grow steadily from this position to the bottom (23 mm from the top). A small fraction of γ′ is > 800 nm.

Fig. 2

Besides primary γ′, secondary γ′ with sizes ranging from 5 to 50 nm were also found. These secondary γ′ precipitates, as seen in Fig. 1f, were present only in the bottom and middle regions. A detailed analysis of the multimodal size distribution of γ′ can be found in [16]. There is no significant variation in the phase fraction of the γ′ along the build. The phase fraction is ∼ 52%, as displayed in Fig. 2. It is worth mentioning that the total phase fraction of γ′ was estimated based on the primary γ′ phase fraction because of the small size of secondary γ′. Spherical MC carbides with sizes ranging from 50 to 400 nm and a phase fraction of 0.8% were also observed throughout the build. The carbides are the light grey precipitates in Fig. 1g. The light grey shade of carbides in the SEM images is due to their composition and crystal structure [52]. These carbides are not visible in Fig. 1b-e because they were dissolved during electro-etching carried out after electropolishing. In Fig. 1g, however, the sample was examined directly after electropolishing, without electro-etching.

Table 2 shows the nominal and measured composition of γ′ precipitates throughout the build by atom probe microscopy as determined in our previous study [17]. No build height-dependent composition difference was observed in either of the γ′ precipitate populations. However, there was a slight disparity between the composition of primary and secondary γ′. Among the main γ′ forming elements, the primary γ′ has a high Ti concentration while secondary γ′ has a high Al concentration. A detailed description of the atom distribution maps and the proxigrams of the constituent elements of γ′ throughout the build can be found in [17].

Table 2. Bulk IN738 composition determined using inductively coupled plasma atomic emission spectroscopy (ICP-AES). Compositions of γ, primary γ′, and secondary γ′ at various locations in the build measured by APT. This information is reproduced from data in Ref. [17] with permission.

at%NiCrCoAlMoWTiNbCBZrTaOthers
Bulk59.1217.478.487.001.010.813.960.490.470.050.090.560.46
γ matrix
Top50.4832.9111.591.941.390.820.440.80.030.030.020.24
Mid50.3732.6111.931.791.540.890.440.10.030.020.020.010.23
Bot48.1034.5712.082.141.430.880.480.080.040.030.010.12
Primary γ′
Top72.172.513.4412.710.250.397.780.560.030.020.050.08
Mid71.602.573.2813.550.420.687.040.730.010.030.040.04
Bot72.342.473.8612.500.260.447.460.500.050.020.020.030.04
Secondary γ′
Mid70.424.203.2314.190.631.035.340.790.030.040.040.05
Bot69.914.063.6814.320.811.045.220.650.050.100.020.11

3.2. Hardness

Fig. 3a shows the Vickers hardness mapping performed along the entire X-Z surface, while Fig. 3b shows the plot of average hardness at different build heights. This hardness distribution is consistent with the γ′ precipitate size gradient across the build direction in Fig. 1Fig. 2. The maximum hardness of ∼530 HV1 is found at ∼0.5 mm away from the top surface (Z = 22.5), where γ′ particles exhibit the smallest observed size in Fig. 2b. Further down the build (∼ 2 mm from the top), the hardness drops to the 440–490 HV1 range. This represents the region where γ′ begins to coarsen. The hardness drops further to 380–430 HV1 at the bottom of the build.

Fig. 3

3.3. Modeling of the microstructural evolution during E-PBF

3.3.1. Thermal profile modeling

Fig. 4 shows the simulated thermal profile of the E-PBF build at a location of 23 mm from the top of the build, using a semi-analytical heat conduction model. This profile consists of the time taken to deposit 460 layers until final cooling, as shown in Fig. 4a. Fig. 4b-d show the magnified regions of Fig. 4a and reveal the first 20 layers from the top, a single layer (first layer from the top), and the time taken for the build to cool after the last layer deposition, respectively.

Fig. 4

The peak temperatures experienced by previous layers decrease progressively as the number of layers increases but never fall below the build preheat temperature (1000 °C). Our simulated thermal cycle may not completely capture the complexity of the actual thermal cycle utilized in the E-PBF build. For instance, the top layer (Fig. 4c), also representing the first deposit’s thermal profile without additional cycles (from powder heating, melting, to solidification), recorded the highest peak temperature of 1390 °C. Although this temperature is above the melting range of the alloy (1230–1360 °C) [62], we believe a much higher temperature was produced by the electron beam to melt the powder. Nevertheless, the solidification temperature and dynamics are outside the scope of this study as our focus is on the solid-state phase transformations during deposition. It takes ∼25 s for each layer to be deposited and cooled to the build temperature. The interlayer dwell time is 125 s. The time taken for the build to cool to room temperature (RT) after final layer deposition is ∼4.7 hrs (17,000 s).

3.3.2. MatCalc simulation

During the MatCalc simulation, the matrix phase is defined as γ. γ′, and MC carbide are included as possible precipitates. The domain of these precipitates is set to be the matrix (γ), and nucleation is assumed to be homogenous. In homogeneous nucleation, all atoms of the unit volume are assumed to be potential nucleation sitesTable 3 shows the computational parameters used in the simulation. All other parameters were set at default values as recommended in the version 6.04.0011 of MatCalc. The values for the interfacial energies are automatically calculated according to the generalized nearest neighbor broken bond model and is one of the most outstanding features in MatCalc [56][57][58]. It should be noted that the elastic misfit strain was not included in the calculation. The output of MatCalc includes phase fraction, size, nucleation rate, and composition of the precipitates. The phase fraction in MatCalc is the volume fraction. Although the experimental phase fraction is the measured area fraction, it is relatively similar to the volume fraction. This is because of the generally larger precipitate size and similar morphology at the various locations along the build [63]. A reliable phase fraction comparison between experiment and simulation can therefore be made.

Table 3. Computational parameters used in the simulation.

Precipitation domainγ
Nucleation site γ′Bulk (homogenous)
Nucleation site MC carbideBulk (Homogenous)
Precipitates class size250
Regular solution critical temperature γ′2500 K[64]
Calculated interfacial energyγ′ = 0.080–0.140 J/m2 and MC carbide = 0.410–0.430 J/m2
3.3.2.1. Precipitate phase fraction

Fig. 5a shows the simulated phase fraction of γ′ and MC carbide during thermal cycling. Fig. 5b is a magnified view of 5a showing the simulated phase fraction at the center points of the top 70 layers, whereas Fig. 5c corresponds to the first two layers from the top. As mentioned earlier, the top layer (460th layer) represents the microstructure after solidification. The microstructure of the layers below is determined by the number of thermal cycles, which increases with distance to the top. For example, layers 459, 458, 457, up to layer 1 (region of interest) experience 1, 2, 3 and 459 thermal cycles, respectively. In the top layer in Fig. 5c, the volume fraction of γ′ and carbides increases with temperature. For γ′, it decreases to zero when the temperature is above the solvus temperature after a few seconds. Carbides, however, remain constant in their volume fraction reaching equilibrium (phase fraction ∼ 0.9%) in a short time. The topmost layer can be compared to the first deposit, and the peak in temperature symbolizes the stage where the electron beam heats the powder until melting. This means γ′ and carbide precipitation might have started in the powder particles during heating from the build temperature and electron beam until the onset of melting, where γ′ dissolves, but carbides remain stable [28].

Fig. 5

During cooling after deposition, γ′ reprecipitates at a temperature of 1085 °C, which is below its solvus temperature. As cooling progresses, the phase fraction increases steadily to ∼27% and remains constant at 1000 °C (elevated build temperature). The calculated equilibrium fraction of phases by MatCalc is used to show the complex precipitation characteristics in this alloy. Fig. 6 shows that MC carbides form during solidification at 1320 °C, followed by γ′, which precipitate when the solidified layer cools to 1140 °C. This indicates that all deposited layers might contain a negligible amount of these precipitates before subsequent layer deposition, while being at the 1000 °C build temperature or during cooling to RT. The phase diagram also shows that the equilibrium fraction of the γ′ increases as temperature decreases. For instance, at 1000, 900, and 800 °C, the phase fractions are ∼30%, 38%, and 42%, respectively.

Fig. 6

Deposition of subsequent layers causes previous layers to undergo phase transformations as they are exposed to several thermal cycles with different peak temperatures. In Fig. 5c, as the subsequent layer is being deposited, γ′ in the previous layer (459th layer) begins to dissolve as the temperature crosses the solvus temperature. This is witnessed by the reduction of the γ′ phase fraction. This graph also shows how this phase dissolves during heating. However, the phase fraction of MC carbide remains stable at high temperatures and no dissolution is seen during thermal cycling. Upon cooling, the γ′ that was dissolved during heating reprecipitates with a surge in the phase fraction until 1000 °C, after which it remains constant. This microstructure is similar to the solidification microstructure (layer 460), with a similar γ′ phase fraction (∼27%).

The complete dissolution and reprecipitation of γ′ continue for several cycles until the 50th layer from the top (layer 411), where the phase fraction does not reach zero during heating to the peak temperature (see Fig. 5d). This indicates the ‘partial’ dissolution of γ′, which continues progressively with additional layers. It should be noted that the peak temperatures for layers that underwent complete dissolution were much higher (1170–1300 °C) than the γ′ solvus.

The dissolution and reprecipitation of γ′ during thermal cycling are further confirmed in Fig. 7, which summarizes the nucleation rate, phase fraction, and concentration of major elements that form γ′ in the matrix. Fig. 7b magnifies a single layer (3rd layer from top) within the full dissolution region in Fig. 7a to help identify the nucleation and growth mechanisms. From Fig. 7b, γ′ nucleation begins during cooling whereby the nucleation rate increases to reach a maximum value of approximately 1 × 1020 m−3s−1. This fast kinetics implies that some rearrangement of atoms is required for γ′ precipitates to form in the matrix [65][66]. The matrix at this stage is in a non-equilibrium condition. Its composition is similar to the nominal composition and remains unchanged. The phase fraction remains insignificant at this stage although nucleation has started. The nucleation rate starts declining upon reaching the peak value. Simultaneously, diffusion-controlled growth of existing nuclei occurs, depleting the matrix of γ′ forming elements (Al and Ti). Thus, from (7)(11), ∆�vol continuously decreases until nucleation ceases. The growth of nuclei is witnessed by the increase in phase fraction until a constant level is reached at 27% upon cooling to and holding at build temperature. This nucleation event is repeated several times.

Fig. 7

At the onset of partial dissolution, the nucleation rate jumps to 1 × 1021 m−3s−1, and then reduces sharply at the middle stage of partial dissolution. The nucleation rate reaches 0 at a later stage. Supplementary Fig. S1 shows a magnified view of the nucleation rate, phase fraction, and thermal profile, underpinning this trend. The jump in nucleation rate at the onset is followed by a progressive reduction in the solute content of the matrix. The peak temperatures (∼1130–1160 °C) are lower than those in complete dissolution regions but still above or close to the γ′ solvus. The maximum phase fraction (∼27%) is similar to that of the complete dissolution regions. At the middle stage, the reduction in nucleation rate is accompanied by a sharp drop in the matrix composition. The γ′ fraction drops to ∼24%, where the peak temperatures of the layers are just below or at γ′ solvus. The phase fraction then increases progressively through the later stage of partial dissolution to ∼30% towards the end of thermal cycling. The matrix solute content continues to drop although no nucleation event is seen. The peak temperatures are then far below the γ′ solvus. It should be noted that the matrix concentration after complete dissolution remains constant. Upon cooling to RT after final layer deposition, the nucleation rate increases again, indicating new nucleation events. The phase fraction reaches ∼40%, with a further depletion of the matrix in major γ′ forming elements.

3.3.2.2. γ′ size distribution

Fig. 8 shows histograms of the γ′ precipitate size distributions (PSD) along the build height during deposition. These PSDs are predicted at the end of each layer of interest just before final cooling to room temperature, to separate the role of thermal cycles from final cooling on the evolution of γ′. The PSD for the top layer (layer 460) is shown in Fig. 8a (last solidified region with solidification microstructure). The γ′ size ranges from 120 to 230 nm and is similar to the 44 layers below (2.2 mm from the top).

Fig. 8

Further down the build, γ′ begins to coarsen after layer 417 (44th layer from top). Fig. 8c shows the PSD after the 44th layer, where the γ′ size exhibits two peaks at ∼120–230 and ∼300 nm, with most of the population being in the former range. This is the onset of partial dissolution where simultaneously with the reprecipitation and growth of fresh γ′, the undissolved γ′ grows rapidly through diffusive transport of atoms to the precipitates. This is shown in Fig. 8c, where the precipitate class sizes between 250 and 350 represent the growth of undissolved γ′. Although this continues in the 416th layer, the phase fractions plot indicates that the onset of partial dissolution begins after the 411th layer. This implies that partial dissolution started early, but the fraction of undissolved γ′ was too low to impact the phase fraction. The reprecipitated γ′ are mostly in the 100–220 nm class range and similar to those observed during full dissolution.

As the number of layers increases, coarsening intensifies with continued growth of more undissolved γ′, and reprecipitation and growth of partially dissolved ones. Fig. 8d, e, and f show this sequence. Further down the build, coarsening progresses rapidly, as shown in Figs. 8d, 8e, and 8f. The γ′ size ranges from 120 to 1100 nm, with the peaks at 160, 180, and 220 nm in Figs. 8d, 8e, and 8f, respectively. Coarsening continues until nucleation ends during dissolution, where only the already formed γ′ precipitates continue to grow during further thermal cycling. The γ′ size at this point is much larger, as observed in layers 361 and 261, and continues to increase steadily towards the bottom (layer 1). Two populations in the ranges of ∼380–700 and ∼750–1100 nm, respectively, can be seen. The steady growth of γ′ towards the bottom is confirmed by the gradual decrease in the concentration of solute elements in the matrix (Fig. 7a). It should be noted that for each layer, the γ′ class with the largest size originates from continuous growth of the earliest set of the undissolved precipitates.

Fig. 9Fig. 10 and supplementary Figs. S2 and S3 show the γ′ size evolution during heating and cooling of a single layer in the full dissolution region, and early, middle stages, and later stages of partial dissolution, respectively. In all, the size of γ′ reduces during layer heating. Depending on the peak temperature of the layer which varies with build height, γ′ are either fully or partially dissolved as mentioned earlier. Upon cooling, the dissolved γ′ reprecipitate.

Fig. 9
Fig. 10

In Fig. 9, those layers that underwent complete dissolution (top layers) were held above γ′ solvus temperature for longer. In Fig. 10, layers at the early stage of partial dissolution spend less time in the γ′ solvus temperature region during heating, leading to incomplete dissolution. In such conditions, smaller precipitates are fully dissolved while larger ones shrink [67]. Layers in the middle stages of partial dissolution have peak temperatures just below or at γ′ solvus, not sufficient to achieve significant γ′ dissolution. As seen in supplementary Fig. S2, only a few smaller γ′ are dissolved back into the matrix during heating, i.e., growth of precipitates is more significant than dissolution. This explains the sharp decrease in concentration of Al and Ti in the matrix in this layer.

The previous sections indicate various phenomena such as an increase in phase fraction, further depletion of matrix composition, and new nucleation bursts during cooling. Analysis of the PSD after the final cooling of the build to room temperature allows a direct comparison to post-printing microstructural characterization. Fig. 11 shows the γ′ size distribution of layer 1 (460th layer from the top) after final cooling to room temperature. Precipitation of secondary γ′ is observed, leading to the multimodal size distribution of secondary and primary γ′. The secondary γ′ size falls within the 10–80 nm range. As expected, a further growth of the existing primary γ′ is also observed during cooling.

Fig. 11
3.3.2.3. γ′ chemistry after deposition

Fig. 12 shows the concentration of the major elements that form γ′ (Al, Ti, and Ni) in the primary and secondary γ′ at the bottom of the build, as calculated by MatCalc. The secondary γ′ has a higher Al content (13.5–14.5 at% Al), compared to 13 at% Al in the primary γ′. Additionally, within the secondary γ′, the smallest particles (∼10 nm) have higher Al contents than larger ones (∼70 nm). In contrast, for the primary γ′, there is no significant variation in the Al content as a function of their size. The Ni concentration in secondary γ′ (71.1–72 at%) is also higher in comparison to the primary γ′ (70 at%). The smallest secondary γ′ (∼10 nm) have higher Ni contents than larger ones (∼70 nm), whereas there is no substantial change in the Ni content of primary γ′, based on their size. As expected, Ti shows an opposite size-dependent variation. It ranges from ∼ 7.7–8.7 at% Ti in secondary γ′ to ∼9.2 at% in primary γ′. Similarly, within the secondary γ′, the smallest (∼10 nm) have lower Al contents than the larger ones (∼70 nm). No significant variation is observed for Ti content in primary γ′.

Fig. 12

4. Discussion

A combined modelling method is utilized to study the microstructural evolution during E-PBF of IN738. The presented results are discussed by examining the precipitation and dissolution mechanism of γ′ during thermal cycling. This is followed by a discussion on the phase fraction and size evolution of γ′ during thermal cycling and after final cooling. A brief discussion on carbide morphology is also made. Finally, a comparison is made between the simulation and experimental results to assess their agreement.

4.1. γ′ morphology as a function of build height

4.1.1. Nucleation of γ′

The fast precipitation kinetics of the γ′ phase enables formation of γ′ upon quenching from higher temperatures (above solvus) during thermal cycling [66]. In Fig. 7b, for a single layer in the full dissolution region, during cooling, the initial increase in nucleation rate signifies the first formation of nuclei. The slight increase in nucleation rate during partial dissolution, despite a decrease in the concentration of γ′ forming elements, may be explained by the nucleation kinetics. During partial dissolution and as the precipitates shrink, it is assumed that the regions at the vicinity of partially dissolved precipitates are enriched in γ′ forming elements [68][69]. This differs from the full dissolution region, in which case the chemical composition is evenly distributed in the matrix. Several authors have attributed the solute supersaturation of the matrix around primary γ′ to partial dissolution during isothermal ageing [69][70][71][72]. The enhanced supersaturation in the regions close to the precipitates results in a much higher driving force for nucleation, leading to a higher nucleation rate upon cooling. This phenomenon can be closely related to the several nucleation bursts upon continuous cooling of Ni-based superalloys, where second nucleation bursts exhibit higher nucleation rates [38][68][73][74].

At middle stages of partial dissolution, the reduction in the nucleation rate indicates that the existing composition and low supersaturation did not trigger nucleation as the matrix was closer to the equilibrium state. The end of a nucleation burst means that the supersaturation of Al and Ti has reached a low level, incapable of providing sufficient driving force during cooling to or holding at 1000 °C for further nucleation [73]. Earlier studies on Ni-based superalloys have reported the same phenomenon during ageing or continuous cooling from the solvus temperature to RT [38][73][74].

4.1.2. Dissolution of γ′ during thermal cycling

γ′ dissolution kinetics during heating are fast when compared to nucleation due to exponential increase in phase transformation and diffusion activities with temperature [65]. As shown in Fig. 9Fig. 10, and supplementary Figs. S2 and S3, the reduction in γ′ phase fraction and size during heating indicates γ′ dissolution. This is also revealed in Fig. 5 where phase fraction decreases upon heating. The extent of γ′ dissolution mostly depends on the temperature, time spent above γ′ solvus, and precipitate size [75][76][77]. Smaller γ′ precipitates are first to be dissolved [67][77][78]. This is mainly because more solute elements need to be transported away from large γ′ precipitates than from smaller ones [79]. Also, a high temperature above γ′ solvus temperature leads to a faster dissolution rate [80]. The equilibrium solvus temperature of γ′ in IN738 in our MatCalc simulation (Fig. 6) and as reported by Ojo et al. [47] is 1140 °C and 1130–1180 °C, respectively. This means the peak temperature experienced by previous layers decreases progressively from γ′ supersolvus to subsolvus, near-solvus, and far from solvus as the number of subsequent layers increases. Based on the above, it can be inferred that the degree of dissolution of γ′ contributes to the gradient in precipitate distribution.

Although the peak temperatures during later stages of partial dissolution are much lower than the equilibrium γ′ solvus, γ′ dissolution still occurs but at a significantly lower rate (supplementary Fig. S3). Wahlmann et al. [28] also reported a similar case where they observed the rapid dissolution of γ′ in CMSX-4 during fast heating and cooling cycles at temperatures below the γ′ solvus. They attributed this to the γ′ phase transformation process taking place in conditions far from the equilibrium. While the same reasoning may be valid for our study, we further believe that the greater surface area to volume ratio of the small γ′ precipitates contributed to this. This ratio means a larger area is available for solute atoms to diffuse into the matrix even at temperatures much below the solvus [81].

4.2. γ′ phase fraction and size evolution

4.2.1. During thermal cycling

In the first layer, the steep increase in γ′ phase fraction during heating (Fig. 5), which also represents γ′ precipitation in the powder before melting, has qualitatively been validated in [28]. The maximum phase fraction of 27% during the first few layers of thermal cycling indicates that IN738 theoretically could reach the equilibrium state (∼30%), but the short interlayer time at the build temperature counteracts this. The drop in phase fraction at middle stages of partial dissolution is due to the low number of γ′ nucleation sites [73]. It has been reported that a reduction of γ′ nucleation sites leads to a delay in obtaining the final volume fraction as more time is required for γ′ precipitates to grow and reach equilibrium [82]. This explains why even upon holding for 150 s before subsequent layer deposition, the phase fraction does not increase to those values that were observed in the previous full γ′ dissolution regions. Towards the end of deposition, the increase in phase fraction to the equilibrium value of 30% is as a result of the longer holding at build temperature or close to it [83].

During thermal cycling, γ′ particles begin to grow immediately after they first precipitate upon cooling. This is reflected in the rapid increase in phase fraction and size during cooling in Fig. 5 and supplementary Fig. S2, respectively. The rapid growth is due to the fast diffusion of solute elements at high temperatures [84]. The similar size of γ′ for the first 44 layers from the top can be attributed to the fact that all layers underwent complete dissolution and hence, experienced the same nucleation event and growth during deposition. This corresponds with the findings by Balikci et al. [85], who reported that the degree of γ′ precipitation in IN738LC does not change when a solution heat treatment is conducted above a certain critical temperature.

The increase in coarsening rate (Fig. 8) during thermal cycling can first be ascribed to the high peak temperature of the layers [86]. The coarsening rate of γ′ is known to increase rapidly with temperature due to the exponential growth of diffusion activity. Also, the simultaneous dissolution with coarsening could be another reason for the high coarsening rate, as γ′ coarsening is a diffusion-driven process where large particles grow by consuming smaller ones [78][84][86][87]. The steady growth of γ′ towards the bottom of the build is due to the much lower layer peak temperature, which is almost close to the build temperature, and reduced dissolution activity, as is seen in the much lower solute concentration in γ′ compared to those in the full and partial dissolution regions.

4.2.2. During cooling

The much higher phase fraction of ∼40% upon cooling signifies the tendency of γ′ to reach equilibrium at lower temperatures (Fig. 4). This is due to the precipitation of secondary γ′ and a further increase in the size of existing primary γ′, which leads to a multimodal size distribution of γ′ after cooling [38][73][88][89][90]. The reason for secondary γ′ formation during cooling is as follows: As cooling progresses, it becomes increasingly challenging to redistribute solute elements in the matrix owing to their lower mobility [38][73]. A higher supersaturation level in regions away from or free of the existing γ′ precipitates is achieved, making them suitable sites for additional nucleation bursts. More cooling leads to the growth of these secondary γ′ precipitates, but as the temperature and in turn, the solute diffusivity is low, growth remains slow.

4.3. Carbides

MC carbides in IN738 are known to have a significant impact on the high-temperature strength. They can also act as effective hardening particles and improve the creep resistance [91]. Precipitation of MC carbides in IN738 and several other superalloys is known to occur during solidification or thermal treatments (e.g., hot isostatic pressing) [92]. In our case, this means that the MC carbides within the E-PBF build formed because of the thermal exposure from the E-PBF thermal cycle in addition to initial solidification. Our simulation confirms this as MC carbides appear during layer heating (Fig. 5). The constant and stable phase fraction of MC carbides during thermal cycling can be attributed to their high melting point (∼1360 °C) and the short holding time at peak temperatures [75][93][94]. The solvus temperature for most MC carbides exceeds most of the peak temperatures observed in our simulation, and carbide dissolution kinetics at temperatures above the solvus are known to be comparably slow [95]. The stable phase fraction and random distribution of MC carbides signifies the slight influence on the gradient in hardness.

4.4. Comparison of simulations and experiments

4.4.1. Precipitate phase fraction and morphology as a function of build height

A qualitative agreement is observed for the phase fraction of carbides, i.e. ∼0.8% in the experiment and ∼0.9% in the simulation. The phase fraction of γ′ differs, with the experiment reporting a value of ∼51% and the simulation, 40%. Despite this, the size distribution of primary γ′ along the build shows remarkable consistency between experimental and computational analyses. It is worth noting that the primary γ′ morphology in the experimental analysis is observed in the as-fabricated state, whereas the simulation (Fig. 8) captures it during deposition process. The primary γ′ size in the experiment is expected to experience additional growth during the cooling phase. Regardless, both show similar trends in primary γ′ size increments from the top to the bottom of the build. The larger primary γ’ size in the simulation versus the experiment can be attributed to the fact that experimental and simulation results are based on 2D and 3D data, respectively. The absence of stereological considerations [96] in our analysis could have led to an underestimation of the precipitate sizes from SEM measurements. The early starts of coarsening (8th layer) in the experiment compared to the simulation (45th layer) can be attributed to a higher actual γ′ solvus temperature than considered in our simulation [47]. The solvus temperature of γ′ in a Ni-based superalloy is mainly determined by the detailed composition. A high amount of Cr and Co are known to reduce the solvus temperature, whereas Ta and Mo will increase it [97][98][99]. The elemental composition from our experimental work was used for the simulation except for Ta. It should be noted that Ta is not included in the thermodynamic database in MatCalc used, and this may have reduced the solvus temperature. This could also explain the relatively higher γ′ phase fraction in the experiment than in simulation, as a higher γ′ solvus temperature will cause more γ′ to precipitate and grow early during cooling [99][100].

Another possible cause of this deviation can be attributed to the extent of γ′ dissolution, which is mainly determined by the peak temperature. It can be speculated that individual peak temperatures at different layers in the simulation may have been over-predicted. However, one needs to consider that the true thermal profile is likely more complicated in the actual E-PBF process [101]. For example, the current model assumes that the thermophysical properties of the material are temperature-independent, which is not realistic. Many materials, including IN738, exhibit temperature-dependent properties such as thermal conductivityspecific heat capacity, and density [102]. This means that heat transfer simulations may underestimate or overestimate the temperature gradients and cooling rates within the powder bed and the solidified part. Additionally, the model does not account for the reduced thermal diffusivity through unmelted powder, where gas separating the powder acts as insulation, impeding the heat flow [1]. In E-PBF, the unmelted powder regions with trapped gas have lower thermal diffusivity compared to the fully melted regions, leading to localized temperature variations, and altered solidification behavior. These limitations can impact the predictions, particularly in relation to the carbide dissolution, as the peak temperatures may be underestimated.

While acknowledging these limitations, it is worth emphasizing that achieving a detailed and accurate representation of each layer’s heat source would impose tough computational challenges. Given the substantial layer count in E-PBF, our decision to employ a semi-analytical approximation strikes a balance between computational feasibility and the capture of essential trends in thermal profiles across diverse build layers. In future work, a dual-calibration strategy is proposed to further reduce simulation-experiment disparities. By refining temperature-independent thermophysical property approximations and absorptivity in the heat source model, and by optimizing interfacial energy descriptions in the kinetic model, the predictive precision could be enhanced. Further refining the simulation controls, such as adjusting the precipitate class size may enhance quantitative comparisons between modeling outcomes and experimental data in future work.

4.4.2. Multimodal size distribution of γ′ and concentration

Another interesting feature that sees qualitative agreement between the simulation and the experiment is the multimodal size distribution of γ′. The formation of secondary γ′ particles in the experiment and most E-PBF Ni-based superalloys is suggested to occur at low temperatures, during final cooling to RT [16][73][90]. However, so far, this conclusion has been based on findings from various continuous cooling experiments, as the study of the evolution during AM would require an in-situ approach. Our simulation unambiguously confirms this in an AM context by providing evidence for secondary γ′ precipitation during slow cooling to RT. Additionally, it is possible to speculate that the chemical segregation occurring during solidification, due to the preferential partitioning of certain elements between the solid and liquid phases, can contribute to the multimodal size distribution during deposition [51]. This is because chemical segregation can result in variations in the local composition of superalloys, which subsequently affects the nucleation and growth of γ′. Regions with higher concentrations of alloying elements will encourage the formation of larger γ′ particles, while regions with lower concentrations may favor the nucleation of smaller precipitates. However, it is important to acknowledge that the elevated temperature during the E-PBF process will largely homogenize these compositional differences [103][104].

A good correlation is also shown in the composition of major γ′ forming elements (Al and Ti) in primary and secondary γ′. Both experiment and simulation show an increasing trend for Al content and a decreasing trend for Ti content from primary to secondary γ′. The slight composition differences between primary and secondary γ′ particles are due to the different diffusivity of γ′ stabilizers at different thermal conditions [105][106]. As the formation of multimodal γ′ particles with different sizes occurs over a broad temperature range, the phase chemistry of γ′ will be highly size dependent. The changes in the chemistry of various γ′ (primary, secondary, and tertiary) have received significant attention since they have a direct influence on the performance [68][105][107][108][109]. Chen et al. [108][109], reported a high Al content in the smallest γ′ precipitates compared to the largest, while Ti showed an opposite trend during continuous cooling in a RR1000 Ni-based superalloy. This was attributed to the temperature and cooling rate at which the γ′ precipitates were formed. The smallest precipitates formed last, at the lowest temperature and cooling rate. A comparable observation is evident in the present investigation, where the secondary γ′ forms at a low temperature and cooling rate in comparison to the primary. The temperature dependence of γ′ chemical composition is further evidenced in supplementary Fig. S4, which shows the equilibrium chemical composition of γ′ as a function of temperature.

5. Conclusions

A correlative modelling approach capable of predicting solid-state phase transformations kinetics in metal AM was developed. This approach involves computational simulations with a semi-analytical heat transfer model and the MatCalc thermo-kinetic software. The method was used to predict the phase transformation kinetics and detailed morphology and chemistry of γ′ and MC during E-PBF of IN738 Ni-based superalloy. The main conclusions are:

  • 1.The computational simulations are in qualitative agreement with the experimental observations. This is particularly true for the γ′ size distribution along the build height, the multimodal size distribution of particles, and the phase fraction of MC carbides.
  • 2.The deviations between simulation and experiment in terms of γ′ phase fraction and location in the build are most likely attributed to a higher γ′ solvus temperature during the experiment than in the simulation, which is argued to be related to the absence of Ta in the MatCalc database.
  • 3.The dissolution and precipitation of γ′ occur fast and under non-equilibrium conditions. The level of γ′ dissolution determines the gradient in γ′ size distribution along the build. After thermal cycling, the final cooling to room temperature has further significant impacts on the final γ′ size, morphology, and distribution.
  • 4.A negligible amount of γ′ forms in the first deposited layer before subsequent layer deposition, and a small amount of γ′ may also form in the powder induced by the 1000 °C elevated build temperature before melting.

Our findings confirm the suitability of MatCalc to predict the microstructural evolution at various positions throughout a build in a Ni-based superalloy during E-PBF. It also showcases the suitability of a tool which was originally developed for traditional thermo-mechanical processing of alloys to the new additive manufacturing context. Our simulation capabilities are likely extendable to other alloy systems that undergo solid-state phase transformations implemented in MatCalc (various steels, Ni-based superalloys, and Al-alloys amongst others) as well as other AM processes such as L-DED and L-PBF which have different thermal cycle characteristics. New tools to predict the microstructural evolution and properties during metal AM are important as they provide new insights into the complexities of AM. This will enable control and design of AM microstructures towards advanced materials properties and performances.

CRediT authorship contribution statement

Primig Sophie: Writing – review & editing, Supervision, Resources, Project administration, Funding acquisition, Conceptualization. Adomako Nana Kwabena: Writing – original draft, Writing – review & editing, Visualization, Software, Investigation, Formal analysis, Conceptualization. Haghdadi Nima: Writing – review & editing, Supervision, Project administration, Methodology, Conceptualization. Dingle James F.L.: Methodology, Conceptualization, Software, Writing – review & editing, Visualization. Kozeschnik Ernst: Writing – review & editing, Software, Methodology. Liao Xiaozhou: Writing – review & editing, Project administration, Funding acquisition. Ringer Simon P: Writing – review & editing, Project administration, Funding acquisition.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This research was sponsored by the Department of Industry, Innovation, and Science under the auspices of the AUSMURI program – which is a part of the Commonwealth’s Next Generation Technologies Fund. The authors acknowledge the facilities and the scientific and technical assistance at the Electron Microscope Unit (EMU) within the Mark Wainwright Analytical Centre (MWAC) at UNSW Sydney and Microscopy Australia. Nana Adomako is supported by a UNSW Scientia PhD scholarship. Michael Haines’ (UNSW Sydney) contribution to the revised version of the original manuscript is thankfully acknowledged.

Appendix A. Supplementary material

Download : Download Word document (462KB)

Supplementary material.

Data Availability

Data will be made available on request.

References

Fig. 7.Simulation results by single external force (left: rainfall, right: storm surge)

연안 지역의 복합 외력에 의한 침수 특성 분석

Analysis on inundation characteristics by compound external forces in coastal areas

연안 지역의 복합 외력에 의한 침수 특성 분석

Taeuk Kanga, Dongkyun Sunb, Sangho Leec*
강 태욱a, 선 동균b, 이 상호c*

aResearch Professor, Disaster Prevention Research Institute, Pukyong National University, Busan, Korea
bResearcher, Disaster Prevention Research Institute, Pukyong National University, Busan, Korea
cProfessor, Department of Civil Engineering, Pukyong National University, Busan, Korea
a부경대학교 방재연구소 전임연구교수
b부경대학교 방재연구소 연구원
c부경대학교 공과대학 토목공학과 교수
*Corresponding Author

ABSTRACT

연안 지역은 강우, 조위, 월파 등 여러가지 외력에 의해 침수가 발생될 수 있다. 이에 이 연구에서는 연안 지역에서 발생될 수 있는 단일 및 복합 외력에 의한 지역별 침수 특성을 분석하였다. 연구에서 고려한 외력은 강우와 폭풍 해일에 의한 조위 및 월파이고, 분석 대상지역은 남해안 및 서해안의 4개 지역이다. 유역의 강우-유출 및 2차원 지표면 침수 분석에는 XP-SWMM이 사용되었고, 폭풍 해일에 의한 외력인 조위 및 월파량 산정에는 ADCSWAN (ADCIRC와 UnSWAN) 모형과 FLOW-3D 모형이 각각 활용되었다. 단일 외력을 이용한 분석 결과, 대부분의 연안 지역에서는 강우에 의한 침수 영향보다 폭풍 해일에 의한 침수 영향이 크게 나타났다. 복합 외력에 의한 침수 분석 결과는 대체로 단일 외력에 의한 침수 모의 결과를 중첩시켜 나타낸 결과와 유사하였다. 다만, 특정 지역에서는 복합 외력을 고려함에 따라 단일 외력만을 고려한 침수모의에서 나타나지 않았던 새로운 침수 영역이 발생하기도 하였다. 이러한 지역의 침수 피해 저감을 위해서는 복합 외력을 고려한 분석이 요구되는 것으로 판단되었다.

키워드

연안 지역

침수 분석

강우

폭풍 해일

복합 외력

The various external forces can cause inundation in coastal areas. This study is to analyze regional characteristics caused by single or compound external forces that can occur in coastal areas. Storm surge (tide level and wave overtopping) and rainfall were considered as the external forces in this study. The inundation analysis were applied to four coastal areas, located on the west and south coast in Republic of Korea. XP-SWMM was used to simulate rainfall-runoff phenomena and 2D ground surface inundation for watershed. A coupled model of ADCIRC and SWAN (ADCSWAN) was used to analyze tide level by storm surge and the FLOW-3D model was used to estimate wave overtopping. As a result of using a single external force, the inundation influence due to storm surge in most of the coastal areas was greater than rainfall. The results of using compound external forces were quite similar to those combined using one external force independently. However, a case of considering compound external forces sometimes created new inundation areas that didn’t appear when considering only a single external force. The analysis considering compound external forces was required to reduce inundation damage in these areas.

Keywords

Coastal area

Inundation analysis

Rainfall

Storm surge

Compound external forces

MAIN

1. 서 론

우리나라는 반도에 위치하여 삼면이 바다로 둘러싸여 있는 지리적 특성을 가지고 있다. 이에 따라 해양 산업을 중심으로 부산, 인천, 울산 등 대규모의 광역도시가 발달하였을 뿐만 아니라, 창원, 포항, 군산, 목포, 여수 등의 중․소규모 도시들도 발달되어 있다. 또한, 최근에는 연안 지역이 바다를 전망으로 하는 입지 조건을 가지고 있어 개발 선호도가 높고, 이에 따라 부산시 해운대의 마린시티, 엘시티와 같은 주거 및 상업시설의 개발이 지속되고 있다(Kang et al., 2019b).

한편, 최근 기후변화에 따른 지구 온난화 현상으로 평균 해수면이 상승하고, 해수면 온도도 상승하면서 태풍 및 강우의 강도가 커지고 있어 전 세계적으로 자연 재해로 인한 피해가 증가하고 있다(Kim et al., 2016). 실제로 2020년에는 최장기간의 장마가 발생하여 부산, 울산은 물론, 전국에서 50명의 인명 피해와 3,489세대의 이재민이 발생하였다1). 특히, 연안 지역은 강우, 만조 시 해수면 상승, 폭풍 해일(storm surge)에 의한 월파(wave overtopping) 등 복합적인 외력(compound external forces)에 의해 침수될 수 있다(Lee et al., 2020). 일례로, 2016년 태풍 차바 시 부산시 해운대구의 마린시티는 강우와 폭풍 해일에 의한 월파가 발생함에 따라 대규모 침수를 유발하였다(Kang et al., 2019b). 또한, 2020년 7월 23일에 부산에서는 시간당 81.6 mm의 집중호우와 약최고고조위를 상회하는 만조가 동시에 발생하였고, 이로 인해 감조 하천인 동천의 수위가 크게 상승하여 하천이 범람하였다(KSCE, 2021).

연안 지역의 복합 외력을 고려한 침수 분석에 관한 사례로서, 우선 강우와 조위를 고려한 연구 사례는 다음과 같다. Han et al. (2014)은 XP-SWMM을 이용하여 창원시 배수 구역을 대상으로 침수 모의를 수행하였는데, 연안 도시의 침수 모의에는 조위의 영향을 반드시 고려해야 함을 제시하였다. Choi et al. (2018a)은 경남 사천시 선구동 일대에 대하여 초과 강우 및 해수면 상승 시나리오를 조합하여 침수 분석을 수행하였다. Choi et al. (2018b)은 XP-SWMM을 이용하여 여수시 연등천 및 여수시청 지역에 대하여 강우 시나리오와 해수위 상승 시나리오를 고려한 복합 원인에 의한 침수 모의를 수행하여 홍수예경보 기준표를 작성하였다. 한편, 강우, 조위, 월파를 고려한 연구 사례로서, Song et al. (2017)은 부산시 해운대구 수영만 일원에 대하여 XP-SWMM으로 월파량의 적용 유무에 따른 침수 면적을 비교하였다. Suh and Kim (2018)은 부산시 마린시티 지역을 대상으로 태풍 차바 때 EurOtop의 경험식을 ADSWAN에 적용하여 월파량을 반영하였다. Chen et al. (2017)은 TELEMAC-2D 및 SWMM을 기반으로 한 극한 강우, 월파 및 조위를 고려하여 중국 해안 원자력 발전소의 침수를 예측하고 분석하기 위한 결합 모델을 개발한 바 있다. 한편, Lee et al. (2020)은 수리‧수문학 분야와 해양공학 분야에서 사용되는 물리 모형의 기술적 연계를 통해 연안 지역의 침수 모의의 재현성을 높였다.

상기의 연구들은 공통적으로 연안 지역에 대하여 복합 외력을 고려했을 때 발생되는 침수 현상의 재현 또는 예측을 목적으로 수행되었다. 이 연구는 이와 차별하여 복합 외력을 고려하는 경우 나타날 수 있는 연안 지역의 침수 특성 분석을 목적으로 수행되었다. 이를 위해 단일 외력을 독립적으로 고려했을 때 발생되는 침수 양상과 동시에 고려하는 경우의 침수 현상을 비교, 분석하였다. 복합 외력에 의한 지역적 침수 특성 분석은 우리나라 남해안과 서해안에 위치한 4개 지역에 대하여 적용되었다.

1) 장연제, 47일째 이어진 긴 장마, 50명 인명피해… 9년만에 최대, 동아닷컴, 2020년 8월 9일 수정, 2021년 3월 4일 접속, https://www.donga.com/news/article/all/20200809/102369692/2

2. 연구 방법

2.1 연안 지역의 침수 영향 인자

연안 지역의 침수는 크게 세 가지의 메카니즘으로 발생될 수 있다. 우선, 연안 지역은 바다와 인접하고 있기 때문에 그 영향을 직접적으로 받는다. Kim (2018)에 의하면, 연안 지역의 침수는 폭풍 해일에 의해 상승한 조위와 월파로 인해 발생될 수 있다(Table 1). 특히, 경상남도의 창원과 통영, 인천광역시의 소래포구 어시장 등 남해안 및 서해안 지역의 일부는 백중사리, 슈퍼문(super moon) 등 만조 시 조위의 상승으로 인한 침수가 발생하는 지역이 존재한다(Kang et al., 2019a). 두 번째는 강우에 의한 내수 침수 발생이다. ME (2011)에서는 도시 지역의 우수 관거를 10 ~ 30년 빈도로 계획하도록 지정하고 있고, 펌프 시설은 30 ~ 50년 빈도의 홍수를 배수시킬 수 있도록 정하고 있다. 하지만 최근에는 기후변화의 영향으로 도시 지역 배수시설의 설계 빈도를 초과하는 강우가 빈번하게 나타나고 있다. 실제로 2016년의 태풍 차바 시 울산 기상관측소에 관측된 시간 최대 강우량은 106.0 mm로서, 이는 300년 빈도 이상의 강우량에 해당하였다(Kang et al., 2019a). 따라서 배수시설의 설계 빈도 이상의 강우는 연안 도시 지역의 침수를 유발할 수 있다. 세 번째, 하천이 인접한 연안 도시에서는 하천의 범람으로 인해 침수가 발생할 수 있다. 하천의 경우, 기본계획이 수립되기는 하지만, 설계 빈도를 상회하는 강우의 발생, 제방, 수문 등 홍수 방어시설의 기능 저하, 예산 등의 문제로 하천기본계획 이행의 지연 등에 의해 범람할 가능성이 존재한다.

Table 1.

Type of natural hazard damage in coastal areas (Kim, 2018)

ItemRisk factor
Facilities damage∙ Breaking of coastal facilities by wave
– Breakwater, revetment, lighters wharf etc.
∙ Local scouring at the toe of the structures by wave
∙ Road collapse by wave overtopping
Inundation damage∙ Inundation damage by wave overtopping
∙ Inundation of coastal lowlands by storm surge
Erosion damage∙ Backshore erosion due to high swell waves
∙ Shoreline changes caused by construction of coastal erosion control structure
∙ Sediment transport due to the construction of artificial structures

상기의 내용을 종합하면, 연안 지역은 조위 및 월파에 의한 침수, 강우에 의한 내수 침수, 하천 범람에 의한 침수로 구분될 수 있다. 이 연구에서는 폭풍 해일에 의한 조위 상승 및 월파와 강우를 연안 지역의 침수 유발 외력으로 고려하였다. 하천 범람의 경우, 상대적으로 사례가 희소하여 제외하였다.

2.2 복합 외력을 고려한 침수 모의 방법

이 연구에서는 조위 및 월파와 강우를 연안 지역의 침수 발생에 관한 외력 조건으로 고려하였다. 따라서 해당 외력 조건을 고려하여 침수 분석을 수행할 수 있어야 한다. 이와 관련하여 Lee et al. (2020)은 Fig. 1과 같이 수리‧수문 및 해양공학 분야에서 사용되는 물리 기반 모형의 연계를 통해 조위, 월파, 강우를 고려한 침수 분석 방법을 제시하였고, 이 연구에서는 해당 방법을 이용하였다.

https://static.apub.kr/journalsite/sites/kwra/2021-054-07/N0200540702/images/kwra_54_07_02_F1.jpg
Fig. 1.

Connection among the models for inundation analysis in coastal areas (Lee et al., 2020)

우선, 태풍에 의해 발생되는 폭풍 해일의 영향을 분석하기 위해서는 태풍에 의해 발생되는 기압 강하, 해상풍, 진행 속도 등을 고려하여 해수면의 변화 양상 및 조석-해일-파랑을 충분히 재현 가능해야 한다. 이 연구에서는 국내․외에서 검증 및 공인된 폭풍 해일 모형인 ADCIRC 모형과 파랑 모형인 UnSWAN이 결합된 ADCSWAN (coupled model of ADCIRC and UnSWAN)을 이용하였다. 정수압 가정의 ADCSWAN은 월파량 산정에 단순 경험식을 적용하는 단점이 있지만 넓은 영역을 모의할 수 있고, FLOW-3D는 해안선의 경계를 고해상도로 재현이 가능하다. 이에 연구에서는 먼 바다 영역에 대해서는 ADCSWAN을 이용하여 분석하였고, 연안 주변의 바다 영역과 월파량 산정에 대해서는 FLOW-3D 모형을 이용하였다. 한편, 연안 지역의 침수 모의를 위해서는 유역에서 발생하는 강우-유출 현상과 우수 관거 등의 배수 체계에 대한 분석이 가능해야 한다. 또한, 배수 체계로부터 범람한 물이 지표면을 따라 흘러가는 현상을 해석할 수 있어야 하고, 바다의 조위 및 월파량을 경계조건으로 반영할 수 있어야 한다. 이 연구에서는 이러한 현상을 모의할 수 있고, 도시 침수 모의에 활용도가 높은 XP-SWMM을 이용하였다.

2.3 침수 분석 대상지역

연구의 대상지역은 조위 및 월파에 의한 침수와 강우에 의한 내수 침수의 영향이 복합적으로 발생할 수 있는 남해안과 서해안에 위치한 4개 지역이다. Table 2는 침수 분석 대상지역을 정리하여 나타낸 표이고, Fig. 2는 각 지역의 유역 경계를 나타낸 그림이다.

Table 2.

Target region for inundation analysis

ClassificationAdministrative districtTarget regionArea
(km2)
Main cause of inundationPump
facility
Number of
major outfall
The south
coast
Haundae-gu, BusanMarine City area0.53Wave overtopping9
Haundae-gu, BusanCentum City area4.76Poor interior drainage at high tide level12
The west
coast
GunsanJungang-dong area0.79Poor interior drainage at high tide level23
BoryeongOcheon Port area0.41High tide level5
https://static.apub.kr/journalsite/sites/kwra/2021-054-07/N0200540702/images/kwra_54_07_02_F2.jpg
Fig. 2.

Watershed area

남해안의 분석 대상지역 중 부산시 해운대구의 마린시티는 바다 조망을 중심으로 조성된 주거지 및 상업시설 중심의 개발지역이다. 마린시티는 2016년 태풍 차바 및 2018년 태풍 콩레이 등 태풍 내습 시 월파에 의한 해수 월류로 인해 도로 및 상가 일부가 침수를 겪은 지역이다. 부산시 해운대구의 센텀시티는 과거 수영만 매립지였던 곳에 조성된 주거지 및 상업시설 중심의 신도시 지역이다. 센텀시티 유역의 북쪽은 해발고도 El. 634 m의 장산이 위치하는 등 산지 특성도 가지고 있어 상대적으로 유역 면적이 넓고, 배수시설의 규모도 크고 복잡하다. 하지만 수영강 하구의 저지대 지역에 위치함에 따라 강우 시 내수 배제가 불량하고, 특히 만조 시 침수가 잦은 지역이다.

서해안 분석 대상지역 중 전라북도 군산시의 중앙동 일원은 군산시 내항 내측에 조성된 구도시로서, 금강 및 경포천 하구에 위치하는 저지대이다. 이에 따라 군산시 풍수해저감종합계획에서는 해당 지역을 3개의 영역으로 구분하여 내수재해 위험지구(영동지구, 중동지구, 경암지구)로 지정하였고, 이 연구에서는 해당 지역을 모두 고려하였다. 한편, 군산시 중앙동 일원은 특히, 만조 시 내수 배제가 매우 불량하여 2개의 펌프시설이 운영되고 있다. 충청남도 보령시의 오천면에 위치한 오천항은 배후의 산지를 포함한 소규모 유역에 위치한다. 서해안의 특성에 따라 조석 간만의 차가 크고, 특히 태풍 내습 시 폭풍 해일에 의한 침수가 잦은 지역이다. 산지의 강우-유출수는 복개된 2개의 수로를 통해 바다로 배제되고, 상가들이 위치한 연안 주변 지역에는 강우-유출수 배제를 위한 3개의 배수 체계가 구성되어 있다.

3. 연구 결과

3.1 침수 모의 모형 구축

XP-SWMM을 이용하여 분석 대상지역별 침수 모의 모형을 구축하였다. 적절한 침수 분석 수행을 위해 지역별 수치지형도, 도시 공간 정보 시스템(urban information system, UIS), 하수 관망도 등의 수치 자료와 현장 조사를 통해 유역의 배수 체계를 구성하였다. 그리고 2차원 침수 분석을 위해 무인 드론 및 육상 라이다(LiDAR) 측량을 수행하여 평면해상도가 1 m 이하인 고해상도 수치지형모형(digital terrain model, DTM)을 구성하였고, 침수 모의 격자를 생성하였다.

Fig. 3은 XP-SWMM의 상세 구축 사례로서 부산시 마린시티 배수 유역에 대한 소유역 및 관거 분할 등을 통해 구성한 배수 체계와 고해상도 측량 결과를 이용하여 구성한 수치표면모형(digital surface model, DSM)을 나타낸다. Fig. 4는 각 대상지역에 대해 XP-SWMM을 이용하여 구축한 침수 모의 모형을 나타낸다. 침수 분석을 위해서는 침수 모의 영역에 대한 설정이 필요한데, 다수의 사전 모의를 통해 유역 내에서 침수가 발생되는 지역을 검토하여 결정하였다.

https://static.apub.kr/journalsite/sites/kwra/2021-054-07/N0200540702/images/kwra_54_07_02_F3.jpg
Fig. 3.

Analysis of watershed drainage system and high-resolution survey for Marine City

https://static.apub.kr/journalsite/sites/kwra/2021-054-07/N0200540702/images/kwra_54_07_02_F4.jpg
Fig. 4.

Simulation model for inundation analysis by target region using XP-SWMM

한편, 이 연구에서는 월파량 및 조위의 산정 과정과 침수 모의 모형의 보정에 관한 내용 등은 다루지 않았다. 관련된 내용은 선행 연구인 Kang et al. (2019b)와 Lee et al. (2020)을 참조할 수 있다.

3.2 침수 모의 설정

3.2.1 분석 방법

복합 외력에 의한 침수 영향을 검토하기 위해서는 외력 조건에 대한 빈도와 지속기간의 설정이 필요하다. 이 연구에서는 재해 현상이 충분히 나타날 수 있도록 강우와 조위 및 월파의 빈도를 모두 100년으로 설정하였다. 이때, 조위와 월파량의 산정에는 만조(약최고고조위) 시, 100년 빈도에 해당하는 태풍 내습에 따른 폭풍 해일의 발생 조건을 고려하였다.

지역별 강우 발생 특성과 유역 특성을 고려하기 위해 MOIS (2017)의 방재성능목표 기준에 따라 임계 지속기간을 결정하여 대상지역별 강우의 지속기간으로 설정하였다. 이때, 강우의 시간 분포는 MLTM (2011)의 Huff 3분위를 이용하였다. 그리고 조위와 월파의 경우, 일반적인 폭풍 해일의 지속기간을 고려하여 5시간으로 결정하였다. 한편, 침수 모의를 위한 계산 시간 간격, 2차원 모의 격자 등의 입력자료는 분석 대상지역의 유역 규모와 침수 분석 대상 영역을 고려하여 결정하였다. 참고로 침수 분석에 사용된 수치지형모형은 1 m 급의 고해상도로 구성되었지만, 2차원 침수 모의 격자의 크기는 지역별로 3 ~ 4 m이다. 이는 연구에서 사용된 XP-SWMM의 격자 수(100,000개) 제약에 따른 설정이나, Sun (2021)은 민감도 분석을 통해 2차원 침수 분석을 위한 적정 격자 크기를 3 ~ 4.5 m로 제시한 바 있다.

Table 3은 이 연구에서 설정한 침수 모의 조건과 분석 방법을 정리하여 나타낸 표이다.

Table 3.

Simulation condition and method

ClassificationTarget regionSimulation conditionSimulation method
RainfallStorm surgeSimulation time interval2D
grid size
Return
period
DurationTemporal
distribution
Return
period
DurationWatershed
routing
Channel
routing
2D
inundation
The south coastMarine City area100 yr1 hr3rd quartile
of Huff’s
method
1005 hr5 min10 sec1 sec3 m
Centum City area1 hr1005 min10 sec1 sec4 m
The west coastJungang-dong area2 hr1005 min10 sec1 sec3.5 m
Ocheon Port area1 hr1001 min10 sec1 sec3 m

3.2.2 복합 재해의 동시 고려

이 연구의 대상지역들은 모두 소규모의 해안가 도시지역이고, 이러한 지역에 대한 강우의 임계지속기간은 1시간 ~ 2시간이나, 이 연구에서 분석한 폭풍 해일의 지속기간은 5시간으로 강우의 지속기간과 폭풍 해일의 지속기간이 상이하다. 이에 이 연구에서는 서로 다른 지속기간을 가진 강우와 폭풍 해일 또는 조위를 고려하기 위해 강우의 중심과 폭풍 해일의 중심이 동일한 시간에 위치하도록 설정하였다(Fig. 5).

XP-SWMM은 폭풍 해일이 지속되는 5시간 전체를 모의하도록 설정하였고, 폭풍 해일이 가장 큰 시점에 강우의 중심이 위치하도록 강우 발생 시기를 결정하였다. 다만, 부산 마린시티의 경우, 폭풍 해일에 의한 피해가 주로 월파에 의해 발생되므로 강우의 중심과 월파의 중심을 일치시켰고(Fig. 5(a)), 상대적으로 조위의 영향이 큰 3개 지역은 강우의 중심과 조위의 중심을 맞추었다. Fig. 5(b)는 군산시 중앙동 지역의 복합 외력에 의한 침수 분석에 사용된 강우와 조위의 조합이다.

한편, 100년 빈도의 확률강우량만을 고려한 침수 분석에서는 유역 유출부의 경계조건으로 우수 관거의 설계 조건을 고려하여 약최고고조위가 일정하게 유지되도록 설정하였다.

https://static.apub.kr/journalsite/sites/kwra/2021-054-07/N0200540702/images/kwra_54_07_02_F5.jpg
Fig. 5.

Consideration of external force conditions with different durations

3.2.3 XP-SWMM의 월파량 고려

XP-SWMM에 ADCSWAN 및 FLOW-3D 모형에 의해 산정된 월파량을 입력하기 위해 해안가 지역에 절점을 생성하여 월파 현상을 구현하였다. XP-SWMM에서 월파량을 입력하기 위한 절점의 위치는 FLOW-3D 모형에서 월파량을 산정한 격자의 중심 위치이다.

Fig. 6(a)는 마린시티 지역에 대한 월파량 입력 지점을 나타낸 것으로서, 유역 경계 주변에 동일 간격으로 원으로 표시한 지점들이 해당된다. Fig. 6(b)는 XP-SWMM에 월파량 입력 지점들을 반영하고, 하나의 절점에 월파량 시계열을 입력한 화면을 나타낸다.

https://static.apub.kr/journalsite/sites/kwra/2021-054-07/N0200540702/images/kwra_54_07_02_F6.jpg
Fig. 6.

Considering wave overtopping on XP-SWMM

3.3 침수 모의 결과

3.3.1 단일 외력에 의한 침수 모의 결과

Fig. 7은 단일 외력을 고려한 지역별 침수 모의 결과이다. 즉, Fig. 7의 왼쪽 그림들은 지역별로 100년 빈도 강우에 의한 침수 모의 결과를 나타내고, Fig. 7의 오른쪽 그림들은 만조 시 100년 빈도 폭풍 해일에 의한 침수 모의 결과이다. 대체로 강우에 의한 침수 영역은 유역 중․상류 지역의 유역 전반에 걸쳐 발생하였고, 폭풍 해일에 의한 침수 영역은 해안가 전면부에 위치하는 것을 볼 수 있다. 이는 폭풍 해일에 의한 조위 상승과 월파의 영향이 상류로 갈수록 감소하기 때문이다.

한편, 4개 지역 모두에서 공통적으로 강우에 비해 폭풍 해일에 의한 침수 영향이 상대적으로 크게 분석되었다. 이러한 결과는 연안 지역의 경우, 폭풍 해일에 대비한 침수 피해 저감 노력이 보다 중요함을 의미한다.

https://static.apub.kr/journalsite/sites/kwra/2021-054-07/N0200540702/images/kwra_54_07_02_F7.jpg
Fig. 7.

Simulation results by single external force (left: rainfall, right: storm surge)

3.3.2 복합 외력에 의한 침수 모의 결과

Fig. 8은 복합 외력을 고려한 지역별 침수 모의 결과이다. 즉, 강우 및 폭풍 해일을 동시에 고려함에 따라 발생된 침수 영역을 나타낸다. 복합 외력을 고려하는 경우, 단일 외력만을 고려한 분석 결과(Fig. 7)보다 침수 영역은 넓어졌고, 침수심은 깊어졌다.

복합 외력에 의한 침수 분석 결과는 대체로 단일 외력에 의한 침수 모의 결과를 중첩시켜 나타낸 결과와 유사하였고, 이는 일반적으로 예상할 수 있는 결과이다. 주목할만한 결과는 군산시 중앙동의 침수 분석에서 나타났다. 즉, 군산시 중앙동의 경우, 단일 외력만을 고려한 침수 모의 결과에서 나타나지 않았던 새로운 침수 영역이 발생하였다(Fig. 8(c)). 이와 관련된 상세 내용은 3.4절의 고찰에서 기술하였다.

https://static.apub.kr/journalsite/sites/kwra/2021-054-07/N0200540702/images/kwra_54_07_02_F8.jpg
Fig. 8.

Simulation results by compound external forces

3.4 결과 고찰

외력 조건별 침수의 영향을 정량적으로 비교하기 위해 침수 면적을 이용하였다. 이 연구에서는 강우만에 의해 유발된 침수 면적을 기준(기준값: 1)으로 하고, 폭풍 해일(조위+월파량)에 의한 침수 면적과 복합 외력에 의한 침수 면적의 상대적 비율로 분석하였다(Table 4).

Table 4.

Impact evaluation for inundation area by external force

ConditionMarine City, BusanCentum City, BusanJungang-dong area,
Gunsan
Ocheon Port area,
Boryeong
Inundation area
(km2)
RateInundation area
(km2)
RateInundation area
(km2)
RateInundation area
(km2)
Rate
Single
external force
Rainfall (①)0.01641.00.07591.00.04571.00.01751.0
Storm surge (②)0.03632.210.06850.900.14633.200.04122.35
Compound
external forces
Combination
(①+②)
0.05243.190.15051.980.26325.760.04732.70

분석 결과, 부산 센텀시티를 제외한 3개 지역은 모두 폭풍 해일에 의한 침수 면적이 강우에 의한 침수 면적에 비해 2.2 ~ 3.2배 넓은 것으로 분석되었다. 한편, 복합 외력에 의한 침수 면적은 마린시티와 센텀시티의 경우, 각각의 외력에 의한 침수 면적의 합과 유사하게 나타났다. 이는 각각의 외력에 의한 침수 영역이 상이하여 거의 중복되지 않음을 의미한다. 반면에, 오천항에서는 각각의 외력에 의한 침수 면적의 합이 복합 외력에 의한 면적보다 크게 나타났다. 이는 오천항의 경우, 유역면적이 작고 배수 체계가 비교적 단순하여 강우와 폭풍 해일에 의한 침수 영역이 중복되기 때문인 것으로 분석되었다(Fig. 7(d)).

군산시 중앙동 일대의 경우, 복합 외력에 의한 침수 면적이 각각의 독립적인 외력 조건에 의한 침수 면적의 합에 비해 37.1% 크게 나타났다. 이러한 현상의 원인을 분석하기 위해 복합 외력 조건에서만 나타난 우수 관거(Fig. 8(c)의 A 구간)에 대하여 종단을 검토하였다(Fig. 9). Fig. 9(a)는 강우만에 의해 분석된 우수 관거 내 흐름 종단을 나타내고, Fig. 9(b)는 폭풍 해일만에 의한 우수 관거의 종단이다. 그림을 통해 각각의 독립적인 외력 조건 하에서는 해당 구간에서 침수가 발생되지 않은 것을 볼 수 있다. 다만, 강우만을 고려하더라도 우수 관거는 만관이 된 상태를 확인할 수 있다(Fig. 9(a)). 반면에, 만관 상태에서 폭풍 해일이 함께 고려됨에 따라 해수 범람과 조위 상승에 의해 우수 배제가 불량하게 되었고, 이로 인해 침수가 유발된 것으로 분석되었다(Fig. 9(c)). 따라서 이러한 지역은 복합 외력에 대한 취약지구로 판단할 수 있고, 단일 외력의 고려만으로는 침수를 예상하기 어려운 지역임을 알 수 있다.

https://static.apub.kr/journalsite/sites/kwra/2021-054-07/N0200540702/images/kwra_54_07_02_F9.jpg
Fig. 9.

A part of drainage profiles by external force in Jungang-dong area, Gunsan

4. 결 론

이 연구에서는 외력 조건에 따른 연안 지역의 침수 특성을 분석하였다. 연구에서 고려된 외력 조건은 두 가지로서 강우와 폭풍 해일(조위와 월파)이다. 분석 대상 연안 지역으로는 남해안에 위치하는 2개 지역(부산시 해운대구의 마린시티와 센텀시티)과 서해안의 2개 지역(군산시 중앙동 일원 및 보령시 오천항)이 선정되었다.

복합 외력을 고려한 연안 지역의 침수 모의를 위해서는 유역의 강우-유출 현상과 바다의 조위 및 월파량을 경계조건으로 반영할 수 있는 침수 모의 모형이 요구되는데, 이 연구에서는 XP-SWMM을 이용하였다. 한편, 조위 및 월파량 산정에는 ADCSWAN (ADCIRC와 UnSWAN) 및 FLOW-3D 모형이 이용되었다.

연안 지역별 침수 모의는 100년 빈도의 강우와 폭풍 해일을 독립적으로 고려한 경우와 복합적으로 고려한 경우를 구분하여 수행되었다. 우선, 외력을 독립적으로 고려한 결과, 대체로 폭풍 해일만 고려한 경우가 강우만 고려한 경우에 비해 침수 영향이 크게 나타났다. 따라서 연안 지역의 경우, 폭풍 해일에 의한 침수 피해 방지 계획이 상대적으로 중요한 것으로 분석되었다. 두 번째, 복합 외력에 의한 침수 분석 결과는 대체로 단일 외력에 의한 침수 모의 결과를 중첩시켜 나타낸 결과와 유사하였다. 다만, 특정 지역에서는 복합 외력을 고려함에 따라 단일 외력만을 고려한 침수 모의에서 나타나지 않았던 새로운 침수 영역이 발생하기도 하였다. 이러한 결과는 독립적인 외력 조건에서는 우수 관거가 만관 또는 그 이하의 상태가 되지만, 두 가지의 외력이 동시에 고려됨에 따라 우수 관거의 통수능 한계를 초과하여 나타났다. 이러한 지역은 복합 외력에 대한 취약지구로 판단되었고, 해당 지역의 적절한 침수 방지 대책 수립을 위해서는 복합적인 외력 조건이 고려되어야 함을 시사하였다.

현행, 자연재해저감종합계획에서는 침수와 관련된 재해 원인 지역을 내수재해, 해안재해, 하천재해 등으로 구분하고 있다. 하지만 이 연구에서 검토된 바와 같이, 연안 지역의 침수 원인은 복합적으로 나타날 뿐만 아니라, 복합 외력을 고려함에 따라 추가적으로 나타날 수 있는 침수 위험 지역도 존재한다. 따라서 기존의 획일적인 재해 원인의 구분보다는 지역의 특성에 맞는 복합적인 재해 원인을 검토할 필요가 있음을 제안한다.

Acknowledgements

본 논문은 행정안전부 극한 재난대응 기반기술 개발사업의 일환인 “해안가 복합재난 위험지역 피해저감 기술개발(연구과제번호: 2018-MOIS31-008)”의 지원으로 수행되었습니다.

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The distribution of the computed maximum current speed during the entire duration of the NAMI DANCE and FLOW-3D simulations. The resolution of computational domain is 10 m

Performance Comparison of NAMI DANCE and FLOW-3D® Models in Tsunami Propagation, Inundation and Currents using NTHMP Benchmark Problems

NTHMP 벤치마크 문제를 사용하여 쓰나미 전파, 침수 및 해류에서 NAMI DANCE 및 FLOW-3D® 모델의 성능 비교

Pure and Applied Geophysics volume 176, pages3115–3153 (2019)Cite this article

Abstract

Field observations provide valuable data regarding nearshore tsunami impact, yet only in inundation areas where tsunami waves have already flooded. Therefore, tsunami modeling is essential to understand tsunami behavior and prepare for tsunami inundation. It is necessary that all numerical models used in tsunami emergency planning be subject to benchmark tests for validation and verification. This study focuses on two numerical codes, NAMI DANCE and FLOW-3D®, for validation and performance comparison. NAMI DANCE is an in-house tsunami numerical model developed by the Ocean Engineering Research Center of Middle East Technical University, Turkey and Laboratory of Special Research Bureau for Automation of Marine Research, Russia. FLOW-3D® is a general purpose computational fluid dynamics software, which was developed by scientists who pioneered in the design of the Volume-of-Fluid technique. The codes are validated and their performances are compared via analytical, experimental and field benchmark problems, which are documented in the ‘‘Proceedings and Results of the 2011 National Tsunami Hazard Mitigation Program (NTHMP) Model Benchmarking Workshop’’ and the ‘‘Proceedings and Results of the NTHMP 2015 Tsunami Current Modeling Workshop”. The variations between the numerical solutions of these two models are evaluated through statistical error analysis.

현장 관찰은 연안 쓰나미 영향에 관한 귀중한 데이터를 제공하지만 쓰나미 파도가 이미 범람한 침수 지역에서만 가능합니다. 따라서 쓰나미 모델링은 쓰나미 행동을 이해하고 쓰나미 범람에 대비하는 데 필수적입니다.

쓰나미 비상 계획에 사용되는 모든 수치 모델은 검증 및 검증을 위한 벤치마크 테스트를 받아야 합니다. 이 연구는 검증 및 성능 비교를 위해 NAMI DANCE 및 FLOW-3D®의 두 가지 숫자 코드에 중점을 둡니다.

NAMI DANCE는 터키 중동 기술 대학의 해양 공학 연구 센터와 러시아 해양 연구 자동화를 위한 특별 조사국 연구소에서 개발한 사내 쓰나미 수치 모델입니다. FLOW-3D®는 Volume-of-Fluid 기술의 설계를 개척한 과학자들이 개발한 범용 전산 유체 역학 소프트웨어입니다.

코드의 유효성이 검증되고 분석, 실험 및 현장 벤치마크 문제를 통해 코드의 성능이 비교되며, 이는 ‘2011년 NTHMP(National Tsunami Hazard Mitigation Program) 모델 벤치마킹 워크숍의 절차 및 결과’와 ”절차 및 NTHMP 2015 쓰나미 현재 모델링 워크숍 결과”. 이 두 모델의 수치 해 사이의 변동은 통계적 오류 분석을 통해 평가됩니다.

The distribution of the computed maximum current speed during the entire duration of the NAMI DANCE and FLOW-3D simulations. The resolution of computational domain is 10 m
The distribution of the computed maximum current speed during the entire duration of the NAMI DANCE and FLOW-3D simulations. The resolution of computational domain is 10 m

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Acknowledgements

The authors wish to thank Dr. Andrey Zaytsev due to his undeniable contributions to the development of in-house numerical model, NAMI DANCE. The Turkish branch of Flow Science, Inc. is also acknowledged. Finally, the National Tsunami Hazard Mitigation Program (NTHMP), who provided most of the benchmark data, is appreciated. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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  1. Deniz Velioglu SogutPresent address: 1212 Computer Science, Department of Civil Engineering, Stony Brook University, Stony Brook, NY, 11794, USA

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  1. Middle East Technical University, 06800, Ankara, TurkeyDeniz Velioglu Sogut & Ahmet Cevdet Yalciner

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Correspondence to Deniz Velioglu Sogut.

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Velioglu Sogut, D., Yalciner, A.C. Performance Comparison of NAMI DANCE and FLOW-3D® Models in Tsunami Propagation, Inundation and Currents using NTHMP Benchmark Problems. Pure Appl. Geophys. 176, 3115–3153 (2019). https://doi.org/10.1007/s00024-018-1907-9

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  • Received22 December 2017
  • Revised16 May 2018
  • Accepted24 May 2018
  • Published07 June 2018
  • Issue Date01 July 2019
  • DOIhttps://doi.org/10.1007/s00024-018-1907-9

Keywords

  • Tsunami
  • depth-averaged shallow water
  • Reynolds-averaged Navier–Stokes
  • benchmarking
  • NAMI DANCE
  • FLOW-3D®

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FLOW-3D 소프트웨어 제품군의 모든 제품은 2023R1에서 IT 관련 개선 사항을 받았습니다. FLOW-3D 2023R1은 이제 Windows 11 및 RHEL 8을 지원합니다. 누락된 종속성을 보고하도록 Linux 설치 프로그램이 개선되었으며 더 이상 루트 수준 권한이 필요하지 않으므로 설치가 더 쉽고 안전해집니다. 또한 워크플로를 자동화한 사용자를 위해 입력 파일 변환기에 명령줄 인터페이스를 추가하여 스크립트 환경에서도 워크플로가 업데이트된 입력 파일로 작동하는지 확인할 수 있습니다.

확장된 PQ 2 분석

제조에 사용되는 유압 시스템은 PQ 2 곡선을 사용하여 모델링할 수 있습니다. 장치의 세부 사항을 건너뛰고 흐름에 미치는 영향을 포함하기 위해 질량-운동량 소스 또는 속도 경계 조건을 사용하여 유압 시스템을 근사화하는 것이 편리한 단순화인 경우가 많습니다. 기존 PQ 2 분석 모델을 확장하여 이러한 유형의 기하학적 단순화를 허용하면서도 여전히 현실적인 결과를 제공합니다. 이것은 시뮬레이션 시간과 모델 복잡성의 감소로 해석됩니다.

FLOW-3D 2022R2 의 새로운 기능

FLOW-3D 2022R2 제품군 의 출시와 함께 Flow Science는 워크스테이션과 FLOW-3D 의 HPC 버전 을 통합하여 단일 노드 CPU 구성에서 다중 구성에 이르기까지 모든 유형의 하드웨어 아키텍처를 활용할 수 있는 단일 솔버 엔진을 제공합니다. 노드 병렬 고성능 컴퓨팅 실행. 추가 개발에는 점탄성 흐름을 위한 새로운 로그 구조 텐서 방법, 지속적인 솔버 속도 성능 개선, 고급 냉각 채널 및 팬텀 구성 요소 제어, 향상된 연행 공기 기능이 포함됩니다.

통합 솔버

FLOW-3D 제품을 단일 통합 솔버로 마이그레이션하여  로컬 워크스테이션 또는 고성능 컴퓨팅 하드웨어 환경에서 원활하게 실행했습니다.

많은 사용자가 노트북이나 로컬 워크스테이션에서 모델을 실행하지만 고성능 컴퓨팅 클러스터에서 더 큰 모델을 실행합니다. 2022R2 릴리스에서는 통합 솔버를 통해 사용자가 HPC 솔루션에서 OpenMP/MPI 하이브리드 병렬화의 동일한 이점을 활용하여 워크스테이션 및 노트북에서 실행할 수 있습니다.

성능 확장의 예
점점 더 많은 수의 CPU 코어를 사용하는 성능 확장의 예
메쉬 분해의 예
OpenMP/MPI 하이브리드 병렬화를 위한 메시 분해의 예

솔버 성능 개선

멀티 소켓 워크스테이션

멀티 소켓 워크스테이션은 이제 매우 일반적이며 대규모 시뮬레이션을 실행할 수 있습니다. 새로운 통합 솔버를 통해 이러한 유형의 하드웨어를 사용하는 사용자는 일반적으로 HPC 클러스터 구성에서만 사용할 수 있었던 OpenMP/MPI 하이브리드 병렬화를 활용하여 모델을 실행할 수 있는 성능 이점을 볼 수 있습니다.

낮은 수준의 루틴으로 벡터화 및 메모리 액세스 개선

대부분의 테스트 사례에서 10%에서 20% 정도의 성능 향상이 관찰되었으며 일부 사례에서는 20%를 초과하는 런타임 이점이 있었습니다.

정제된 체적 대류 안정성 한계

시간 단계 안정성 한계는 모델 런타임의 주요 동인입니다. 2022R2에서는 새로운 시간 단계 안정성 한계인 3D 대류 안정성 한계를 숫자 위젯에서 사용할 수 있습니다. 실행 중이고 대류가 제한된(cx, cy 또는 cz 제한) 모델의 경우 새 옵션은 30% 정도의 일반적인 속도 향상을 보여주었습니다.

압력 솔버 프리 컨디셔너

경우에 따라 까다로운 흐름 구성의 경우 과도한 압력 솔버 반복으로 인해 실행 시간이 길어질 수 있습니다. 어려운 경우 2022R2에서는 모델이 너무 많이 반복될 때 FLOW-3D가 자동으로 새로운 프리 컨디셔너를 활성화하여 압력 수렴을 돕습니다. 테스트의 런타임이 1.9배에서 335배까지 빨라졌습니다!

점탄성 유체에 대한 로그 형태 텐서 방법

점탄성 유체에 대한 새로운 솔버 옵션을 사용자가 사용할 수 있으며 특히 높은 Weissenberg 수치에 효과적입니다.

점탄성 흐름을 위한 개선된 솔루션
로그 구조 텐서 솔루션을 사용하여 점탄성 흐름에 대한 높은 Weissenberg 수에서 개선된 솔루션의 예. Courtesy MF Tome, et al., J. Non-Newton. 체액. 기계 175-176 (2012) 44–54

활성 시뮬레이션 제어 확장

능동 시뮬레이션 제어 기능은 연속 주조 및 적층 제조 응용 프로그램과 주조 및 기타 여러 열 관리 응용 프로그램에 사용되는 냉각 채널에 일반적으로 사용되는 팬텀 개체를 포함하도록 확장되었습니다.

동적 열 제어의 예
융합 증착 모델링 애플리케이션을 위한 동적 열 제어의 예
가상 물체 속도 제어의 예
산업용 탱크 적용을 위한 동적 냉각 채널 제어의 예
동적 열 제어의 예
연속 주조 애플리케이션을 위한 팬텀 물체 속도 제어의 예

연행 공기 기능 개선

디퓨저 및 유사한 산업용 기포 흐름 응용 분야의 경우 이제 대량 공급원을 사용하여 물 기둥에 공기를 도입할 수 있습니다. 또한 혼입 공기 및 용존 산소의 난류 확산에 대한 기본값이 업데이트되었으며 매우 낮은 공기 농도에 대한 모델 정확도가 향상되었습니다.

디퓨저 모델의 예
디퓨저 모델의 예: 질량원을 사용하여 물기둥에 공기를 도입할 수 있습니다.
Figure 3. Different parts of a Searaser; 1) Buoy 2) Chamber 3) Valves 4) Generator 5) Anchor system

데이터 기반 방법을 활용한 재생 가능 에너지 변환기의 전력 및 수소 생성 예측 지속 가능한 스마트 그리드 사례 연구

Fatemehsadat Mirshafiee1, Emad Shahbazi 2, Mohadeseh Safi 3, Rituraj Rituraj 4,*
1Department of Electrical and Computer Engineering, K.N. Toosi University of Technology, Tehran 1999143344 , Iran
2Department of Mechatronic, Amirkabir University of Technology, Tehran 158754413, Iran
3Department of Mechatronic, Electrical and Computer Engineering, University of Tehran, Tehran 1416634793, Iran
4 Faculty of Informatics, Obuda University, 1023, Budapest, Hungary

  • Correspondence: rituraj88@stud.uni-obuda.hu

ABSTRACT

본 연구는 지속가능한 에너지 변환기의 전력 및 수소 발생 모델링을 위한 데이터 기반 방법론을 제안합니다. 파고와 풍속을 달리하여 파고와 수소생산을 예측합니다.

또한 이 연구는 파도에서 수소를 추출할 수 있는 가능성을 강조하고 장려합니다. FLOW-3D 소프트웨어 시뮬레이션에서 추출한 데이터와 해양 특수 테스트의 실험 데이터를 사용하여 두 가지 데이터 기반 학습 방법의 비교 분석을 수행합니다.

결과는 수소 생산의 양은 생성된 전력의 양에 비례한다는 것을 보여줍니다. 제안된 재생 에너지 변환기의 신뢰성은 지속 가능한 스마트 그리드 애플리케이션으로 추가로 논의됩니다.

This study proposes a data-driven methodology for modeling power and hydrogen generation of a sustainable energy converter. The wave and hydrogen production at different wave heights and wind speeds are predicted. Furthermore, this research emphasizes and encourages the possibility of extracting hydrogen from ocean waves. By using the extracted data from FLOW-3D software simulation and the experimental data from the special test in the ocean, the comparison analysis of two data-driven learning methods is conducted. The results show that the amount of hydrogen production is proportional to the amount of generated electrical power. The reliability of the proposed renewable energy converter is further discussed as a sustainable smart grid application.

Key words

Cavity, Combustion efficiency, hydrogen fuel, Computational Fluent and Gambit.

Figure 1. The process of power and hydrogen production with Searaser.
Figure 1. The process of power and hydrogen production with Searaser.
Figure 2. The cross-section A-A of the two essential parts of a Searaser
Figure 2. The cross-section A-A of the two essential parts of a Searaser
Figure 3. Different parts of a Searaser; 1) Buoy 2) Chamber 3) Valves 4) Generator 5) Anchor system
Figure 3. Different parts of a Searaser; 1) Buoy 2) Chamber 3) Valves 4) Generator 5) Anchor system
Figure 4. The boundary conditions of the control volume
Figure 4. The boundary conditions of the control volume
Figure 5. The wind velocity during the period of the experimental test
Figure 5. The wind velocity during the period of the experimental test

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Figure 14. Defects: (a) Unmelt defects(Scheme NO.4);(b) Pores defects(Scheme NO.1); (c); Spattering defect (Scheme NO.3); (d) Low overlapping rate defects(Scheme NO.5).

Molten pool structure, temperature and velocity
flow in selective laser melting AlCu5MnCdVA alloy

용융 풀 구조, 선택적 온도 및 속도 흐름 레이저 용융 AlCu5MnCdVA 합금

Pan Lu1 , Zhang Cheng-Lin2,6,Wang Liang3, Liu Tong4 and Liu Jiang-lin5
1 Aviation and Materials College, Anhui Technical College of Mechanical and Electrical Engineering, Wuhu Anhui 241000, People’s
Republic of China 2 School of Engineering Science, University of Science and Technology of China, Hefei Anhui 230026, People’s Republic of China 3 Anhui Top Additive Manufacturing Technology Co., Ltd., Wuhu Anhui 241300, People’s Republic of China 4 Anhui Chungu 3D Printing Institute of Intelligent Equipment and Industrial Technology, Anhui 241300, People’s Republic of China 5 School of Mechanical and Transportation Engineering, Taiyuan University of Technology, Taiyuan Shanxi 030024, People’s Republic of
China 6 Author to whom any correspondence should be addressed.
E-mail: ahjdpanlu@126.com, jiao__zg@126.com, ahjdjxx001@126.com,tongliu1988@126.com and liujianglin@tyut.edu.cn

Keywords

SLM, molten pool, AlCu5MnCdVA alloy, heat flow, velocity flow, numerical simulation

Abstract

선택적 레이저 용융(SLM)은 열 전달, 용융, 상전이, 기화 및 물질 전달을 포함하는 복잡한 동적 비평형 프로세스인 금속 적층 제조(MAM)에서 가장 유망한 기술 중 하나가 되었습니다. 용융 풀의 특성(구조, 온도 흐름 및 속도 흐름)은 SLM의 최종 성형 품질에 결정적인 영향을 미칩니다. 이 연구에서는 선택적 레이저 용융 AlCu5MnCdVA 합금의 용융 풀 구조, 온도 흐름 및 속도장을 연구하기 위해 수치 시뮬레이션과 실험을 모두 사용했습니다.

그 결과 용융풀의 구조는 다양한 형태(깊은 오목 구조, 이중 오목 구조, 평면 구조, 돌출 구조 및 이상적인 평면 구조)를 나타냈으며, 용융 풀의 크기는 약 132 μm × 107 μm × 50 μm였습니다. : 용융풀은 초기에는 여러 구동력에 의해 깊이 15μm의 깊은 오목형상이었으나, 성형 후기에는 장력구배에 의해 높이 10μm의 돌출형상이 되었다. 용융 풀 내부의 금속 흐름은 주로 레이저 충격력, 금속 액체 중력, 표면 장력 및 반동 압력에 의해 구동되었습니다.

AlCu5MnCdVA 합금의 경우, 금속 액체 응고 속도가 매우 빠르며(3.5 × 10-4 S), 가열 속도 및 냉각 속도는 각각 6.5 × 107 K S-1 및 1.6 × 106 K S-1 에 도달했습니다. 시각적 표준으로 표면 거칠기를 선택하고, 낮은 레이저 에너지 AlCu5MnCdVA 합금 최적 공정 매개변수 창을 수치 시뮬레이션으로 얻었습니다: 레이저 출력 250W, 부화 공간 0.11mm, 층 두께 0.03mm, 레이저 스캔 속도 1.5m s-1 .

또한, 실험 프린팅과 수치 시뮬레이션과 비교할 때, 용융 풀의 폭은 각각 약 205um 및 약 210um이었고, 인접한 두 용융 트랙 사이의 중첩은 모두 약 65um이었다. 결과는 수치 시뮬레이션 결과가 실험 인쇄 결과와 기본적으로 일치함을 보여 수치 시뮬레이션 모델의 정확성을 입증했습니다.

Selective Laser Melting (SLM) has become one of the most promising technologies in Metal Additive Manufacturing (MAM), which is a complex dynamic non-equilibrium process involving heat transfer, melting, phase transition, vaporization and mass transfer. The characteristics of the molten pool (structure, temperature flow and velocity flow) have a decisive influence on the final forming quality of SLM. In this study, both numerical simulation and experiments were employed to study molten pool structure, temperature flow and velocity field in Selective Laser Melting AlCu5MnCdVA alloy. The results showed the structure of molten pool showed different forms(deep-concave structure, double-concave structure, plane structure, protruding structure and ideal planar structure), and the size of the molten pool was approximately 132 μm × 107 μm × 50 μm: in the early stage, molten pool was in a state of deep-concave shape with a depth of 15 μm due to multiple driving forces, while a protruding shape with a height of 10 μm duo to tension gradient in the later stages of forming. The metal flow inside the molten pool was mainly driven by laser impact force, metal liquid gravity, surface tension and recoil pressure. For AlCu5MnCdVA alloy, metal liquid solidification speed was extremely fast(3.5 × 10−4 S), the heating rate and cooling rate reached 6.5 × 107 K S−1 and 1.6 × 106 K S−1 , respectively. Choosing surface roughness as a visual standard, low-laser energy AlCu5MnCdVA alloy optimum process parameters window was obtained by numerical simulation: laser power 250 W, hatching space 0.11 mm, layer thickness 0.03 mm, laser scanning velocity 1.5 m s−1 . In addition, compared with experimental printing and numerical simulation, the width of the molten pool was about 205 um and about 210 um, respectively, and overlapping between two adjacent molten tracks was all about 65 um. The results showed that the numerical simulation results were basically consistent with the experimental print results, which proved the correctness of the numerical simulation model.

Figure 1. AlCu5MnCdVA powder particle size distribution.
Figure 1. AlCu5MnCdVA powder particle size distribution.
Figure 2. AlCu5MnCdVA powder
Figure 2. AlCu5MnCdVA powder
Figure 3. Finite element model and calculation domains of SLM.
Figure 3. Finite element model and calculation domains of SLM.
Figure 4. SLM heat transfer process.
Figure 4. SLM heat transfer process.
Figure 14. Defects: (a) Unmelt defects(Scheme NO.4);(b) Pores defects(Scheme NO.1); (c); Spattering defect (Scheme NO.3); (d) Low
overlapping rate defects(Scheme NO.5).
Figure 17. Two-pass molten tracks overlapping for Scheme NO.2.
Figure 17. Two-pass molten tracks overlapping for Scheme NO.2.

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Figure 5 A schematic of the water model of reactor URO 200.

Physical and Numerical Modeling of the Impeller Construction Impact on the Aluminum Degassing Process

알루미늄 탈기 공정에 미치는 임펠러 구성의 물리적 및 수치적 모델링

Kamil Kuglin,1 Michał Szucki,2 Jacek Pieprzyca,3 Simon Genthe,2 Tomasz Merder,3 and Dorota Kalisz1,*

Mikael Ersson, Academic Editor

Author information Article notes Copyright and License information Disclaimer

Associated Data

Data Availability Statement

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Abstract

This paper presents the results of tests on the suitability of designed heads (impellers) for aluminum refining. The research was carried out on a physical model of the URO-200, followed by numerical simulations in the FLOW 3D program. Four design variants of impellers were used in the study. The degree of dispersion of the gas phase in the model liquid was used as a criterion for evaluating the performance of each solution using different process parameters, i.e., gas flow rate and impeller speed. Afterward, numerical simulations in Flow 3D software were conducted for the best solution. These simulations confirmed the results obtained with the water model and verified them.

Keywords: aluminum, impeller construction, degassing process, numerical modeling, physical modeling

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1. Introduction

Constantly increasing requirements concerning metallurgical purity in terms of hydrogen content and nonmetallic inclusions make casting manufacturers use effective refining techniques. The answer to this demand is the implementation of the aluminum refining technique making use of a rotor with an original design guaranteeing efficient refining [1,2,3,4]. The main task of the impeller (rotor) is to reduce the contamination of liquid metal (primary and recycled aluminum) with hydrogen and nonmetallic inclusions. An inert gas, mainly argon or a mixture of gases, is introduced through the rotor into the liquid metal to bring both hydrogen and nonmetallic inclusions to the metal surface through the flotation process. Appropriately and uniformly distributed gas bubbles in the liquid metal guarantee achieving the assumed level of contaminant removal economically. A very important factor in deciding about the obtained degassing effect is the optimal rotor design [5,6,7,8]. Thanks to the appropriate geometry of the rotor, gas bubbles introduced into the liquid metal are split into smaller ones, and the spinning movement of the rotor distributes them throughout the volume of the liquid metal bath. In this solution impurities in the liquid metal are removed both in the volume and from the upper surface of the metal. With a well-designed impeller, the costs of refining aluminum and its alloys can be lowered thanks to the reduced inert gas and energy consumption (optimal selection of rotor rotational speed). Shorter processing time and a high degree of dehydrogenation decrease the formation of dross on the metal surface (waste). A bigger produced dross leads to bigger process losses. Consequently, this means that the choice of rotor geometry has an indirect impact on the degree to which the generated waste is reduced [9,10].

Another equally important factor is the selection of process parameters such as gas flow rate and rotor speed [11,12]. A well-designed gas injection system for liquid metal meets two key requirements; it causes rapid mixing of the liquid metal to maintain a uniform temperature throughout the volume and during the entire process, to produce a chemically homogeneous metal composition. This solution ensures effective degassing of the metal bath. Therefore, the shape of the rotor, the arrangement of the nozzles, and their number are significant design parameters that guarantee the optimum course of the refining process. It is equally important to complete the mixing of the metal bath in a relatively short time, as this considerably shortens the refining process and, consequently, reduces the process costs. Another important criterion conditioning the implementation of the developed rotor is the generation of fine diffused gas bubbles which are distributed throughout the metal volume, and whose residence time will be sufficient for the bubbles to collide and adsorb the contaminants. The process of bubble formation by the spinning rotors differs from that in the nozzles or porous molders. In the case of a spinning rotor, the shear force generated by the rotor motion splits the bubbles into smaller ones. Here, the rotational speed, mixing force, surface tension, and fluid density have a key effect on the bubble size. The velocity of the bubbles, which depends mainly on their size and shape, determines their residence time in the reactor and is, therefore, very important for the refining process, especially since gas bubbles in liquid aluminum may remain steady only below a certain size [13,14,15].

The impeller designs presented in the article were developed to improve the efficiency of the process and reduce its costs. The impellers used so far have a complicated structure and are very pricey. The success of the conducted research will allow small companies to become independent of external supplies through the possibility of making simple and effective impellers on their own. The developed structures were tested on the water model. The results of this study can be considered as pilot.

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2. Materials and Methods

Rotors were realized with the SolidWorks computer design technique and a 3D printer. The developed designs were tested on a water model. Afterward, the solution with the most advantageous refining parameters was selected and subjected to calculations with the Flow3D package. As a result, an impeller was designed for aluminum refining. Its principal lies in an even distribution of gas bubbles in the entire volume of liquid metal, with the largest possible participation of the bubble surface, without disturbing the metal surface. This procedure guarantees the removal of gaseous, as well as metallic and nonmetallic, impurities.

2.1. Rotor Designs

The developed impeller constructions, shown in Figure 1Figure 2Figure 3 and Figure 4, were printed on a 3D printer using the PLA (polylactide) material. The impeller design models differ in their shape and the number of holes through which the inert gas flows. Figure 1Figure 2 and Figure 3 show the same impeller model but with a different number of gas outlets. The arrangement of four, eight, and 12 outlet holes was adopted in the developed design. A triangle-shaped structure equipped with three gas outlet holes is presented in Figure 4.

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Figure 1

A 3D model—impeller with four holes—variant B4.

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Figure 2

A 3D model—impeller with eight holes—variant B8.

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Figure 3

A 3D model—impeller with twelve holes—variant B12.

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Figure 4

A 3D model—‘red triangle’ impeller with three holes—variant RT3.

2.2. Physical Models

Investigations were carried out on a water model of the URO 200 reactor of the barbotage refining process (see Figure 5).

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Figure 5

A schematic of the water model of reactor URO 200.

The URO 200 reactor can be classified as a cyclic reactor. The main element of the device is a rotor, which ends the impeller. The whole system is attached to a shaft via which the refining gas is supplied. Then, the shaft with the rotor is immersed in the liquid metal in the melting pot or the furnace chamber. In URO 200 reactors, the refining process lasts 600 s (10 min), the gas flow rate that can be obtained ranges from 5 to 20 dm3·min−1, and the speed at which the rotor can move is 0 to 400 rpm. The permissible quantity of liquid metal for barbotage refining is 300 kg or 700 kg [8,16,17]. The URO 200 has several design solutions which improve operation and can be adapted to the existing equipment in the foundry. These solutions include the following [8,16]:

  • URO-200XR—used for small crucible furnaces, the capacity of which does not exceed 250 kg, with no control system and no control of the refining process.
  • URO-200SA—used to service several crucible furnaces of capacity from 250 kg to 700 kg, fully automated and equipped with a mechanical rotor lift.
  • URO-200KA—used for refining processes in crucible furnaces and allows refining in a ladle. The process is fully automated, with a hydraulic rotor lift.
  • URO-200KX—a combination of the XR and KA models, designed for the ladle refining process. Additionally, refining in heated crucibles is possible. The unit is equipped with a manual hydraulic rotor lift.
  • URO-200PA—designed to cooperate with induction or crucible furnaces or intermediate chambers, the capacity of which does not exceed one ton. This unit is an integral part of the furnace. The rotor lift is equipped with a screw drive.

Studies making use of a physical model can be associated with the observation of the flow and circulation of gas bubbles. They require meeting several criteria regarding the similarity of the process and the object characteristics. The similarity conditions mainly include geometric, mechanical, chemical, thermal, and kinetic parameters. During simulation of aluminum refining with inert gas, it is necessary to maintain the geometric similarity between the model and the real object, as well as the similarity related to the flow of liquid metal and gas (hydrodynamic similarity). These quantities are characterized by the Reynolds, Weber, and Froude numbers. The Froude number is the most important parameter characterizing the process, its magnitude is the same for the physical model and the real object. Water was used as the medium in the physical modeling. The factors influencing the choice of water are its availability, relatively low cost, and kinematic viscosity at room temperature, which is very close to that of liquid aluminum.

The physical model studies focused on the flow of inert gas in the form of gas bubbles with varying degrees of dispersion, particularly with respect to some flow patterns such as flow in columns and geysers, as well as disturbance of the metal surface. The most important refining parameters are gas flow rate and rotor speed. The barbotage refining studies for the developed impeller (variants B4, B8, B12, and RT3) designs were conducted for the following process parameters:

  • Rotor speed: 200, 300, 400, and 500 rpm,
  • Ideal gas flow: 10, 20, and 30 dm3·min−1,
  • Temperature: 293 K (20 °C).

These studies were aimed at determining the most favorable variants of impellers, which were then verified using the numerical modeling methods in the Flow-3D program.

2.3. Numerical Simulations with Flow-3D Program

Testing different rotor impellers using a physical model allows for observing the phenomena taking place while refining. This is a very important step when testing new design solutions without using expensive industrial trials. Another solution is modeling by means of commercial simulation programs such as ANSYS Fluent or Flow-3D [18,19]. Unlike studies on a physical model, in a computer program, the parameters of the refining process and the object itself, including the impeller design, can be easily modified. The simulations were performed with the Flow-3D program version 12.03.02. A three-dimensional system with the same dimensions as in the physical modeling was used in the calculations. The isothermal flow of liquid–gas bubbles was analyzed. As in the physical model, three speeds were adopted in the numerical tests: 200, 300, and 500 rpm. During the initial phase of the simulations, the velocity field around the rotor generated an appropriate direction of motion for the newly produced bubbles. When the required speed was reached, the generation of randomly distributed bubbles around the rotor was started at a rate of 2000 per second. Table 1 lists the most important simulation parameters.

Table 1

Values of parameters used in the calculations.

ParameterValueUnit
Maximum number of gas particles1,000,000
Rate of particle generation20001·s−1
Specific gas constant287.058J·kg−1·K−1
Atmospheric pressure1.013 × 105Pa
Water density1000kg·m−3
Water viscosity0.001kg·m−1·s−1
Boundary condition on the wallsNo-slip
Size of computational cell0.0034m

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In the case of the CFD analysis, the numerical solutions require great care when generating the computational mesh. Therefore, computational mesh tests were performed prior to the CFD calculations. The effect of mesh density was evaluated by taking into account the velocity of water in the tested object on the measurement line A (height of 0.065 m from the bottom) in a characteristic cross-section passing through the object axis (see Figure 6). The mesh contained 3,207,600, 6,311,981, 7,889,512, 11,569,230, and 14,115,049 cells.

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Figure 6

The velocity of the water depending on the size of the computational grid.

The quality of the generated computational meshes was checked using the criterion skewness angle QEAS [18]. This criterion is described by the following relationship:

QEAS=max{βmax−βeq180−βeq,βeq−βminβeq},

(1)

where βmaxβmin are the maximal and minimal angles (in degrees) between the edges of the cell, and βeq is the angle corresponding to an ideal cell, which for cubic cells is 90°.

Normalized in the interval [0;1], the value of QEAS should not exceed 0.75, which identifies the permissible skewness angle of the generated mesh. For the computed meshes, this value was equal to 0.55–0.65.

Moreover, when generating the computational grids in the studied facility, they were compacted in the areas of the highest gradients of the calculated values, where higher turbulence is to be expected (near the impeller). The obtained results of water velocity in the studied object at constant gas flow rate are shown in Figure 6.

The analysis of the obtained water velocity distributions (see Figure 6) along the line inside the object revealed that, with the density of the grid of nodal points, the velocity changed and its changes for the test cases of 7,889,512, 11,569,230, and 14,115,049 were insignificant. Therefore, it was assumed that a grid containing not less than 7,900,000 (7,889,512) cells would not affect the result of CFD calculations.

A single-block mesh of regular cells with a size of 0.0034 m was used in the numerical calculations. The total number of cells was approximately 7,900,000 (7,889,512). This grid resolution (see Figure 7) allowed the geometry of the system to be properly represented, maintaining acceptable computation time (about 3 days on a workstation with 2× CPU and 12 computing cores).

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Figure 7

Structured equidistant mesh used in numerical calculations: (a) mesh with smoothed, surface cells (the so-called FAVOR method) used in Flow-3D; (b) visualization of the applied mesh resolution.

The calculations were conducted with an explicit scheme. The timestep was selected by the program automatically and controlled by stability and convergence. From the moment of the initial velocity field generation (start of particle generation), it was 0.0001 s.

When modeling the degassing process, three fluids are present in the system: water, gas supplied through the rotor head (impeller), and the surrounding air. Modeling such a multiphase flow is a numerically very complex issue. The necessity to overcome the liquid backpressure by the gas flowing out from the impeller leads to the formation of numerical instabilities in the volume of fluid (VOF)-based approach used by Flow-3D software. Therefore, a mixed description of the analyzed flow was used here. In this case, water was treated as a continuous medium, while, in the case of gas bubbles, the discrete phase model (DPM) model was applied. The way in which the air surrounding the system was taken into account is later described in detail.

The following additional assumptions were made in the modeling:

  • —The liquid phase was considered as an incompressible Newtonian fluid.
  • —The effect of chemical reactions during the refining process was neglected.
  • —The composition of each phase (gas and liquid) was considered homogeneous; therefore, the viscosity and surface tension were set as constants.
  • —Only full turbulence existed in the liquid, and the effect of molecular viscosity was neglected.
  • —The gas bubbles were shaped as perfect spheres.
  • —The mutual interaction between gas bubbles (particles) was neglected.

2.3.1. Modeling of Liquid Flow 

The motion of the real fluid (continuous medium) is described by the Navier–Stokes Equation [20].

dudt=−1ρ∇p+ν∇2u+13ν∇(∇⋅ u)+F,

(2)

where du/dt is the time derivative, u is the velocity vector, t is the time, and F is the term accounting for external forces including gravity (unit components denoted by XYZ).

In the simulations, the fluid flow was assumed to be incompressible, in which case the following equation is applicable:

∂u∂t+(u⋅∇)u=−1ρ∇p+ν∇2u+F.

(3)

Due to the large range of liquid velocities during flows, the turbulence formation process was included in the modeling. For this purpose, the k–ε model turbulence kinetic energy k and turbulence dissipation ε were the target parameters, as expressed by the following equations [21]:

∂(ρk)∂t+∂(ρkvi)∂xi=∂∂xj[(μ+μtσk)⋅∂k∂xi]+Gk+Gb−ρε−Ym+Sk,

(4)

∂(ρε)∂t+∂(ρεui)∂xi=∂∂xj[(μ+μtσε)⋅∂k∂xi]+C1εεk(Gk+G3εGb)+C2ερε2k+Sε,

(5)

where ρ is the gas density, σκ and σε are the Prandtl turbulence numbers, k and ε are constants of 1.0 and 1.3, and Gk and Gb are the kinetic energy of turbulence generated by the average velocity and buoyancy, respectively.

As mentioned earlier, there are two gas phases in the considered problem. In addition to the gas bubbles, which are treated here as particles, there is also air, which surrounds the system. The boundary of phase separation is in this case the free surface of the water. The shape of the free surface can change as a result of the forming velocity field in the liquid. Therefore, it is necessary to use an appropriate approach to free surface tracking. The most commonly used concept in liquid–gas flow modeling is the volume of fluid (VOF) method [22,23], and Flow-3D uses a modified version of this method called TrueVOF. It introduces the concept of the volume fraction of the liquid phase fl. This parameter can be used for classifying the cells of a discrete grid into areas filled with liquid phase (fl = 1), gaseous phase, or empty cells (fl = 0) and those through which the phase separation boundary (fl ∈ (0, 1)) passes (free surface). To determine the local variations of the liquid phase fraction, it is necessary to solve the following continuity equation:

dfldt=0.

(6)

Then, the fluid parameters in the region of coexistence of the two phases (the so-called interface) depend on the volume fraction of each phase.

ρ=flρl+(1−fl)ρg,

(7)

ν=flνl+(1−fl)νg,

(8)

where indices l and g refer to the liquid and gaseous phases, respectively.

The parameter of fluid velocity in cells containing both phases is also determined in the same way.

u=flul+(1−fl)ug.

(9)

Since the processes taking place in the surrounding air can be omitted, to speed up the calculations, a single-phase, free-surface model was used. This means that no calculations were performed in the gas cells (they were treated as empty cells). The liquid could fill them freely, and the air surrounding the system was considered by the atmospheric pressure exerted on the free surface. This approach is often used in modeling foundry and metallurgical processes [24].

2.3.2. Modeling of Gas Bubble Flow 

As stated, a particle model was used to model bubble flow. Spherical particles (gas bubbles) of a given size were randomly generated in the area marked with green in Figure 7b. In the simulations, the gas bubbles were assumed to have diameters of 0.016 and 0.02 m corresponding to the gas flow rates of 10 and 30 dm3·min−1, respectively.

Experimental studies have shown that, as a result of turbulent fluid motion, some of the bubbles may burst, leading to the formation of smaller bubbles, although merging of bubbles into larger groupings may also occur. Therefore, to be able to observe the behavior of bubbles of different sizes (diameter), the calculations generated two additional particle types with diameters twice smaller and twice larger, respectively. The proportion of each species in the system was set to 33.33% (Table 2).

Table 2

Data assumed for calculations.

NoRotor Speed (Rotational Speed)
rpm
Bubbles Diameter
m
Corresponding Gas Flow Rate
dm3·min−1
NoRotor Speed (Rotational Speed)
rpm
Bubbles Diameter
m
Corresponding Gas Flow Rate
dm3·min−1
A2000.01610D2000.0230
0.0080.01
0.0320.04
B3000.01610E3000.0230
0.0080.01
0.0320.04
C5000.01610F5000.0230
0.0080.01
0.0320.04

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The velocity of the particle results from the generated velocity field (calculated from Equation (3) in the liquid ul around it and its velocity resulting from the buoyancy force ub. The effect of particle radius r on the terminal velocity associated with buoyancy force can be determined according to Stokes’ law.

ub=29 (ρg−ρl)μlgr2,

(10)

where g is the acceleration (9.81).

The DPM model was used for modeling the two-phase (water–air) flow. In this model, the fluid (water) is treated as a continuous phase and described by the Navier–Stokes equation, while gas bubbles are particles flowing in the model fluid (discrete phase). The trajectories of each bubble in the DPM system are calculated at each timestep taking into account the mass forces acting on it. Table 3 characterizes the DPM model used in our own research [18].

Table 3

Characteristic of the DPM model.

MethodEquations
Euler–LagrangeBalance equation:
dugdt=FD(u−ug)+g(ϱg−ϱ)ϱg+F.
FD (u − up) denotes the drag forces per mass unit of a bubble, and the expression for the drag coefficient FD is of the form
FD=18μCDReϱ⋅gd2g24.
The relative Reynolds number has the form
Re≡ρdg|ug−u|μ.
On the other hand, the force resulting from the additional acceleration of the model fluid has the form
F=12dρdtρg(u−ug),
where ug is the gas bubble velocity, u is the liquid velocity, dg is the bubble diameter, and CD is the drag coefficient.

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3. Results and Discussion

3.1. Calculations of Power and Mixing Time by the Flowing Gas Bubbles

One of the most important parameters of refining with a rotor is the mixing power induced by the spinning rotor and the outflowing gas bubbles (via impeller). The mixing power of liquid metal in a ladle of height (h) by gas injection can be determined from the following relation [15]:

pgVm=ρ⋅g⋅uB,

(11)

where pg is the mixing power, Vm is the volume of liquid metal in the reactor, ρ is the density of liquid aluminum, and uB is the average speed of bubbles, given below.

uB=n⋅R⋅TAc⋅Pm⋅t,

(12)

where n is the number of gas moles, R is the gas constant (8.314), Ac is the cross-sectional area of the reactor vessel, T is the temperature of liquid aluminum in the reactor, and Pm is the pressure at the middle tank level. The pressure at the middle level of the tank is calculated by a function of the mean logarithmic difference.

Pm=(Pa+ρ⋅g⋅h)−Paln(Pa+ρ⋅g⋅h)Pa,

(13)

where Pa is the atmospheric pressure, and h is the the height of metal in the reactor.

Themelis and Goyal [25] developed a model for calculating mixing power delivered by gas injection.

pg=2Q⋅R⋅T⋅ln(1+m⋅ρ⋅g⋅hP),

(14)

where Q is the gas flow, and m is the mass of liquid metal.

Zhang [26] proposed a model taking into account the temperature difference between gas and alloy (metal).

pg=QRTgVm[ln(1+ρ⋅g⋅hPa)+(1−TTg)],

(15)

where Tg is the gas temperature at the entry point.

Data for calculating the mixing power resulting from inert gas injection into liquid aluminum are given below in Table 4. The design parameters were adopted for the model, the parameters of which are shown in Figure 5.

Table 4

Data for calculating mixing power introduced by an inert gas.

ParameterValueUnit
Height of metal column0.7m
Density of aluminum2375kg·m−3
Process duration20s
Gas temperature at the injection site940K
Cross-sectional area of ladle0.448m2
Mass of liquid aluminum546.25kg
Volume of ladle0.23M3
Temperature of liquid aluminum941.15K

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Table 5 presents the results of mixing power calculations according to the models of Themelis and Goyal and of Zhang for inert gas flows of 10, 20, and 30 dm3·min−1. The obtained calculation results significantly differed from each other. The difference was an order of magnitude, which indicates that the model is highly inaccurate without considering the temperature of the injected gas. Moreover, the calculations apply to the case when the mixing was performed only by the flowing gas bubbles, without using a rotor, which is a great simplification of the phenomenon.

Table 5

Mixing power calculated from mathematical models.

Mathematical ModelMixing Power (W·t−1)
for a Given Inert Gas Flow (dm3·min−1)
102030
Themelis and Goyal11.4923.3335.03
Zhang0.821.662.49

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The mixing time is defined as the time required to achieve 95% complete mixing of liquid metal in the ladle [27,28,29,30]. Table 6 groups together equations for the mixing time according to the models.

Table 6

Models for calculating mixing time.

AuthorsModelRemarks
Szekely [31]τ=800ε−0.4ε—W·t−1
Chiti and Paglianti [27]τ=CVQlV—volume of reactor, m3
Ql—flow intensity, m3·s−1
Iguchi and Nakamura [32]τ=1200⋅Q−0.4D1.97h−1.0υ0.47υ—kinematic viscosity, m2·s−1
D—diameter of ladle, m
h—height of metal column, m
Q—liquid flow intensity, m3·s−1

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Figure 8 and Figure 9 show the mixing time as a function of gas flow rate for various heights of the liquid column in the ladle and mixing power values.

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Figure 8

Mixing time as a function of gas flow rate for various heights of the metal column (Iguchi and Nakamura model).

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Figure 9

Mixing time as a function of mixing power (Szekly model).

3.2. Determining the Bubble Size

The mechanisms controlling bubble size and mass transfer in an alloy undergoing refining are complex. Strong mixing conditions in the reactor promote impurity mass transfer. In the case of a spinning rotor, the shear force generated by the rotor motion separates the bubbles into smaller bubbles. Rotational speed, mixing force, surface tension, and liquid density have a strong influence on the bubble size. To characterize the kinetic state of the refining process, parameters k and A were introduced. Parameters kA, and uB can be calculated using the below equations [33].

k=2D⋅uBdB⋅π−−−−−−√,

(16)

A=6Q⋅hdB⋅uB,

(17)

uB=1.02g⋅dB,−−−−−√

(18)

where D is the diffusion coefficient, and dB is the bubble diameter.

After substituting appropriate values, we get

dB=3.03×104(πD)−2/5g−1/5h4/5Q0.344N−1.48.

(19)

According to the last equation, the size of the gas bubble decreases with the increasing rotational speed (see Figure 10).

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Figure 10

Effect of rotational speed on the bubble diameter.

In a flow of given turbulence intensity, the diameter of the bubble does not exceed the maximum size dmax, which is inversely proportional to the rate of kinetic energy dissipation in a viscous flow ε. The size of the gas bubble diameter as a function of the mixing energy, also considering the Weber number and the mixing energy in the negative power, can be determined from the following equations [31,34]:

  • —Sevik and Park:

dBmax=We0.6kr⋅(σ⋅103ρ⋅10−3)0.6⋅(10⋅ε)−0.4⋅10−2.

(20)

  • —Evans:

dBmax=⎡⎣Wekr⋅σ⋅1032⋅(ρ⋅10−3)13⎤⎦35 ⋅(10⋅ε)−25⋅10−2.

(21)

The results of calculating the maximum diameter of the bubble dBmax determined from Equation (21) are given in Table 7.

Table 7

The results of calculating the maximum diameter of the bubble using Equation (21).

ModelMixing Energy
ĺ (m2·s−3)
Weber Number (Wekr)
0.591.01.2
Zhang and Taniguchi
dmax
0.10.01670.02300.026
0.50.00880.01210.013
1.00.00670.00910.010
1.50.00570.00780.009
Sevik and Park
dBmax
0.10.2650.360.41
0.50.1390.190.21
1.00.1060.140.16
1.50.0900.120.14
Evans
dBmax
0.10.2470.3400.38
0.50.1300.1780.20
1.00.0980.1350.15
1.50.0840.1150.13

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3.3. Physical Modeling

The first stage of experiments (using the URO-200 water model) included conducting experiments with impellers equipped with four, eight, and 12 gas outlets (variants B4, B8, B12). The tests were carried out for different process parameters. Selected results for these experiments are presented in Figure 11Figure 12Figure 13 and Figure 14.

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Figure 11

Impeller variant B4—gas bubbles dispersion registered for a gas flow rate of 10 dm3·min−1 and rotor speed of (a) 200, (b) 300, (c) 400, and (d) 500 rpm.

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Figure 12

Impeller variant B8—gas bubbles dispersion registered for a gas flow rate of 10 dm3·min−1 and rotor speed of (a) 200, (b) 300, (c) 400, and (d) 500 rpm.

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Figure 13

Gas bubble dispersion registered for different processing parameters (impeller variant B12).

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Figure 14

Gas bubble dispersion registered for different processing parameters (impeller variant RT3).

The analysis of the refining variants presented in Figure 11Figure 12Figure 13 and Figure 14 reveals that the proposed impellers design model is not useful for the aluminum refining process. The number of gas outlet orifices, rotational speed, and flow did not affect the refining efficiency. In all the variants shown in the figures, very poor dispersion of gas bubbles was observed in the object. The gas bubble flow had a columnar character, and so-called dead zones, i.e., areas where no inert gas bubbles are present, were visible in the analyzed object. Such dead zones were located in the bottom and side zones of the ladle, while the flow of bubbles occurred near the turning rotor. Another negative phenomenon observed was a significant agitation of the water surface due to excessive (rotational) rotor speed and gas flow (see Figure 13, cases 20; 400, 30; 300, 30; 400, and 30; 500).

Research results for a ‘red triangle’ impeller equipped with three gas supply orifices (variant RT3) are presented in Figure 14.

In this impeller design, a uniform degree of bubble dispersion in the entire volume of the modeling fluid was achieved for most cases presented (see Figure 14). In all tested variants, single bubbles were observed in the area of the water surface in the vessel. For variants 20; 200, 30; 200, and 20; 300 shown in Figure 14, the bubble dispersion results were the worst as the so-called dead zones were identified in the area near the bottom and sidewalls of the vessel, which disqualifies these work parameters for further applications. Interestingly, areas where swirls and gas bubble chains formed were identified only for the inert gas flows of 20 and 30 dm3·min−1 and 200 rpm in the analyzed model. This means that the presented model had the best performance in terms of dispersion of gas bubbles in the model liquid. Its design with sharp edges also differed from previously analyzed models, which is beneficial for gas bubble dispersion, but may interfere with its suitability in industrial conditions due to possible premature wear.

3.4. Qualitative Comparison of Research Results (CFD and Physical Model)

The analysis (physical modeling) revealed that the best mixing efficiency results were obtained with the RT3 impeller variant. Therefore, numerical calculations were carried out for the impeller model with three outlet orifices (variant RT3). The CFD results are presented in Figure 15 and Figure 16.

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Figure 15

Simulation results of the impeller RT3, for given flows and rotational speeds after a time of 1 s: simulation variants (a) A, (b) B, (c) C, (d) D, (e) E, and (f) F.

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Figure 16

Simulation results of the impeller RT3, for given flows and rotational speeds after a time of 5.4 s.: simulation variants (a) A, (b) B, (c) C, (d) D, (e) E, and (f) F.

CFD results are presented for all analyzed variants (impeller RT3) at two selected calculation timesteps of 1 and 5.40 s. They show the velocity field of the medium (water) and the dispersion of gas bubbles.

Figure 15 shows the initial refining phase after 1 s of the process. In this case, the gas bubble formation and flow were observed in an area close to contact with the rotor. Figure 16 shows the phase when the dispersion and flow of gas bubbles were advanced in the reactor area of the URO-200 model.

The quantitative evaluation of the obtained results of physical and numerical model tests was based on the comparison of the degree of gas dispersion in the model liquid. The degree of gas bubble dispersion in the volume of the model liquid and the areas of strong turbulent zones formation were evaluated during the analysis of the results of visualization and numerical simulations. These two effects sufficiently characterize the required course of the process from the physical point of view. The known scheme of the below description was adopted as a basic criterion for the evaluation of the degree of dispersion of gas bubbles in the model liquid.

  • Minimal dispersion—single bubbles ascending in the region of their formation along the ladle axis; lack of mixing in the whole bath volume.
  • Accurate dispersion—single and well-mixed bubbles ascending toward the bath mirror in the region of the ladle axis; no dispersion near the walls and in the lower part of the ladle.
  • Uniform dispersion—most desirable; very good mixing of fine bubbles with model liquid.
  • Excessive dispersion—bubbles join together to form chains; large turbulence zones; uneven flow of gas.

The numerical simulation results give a good agreement with the experiments performed with the physical model. For all studied variants (used process parameters), the single bubbles were observed in the area of water surface in the vessel. For variants presented in Figure 13 (200 rpm, gas flow 20 and dm3·min−1) and relevant examples in numerical simulation Figure 16, the worst bubble dispersion results were obtained because the dead zones were identified in the area near the bottom and sidewalls of the vessel, which disqualifies these work parameters for further use. The areas where swirls and gas bubble chains formed were identified only for the inert gas flows of 20 and 30 dm3·min−1 and 200 rpm in the analyzed model (physical model). This means that the presented impeller model had the best performance in terms of dispersion of gas bubbles in the model liquid. The worst bubble dispersion results were obtained because the dead zones were identified in the area near the bottom and side walls of the vessel, which disqualifies these work parameters for further use.

Figure 17 presents exemplary results of model tests (CFD and physical model) with marked gas bubble dispersion zones. All variants of tests were analogously compared, and this comparison allowed validating the numerical model.

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Figure 17

Compilations of model research results (CFD and physical): A—single gas bubbles formed on the surface of the modeling liquid, B—excessive formation of gas chains and swirls, C—uniform distribution of gas bubbles in the entire volume of the tank, and D—dead zones without gas bubbles, no dispersion. (a) Variant B; (b) variant F.

It should be mentioned here that, in numerical simulations, it is necessary to make certain assumptions and simplifications. The calculations assumed three particle size classes (Table 2), which represent the different gas bubbles that form due to different gas flow rates. The maximum number of particles/bubbles (Table 1) generated was assumed in advance and related to the computational capabilities of the computer. Too many particles can also make it difficult to visualize and analyze the results. The size of the particles, of course, affects their behavior during simulation, while, in the figures provided in the article, the bubbles are represented by spheres (visualization of the results) of the same size. Please note that, due to the adopted Lagrangian–Eulerian approach, the simulation did not take into account phenomena such as bubble collapse or fusion. However, the obtained results allow a comprehensive analysis of the behavior of gas bubbles in the system under consideration.

The comparative analysis of the visualization (quantitative) results obtained with the water model and CFD simulations (see Figure 17) generated a sufficient agreement from the point of view of the trends. A precise quantitative evaluation is difficult to perform because of the lack of a refraction compensating system in the water model. Furthermore, in numerical simulations, it is not possible to determine the geometry of the forming gas bubbles and their interaction with each other as opposed to the visualization in the water model. The use of both research methods is complementary. Thus, a direct comparison of images obtained by the two methods requires appropriate interpretation. However, such an assessment gives the possibility to qualitatively determine the types of the present gas bubble dispersion, thus ultimately validating the CFD results with the water model.

A summary of the visualization results for impellers RT3, i.e., analysis of the occurring gas bubble dispersion types, is presented in Table 8.

Table 8

Summary of visualization results (impeller RT3)—different types of gas bubble dispersion.

No Exp.ABCDEF
Gas flow rate, dm3·min−11030
Impeller speed, rpm200300500200300500
Type of dispersionAccurateUniformUniform/excessiveMinimalExcessiveExcessive

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Tests carried out for impeller RT3 confirmed the high efficiency of gas bubble distribution in the volume of the tested object at a low inert gas flow rate of 10 dm3·min−1. The most optimal variant was variant B (300 rpm, 10 dm3·min−1). However, the other variants A and C (gas flow rate 10 dm3·min−1) seemed to be favorable for this type of impeller and are recommended for further testing. The above process parameters will be analyzed in detail in a quantitative analysis to be performed on the basis of the obtained efficiency curves of the degassing process (oxygen removal). This analysis will give an unambiguous answer as to which process parameters are the most optimal for this type of impeller; the results are planned for publication in the next article.

It should also be noted here that the high agreement between the results of numerical calculations and physical modelling prompts a conclusion that the proposed approach to the simulation of a degassing process which consists of a single-phase flow model with a free surface and a particle flow model is appropriate. The simulation results enable us to understand how the velocity field in the fluid is formed and to analyze the distribution of gas bubbles in the system. The simulations in Flow-3D software can, therefore, be useful for both the design of the impeller geometry and the selection of process parameters.

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4. Conclusions

The results of experiments carried out on the physical model of the device for the simulation of barbotage refining of aluminum revealed that the worst results in terms of distribution and dispersion of gas bubbles in the studied object were obtained for the black impellers variants B4, B8, and B12 (multi-orifice impellers—four, eight, and 12 outlet holes, respectively).

In this case, the control of flow, speed, and number of gas exit orifices did not improve the process efficiency, and the developed design did not meet the criteria for industrial tests. In the case of the ‘red triangle’ impeller (variant RT3), uniform gas bubble dispersion was achieved throughout the volume of the modeling fluid for most of the tested variants. The worst bubble dispersion results due to the occurrence of the so-called dead zones in the area near the bottom and sidewalls of the vessel were obtained for the flow variants of 20 dm3·min−1 and 200 rpm and 30 dm3·min−1 and 200 rpm. For the analyzed model, areas where swirls and gas bubble chains were formed were found only for the inert gas flow of 20 and 30 dm3·min−1 and 200 rpm. The model impeller (variant RT3) had the best performance compared to the previously presented impellers in terms of dispersion of gas bubbles in the model liquid. Moreover, its design differed from previously presented models because of its sharp edges. This can be advantageous for gas bubble dispersion, but may negatively affect its suitability in industrial conditions due to premature wearing.

The CFD simulation results confirmed the results obtained from the experiments performed on the physical model. The numerical simulation of the operation of the ‘red triangle’ impeller model (using Flow-3D software) gave good agreement with the experiments performed on the physical model. This means that the presented model impeller, as compared to other (analyzed) designs, had the best performance in terms of gas bubble dispersion in the model liquid.

In further work, the developed numerical model is planned to be used for CFD simulations of the gas bubble distribution process taking into account physicochemical parameters of liquid aluminum based on industrial tests. Consequently, the obtained results may be implemented in production practice.

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Funding Statement

This paper was created with the financial support grants from the AGH-UST, Faculty of Foundry Engineering, Poland (16.16.170.654 and 11/990/BK_22/0083) for the Faculty of Materials Engineering, Silesian University of Technology, Poland.

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Author Contributions

Conceptualization, K.K. and D.K.; methodology, J.P. and T.M.; validation, M.S. and S.G.; formal analysis, D.K. and T.M.; investigation, J.P., K.K. and S.G.; resources, M.S., J.P. and K.K.; writing—original draft preparation, D.K. and T.M.; writing—review and editing, D.K. and T.M.; visualization, J.P., K.K. and S.G.; supervision, D.K.; funding acquisition, D.K. and T.M. All authors have read and agreed to the published version of the manuscript.

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Institutional Review Board Statement

Not applicable.

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Informed Consent Statement

Not applicable.

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Data Availability Statement

Data are contained within the article.

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Conflicts of Interest

The authors declare no conflict of interest.

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Footnotes

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Figure 4.24 - Model with virtual valves in the extremities of the geometries to simulate the permeability of the mold promoting a more uniformed filling

Optimization of filling systems for low pressure by Flow-3D

Dissertação de Mestrado
Ciclo de Estudos Integrados Conducentes ao
Grau de Mestre em Engenharia Mecânica
Trabalho efectuado sob a orientação do
Doutor Hélder de Jesus Fernades Puga
Professor Doutor José Joaquim Carneiro Barbosa

ABSTRACT

논문의 일부로 튜터 선택 가능성과 해결해야 할 주제가 설정되는 매개변수를 염두에 두고 개발 주제 ‘Flow- 3D ®에 의한 저압 충전 시스템 최적화’가 선택되었습니다. 이를 위해서는 달성해야 할 목표와 이를 달성하기 위한 방법을 정의하는 것이 필요했습니다.

충전 시스템을 시뮬레이션하고 검증할 수 있는 광범위한 소프트웨어에도 불구하고 Flow-3D®는 시장에서 최고의 도구 중 하나로 표시되어 전체 충전 프로세스 및 행동 표현과 관련하여 탁월한 정확도로 시뮬레이션하는 능력을 입증했습니다.

이를 위해 관련 프로세스를 더 잘 이해하고 충진 시스템 시뮬레이션을 위한 탐색적 기반 역할을 하기 위해 이 도구를 탐색하는 것이 중요합니다. 지연 및 재료 낭비에 반영되는 실제적인 측면에서 충전 장치의 치수를 완벽하게 만드는 비용 및 시간 낭비. 이러한 방식으로 저압 주조 공정에서 충진 시스템을 설계하고 물리적 모델을 탐색하여 특성화하는 방법론을 검증하기 위한 것입니다.

이를 위해 다음 주요 단계를 고려하십시오.

시뮬레이션 소프트웨어 Flow 3D® 탐색;
충전 시스템 모델링;
모델의 매개변수를 탐색하여 모델링된 시스템의 시뮬레이션, 검증 및 최적화.

따라서 연구 중인 압력 곡선과 주조 분석에서 가장 관련성이 높은 정보의 최종 마이닝을 검증하기 위한 것입니다.

사용된 압력 곡선은 수집된 문헌과 이전에 수행된 실제 작업을 통해 얻었습니다. 결과를 통해 3단계 압력 곡선이 층류 충진 체계의 의도된 목적과 관련 속도가 0.5 𝑚/𝑠를 초과하지 않는다는 결론을 내릴 수 있었습니다.

충전 수준이 2인 압력 곡선은 0.5 𝑚/𝑠 이상의 속도로 영역을 채우는 더 난류 시스템을 갖습니다. 열전달 매개변수는 이전에 얻은 값이 주물에 대한 소산 거동을 확증하지 않았기 때문에 연구되었습니다.

이러한 방식으로 주조 공정에 더 부합하는 새로운 가치를 얻었습니다. 달성된 결과는 유사한 것으로 나타난 NovaFlow & Solid®에 의해 생성된 결과와 비교되어 시뮬레이션에서 설정된 매개변수를 검증했습니다. Flow 3D®는 주조 부품 시뮬레이션을 위한 강력한 도구로 입증되었습니다.

As part of the dissertation and bearing in mind the parameters in which the possibility of a choice of tutor and the subject to be addressed is established, the subject for development ’Optimization of filling systems for low pressure by Flow 3D ®’ was chosen. For this it was necessary to define the objectives to achieve and the methods to attain them. Despite the wide range of software able to simulate and validate filling systems, Flow 3D® has been shown as one of the best tools in the market, demonstrating its ability to simulate with distinctive accuracy with respect to the entire process of filling and the behavioral representation of the fluid obtained. To this end, it is important to explore this tool for a better understanding of the processes involved and to serve as an exploratory basis for the simulation of filling systems, simulation being one of the great strengths of the current industry due to the need to reduce costs and time waste, in practical terms, that lead to the perfecting of the dimensioning of filling devices, which are reflected in delays and wasted material. In this way it is intended to validate the methodology to design a filling system in lowpressure casting process, exploring their physical models and thus allowing for its characterization. For this, consider the following main phases: The exploration of the simulation software Flow 3D®; modeling of filling systems; simulation, validation and optimization of systems modeled by exploring the parameters of the models. Therefore, it is intended to validate the pressure curves under study and the eventual mining of the most relevant information in a casting analysis. The pressure curves that were used were obtained through the gathered literature and the practical work previously performed. Through the results it was possible to conclude that the pressure curve with 3 levels meets the intended purpose of a laminar filling regime and associated speeds never exceeding 0.5 𝑚/𝑠. The pressure curve with 2 filling levels has a more turbulent system, having filling areas with velocities above 0.5 𝑚/𝑠. The heat transfer parameter was studied due to the values previously obtained didn’t corroborate the behavior of dissipation regarding to the casting. In this way, new values, more in tune with the casting process, were obtained. The achieved results were compared with those generated by NovaFlow & Solid®, which were shown to be similar, validating the parameters established in the simulations. Flow 3D® was proven a powerful tool for the simulation of casting parts.

키워드

저압, Flow 3D®, 시뮬레이션, 파운드리, 압력-시간 관계,Low Pressure, Flow 3D®, Simulation, Foundry, Pressure-time relation

Figure 4.24 - Model with virtual valves in the extremities of the geometries to simulate the permeability of the mold promoting a more uniformed filling
Figure 4.24 – Model with virtual valves in the extremities of the geometries to simulate the permeability of the mold promoting a more uniformed filling
Figure 4.39 - Values of temperature contours using full energy heat transfer parameter for simula
Figure 4.39 – Values of temperature contours using full energy heat transfer parameter for simula
Figure 4.40 – Comparison between software simulations (a) Flow 3D® simulation,
(b) NovaFlow & Solid® simulation
Figure 4.40 – Comparison between software simulations (a) Flow 3D® simulation, (b) NovaFlow & Solid® simulation

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Figure 1: Mold drawings

3D Flow and Temperature Analysis of Filling a Plutonium Mold

플루토늄 주형 충전의 3D 유동 및 온도 분석

Authors: Orenstein, Nicholas P. [1]

Publication Date:2013-07-24
Research Org.: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.: DOE/LANL
OSTI Identifier: 1088904
Report Number(s): LA-UR-13-25537
DOE Contract Number: AC52-06NA25396
Resource Type: Technical Report
Country of Publication: United States
Language: English
Subject: Engineering(42); Materials Science(36); Radiation Chemistry, Radiochemistry, & Nuclear Chemistry(38)

Introduction

The plutonium foundry at Los Alamos National Laboratory casts products for various special nuclear applications. However, plutonium’s radioactivity, material properties, and security constraints complicate the ability to perform experimental analysis of mold behavior. The Manufacturing Engineering and Technologies (MET-2) group previously developed a graphite mold to vacuum cast small plutonium disks to be used by the Department of Homeland Security as point sources for radiation sensor testing.

A two-stage pouring basin consisting of a funnel and an angled cavity directs the liquid into a vertical runner. A stack of ten disk castings connect to the runner by horizontal gates. Volumetric flow rates were implemented to limit overflow into the funnel and minimize foundry returns. Models using Flow-3D computational fluid dynamics software are employed here to determine liquid Pu flow paths, optimal pour regimes, temperature changes, and pressure variations.

Setup

Hardcopy drawings provided necessary information to create 3D .stl models for import into Flow-3D (Figs. 1 and 2). The mesh was refined over several iterations to isolate the disk cavities, runner, angled cavity, funnel, and input pour. The final flow and mold-filling simulation utilizes a fine mesh with ~5.5 million total cells. For the temperature study, the mesh contained 1/8 as many cells to reduce computational time and set temperatures to 850 °C for the molten plutonium and 500 °C for the solid graphite mold components (Fig. 3).

Flow-3D solves mass continuity and Navier-Stokes momentum equations over the structured rectangular grid model using finite difference and finite volume numerical algorithms. The solver includes terms in the momentum equation for body and viscous accelerations and uses convective heat transfer.

Simulation settings enabled Flow-3D physics calculations for gravity at 980.665 cm/s 2 in the negative Z direction (top of mold to bottom); viscous, turbulent, incompressible flow using dynamically-computed Renormalized Group Model turbulence calculations and no-slip/partial slip wall shear, and; first order, full energy equation heat transfer.

Mesh boundaries were all set to symmetric boundary conditions except for the Zmin boundary set to outflow and the Zmax boundary set to a volume flow. Vacuum casting conditions and the high reactivity of remaining air molecules with Pu validate the assumption of an initially fluidless void.

Results

The flow follows a unique three-dimensional path. The mold fills upwards with two to three disks receiving fluid in a staggered sequence. Figures 5-9 show how the fluid fills the cavity, and Figure 7 includes the color scale for pressure levels in these four figures. The narrow gate causes a high pressure region which forces the fluid to flow down the cavity centerline.

It proceeds to splash against the far wall and then wrap around the circumference back to the gate (Figs. 5 and 6). Flow in the angled region of the pouring basin cascades over the bottom ledge and attaches to the far wall of the runner, as seen in Figure 7.

This channeling becomes less pronounced as fluid volume levels increase. Finally, two similar but non-uniform depressed regions form about the centerline. These regions fill from their perimeter and bottom until completion (Fig. 8). Such a pattern is counter, for example, to a steady scenario in which a circle of molten Pu encompassing the entire bottom surface rises as a growing cylinder.

Cavity pressure becomes uniform when the cavity is full. Pressure levels build in the rising well section of the runner, where impurities were found to settle in actual casting. Early test simulations optimized the flow as three pours so that the fluid would never overflow to the funnel, the cavities would all fill completely, and small amounts of fluid would remain as foundry returns in the angled cavity.

These rates and durations were translated to the single 2.7s pour at 100 cm 3 per second used here. Figure 9 shows anomalous pressure fluctuations which occurred as the cavities became completely filled. Multiple simulations exhibited a rapid change in pressure from positive to negative and back within the newly-full disk and surrounding, already-full disks.

The time required to completely fill each cavity is plotted in Figure 10. Results show negligible temperature change within the molten Pu during mold filling and, as seen in Figure 11, at fill completion.

Figure 1: Mold drawings
Figure 1: Mold drawings
Figure 2: Mold Assembly
Figure 2: Mold Assembly
Figure 4: Actual mold and cast Pu
Figure 4: Actual mold and cast Pu
Figure 5: Bottom cavity filling
from runner
Figure 5: Bottom cavity filling from runner
Figure 6: Pouring and filling
Figure 6: Pouring and filling
Figure 8: Edge detection of cavity fill geometry. Two similar depressed areas form
about the centerline. Top cavity shown; same pressure scale as other figures
Figure 8: Edge detection of cavity fill geometry. Two similar depressed areas form about the centerline. Top cavity shown; same pressure scale as other figures
Figure 10: Cavity fill times,from first fluid contact with pouring basin, Figure 11:Fluid temperature remains essentially constant
Figure 10: Cavity fill times,from first fluid contact with pouring basin, Figure 11:Fluid temperature remains essentially constant

Conclusions

Non-uniform cavity filling could cause crystal microstructure irregularities during solidification. However, the small temperature changes seen – due to large differences in specific heat between Pu and graphite – over a relatively short time make such problems unlikely in this case.

In the actual casting, cooling required approximately ten minutes. This large difference in time scales further reduces the chance for temperature effects in such a superheated scenario. Pouring basin emptying decreases pressure at the gate which extends fill time of the top two cavities.

The bottom cavity takes longer to fill because fluid must first enter the runner and fill the well. Fill times continue linearly until the top two cavities. The anomalous pressure fluctuations may be due to physical attempts by the system to reach equilibrium, but they are more likely due to numerical errors in the Flow3D solver.

Unsuccessful tests were performed to remove them by halving fluid viscosity. The fine mesh reduced, but did not eliminate, the extent of the fluctuations. Future work is planned to study induction and heat transfer in the full Pu furnace system, including quantifying temporal lag of the cavity void temperature to the mold wall temperature during pre-heat and comparing heat flux levels between furnace components during cool-down.

Thanks to Doug Kautz for the opportunity to work with MET-2 and for assigning an interesting unclassified project. Additional thanks to Mike Bange for CFD guidance, insight of the project’s history, and draft review.

Development of macro-defect-free PBF-EB-processed Ti–6Al–4V alloys with superior plasticity using PREP-synthesized powder and machine learning-assisted process optimization

Development of macro-defect-free PBF-EB-processed Ti–6Al–4V alloys with superior plasticity using PREP-synthesized powder and machine learning-assisted process optimization

Yunwei GuiabKenta Aoyagib Akihiko Chibab
aDepartment of Materials Processing, Graduate School of Engineering, Tohoku University, 6-6 Aramaki Aza Aoba, Aoba-ku, Sendai, 980-8579, Japan
bInstitute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, 980-8577, Japan

Received 14 October 2022, Revised 23 December 2022, Accepted 3 January 2023, Available online 5 January 2023.Show lessAdd to MendeleyShareCite

https://doi.org/10.1016/j.msea.2023.144595Get rights and content

Abstract

The elimination of internal macro-defects is a key issue in Ti–6Al–4V alloys fabricated via powder bed fusion using electron beams (PBF-EB), wherein internal macro-defects mainly originate from the virgin powder and inappropriate printing parameters. This study compares different types powders by combining support vector machine techniques to determine the most suitable powder for PBF-EB and to predict the processing window for the printing parameters without internal macro-defects. The results show that powders fabricated via plasma rotating electrode process have the best sphericity, flowability, and minimal porosity and are most suitable for printing. Surface roughness criterion was also applied to determine the quality of the even surfaces, and support vector machine was used to construct processing maps capable of predicting a wide range of four-dimensional printing parameters to obtain macro-defect-free samples, offering the possibility of subsequent development of Ti–6Al–4V alloys with excellent properties. The macro-defect-free samples exhibited good elongation, with the best overall mechanical properties being the ultimate tensile strength and elongation of 934.7 MPa and 24.3%, respectively. The elongation of the three macro-defect-free samples was much higher than that previously reported for additively manufactured Ti–6Al–4V alloys. The high elongation of the samples in this work is mainly attributed to the elimination of internal macro-defects.

Introduction

Additive manufacturing (AM) technologies can rapidly manufacture complex or custom parts, reducing process steps and saving manufacturing time [[1], [2], [3], [4]], and are widely used in the aerospace, automotive, and other precision industries [5,6]. Powder bed fusion using an electron beam (PBF-EB) is an additive manufacturing method that uses a high-energy electron beam to melt metal powders layer by layer to produce parts. In contrast to selective laser melting, PBF-EB involves the preparation of samples in a high vacuum environment, which effectively prevents the introduction of impurities such as O and N. It also involves a preheating process for the print substrate and powder, which reduces residual thermal stress on the sample and subsequent heat treatment processes [[2], [3], [4],7]. Due to these features and advantages, PBF-EB technology is a very important AM technology with great potential in metallic materials. Moreover, PBF-EB is the ideal AM technology for the manufacture of complex components made of many alloys, such as titanium alloys, nickel-based superalloys, aluminum alloys and stainless steels [[2], [3], [4],8].

Ti–6Al–4V alloy is one of the prevalent commercial titanium alloys possessing high specific strength, excellent mechanical properties, excellent corrosion resistance, and good biocompatibility [9,10]. It is widely used in applications requiring low density and excellent corrosion resistance, such as the aerospace industry and biomechanical applications [11,12]. The mechanical properties of PBF-EB-processed Ti–6Al–4V alloys are superior to those fabricated by casting or forging, because the rapid cooling rate in PBF-EB results in finer grains [[12], [13], [14], [15], [16], [17], [18]]. However, the PBF-EB-fabricated parts often include internal macro-defects, which compromises their mechanical properties [[19], [20], [21], [22]]. This study focused on the elimination of macro-defects, such as porosity, lack of fusion, incomplete penetration and unmelted powders, which distinguishes them from micro-defects such as vacancies, dislocations, grain boundaries and secondary phases, etc. Large-sized fusion defects cause a severe reduction in mechanical strength. Smaller defects, such as pores and cracks, lead to the initiation of fatigue cracking and rapidly accelerate the cracking process [23]. The issue of internal macro-defects must be addressed to expand the application of the PBF-EB technology. The main studies for controlling internal macro-defects are online monitoring of defects, remelting and hot isostatic pressing (HIP). The literatures [24,25] report the use of infrared imaging or other imaging techniques to identify defects, but the monitoring of smaller sized defects is still not adequate. And in some cases remelting does not reduce the internal macro-defects of the part, but instead causes coarsening of the macrostructure and volatilization of some metal elements [23]. The HIP treatment does not completely eliminate the internal macro-defects, the original defect location may still act as a point of origin of the crack, and the subsequent treatment will consume more time and economic costs [23]. Therefore, optimizing suitable printing parameters to avoid internal macro-defects in printed parts at source is of great industrial value and research significance, and is an urgent issue in PBF-EB related technology.

There are two causes of internal macro-defects in the AM process: gas pores trapped in the virgin powder and the inappropriate printing parameters [7,23]. Gui et al. [26] classify internal macro-defects during PBF-EB process according to their shape, such as spherical defects, elongated shape defects, flat shape defects and other irregular shape defects. Of these, spherical defects mainly originate from raw material powders. Other shape defects mainly originate from lack of fusion or unmelted powders caused by unsuitable printing parameters, etc. The PBF-EB process requires powders with good flowability, and spherical powders are typically chosen as raw materials. The prevalent techniques for the fabrication of pre-alloyed powders are gas atomization (GA), plasma atomization (PA), and the plasma rotating electrode process (PREP) [27,28]. These methods yield powders with different characteristics that affect the subsequent fabrication. The selection of a suitable powder for PBF-EB is particularly important to produce Ti–6Al–4V alloys without internal macro-defects. The need to optimize several printing parameters such as beam current, scan speed, line offset, and focus offset make it difficult to eliminate internal macro-defects that occur during printing [23]. Most of the studies [11,12,22,[29], [30], [31], [32], [33]] on the optimization of AM processes for Ti–6Al–4V alloys have focused on samples with a limited set of parameters (e.g., power–scan speed) and do not allow for the guidance and development of unknown process windows for macro-defect-free samples. In addition, process optimization remains a time-consuming problem, with the traditional ‘trial and error’ method demanding considerable time and economic costs. The development of a simple and efficient method to predict the processing window for alloys without internal macro-defects is a key issue. In recent years, machine learning techniques have increasingly been used in the field of additive manufacturing and materials development [[34], [35], [36], [37]]. Aoyagi et al. [38] recently proposed a novel and efficient method based on a support vector machine (SVM) to optimize the two-dimensional process parameters (current and scan speed) and obtain PBF-EB-processed CoCr alloys without internal macro-defects. The method is one of the potential approaches toward effective optimization of more than two process parameters and makes it possible for the machine learning techniques to accelerate the development of alloys without internal macro-defects.

Herein, we focus on the elimination of internal macro-defects, such as pores, lack of fusion, etc., caused by raw powders and printing parameters. The Ti–6Al–4V powders produced by three different methods were compared, and the powder with the best sphericity, flowability, and minimal porosity was selected as the feedstock for subsequent printing. The relationship between the surface roughness and internal macro-defects in the Ti–6Al–4V components was also investigated. The combination of SVM and surface roughness indices (Sdr) predicted a wider four-dimensional processing window for obtaining Ti–6Al–4V alloys without internal macro-defects. Finally, we investigated the tensile properties of Ti–6Al–4V alloys at room temperature with different printing parameters, as well as the corresponding microstructures and fracture types.

Section snippets

Starting materials

Three types of Ti–6Al–4V alloy powders, produced by GA, PA, and PREP, were compared. The particle size distribution of the powders was determined using a laser particle size analyzer (LS230, Beckman Coulter, USA), and the flowability was measured using a Hall flowmeter (JIS-Z2502, Tsutsui Scientific Instruments Co., Ltd., Japan), according to the ASTM B213 standard. The powder morphology and internal macro-defects were determined using scanning electron microscopy (SEM, JEOL JCM-6000) and X-ray 

Comparison of the characteristics of GA, PA, and PREP Ti–6Al–4V powders

The particle size distributions (PSDs) and flowability of the three types of Ti–6Al–4V alloy powders produced by GA, PA, and PREP are shown in Fig. 2. Although the average particle sizes are similar (89.4 μm for GA, 82.5 μm for PA, and 86.1μm for PREP), the particle size range is different for the three types of powder (6.2–174.8 μm for GA, 27.3–139.2 μm for PA, and 39.4–133.9 μm for PREP). The flowability of the GA, PA, and PREP powders was 30.25 ± 0.98, 26.54 ± 0.37, and 25.03 ± 0.22 (s/50

Conclusions

The characteristics of the three types of Ti–6Al–4V alloy powders produced via GA, PA, and PREP were compared. The PREP powder with the best sphericity, flowability, and low porosity was found to be the most favorable powder for subsequent printing of Ti–6Al–4V alloys without internal macro-defects. The quantitative criterion of Sdr <0.015 for even surfaces was also found to be applicable to Ti–6Al–4V alloys. The process maps of Ti–6Al–4V alloys include two regions, high beam current/scan speed 

Uncited references

[55]; [56]; [57]; [58]; [59]; [60]; [61]; [62]; [63]; [64]; [65].

CRediT authorship contribution statement

Yunwei Gui: Writing – original draft, Visualization, Validation, Investigation. Kenta Aoyagi: Writing – review & editing, Supervision, Resources, Methodology, Funding acquisition, Conceptualization. Akihiko Chiba: Supervision, Funding acquisition.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This study was based on the results obtained from project JPNP19007, commissioned by the New Energy and Industrial Technology Development Organization (NEDO). This work was also supported by JSPS KAKENHI (Proposal No. 21K03801) and the Inter-University Cooperative Research Program (Proposal nos. 18G0418, 19G0411, and 20G0418) of the Cooperative Research and Development Center for Advanced Materials, Institute for Materials Research, Tohoku University. It was also supported by the Council for

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Figura 7. Influencia del modelo de turbulencia. Qmodelo=27.95l/s.

Flow-3D를 사용하여 전산유체역학(CFD)을 적용한 빠른 단계의 플러시 유동 수치 모델링

Numerical Modeling of Flush Flow in a Rapid Step Applying Computational Fluid Dynamics (CFD) Using Flow-3D.

레브 폴리텍. (Quito) [온라인]. 2018, vol.41, n.2, pp.53-64. ISSN 2477-8990.

이 프로젝트의 주요 목표는 FLOW-3D를 사용하여 계단식 여수로에서 스키밍 흐름의 수치 모델링을 개발하는 것입니다. 이러한 구조의 설계는 물리적 모델링에서 얻은 경험적 표현과 CFD 코드를 지원하는 계단식 여수로를 통한 흐름의 수치 모델링에서 보완 연구를 기반으로 합니다. 수치 모델은 균일한 영역의 유속과 계단 여수로의 마찰 계수를 추정하는 데 사용됩니다(ϴ = 45º, Hd=4.61m). 흐름에 대한 자동 통기의 표현은 복잡하므로 프로그램은 공기 연행 모델을 사용하여 특정 제한이 있는 솔루션에 근접합니다.

The main objective of this project is to develop the numerical modeling of the skimming flow in a stepped spillway using FLOW-3D. The design of these structures is based on the use of empirical expressions obtained from physical modeling and complementary studies in the numerical modeling of flow over the stepped spillway with support of CFD code. The numerical model is used to estimate the flow velocity in the uniform region and the friction coefficient of the stepped spillway (ϴ = 45º, Hd=4.61m). The representation of auto aeration a flow is complex, so the program approximates the solution with certain limitations, using an air entrainment model; drift flux model and turbulence model k-ԑ RNG. The results obtained with numerical modeling and physical modeling at the beginning of natural auto aeration of flow and depth of the biphasic flow in the uniform region presents deviations above to 10% perhaps the flow is highly turbulent.

Keywords : Stepped spillway; skimming flow; air entrainment; drift flux; numerical modeling; FLOW-3D.

Keywords : 계단식 여수로; 스키밍 흐름; 공기 연행; 드리프트 플럭스; 수치 모델링; 흐름-3D.· 

스페인어로 된 초록 · 스페인어 로 된 텍스트 · 스페인어로 된 텍스트( pdf 

Figure 1. Grazing flow over a rapid step.
Figure 1. Grazing flow over a rapid step.
Figura 2. Principales regiones existentes en un flujo rasante.
Figura 2. Principales regiones existentes en un flujo rasante.
Figure 3. Dimensions of the El Batán stepped rapid.
Figure 3. Dimensions of the El Batán stepped rapid.
Figure 4. 3D physical model of the El Batán stepped rapid
Figure 4. 3D physical model of the El Batán stepped rapid
Figura 7. Influencia del modelo de turbulencia. Qmodelo=27.95l/s.
Figura 7. Influencia del modelo de turbulencia. Qmodelo=27.95l/s.

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Figure 5: 3D & 2D views of simulated fill sequence of a hollow cylinder at 1000 rpm and 1500 rpm at various time intervals during filling.

Computer Simulation of Centrifugal Casting Process using FLOW-3D

Aneesh Kumar J1, a, K. Krishnakumar1, b and S. Savithri2, c 1 Department of Mechanical Engineering, College of Engineering, Thiruvananthapuram, Kerala, 2 Computational Modelling& Simulation Division, Process Engineering & Environmental Technology Division CSIR-National Institute for Interdisciplinary Science & Technology
Thiruvananthapuram, Kerala, India.
a aneesh82kj@gmail.com, b kkk@cet.ac.in, c sivakumarsavi@gmail.com, ssavithri@niist.res.in Key words: Mold filling, centrifugal casting process, computer simulation, FLOW- 3D™

Abstract

원심 주조 공정은 기능적으로 등급이 지정된 재료, 즉 구성 요소 간에 밀도 차이가 큰 복합 재료 또는 금속 재료를 생산하는 데 사용되는 잠재적인 제조 기술 중 하나입니다. 이 공정에서 유체 흐름이 중요한 역할을 하며 복잡한 흐름 공정을 이해하는 것은 결함 없는 주물을 생산하는 데 필수입니다. 금형이 고속으로 회전하고 금형 벽이 불투명하기 때문에 흐름 패턴을 실시간으로 시각화하는 것은 불가능합니다. 따라서 현재 연구에서는 상용 CFD 코드 FLOW-3D™를 사용하여 수직 원심 주조 공정 중 단순 중공 원통형 주조에 대한 금형 충전 시퀀스를 시뮬레이션했습니다. 수직 원심주조 공정 중 다양한 방사 속도가 충전 패턴에 미치는 영향을 조사하고 있습니다.

Centrifugal casting process is one of the potential manufacturing techniques used for producing functionally graded materials viz., composite materials or metallic materials which have high differences of density among constituents. In this process, the fluid flow plays a major role and understanding the complex flow process is a must for the production of defect-free castings. Since the mold spins at a high velocity and the mold wall being opaque, it is impossible to visualise the flow patterns in real time. Hence, in the present work, the commercial CFD code FLOW-3D™, has been used to simulate the mold filling sequence for a simple hollow cylindrical casting during vertical centrifugal casting process. Effect of various spinning velocities on the fill pattern during vertical centrifugal casting process is being investigated.

Figure 1: (a) Mold geometry and (b) Computational mesh
Figure 1: (a) Mold geometry and (b) Computational mesh
Figure 2: Experimental data on height of
vertex formed [8]  / Figure 3: Vertex height as a function of time
Figure 2: Experimental data on height of vertex formed [8]/Figure 3: Vertex height as a function of time
Figure 4: Free surface contours for water model at 10 s, 15 s and 20 s.
Figure 4: Free surface contours for water model at 10 s, 15 s and 20 s.
Figure 5: 3D & 2D views of simulated fill sequence of a hollow cylinder at 1000 rpm and 1500 rpm at various time intervals during filling.
Figure 5: 3D & 2D views of simulated fill sequence of a hollow cylinder at 1000 rpm and 1500 rpm at various time intervals during filling.

References

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Figure 2. Different PKW Types.

A review of Piano Key Weir as a superior alternative for dam rehabilitation

댐 복구를 위한 우수한 대안으로서의 Piano Key Weir에 대한 검토

Amiya Abhash &

K. K. Pandey

Pages 541-551 | Received 03 Mar 2020, Accepted 07 May 2020, Published online: 21 May 2020

ABSTRACT

Dams fall in ‘installations containing dangerous forces’ because of their massive impact on the environment and civilian life and property as per International humanitarian law. As such, it becomes vital for hydraulic engineers to refurbish various solutions for dam rehabilitation. This paper presents a review of a new type of weir installation called Piano Key Weir (PKW), which is becoming popular around the world for its higher spillway capacity both for existing and new dam spillway installations. This paper reviews the geometry along with structural integrity, discharging capacity, economic aspects, aeration requirements, sediment transport and erosion aspects of Piano Key Weir (PKW) as compared with other traditional spillway structures and alternatives from literature. The comparison with other alternatives shows PKW to be an excellent alternative for dam risk mitigation owing to its high spillway capabilities and economy, along with its use in both existing and new hydraulic structures.

댐은 국제 인도법에 따라 환경과 민간인 생활 및 재산에 막대한 영향을 미치기 때문에 ‘위험한 힘을 포함하는 시설물’에 속합니다. 따라서 유압 엔지니어는 댐 복구를 위한 다양한 솔루션을 재정비해야 합니다.

이 백서에서는 PKW(Piano Key Weir)라는 새로운 유형의 둑 설치에 대한 검토를 제공합니다. PKW는 기존 및 신규 댐 방수로 설치 모두에서 더 높은 방수로 용량으로 전 세계적으로 인기를 얻고 있습니다.

이 백서에서는 구조적 무결성, 배출 용량, 경제적 측면, 폭기 요구 사항, 퇴적물 운반 및 PKW(Piano Key Weir)의 침식 측면과 함께 다른 전통적인 여수로 구조 및 문헌의 대안과 비교하여 기하학을 검토합니다.

다른 대안과의 비교는 PKW가 높은 여수로 기능과 경제성으로 인해 댐 위험 완화를 위한 탁월한 대안이며 기존 및 새로운 수력 구조물 모두에 사용됨을 보여줍니다.

KEYWORDS: 

Figure 2. Different PKW Types.
Figure 2. Different PKW Types.

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Extratropical cyclone damage to the seawall in Dawlish, UK: eyewitness accounts, sea level analysis and numerical modelling

영국 Dawlish의 방파제에 대한 온대 저기압 피해: 목격자 설명, 해수면 분석 및 수치 모델링

Extratropical cyclone damage to the seawall in Dawlish, UK: eyewitness accounts, sea level analysis and numerical modelling

Natural Hazards (2022)Cite this article

Abstract

2014년 2월 영국 해협(영국)과 특히 Dawlish에 영향을 미친 온대 저기압 폭풍 사슬은 남서부 지역과 영국의 나머지 지역을 연결하는 주요 철도에 심각한 피해를 입혔습니다.

이 사건으로 라인이 두 달 동안 폐쇄되어 5천만 파운드의 피해와 12억 파운드의 경제적 손실이 발생했습니다. 이 연구에서는 폭풍의 파괴력을 해독하기 위해 목격자 계정을 수집하고 해수면 데이터를 분석하며 수치 모델링을 수행합니다.

우리의 분석에 따르면 이벤트의 재난 관리는 성공적이고 효율적이었으며 폭풍 전과 도중에 인명과 재산을 구하기 위해 즉각적인 조치를 취했습니다. 파도 부이 분석에 따르면 주기가 4–8, 8–12 및 20–25초인 복잡한 삼중 봉우리 바다 상태가 존재하는 반면, 조위계 기록에 따르면 최대 0.8m의 상당한 파도와 최대 1.5m의 파도 성분이 나타났습니다.

이벤트에서 가능한 기여 요인으로 결합된 진폭. 최대 286 KN의 상당한 임펄스 파동이 손상의 시작 원인일 가능성이 가장 높았습니다. 수직 벽의 반사는 파동 진폭의 보강 간섭을 일으켜 파고가 증가하고 최대 16.1m3/s/m(벽의 미터 너비당)의 상당한 오버탑핑을 초래했습니다.

이 정보와 우리의 공학적 판단을 통해 우리는 이 사고 동안 다중 위험 계단식 실패의 가장 가능성 있는 순서는 다음과 같다고 결론을 내립니다. 조적 파괴로 이어지는 파도 충격력, 충전물 손실 및 연속적인 조수에 따른 구조물 파괴.

The February 2014 extratropical cyclonic storm chain, which impacted the English Channel (UK) and Dawlish in particular, caused significant damage to the main railway connecting the south-west region to the rest of the UK. The incident caused the line to be closed for two months, £50 million of damage and an estimated £1.2bn of economic loss. In this study, we collate eyewitness accounts, analyse sea level data and conduct numerical modelling in order to decipher the destructive forces of the storm. Our analysis reveals that the disaster management of the event was successful and efficient with immediate actions taken to save lives and property before and during the storm. Wave buoy analysis showed that a complex triple peak sea state with periods at 4–8, 8–12 and 20–25 s was present, while tide gauge records indicated that significant surge of up to 0.8 m and wave components of up to 1.5 m amplitude combined as likely contributing factors in the event. Significant impulsive wave force of up to 286 KN was the most likely initiating cause of the damage. Reflections off the vertical wall caused constructive interference of the wave amplitudes that led to increased wave height and significant overtopping of up to 16.1 m3/s/m (per metre width of wall). With this information and our engineering judgement, we conclude that the most probable sequence of multi-hazard cascading failure during this incident was: wave impact force leading to masonry failure, loss of infill and failure of the structure following successive tides.

Introduction

The progress of climate change and increasing sea levels has started to have wide ranging effects on critical engineering infrastructure (Shakou et al. 2019). The meteorological effects of increased atmospheric instability linked to warming seas mean we may be experiencing more frequent extreme storm events and more frequent series or chains of events, as well as an increase in the force of these events, a phenomenon called storminess (Mölter et al. 2016; Feser et al. 2014). Features of more extreme weather events in extratropical latitudes (30°–60°, north and south of the equator) include increased gusting winds, more frequent storm squalls, increased prolonged precipitation and rapid changes in atmospheric pressure and more frequent and significant storm surges (Dacre and Pinto 2020). A recent example of these events impacting the UK with simultaneous significant damage to coastal infrastructure was the extratropical cyclonic storm chain of winter 2013/2014 (Masselink et al. 2016; Adams and Heidarzadeh 2021). The cluster of storms had a profound effect on both coastal and inland infrastructure, bringing widespread flooding events and large insurance claims (RMS 2014).

The extreme storms of February 2014, which had a catastrophic effect on the seawall of the south Devon stretch of the UK’s south-west mainline, caused a two-month closure of the line and significant disruption to the local and regional economy (Fig. 1b) (Network Rail 2014; Dawson et al. 2016; Adams and Heidarzadeh 2021). Restoration costs were £35 m, and economic effects to the south-west region of England were estimated up to £1.2bn (Peninsula Rail Taskforce 2016). Adams and Heidarzadeh (2021) investigated the disparate cascading failure mechanisms which played a part in the failure of the railway through Dawlish and attempted to put these in the context of the historical records of infrastructure damage on the line. Subsequent severe storms in 2016 in the region have continued to cause damage and disruption to the line in the years since 2014 (Met Office 2016). Following the events of 2014, Network Rail Footnote1 who owns the network has undertaken a resilience study. As a result, it has proposed a £400 m refurbishment of the civil engineering assets that support the railway (Fig. 1) (Network Rail 2014). The new seawall structure (Fig. 1a,c), which is constructed of pre-cast concrete sections, encases the existing Brunel seawall (named after the project lead engineer, Isambard Kingdom Brunel) and has been improved with piled reinforced concrete foundations. It is now over 2 m taller to increase the available crest freeboard and incorporates wave return features to minimise wave overtopping. The project aims to increase both the resilience of the assets to extreme weather events as well as maintain or improve amenity value of the coastline for residents and visitors.

figure 1
Fig. 1

In this work, we return to the Brunel seawall and the damage it sustained during the 2014 storms which affected the assets on the evening of the 4th and daytime of the 5th of February and eventually resulted in a prolonged closure of the line. The motivation for this research is to analyse and model the damage made to the seawall and explain the damage mechanisms in order to improve the resilience of many similar coastal structures in the UK and worldwide. The innovation of this work is the multidisciplinary approach that we take comprising a combination of analysis of eyewitness accounts (social science), sea level and wave data analysis (physical science) as well as numerical modelling and engineering judgement (engineering sciences). We investigate the contemporary wave climate and sea levels by interrogating the real-time tide gauge and wave buoys installed along the south-west coast of the English Channel. We then model a typical masonry seawall (Fig. 2), applying the computational fluid dynamics package FLOW3D-Hydro,Footnote2 to quantify the magnitude of impact forces that the seawall would have experienced leading to its failure. We triangulate this information to determine the probable sequence of failures that led to the disaster in 2014.

figure 2
Fig. 2

Data and methods

Our data comprise eyewitness accounts, sea level records from coastal tide gauges and offshore wave buoys as well as structural details of the seawall. As for methodology, we analyse eyewitness data, process and investigate sea level records through Fourier transform and conduct numerical simulations using the Flow3D-Hydro package (Flow Science 2022). Details of the data and methodology are provided in the following.

Eyewitness data

The scale of damage to the seawall and its effects led the local community to document the first-hand accounts of those most closely affected by the storms including residents, local businesses, emergency responders, politicians and engineering contractors involved in the post-storm restoration work. These records now form a permanent exhibition in the local museum in DawlishFootnote3, and some of these accounts have been transcribed into a DVD account of the disaster (Dawlish Museum 2015). We have gathered data from the Dawlish Museum, national and international news reports, social media tweets and videos. Table 1 provides a summary of the eyewitness accounts. Overall, 26 entries have been collected around the time of the incident. Our analysis of the eyewitness data is provided in the third column of Table 1 and is expanded in Sect. 3.Table 1 Eyewitness accounts of damage to the Dawlish railway due to the February 2014 storm and our interpretations

Full size table

Sea level data and wave environment

Our sea level data are a collection of three tide gauge stations (Newlyn, Devonport and Swanage Pier—Fig. 5a) owned and operated by the UK National Tide and Sea Level FacilityFootnote4 for the Environment Agency and four offshore wave buoys (Dawlish, West Bay, Torbay and Chesil Beach—Fig. 6a). The tide gauge sites are all fitted with POL-EKO (www.pol-eko.com.pl) data loggers. Newlyn has a Munro float gauge with one full tide and one mid-tide pneumatic bubbler system. Devonport has a three-channel data pneumatic bubbler system, and Swanage Pier consists of a pneumatic gauge. Each has a sampling interval of 15 min, except for Swanage Pier which has a sampling interval of 10 min. The tide gauges are located within the port areas, whereas the offshore wave buoys are situated approximately 2—3.3 km from the coast at water depths of 10–15 m. The wave buoys are all Datawell Wavemaker Mk III unitsFootnote5 and come with sampling interval of 0.78 s. The buoys have a maximum saturation amplitude of 20.5 m for recording the incident waves which implies that every wave larger than this threshold will be recorded at 20.5 m. The data are provided by the British Oceanographic Data CentreFootnote6 for tide gauges and the Channel Coastal ObservatoryFootnote7 for wave buoys.

Sea level analysis

The sea level data underwent quality control to remove outliers and spikes as well as gaps in data (e.g. Heidarzadeh et al. 2022; Heidarzadeh and Satake 2015). We processed the time series of the sea level data using the Matlab signal processing tool (MathWorks 2018). For calculations of the tidal signals, we applied the tidal package TIDALFIT (Grinsted 2008), which is based on fitting tidal harmonics to the observed sea level data. To calculate the surge signals, we applied a 30-min moving average filter to the de-tided data in order to remove all wind, swell and infra-gravity waves from the time series. Based on the surge analysis and the variations of the surge component before the time period of the incident, an error margin of approximately ± 10 cm is identified for our surge analysis. Spectral analysis of the wave buoy data is performed using the fast Fourier transform (FFT) of Matlab package (Mathworks 2018).

Numerical modelling

Numerical modelling of wave-structure interaction is conducted using the computational fluid dynamics package Flow3D-Hydro version 1.1 (Flow Science 2022). Flow3D-Hydro solves the transient Navier–Stokes equations of conservation of mass and momentum using a finite difference method and on Eulerian and Lagrangian frameworks (Flow Science 2022). The aforementioned governing equations are:

∇.u=0∇.u=0

(1)

∂u∂t+u.∇u=−∇Pρ+υ∇2u+g∂u∂t+u.∇u=−∇Pρ+υ∇2u+g

(2)

where uu is the velocity vector, PP is the pressure, ρρ is the water density, υυ is the kinematic viscosity and gg is the gravitational acceleration. A Fractional Area/Volume Obstacle Representation (FAVOR) is adapted in Flow3D-Hydro, which applies solid boundaries within the Eulerian grid and calculates the fraction of areas and volume in partially blocked volume in order to compute flows on corresponding boundaries (Hirt and Nichols 1981). We validated the numerical modelling through comparing the results with Sainflou’s analytical equation for the design of vertical seawalls (Sainflou 1928; Ackhurst 2020), which is as follows:

pd=ρgHcoshk(d+z)coshkdcosσtpd=ρgHcoshk(d+z)coshkdcosσt

(3)

where pdpd is the hydrodynamic pressure, ρρ is the water density, gg is the gravitational acceleration, HH is the wave height, dd is the water depth, kk is the wavenumber, zz is the difference in still water level and mean water level, σσ is the angular frequency and tt is the time. The Sainflou’s equation (Eq. 3) is used to calculate the dynamic pressure from wave action, which is combined with static pressure on the seawall.

Using Flow3D-Hydro, a model of the Dawlish seawall was made with a computational domain which is 250.0 m in length, 15.0 m in height and 0.375 m in width (Fig. 3a). The computational domain was discretised using a single uniform grid with a mesh size of 0.125 m. The model has a wave boundary at the left side of the domain (x-min), an outflow boundary on the right side (x-max), a symmetry boundary at the bottom (z-min) and a wall boundary at the top (z-max). A wall boundary implies that water or waves are unable to pass through the boundary, whereas a symmetry boundary means that the two edges of the boundary are identical and therefore there is no flow through it. The water is considered incompressible in our model. For volume of fluid advection for the wave boundary (i.e. the left-side boundary) in our simulations, we utilised the “Split Lagrangian Method”, which guarantees the best accuracy (Flow Science, 2022).

figure 3
Fig. 3

The stability of the numerical scheme is controlled and maintained through checking the Courant number (CC) as given in the following:

C=VΔtΔxC=VΔtΔx

(4)

where VV is the velocity of the flow, ΔtΔt is the time step and ΔxΔx is the spatial step (i.e. grid size). For stability and convergence of the numerical simulations, the Courant number must be sufficiently below one (Courant et al. 1928). This is maintained by a careful adjustment of the ΔxΔx and ΔtΔt selections. Flow3D-Hydro applies a dynamic Courant number, meaning the program adjusts the value of time step (ΔtΔt) during the simulations to achieve a balance between accuracy of results and speed of simulation. In our simulation, the time step was in the range ΔtΔt = 0.0051—0.051 s.

In order to achieve the most efficient mesh resolution, we varied cell size for five values of ΔxΔx = 0.1 m, 0.125 m, 0.15 m, 0.175 m and 0.20 m. Simulations were performed for all mesh sizes, and the results were compared in terms of convergence, stability and speed of simulation (Fig. 3). A linear wave with an amplitude of 1.5 m and a period of 6 s was used for these optimisation simulations. We considered wave time histories at two gauges A and B and recorded the waves from simulations using different mesh sizes (Fig. 3). Although the results are close (Fig. 3), some limited deviations are observed for larger mesh sizes of 0.20 m and 0.175 m. We therefore selected mesh size of 0.125 m as the optimum, giving an extra safety margin as a conservative solution.

The pressure from the incident waves on the vertical wall is validated in our model by comparing them with the analytical equation of Sainflou (1928), Eq. (3), which is one of the most common set of equations for design of coastal structures (Fig. 4). The model was tested by running a linear wave of period 6 s and wave amplitude of 1.5 m against the wall, with a still water level of 4.5 m. It can be seen that the model results are very close to those from analytical equations of Sainflou (1928), indicating that our numerical model is accurately modelling the wave-structure interaction (Fig. 4).

figure 4
Fig. 4

Eyewitness account analysis

Contemporary reporting of the 4th and 5th February 2014 storms by the main national news outlets in the UK highlights the extreme nature of the events and the significant damage and disruption they were likely to have on the communities of the south-west of England. In interviews, this was reinforced by Network Rail engineers who, even at this early stage, were forecasting remedial engineering works to last for at least 6 weeks. One week later, following subsequent storms the cascading nature of the events was obvious. Multiple breaches of the seawall had taken place with up to 35 separate landslide events and significant damage to parapet walls along the coastal route also were reported. Residents of the area reported extreme effects of the storm, one likening it to an earthquake and reporting water ingress through doors windows and even through vertical chimneys (Table 1). This suggests extreme wave overtopping volumes and large wave impact forces. One resident described the structural effects as: “the house was jumping up and down on its footings”.

Disaster management plans were quickly and effectively put into action by the local council, police service and National Rail. A major incident was declared, and decisions regarding evacuation of the residents under threat were taken around 2100 h on the night of 4th February when reports of initial damage to the seawall were received (Table 1). Local hotels were asked to provide short-term refuge to residents while local leisure facilities were prepared to accept residents later that evening. Initial repair work to the railway line was hampered by successive high spring tides and storms in the following days although significant progress was still made when weather conditions permitted (Table 1).

Sea level observations and spectral analysis

The results of surge and wave analyses are presented in Figs. 5 and 6. A surge height of up to 0.8 m was recorded in the examined tide gauge stations (Fig. 5b-d). Two main episodes of high surge heights are identified: the first surge started on 3rd February 2014 at 03:00 (UTC) and lasted until 4th of February 2014 at 00:00; the second event occurred in the period 4th February 2014 15:00 to 5th February 2014 at 17:00 (Fig. 5b-d). These data imply surge durations of 21 h and 26 h for the first and the second events, respectively. Based on the surge data in Fig. 5, we note that the storm event of early February 2014 and the associated surges was a relatively powerful one, which impacted at least 230 km of the south coast of England, from Land’s End to Weymouth, with large surge heights.

figure 5
Fig. 5
figure 6
Fig. 6

Based on wave buoy records, the maximum recorded amplitudes are at least 20.5 m in Dawlish and West Bay, 1.9 m in Tor Bay and 4.9 m in Chesil (Fig. 6a-b). The buoys at Tor Bay and Chesil recorded dual peak period bands of 4–8 and 8–12 s, whereas at Dawlish and West Bay registered triple peak period bands at 4–8, 8–12 and 20–25 s (Fig. 6c, d). It is important to note that the long-period waves at 20–25 s occur with short durations (approximately 2 min) while the waves at the other two bands of 4–8 and 8–12 s appear to be present at all times during the storm event.

The wave component at the period band of 4–8 s can be most likely attributed to normal coastal waves while the one at 8–12 s, which is longer, is most likely the swell component of the storm. Regarding the third component of the waves with long period of 20 -25 s, which occurs with short durations of 2 min, there are two hypotheses; it is either the result of a local (port and harbour) and regional (the Lyme Bay) oscillations (eg. Rabinovich 1997; Heidarzadeh and Satake 2014; Wang et al. 1992), or due to an abnormally long swell. To test the first hypothesis, we consider various water bodies such as Lyme Bay (approximate dimensions of 70 km × 20 km with an average water depth of 30 m; Fig. 6), several local bays (approximate dimensions of 3.6 km × 0.6 km with an average water depth of 6 m) and harbours (approximate dimensions of 0.5 km × 0.5 km with an average water depth of 4 m). Their water depths are based on the online Marine navigation website.Footnote8 According to Rabinovich (2010), the oscillation modes of a semi-enclosed rectangle basin are given by the following equation:

Tmn=2gd−−√[(m2L)2+(nW)2]−1/2Tmn=2gd[(m2L)2+(nW)2]−1/2

(5)

where TmnTmn is the oscillation period, gg is the gravitational acceleration, dd is the water depth, LL is the length of the basin, WW is the width of the basin, m=1,2,3,…m=1,2,3,… and n=0,1,2,3,…n=0,1,2,3,…; mm and nn are the counters of the different modes. Applying Eq. (5) to the aforementioned water bodies results in oscillation modes of at least 5 min, which is far longer than the observed period of 20–25 s. Therefore, we rule out the first hypothesis and infer that the long period of 20–25 s is most likely a long swell wave coming from distant sources. As discussed by Rabinovich (1997) and Wang et al. (2022), comparison between sea level spectra before and after the incident is a useful method to distinguish the spectrum of the weather event. A visual inspection of Fig. 6 reveals that the forcing at the period band of 20–25 s is non-existent before the incident.

Numerical simulations of wave loading and overtopping

Based on the results of sea level data analyses in the previous section (Fig. 6), we use a dual peak wave spectrum with peak periods of 10.0 s and 25.0 s for numerical simulations because such a wave would be comprised of the most energetic signals of the storm. For variations of water depth (2.0–4.0 m), coastal wave amplitude (0.5–1.5 m) (Fig. 7) and storm surge height (0.5–0.8 m) (Fig. 5), we developed 20 scenarios (Scn) which we used in numerical simulations (Table 2). Data during the incident indicated that water depth was up to the crest level of the seawall (approximately 4 m water depth); therefore, we varied water depth from 2 to 4 m in our simulation scenarios. Regarding wave amplitudes, we referred to the variations at a nearby tide gauge station (West Bay) which showed wave amplitude up to 1.2 m (Fig. 7). Therefore, wave amplitude was varied from 0.5 m to 1.5 m by considering a factor a safety of 25% for the maximum wave amplitude. As for the storm surge component, time series of storm surges calculated at three coastal stations adjacent to Dawlish showed that it was in the range of 0.5 m to 0.8 m (Fig. 5). These 20 scenarios would help to study uncertainties associated with wave amplitudes and pressures. Figure 8 shows snapshots of wave propagation and impacts on the seawall at different times.

figure 7
Fig. 7

Table 2 The 20 scenarios considered for numerical simulations in this study

Full size table

figure 8
Fig. 8

Results of wave amplitude simulations

Large wave amplitudes can induce significant wave forcing on the structure and cause overtopping of the seawall, which could eventually cascade to other hazards such as erosion of the backfill and scour (Adams and Heidarzadeh, 2021). The first 10 scenarios of our modelling efforts are for the same incident wave amplitudes of 0.5 m, which occur at different water depths (2.0–4.0 m) and storm surge heights (0.5–0.8 m) (Table 2 and Fig. 9). This is because we aim at studying the impacts of effective water depth (deff—the sum of mean sea level and surge height) on the time histories of wave amplitudes as the storm evolves. As seen in Fig. 9a, by decreasing effective water depth, wave amplitude increases. For example, for Scn-1 with effective depth of 4.5 m, the maximum amplitude of the first wave is 1.6 m, whereas it is 2.9 m for Scn-2 with effective depth of 3.5 m. However, due to intensive reflections and interferences of the waves in front of the vertical seawall, such a relationship is barely seen for the second and the third wave peaks. It is important to note that the later peaks (second or third) produce the largest waves rather than the first wave. Extraordinary wave amplifications are seen for the Scn-2 (deff = 3.5 m) and Scn-7 (deff = 3.3 m), where the corresponding wave amplitudes are 4.5 m and 3.7 m, respectively. This may indicate that the effective water depth of deff = 3.3–3.5 m is possibly a critical water depth for this structure resulting in maximum wave amplitudes under similar storms. In the second wave impact, the combined wave height (i.e. the wave amplitude plus the effective water depth), which is ultimately an indicator of wave overtopping, shows that the largest wave heights are generated by Scn-2, 7 and 8 (Fig. 9a) with effective water depths of 3.5 m, 3.3 m and 3.8 m and combined heights of 8.0 m, 7.0 m and 6.9 m (Fig. 9b). Since the height of seawall is 5.4 m, the combined wave heights for Scn-2, 7 and 8 are greater than the crest height of the seawall by 2.6 m, 1.6 m and 1.5 m, respectively, which indicates wave overtopping.

figure 9
Fig. 9

For scenarios 11–20 (Fig. 10), with incident wave amplitudes of 1.5 m (Table 2), the largest wave amplitudes are produced by Scn-17 (deff = 3.3 m), Scn-13 (deff = 2.5 m) and Scn-12 (deff = 3.5 m), which are 5.6 m, 5.1 m and 4.5 m. The maximum combined wave heights belong to Scn-11 (deff = 4.5 m) and Scn-17 (deff = 3.3 m), with combined wave heights of 9.0 m and 8.9 m (Fig. 10b), which are greater than the crest height of the seawall by 4.6 m and 3.5 m, respectively.

figure 10
Fig. 10

Our simulations for all 20 scenarios reveal that the first wave is not always the largest and wave interactions, reflections and interferences play major roles in amplifying the waves in front of the seawall. This is primarily because the wall is fully vertical and therefore has a reflection coefficient of close to one (i.e. full reflection). Simulations show that the combined wave height is up to 4.6 m higher than the crest height of the wall, implying that severe overtopping would be expected.

Results of wave loading calculations

The pressure calculations for scenarios 1–10 are given in Fig. 11 and those of scenarios 11–20 in Fig. 12. The total pressure distribution in Figs. 1112 mostly follows a triangular shape with maximum pressure at the seafloor as expected from the Sainflou (1928) design equations. These pressure plots comprise both static (due to mean sea level in front of the wall) and dynamic (combined effects of surge and wave) pressures. For incident wave amplitudes of 0.5 m (Fig. 11), the maximum wave pressure varies in the range of 35–63 kPa. At the sea surface, it is in the range of 4–20 kPa (Fig. 11). For some scenarios (Scn-2 and 7), the pressure distribution deviates from a triangular shape and shows larger pressures at the top, which is attributed to the wave impacts and partial breaking at the sea surface. This adds an additional triangle-shaped pressure distribution at the sea surface elevation consistent with the design procedure developed by Goda (2000) for braking waves. The maximum force on the seawall due to scenarios 1–10, which is calculated by integrating the maximum pressure distribution over the wave-facing surface of the seawall, is in the range of 92–190 KN (Table 2).

figure 11
Fig. 11
figure 12
Fig. 12

For scenarios 11–20, with incident wave amplitude of 1.5 m, wave pressures of 45–78 kPa and 7–120 kPa, for  the bottom and top of the wall, respectively, were observed (Fig. 12). Most of the plots show a triangular pressure distribution, except for Scn-11 and 15. A significant increase in wave impact pressure is seen for Scn-15 at the top of the structure, where a maximum pressure of approximately 120 kPa is produced while other scenarios give a pressure of 7–32 kPa for the sea surface. In other words, the pressure from Scn-15 is approximately four times larger than the other scenarios. Such a significant increase of the pressure at the top is most likely attributed to the breaking wave impact loads as detailed by Goda (2000) and Cuomo et al. (2010). The wave simulation snapshots in Fig. 8 show that the wave breaks before reaching the wall. The maximum force due to scenarios 11–20 is 120–286 KN.

The breaking wave impacts peaking at 286 KN in our simulations suggest destabilisation of the upper masonry blocks, probably by grout malfunction. This significant impact force initiated the failure of the seawall which in turn caused extensive ballast erosion. Wave impact damage was proposed by Adams and Heidarzadeh (2021) as one of the primary mechanisms in the 2014 Dawlish disaster. In the multi-hazard risk model proposed by these authors, damage mechanism III (failure pathway 5 in Adams and Heidarzadeh, 2021) was characterised by wave impact force causing damage to the masonry elements, leading to failure of the upper sections of the seawall and loss of infill material. As blocks were removed, access to the track bed was increased for inbound waves allowing infill material from behind the seawall to be fluidised and subsequently removed by backwash. The loss of infill material critically compromised the stability of the seawall and directly led to structural failure. In parallel, significant wave overtopping (discussed in the next section) led to ballast washout and cascaded, in combination with masonry damage, to catastrophic failure of the wall and suspension of the rails in mid-air (Fig. 1b), leaving the railway inoperable for two months.

Wave Overtopping

The two most important factors contributing to the 2014 Dawlish railway catastrophe were wave impact forces and overtopping. Figure 13 gives the instantaneous overtopping rates for different scenarios, which experienced overtopping. It can be seen that the overtopping rates range from 0.5 m3/s/m to 16.1 m3/s/m (Fig. 13). Time histories of the wave overtopping rates show that the phenomenon occurs intermittently, and each time lasts 1.0–7.0 s. It is clear that the longer the overtopping time, the larger the volume of the water poured on the structure. The largest wave overtopping rates of 16.1 m3/s/m and 14.4 m3/s/m belong to Scn-20 and 11, respectively. These are the two scenarios that also give the largest combined wave heights (Fig. 10b).

figure 13
Fig. 13

The cumulative overtopping curves (Figs. 1415) show the total water volume overtopped the structure during the entire simulation time. This is an important hazard factor as it determines the level of soil saturation, water pore pressure in the soil and soil erosion (Van der Meer et al. 2018). The maximum volume belongs to Scn-20, which is 65.0 m3/m (m-cubed of water per metre length of the wall). The overtopping volumes are 42.7 m3/m for Scn-11 and 28.8 m3/m for Scn-19. The overtopping volume is in the range of 0.7–65.0 m3/m for all scenarios.

figure 14
Fig. 14
figure 15
Fig. 15

For comparison, we compare our modelling results with those estimated using empirical equations. For the case of the Dawlish seawall, we apply the equation proposed by Van Der Meer et al. (2018) to estimate wave overtopping rates, based on a set of decision criteria which are the influence of foreshore, vertical wall, possible breaking waves and low freeboard:

qgH3m−−−−√=0.0155(Hmhs)12e(−2.2RcHm)qgHm3=0.0155(Hmhs)12e(−2.2RcHm)

(6)

where qq is the mean overtopping rate per metre length of the seawall (m3/s/m), gg is the acceleration due to gravity, HmHm is the incident wave height at the toe of the structure, RcRc is the wall crest height above mean sea level, hshs is the deep-water significant wave height and e(x)e(x) is the exponential function. It is noted that Eq. (6) is valid for 0.1<RcHm<1.350.1<RcHm<1.35. For the case of the Dawlish seawall and considering the scenarios with larger incident wave amplitude of 1.5 m (hshs= 1.5 m), the incident wave height at the toe of the structure is HmHm = 2.2—5.6 m, and the wall crest height above mean sea level is RcRc = 0.6–2.9 m. As a result, Eq. (6) gives mean overtopping rates up to approximately 2.9 m3/s/m. A visual inspection of simulated overtopping rates in Fig. 13 for Scn 11–20 shows that the mean value of the simulated overtopping rates (Fig. 13) is close to estimates using Eq. (6).

Discussion and conclusions

We applied a combination of eyewitness account analysis, sea level data analysis and numerical modelling in combination with our engineering judgement to explain the damage to the Dawlish railway seawall in February 2014. Main findings are:

  • Eyewitness data analysis showed that the extreme nature of the event was well forecasted in the hours prior to the storm impact; however, the magnitude of the risks to the structures was not well understood. Multiple hazards were activated simultaneously, and the effects cascaded to amplify the damage. Disaster management was effective, exemplified by the establishment of an emergency rendezvous point and temporary evacuation centre during the storm, indicating a high level of hazard awareness and preparedness.
  • Based on sea level data analysis, we identified triple peak period bands at 4–8, 8–12 and 20–25 s in the sea level data. Storm surge heights and wave oscillations were up to 0.8 m and 1.5 m, respectively.
  • Based on the numerical simulations of 20 scenarios with different water depths, incident wave amplitudes, surge heights and peak periods, we found that the wave oscillations at the foot of the seawall result in multiple wave interactions and interferences. Consequently, large wave amplitudes, up to 4.6 m higher than the height of the seawall, were generated and overtopped the wall. Extreme impulsive wave impact forces of up to 286 KN were generated by the waves interacting with the seawall.
  • We measured maximum wave overtopping rates of 0.5–16.1 m3/s/m for our scenarios. The cumulative overtopping water volumes per metre length of the wall were 0.7–65.0 m3/m.
  • Analysis of all the evidence combined with our engineering judgement suggests that the most likely initiating cause of the failure was impulsive wave impact forces destabilising one or more grouted joints between adjacent masonry blocks in the wall. Maximum observed pressures of 286 KN in our simulations are four times greater in magnitude than background pressures leading to block removal and initiating failure. Therefore, the sequence of cascading events was :1) impulsive wave impact force causing damage to masonry, 2) failure of the upper sections of the seawall, 3) loss of infill resulting in a reduction of structural strength in the landward direction, 4) ballast washout as wave overtopping and inbound wave activity increased and 5) progressive structural failure following successive tides.

From a risk mitigation point of view, the stability of the seawall in the face of future energetic cyclonic storm events and sea level rise will become a critical factor in protecting the rail network. Mitigation efforts will involve significant infrastructure investment to strengthen the civil engineering assets combined with improved hazard warning systems consisting of meteorological forecasting and real-time wave observations and instrumentation. These efforts must take into account the amenity value of coastal railway infrastructure to local communities and the significant number of tourists who visit every year. In this regard, public awareness and active engagement in the planning and execution of the project will be crucial in order to secure local stakeholder support for the significant infrastructure project that will be required for future resilience.

Notes

  1. https://www.networkrail.co.uk/..
  2. https://www.flow3d.com/products/flow-3d-hydro/.
  3. https://www.devonmuseums.net/Dawlish-Museum/Devon-Museums/.
  4. https://ntslf.org/.
  5. https://www.datawell.nl/Products/Buoys/DirectionalWaveriderMkIII.aspx.
  6. https://www.bodc.ac.uk/.
  7. https://coastalmonitoring.org/cco/.
  8. https://webapp.navionics.com/#boating@8&key=iactHlwfP.

References

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Acknowledgements

We are grateful to Brunel University London for administering the scholarship awarded to KA. The Flow3D-Hydro used in this research for numerical modelling is licenced to Brunel University London through an academic programme contract. We sincerely thank Prof Harsh Gupta (Editor-in-Chief) and two anonymous reviewers for their constructive review comments.

Funding

This project was funded by the UK Engineering and Physical Sciences Research Council (EPSRC) through a PhD scholarship to Keith Adams.

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  1. Department of Civil and Environmental Engineering, Brunel University London, Uxbridge, UB8 3PH, UKKeith Adams
  2. Department of Architecture and Civil Engineering, University of Bath, Bath, BA2 7AY, UKMohammad Heidarzadeh

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Correspondence to Keith Adams.

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Adams, K., Heidarzadeh, M. Extratropical cyclone damage to the seawall in Dawlish, UK: eyewitness accounts, sea level analysis and numerical modelling. Nat Hazards (2022). https://doi.org/10.1007/s11069-022-05692-2

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  • Received17 May 2022
  • Accepted17 October 2022
  • Published14 November 2022
  • DOIhttps://doi.org/10.1007/s11069-022-05692-2

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Keywords

  • Storm surge
  • Cyclone
  • Railway
  • Climate change
  • Infrastructure
  • Resilience
Fig. 1. (a) Dimensions of the casting with runners (unit: mm), (b) a melt flow simulation using Flow-3D software together with Reilly's model[44], predicted that a large amount of bifilms (denoted by the black particles) would be contained in the final casting. (c) A solidification simulation using Pro-cast software showed that no shrinkage defect was contained in the final casting.

AZ91 합금 주물 내 연행 결함에 대한 캐리어 가스의 영향

TianLiabJ.M.T.DaviesaXiangzhenZhuc
aUniversity of Birmingham, Birmingham B15 2TT, United Kingdom
bGrainger and Worrall Ltd, Bridgnorth WV15 5HP, United Kingdom
cBrunel Centre for Advanced Solidification Technology, Brunel University London, Kingston Ln, London, Uxbridge UB8 3PH, United Kingdom

Abstract

An entrainment defect (also known as a double oxide film defect or bifilm) acts a void containing an entrapped gas when submerged into a light-alloy melt, thus reducing the quality and reproducibility of the final castings. Previous publications, carried out with Al-alloy castings, reported that this trapped gas could be subsequently consumed by the reaction with the surrounding melt, thus reducing the void volume and negative effect of entrainment defects. Compared with Al-alloys, the entrapped gas within Mg-alloy might be more efficiently consumed due to the relatively high reactivity of magnesium. However, research into the entrainment defects within Mg alloys has been significantly limited. In the present work, AZ91 alloy castings were produced under different carrier gas atmospheres (i.e., SF6/CO2, SF6/air). The evolution processes of the entrainment defects contained in AZ91 alloy were suggested according to the microstructure inspections and thermodynamic calculations. The defects formed in the different atmospheres have a similar sandwich-like structure, but their oxide films contained different combinations of compounds. The use of carrier gases, which were associated with different entrained-gas consumption rates, affected the reproducibility of AZ91 castings.

연행 결함(이중 산화막 결함 또는 이중막이라고도 함)은 경합금 용융물에 잠길 때 갇힌 가스를 포함하는 공극으로 작용하여 최종 주물의 품질과 재현성을 저하시킵니다. Al-합금 주물을 사용하여 수행된 이전 간행물에서는 이 갇힌 가스가 주변 용융물과의 반응에 의해 후속적으로 소모되어 공극 부피와 연행 결함의 부정적인 영향을 줄일 수 있다고 보고했습니다. Al-합금에 비해 마그네슘의 상대적으로 높은 반응성으로 인해 Mg-합금 내에 포집된 가스가 더 효율적으로 소모될 수 있습니다. 그러나 Mg 합금 내 연행 결함에 대한 연구는 상당히 제한적이었습니다. 현재 작업에서 AZ91 합금 주물은 다양한 캐리어 가스 분위기(즉, SF6/CO2, SF6/공기)에서 생산되었습니다. AZ91 합금에 포함된 연행 결함의 진화 과정은 미세 조직 검사 및 열역학 계산에 따라 제안되었습니다. 서로 다른 분위기에서 형성된 결함은 유사한 샌드위치 구조를 갖지만 산화막에는 서로 다른 화합물 조합이 포함되어 있습니다. 다른 동반 가스 소비율과 관련된 운반 가스의 사용은 AZ91 주물의 재현성에 영향을 미쳤습니다.

Keywords

Magnesium alloy, Casting, Oxide film, Bifilm, Entrainment defect, Reproducibility

1. Introduction

As the lightest structural metal available on Earth, magnesium became one of the most attractive light metals over the last few decades. The magnesium industry has consequently experienced a rapid development in the last 20 years [1,2], indicating a large growth in demand for Mg alloys all over the world. Nowadays, the use of Mg alloys can be found in the fields of automobiles, aerospace, electronics and etc.[3,4]. It has been predicted that the global consumption of Mg metals will further increase in the future, especially in the automotive industry, as the energy efficiency requirement of both traditional and electric vehicles further push manufactures lightweight their design [3,5,6].

The sustained growth in demand for Mg alloys motivated a wide interest in the improvement of the quality and mechanical properties of Mg-alloy castings. During a Mg-alloy casting process, surface turbulence of the melt can lead to the entrapment of a doubled-over surface film containing a small quantity of the surrounding atmosphere, thus forming an entrainment defect (also known as a double oxide film defect or bifilm) [7][8][9][10]. The random size, quantity, orientation, and placement of entrainment defects are widely accepted to be significant factors linked to the variation of casting properties [7]. In addition, Peng et al. [11] found that entrained oxides films in AZ91 alloy melt acted as filters to Al8Mn5 particles, trapping them as they settle. Mackie et al. [12] further suggested that entrained oxide films can act to trawl the intermetallic particles, causing them to cluster and form extremely large defects. The clustering of intermetallic compounds made the entrainment defects more detrimental for the casting properties.

Most of the previous studies regarding entrainment defects were carried out on Al-alloys [7,[13][14][15][16][17][18], and a few potential methods have been suggested for diminishing their negative effect on the quality of Al-alloy castings. Nyahumwa et al.,[16] shows that the void volume within entrainment defects could be reduced by a hot isostatic pressing (HIP) process. Campbell [7] suggested the entrained gas within the defects could be consumed due to reaction with the surrounding melt, which was further verified by Raiszedeh and Griffiths [19].The effect of the entrained gas consumption on the mechanical properties of Al-alloy castings has been investigated by [8,9], suggesting that the consumption of the entrained gas promoted the improvement of the casting reproducibility.

Compared with the investigation concerning the defects within Al-alloys, research into the entrainment defects within Mg-alloys has been significantly limited. The existence of entrainment defects has been demonstrated in Mg-alloy castings [20,21], but their behaviour, evolution, as well as entrained gas consumption are still not clear.

In a Mg-alloy casting process, the melt is usually protected by a cover gas to avoid magnesium ignition. The cavities of sand or investment moulds are accordingly required to be flushed with the cover gas prior to the melt pouring [22]. Therefore, the entrained gas within Mg-alloy castings should contain the cover gas used in the casting process, rather than air only, which may complicate the structure and evolution of the corresponding entrainment defects.

SF6 is a typical cover gas widely used for Mg-alloy casting processes [23][24][25]. Although this cover gas has been restricted to use in European Mg-alloy foundries, a commercial report has pointed out that this cover is still popular in global Mg-alloy industry, especially in the countries which dominated the global Mg-alloy production, such as China, Brazil, India, etc. [26]. In addition, a survey in academic publications also showed that this cover gas was widely used in recent Mg-alloy studies [27]. The protective mechanism of SF6 cover gas (i.e., the reaction between liquid Mg-alloy and SF6 cover gas) has been investigated by several previous researchers, but the formation process of the surface oxide film is still not clearly understood, and even some published results are conflicting with each other. In early 1970s, Fruehling [28] found that the surface film formed under SF6 was MgO mainly with traces of fluorides, and suggested that SF6 was absorbed in the Mg-alloy surface film. Couling [29] further noticed that the absorbed SF6 reacted with the Mg-alloy melt to form MgF2. In last 20 years, different structures of the Mg-alloy surface films have been reported, as detailed below.(1)

Single-layered film. Cashion [30,31] used X-ray Photoelectron Spectroscopy (XPS) and Auger Spectroscopy (AES) to identify the surface film as MgO and MgF2. He also found that composition of the film was constant throughout the thickness and the whole experimental holding time. The film observed by Cashion had a single-layered structure created from a holding time from 10 min to 100 min.(2)

Double-layered film. Aarstad et. al [32] reported a doubled-layered surface oxide film in 2003. They observed several well-distributed MgF2 particles attached to the preliminary MgO film and grew until they covered 25–50% of the total surface area. The inward diffusion of F through the outer MgO film was the driving force for the evolution process. This double-layered structure was also supported by Xiong’s group [25,33] and Shih et al. [34].(3)

Triple-layered film. The triple-layered film and its evolution process were reported in 2002 by Pettersen [35]. Pettersen found that the initial surface film was a MgO phase and then gradually evolved to the stable MgF2 phase by the inward diffusion of F. In the final stage, the film has a triple-layered structure with a thin O-rich interlayer between the thick top and bottom MgF2 layers.(4)

Oxide film consisted of discrete particles. Wang et al [36] stirred the Mg-alloy surface film into the melt under a SF6 cover gas, and then inspect the entrained surface film after the solidification. They found that the entrained surface films were not continues as the protective surface films reported by other researchers but composed of discrete particles. The young oxide film was composed of MgO nano-sized oxide particles, while the old oxide films consist of coarse particles (about 1  µm in average size) on one side that contained fluorides and nitrides.

The oxide films of a Mg-alloy melt surface or an entrained gas are both formed due to the reaction between liquid Mg-alloy and the cover gas, thus the above-mentioned research regarding the Mg-alloy surface film gives valuable insights into the evolution of entrainment defects. The protective mechanism of SF6 cover gas (i.e., formation of a Mg-alloy surface film) therefore indicated a potential complicated evolution process of the corresponding entrainment defects.

However, it should be noted that the formation of a surface film on a Mg-alloy melt is in a different situation to the consumption of an entrained gas that is submerged into the melt. For example, a sufficient amount of cover gas was supported during the surface film formation in the studies previously mentioned, which suppressed the depletion of the cover gas. In contrast, the amount of entrained gas within a Mg-alloy melt is finite, and the entrained gas may become fully depleted. Mirak [37] introduced 3.5%SF6/air bubbles into a pure Mg-alloy melt solidifying in a specially designed permanent mould. It was found that the gas bubbles were entirely consumed, and the corresponding oxide film was a mixture of MgO and MgF2. However, the nucleation sites (such as the MgF2 spots observed by Aarstad [32] and Xiong [25,33]) were not observed. Mirak also speculated that the MgF2 formed prior to MgO in the oxide film based on the composition analysis, which was opposite to the surface film formation process reported in previous literatures (i.e., MgO formed prior to MgF2). Mirak’s work indicated that the oxide-film formation of an entrained gas may be quite different from that of surface films, but he did not reveal the structure and evolution of the oxide films.

In addition, the use of carrier gas in the cover gases also influenced the reaction between the cover gas and the liquid Mg-alloy. SF6/air required a higher content of SF6 than did a SF6/CO2 carrier gas [38], to avoid the ignition of molten magnesium, revealing different gas-consumption rates. Liang et.al [39] suggested that carbon was formed in the surface film when CO2 was used as a carrier gas, which was different from the films formed in SF6/air. An investigation into Mg combustion [40] reported a detection of Mg2C3 in the Mg-alloy sample after burning in CO2, which not only supported Liang’s results, but also indicated a potential formation of Mg carbides in double oxide film defects.

The work reported here is an investigation into the behaviour and evolution of entrainment defects formed in AZ91 Mg-alloy castings, protected by different cover gases (i.e., SF6/air and SF6/CO2). These carrier gases have different protectability for liquid Mg alloy, which may be therefore associated with different consumption rates and evolution processes of the corresponding entrained gases. The effect of the entrained-gas consumption on the reproducibility of AZ91 castings was also studied.

2. Experiment

2.1. Melting and casting

Three kilograms AZ91 alloy was melted in a mild steel crucible at 700 ± 5 °C. The composition of the AZ91 alloy has been shown in Table 1. Prior to heating, all oxide scale on the ingot surface was removed by machining. The cover gases used were 0.5%SF6/air or 0.5%SF6/CO2 (vol.%) at a flow rate of 6 L/min for different castings. The melt was degassed by argon with a flow rate of 0.3 L/min for 15 min [41,42], and then poured into sand moulds. Prior to pouring, the sand mould cavity was flushed with the cover gas for 20 min [22]. The residual melt (around 1 kg) was solidified in the crucible.

Table 1. Composition (wt.%) of the AZ91 alloy used in this study.

AlZnMnSiFeNiMg
9.40.610.150.020.0050.0017Residual

Fig. 1(a) shows the dimensions of the casting with runners. A top-filling system was deliberately used to generate entrainment defects in the final castings. Green and Campbell [7,43] suggested that a top-filling system caused more entrainment events (i.e., bifilms) during a casting process, compared with a bottom-filling system. A melt flow simulation (Flow-3D software) of this mould, using Reilly’s model [44] regarding the entrainment events, also predicted that a large amount of bifilms would be contained in the final casting (denoted by the black particles in Fig. 1b).

Fig. 1. (a) Dimensions of the casting with runners (unit: mm), (b) a melt flow simulation using Flow-3D software together with Reilly's model[44], predicted that a large amount of bifilms (denoted by the black particles) would be contained in the final casting. (c) A solidification simulation using Pro-cast software showed that no shrinkage defect was contained in the final casting.

Shrinkage defects also affect the mechanical properties and reproducibility of castings. Since this study focused on the effect of bifilms on the casting quality, the mould has been deliberately designed to avoid generating shrinkage defects. A solidification simulation using ProCAST software showed that no shrinkage defect would be contained in the final casting, as shown in Fig. 1c. The casting soundness has also been confirmed using a real time X-ray prior to the test bar machining.

The sand moulds were made from resin-bonded silica sand, containing 1wt. % PEPSET 5230 resin and 1wt. % PEPSET 5112 catalyst. The sand also contained 2 wt.% Na2SiF6 to act as an inhibitor [45]. The pouring temperature was 700 ± 5 °C. After the solidification, a section of the runner bars was sent to the Sci-Lab Analytical Ltd for a H-content analysis (LECO analysis), and all the H-content measurements were carried out on the 5th day after the casting process. Each of the castings was machined into 40 test bars for a tensile strength test, using a Zwick 1484 tensile test machine with a clip extensometer. The fracture surfaces of the broken test bars were examined using Scanning Electron Microscope (SEM, Philips JEOL7000) with an accelerating voltage of 5–15 kV. The fractured test bars, residual Mg-alloy solidified in the crucible, and the casting runners were then sectioned, polished and also inspected using the same SEM. The cross-section of the oxide film found on the test-bar fracture surface was exposed by the Focused Ion Beam milling technique (FIB), using a CFEI Quanta 3D FEG FIB-SEM. The oxide film required to be analysed was coated with a platinum layer. Then, a gallium ion beam, accelerated to 30 kV, milled the material substrate surrounding the platinum coated area to expose the cross section of the oxide film. EDS analysis of the oxide film’s cross section was carried out using the FIB equipment at accelerating voltage of 30 kV.

2.2. Oxidation cell

As previously mentioned, several past researchers investigated the protective film formed on a Mg-alloy melt surface [38,39,[46][47][48][49][50][51][52]. During these experiments, the amount of cover gas used was sufficient, thus suppressing the depletion of fluorides in the cover gas. The experiment described in this section used a sealed oxidation cell, which limited the supply of cover gas, to study the evolution of the oxide films of entrainment defects. The cover gas contained in the oxidation cell was regarded as large-size “entrained bubble”.

As shown in Fig. 2, the main body of the oxidation cell was a closed-end mild steel tube which had an inner length of 400 mm, and an inner diameter of 32 mm. A water-cooled copper tube was wrapped around the upper section of the cell. When the tube was heated, the cooling system created a temperature difference between the upper and lower sections, causing the interior gas to convect within the tube. The temperature was monitored by a type-K thermocouple located at the top of the crucible. Nie et al. [53] suggested that the SF6 cover gas would react with the steel wall of the holding furnace when they investigated the surface film of a Mg-alloy melt. To avoid this reaction, the interior surface of the steel oxidation cell (shown in Fig. 2) and the upper half section of the thermocouple were coated with boron nitride (the Mg-alloy was not in contact with boron nitride).

Fig. 2. Schematic of the oxidation cell used to study the evolution of the oxide films of the entrainment defects (unit mm).

During the experiment, a block of solid AZ91 alloy was placed in a magnesia crucible located at the bottom of the oxidation cell. The cell was heated to 100 °C in an electric resistance furnace under a gas flow rate of 1 L/min. The cell was held at this temperature for 20 min, to replace the original trapped atmosphere (i.e. air). Then, the oxidation cell was further heated to 700 °C, melting the AZ91 sample. The gas inlet and exit valves were then closed, creating a sealed environment for oxidation under a limited supply of cover gas. The oxidation cell was then held at 700 ± 10 °C for periods of time from 5 min to 30 min in 5-min intervals. At the end of each holding time, the cell was quenched in water. After cooling to room temperature, the oxidised sample was sectioned, polished, and subsequently examined by SEM.

3. Results

3.1. Structure and composition of the entrainment defects formed in SF6/air

The structure and composition of the entrainment defect formed in the AZ91 castings under a cover gas of 0.5%SF6/air was observed by SEM and EDS. The results indicate that there exist two types of entrainment defects which are sketched in Fig. 3: (1) Type A defect whose oxide film has a traditional single-layered structure and (2) Type B defect, whose oxide film has two layers. The details of these defects were introduced in the following. Here it should be noticed that, as the entrainment defects are also known as biofilms or double oxide film, the oxide films of Type B defect were referred to as “multi-layered oxide film” or “multi-layered structure” in the present work to avoid a confusing description such as “the double-layered oxide film of a double oxide film defect”.

Fig. 3. Schematic of the different types of entrainment defects found in AZ91 castings. (a) Type A defect with a single-layered oxide film and (b) Type B defect with two-layered oxide film.

Fig. 4(a-b) shows a Type A defect having a compact single-layered oxide film with about 0.4 µm thickness. Oxygen, fluorine, magnesium and aluminium were detected in this film (Fig. 4c). It is speculated that oxide film is the mixture of fluoride and oxide of magnesium and aluminium. The detection of fluorine revealed that an entrained cover gas was contained in the formation of this defect. That is to say that the pores shown in Fig. 4(a) were not shrinkage defects or hydrogen porosity, but entrainment defects. The detection of aluminium was different with Xiong and Wang’s previous study [47,48], which showed that no aluminium was contained in their surface film of an AZ91 melt protected by a SF6 cover gas. Sulphur could not be clearly recognized in the element map, but there was a S-peak in the corresponding ESD spectrum.

Fig. 4. (a) A Type A entrainment defect formed in SF6/air and having a single-layered oxide film, (b) the oxide film of this defect, (c) SEM-EDS element maps (using Philips JEOL7000) corresponding to the area highlighted in (b).

Fig. 5(a-b) shows a Type B entrainment defect having a multi-layered oxide film. The compact outer layers of the oxide films were enriched with fluorine and oxygen (Fig. 5c), while their relatively porous inner layers were only enriched with oxygen (i.e., poor in fluorine) and partly grew together, thus forming a sandwich-like structure. Therefore, it is speculated that the outer layer is the mixture of fluoride and oxide, while the inner layer is mainly oxide. Sulphur could only be recognized in the EDX spectrum and could not be clearly identified in the element map, which might be due to the small S-content in the cover gas (i.e., 0.5% volume content of SF6 in the cover gas). In this oxide film, aluminium was contained in the outer layer of this oxide film but could not be clearly detected in the inner layer. Moreover, the distribution of Al seems to be uneven. It can be found that, in the right side of the defect, aluminium exists in the film but its concentration can not be identified to be higher than the matrix. However, there is a small area with much higher aluminium concentration in the left side of the defect. Such an uneven distribution of aluminium was also observed in other defects (shown in the following), and it is the result of the formation of some oxide particles in or under the film.

Fig. 5. (a) A Type B entrainment defect formed in SF6/air and having a multi-layered oxide film, (b) the oxide films of this defect have grown together, (c) SEM-EDS element maps (using Philips JEOL7000) corresponding to the area shown in (b).

Figs. 4 and 5 show cross sectional observations of the entrainment defects formed in the AZ91 alloy sample cast under a cover gas of SF6/air. It is not sufficient to characterize the entrainment defects only by the figures observed from the two-dimensional section. To have a further understanding, the surface of the entrainment defects (i.e. the oxide film) was further studied by observing the fracture surface of the test bars.

Fig. 6(a) shows fracture surfaces of an AZ91 alloy tensile test bar produced in SF6/air. Symmetrical dark regions can be seen on both sides of the fracture surfaces. Fig. 6(b) shows boundaries between the dark and bright regions. The bright region consisted of jagged and broken features, while the surface of the dark region was relatively smooth and flat. In addition, the EDS results (Fig. 6c-d and Table 2) show that fluorine, oxygen, sulphur, and nitrogen were only detected in the dark regions, indicating that the dark regions were surface protective films entrained into the melt. Therefore, it could be suggested that the dark regions were an entrainment defect with consideration of their symmetrical nature. Similar defects on fracture surfaces of Al-alloy castings have been previously reported [7]Nitrides were only found in the oxide films on the test-bar fracture surfaces but never detected in the cross-sectional samples shown in Figs. 4 and 5. An underlying reason is that the nitrides contained in these samples may have hydrolysed during the sample polishing process [54].

Fig. 6. (a) A pair of the fracture surfaces of a AZ91 alloy tensile test bar produced under a cover gas of SF6/air. The dimension of the fracture surface is 5 mm × 6 mm, (b) a section of the boundary between the dark and bright regions shown in (a), (c-d) EDS spectrum of the (c) bright regions and (d) dark regions, (e) schematic of an entrainment defect contained in a test bar.

Table 2. EDS results (wt.%) corresponding to the regions shown in Fig. 6 (cover gas: SF6/air).

Empty CellCOMgFAlZnSN
Dark region in Fig. 6(b)3.481.3279.130.4713.630.570.080.73
Bright region in Fig. 6(b)3.5884.4811.250.68

In conjunction with the cross-sectional observation of the defects shown in Figs. 4 and 5, the structure of an entrainment defect contained in a tensile test bar was sketched as shown in Fig. 6(e). The defect contained an entrained gas enclosed by its oxide film, creating a void section inside the test bar. When the tensile force applied on the defect during the fracture process, the crack was initiated at the void section and propagated along the entrainment defect, since cracks would be propagated along the weakest path [55]. Therefore, when the test bar was finally fractured, the oxide films of entrainment defect appeared on both fracture surfaces of the test bar, as shown in Fig. 6(a).

3.2. Structure and composition of the entrainment defects formed in SF6/CO2

Similar to the entrainment defect formed in SF6/air, the defects formed under a cover gas of 0.5%SF6/CO2 also had two types of oxide films (i.e., single-layered and multi-layered types). Fig. 7(a) shows an example of the entrainment defects containing a multi-layered oxide film. A magnified observation to the defect (Fig. 7b) shows that the inner layers of the oxide films had grown together, presenting a sandwich-like structure, which was similar to the defects formed in an atmosphere of SF6/air (Fig. 5b). An EDS spectrum (Fig. 7c) revealed that the joint area (inner layer) of this sandwich-like structure mainly contained magnesium oxides. Peaks of fluorine, sulphur, and aluminium were recognized in this EDS spectrum, but their amount was relatively small. In contrast, the outer layers of the oxide films were compact and composed of a mixture of fluorides and oxides (Fig. 7d-e).

Fig. 7. (a) An example of entrainment defects formed in SF6/CO2 and having a multi-layered oxide film, (b) magnified observation of the defect, showing the inner layer of the oxide films has grown together, (c) EDS spectrum of the point denoted in (b), (d) outer layer of the oxide film, (e) SEM-EDS element maps (using Philips JEOL7000) corresponding to the area shown in (d).

Fig. 8(a) shows an entrainment defect on the fracture surfaces of an AZ91 alloy tensile test bar, which was produced in an atmosphere of 0.5%SF6/CO2. The corresponding EDS results (Table 3) showed that oxide film contained fluorides and oxides. Sulphur and nitrogen were not detected. Besides, a magnified observation (Fig. 8b) indicated spots on the oxide film surface. The diameter of the spots ranged from hundreds of nanometres to a few micron meters.

Fig. 8. (a) A pair of the fracture surfaces of a AZ91 alloy tensile test bar, produced in an atmosphere of SF6/CO2. The dimension of the fracture surface is 5 mm × 6 mm, (b) surface appearance of the oxide films on the fracture surfaces, showing spots on the film surface.

To further reveal the structure and composition of the oxide film clearly, the cross-section of the oxide film on a test-bar fracture surface was onsite exposed using the FIB technique (Fig. 9). As shown in Fig. 9a, a continuous oxide film was found between the platinum coating layer and the Mg-Al alloy substrate. Fig. 9 (b-c) shows a magnified observation to oxide films, indicating a multi-layered structure (denoted by the red box in Fig. 9c). The bottom layer was enriched with fluorine and oxygen and should be the mixture of fluoride and oxide, which was similar to the “outer layer” shown in Figs. 5 and 7, while the only-oxygen-enriched top layer was similar to the “inner layer” shown in Figs. 5 and 7.

Fig. 9. (a) A cross-sectional observation of the oxide film on the fracture surface of the AZ91 casting produced in SF6/CO2, exposed by FIB, (b) a magnified observation of area highlighted in (a), and (c) SEM-EDS elements map of the area shown in (b), obtained by CFEI Quanta 3D FEG FIB-SEM.

Except the continuous film, some individual particles were also observed in or below the continuous film, as shown in Fig. 9. An Al-enriched particle was detected in the left side of the oxide film shown in Fig. 9b and might be speculated to be spinel Mg2AlO4 because it also contains abundant magnesium and oxygen elements. The existing of such Mg2AlO4 particles is responsible for the high concentration of aluminium in small areas of the observed film and the uneven distribution of aluminium, as shown in Fig. 5(c). Here it should be emphasized that, although the other part of the bottom layer of the continuous oxide film contains less aluminium than this Al-enriched particle, the Fig. 9c indicated that the amount of aluminium in this bottom layer was still non-negligible, especially when comparing with the outer layer of the film. Below the right side of the oxide film shown in Fig. 9b, a particle was detected and speculated to be MgO because it is rich in Mg and O. According to Wang’s result [56], lots of discrete MgO particles can be formed on the surface of the Mg melt by the oxidation of Mg melt and Mg vapor. The MgO particles observed in our present work may be formed due to the same reasons. While, due to the differences in experimental conditions, less Mg melt can be vapored or react with O2, thus only a few of MgO particles formed in our work. An enrichment of carbon was also found in the film, revealing that CO2 was able to react with the melt, thus forming carbon or carbides. This carbon concentration was consistent with the relatively high carbon content of the oxide film shown in Table 3 (i.e., the dark region). In the area next to the oxide film.

Table 3. EDS results (wt.%) corresponding to the regions shown in Fig. 8 (cover gas: SF6/ CO2).

Empty CellCOMgFAlZnSN
Dark region in Fig. 8(a)7.253.6469.823.827.030.86
Bright region in Fig. 8(a)2.100.4482.8313.261.36

This cross-sectional observation of the oxide film on a test bar fracture surface (Fig. 9) further verified the schematic of the entrainment defect shown in Fig. 6(e). The entrainment defects formed in different atmospheres of SF6/CO2 and SF6/air had similar structures, but their compositions were different.

3.3. Evolution of the oxide films in the oxidation cell

The results in Section 3.1 and 3.2 have shown the structures and compositions of entrainment defects formed in AZ91 castings under cover gases of SF6/air and SF6/CO2. Different stages of the oxidation reaction may lead to the different structures and compositions of entrainment defects. Although Campbell has conjectured that an entrained gas may react with the surrounding melt, it is rarely reported that the reaction occurring between the Mg-alloy melt and entrapped cover gas. Previous researchers normally focus on the reaction between a Mg-alloy melt and the cover gas in an open environment [38,39,[46][47][48][49][50][51][52], which was different from the situation of a cover gas trapped into the melt. To further understand the formation of the entrainment defect in an AZ91 alloy, the evolution process of oxide films of the entrainment defect was further studied using an oxidation cell.

Fig. 10 (a and d) shows a surface film held for 5 min in the oxidation cell, protected by 0.5%SF6/air. There was only one single layer consisting of fluoride and oxide (MgF2 and MgO). In this surface film. Sulphur was detected in the EDS spectrum, but its amount was too small to be recognized in the element map. The structure and composition of this oxide film was similar to the single-layered films of entrainment defects shown in Fig. 4.

Fig. 10. Oxide films formed in the oxidation cell under a cover gas of 0.5%SF6/air and held at 700 °C for (a) 5 min; (b) 10 min; (c) 30 min, and (d-f) the SEM-EDS element maps (using Philips JEOL7000) corresponding to the oxide film shown in (a-c) respectively, (d) 5 min; (e) 10 min; (f) 30 min. The red points in (c and f) are the location references, denoting the boundary of the F-enriched layer in different element maps.

After a holding time of 10 min, a thin (O, S)-enriched top layer (around 700 nm) appeared upon the preliminary F-enriched film, forming a multi-layered structure, as shown in Fig. 10(b and e). The thickness of the (O, S)-enriched top layer increased with increased holding time. As shown in Fig. 10(c and f), the oxide film held for 30 min also had a multi-layered structure, but the thickness of its (O, S)-enriched top layer (around 2.5 µm) was higher than the that of the 10-min oxide film. The multi-layered oxide films shown in Fig. 10(b-c) presented a similar appearance to the films of the sandwich-like defect shown in Fig. 5.

The different structures of the oxide films shown in Fig. 10 indicated that fluorides in the cover gas would be preferentially consumed due to the reaction with the AZ91 alloy melt. After the depletion of fluorides, the residual cover gas reacted further with the liquid AZ91 alloy, forming the top (O, S)-enriched layer in the oxide film. Therefore, the different structures and compositions of entrainment defects shown in Figs. 4 and 5 may be due to an ongoing oxidation reaction between melt and entrapped cover gas.

This multi-layered structure has not been reported in previous publications concerning the protective surface film formed on a Mg-alloy melt [38,[46][47][48][49][50][51]. This may be due to the fact that previous researchers carried out their experiments with an un-limited amount of cover gas, creating a situation where the fluorides in the cover gas were not able to become depleted. Therefore, the oxide film of an entrainment defect had behaviour traits similar to the oxide films shown in Fig. 10, but different from the oxide films formed on the Mg-alloy melt surface reported in [38,[46][47][48][49][50][51].

Similar with the oxide films held in SF6/air, the oxide films formed in SF6/CO2 also had different structures with different holding times in the oxidation cell. Fig. 11(a) shows an oxide film, held on an AZ91 melt surface under a cover gas of 0.5%SF6/CO2 for 5 min. This film had a single-layered structure consisting of MgF2. The existence of MgO could not be confirmed in this film. After the holding time of 30 min, the film had a multi-layered structure; the inner layer was of a compact and uniform appearance and composed of MgF2, while the outer layer is the mixture of MgF2 and MgO. Sulphur was not detected in this film, which was different from the surface film formed in 0.5%SF6/air. Therefore, fluorides in the cover gas of 0.5%SF6/CO2 were also preferentially consumed at an early stage of the film growth process. Compared with the film formed in SF6/air, the MgO in film formed in SF6/CO2 appeared later and sulphide did not appear within 30 min. It may mean that the formation and evolution of film in SF6/air is faster than SF6/CO2. CO2 may have subsequently reacted with the melt to form MgO, while sulphur-containing compounds accumulated in the cover gas and reacted to form sulphide in very late stage (may after 30 min in oxidation cell).

Fig. 11. Oxide films formed in the oxidation cell under a cover gas of 0.5%SF6/CO2, and their SEM-EDS element maps (using Philips JEOL7000). They were held at 700 °C for (a) 5 min; (b) 30 min. The red points in (b) are the location references, denoting the boundary between the top and bottom layers in the oxide film.

4. Discussion

4.1. Evolution of entrainment defects formed in SF6/air

HSC software from Outokumpu HSC Chemistry for Windows (http://www.hsc-chemistry.net/) was used to carry out thermodynamic calculations needed to explore the reactions which might occur between the trapped gases and liquid AZ91 alloy. The solutions to the calculations suggest which products are most likely to form in the reaction process between a small amount of cover gas (i.e., the amount within a trapped bubble) and the AZ91-alloy melt.

In the trials, the pressure was set to 1 atm, and the temperature set to 700 °C. The amount of the cover gas was assumed to be 7 × 10−7 kg, with a volume of approximately 0.57 cm3 (3.14 × 10−8 kmol) for 0.5%SF6/air, and 0.35 cm3 (3.12 × 10−8 kmol) for 0.5%SF6/CO2. The amount of the AZ91 alloy melt in contact with the trapped gas was assumed to be sufficient to complete all reactions. The decomposition products of SF6 were SF5, SF4, SF3, SF2, F2, S(g), S2(g) and F(g) [57][58][59][60].

Fig. 12 shows the equilibrium diagram of the thermodynamic calculation of the reaction between the AZ91 alloy and 0.5%SF6/air. In the diagram, the reactants and products with less than 10−15 kmol have not been shown, as this was 5 orders of magnitude less than the amount of SF6 present (≈ 1.57 × 10−10 kmol) and therefore would not affect the observed process in a practical way.

Fig. 12. An equilibrium diagram for the reaction between 7e-7 kg 0.5%SF6/air and a sufficient amount of AZ91 alloy. The X axis is the amount of AZ91 alloy melt having reacted with the entrained gas, and the vertical Y-axis is the amount of the reactants and products.

This reaction process could be divided into 3 stages.

Stage 1: The formation of fluorides. the AZ91 melt preferentially reacted with SF6 and its decomposition products, producing MgF2, AlF3, and ZnF2. However, the amount of ZnF2 may have been too small to be detected practically (1.25 × 10−12 kmol of ZnF2 compared with 3 × 10−10 kmol of MgF2), which may be the reason why Zn was not detected in any the oxide films shown in Sections 3.13.3. Meanwhile, sulphur accumulated in the residual gas as SO2.

Stage 2: The formation of oxides. After the liquid AZ91 alloy had depleted all the available fluorides in the entrapped gas, the amount of AlF3 and ZnF2 quickly reduced due to a reaction with Mg. O2(g) and SO2 reacted with the AZ91 melt, forming MgO, Al2O3, MgAl2O4, ZnO, ZnSO4 and MgSO4. However, the amount of ZnO and ZnSO4 would have been too small to be found practically by EDS (e.g. 9.5 × 10−12 kmol of ZnO,1.38 × 10−14 kmol of ZnSO4, in contrast to 4.68 × 10−10 kmol of MgF2, when the amount of AZ91 on the X-axis is 2.5 × 10−9 kmol). In the experimental cases, the concentration of F in the cover gas is very low, whole the concentration f O is much higher. Therefore, the stage 1 and 2, i.e, the formation of fluoride and oxide may happen simultaneously at the beginning of the reaction, resulting in the formation of a singer-layered mixture of fluoride and oxide, as shown in Figs. 4 and 10(a). While an inner layer consisted of oxides but fluorides could form after the complete depletion of F element in the cover gas.

Stages 1- 2 theoretically verified the formation process of the multi-layered structure shown in Fig. 10.

The amount of MgAl2O4 and Al2O3 in the oxide film was of a sufficient amount to be detected, which was consistent with the oxide films shown in Fig. 4. However, the existence of aluminium could not be recognized in the oxide films grown in the oxidation cell, as shown in Fig. 10. This absence of Al may be due to the following reactions between the surface film and AZ91 alloy melt:(1)

Al2O3 + 3Mg + = 3MgO + 2Al, △G(700 °C) = -119.82 kJ/mol(2)

Mg + MgAl2O4 = MgO + Al, △G(700 °C) =-106.34 kJ/molwhich could not be simulated by the HSC software since the thermodynamic calculation was carried out under an assumption that the reactants were in full contact with each other. However, in a practical process, the AZ91 melt and the cover gas would not be able to be in contact with each other completely, due to the existence of the protective surface film.

Stage 3: The formation of Sulphide and nitride. After a holding time of 30 min, the gas-phase fluorides and oxides in the oxidation cell had become depleted, allowing the melt reaction with the residual gas, forming an additional sulphur-enriched layer upon the initial F-enriched or (F, O)-enriched surface film, thus resulting in the observed multi-layered structure shown in Fig. 10 (b and c). Besides, nitrogen reacted with the AZ91 melt until all reactions were completed. The oxide film shown in Fig. 6 may correspond to this reaction stage due to its nitride content. However, the results shows that the nitrides were not detected in the polished samples shown in Figs. 4 and 5, but only found on the test bar fracture surfaces. The nitrides may have hydrolysed during the sample preparation process, as follows [54]:(3)

Mg3N2 + 6H2O =3Mg(OH)2 + 2NH3↑(4)

AlN+ 3H2O =Al(OH)3 + NH3

In addition, Schmidt et al. [61] found that Mg3N2 and AlN could react to form ternary nitrides (Mg3AlnNn+2, n= 1, 2, 3…). HSC software did not contain the database of ternary nitrides, and it could not be added into the calculation. The oxide films in this stage may also contain ternary nitrides.

4.2. Evolution of entrainment defects formed in SF6/CO2

Fig. 13 shows the results of the thermodynamic calculation between AZ91 alloy and 0.5%SF6/CO2. This reaction processes can also be divided into three stages.

Fig. 13. An equilibrium diagram for the reaction between 7e-7 kg 0.5%SF6/CO2 and a sufficient amount of AZ91 alloy. The X axis denotes the amount of Mg alloy melt having reacted with the entrained gas, and the vertical Y-axis denotes the amounts of the reactants and products.

Stage 1: The formation of fluorides. SF6 and its decomposition products were consumed by the AZ91 melt, forming MgF2, AlF3, and ZnF2. As in the reaction of AZ91 in 0.5%SF6/air, the amount of ZnF2 was too small to be detected practically (1.51 × 10−13 kmol of ZnF2 compared with 2.67 × 10−10 kmol of MgF2). Sulphur accumulated in the residual trapped gas as S2(g) and a portion of the S2(g) reacted with CO2, to form SO2 and CO. The products in this reaction stage were consistent with the film shown in Fig. 11(a), which had a single layer structure that contained fluorides only.

Stage 2: The formation of oxides. AlF3 and ZnF2 reacted with the Mg in the AZ91 melt, forming MgF2, Al and Zn. The SO2 began to be consumed, producing oxides in the surface film and S2(g) in the cover gas. Meanwhile, the CO2 directly reacted with the AZ91 melt, forming CO, MgO, ZnO, and Al2O3. The oxide films shown in Figs. 9 and 11(b) may correspond to this reaction stage due to their oxygen-enriched layer and multi-layered structure.

The CO in the cover gas could further react with the AZ91 melt, producing C. This carbon may further react with Mg to form Mg carbides, when the temperature reduced (during solidification period) [62]. This may be the reason for the high carbon content in the oxide film shown in Figs. 89. Liang et al. [39] also reported carbon-detection in an AZ91 alloy surface film protected by SO2/CO2. The produced Al2O3 may be further combined with MgO, forming MgAl2O4 [63]. As discussed in Section 4.1, the alumina and spinel can react with Mg, causing an absence of aluminium in the surface films, as shown in Fig. 11.

Stage 3: The formation of Sulphide. the AZ91 melt began to consume S2(g) in the residual entrapped gas, forming ZnS and MgS. These reactions did not occur until the last stage of the reaction process, which could be the reason why the S-content in the defect shown Fig. 7(c) was small.

In summary, thermodynamic calculations indicate that the AZ91 melt will react with the cover gas to form fluorides firstly, then oxides and sulphides in the last. The oxide film in the different reaction stages would have different structures and compositions.

4.3. Effect of the carrier gases on consumption of the entrained gas and the reproducibility of AZ91 castings

The evolution processes of entrainment defects, formed in SF6/air and SF6/CO2, have been suggested in Sections 4.1 and 4.2. The theoretical calculations were verified with respect to the corresponding oxide films found in practical samples. The atmosphere within an entrainment defect could be efficiently consumed due to the reaction with liquid Mg-alloy, in a scenario dissimilar to the Al-alloy system (i.e., nitrogen in an entrained air bubble would not efficiently react with Al-alloy melt [64,65], however, nitrogen would be more readily consumed in liquid Mg alloys, commonly referred to as “nitrogen burning” [66]).

The reaction between the entrained gas and the surrounding liquid Mg-alloy converted the entrained gas into solid compounds (e.g. MgO) within the oxide film, thus reducing the void volume of the entrainment defect and hence probably causing a collapse of the defect (e.g., if an entrained gas of air was depleted by the surrounding liquid Mg-alloy, under an assumption that the melt temperature is 700 °C and the depth of liquid Mg-alloy is 10 cm, the total volume of the final solid products would be 0.044% of the initial volume taken by the entrapped air).

The relationship between the void volume reduction of entrainment defects and the corresponding casting properties has been widely studied in Al-alloy castings. Nyahumwa and Campbell [16] reported that the Hot Isostatic Pressing (HIP) process caused the entrainment defects in Al-alloy castings to collapse and their oxide surfaces forced into contact. The fatigue lives of their castings were improved after HIP. Nyahumwa and Campbell [16] also suggested a potential bonding of the double oxide films that were in contact with each other, but there was no direct evidence to support this. This binding phenomenon was further investigated by Aryafar et.al.[8], who re-melted two Al-alloy bars with oxide skins in a steel tube and then carried out a tensile strength test on the solidified sample. They found that the oxide skins of the Al-alloy bars strongly bonded with each other and became even stronger with an extension of the melt holding time, indicating a potential “healing” phenomenon due to the consumption of the entrained gas within the double oxide film structure. In addition, Raidszadeh and Griffiths [9,19] successfully reduced the negative effect of entrainment defects on the reproducibility of Al-alloy castings, by extending the melt holding time before solidification, which allowed the entrained gas to have a longer time to react with the surrounding melt.

With consideration of the previous work mentioned, the consumption of the entrained gas in Mg-alloy castings may diminish the negative effect of entrainment defects in the following two ways.

(1) Bonding phenomenon of the double oxide films. The sandwich-like structure shown in Fig. 5 and 7 indicated a potential bonding of the double oxide film structure. However, more evidence is required to quantify the increase in strength due to the bonding of the oxide films.

(2) Void volume reduction of entrainment defects. The positive effect of void-volume reduction on the quality of castings has been widely demonstrated by the HIP process [67]. As the evolution processes discussed in Section 4.14.2, the oxide films of entrainment defects can grow together due to an ongoing reaction between the entrained gas and surrounding AZ91 alloy melt. The volume of the final solid products was significant small compared with the entrained gas (i.e., 0.044% as previously mentioned).

Therefore, the consumption rate of the entrained gas (i.e., the growth rate of oxide films) may be a critical parameter for improving the quality of AZ91 alloy castings. The oxide film growth rate in the oxidization cell was accordingly further investigated.

Fig. 14 shows a comparison of the surface film growth rates in different cover gases (i.e., 0.5%SF6/air and 0.5%SF6/CO2). 15 random points on each sample were selected for film thickness measurements. The 95% confidence interval (95%CI) was computed under an assumption that the variation of the film thickness followed a Gaussian distribution. It can be seen that all the surface films formed in 0.5%SF6/air grew faster than those formed in 0.5%SF6/CO2. The different growth rates suggested that the entrained-gas consumption rate of 0.5%SF6/air was higher than that of 0.5%SF6/CO2, which was more beneficial for the consumption of the entrained gas.

Fig. 14. A comparison of the AZ91 alloy oxide film growth rates in 0.5%SF6/air and 0.5%SF6/CO2

It should be noted that, in the oxidation cell, the contact area of liquid AZ91 alloy and cover gas (i.e. the size of the crucible) was relatively small with consideration of the large volume of melt and gas. Consequently, the holding time for the oxide film growth within the oxidation cell was comparatively long (i.e., 5–30 min). However, the entrainment defects contained in a real casting are comparatively very small (i.e., a few microns size as shown in Figs. 36, and [7]), and the entrained gas is fully enclosed by the surrounding melt, creating a relatively large contact area. Hence the reaction time for cover gas and the AZ91 alloy melt may be comparatively short. In addition, the solidification time of real Mg-alloy sand castings can be a few minutes (e.g. Guo [68] reported that a Mg-alloy sand casting with 60 mm diameter required 4 min to be solidified). Therefore, it can be expected that an entrained gas trapped during an Mg-alloy melt pouring process will be readily consumed by the surrounding melt, especially for sand castings and large-size castings, where solidification times are long.

Therefore, the different cover gases (0.5%SF6/air and 0.5%SF6/CO2) associated with different consumption rates of the entrained gases may affect the reproducibility of the final castings. To verify this assumption, the AZ91 castings produced in 0.5%SF6/air and 0.5%SF6/CO2 were machined into test bars for mechanical evaluation. A Weibull analysis was carried out using both linear least square (LLS) method and non-linear least square (non-LLS) method [69].

Fig. 15(a-b) shows a traditional 2-p linearized Weibull plot of the UTS and elongation of the AZ91 alloy castings, obtained by the LLS method. The estimator used is P= (i-0.5)/N, which was suggested to cause the lowest bias among all the popular estimators [69,70]. The casting produced in SF6/air has an UTS Weibull moduli of 16.9, and an elongation Weibull moduli of 5.0. In contrast, the UTS and elongation Weibull modulus of the casting produced in SF6/CO2 are 7.7 and 2.7 respectively, suggesting that the reproducibility of the casting protected by SF6/CO2 were much lower than that produced in SF6/air.

Fig. 15. The Weibull modulus of AZ91 castings produced in different atmospheres, estimated by (a-b) the linear least square method, (c-d) the non-linear least square method, where SSR is the sum of residual squares.

In addition, the author’s previous publication [69] demonstrated a shortcoming of the linearized Weibull plots, which may cause a higher bias and incorrect R2 interruption of the Weibull estimation. A Non-LLS Weibull estimation was therefore carried out, as shown in Fig. 15 (c-d). The UTS Weibull modulus of the SF6/air casting was 20.8, while the casting produced under SF6/CO2 had a lower UTS Weibull modulus of 11.4, showing a clear difference in their reproducibility. In addition, the SF6/air elongation (El%) dataset also had a Weibull modulus (shape = 5.8) higher than the elongation dataset of SF6/CO2 (shape = 3.1). Therefore, both the LLS and Non-LLS estimations suggested that the SF6/air casting has a higher reproducibility than the SF6/CO2 casting. It supports the method that the use of air instead of CO2 contributes to a quicker consumption of the entrained gas, which may reduce the void volume within the defects. Therefore, the use of 0.5%SF6/air instead of 0.5%SF6/CO2 (which increased the consumption rate of the entrained gas) improved the reproducibility of the AZ91 castings.

However, it should be noted that not all the Mg-alloy foundries followed the casting process used in present work. The Mg-alloy melt in present work was degassed, thus reducing the effect of hydrogen on the consumption of the entrained gas (i.e., hydrogen could diffuse into the entrained gas, potentially suppressing the depletion of the entrained gas [7,71,72]). In contrast, in Mg-alloy foundries, the Mg-alloy melt is not normally degassed, since it was widely believed that there is not a ‘gas problem’ when casting magnesium and hence no significant change in tensile properties [73]. Although studies have shown the negative effect of hydrogen on the mechanical properties of Mg-alloy castings [41,42,73], a degassing process is still not very popular in Mg-alloy foundries.

Moreover, in present work, the sand mould cavity was flushed with the SF6 cover gas prior to pouring [22]. However, not all the Mg-alloy foundries flushed the mould cavity in this way. For example, the Stone Foundry Ltd (UK) used sulphur powder instead of the cover-gas flushing. The entrained gas within their castings may be SO2/air, rather than the protective gas.

Therefore, although the results in present work have shown that using air instead of CO2 improved the reproducibility of the final casting, it still requires further investigations to confirm the effect of carrier gases with respect to different industrial Mg-alloy casting processes.

7. Conclusion

Entrainment defects formed in an AZ91 alloy were observed. Their oxide films had two types of structure: single-layered and multi-layered. The multi-layered oxide film can grow together forming a sandwich-like structure in the final casting.2.

Both the experimental results and the theoretical thermodynamic calculations demonstrated that fluorides in the trapped gas were depleted prior to the consumption of sulphur. A three-stage evolution process of the double oxide film defects has been suggested. The oxide films contained different combinations of compounds, depending on the evolution stage. The defects formed in SF6/air had a similar structure to those formed in SF6/CO2, but the compositions of their oxide films were different. The oxide-film formation and evolution process of the entrainment defects were different from that of the Mg-alloy surface films previous reported (i.e., MgO formed prior to MgF2).3.

The growth rate of the oxide film was demonstrated to be greater under SF6/air than SF6/CO2, contributing to a quicker consumption of the damaging entrapped gas. The reproducibility of an AZ91 alloy casting improved when using SF6/air instead of SF6/CO2.

Acknowledgements

The authors acknowledge funding from the EPSRC LiME grant EP/H026177/1, and the help from Dr W.D. Griffiths and Mr. Adrian Carden (University of Birmingham). The casting work was carried out in University of Birmingham.

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Fig. 8. Variation of water surface profile (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.

Numerical study of the dam-break waves and Favre waves down sloped wet rigid-bed at laboratory scale

WenjunLiuaBoWangaYakunGuobaState Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resource and Hydropower, Sichuan University, Chengdu 610065, ChinabFaculty of Engineering & Informatics, University of Bradford, BD7 1DP, UK

Highlights

경사진 습윤층에서 댐파괴유동과 FFavre 파를 수치적으로 조사하였다.
수직 대 수평 속도의 비율이 먼저 정량화됩니다.
유동 상태는 유상 경사가 큰 후기 단계에서 크게 변경됩니다.
Favre 파도는 수직 속도와 수직 가속도에 큰 영향을 미칩니다.
베드 전단응력의 변화는 베드 기울기와 꼬리물의 영향을 받습니다.

Abstract

The bed slope and the tailwater depth are two important ones among the factors that affect the propagation of the dam-break flood and Favre waves. Most previous studies have only focused on the macroscopic characteristics of the dam-break flows or Favre waves under the condition of horizontal bed, rather than the internal movement characteristics in sloped channel. The present study applies two numerical models, namely, large eddy simulation (LES) and shallow water equations (SWEs) models embedded in the CFD software package FLOW-3D to analyze the internal movement characteristics of the dam-break flows and Favre waves, such as water level, the velocity distribution, the fluid particles acceleration and the bed shear stress, under the different bed slopes and water depth ratios. The results under the conditions considered in this study show that there is a flow state transition in the flow evolution for the steep bed slope even in water depth ratio α = 0.1 (α is the ratio of the tailwater depth to the reservoir water depth). The flow state transition shows that the wavefront changes from a breaking state to undular. Such flow transition is not observed for the horizontal slope and mild bed slope. The existence of the Favre waves leads to a significant increase of the vertical velocity and the vertical acceleration. In this situation, the SWEs model has poor prediction. Analysis reveals that the variation of the maximum bed shear stress is affected by both the bed slope and tailwater depth. Under the same bed slope (e.g., S0 = 0.02), the maximum bed shear stress position develops downstream of the dam when α = 0.1, while it develops towards the end of the reservoir when α = 0.7. For the same water depth ratio (e.g., α = 0.7), the maximum bed shear stress position always locates within the reservoir at S0 = 0.02, while it appears in the downstream of the dam for S0 = 0 and 0.003 after the flow evolves for a while. The comparison between the numerical simulation and experimental measurements shows that the LES model can predict the internal movement characteristics with satisfactory accuracy. This study improves the understanding of the effect of both the bed slope and the tailwater depth on the internal movement characteristics of the dam-break flows and Favre waves, which also provides a valuable reference for determining the flood embankment height and designing the channel bed anti-scouring facility.

Fig. 1. Sketch of related variables involved in shallow water model.
Fig. 1. Sketch of related variables involved in shallow water model.
Fig. 2. Flume model in numerical simulation.
Fig. 2. Flume model in numerical simulation.
Fig. 3. Grid sensitivity analysis (a) water surface profile; (b) velocity profile.
Fig. 3. Grid sensitivity analysis (a) water surface profile; (b) velocity profile.
Fig. 4. Sketch of experimental set-up for validating the velocity profile.
Fig. 4. Sketch of experimental set-up for validating the velocity profile.
Fig. 5. Sketch of experimental set-up for validating the bed shear stress.
Fig. 5. Sketch of experimental set-up for validating the bed shear stress.
Fig. 6. Model validation results (a) variation of the velocity profile; (b) error value of the velocity profile; (c) variation of the bed shear stress; (d) error value of the bed shear stress.
Fig. 6. Model validation results (a) variation of the velocity profile; (b) error value of the velocity profile; (c) variation of the bed shear stress; (d) error value of the bed shear stress.
Fig. 7. Schematic diagram of regional division.
Fig. 7. Schematic diagram of regional division.
Fig. 8. Variation of water surface profile (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 8. Variation of water surface profile (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 8. (continued).
Fig. 8. (continued).
Fig. 8. (continued).
Fig. 8. (continued).
Fig. 8. (continued).
Fig. 8. (continued).
Fig. 9. Froude number for α = 0.1 (a) variation with time; (b) variation with wavefront position.
Fig. 9. Froude number for α = 0.1 (a) variation with time; (b) variation with wavefront position.
Fig. 10. Characteristics of velocity distribution (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 10. Characteristics of velocity distribution (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 11. Average proportion of the vertical velocity (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 11. Average proportion of the vertical velocity (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 12. Bed shear stress distribution (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 12. Bed shear stress distribution (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 12. (continued).
Fig. 12. (continued).
Fig. 13. Variation of the maximum bed shear stress position with time (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 13. Variation of the maximum bed shear stress position with time (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 14. Time when the maximum bed shear stress appears at different positions (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 14. Time when the maximum bed shear stress appears at different positions (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 15. Movement characteristics of the fluid particles (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 15. Movement characteristics of the fluid particles (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 15. (continued).
Fig. 15. (continued).

Keywords

Dam-break flow, Bed slope, Wet bed, Velocity profile, Bed shear stress, Large eddy simulation

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Figure 3. Comparison of water surface profiles over porous media with 12 mm particle diameter in laboratory measurements (symbols) and numerical results (lines).

다공층에 대한 돌발 댐 붕괴의 3차원 유동 수치해석 시뮬레이션

A. Safarzadeh1*, P. Mohsenzadeh2, S. Abbasi3
1 Professor of Civil Eng., Water Engineering and Mineral Waters Research Center, Univ. of Mohaghegh Ardabili,Ardabil, Iran
2 M.Sc., Graduated of Civil-Hydraulic Structures Eng., Faculty of Eng., Univ. of Mohaghegh Ardabili, Ardabil, Iran
3 M.Sc., Graduated of Civil -Hydraulic Structures Eng., Faculty of Eng., Univ. of Mohaghegh Ardabili, Ardabil, Iran Safarzadeh@uma.ac.ir

Highlights

유체 이동에 의해 생성된 RBF는 Ls-Dyna에서 Fluent, ICFD ALE 및 SPH 방법으로 시뮬레이션되었습니다.
RBF의 과예측은 유체가 메인 도메인에서 고속으로 분리될 때 발생합니다.
이 과잉 예측은 요소 크기, 시간 단계 크기 및 유체 모델에 따라 다릅니다.
유체 성능을 검증하려면 최대 RBF보다 임펄스가 권장됩니다.

Abstract

Dam break is a very important problem due to its effects on economy, security, human casualties and environmental consequences. In this study, 3D flow due to dam break over the porous substrate is numerically simulated and the effect of porosity, permeability and thickness of the porous bed and the water depth in the porous substrate are investigated. Classic models of dam break over a rigid bed and water infiltration through porous media were studied and results of the numerical simulations are compared with existing laboratory data. Validation of the results is performed by comparing the water surface profiles and wave front position with dam break on rigid and porous bed. Results showed that, due to the effect of dynamic wave in the initial stage of dam break, a local peak occurs in the flood hydrograph. The presence of porous bed reduces the acceleration of the flood wave relative to the flow over the solid bed and it decreases with the increase of the permeability of the bed. By increasing the permeability of the bed, the slope of the ascending limb of the flood hydrograph and the peak discharge drops. Furthermore, if the depth and permeability of the bed is such that the intrusive flow reaches the rigid substrate under the porous bed, saturation of the porous bed, results in a sharp increase in the slope of the flood hydrograph. The maximum values of the peak discharge at the end of the channel with porous bed occurred in saturated porous bed conditions.

댐 붕괴는 경제, 보안, 인명 피해 및 환경적 영향으로 인해 매우 중요한 문제입니다. 본 연구에서는 다공성 기재에 대한 댐 파괴로 인한 3차원 유동을 수치적으로 시뮬레이션하고 다공성 기재의 다공성, 투과도 및 다공성 층의 두께 및 수심의 영향을 조사합니다. 단단한 바닥에 대한 댐 파괴 및 다공성 매체를 통한 물 침투의 고전 모델을 연구하고 수치 시뮬레이션 결과를 기존 실험실 데이터와 비교합니다. 결과 검증은 강체 및 다공성 베드에서 댐 파단과 수면 프로파일 및 파면 위치를 비교하여 수행됩니다. 그 결과 댐파괴 초기의 동적파동의 영향으로 홍수수문곡선에서 국부첨두가 발생하는 것으로 나타났다. 다공성 베드의 존재는 고체 베드 위의 유동에 대한 홍수파의 가속을 감소시키고 베드의 투과성이 증가함에 따라 감소합니다. 베드의 투수성을 증가시켜 홍수 수문곡선의 오름차순 경사와 첨두방류량이 감소한다. 더욱이, 만약 층의 깊이와 투과성이 관입 유동이 다공성 층 아래의 단단한 기질에 도달하는 정도라면, 다공성 층의 포화는 홍수 수문곡선의 기울기의 급격한 증가를 초래합니다. 다공층이 있는 채널의 끝단에서 최대 방전 피크값은 포화 다공층 조건에서 발생하였다.

Keywords

Keywords: Dams Break, 3D modeling, Porous Bed, Permeability, Flood wave

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Fig. 9 Test facility a plan view, b the bottom elevation of the reservoir to the channel (Bell et al. 1992)

2-D Dam-Break Flow Modeling Based on Weighted Average Flux Method

Iranian Journal of Science and Technology, Transactions of Civil Engineering volume 46, pages1515–1525 (2022)Cite this article

Abstract

천해 방정식을 기반으로 하는 2차원 흐름 모델은 댐 붕괴 흐름을 모델링하기 위해 개발되었습니다. 공간 이산화는 유한 체적 셀 중심 유형 방법에 의해 얻어집니다.

수치 시스템은 명시적인 방식으로 해결됩니다. 플럭스 모델링은 시간과 공간 모두에서 2차 정확도로 TVD WAF 방식으로 배포되었습니다. 로컬 리만 문제는 셀 인터페이스에서 HLLC 방법으로 해결됩니다. 수치 모델은 모델 결과와 해석 솔루션을 비교하여 검증합니다.

그런 다음 수치 모델의 결과는 90° 및 180° 편차 각도를 갖는 수로 및 삼각형 바텀 씰 위의 직선 수로에서 사용 가능한 실험 데이터와 비교됩니다. 결과는 댐 파괴파를 예측하는 현재 모델의 합리적인 성능을 확인합니다.

A two-dimensional flow model based on shallow water equations is developed for modeling dam-break flows. The spatial discretization is obtained by the finite volume cell centered type method. The numerical system is solved in explicit way. The flux modeling has been deployed by TVD WAF scheme with a second-order accuracy in both time and space. The local Riemann problem is solved by the HLLC method in the interface of the cells. The numerical model is verified by comparison of model results and analytical solutions. Then the results of numerical model are compared with available experimental data of dam-break waves in a channel with 90° and 180° deviation angle and in a straight channel over a triangular bottom sill. The results confirm the reasonable performance of the present model in predicting dam-break waves.

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Keywords

  • Finite volume
  • Shallow water equations
  • Dam-break
  • HLLC
  • TVD
  • WAF
Fig. 2 Generic control volume and notations
Fig. 2 Generic control volume and notations
Fig. 1 The generated grid for a channel with a 180° bend
Fig. 1 The generated grid for a channel with a 180° bend
Fig. 4 a Water surface profle and b velocity profle of dam-break problem with left dry bed
Fig. 4 a Water surface profle and b velocity profle of dam-break problem with left dry bed
Fig. 5 a Water surface profle and b velocity profle of appearance dry region
Fig. 5 a Water surface profle and b velocity profle of appearance dry region
Fig. 6 Comparison of the present model results and exact solution for transcritical fow over a bump with a shock
Fig. 6 Comparison of the present model results and exact solution for transcritical fow over a bump with a shock
Fig. 7 Geometry of the reservoir and L-shaped channel: plan view (Soares-Frazao et al. 2019)
Fig. 7 Geometry of the reservoir and L-shaped channel: plan view (Soares-Frazao et al. 2019)
Fig. 9 Test facility a plan view, b the bottom elevation of the reservoir to the channel (Bell et al. 1992)
Fig. 9 Test facility a plan view, b the bottom elevation of the reservoir to the channel (Bell et al. 1992)

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Figure 2.1: Types of Landslides[2]

Landslide flow path modelling
A Case Study on Aranayaka
Landslide

산사태 유로 모델링 : Aranayaka 산사태 사례 연구

Authors:

Malithi De Silva : University of Kelaniya

N.M.T De Silva
University of Colombo School of Computing
2018

Abstract

산사태가 발생하기 쉬운 구릉 지역 근처에서 발생하는 최근 인구 증가 및 개발은 취약성을 증가시킵니다. 기후 변화의 영향은 산사태 위험의 가능성을 더욱 높입니다. 따라서 인명 및 재산 피해를 방지하기 위해서는 불안정한 경사면 거동에 대한 적절한 관찰과 분석이 중요합니다.

산사태 흐름 경로 예측은 산사태 흐름 경로를 결정하는 데 중요하며 위험 매핑의 필수 요소입니다. 그러나 현상의 복잡한 특성과 관련 매개변수의 불확실성으로 인해 흐름 경로 예측은 어려운 작업입니다. 이 작업에서는 Kegalle 지역의 Aranayaka 지역의 주요 산사태 사고를 흐름 경로를 모델링하기 위한 사례 연구로 사용합니다.

위치에서 디지털 고도 모델을 기반으로 잠재적 소스 영역이 식별되었습니다. 확산 영역 평가는 D8 및 다중 방향 흐름 알고리즘이라는 두 가지 흐름 방향 알고리즘을 기반으로 했습니다. 이 프로토타입 모델을 사용하여 사용자는 슬라이드의 최대 너비, 런아웃 거리 및 슬립 표면적과 같은 산사태 관련 통계를 대화식으로 얻을 수 있습니다.

모델에서 얻은 결과는 실제 Aranayaka 산사태 데이터 세트와 해당 지역의 산사태 위험 지도와 비교되었습니다. D8 알고리즘을 사용하여 구현된 도구에서 생성된 산사태 흐름 경로는 65% 이상의 일치를 나타내고 다중 방향 흐름 알고리즘은 실제 흐름 경로 및 기타 관련 통계와 69% 이상의 일치를 나타냅니다.

또한, 생성된 유동 경로 방향과 예상되는 산사태 시작 지점이 실제 산사태 경계 내부에 잘 일치합니다.

Recent population growth and developments taking place close to landslides prone
hilly areas increase their vulnerability. Climate change impacts further raise the
potential of landslide hazard. Therefore, to prevent loss of lives and damage to
property, proper observation and analysis of unstable slope behavior is crucial.
Landslide flow path forecasting is important for determining a landslide flow route and
it is an essential element in hazard mapping. However, due to the complex nature of
the phenomenon and the uncertainties of associated parameters flow path prediction is
a challenging task.
In this work, the major landslide incident at Aranayaka area in Kegalle district is taken
as the case study to model the flow path. At the location, potential source areas were
identified on the basis of the Digital Elevation Model. Spreading area assessment was
based on two flow directional algorithms namely D8 and Multiple Direction Flow
Algorithm. Using this prototype model, a user can interactively get landslide specific
statistics such as the maximum width of the slide, runout distance, and slip surface area.
Results obtained by the model were compared with the actual Aranayaka landslide data
set the landslide hazard map of the area.
Landslide flow paths generated from the implemented tool using D8 algorithm shows
more than 65% agreement and Multiple Direction Flow Algorithm shows more than
69% agreement with the actual flow paths and other related statistics. Also, the
generated flow path directions and predicted possible landslide initiation points fit
inside the actual landslide boundary with good agreement.

Figure 2.1: Types of Landslides[2]
Figure 2.1: Types of Landslides[2]
Figure 2.2: Landslide Glossary [2]
Figure 2.2: Landslide Glossary [2]

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Fig. 1. Model geometry with the computational domain, extrusion nozzle, toolpath, and boundary conditions. The model is presented while printing the fifth layer.

재료 압출 적층 제조에서 증착된 층의 안정성 및 변형

Md Tusher Mollah Raphaël 사령관 Marcin P. Serdeczny David B. Pedersen Jon Spangenberg덴마크 공과 대학 기계 공학과, Kgs. 덴마크 링비

2020년 12월 22일 접수, 2021년 5월 1일 수정, 2021년 7월 15일 수락, 2021년 7월 21일 온라인 사용 가능, 기록 버전 2021년 8월 17일 .

Abstract

이 문서는 재료 압출 적층 제조 에서 여러 레이어를 인쇄하는 동안 증착 흐름의 전산 유체 역학 시뮬레이션 을 제공합니다 개발된 모델은 증착된 레이어의 형태를 예측하고 점소성 재료 를 인쇄하는 동안 레이어 변형을 캡처합니다 . 물리학은 일반화된 뉴턴 유체 로 공식화된 Bingham 구성 모델의 연속성 및 운동량 방정식에 의해 제어됩니다. . 증착된 층의 단면 모양이 예측되고 재료의 다양한 구성 매개변수에 대해 층의 변형이 연구됩니다. 층의 변형은 인쇄물의 정수압과 압출시 압출압력으로 인한 것임을 알 수 있다. 시뮬레이션에 따르면 항복 응력이 높을수록 변형이 적은 인쇄물이 생성되는 반면 플라스틱 점도 가 높을수록 증착된 레이어에서변형이 커 집니다 . 또한, 인쇄 속도, 압출 속도 의 영향, 층 높이 및 인쇄된 층의 변형에 대한 노즐 직경을 조사합니다. 마지막으로, 이 모델은 후속 인쇄된 레이어의 정수압 및 압출 압력을 지원하기 위해 증착 후 점소성 재료가 요구하는 항복 응력의 필요한 증가에 대한 보수적인 추정치를 제공합니다.

This paper presents computational fluid dynamics simulations of the deposition flow during printing of multiple layers in material extrusion additive manufacturing. The developed model predicts the morphology of the deposited layers and captures the layer deformations during the printing of viscoplastic materials. The physics is governed by the continuity and momentum equations with the Bingham constitutive model, formulated as a generalized Newtonian fluid. The cross-sectional shapes of the deposited layers are predicted, and the deformation of layers is studied for different constitutive parameters of the material. It is shown that the deformation of layers is due to the hydrostatic pressure of the printed material, as well as the extrusion pressure during the extrusion. The simulations show that a higher yield stress results in prints with less deformations, while a higher plastic viscosity leads to larger deformations in the deposited layers. Moreover, the influence of the printing speed, extrusion speed, layer height, and nozzle diameter on the deformation of the printed layers is investigated. Finally, the model provides a conservative estimate of the required increase in yield stress that a viscoplastic material demands after deposition in order to support the hydrostatic and extrusion pressure of the subsequently printed layers.

Fig. 1. Model geometry with the computational domain, extrusion nozzle, toolpath, and boundary conditions. The model is presented while printing the fifth layer.
Fig. 1. Model geometry with the computational domain, extrusion nozzle, toolpath, and boundary conditions. The model is presented while printing the fifth layer.

키워드

점성 플라스틱 재료, 재료 압출 적층 제조(MEX-AM), 다층 증착, 전산유체역학(CFD), 변형 제어
Viscoplastic Materials, Material Extrusion Additive Manufacturing (MEX-AM), Multiple-Layers Deposition, Computational Fluid Dynamics (CFD), Deformation Control

Introduction

Three-dimensional printing of viscoplastic materials has grown in popularity over the recent years, due to the success of Material Extrusion Additive Manufacturing (MEX-AM) [1]. Viscoplastic materials, such as ceramic pastes [2,3], hydrogels [4], thermosets [5], and concrete [6], behave like solids when the applied load is below their yield stress, and like a fluid when the applied load exceeds their yield stress [7]. Viscoplastic materials are typically used in MEX-AM techniques such as Robocasting [8], and 3D concrete printing [9,10]. The differences between these technologies lie in the processing of the material before the extrusion and in the printing scale (from microscale to big area additive manufacturing). In these extrusion-based technologies, the structure is fabricated in a layer-by-layer approach onto a solid surface/support [11, 12]. During the process, the material is typically deposited on top of the previously printed layers that may be already solidified (wet-on-dry printing) or still deformable (wet-on-wet printing) [1]. In wet-on-wet printing, control over the deformation of layers is important for the stability and geometrical accuracy of the prints. If the material is too liquid after the deposition, it cannot support the pressure of the subsequently deposited layers. On the other hand, the material flowability is a necessity during extrusion through the nozzle. Several experimental studies have been performed to analyze the physics of the extrusion and deposition of viscoplastic materials, as reviewed in Refs. [13–16]. The experimental measurements can be supplemented with Computational Fluid Dynamics (CFD) simulations to gain a more complete picture of MEX-AM. A review of the CFD studies within the material processing and deposition in 3D concrete printing was presented by Roussel et al. [17]. Wolfs et al. [18] predicted numerically the failure-deformation of a cylindrical structure due to the self-weight by calculating the stiffness and strength of the individual layers. It was found that the deformations can take place in all layers, however the most critical deformation occurs in the bottom layer. Comminal et al. [19,20] presented three-dimensional simulations of the material deposition in MEX-AM, where the fluid was approximated as Newtonian. Subsequently, the model was experimentally validated in Ref. [21] for polymer-based MEX-AM, and extended to simulate the deposition of multiple layers in Ref. [22], where the previously printed material was assumed solid. Xia et al. [23] simulated the influence of the viscoelastic effects on the shape of deposited layers in MEX-AM. A numerical model for simulating the deposition of a viscoplastic material was recently presented and experimentally validated in Refs. [24] and [25]. These studies focused on predicting the cross-sectional shape of a single printed layer for different processing conditions (relative printing speed, and layer height). Despite these research efforts, a limited number of studies have focused on investigating the material deformations in wet-on-wet printing when multiple layers are deposited on top of each other. This paper presents CFD simulations of the extrusion-deposition flow of a viscoplastic material for several subsequent layers (viz. three- and five-layers). The material is continuously printed one layer over another on a fixed solid surface. The rheology of the viscoplastic material is approximated by the Bingham constitutive equation that is formulated using the Generalized Newtonian Fluid (GNF) model. The CFD model is used to predict the cross-sectional shapes of the layers and their deformations while printing the next layers on top. Moreover, the simulations are used to quantify the extrusion pressure applied by the deposited material on the substrate, and the previously printed layers. Numerically, it is investigated how the process parameters (i.e., the extrusion speed, printing speed, nozzle diameter, and layer height) and the material rheology affect the deformations of the deposited layers. Section 2 describes the methodology of the study. Section 3 presents and discusses the results. The study is summarized and concluded in Section 4.

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하류하천의 영향 최소화를 위한 보조 여수로 최적 활용방안 검토

The Optimal Operation on Auxiliary Spillway to Minimize the Flood Damage in Downstream River with Various Outflow Conditions

하류하천의 영향 최소화를 위한 보조 여수로 최적 활용방안 검토

Hyung Ju Yoo1, Sung Sik Joo2, Beom Jae Kwon3, Seung Oh Lee4*

유 형주1, 주 성식2, 권 범재3, 이 승오4*

1Ph.D Student, Dept. of Civil & Environmental Engineering, Hongik University
2Director, Water Resources & Environment Department, HECOREA
3Director, Water Resources Department, ISAN
4Professor, Dept. of Civil & Environmental Engineering, Hongik University

1홍익대학교 건설환경공학과 박사과정
2㈜헥코리아 수자원환경사업부 이사
3㈜이산 수자원부 이사
4홍익대학교 건설환경공학과 교수

ABSTRACT

최근 기후변화로 인해 강우강도 및 빈도의 증가에 따른 집중호우의 영향 및 기존 여수로의 노후화에 대비하여 홍수 시 하류 하천의 영향을 최소화할 수 있는 보조 여수로 활용방안 구축이 필요한 실정이다. 이를 위해, 수리모형 실험 및 수치모형 실험을 통하여 보조 여수로 운영에 따른 흐름특성 변화 검토에 관한 연구가 많이 진행되어 왔다. 그러나 대부분의 연구는 여수로에서의 흐름특성 및 기능성에 대한 검토를 수행하였을 뿐 보조 여수로의 활용방안에 따른 하류하천 영향 검토 및 호안 안정성 검토에 관한 연구는 미비한 실정이다. 이에 본 연구에서는 기존 여수로 및 보조 여수로 방류 조건에 따른 하류영향 분석 및 호안 안정성 측면에서 최적 방류 시나리오 검토를 3차원 수치모형인 FLOW-3D를 사용하여 검토하였다. 또한 FLOW-3D 수치모의 수행을 통한 유속, 수위 결과와 소류력 산정 결과를 호안 설계허용 기준과 비교하였다. 수문 완전 개도 조건으로 가정하고 계획홍수량 유입 시 다양한 보조 여수로 활용방안에 대하여 수치모의를 수행한 결과, 보조 여수로 단독 운영 시 기존 여수로 단독운영에 비하여 최대유속 및 최대 수위의 감소효과를 확인하였다. 다만 계획홍수량의 45% 이하 방류 조건에서 대안부의 호안 안정성을 확보하였고 해당 방류량 초과 경우에는 처오름 현상이 발생하여 월류에 대한 위험성 증가를 확인하였다. 따라서 기존 여수로와의 동시 운영 방안 도출이 중요하다고 판단하였다. 여수로의 배분 비율 및 총 허용 방류량에 대하여 검토한 결과 보조 여수로의 방류량이 기존 여수로의 방류량보다 큰 경우 하류하천의 흐름이 중심으로 집중되어 대안부의 유속 저감 및 수위 감소를 확인하였고, 계획 홍수량의 77% 이하의 조건에서 호안의 허용 유속 및 허용 소류력 조건을 만족하였다. 이를 통하여 본 연구에서 제안한 보조 여수로 활용방안으로는 기존 여수로와 동시 운영 시 총 방류량에 대하여 보조 여수로의 배분량이 기존 여수로의 배분량보다 크게 설정하는 것이 하류하천의 영향을 최소화 할 수 있는 것으로 나타났다. 그러나 본 연구는 여수로 방류에 따른 대안부에서의 영향에 대해서만 검토하였고 수문 전면 개도 조건에서 검토하였다는 한계점은 분명히 있다. 이에 향후에는 다양한 수문 개도 조건 및 방류 시나리오를 적용 및 검토한다면 보다 효율적이고, 효과적인 보조 여수로 활용방안을 도출이 가능할 것으로 기대 된다.

키워드 : 보조 여수로, FLOW-3D, 수치모의, 호안 안정성, 소류력

1. 서 론

최근 기후변화로 인한 집중호우의 영향으로 홍수 시 댐으로 유입되는 홍수량이 설계 홍수량보다 증가하여 댐 안정성 확보가 필요한 실정이다(Office for Government Policy Coordination, 2003). MOLIT & K-water(2004)에서는 기존댐의 수문학적 안정성 검토를 수행하였으며 이상홍수 발생 시 24개 댐에서 월류 등으로 인한 붕괴위험으로 댐 하류지역의 극심한 피해를 예상하여 보조여수로 신설 및 기존여수로 확장 등 치수능력 증대 기본계획을 수립하였고 이를 통하여 극한홍수 발생 시 홍수량 배제능력을 증대하여 기존댐의 안전성 확보 및 하류지역의 피해를 방지하고자 하였다. 여기서 보조 여수로는 기존 여수로와 동시 또는 별도 운영하는 여수로로써 비상상황 시 방류 기능을 포함하고 있고(K-water, 2021), 최근에는 기존 여수로의 노후화에 따라 보조여수로의 활용방안에 대한 관심이 증가하고 있다. 따라서 본 연구에서는 3차원 수치해석을 수행하여 기존 및 보조 여수로의 방류량 조합에 따른 하류 영향을 분석하고 하류 호안 안정성 측면에서 최적 방류 시나리오를 검토하고자 한다.

기존의 댐 여수로 검토에 관한 연구는 주로 수리실험을 통하여 방류조건 별 흐름특성을 검토하였으나 최근에는 수치모형 실험결과가 수리모형실험과 비교하여 근사한 것을 확인하는 등 점차 수치모형실험을 수리모형실험의 대안으로 활용하고 있다(Jeon et al., 2006Kim, 2007Kim et al., 2008). 국내의 경우, Jeon et al.(2006)은 수리모형 실험과 수치모의를 이용하여 임하댐 바상여수로의 기본설계안을 도출하였고, Kim et al.(2008)은 가능최대홍수량 유입 시 비상여수로 방류에 따른 수리학적 안정성과 기능성을 3차원 수치모형인 FLOW-3D를 활용하여 검토하였다. 또한 Kim and Kim(2013)은 충주댐의 홍수조절 효과 검토 및 방류량 변화에 따른 상·하류의 수위 변화를 수치모형을 통하여 검토하였다. 국외의 경우 Zeng et al.(2017)은 3차원 수치모형인 Fluent를 활용한 여수로 방류에 따른 흐름특성 결과와 측정결과를 비교하여 수치모형 결과의 신뢰성을 검토하였다. Li et al.(2011)은 가능 최대 홍수량(Probable Maximum Flood, PMF)조건에서 기존 여수로와 신규 보조 여수로 유입부 주변의 흐름특성에 대하여 3차원 수치모형 Fluent를 활용하여 검토하였고, Lee et al.(2019)는 서로 근접해있는 기존 여수로와 보조여수로 동시 운영 시 방류능 검토를 수리모형 실험 및 수치모형 실험(FLOW-3D)을 통하여 수행하였으며 기존 여수로와 보조 여수로를 동시운영하게 되면 배수로 간섭으로 인하여 총 방류량이 7.6%까지 감소되어 댐의 방류능력이 감소하였음을 확인하였다.

그러나 대부분의 여수로 검토에 대한 연구는 여수로 내에서의 흐름특성 및 기능성에 대한 검토를 수행하였고. 이에 기존 여수로와 보조 여수로 방류운영에 따른 하류하천의 흐름특성 변화 및 호안 안정성 평가에 관한 추가적인 검토가 필요한 실정이다. 따라서 본 연구에서는 기존 여수로 및 보조 여수로 방류 조건에 따른 하류하천의 흐름특성 및 호안 안정성분석을 3차원 수치모형인 FLOW-3D를 이용하여 검토하였다. 또한 다양한 방류 배분 비율 및 허용 방류량 조건 변화에 따른 하류하천의 흐름특성 및 소류력 분석결과를 호안 설계 허용유속 및 허용 소류력 기준과 비교하여 하류하천의 영향을 최소화 할 수 있는 최적의 보조 여수로 활용방안을 도출하고자 한다.

2. 본 론

2.1 이론적 배경

2.1.1 3차원 수치모형의 기본이론

FLOW-3D는 미국 Flow Science, Inc에서 개발한 범용 유체역학 프로그램(CFD, Computational Fluid Dynamics)으로 자유 수면을 갖는 흐름모의에 사용되는 3차원 수치해석 모형이다. 난류모형을 통해 난류 해석이 가능하고, 댐 방류에 따른 하류 하천의 흐름 해석에도 많이 사용되어 왔다(Flow Science, 2011). 본 연구에서는 FLOW-3D(version 12.0)을 이용하여 홍수 시 기존 여수로의 노후화에 대비하여 보조 여수로의 활용방안에 대한 검토를 하류하천의 호안 안정성 측면에서 검토하였다.

2.1.2 유동해석의 지배방정식

1) 연속 방정식(Continuity Equation)

FLOW-3D는 비압축성 유체에 대하여 연속방정식을 사용하며, 밀도는 상수항으로 적용된다. 연속 방정식은 Eqs. (1)(2)와 같다.

(1)

∇·v=0

(2)

∂∂x(uAx)+∂∂y(vAy)+∂∂z(wAz)=RSORρ

여기서, ρ는 유체 밀도(kg/m3), u, v, w는 x, y, z방향의 유속(m/s), Ax, Ay, Az는 각 방향의 요소면적(m2), RSOR는 질량 생성/소멸(mass source/sink)항을 의미한다.

2) 운동량 방정식(Momentum Equation)

각 방향 속도성분 u, v, w에 대한 운동방정식은 Navier-Stokes 방정식으로 다음 Eqs. (3)(4)(5)와 같다.

(3)

∂u∂t+1VF(uAx∂u∂x+vAy∂v∂y+wAz∂w∂z)=-1ρ∂p∂x+Gx+fx-bx-RSORρVFu

(4)

∂v∂t+1VF(uAx∂u∂x+vAy∂v∂y+wAz∂w∂z)=-1ρ∂p∂y+Gy+fy-by-RSORρVFv

(5)

∂w∂t+1VF(uAx∂u∂x+vAy∂v∂y+wAz∂w∂z)=-1ρ∂p∂z+Gz+fz-bz-RSORρVFw

여기서, Gx, Gy, Gz는 체적력에 의한 가속항, fx, fy, fz는 점성에 의한 가속항, bx, by, bz는 다공성 매체에서의 흐름손실을 의미한다.

2.1.3 소류력 산정

호안설계 시 제방사면 호안의 안정성 확보를 위해서는 하천의 흐름에 의하여 호안에 작용하는 소류력에 저항할 수 있는 재료 및 공법 선택이 필요하다. 국내의 경우 하천공사설계실무요령(MOLIT, 2016)에서 계획홍수량 유하 시 소류력 산정 방법을 제시하고 있다. 소류력은 하천의 평균유속을 이용하여 산정할 수 있으며, 소류력 산정식은 Eqs. (6)(7)과 같다.

1) Schoklitsch 공식

Schoklitsch(1934)는 Chezy 유속계수를 적용하여 소류력을 산정하였다.

(6)

τ=γRI=γC2V2

여기서, τ는 소류력(N/m2), R은 동수반경(m), γ는 물의 단위중량(10.0 kN/m3), I는 에너지경사, C는 Chezy 유속계수, V는 평균유속(m/s)을 의미한다.

2) Manning 조도계수를 고려한 공식

Chezy 유속계수를 대신하여 Manning의 조도계수를 고려하여 소류력을 산정할 수 있다.

(7)

τ=γn2V2R1/3

여기서, τ는 소류력(N/m2), R은 동수반경(m), γ는 물의 단위중량(10.0 kN/m3), n은 Manning의 조도계수, V는 평균유속(m/s)을 의미한다.

FLOW-3D 수치모의 수행을 통하여 하천의 바닥 유속을 도출할 수 있으며, 본 연구에서는 Maning 조도계수롤 고려하여 소류력을 산정하고자 한다. 소류력을 산정하기 위해서 여수로 방류에 따른 대안부의 바닥유속 변화를 검토하여 최대 유속 값을 이용하였다. 최종적으로 산정한 소류력과 호안의 재료 및 공법에 따른 허용 소류력과 비교하여 제방사면 호안의 안정성 검토를 수행하게 된다.

2.2 하천호안 설계기준

하천 호안은 계획홍수위 이하의 유수작용에 대하여 안정성이 확보되도록 계획하여야 하며, 호안의 설계 시에는 사용재료의 확보용이성, 시공상의 용이성, 세굴에 대한 굴요성(flexibility) 등을 고려하여 호안의 형태, 시공방법 등을 결정한다(MOLIT, 2019). 국내의 경우, 하천공사설계실무요령(MOLIT, 2016)에서는 다양한 호안공법에 대하여 비탈경사에 따라 설계 유속을 비교하거나, 허용 소류력을 비교함으로써 호안의 안정성을 평가한다. 호안에 대한 국외의 설계기준으로 미국의 경우, ASTM(미국재료시험학회)에서 호안블록 및 식생매트 시험방법을 제시하였고 제품별로 ASTM 시험에 의한 허용유속 및 허용 소류력을 제시하였다. 일본의 경우, 호안 블록에 대한 축소실험을 통하여 항력을 측정하고 이를 통해서 호안 블록에 대한 항력계수를 제시하고 있다. 설계 시에는 항력계수에 의한 블록의 안정성을 평가하고 있으나, 최근에는 세굴의 영향을 고려할 수 있는 호안 안정성 평가의 필요성을 제기하고 있다(MOLIT, 2019). 관련된 국내·외의 하천호안 설계기준은 Table 1에 정리하여 제시하였고, 본 연구에서 하천 호안 안정성 평가 시 하천공사설계실무요령(MOLIT, 2016)과 ASTM 시험에서 제시한 허용소류력 및 허용유속 기준을 비교하여 각각 0.28 kN/m2, 5.0 m/s 미만일 경우 호안 안정성을 확보하였다고 판단하였다.

Table 1.

Standard of Permissible Velocity and Shear on Revetment

Country (Reference)MaterialPermissible velocity (Vp, m/s)Permissible Shear (τp, kN/m2)
KoreaRiver Construction Design Practice Guidelines
(MOLIT, 2016)
Vegetated5.00.50
Stone5.00.80
USAASTM D’6460Vegetated6.10.81
Unvegetated5.00.28
JAPANDynamic Design Method of Revetment5.0

2.3. 보조여수로 운영에 따른 하류하천 영향 분석

2.3.1 모형의 구축 및 경계조건

본 연구에서는 기존 여수로의 노후화에 대비하여 홍수 시 보조여수로의 활용방안에 따른 하류하천의 흐름특성 및 호안안정성 평가를 수행하기 위해 FLOW-3D 모형을 이용하였다. 기존 여수로 및 보조 여수로는 치수능력 증대사업(MOLIT & K-water, 2004)을 통하여 완공된 ○○댐의 제원을 이용하여 구축하였다. ○○댐은 설계빈도(100년) 및 200년빈도 까지는 계획홍수위 이내로 기존 여수로를 통하여 운영이 가능하나 그 이상 홍수조절은 보조여수로를 통하여 조절해야 하며, 또한 2011년 기존 여수로 정밀안전진단 결과 사면의 표층 유실 및 옹벽 밀림현상 등이 확인되어 노후화에 따른 보수·보강이 필요한 상태이다. 이에 보조여수로의 활용방안 검토가 필요한 것으로 판단하여 본 연구의 대상댐으로 선정하였다. 하류 하천의 흐름특성을 예측하기 위하여 격자간격을 0.99 ~ 8.16 m의 크기로 하여 총 격자수는 49,102,500개로 구성하였으며, 여수로 방류에 따른 하류하천의 흐름해석을 위한 경계조건으로 상류는 유입유량(inflow), 바닥은 벽면(wall), 하류는 수위(water surface elevation)조건으로 적용하도록 하였다(Table 2Fig. 1 참조). FLOW-3D 난류모형에는 혼합길이 모형, 난류에너지 모형, k-ϵ모형, RNG(Renormalized Group Theory) k-ϵ모형, LES 모형 등이 있으며, 본 연구에서는 여수로 방류에 따른 복잡한 난류 흐름 및 높은 전단흐름을 정확하게 모의(Flow Science, 2011)할 수 있는 RNG k-ϵ모형을 사용하였고, 하류하천 호안의 안정성 측면에서 보조여수로의 활용방안을 검토하기 위하여 방류시나리오는 Table 3에 제시된 것 같이 설정하였다. Case 1 및 Case 2를 통하여 계획홍수량에 대하여 기존 여수로와 보조 여수로의 단독 운영이 하류하천에 미치는 영향을 확인하였고 보조 여수로의 방류량 조절을 통하여 호안 안정성 측면에서 보조 여수로 방류능 검토를 수행하였다(Case 3 ~ Case 6). 또한 기존 여수로와 보조 여수로의 방류량 배분에 따른 하류하천의 영향 검토(Case 7 ~ Case 10) 및 방류 배분에 따른 허용 방류량을 호안 안정성 측면에서 검토를 수행하였다(Case 11 ~ Case 14).

수문은 완전개도 조건으로 가정하였으며 하류하천의 계획홍수량에 대한 기존 여수로와 보조여수로의 배분량을 조절하여 모의를 수행하였다. 여수로는 콘크리트의 조도계수 값(Chow, 1959)을 채택하였고, 댐 하류하천의 조도계수는 하천기본계획(Busan Construction and Management Administration, 2009) 제시된 조도계수 값을 채택하였으며 FLOW-3D의 적용을 위하여 Manning-Strickler 공식(Vanoni, 2006)을 이용하여 조도계수를 조고값으로 변환하여 사용하였다. Manning-Strickler 공식은 Eq. (8)과 같으며, FLOW-3D에 적용한 조도계수 및 조고는 Table 4와 같다.

(8)

n=ks1/68.1g1/2

여기서, kS는 조고 (m), n은 Manning의 조도계수, g는 중력가속도(m/s2)를 의미한다.

시간에 따라 동일한 유량이 일정하게 유입되도록 모의를 수행하였으며, 시간간격(Time Step)은 0.0001초로 설정(CFL number < 1.0) 하였다. 또한 여수로 수문을 통한 유량의 변동 값이 1.0%이내일 경우는 연속방정식을 만족하고 있다고 가정하였다. 이는, 유량의 변동 값이 1.0%이내일 경우 유속의 변동 값 역시 1.0%이내이며, 수치모의 결과 1.0%의 유속변동은 호안의 유속설계기준에 크게 영향을 미치지 않는다고 판단하였다. 그 결과 모든 수치모의 Case에서 2400초 이내에 결과 값이 수렴하는 것을 확인하였다.

Table 2.

Mesh sizes and numerical conditions

MeshNumbers49,102,500 EA
Increment (m)DirectionExisting SpillwayAuxiliary Spillway
∆X0.99 ~ 4.301.00 ~ 4.30
∆Y0.99 ~ 8.161.00 ~ 5.90
∆Z0.50 ~ 1.220.50 ~ 2.00
Boundary ConditionsXmin / YmaxInflow / Water Surface Elevation
Xmax, Ymin, Zmin / ZmaxWall / Symmetry
Turbulence ModelRNG model
Table 3.

Case of numerical simulation (Qp : Design flood discharge)

CaseExisting Spillway (Qe, m3/s)Auxiliary Spillway (Qa, m3/s)Remarks
1Qp0Reference case
20Qp
300.58QpReview of discharge capacity on
auxiliary spillway
400.48Qp
500.45Qp
600.32Qp
70.50Qp0.50QpDetermination of optimal division
ratio on Spillways
80.61Qp0.39Qp
90.39Qp0.61Qp
100.42Qp0.58Qp
110.32Qp0.45QpDetermination of permissible
division on Spillways
120.35Qp0.48Qp
130.38Qp0.53Qp
140.41Qp0.56Qp
Table 4.

Roughness coefficient and roughness height

CriteriaRoughness coefficient (n)Roughness height (ks, m)
Structure (Concrete)0.0140.00061
River0.0330.10496
/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F1.jpg
Fig. 1

Layout of spillway and river in this study

2.3.2 보조 여수로의 방류능 검토

본 연구에서는 기존 여수로와 보조 여수로의 방류량 배분에 따른 하류하천 대안부의 유속분포 및 수위분포를 검토하기 위해 수치모의 Case 별 다음과 같이 관심구역을 설정하였다(Fig. 2 참조). 관심구역(대안부)의 길이(L)는 총 1.3 km로 10 m 등 간격으로 나누어 검토하였으며, Section 1(0 < X/L < 0.27)은 기존 여수로 방류에 따른 영향이 지배적인 구간, Section 2(0.27 < X/L < 1.00)는 보조 여수로 방류에 따른 영향이 지배적인 구간으로 각 구간에서의 수위, 유속, 수심결과를 확인하였다. 기존 여수로의 노후화에 따른 보조 여수로의 방류능 검토를 위하여 Case 1 – Case 6까지의 결과를 비교하였다.

보조 여수로의 단독 운영 시 기존 여수로 운영 시 보다 하류하천의 대안부의 최대 유속(Vmax)은 약 3% 감소하였으며, 이는 보조 여수로의 하천 유입각이 기존 여수로 보다 7°작으며 유입하천의 폭이 증가하여 유속이 감소한 것으로 판단된다. 대안부의 최대 유속 발생위치는 하류 쪽으로 이동하였으며 교량으로 인한 단면의 축소로 최대유속이 발생하는 것으로 판단된다. 또한 보조 여수로의 배분량(Qa)이 증가함에 따라 하류하천 대안부의 최대 유속이 증가하였다. 하천호안 설계기준에서 제시하고 있는 허용유속(Vp)과 비교한 결과, 계획홍수량(Qp)의 45% 이하(Case 5 & 6)를 보조 여수로에서 방류하게 되면 허용 유속(5.0 m/s)조건을 만족하여 호안안정성을 확보하였다(Fig. 3 참조). 허용유속 외에도 대안부에서의 소류력을 산정하여 하천호안 설계기준에서 제시한 허용 소류력(τp)과 비교한 결과, 유속과 동일하게 보조 여수로의 방류량이 계획홍수량의 45% 이하일 경우 허용소류력(0.28 kN/m2) 조건을 만족하였다(Fig. 4 참조). 각 Case 별 호안설계조건과 비교한 결과는 Table 5에 제시하였다.

하류하천의 수위도 기존 여수로 운영 시 보다 보조 여수로 단독 운영 시 최대 수위(ηmax)가 약 2% 감소하는 효과를 보였으며 최대 수위 발생위치는 수충부로 여수로 방류시 처오름에 의한 수위 상승으로 판단된다. 기존 여수로의 단독운영(Case 1)의 수위(ηref)를 기준으로 보조 여수로의 방류량이 증가함에 따라 수위는 증가하였으나 계획홍수량의 58%까지 방류할 경우 월류에 대한 안정성(ηmax/ηref<0.97(=기설제방고))은 확보되었다(Fig. 5 참조). 그러나 계획홍수량 조건에서는 월류에 대한 위험성이 존재하기 때문에 기존여수로와 보조여수로의 적절한 방류량 배분 조합을 도출하는 것이 중요하다고 판단되어 진다.

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F2.jpg
Fig. 2

Region of interest in this study

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F3.jpg
Fig. 3

Maximum velocity and location of Vmax according to Qa

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F4.jpg
Fig. 4

Maximum shear according to Qa

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F5.jpg
Fig. 5

Maximum water surface elevation and location of ηmax according to Qa

Table 5.

Numerical results for each cases (Case 1 ~ Case 6)

CaseMaximum Velocity
(Vmax, m/s)
Maximum Shear
(τmax, kN/m2)
Evaluation
in terms of Vp
Evaluation
in terms of τp
1
(Qa = 0)
9.150.54No GoodNo Good
2
(Qa = Qp)
8.870.56No GoodNo Good
3
(Qa = 0.58Qp)
6.530.40No GoodNo Good
4
(Qa = 0.48Qp)
6.220.36No GoodNo Good
5
(Qa = 0.45Qp)
4.220.12AccpetAccpet
6
(Qa = 0.32Qp)
4.040.14AccpetAccpet

2.3.3 기존 여수로와 보조 여수로 방류량 배분 검토

기존 여수로 및 보조 여수로 단독운영에 따른 하류하천 및 호안의 안정성 평가를 수행한 결과 계획홍수량 방류 시 하류하천 대안부에서 호안 설계 조건(허용유속 및 허용 소류력)을 초과하였으며, 처오름에 의한 수위 상승으로 월류에 대한 위험성 증가를 확인하였다. 따라서 계획 홍수량 조건에서 기존 여수로와 보조 여수로의 방류량 배분을 통하여 호안 안정성을 확보하고 하류하천에 방류로 인한 피해를 최소화할 수 있는 배분조합(Case 7 ~ Case 10)을 검토하였다. Case 7은 기존 여수로와 보조여수로의 배분 비율을 균등하게 적용한 경우이고, Case 8은 기존 여수로의 배분량이 보조 여수로에 비하여 많은 경우, Case 9는 보조 여수로의 배분량이 기존 여수로에 비하여 많은 경우를 의미한다. 최대유속을 비교한 결과 보조 여수로의 배분 비율이 큰 경우 기존 여수로의 배분량에 의하여 흐름이 하천 중심에 집중되어 대안부의 유속을 저감하는 효과를 확인하였다. 보조여수로의 방류량 배분 비율이 증가할수록 기존 여수로 대안부 측(0.00<X/L<0.27, Section 1) 유속 분포는 감소하였으나, 신규여수로 대안부 측(0.27<X/L<1.00, Section 2) 유속은 증가하는 것을 확인하였다(Fig. 6 참조). 그러나 유속 저감 효과에도 대안부 전구간에서 설계 허용유속 조건을 초과하여 제방의 안정성을 확보하지는 못하였다. 소류력 산정 결과 유속과 동일하게 보조 여수로의 방류량이 기존 여수로의 방류량 보다 크면 감소하는 것을 확인하였고 일부 구간에서는 허용 소류력 조건을 만족하는 것을 확인하였다(Fig. 7 참조).

따라서 유속 저감효과가 있는 배분 비율 조건(Qa>Qe)에서 Section 2에 유속 저감에 영향을 미치는 기존 여수로 방류량 배분 비율을 증가시켜 추가 검토(Case 10)를 수행하였다. 단독운영과 비교 시 하류하천에 유입되는 유량은 증가하였음에도 불구하고 기존 여수로 방류량에 의해 흐름이 하천 중심으로 집중되는 현상에 따라 대안부의 유속은 단독 운영에 비하여 감소하는 것을 확인하였고(Fig. 8 참조), 호안 설계 허용유속 및 허용 소류력 조건을 만족하는 구간이 발생하여 호안 안정성도 확보한 것으로 판단되었다. 최종적으로 각 Case 별 수위 결과의 경우 여수로 동시 운영을 수행하게 되면 대안부 전 구간에서 월류에 대한 안정성(ηmax/ηref<0.97(=기설제방고))은 확보하였다(Fig. 9 참조). 각 Case 별 대안부에서 최대 유속결과 및 산정한 소류력은 Table 6에 제시하였다.

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F6.jpg
Fig. 6

Maximum velocity on section 1 & 2 according to Qa

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F7.jpg
Fig. 7

Maximum shear on section 1 & 2 according to Qa

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F8.jpg
Fig. 8

Velocity results of FLOW-3D (a: auxiliary spillway operation only , b : simultaneous operation of spillways)

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F9.jpg
Fig. 9

Maximum water surface elevation on section 1 & 2 according to Qa

Table 6.

Numerical results for each cases (Case 7 ~ Case 10)

Case (Qe &amp; Qa)Maximum Velocity (Vmax, m/s)Maximum Shear
(τmax, kN/m2)
Evaluation in terms of VpEvaluation in terms of τp
Section 1Section 2Section 1Section 2Section 1Section 2Section 1Section 2
7
Qe : 0.50QpQa : 0.50Qp
8.106.230.640.30No GoodNo GoodNo GoodNo Good
8
Qe : 0.61QpQa : 0.39Qp
8.886.410.610.34No GoodNo GoodNo GoodNo Good
9
Qe : 0.39QpQa : 0.61Qp
6.227.330.240.35No GoodNo GoodAcceptNo Good
10
Qe : 0.42QpQa : 0.58Qp
6.394.790.300.19No GoodAcceptNo GoodAccept

2.3.4 방류량 배분 비율의 허용 방류량 검토

계획 홍수량 방류 시 기존 여수로와 보조 여수로의 배분 비율 검토 결과 Case 10(Qe = 0.42Qp, Qa = 0.58Qp)에서 방류에 따른 하류 하천의 피해를 최소화시킬 수 있는 것을 확인하였다. 그러나 대안부 전 구간에 대하여 호안 설계조건을 만족하지 못하였다. 따라서 기존 여수로와 보조 여수로의 방류 배분 비율을 고정시킨 후 총 방류량을 조절하여 허용 방류량을 검토하였다(Case 11 ~ Case 14).

호안 안정성 측면에서 검토한 결과 계획홍수량 대비 총 방류량이 감소하면 최대 유속 및 최대 소류력이 감소하고 최종적으로 계획 홍수량의 77%를 방류할 경우 하류하천의 대안부에서 호안 설계조건을 모두 만족하는 것을 확인하였다(Fig. 10Fig. 11 참조). 각 Case 별 대안부에서 최대 유속결과 및 산정한 소류력은 Table 7에 제시하였다. 또한 Case 별 수위 검토 결과 처오름으로 인한 대안부 전 구간에서 월류에 대한 안정성(ηmax/ηref<0.97(=기설제방고))은 확보하였다(Fig. 12 참조).

Table 7.

Numerical results for each cases (Case 11 ~ Case 14)

Case (Qe &amp; Qa)Maximum Velocity
(Vmax, m/s)
Maximum Shear
(τmax, kN/m2)
Evaluation in terms of VpEvaluation in terms of τp
Section 1Section 2Section 1Section 2Section 1Section 2Section 1Section 2
11
Qe : 0.32QpQa : 0.45Qp
3.634.530.090.26AcceptAcceptAcceptAccept
12
Qe : 0.35QpQa : 0.48Qp
5.745.180.230.22No GoodNo GoodAcceptAccept
13
Qe : 0.38QpQa : 0.53Qp
6.704.210.280.11No GoodAcceptAcceptAccept
14
Qe : 0.41QpQa : 0.56Qp
6.545.240.280.24No GoodNo GoodAcceptAccept
/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F10.jpg
Fig. 10

Maximum velocity on section 1 & 2 according to total outflow

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F11.jpg
Fig. 11

Maximum shear on section 1 & 2 according to total outflow

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F12.jpg
Fig. 12

Maximum water surface elevation on section 1 & 2 according to total outflow

3. 결 론

본 연구에서는 홍수 시 기존 여수로의 노후화로 인한 보조 여수로의 활용방안에 대하여 하류하천의 호안 안정성 측면에서 검토하였다. 여수로 방류로 인한 하류하천의 흐름특성을 검토하기 위하여 3차원 수치모형인 FLOW-3D를 활용하였고, 여수로 지형은 치수능력 증대사업을 통하여 완공된 ○○댐의 제원을 이용하였다. 하류하천 조도 계수 및 여수로 방류량은 하천기본계획을 참고하여 적용하였다. 최종적으로 여수로 방류로 인한 하류하천의 피해를 최소화 시킬 수 있는 적절한 보조 여수로의 활용방안을 도출하기 위하여 보조 여수로 단독 운영과 기존 여수로와의 동시 운영에 따른 하류 하천의 흐름특성 및 소류력의 변화를 검토하였다.

수문은 완전 개도 상태에서 방류한다는 가정으로 계획 홍수량 조건에서 보조 여수로 단독 운영 시 하류하천 대안부의 유속 및 수위를 검토한 결과 기존 여수로 단독운영에 비하여 최대 유속 및 최대 수위가 감소하는 것을 확인할 수 있었으며, 이는 보조 여수로 단독 운영 시 하류하천으로 유입각도가 작아지고, 유입되는 하천의 폭이 증가되기 때문이다. 그러나 계획 홍수량 조건에서 하천호안 설계기준에서 제시한 허용 유속(5.0 m/s)과 허용 소류력(0.28 kN/m2)과 비교하였을 때 호안 안정성을 확보하지 못하였으며, 계획홍수량의 45% 이하 방류 시에 대안부의 호안 안정성을 확보하였다. 수위의 경우 여수로 방류에 따른 대안부에서 처오름 현상이 발생하여 월류에 대한 위험성을 확인하였고 이를 통하여 기존 여수로와의 동시 운영 방안을 도출하는 것이 중요하다고 판단된다. 따라서 기존 여수로와의 동시 운영 측면에서 기존 여수로와 보조 여수로의 배분 비율 및 총 방류량을 변화시켜가며 하류 하천의 흐름특성 및 소류력의 변화를 검토하였다. 배분 비율의 경우 기존 여수로와 보조 여수로의 균등 배분(Case 7) 및 편중 배분(Case 8 & Case 9)을 검토하여 보조 여수로의 방류량이 기존 여수로의 방류량보다 큰 경우 하류하천의 중심부로 집중되어 대안부의 최대유속, 최대소류력 및 최대수위가 감소하는 것을 확인하였다. 이를 근거로 기존 여수로의 방류 비율을 증가(Qe=0.42Qp, Qa=0.58Qp)시켜 검토한 결과 대안부 일부 구간에서 허용 유속 및 허용소류력 조건을 만족하는 것을 확인하였다. 이를 통하여 기존 여수로와 보조 여수로의 동시 운영을 통하여 적절한 방류량 배분 비율을 도출하는 것이 방류로 인한 하류하천의 피해를 저감하는데 효과적인 것으로 판단된다. 그러나 설계홍수량 방류 시 전 구간에서 허용 유속 및 소류력 조건을 만족하지 못하였다. 최종적으로 전체 방류량에서 기존 여수로의 방류 비율을 42%, 보조 여수로의 방류 비율을 58%로 설정하여 허용방류량을 검토한 결과, 계획홍수량의 77%이하로 방류 시 대안부의 최대유속은 기존여수로 방류의 지배영향구간(section 1)에서 3.63 m/s, 기존 여수로와 보조 여수로 방류의 영향구간(section 2)에서 4.53 m/s로 허용유속 조건을 만족하였고, 산정한 소류력도 각각 0.09 kN/m2 및 0.26 kN/m2로 허용 소류력 조건을 만족하여 대안부 호안의 안정성을 확보하였다고 판단된다.

본 연구 결과는 기후변화 및 기존여수로의 노후화로 인하여 홍수 시 기존여수로의 단독운영으로 하류하천의 피해가 발생할 수 있는 현시점에서 치수증대 사업으로 완공된 보조 여수로의 활용방안에 대한 기초자료로 활용될 수 있고, 향후 계획 홍수량 유입 시 최적의 배분 비율 및 허용 방류량 도출에 이용할 수 있다. 다만 본 연구는 여수로 방류에 따른 제방에 작용하는 수충력은 검토하지 못하고, 허용 유속 및 허용소류력은 제방과 유수의 방향이 일정한 구간에 대하여 검토하였다. 또한 여수로 방류에 따른 대안부에서의 영향에 대해서만 검토하였고 수문 전면 개도 조건에서 검토하였다는 한계점은 분명히 있다. 이에 향후에는 다양한 수문 개도 조건 및 방류 시나리오를 적용 및 검토하여 보다 효율적이고, 효과적인 보조 여수로 활용방안을 도출하고자 한다.

Acknowledgements

본 결과물은 K-water에서 수행한 기존 및 신규 여수로 효율적 연계운영 방안 마련(2021-WR-GP-76-149)의 지원을 받아 연구되었습니다.

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Gating System Design Based on Numerical Simulation and Production Experiment Verification of Aluminum Alloy Bracket Fabricated by Semi-solid Rheo-Die Casting Process

Gating System Design Based on Numerical Simulation and Production Experiment Verification of Aluminum Alloy Bracket Fabricated by Semi-solid Rheo-Die Casting Process

반고체 레오 다이 캐스팅 공정으로 제작된 알루미늄 합금 브래킷의 수치 시뮬레이션 및 생산 실험 검증을 기반으로 한 게이팅 시스템 설계

International Journal of Metalcasting volume 16, pages878–893 (2022)Cite this article

Abstract

In this study a gating system including sprue, runner and overflows for semi-solid rheocasting of aluminum alloy was designed by means of numerical simulations with a commercial software. The effects of pouring temperature, mold temperature and injection speed on the filling process performance of semi-solid die casting were studied. Based on orthogonal test analysis, the optimal die casting process parameters were selected, which were metal pouring temperature 590 °C, mold temperature 260 °C and injection velocity 0.5 m/s. Semi-solid slurry preparation process of Swirled Enthalpy Equilibration Device (SEED) was used for die casting production experiment. Aluminum alloy semi-solid bracket components were successfully produced with the key die casting process parameters selected, which was consistent with the simulation result. The design of semi-solid gating system was further verified by observing and analyzing the microstructure of different zones of the casting. The characteristic parameters, particle size and shape factor of microstructure of the produced semi-solid casting showed that the semi-solid aluminum alloy components are of good quality.

이 연구에서 알루미늄 합금의 반고체 레오캐스팅을 위한 스프루, 러너 및 오버플로를 포함하는 게이팅 시스템은 상용 소프트웨어를 사용한 수치 시뮬레이션을 통해 설계되었습니다. 주입 온도, 금형 온도 및 사출 속도가 반고체 다이캐스팅의 충전 공정 성능에 미치는 영향을 연구했습니다. 직교 테스트 분석을 기반으로 금속 주입 온도 590°C, 금형 온도 260°C 및 사출 속도 0.5m/s인 최적의 다이 캐스팅 공정 매개변수가 선택되었습니다. Swirled Enthalpy Equilibration Device(SEED)의 반고체 슬러리 제조 공정을 다이캐스팅 생산 실험에 사용하였다. 알루미늄 합금 반고체 브래킷 구성 요소는 시뮬레이션 결과와 일치하는 주요 다이 캐스팅 공정 매개변수를 선택하여 성공적으로 생산되었습니다. 반고체 게이팅 시스템의 설계는 주조의 다른 영역의 미세 구조를 관찰하고 분석하여 추가로 검증되었습니다. 생산된 반고체 주조물의 특성 매개변수, 입자 크기 및 미세 구조의 형상 계수는 반고체 알루미늄 합금 부품의 품질이 양호함을 보여주었습니다.

Gating System Design Based on Numerical Simulation and Production Experiment Verification of Aluminum Alloy Bracket Fabricated by Semi-solid Rheo-Die Casting Process
Gating System Design Based on Numerical Simulation and Production Experiment Verification of Aluminum Alloy Bracket Fabricated by Semi-solid Rheo-Die Casting Process

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Keywords

  • semi-solid rheo-die casting
  • gating system
  • process parameters
  • numerical simulation
  • microstructure
Fig. 1. Modified Timelli mold design.

Characterization of properties of Vanadium, Boron and Strontium addition on HPDC of A360 alloy

A360 합금의 HPDC에 대한 바나듐, 붕소 및 스트론튬 첨가 특성 특성

OzenGursoya
MuratColakb
KazimTurc
DeryaDispinarde

aUniversity of Padova, Department of Management and Engineering, Vicenza, Italy
bUniversity of Bayburt, Mechanical Engineering, Bayburt, Turkey
cAtilim University, Metallurgical and Materials Engineering, Ankara, Turkey
dIstanbul Technical University, Metallurgical and Materials Engineering, Istanbul, Turkey
eCenter for Critical and Functional Materials, ITU, Istanbul, Turkey

ABSTRACT

The demand for lighter weight decreased thickness and higher strength has become the focal point in the
automotive industry. In order to meet such requirements, the addition of several alloying elements has been started to be investigated. In this work, the additions of V, B, and Sr on feedability and tensile properties of A360 has been studied. A mold design that consisted of test bars has been produced. Initially, a simulation was carried out to optimize the runners, filling, and solidification parameters. Following the tests, it was found that V addition revealed the highest UTS but low elongation at fracture, while B addition exhibited visa verse. On the other hand, impact energy was higher with B additions.

더 가벼운 무게의 감소된 두께와 더 높은 강도에 대한 요구는 자동차 산업의 초점이 되었습니다. 이러한 요구 사항을 충족하기 위해 여러 합금 원소의 추가가 조사되기 시작했습니다. 이 연구에서는 A360의 이송성 및 인장 특성에 대한 V, B 및 Sr의 첨가가 연구되었습니다. 시험봉으로 구성된 금형 설계가 제작되었습니다. 처음에는 러너, 충전 및 응고 매개변수를 최적화하기 위해 시뮬레이션이 수행되었습니다. 시험 결과, V 첨가는 UTS가 가장 높지만 파단 연신율은 낮았고, B 첨가는 visa verse를 나타냈다. 반면에 충격 에너지는 B 첨가에서 더 높았다.

Fig. 1. Modified Timelli mold design.
Fig. 1. Modified Timelli mold design.
Fig. 2. Microstructural images (a) unmodified alloy, (b) Sr modified, (c) V added, (d) B added.
Fig. 2. Microstructural images (a) unmodified alloy, (b) Sr modified, (c) V added, (d) B added.
Fig. 3. Effect of Sr and V addition on the tensile properties of A360
Fig. 3. Effect of Sr and V addition on the tensile properties of A360
Fig. 4. Effect of Sr and B addition on the tensile properties of A360.
Fig. 4. Effect of Sr and B addition on the tensile properties of A360.
Fig. 5. Bubbles chart of tensile properties values obtained from Weibull statistics. | Fig. 6. Effect of Sr, V and B addition on the impact properties of A360.
Fig. 5. Bubbles chart of tensile properties values obtained from Weibull statistics.
Fig. 6. Effect of Sr, V and B addition on the impact properties of A360.
Fig. 7. SEM images on the fracture surfaces (a) V added, (b) B added.
Fig. 7. SEM images on the fracture surfaces (a) V added, (b) B added.

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Fig. 5. The predicted shapes of initial breach (a) Rectangular (b) V-notch. Fig. 6. Dam breaching stages.

Investigating the peak outflow through a spatial embankment dam breach

공간적 제방댐 붕괴를 통한 최대 유출량 조사

Mahmoud T.GhonimMagdy H.MowafyMohamed N.SalemAshrafJatwaryFaculty of Engineering, Zagazig University, Zagazig 44519, Egypt

Abstract

Investigating the breach outflow hydrograph is an essential task to conduct mitigation plans and flood warnings. In the present study, the spatial dam breach is simulated by using a three-dimensional computational fluid dynamics model, FLOW-3D. The model parameters were adjusted by making a comparison with a previous experimental model. The different parameters (initial breach shape, dimensions, location, and dam slopes) are studied to investigate their effects on dam breaching. The results indicate that these parameters have a significant impact. The maximum erosion rate and peak outflow for the rectangular shape are higher than those for the V-notch by 8.85% and 5%, respectively. Increasing breach width or decreasing depth by 5% leads to increasing maximum erosion rate by 11% and 15%, respectively. Increasing the downstream slope angle by 4° leads to an increase in both peak outflow and maximum erosion rate by 2.0% and 6.0%, respectively.

유출 유출 수문곡선을 조사하는 것은 완화 계획 및 홍수 경보를 수행하는 데 필수적인 작업입니다. 본 연구에서는 3차원 전산유체역학 모델인 FLOW-3D를 사용하여 공간 댐 붕괴를 시뮬레이션합니다. 이전 실험 모델과 비교하여 모델 매개변수를 조정했습니다.

다양한 매개변수(초기 붕괴 형태, 치수, 위치 및 댐 경사)가 댐 붕괴에 미치는 영향을 조사하기 위해 연구됩니다. 결과는 이러한 매개변수가 상당한 영향을 미친다는 것을 나타냅니다. 직사각형 형태의 최대 침식율과 최대 유출량은 V-notch보다 각각 8.85%, 5% 높게 나타났습니다.

위반 폭을 늘리거나 깊이를 5% 줄이면 최대 침식률이 각각 11% 및 15% 증가합니다. 하류 경사각을 4° 증가시키면 최대 유출량과 최대 침식률이 각각 2.0% 및 6.0% 증가합니다.

Keywords

Spatial dam breach; FLOW-3D; Overtopping erosion; Computational fluid dynamics (CFD)

1. Introduction

There are many purposes for dam construction, such as protection from flood disasters, water storage, and power generationEmbankment failures may have a catastrophic impact on lives and infrastructure in the downstream regions. One of the most common causes of embankment dam failure is overtopping. Once the overtopping of the dam begins, the breach formation will start in the dam body then end with the dam failure. This failure occurs within a very short time, which threatens to be very dangerous. Therefore, understanding and modeling the embankment breaching processes is essential for conducting mitigation plans, flood warnings, and forecasting flood damage.

The analysis of the dam breaching process is implemented by different techniques: comparative methods, empirical models with dimensional and dimensionless solutions, physical-based models, and parametric models. These models were described in detail [1]Parametric modeling is commonly used to simulate breach growth as a time-dependent linear process and calculate outflow discharge from the breach using hydraulics principles [2]. Alhasan et al. [3] presented a simple one-dimensional mathematical model and a computer code to simulate the dam breaching process. These models were validated by small dams breaching during the floods in 2002 in the Czech Republic. Fread [4] developed an erosion model (BREACH) based on hydraulics principles, sediment transport, and soil mechanics to estimate breach size, time of formation, and outflow discharge. Říha et al. [5] investigated the dam break process for a cascade of small dams using a simple parametric model for piping and overtopping erosion, as well as a 2D shallow-water flow model for the flood in downstream areas. Goodarzi et al. [6] implemented mathematical and statistical methods to assess the effect of inflows and wind speeds on the dam’s overtopping failure.

Dam breaching studies can be divided into two main modes of erosion. The first mode is called “planar dam breach” where the flow overtops the whole dam width. While the second mode is called “spatial dam breach” where the flow overtops through the initial pilot channel (i.e., a channel created in the dam body). Therefore, the erosion will be in both vertical and horizontal directions [7].

The erosion process through the embankment dams occurs due to the shear stress applied by water flows. The dam breaching evolution can be divided into three stages [8][9], but Y. Yang et al. [10] divided the breach development into five stages: Stage I, the seepage erosion; Stage II, the initial breach formation; Stage III, the head erosion; Stage IV, the breach expansion; and Stage V, the re-equilibrium of the river channel through the breach. Many experimental tests have been carried out on non-cohesive embankment dams with an initial breach to examine the effect of upstream inflow discharges on the longitudinal profile evolution and the time to inflection point [11].

Zhang et al. [12] studied the effect of changing downstream slope angle, sediment grain size, and dam crest length on erosion rates. They noticed that increasing dam crest length and decreasing downstream slope angle lead to decreasing sediment transport rate. While the increase in sediment grain size leads to an increased sediment transport rate at the initial stages. Höeg et al. [13] presented a series of field tests to investigate the stability of embankment dams made of various materials. Overtopping and piping were among the failure tests carried out for the dams composed of homogeneous rock-fill, clay, or gravel with a height of up to 6.0 m. Hakimzadeh et al. [14] constructed 40 homogeneous cohesive and non-cohesive embankment dams to study the effect of changing sediment diameter and dam height on the breaching process. They also used genetic programming (GP) to estimate the breach outflow. Refaiy et al. [15] studied different scenarios for the downstream drain geometry, such as length, height, and angle, to minimize the effect of piping phenomena and therefore increase dam safety.

Zhu et al. [16] examined the effect of headcut erosion on dam breach growth, especially in the case of cohesive dams. They found that the breach growth in non-cohesive embankments is slower than cohesive embankments due to the little effect of headcut. Schmocker and Hager [7] proposed a relationship for estimating peak outflow from the dam breach process.(1)QpQin-1=1.7exp-20hc23d5013H0

where: Qp = peak outflow discharge.

Qin = inflow discharge.

hc = critical flow depth.

d50 = mean sediment diameter.

Ho = initial dam height.

Yu et al. [17] carried out an experimental study for homogeneous non-cohesive embankment dams in a 180° bending rectangular flume to determine the effect of overtopping flows on breaching formation. They found that the main factors influencing breach formation are water level, river discharge, and embankment material diameter.

Wu et al. [18] carried out a series of experiments to investigate the effect of breaching geometry on both non-cohesive and cohesive embankment dams in a U-bend flume due to overtopping flows. In the case of non-cohesive embankments, the non-symmetrical lateral expansion was noticed during the breach formation. This expansion was described by a coefficient ranging from 2.7 to 3.3.

The numerical models of the dam breach can be categorized according to different parameters, such as flow dimensions (1D, 2D, or 3D), flow governing equations, and solution methods. The 1D models are mainly used to predict the outflow hydrograph from the dam breach. Saberi et al. [19] applied the 1D Saint-Venant equation, which is solved by the finite difference method to investigate the outflow hydrograph during dam overtopping failure. Because of the ability to study dam profile evolution and breach formation, 2D models are more applicable than 1D models. Guan et al. [20] and Wu et al. [21] employed both 2D shallow water equations (SWEs) and sediment erosion equations, which are solved by the finite volume method to study the effect of the dam’s geometry parameters on outflow hydrograph and dam profile evolution. Wang et al. [22] also proposed a second-order hybrid-type of total variation diminishing (TVD) finite-difference to estimate the breach outflow by solving the 2D (SWEs). The accuracy of (SWEs) for both vertical flow contraction and surface roughness has been assessed [23]. They noted that the accuracy of (SWEs) is acceptable for milder slopes, but in the case of steeper slopes, modelers should be more careful. Generally, the accuracy of 2D models is still low, especially with velocity distribution over the flow depth, lateral momentum exchange, density-driven flows, and bottom friction [24]. Therefore, 3D models are preferred. Larocque et al. [25] and Yang et al. [26] started to use three-dimensional (3D) models that depend on the Reynolds-averaged Navier-Stokes (RANS) equations.

Previous experimental studies concluded that there is no clear relationship between the peak outflow from the dam breach and the initial breach characteristics. Some of these studies depend on the sharp-crested weir fixed at the end of the flume to determine the peak outflow from the breach, which leads to a decrease in the accuracy of outflow calculations at the microscale. The main goals of this study are to carry out a numerical simulation for a spatial dam breach due to overtopping flows by using (FLOW-3D) software to find an empirical equation for the peak outflow discharge from the breach and determine the worst-case that leads to accelerating the dam breaching process.

2. Numerical simulation

The current study for spatial dam breach is simulated by using (FLOW-3D) software [27], which is a powerful computational fluid dynamics (CFD) program.

2.1. Geometric presentations

A stereolithographic (STL) file is prepared for each change in the initial breach geometry and dimensions. The CAD program is useful for creating solid objects and converting them to STL format, as shown in Fig. 1.

2.2. Governing equations

The governing equations for water flow are three-dimensional Reynolds Averaged Navier-Stokes equations (RANS).

The continuity equation:(2)∂ui∂xi=0

The momentum equation:(3)∂ui∂t+1VFuj∂ui∂xj=1ρ∂∂xj-pδij+ν∂ui∂xj+∂uj∂xi-ρu`iu`j¯

where u is time-averaged velocity,ν is kinematic viscosity, VF is fractional volume open to flow, p is averaged pressure and -u`iu`j¯ are components of Reynold’s stress. The Volume of Fluid (VOF) technique is used to simulate the free surface profile. Hirt et al. [28] presented the VOF algorithm, which employs the function (F) to express the occupancy of each grid cell with fluid. The value of (F) varies from zero to unity. Zero value refers to no fluid in the grid cell, while the unity value refers to the grid cell being fully occupied with fluid. The free surface is formed in the grid cells having (F) values between zero and unity.(4)∂F∂t+1VF∂∂xFAxu+∂∂yFAyv+∂∂zFAzw=0

where (u, v, w) are the velocity components in (x, y, z) coordinates, respectively, and (AxAyAz) are the area fractions.

2.3. Boundary and initial conditions

To improve the accuracy of the results, the boundary conditions should be carefully determined. In this study, two mesh blocks are used to minimize the time consumed in the simulation. The boundary conditions for mesh block 1 are as follows: The inlet and sides boundaries are defined as a wall boundary condition (wall boundary condition is usually used for bound fluid by solid regions. In the case of viscous flows, no-slip means that the tangential velocity is equal to the wall velocity and the normal velocity is zero), the outlet is defined as a symmetry boundary condition (symmetry boundary condition is usually used to reduce computational effort during CFD simulation. This condition allows the flow to be transferred from one mesh block to another. No inputs are required for this boundary condition except that its location should be defined accurately), the bottom boundary is defined as a uniform flow rate boundary condition, and the top boundary is defined as a specific pressure boundary condition with assigned atmospheric pressure. The boundary conditions for mesh block 2 are as follows: The inlet is defined as a symmetry boundary condition, the outlet is defined as a free flow boundary condition, the bottom and sides boundaries are defined as a wall boundary condition, and the top boundary is defined as a specific pressure boundary condition with assigned atmospheric pressure as shown in Fig. 2. The initial conditions required to be set for the fluid (i.e., water) inside of the domain include configuration, temperature, velocities, and pressure distribution. The configuration of water depends on the dimensions and shape of the dam reservoir. While the other conditions have been assigned as follows: temperature is normal water temperature (25 °c) and pressure distribution is hydrostatic with no initial velocity.

2.4. Numerical method

FLOW-3D uses the finite volume method (FVM) to solve the governing equation (Reynolds-averaged Navier-Stokes) over the computational domain. A finite-volume method is an Eulerian approach for representing and evaluating partial differential equations in algebraic equations form [29]. At discrete points on the mesh geometry, values are determined. Finite volume expresses a small volume surrounding each node point on a mesh. In this method, the divergence theorem is used to convert volume integrals with a divergence term to surface integrals. After that, these terms are evaluated as fluxes at each finite volume’s surfaces.

2.5. Turbulent models

Turbulence is the chaotic, unstable motion of fluids that occurs when there are insufficient stabilizing viscous forces. In FLOW-3D, there are six turbulence models available: the Prandtl mixing length model, the one-equation turbulent energy model, the two-equation (k – ε) model, the Renormalization-Group (RNG) model, the two-equation (k – ω) models, and a large eddy simulation (LES) model. For simulating flow motion, the RNG model is adopted to simulate the motion behavior better than the k – ε and k – ω.

models [30]. The RNG model consists of two main equations for the turbulent kinetic energy KT and its dissipation.εT(5)∂kT∂t+1VFuAx∂kT∂x+vAy∂kT∂y+wAz∂kT∂z=PT+GT+DiffKT-εT(6)∂εT∂t+1VFuAx∂εT∂x+vAy∂εT∂y+wAz∂εT∂z=C1.εTKTPT+c3.GT+Diffε-c2εT2kT

where KT is the turbulent kinetic energy, PT is the turbulent kinetic energy production, GT is the buoyancy turbulence energy, εT is the turbulent energy dissipation rate, DiffKT and Diffε are terms of diffusion, c1, c2 and c3 are dimensionless parameters, in which c1 and c3 have a constant value of 1.42 and 0.2, respectively, c2 is computed from the turbulent kinetic energy (KT) and turbulent production (PT) terms.

2.6. Sediment scour model

The sediment scour model available in FLOW-3D can calculate all the sediment transport processes including Entrainment transport, Bedload transport, Suspended transport, and Deposition. The erosion process starts once the water flows remove the grains from the packed bed and carry them into suspension. It happens when the applied shear stress by water flows exceeds critical shear stress. This process is represented by entrainment transport in the numerical model. After entrained, the grains carried by water flow are represented by suspended load transport. After that, some suspended grains resort to settling because of the combined effect of gravity, buoyancy, and friction. This process is described through a deposition. Finally, the grains sliding motions are represented by bedload transport in the model. For the entrainment process, the shear stress applied by the fluid motion on the packed bed surface is calculated using the standard wall function as shown in Eq.7.(7)ks,i=Cs,i∗d50

where ks,i is the Nikuradse roughness and Cs,i is a user-defined coefficient. The critical bed shear stress is defined by a dimensionless parameter called the critical shields number as expressed in Eq.8.(8)θcr,i=τcr,i‖g‖diρi-ρf

where θcr,i is the critical shields number, τcr,i is the critical bed shear stress, g is the absolute value of gravity acceleration, di is the diameter of the sediment grain, ρi is the density of the sediment species (i) and ρf is the density of the fluid. The value of the critical shields number is determined according to the Soulsby-Whitehouse equation.(9)θcr,i=0.31+1.2d∗,i+0.0551-exp-0.02d∗,i

where d∗,i is the dimensionless diameter of the sediment, given by Eq.10.(10)d∗,i=diρfρi-ρf‖g‖μf213

where μf is the fluid dynamic viscosity. For the sloping bed interface, the value of the critical shields number is modified according to Eq.11.(11)θ`cr,i=θcr,icosψsinβ+cos2βtan2φi-sin2ψsin2βtanφi

where θ`cr,i is the modified critical shields number, φi is the angle of repose for the sediment, β is the angle of bed slope and ψ is the angle between the flow and the upslope direction. The effects of the rolling, hopping, and sliding motions of grains along the packed bed surface are taken by the bedload transport process. The volumetric bedload transport rate (qb,i) per width of the bed is expressed in Eq.12.(12)qb,i=Φi‖g‖ρi-ρfρfdi312

where Φi is the dimensionless bedload transport rate is calculated by using Meyer Peter and Müller equation.(13)Φi=βMPM,iθi-θ`cr,i1.5cb,i

where βMPM,i is the Meyer Peter and Müller user-defined coefficient and cb,i is the volume fraction of species i in the bed material. The suspended load transport is calculated as shown in Eq.14.(14)∂Cs,i∂t+∇∙Cs,ius,i=∇∙∇DCs,i

where Cs,i is the suspended sediment mass concentration, D is the diffusivity, and us,i is the grain velocity of species i. Entrainment and deposition are two opposing processes that take place at the same time. The lifting and settling velocities for both entrainment and deposition processes are calculated according to Eq.15 and Eq.16, respectively.(15)ulifting,i=αid∗,i0.3θi-θ`cr,igdiρiρf-1(16)usettling,i=υfdi10.362+1.049d∗,i3-10.36

where αi is the entrainment coefficient of species i and υf is the kinematic viscosity of the fluid.

2.7. Grid type

Using simple rectangular orthogonal elements in planes and hexahedral in volumes in the (FLOW-3D) program makes the mesh generation process easier, decreases the required memory, and improves numerical accuracy. Two mesh blocks were used in a joined form with a size ratio of 2:1. The first mesh block is coarser, which contains the reservoir water, and the second mesh block is finer, which contains the dam. For achieving accuracy and efficiency in results, the mesh size is determined by using a grid convergence test. The optimum uniform cell size for the first mesh block is 0.012 m and for the second mesh block is 0.006 m.

2.8. Time step

The maximum time step size is determined by using a Courant number, which controls the distance that the flow will travel during the simulation time step. In this study, the Courant number was taken equal to 0.25 to prevent the flow from traveling through more than one cell in the time step. Based on the Courant number, a maximum time step value of 0.00075 s was determined.

2.9. Numerical model validation

The numerical model accuracy was achieved by comparing the numerical model results with previous experimental results. The experimental study of Schmocker and Hager [7] was based on 31 tests with changes in six parameters (d50, Ho, Bo, Lk, XD, and Qin). All experimental tests were conducted in a straight open glass-sided flume. The horizontal flume has a rectangular cross-section with a width of 0.4 m and a height of 0.7 m. The flume was provided with a flow straightener and an intake with a length of 0.66 m. All tested dams were inserted at various distances (XD) from the intake. Test No.1 from this experimental program was chosen to validate the numerical model. The different parameters used in test No.1 are as follows:

(1) uniform sediment with a mean diameter (d50 = 0.31 mm), (2) Ho = 0.2 m, (3) Bo = 0.2 m, (4) Lk = 0.1 m,

(5) XD = 1.0 m, (6) Qin = 6.0 lit/s, (7) Su and Sd = 2:1, (8) mass density (ρs = 2650 kg/m3(9) Homogenous and non-cohesive embankment dam. As shown in Fig. 2, the simulation is contained within a rectangular grid with dimensions: 3.56 m in the x-direction (where 0.66 m is used as inlet, 0.9 m as dam base width, and 1.0 m as outlet), in y-direction 0.2 m (dam length), and in the z-direction 0.3 m, which represents the dam height (0.2 m) with a free distance (0.1 m) above the dam. There are two main reasons that this experimental program is preferred for the validation process. The first reason is that this program deals with homogenous, non-cohesive soil, which is available in FLOW-3D. The second reason is that this program deals with small-scale models which saves time for numerical simulation. Finally, some important assumptions were considered during the validation process. The flow is assumed to be incompressible, viscous, turbulent, and three-dimensional.

By comparing dam profiles at different time instants for the experimental test with the current numerical model, it appears that the numerical model gives good agreement as shown in Fig. 3 and Fig. 4, with an average error percentage of 9% between the experimental results and the numerical model.

3. Analysis and discussions

The current model is used to study the effects of different parameters such as (initial breach shapes, dimensions, locations, upstream and downstream dam slopes) on the peak outflow discharge, QP, time of peak outflow, tP, and rate of erosion, E.

This study consists of a group of scenarios. The first scenario is changing the shapes of the initial breach according to Singh [1], the most predicted shapes are rectangular and V-notch as shown in Fig. 5. The second scenario is changing the initial breach dimensions (i.e., width and depth). While the third scenario is changing the location of the initial breach. Eventually, the last scenario is changing the upstream and downstream dam slopes.

All scenarios of this study were carried out under the same conditions such as inflow discharge value (Qin=1.0lit/s), dimensions of the tested dam, where dam height (Ho=0.20m), crest width.

(Lk=0.1m), dam length (Bo=0.20m), and homogenous & non-cohesive soil with a mean diameter (d50=0.31mm).

3.1. Dam breaching process evolution

The dam breaching process is a very complex process due to the quick changes in hydrodynamic conditions during dam failure. The dam breaching process starts once water flows reach the downstream face of the dam. During the initial stage of dam breaching, the erosion process is relatively quiet due to low velocities of flow. As water flows continuously, erosion rates increase, especially in two main zones: the crest and the downstream face. As soon as the dam crest is totally eroded, the water levels in the dam reservoir decrease rapidly, accompanied by excessive erosion in the dam body. The erosion process continues until the water levels in the dam reservoir equal the remaining height of the dam.

According to Zhou et al. [11], the breaching process consists of three main stages. The first stage starts with beginning overtopping flow, then ends when the erosion point directed upstream and reached the inflection point at the inflection time (ti). The second stage starts from the end of the stage1 until the occurrence of peak outflow discharge at the peak outflow time (tP). The third stage starts from the end of the stage2 until the value of outflow discharge becomes the same as the value of inflow discharge at the final time (tf). The outflow discharge from the dam breach increases rapidly during stage1 and stage2 because of the large dam storage capacity (i.e., the dam reservoir is totally full of water) and excessive erosion. While at stage3, the outflow values start to decrease slowly because most of the dam’s storage capacity was run out. The end of stage3 indicates that the dam storage capacity was totally run out, so the outflow equalized with the inflow discharge as shown in Fig. 6 and Fig. 7.

3.2. The effect of initial breach shape

To identify the effect of the initial breach shape on the evolution of the dam breaching process. Three tests were carried out with different cross-section areas for each shape. The initial breach is created at the center of the dam crest. Each test had an ID to make the process of arranging data easier. The rectangular shape had an ID (Rec5h & 5b), which means that its depth and width are equal to 5% of the dam height, and the V-notch shape had an ID (V-noch5h & 1:1) which means that its depth is equal to 5% of the dam height and its side slope is equal to 1:1. The comparison between rectangular and V-notch shapes is done by calculating the ratio between maximum dam height at different times (ZMax) to the initial dam height (Ho), rate of erosion, and hydrograph of outflow discharge for each test. The rectangular shape achieves maximum erosion rate and minimum inflection time, in addition to a rapid decrease in the dam reservoir levels. Therefore, the dam breaching is faster in the case of a rectangular shape than in a V-notch shape, which has the same cross-section area as shown in Fig. 8.

Also, by comparing the hydrograph for each test, the peak outflow discharge value in the case of a rectangular shape is higher than the V-notch shape by 5% and the time of peak outflow for the rectangular shape is shorter than the V-notch shape by 9% as shown in Fig. 9.

3.3. The effect of initial breach dimensions

The results of the comparison between the different initial breach shapes indicate that the worst initial breach shape is rectangular, so the second scenario from this study concentrated on studying the effect of a change in the initial rectangular breach dimensions. Groups of tests were carried out with different depths and widths for the rectangular initial breach. The first group had a depth of 5% from the dam height and with three different widths of 5,10, and 15% from the dam height, the second group had a depth of 10% with three different widths of 5,10, and 15%, the third group had a depth of 15% with three different widths of 5,10, and 15% and the final group had a width of 15% with three different heights of 5, 10, and 15% for a rectangular breach shape. The comparison was made as in the previous section to determine the worst case that leads to the quick dam failure as shown in Fig. 10.

The results show that the (Rec 5 h&15b) test achieves a maximum erosion rate for a shorter period of time and a minimum ratio for (Zmax / Ho) as shown in Fig. 10, which leads to accelerating the dam failure process. The dam breaching process is faster with the minimum initial breach depth and maximum initial breach width. In the case of a minimum initial breach depth, the retained head of water in the dam reservoir is high and the crest width at the bottom of the initial breach (L`K) is small, so the erosion point reaches the inflection point rapidly. While in the case of the maximum initial breach width, the erosion perimeter is large.

3.4. The effect of initial breach location

The results of the comparison between the different initial rectangular breach dimensions indicate that the worst initial breach dimension is (Rec 5 h&15b), so the third scenario from this study concentrated on studying the effect of a change in the initial breach location. Three locations were checked to determine the worst case for the dam failure process. The first location is at the center of the dam crest, which was named “Center”, the second location is at mid-distance between the dam center and dam edge, which was named “Mid”, and the third location is at the dam edge, which was named “Edge” as shown in Fig. 11. According to this scenario, the results indicate that the time of peak outflow discharge (tP) is the same in the three cases, but the maximum value of the peak outflow discharge occurs at the center location. The difference in the peak outflow values between the three cases is relatively small as shown in Fig. 12.

The rates of erosion were also studied for the three cases. The results show that the maximum erosion rate occurs at the center location as shown in Fig. 13. By making a comparison between the three cases for the dam storage volume. The results show that the center location had the minimum values for the dam storage volume, which means that a large amount of water has passed to the downstream area as shown in Fig. 14. According to these results, the center location leads to increased erosion rate and accelerated dam failure process compared with the two other cases. Because the erosion occurs on both sides, but in the case of edge location, the erosion occurs on one side.

3.5. The effect of upstream and downstream dam slopes

The results of the comparison between the different initial rectangular breach locations indicate that the worst initial breach location is the center location, so the fourth scenario from this study concentrated on studying the effect of a change in the upstream (Su) and downstream (Sd) dam slopes. Three slopes were checked individually for both upstream and downstream slopes to determine the worst case for the dam failure process. The first slope value is (2H:1V), the second slope value is (2.5H:1V), and the third slope value is (3H:1V). According to this scenario, the results show that the decreasing downstream slope angle leads to increasing time of peak outflow discharge (tP) and decreasing value of peak outflow discharge. The difference in the peak outflow values between the three cases for the downstream slope is 2%, as shown in Fig. 15, but changing the upstream slope has a negligible impact on the peak outflow discharge and its time as shown in Fig. 16.

The rates of erosion were also studied in the three cases for both upstream and downstream slopes. The results show that the maximum erosion rate increases by 6.0% with an increasing downstream slope angle by 4°, as shown in Fig. 17. The results also indicate that the erosion rates aren’t affected by increasing or decreasing the upstream slope angle, as shown in Fig. 18. According to these results, increasing the downstream slope angle leads to increased erosion rate and accelerated dam failure process compared with the upstream slope angle. Because of increasing shear stress applied by water flows in case of increasing downstream slope.

According to all previous scenarios, the dimensionless peak outflow discharge QPQin is presented for a fixed dam height (Ho) and inflow discharge (Qin). Fig. 19 illustrates the relationship between QP∗=QPQin and.

Lr=ho2/3∗bo2/3Ho. The deduced relationship achieves R2=0.96.(17)QP∗=2.2807exp-2.804∗Lr

4. Conclusions

A spatial dam breaching process was simulated by using FLOW-3D Software. The validation process was performed by making a comparison between the simulated results of dam profiles and the dam profiles obtained by Schmocker and Hager [7] in their experimental study. And also, the peak outflow value recorded an error percentage of 12% between the numerical model and the experimental study. This model was used to study the effect of initial breach shape, dimensions, location, and dam slopes on peak outflow discharge, time of peak outflow, and the erosion process. By using the parameters obtained from the validation process, the results of this study can be summarized in eight points as follows.1.

The rectangular initial breach shape leads to an accelerating dam failure process compared with the V-notch.2.

The value of peak outflow discharge in the case of a rectangular initial breach is higher than the V-notch shape by 5%.3.

The time of peak outflow discharge for a rectangular initial breach is shorter than the V-notch shape by 9%.4.

The minimum depth and maximum width for the initial breach achieve maximum erosion rates (increasing breach width, b0, or decreasing breach depth, h0, by 5% from the dam height leads to an increase in the maximum rate of erosion by 11% and 15%, respectively), so the dam failure is rapid.5.

The center location of the initial breach leads to an accelerating dam failure compared with the edge location.6.

The initial breach location has a negligible effect on the peak outflow discharge value and its time.7.

Increasing the downstream slope angle by 4° leads to an increase in both peak outflow discharge and maximum rate of erosion by 2.0% and 6.0%, respectively.8.

The upstream slope has a negligible effect on the dam breaching process.

References

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Figure 6. Circular section of the viscosity and shear-rate clouds.

Simulation and Visual Tester Verification of Solid Propellant Slurry Vacuum Plate Casting

Wu Yue,Li Zhuo,Lu RongFirst published: 26 February 2020 https://doi.org/10.1002/prep.201900411Citations: 3

Abstract

Using an improved Carreau constitutive model, a numerical simulation of the casting process of a type of solid propellant slurry vacuum plate casting was carried out using the Flow3D software. Through the flow process in the orifice flow channel and the combustion chamber, the flow velocity of the slurry passing through the plate flow channel was quantitatively analyzed, and the viscosity, shear rate, and leveling characteristics of the slurry in the combustion chamber were qualitatively analyzed and predicted. The pouring time, pouring quality, and flow state predicted by the numerical simulation were verified using a visual tester consisting of a vacuum plate casting system in which a pouring experiment was carried out. Studies have shown that HTPB three-component propellant slurry is a typical yielding pseudoplastic fluid. When the slurry flows through the flower plate and the airfoil, the fluid shear rate reaches its maximum value and the viscosity of the slurry decreases. The visual pouring platform was built and the experiment was controlled according to the numerically-calculated parameters, ensuring the same casting speed. The comparison between the predicted casting quality and the one obtained in the verification test resulted in an error less than 10 %. Moreover, the error between the simulated casting completion time and the process verification test result was also no more than 10 %. Last, the flow state of the slurry during the simulation was consistent with the one during the experimental test. The overall leveling of the slurry in the combustion chamber was adequate and no relatively large holes and flaws developed during the pouring process.

개선된 Carreau 구성 모델을 사용하여 FLOW-3D 소프트웨어를 사용하여 고체 추진제 슬러리 진공판 유형의 Casting Process에 대한 수치 시뮬레이션을 수행했습니다. 오리피스 유로와 연소실에서의 유동과정을 통해 판 유로를 통과하는 슬러리의 유속을 정량적으로 분석하고, 연소실에서 슬러리의 점도, 전단율, 레벨링 특성을 정성적으로 분석하하고, 예측하였습니다.

타설시간, 타설품질, 수치해석으로 예측된 ​​유동상태는 타설실험을 수행한 진공판주조시스템으로 구성된 비주얼 테스터를 이용하여 검증하였습니다.

연구에 따르면 HTPB 3성분 추진제 슬러리는 전형적인 생성 가소성 유체입니다. 슬러리가 플라워 플레이트와 에어포일을 통과할 때 유체 전단율이 최대값에 도달하고 슬러리의 점도가 감소합니다.

시각적 주입 플랫폼이 구축되었고 동일한 주조 속도를 보장하기 위해 수치적으로 계산된 매개변수에 따라 실험이 제어되었습니다. 예측된 casting 품질과 검증 테스트에서 얻은 품질을 비교한 결과 10 % 미만의 오류가 발생했습니다.

또한 모의 casting 완료시간과 공정검증시험 결과의 오차도 10 % 이하로 나타났습니다.

마지막으로 시뮬레이션 중 슬러리의 흐름 상태는 실험 테스트 시와 일치하였다. 연소실에서 슬러리의 전체 레벨링은 적절했으며 주입 과정에서 상대적으로 큰 구멍과 결함이 발생하지 않았습니다.

Figure 1. The equipment used in the vacuum flower-plate pouring process.
Figure 1. The equipment used in the vacuum flower-plate pouring process.
Figure 2. Calculation model.
Figure 2. Calculation model.
Figure 3. Grid block division unit.
Figure 3. Grid block division unit.
Figure 4. Circular section of the speed cloud.
Figure 4. Circular section of the speed cloud.
Figure 5. Viscosity and shear rate distribution cloud pattern flowing through the plate holes.
Figure 5. Viscosity and shear rate distribution cloud pattern flowing through the plate holes.
Figure 6. Circular section of the viscosity and shear-rate clouds.
Figure 6. Circular section of the viscosity and shear-rate clouds.
Figure 7. Volume fraction cloud chart at different time.
Figure 7. Volume fraction cloud chart at different time.
Figure 8. Experimental program.
Figure 8. Experimental program.
Figure 9. Emulation experimental device.
Figure 9. Emulation experimental device.
Figure 10. Visualization of the flow state of the pulp inside the tester.
Figure 10. Visualization of the flow state of the pulp inside the tester.

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그림 1 하천횡단구조물 하류부 횡단구조물 파괴

유입조건에 따른압력변이로 인한하천횡단구조물 하류물받이공 및 바닥보호공설계인자 도출최종보고서

주관연구기관 / 홍익대학교 산학협력단
공동연구기관 / 한국건설기술연구원
공동연구기관 / 주식회사 지티이

연구의 목적 및 내용

하천횡단구조물이 하천설계기준(2009)대로 설계되었음에도 불구하고, 하류부에서 물받이공 및 바닥보호공의 피해가 발생하여, 구조물 본체에 대한 안전성이 현저하 게 낮아지고 있는 실정이다. 하천설계기준이 상류부의 수리특성을 반영하였다고 하나 하류부의 수리특성인 유속의 변동 성분 또는 압력의 변동성분까지 고려하고 있지는 않다. 현재 많은 선행연구에서 이러한 난류적 특성이 구조물에 미치는 영 향에 대해 제시하고 있는 실정이며, 국내 하천에서의 피해 또한 이와 관련이 있다 고 판단된다. 이에 본 연구에서는 난류성분 특히 압력의 변동성분이 물받이공과 바닥보호공에 미치는 영향을 정량적으로 분석하여, 하천 횡단구조물의 치수 안전 성 증대에 기여하고자 한다. 물받이공과 바닥보호공에 미치는 압력의 변동성분 (pressure fluctuation) 영향을 분석하기 위해 크게 3가지로 연구내용을 분류하였 다. 첫 번째는 압력의 변동으로 순간적인 음압구배(adversed pressure gradient) 가 발생할 경우 바닥보호공의 사석 및 블록이 이탈하는 것이다. 이를 확인하기 위 해 정밀한 압력 측정장치를 통해 압력변이를 측정하여, 사석의 이탈 가능성을 검 토할 것이며, 최종적으로 이탈에 대한 한계조건을 도출할 것이다. 두 번째는 압력 의 변동이 물받이공의 진동을 유발시켜 이를 지지하고 있는 지반에 다짐효과를 가 져와 물받이공과 지반사이에 공극이 발생하는 경우이다. 이러한 공극으로 물받이 공은 자중 및 물의 압력을 받게 되어, 결국 휨에 의한 파괴가 발생할 가능성이 있 게 된다. 본 연구에서는 실험을 통하여 압력의 변동과 물받이공의 진동을 동시에 측정하여, 진동이 발생하지 않을 최소 두께를 제시할 것이다. 세 번째는 압력변이 로 인한 물받이공의 진동이 피로파괴로 연결되는 경우이다. 이 현상 또한 수리실 험을 통해 압력변이-피로파괴의 관계를 정량적으로 분석하여, 한계 조건을 제시할 것이다. 본 연구는 국내 보 및 낙차공에서 발생하는 다양한 Jet의 특성을 수리실 험으로 재현해야 하며, 이를 위해 평면 Jet 분사기(plane Jet injector)를 고안/ 제작하여, 효율적인 수리실험을 수행할 것이다. 또한 3차원 수치해석을 통해 실제 스케일에 적용함으로써 연구결과의 활용도 및 적용성을 높이고자 한다.

Keywords

압력변이, 물받이공, 바닥보호공, 난류, 진동

 그림 1 하천횡단구조물 하류부 횡단구조물 파괴
그림 1 하천횡단구조물 하류부 횡단구조물 파괴
그림 2. 시간에 따른 압력의 변동 양상 및 정의
그림 2. 시간에 따른 압력의 변동 양상 및 정의
 그림 3. 하천횡단구조물 하류부 도수현상시 발생하는 압력변이 분포도, Fr=8.0 상태이며, 바닥(slab)에 양압과 음압이 지속적으로 작용한다. (Fiorotto & Rinaldo, 2010)
그림 3. 하천횡단구조물 하류부 도수현상시 발생하는 압력변이 분포도, Fr=8.0 상태이며, 바닥(slab)에 양압과 음압이 지속적으로 작용한다. (Fiorotto & Rinaldo, 2010)
 그림 4. 파괴 개념
그림 4. 파괴 개념
그림 6. PIV 측정 원리(www.photonics.com)
그림 6. PIV 측정 원리(www.photonics.com)
그림 7. LED회로판 및 BIV기법 기본개념
그림 7. LED회로판 및 BIV기법 기본개념
그림 8. BIV측정기법을 적용한 순간이미지 (Lin et al., 2012)
그림 8. BIV측정기법을 적용한 순간이미지 (Lin et al., 2012)
그림 9. 감세공의 분류
그림 9. 감세공의 분류
그림 17 수리실헐 수로시설: (a) 전체수로전경, (b) Weir 보를 포함한 측면도, (c) 도수조건 실험전경
그림 17 수리실헐 수로시설: (a) 전체수로전경, (b) Weir 보를 포함한 측면도, (c) 도수조건 실험전경
그림 18 수리실험 개요도
그림 18 수리실험 개요도
그림 127 난류모형별 압력 Data (측정위치는 그림 125 참조)
그림 127 난류모형별 압력 Data (측정위치는 그림 125 참조)
그림 128 RNG 모형을 이용한 수치모의 결과
그림 128 RNG 모형을 이용한 수치모의 결과
그림 129 LES 모형을 이용한 수치모의 결과
그림 129 LES 모형을 이용한 수치모의 결과
그림 130 압력 Data의 필터링
그림 130 압력 Data의 필터링
그림 134 Case 1의 흐름특성 분포도 및 그래프
그림 134 Case 1의 흐름특성 분포도 및 그래프

참고문헌

국토기술연구센터 (1998) 하상유지공의 구조설계 지침.

감사원 (2013) 감사원 결과보고서- 4대강살리기 사업 주요시설물 품질 밑 수질관리 실태.

국토해양부 (2009) 전국 하천횡단 구조물 설치현황 및 어도 실태조사 보고서. 국토해양부 (2010). 낙동강 살리기 사업 24공구(성주칠곡지구) 실시설계보고서.

국토해양부 (2012) 보도자료-준공대비 점검결과, 4대강 보 안전 재확인.

국토해양부 (2012) 국가 및 지방하천 종합정비 마스터플랜.

국토교통성 (2008) 하천사방기술기준.

농림부 (1996). 농업생산기반정비사업계획 설계기준. 류권규(역자) (2009). 난류의 수치모의(원저자 : 梶島岳夫, 1999).

류권규, 마리안 머스테, 로버트 에테마, 윤병만 (2006). “난류 중 부유사의 속도 지체 측정.” 한국수자원학회논문집, 제39권, 제2호, pp.99-108.

배재현, 이경훈, 신종근, 양용수, 이주희 (2011). “입자영상유속계를 이용한 은어의 유영능력 측정.” 제47권, 제4호, pp.411-418.

우효섭 (2001). 하천수리학. 청문각.

한국수자원학회 (2009). 하천설계기준해설.

한국건설기술연구원 (2014) 입자영상유속계(PIV)를 이용한 하천구조물 주변 유동해석 기법 개발

한국건설기술연구원 (2017) 보와 하상유지공의 안전성 확보를 위한 물받이와 바닥보호공의 성능평가
기법에 대한 원천기술개발

국토기술연구센터 (1998) 하상유지공의 구조설계 지침.

감사원 (2013) 감사원 결과보고서- 4대강살리기 사업 주요시설물 품질 밑 수질관리 실태. 국토해양부 (2009) 전국 하천횡단 구조물 설치현황 및 어도 실태조사 보고서.

국토해양부 (2012) 보도자료-준공대비 점검결과, 4대강 보 안전 재확인. 국토해양부 (2012) 국가 및 지방하천 종합정비 마스터플랜.

국토교통성 (2008) 하천사방기술기준.

농림부 (1996). 농업생산기반정비사업계획 설계기

류권규(역자) (2009). 난류의 수치모의(원저자 : 梶島岳夫, 1999).
류권규, 마리안 머스테, 로버트 에테마, 윤병만 (2006). “난류 중 부유사의 속도 지체 측정.” 한국수자원학회논문집, 제39권, 제2호, pp.99-108.
배재현, 이경훈, 신종근, 양용수, 이주희 (2011). “입자영상유속계를 이용한 은어의 유영능력 측정.” 제47권, 제4호, pp.411-418.
우효섭 (2001). 하천수리학. 청문각. 한국수자원학회 (2009). 하천설계기준해설. 한국건설기술연구원 (2014) 입자영상유속계(PIV)를 이용한 하천구조물 주변 유동해석 기법 개발
한국건설기술연구원 (2017) 보와 하상유지공의 안전성 확보를 위한 물받이와 바닥보호공의 성능평가
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Fig. 4. Numerical modeling of dual spillways: (a) Andong-1; (b) Andong-2; (c) Imha-1; (d) Juam-1; (e) Andong-3; (f) Imha-2; (g) Imha-3; and (h) Juam-3.

Interference of Dual Spillways Operations

Jai Hong Lee, Ph.D., P.E., M.ASCE; Pierre Y. Julien, Ph.D., M.ASCE; and Christopher I. Thornton, Ph.D., P.E., M.ASCE

Abstract

이중 여수로 간섭은 여수로가 서로 가깝게 배치될 때 수압 성능의 손실을 나타냅니다. 배수로 간섭은 물리적 실험과 수치 시뮬레이션을 모두 사용하여 조사됩니다.

이중 여수로 구성의 4개 물리적 모델의 단계 및 배출 측정값을 한국의 4개 댐 부지에서 Flow-3D 계산 결과와 비교합니다.

두 개의 배수로를 함께 사용하는 것을 각 배수로의 단일 작동과 비교합니다. 두 여수로를 동시에 운영할 경우 두 여수로를 통한 총 유량은 최대 7.6%까지 감소합니다.

간섭 계수는 단계 He가 설계 단계 Hd를 초과하고 두 배수로를 분리하는 거리 D가 배수로 너비 W에 비해 짧을 때 가장 중요합니다. 매개변수 DHd/WHe는 계산 및 측정된 간섭 계수와 매우 잘 관련됩니다.

안동댐 설계방류에 대한 홍수경로 예시는 간섭계수를 적용한 경우와 적용하지 않은 경우 저수지 수위의 차이가 42cm임을 보여줍니다. 결과적으로 댐 안전을 위해 추가 여수로의 너비(간섭 계수 포함)를 늘려야 합니다.

Dual spillway interference refers to the loss of hydraulic performance of spillways when they are placed close together. Spillway interference is examined using both physical experiments and numerical simulations. Stage and discharge measurements from four physical models with dual spillways configurations are compared to the Flow-3D computational results at four dam sites in South Korea. The conjunctive use of two spillways is compared with the singular operation of each spillway. When both spillways are operated at the same time, the total flow rate through the two spillways is reduced by up to 7.6%. Interference coefficients are most significant when the stage He exceeds the design stage Hd and when the distance D separating two spillways is short compared to the spillway width W. The parameter DHd/WHecorrelates very well with the calculated and measured interference coefficients. A flood routing example for the design discharge at Andong dam shows a 42 cm difference in reservoir water level with and without application of the interference coefficient. Consequently, the width of additional spillways (including the interference coefficient) should be increased for dam safety.

Fig. 1. Definition sketch for dual spillways
Fig. 1. Definition sketch for dual spillways
Fig. 2. Stage-discharge rating curves for dual spillway operations.
Fig. 2. Stage-discharge rating curves for dual spillway operations.
Fig. 3. Physical modeling of dual spillways: (a) Andong-1; (b) Andong-2; (c) Imha-1; and (d) Juam-1
Fig. 3. Physical modeling of dual spillways: (a) Andong-1; (b) Andong-2; (c) Imha-1; and (d) Juam-1
Fig. 4. Numerical modeling of dual spillways: (a) Andong-1; (b) Andong-2; (c) Imha-1; (d) Juam-1; (e) Andong-3; (f) Imha-2; (g) Imha-3; and (h) Juam-3.
Fig. 4. Numerical modeling of dual spillways: (a) Andong-1; (b) Andong-2; (c) Imha-1; (d) Juam-1; (e) Andong-3; (f) Imha-2; (g) Imha-3; and (h) Juam-3.
Fig. 4. (Continued.)
Fig. 4. (Continued.)
Fig. 5. Meshes and calculation domain for numerical modeling of Andong dam.
Fig. 5. Meshes and calculation domain for numerical modeling of Andong dam.
Fig. 6. Stage-discharge rating curve for existing and additional spillways (Andong-1): (a) existing spillway; (b) additional spillway; and (c) dual spillway simulations.
Fig. 6. Stage-discharge rating curve for existing and additional spillways (Andong-1): (a) existing spillway; (b) additional spillway; and (c) dual spillway simulations.
Fig. 7. Discharge comparison of physical experiments and numerical simulations. The upper panel is the comparative result for the existing spillway (ES) and the lower panel is for the additional spillway (AS) at four dams.
Fig. 7. Discharge comparison of physical experiments and numerical simulations. The upper panel is the comparative result for the existing spillway (ES) and the lower panel is for the additional spillway (AS) at four dams.
Fig. 8. Interference coefficients for dual spillways simulations with various scenarios.
Fig. 8. Interference coefficients for dual spillways simulations with various scenarios.
Fig. 9. Regression model for the distance-width ratio (D=W) and head ratio (Hd=He) by dual spillway simulations
Fig. 9. Regression model for the distance-width ratio (D=W) and head ratio (Hd=He) by dual spillway simulations
Fig. 10. Physical and numerical model validation: (a) numerical modeling; (b) solids of overflow weir of the spillway; and (c) physical models of reservoir and spillway
Fig. 10. Physical and numerical model validation: (a) numerical modeling; (b) solids of overflow weir of the spillway; and (c) physical models of reservoir and spillway
Fig. 11. Interference coefficients for dual spillways operations with various scenarios. The dashed lines indicate the results of the validation model with dual conditions of 1 þ 2, 1 þ 4, 1 þ 6, 3 þ 4, and 4 þ 5.
Fig. 11. Interference coefficients for dual spillways operations with various scenarios. The dashed lines indicate the results of the validation model with dual conditions of 1 þ 2, 1 þ 4, 1 þ 6, 3 þ 4, and 4 þ 5.
Fig. 12. Results of reservoir operations under the PMF at Andong dam.
Fig. 12. Results of reservoir operations under the PMF at Andong dam.

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Forming characteristics and control method of weld bead for GMAW on curved surface

곡면에 GMAW용 용접 비드의 형성 특성 및 제어 방법

Forming characteristics and control method of weld bead for GMAW on curved surface

The International Journal of Advanced Manufacturing Technology (2021)Cite this article

Abstract

곡면에서 GMAW 기반 적층 가공의 용접 성형 특성은 중력의 영향을 크게 받습니다. 성형면의 경사각이 크면 혹 비드(hump bead)와 같은 심각한 결함이 발생합니다.

본 논문에서는 양생면에서 용접 비드 형성의 형성 특성과 제어 방법을 연구하기 위해 용접 용융 풀 유동 역학의 전산 모델을 수립하고 제안된 모델을 검증하기 위해 증착 실험을 수행하였습니다.

결과는 용접 비드 경사각(α)이 증가함에 따라 역류의 속도가 증가하고 상향 용접의 경우 α > 60°일 때 불규칙한 험프 결함이 나타나는 것으로 나타났습니다.

상부 과잉 액체의 하향 압착력과 하부 상향 유동의 반동력과 표면장력 사이의 상호작용은 용접 혹 형성의 주요 요인이었다. 하향 용접의 경우 양호한 형태를 얻을 수 있었으며, 용접 비드 경사각이 증가함에 따라 용접 높이는 감소하고 용접 폭은 증가하였습니다.

하향 및 상향 용접을 위한 곡면의 용융 거동 및 성형 특성을 기반으로 험프 결함을 제어하기 위해 위브 용접을 통한 증착 방법을 제안하였습니다.

성형 궤적의 변화로 인해 용접 방향의 중력 성분이 크게 감소하여 용융 풀 흐름의 안정성이 향상되었으며 복잡한 표면에서 안정적이고 일관된 용접 비드를 얻는 데 유리했습니다.

하향 용접과 상향 용접 사이의 단일 비드의 치수 편차는 7% 이내였으며 하향 및 상향 혼합 혼합 비드 중첩 증착에서 비드의 변동 편차는 0.45로 GMAW 기반 적층 제조 공정에서 허용될 수 있었습니다.

이러한 발견은 GMAW를 기반으로 하는 곡선 적층 적층 제조의 용접 비드 형성 제어에 기여했습니다.

The weld forming characteristics of GMAW-based additive manufacturing on curved surface are dramatically influenced by gravity. Large inclined angle of the forming surface would lead to severe defects such as hump bead. In this paper, a computational model of welding molten pool flow dynamics was established to research the forming characteristic and control method of weld bead forming on cured surface, and deposition experiments were conducted to verify the proposed model. Results indicated that the velocity of backward flows increased with the increase of weld bead tilt angle (α) and irregular hump defects appeared when α > 60° for upward welding. The interaction between the downward squeezing force of the excess liquid at the top and the recoil force of the upward flow at the bottom and the surface tension were primary factors for welding hump formation. For downward welding, a good morphology shape could be obtained, and the weld height decreased and the weld width increased with the increase of weld bead tilt angle. Based on the molten behaviors and forming characteristics on curved surface for downward and upward welding, the method of deposition with weave welding was proposed to control hump defects. Gravity component in the welding direction was significantly reduced due to the change of forming trajectory, which improved the stability of the molten pool flow and was beneficial to obtain stable and consistent weld bead on complex surface. The dimensional deviations of the single bead between downward and upward welding were within 7% and the fluctuation deviation of the bead in multi-bead overlapping deposition with mixing downward and upward welding was 0.45, which could be acceptable in GMAW-based additive manufacturing process. These findings contributed to the weld bead forming control of curve layered additive manufacturing based on GMAW.

Keywords

  • Molten pool behaviors
  • GMAW-based WAAM
  • Deposition with weave welding
  • Welding on curved surface
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Figure 1 Location map of barrier lakes, Sichuan-Tibet region, China

Barrier Lake의 홍수 침수 진행 및 평가지역 생태 시공간 반응 사례 연구 (쓰촨-티베트 지역)

Flood Inundation Evolution of Barrier Lake and Evaluation of Regional Ecological Spatiotemporal Response — A Case Study of Sichuan-Tibet Region

Abstract

중국 쓰촨-티베트 지역은 댐 호수의 발생과 붕괴를 동반한 지진 재해가 빈번한 지역이었습니다. 댐 호수의 붕괴는 하류 직원의 생명과 재산 안전을 심각하게 위협합니다.

동시에 국내외 학자들은 주변의 댐 호수에 대해 우려하고 있으며 호수에 대한 생태 연구는 거의 없으며 댐 호수가 생태에 미치는 영향은 우리 호수 건설 프로젝트에서 매우 중요한 계몽 의의를 가지고 있습니다.

이 기사의 목적은 방벽호의 댐 붕괴 위험을 과학적으로 예측하고 생태 환경에 대한 영향을 조사하며 통제 조치를 제시하는 것입니다. 본 논문은 쓰촨-티베트 지역의 Diexihaizi, Tangjiashan 댐호, Hongshihe 댐의 4대 댐 호수 사건을 기반으로 원격 감지 이미지에서 수역을 추출하고 HEC-RAS 모델을 사용하여 위험이 있는지 여부를 결정합니다.

댐 파손 여부 및 댐의 경로 예측; InVEST 모델을 이용하여 1990년부터 2020년까지 가장 작은 행정 구역(군/구)이 위치한 서식지를 평가 및 분석하고, 홍수 침수 결과를 기반으로 평가합니다. 결과는 공학적 처리 후 안정적인 댐 호수(Diexi Haizi)가 서식지 품질 지수에 안정화 효과가 있음을 보여줍니다.

댐 호수의 형성은 인근 토지 이용 유형과 지역 경관 생태 패턴을 변화 시켰습니다. 서식지 품질 지수는 사이 호수 주변 1km 지역에서 약간 감소하지만 3km 지역과 5km 지역에서 서식지 품질이 향상됩니다. 인공 홍수 방류 및 장벽 호수의 공학적 보강이 필요합니다.

이 논문에서 인간의 통제가 강한 지역은 다른 지역의 서식지 질 지수보다 더 잘 회복될 것입니다.

The Sichuan-Tibet region of China has always been an area with frequent earthquake disasters, accompanied by the occurrence and collapse of dammed lakes. The collapse of dammed lakes seriously threatens the lives and property safety of downstream personnel.

At the same time, domestic and foreign scholars are concerned about the surrounding dammed lake there are few ecological studies on the lake, and the impact of the dammed lake on the ecology has very important enlightenment significance for our lake construction project. It is the purpose of this article to scientifically predict the risk of dam break in a barrier lake, explore its impact on the ecological environment and put forward control measures.

Based on the four major dammed lake events of Diexihaizi, Tangjiashan dammed lake, and Hongshihe dammed lake in the Sichuan-Tibet area, this paper extracts water bodies from remote sensing images and uses the HEC-RAS model to determine whether there is a risk of the dam break and whether Forecast the route of the dam; and use the InVEST model to evaluate and analyze the habitat of the smallest administrative district (county/district) where it is located from 1990 to 2020 and make an evaluation based on the results of flood inundation.

The results show that the stable dammed lake (Diexi Haizi) after engineering treatment has a stabilizing effect on the habitat quality index. The formation of the dammed lake has changed the nearby land-use types and the regional landscape ecological pattern.

The habitat quality index will decrease slightly in the 1 km area around Sai Lake, but the habitat quality will increase in the 3 km area and the 5 km area. Artificial flood discharge and engineering reinforcement of barrier lakes are necessary. In this paper, the areas with strong human control will recover better than other regions’ habitat quality index.

Fengshan Jiang (  florachaing@mail.ynu.edu.cn )
Yunnan University https://orcid.org/0000-0001-6231-6180
Xiaoai Dai
Chengdu University of Technology https://orcid.org/0000-0003-1342-6417
Zhiqiang Xie
Yunnan University
Tong Xu
Yunnan University
Siqiao Yin
Yunnan University
Ge Qu
Chengdu University of Technology
Shouquan Yang
Yunnan University
Yangbin Zhang
Yunnan University
Zhibing Yang
Yunnan University
Jiarui Xu
Yunnan University
Zhiqun Hou
Kunming institute of surveying and mapping

Keywords

dammed lake, regional ecology, flood simulation, habitat quality

Figure 1 Location map of barrier lakes, Sichuan-Tibet region, China
Figure 1 Location map of barrier lakes, Sichuan-Tibet region, China
Figure 8 Habitat quality changes in Maoxian County
Figure 8 Habitat quality changes in Maoxian County
Figure 9 Habitat quality changes in Beichuan County
Figure 9 Habitat quality changes in Beichuan County
Figure 10 Habitat quality change map of Qingchuan County
Figure 10 Habitat quality change map of Qingchuan County

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Figure 2. (a) Scanning electron microscopy images of Ti6Al4V powder particles and (b) simulated powder bed using discrete element modelling

Laser Powder Bed에서 Laser Drilling에 의한 Keyhole 형성 Ti6Al4V 생체 의학 합금의 융합: 메조스코픽 전산유체역학 시뮬레이션 대 경험적 검증을 사용한 수학적 모델링

Keyhole Formation by Laser Drilling in Laser Powder Bed Fusion of Ti6Al4V Biomedical Alloy: Mesoscopic Computational Fluid Dynamics Simulation versus Mathematical Modelling Using Empirical Validation

Asif Ur Rehman 1,2,3,*
,† , Muhammad Arif Mahmood 4,*
,† , Fatih Pitir 1
, Metin Uymaz Salamci 2,3
,
Andrei C. Popescu 4 and Ion N. Mihailescu 4

Abstract

LPBF(Laser Powder Bed fusion) 공정에서 작동 조건은 열 분포를 기반으로 레이저 유도 키홀 영역을 결정하는 데 필수적입니다. 얕은 구멍과 깊은 구멍으로 분류되는 이러한 영역은 LPBF 프로세스에서 확률과 결함 형성 강도를 제어합니다.

LPBF 프로세스의 핵심 구멍을 연구하고 제어하기 위해 수학적 및 CFD(전산 유체 역학) 모델이 제공됩니다. CFD의 경우 이산 요소 모델링 기법을 사용한 유체 체적 방법이 사용되었으며, 분말 베드 보이드 및 표면에 의한 레이저 빔 흡수를 포함하여 수학적 모델이 개발되었습니다.

동적 용융 풀 거동을 자세히 살펴봅니다. 실험적, CFD 시뮬레이션 및 분석적 컴퓨팅 결과 간에 정량적 비교가 수행되어 좋은 일치를 얻습니다.

LPBF에서 레이저 조사 영역 주변의 온도는 높은 내열성과 분말 입자 사이의 공기로 인해 분말층 주변에 비해 급격히 상승하여 레이저 횡방향 열파의 이동이 느려집니다. LPBF에서 키홀은 에너지 밀도에 의해 제어되는 얕고 깊은 키홀 모드로 분류될 수 있습니다. 에너지 밀도를 높이면 얕은 키홀 구멍 모드가 깊은 키홀 구멍 모드로 바뀝니다.

깊은 키홀 구멍의 에너지 밀도는 다중 반사와 키홀 구멍 내의 2차 반사 빔의 집중으로 인해 더 높아져 재료가 빠르게 기화됩니다.

깊은 키홀 구멍 모드에서는 온도 분포가 높기 때문에 액체 재료가 기화 온도에 가까우므로 얕은 키홀 구멍보다 구멍이 형성될 확률이 훨씬 높습니다. 온도가 급격히 상승하면 재료 밀도가 급격히 떨어지므로 비열과 융해 잠열로 인해 유체 부피가 증가합니다.

그 대가로 표면 장력을 낮추고 용융 풀 균일성에 영향을 미칩니다.

In the laser powder bed fusion (LPBF) process, the operating conditions are essential in determining laser-induced keyhole regimes based on the thermal distribution. These regimes, classified into shallow and deep keyholes, control the probability and defects formation intensity in the LPBF process. To study and control the keyhole in the LPBF process, mathematical and computational fluid dynamics (CFD) models are presented. For CFD, the volume of fluid method with the discrete element modeling technique was used, while a mathematical model was developed by including the laser beam absorption by the powder bed voids and surface. The dynamic melt pool behavior is explored in detail. Quantitative comparisons are made among experimental, CFD simulation and analytical computing results leading to a good correspondence. In LPBF, the temperature around the laser irradiation zone rises rapidly compared to the surroundings in the powder layer due to the high thermal resistance and the air between the powder particles, resulting in a slow travel of laser transverse heat waves. In LPBF, the keyhole can be classified into shallow and deep keyhole mode, controlled by the energy density. Increasing the energy density, the shallow keyhole mode transforms into the deep keyhole mode. The energy density in a deep keyhole is higher due to the multiple reflections and concentrations of secondary reflected beams within the keyhole, causing the material to vaporize quickly. Due to an elevated temperature distribution in deep keyhole mode, the probability of pores forming is much higher than in a shallow keyhole as the liquid material is close to the vaporization temperature. When the temperature increases rapidly, the material density drops quickly, thus, raising the fluid volume due to the specific heat and fusion latent heat. In return, this lowers the surface tension and affects the melt pool uniformity.

Keywords: laser powder bed fusion; computational fluid dynamics; analytical modelling; shallow
and deep keyhole modes; experimental correlation

Figure 1. Powder bed schematic with voids.
Figure 1. Powder bed schematic with voids.
Figure 2. (a) Scanning electron microscopy images of Ti6Al4V powder particles and (b) simulated powder bed using discrete element modelling
Figure 2. (a) Scanning electron microscopy images of Ti6Al4V powder particles and (b) simulated powder bed using discrete element modelling
Figure 3. Temperature field contour formation at various time intervals (a) 0.695 ms, (b) 0.795 ms, (c) 0.995 ms and (d) 1.3 ms.
Figure 3. Temperature field contour formation at various time intervals (a) 0.695 ms, (b) 0.795 ms, (c) 0.995 ms and (d) 1.3 ms.
Figure 4. Detailed view of shallow depth melt mode with temperature field at 0.695 ms
Figure 4. Detailed view of shallow depth melt mode with temperature field at 0.695 ms
Figure 5. Melt flow stream traces formation at various time intervals (a) 0.695 ms, (b) 0.795 ms, (c) 0.995 ms and (d) 1.3 ms
Figure 5. Melt flow stream traces formation at various time intervals (a) 0.695 ms, (b) 0.795 ms, (c) 0.995 ms and (d) 1.3 ms
Figure 6. Density evolution of the melt pool at various time intervals (a) 0.695 ms, (b) 0.795 ms, (c) 0.995 ms and (d) 1.3 ms.
Figure 6. Density evolution of the melt pool at various time intervals (a) 0.695 ms, (b) 0.795 ms, (c) 0.995 ms and (d) 1.3 ms.
Figure 7. Un-melted and melted regions at different time intervals (a) 0.695 ms, (b) 0.795 ms, (c) 0.995 ms and (d) 1.3 ms
Figure 7. Un-melted and melted regions at different time intervals (a) 0.695 ms, (b) 0.795 ms, (c) 0.995 ms and (d) 1.3 ms
Figure 8. Transformation from shallow depth melt flow to deep keyhole formation when laser power increased from (a) 170 W to (b) 200 W
Figure 8. Transformation from shallow depth melt flow to deep keyhole formation when laser power increased from (a) 170 W to (b) 200 W
Figure 9. Stream traces and laser beam multiple reflections in deep keyhole melt flow mode
Figure 9. Stream traces and laser beam multiple reflections in deep keyhole melt flow mode
Figure 10. A comparison between analytical and CFD simulation results for peak thermal distribution value in the deep keyhole formation
Figure 10. A comparison between analytical and CFD simulation results for peak thermal distribution value in the deep keyhole formation
Figure 11. A comparison among experiments [49], CFD and analytical simulations for deep keyhole top width and bottom width
Figure 11. A comparison among experiments [49], CFD and analytical simulations for deep keyhole top width and bottom width

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Figure 1 | Original Compound Broad Crested Weir Model (PVC cast).

복합 광대보의 방류계수 예측을 위한 실험적 해석과 CFD 해석의 비교연구

Comparative study of experimental and CFD analysis for predicting discharge coefficient of compound broad crested weir

ABSTRACT

Present study highlights the behavior of weir crest head and width parameter on the discharge coefficient of compound broad crested (CBC) weir. Computational fluid dynamics model (CFD) is validated with laboratory experimental investigations.

In the discharge analysis through broad crested weirs, the upstream head over the weir crest (h) is crucial, where the result is mainly dependent upon the weir crest length (L) in transverse direction to flow, water depth from channel bed. Currently, minimal investigations are known for CFD validations on compound broad crested weirs.

The hydraulic research for measuring discharge numerically is carried out using FLOW 3D software. The model applies renormalized group (RNG) using volume of fluid (VOF) method for improved accuracy in free surface simulations. Structured hexagonal meshes of cubic elements define discretized meshing.

The comparative analysis of the numerical simulations and experimental observations confirm the performance of CBC weir for precise measurement of a wide range of discharges. Series of CFD model studies and experimental validation have led to constant range of discharg coefficients for various head over weir crest. The correlation coefficient of discharge predictions is 0.999 with mean error of 0.28%.

현재 연구에서는 CBC(compound broad crested) 위어의 배출 계수에 대한 위어 볏 머리 및 너비 매개변수의 거동을 강조합니다. 전산 유체 역학 모델(CFD)은 실험실 실험 조사를 통해 검증되었습니다.

넓은 볏이 있는 둑을 통한 유출 분석에서 둑 마루의 상류 수두(h)가 중요합니다. 여기서 결과는 주로 흐름에 대한 횡 방향의 둑 마루 길이(L), 수로 바닥에서 수심에 따라 달라집니다. . 현재 복합 넓은 볏 둑에 대한 CFD 검증에 대해 최소한의 조사가 알려져 있습니다.

수압 연구는 FLOW 3D 소프트웨어를 사용하여 수치적으로 측정합니다. 이 모델은 자유 표면 시뮬레이션의 정확도 향상을 위해 VOF(유체 체적) 방법을 사용하여 RNG(재정규화 그룹)를 적용합니다. 정육면체 요소의 구조화된 육각형 메쉬는 이산화된 메쉬를 정의합니다.

수치 시뮬레이션과 실험적 관찰의 비교 분석을 통해 광범위한 배출의 정확한 측정을 위한 CBC 둑의 성능을 확인했습니다. 일련의 CFD 모델 연구와 실험적 검증을 통해 다양한 head over weir crest에 대한 일정한 범위의 방전 계수가 나타났습니다. 방전 예측의 상관 계수는 0.999이고 평균 오차는 0.28%입니다.

Figure 1 | Original Compound Broad Crested Weir Model (PVC cast).
Figure 1 | Original Compound Broad Crested Weir Model (PVC cast).
Figure 4 | CFD Simulation for max discharge (y2 ¼ 13.557 cm, Qmax ¼ 10 lps) and min discharge (y2 ¼ 6.56 cm, Qmin ¼ 2 lps).
Figure 4 | CFD Simulation for max discharge (y2 ¼ 13.557 cm, Qmax ¼ 10 lps) and min discharge (y2 ¼ 6.56 cm, Qmin ¼ 2 lps).
Figure 5 | (a, b) Velocity profiles corresponding to max discharge (10 lps) and min discharge (2 lps).
Figure 5 | (a, b) Velocity profiles corresponding to max discharge (10 lps) and min discharge (2 lps).
Table 8 | Range of Froude number, Reynold number and Weber number
Table 8 | Range of Froude number, Reynold number and Weber number

Key words

compound weir, flow 3D, flow measurement, numerical technique, open channel

HIGHLIGHTS

• The Head-Discharge relation is established for discharge measurement using compound broad crested weir, experimentally and numerically.
• Assessment of head over weir crest for different step widths of proposed weir on discharge coefficient is executed.
• Experimental and CFD results of weir performance demonstrate good agreement between the theoretical discharges by traditional rectangular weir formulae keeping Cd constant.

CONCLUSION

  1. The head discharge relationship established for compound rectangular broad crested weir for various discharge ranges was validated by CFD technique. A three dimensional simulation software FLOW 3D was used for this purpose.
  2. Original theoretical compound weir model depicts the relative average error between discharge predictions with Flow 3D simulation as 4.96% which is found less than the predictions made by graphical interpolation technique which is 5.33%.
  3. The standard deviation in Cd parameter for CFD simulation model is less i.e. 0.0146 as compared to experimental output of 0.0502.
  4. The correlation coefficient for physical and CFD studies for modified compound weir model is high, around 0.999 with
    error in discharge predictions being 0.28% as compared to the accuracy limits of about +3–5% stated in literature so far.
  5. Discharge coefficient by experimental and CFD approach is maintained constant and equal to design input value of 0.6.
    Thus, the proposed CBC weir can be operated for various discharge ranges by maintaining constant discharge coefficients.
    Good agreement between the theoretical, experimental and CFD simulation results for obtaining discharge through compound broad crested weir ascertains the fact that CFD model can be used as an effective tool towards modeling flow through compound broad crested weir.

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Hydraulic Analysis of Submerged Spillway Flows and Performance Evaluation of Chute Aerator Using CFD Modeling: A Case Study of Mangla Dam Spillway

CFD 모델링을 이용한 침수 배수로 흐름의 수리학적 해석 및 슈트 폭기장치 성능 평가: Mangla Dam 배수로 사례 연구

Hydraulic Analysis of Submerged Spillway Flows and Performance Evaluation of Chute Aerator Using CFD Modeling: A Case Study of Mangla Dam Spillway

Muhammad Kaleem SarwarZohaib NisarGhulam NabiFaraz ul HaqIjaz AhmadMuhammad Masood & Noor Muhammad Khan 

Abstract

대용량 배출구가 있는 수중 여수로는 일반적으로 홍수 처리 및 침전물 세척의 이중 기능을 수행하기 위해 댐 정상 아래에 제공됩니다. 이 방수로를 통과하는 홍수 물은 난류 거동을 나타냅니다. 

게다가 이러한 난류의 수력학적 분석은 어려운 작업입니다. 

따라서 본 연구는 파키스탄 Mangla Dam에 건설된 수중 여수로의 수리학적 거동을 수치해석을 통해 조사하는 것을 목적으로 한다. 또한 다양한 작동 조건에서 화기의 유압 성능을 평가했습니다. 

Mangla Spillway의 흐름을 수치적으로 모델링하는 데 전산 유체 역학 코드 FLOW 3D가 사용되었습니다. 레이놀즈 평균 Navier-Stokes 방정식은 난류 흐름을 수치적으로 모델링하기 위해 FLOW 3D에서 사용됩니다. 

연구 결과에 따르면 개발된 모델은 최대 6%의 허용 오차로 흐름 매개변수를 계산하므로 수중 여수로 흐름을 시뮬레이션할 수 있습니다. 

또한, 여수로 슈트 베드 주변 모델에 의해 계산된 공기 농도는 폭기 장치에 램프를 설치한 후 6% 이상으로 상승한 3%로 개발된 모델도 침수형 폭기 장치의 성능을 평가할 수 있음을 보여주었습니다.

Submerged spillways with large capacity outlets are generally provided below the dam crest to perform the dual functions of flood disposal and sediment flushing. Flood water passing through these spillways exhibits turbulent behavior. Moreover; hydraulic analysis of such turbulent flows is a challenging task. Therefore, the present study aims to use numerical simulations to examine the hydraulic behavior of submerged spillways constructed at Mangla Dam, Pakistan. Besides, the hydraulic performance of aerator was also evaluated at different operating conditions. Computational fluid dynamics code FLOW 3D was used to numerically model the flows of Mangla Spillway. Reynolds-averaged Navier–Stokes equations are used in FLOW 3D to numerically model the turbulent flows. The study results indicated that the developed model can simulate the submerged spillway flows as it computed the flow parameters with an acceptable error of up to 6%. Moreover, air concentration computed by model near spillway chute bed was 3% which raised to more than 6% after the installation of ramp on aerator which showed that developed model is also capable of evaluating the performance of submerged spillway aerator.

Keywords

  • Aerator
  • CFD
  • FLOW 3D
  • Froude number
  • Submerged spillway
  • Fig. 1extended data figure 1Fig. 2extended data figure 2Fig. 3extended data figure 3Fig. 4extended data figure 4Fig. 5extended data figure 5Fig. 6extended data figure 6Fig. 7extended data figure 7Fig. 8

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Watershed area

Analysis on inundation characteristics by compound external forces in coastal areas

연안 지역의 복합 외력에 의한 침수 특성 분석

Taeuk KangaDongkyun SunbSangho Leec*
강 태욱a선 동균b이 상호c*
aResearch Professor, Disaster Prevention Research Institute, Pukyong National University, Busan, KoreabResearcher, Disaster Prevention Research Institute, Pukyong National University, Busan, KoreacProfessor, Department of Civil Engineering, Pukyong National University, Busan, Korea
a부경대학교 방재연구소 전임연구교수b부경대학교 방재연구소 연구원c부경대학교 공과대학 토목공학과 교수*Corresponding Author

ABSTRACT

연안 지역은 강우, 조위, 월파 등 여러가지 외력에 의해 침수가 발생될 수 있다. 이에 이 연구에서는 연안 지역에서 발생될 수 있는 단일 및 복합 외력에 의한 지역별 침수 특성을 분석하였다. 연구에서 고려한 외력은 강우와 폭풍 해일에 의한 조위 및 월파이고, 분석 대상지역은 남해안 및 서해안의 4개 지역이다. 유역의 강우-유출 및 2차원 지표면 침수 분석에는 XP-SWMM이 사용되었고, 폭풍 해일에 의한 외력인 조위 및 월파량 산정에는 ADCSWAN (ADCIRC와 UnSWAN) 모형과 FLOW-3D 모형이 각각 활용되었다. 단일 외력을 이용한 분석 결과, 대부분의 연안 지역에서는 강우에 의한 침수 영향보다 폭풍 해일에 의한 침수 영향이 크게 나타났다. 복합 외력에 의한 침수 분석 결과는 대체로 단일 외력에 의한 침수 모의 결과를 중첩시켜 나타낸 결과와 유사하였다. 다만, 특정 지역에서는 복합 외력을 고려함에 따라 단일 외력만을 고려한 침수모의에서 나타나지 않았던 새로운 침수 영역이 발생하기도 하였다. 이러한 지역의 침수 피해 저감을 위해서는 복합 외력을 고려한 분석이 요구되는 것으로 판단되었다.키워드연안 지역 침수 분석 강우 폭풍 해일 복합 외력

The various external forces can cause inundation in coastal areas. This study is to analyze regional characteristics caused by single or compound external forces that can occur in coastal areas. Storm surge (tide level and wave overtopping) and rainfall were considered as the external forces in this study. The inundation analysis were applied to four coastal areas, located on the west and south coast in Republic of Korea. XP-SWMM was used to simulate rainfall-runoff phenomena and 2D ground surface inundation for watershed. A coupled model of ADCIRC and SWAN (ADCSWAN) was used to analyze tide level by storm surge and the FLOW-3D model was used to estimate wave overtopping. As a result of using a single external force, the inundation influence due to storm surge in most of the coastal areas was greater than rainfall. The results of using compound external forces were quite similar to those combined using one external force independently. However, a case of considering compound external forces sometimes created new inundation areas that didn’t appear when considering only a single external force. The analysis considering compound external forces was required to reduce inundation damage in these areas.KeywordsCoastal area Inundation analysis Rainfall Storm surge Compound external forces

MAIN

1. 서 론

우리나라는 반도에 위치하여 삼면이 바다로 둘러싸여 있는 지리적 특성을 가지고 있다. 이에 따라 해양 산업을 중심으로 부산, 인천, 울산 등 대규모의 광역도시가 발달하였을 뿐만 아니라, 창원, 포항, 군산, 목포, 여수 등의 중․소규모 도시들도 발달되어 있다. 또한, 최근에는 연안 지역이 바다를 전망으로 하는 입지 조건을 가지고 있어 개발 선호도가 높고, 이에 따라 부산시 해운대의 마린시티, 엘시티와 같은 주거 및 상업시설의 개발이 지속되고 있다(Kang et al., 2019b).

한편, 최근 기후변화에 따른 지구 온난화 현상으로 평균 해수면이 상승하고, 해수면 온도도 상승하면서 태풍 및 강우의 강도가 커지고 있어 전 세계적으로 자연 재해로 인한 피해가 증가하고 있다(Kim et al., 2016). 실제로 2020년에는 최장기간의 장마가 발생하여 부산, 울산은 물론, 전국에서 50명의 인명 피해와 3,489세대의 이재민이 발생하였다1). 특히, 연안 지역은 강우, 만조 시 해수면 상승, 폭풍 해일(storm surge)에 의한 월파(wave overtopping) 등 복합적인 외력(compound external forces)에 의해 침수될 수 있다(Lee et al., 2020). 일례로, 2016년 태풍 차바 시 부산시 해운대구의 마린시티는 강우와 폭풍 해일에 의한 월파가 발생함에 따라 대규모 침수를 유발하였다(Kang et al., 2019b). 또한, 2020년 7월 23일에 부산에서는 시간당 81.6 mm의 집중호우와 약최고고조위를 상회하는 만조가 동시에 발생하였고, 이로 인해 감조 하천인 동천의 수위가 크게 상승하여 하천이 범람하였다(KSCE, 2021).

연안 지역의 복합 외력을 고려한 침수 분석에 관한 사례로서, 우선 강우와 조위를 고려한 연구 사례는 다음과 같다. Han et al. (2014)은 XP-SWMM을 이용하여 창원시 배수 구역을 대상으로 침수 모의를 수행하였는데, 연안 도시의 침수 모의에는 조위의 영향을 반드시 고려해야 함을 제시하였다. Choi et al. (2018a)은 경남 사천시 선구동 일대에 대하여 초과 강우 및 해수면 상승 시나리오를 조합하여 침수 분석을 수행하였다. Choi et al. (2018b)은 XP-SWMM을 이용하여 여수시 연등천 및 여수시청 지역에 대하여 강우 시나리오와 해수위 상승 시나리오를 고려한 복합 원인에 의한 침수 모의를 수행하여 홍수예경보 기준표를 작성하였다. 한편, 강우, 조위, 월파를 고려한 연구 사례로서, Song et al. (2017)은 부산시 해운대구 수영만 일원에 대하여 XP-SWMM으로 월파량의 적용 유무에 따른 침수 면적을 비교하였다. Suh and Kim (2018)은 부산시 마린시티 지역을 대상으로 태풍 차바 때 EurOtop의 경험식을 ADSWAN에 적용하여 월파량을 반영하였다. Chen et al. (2017)은 TELEMAC-2D 및 SWMM을 기반으로 한 극한 강우, 월파 및 조위를 고려하여 중국 해안 원자력 발전소의 침수를 예측하고 분석하기 위한 결합 모델을 개발한 바 있다. 한편, Lee et al. (2020)은 수리‧수문학 분야와 해양공학 분야에서 사용되는 물리 모형의 기술적 연계를 통해 연안 지역의 침수 모의의 재현성을 높였다.

상기의 연구들은 공통적으로 연안 지역에 대하여 복합 외력을 고려했을 때 발생되는 침수 현상의 재현 또는 예측을 목적으로 수행되었다. 이 연구는 이와 차별하여 복합 외력을 고려하는 경우 나타날 수 있는 연안 지역의 침수 특성 분석을 목적으로 수행되었다. 이를 위해 단일 외력을 독립적으로 고려했을 때 발생되는 침수 양상과 동시에 고려하는 경우의 침수 현상을 비교, 분석하였다. 복합 외력에 의한 지역적 침수 특성 분석은 우리나라 남해안과 서해안에 위치한 4개 지역에 대하여 적용되었다.

1) 장연제, 47일째 이어진 긴 장마, 50명 인명피해… 9년만에 최대, 동아닷컴, 2020년 8월 9일 수정, 2021년 3월 4일 접속, https://www.donga.com/news/article/all/20200809/102369692/2

2. 연구 방법

2.1 연안 지역의 침수 영향 인자

연안 지역의 침수는 크게 세 가지의 메카니즘으로 발생될 수 있다. 우선, 연안 지역은 바다와 인접하고 있기 때문에 그 영향을 직접적으로 받는다. Kim (2018)에 의하면, 연안 지역의 침수는 폭풍 해일에 의해 상승한 조위와 월파로 인해 발생될 수 있다(Table 1). 특히, 경상남도의 창원과 통영, 인천광역시의 소래포구 어시장 등 남해안 및 서해안 지역의 일부는 백중사리, 슈퍼문(super moon) 등 만조 시 조위의 상승으로 인한 침수가 발생하는 지역이 존재한다(Kang et al., 2019a). 두 번째는 강우에 의한 내수 침수 발생이다. ME (2011)에서는 도시 지역의 우수 관거를 10 ~ 30년 빈도로 계획하도록 지정하고 있고, 펌프 시설은 30 ~ 50년 빈도의 홍수를 배수시킬 수 있도록 정하고 있다. 하지만 최근에는 기후변화의 영향으로 도시 지역 배수시설의 설계 빈도를 초과하는 강우가 빈번하게 나타나고 있다. 실제로 2016년의 태풍 차바 시 울산 기상관측소에 관측된 시간 최대 강우량은 106.0 mm로서, 이는 300년 빈도 이상의 강우량에 해당하였다(Kang et al., 2019a). 따라서 배수시설의 설계 빈도 이상의 강우는 연안 도시 지역의 침수를 유발할 수 있다. 세 번째, 하천이 인접한 연안 도시에서는 하천의 범람으로 인해 침수가 발생할 수 있다. 하천의 경우, 기본계획이 수립되기는 하지만, 설계 빈도를 상회하는 강우의 발생, 제방, 수문 등 홍수 방어시설의 기능 저하, 예산 등의 문제로 하천기본계획 이행의 지연 등에 의해 범람할 가능성이 존재한다.

Table 1.

Type of natural hazard damage in coastal areas (Kim, 2018)

ItemRisk factor
Facilities damage∙ Breaking of coastal facilities by wave
– Breakwater, revetment, lighters wharf etc.
∙ Local scouring at the toe of the structures by wave
∙ Road collapse by wave overtopping
Inundation damage∙ Inundation damage by wave overtopping
∙ Inundation of coastal lowlands by storm surge
Erosion damage∙ Backshore erosion due to high swell waves
∙ Shoreline changes caused by construction of coastal erosion control structure
∙ Sediment transport due to the construction of artificial structures

상기의 내용을 종합하면, 연안 지역은 조위 및 월파에 의한 침수, 강우에 의한 내수 침수, 하천 범람에 의한 침수로 구분될 수 있다. 이 연구에서는 폭풍 해일에 의한 조위 상승 및 월파와 강우를 연안 지역의 침수 유발 외력으로 고려하였다. 하천 범람의 경우, 상대적으로 사례가 희소하여 제외하였다.

2.2 복합 외력을 고려한 침수 모의 방법

이 연구에서는 조위 및 월파와 강우를 연안 지역의 침수 발생에 관한 외력 조건으로 고려하였다. 따라서 해당 외력 조건을 고려하여 침수 분석을 수행할 수 있어야 한다. 이와 관련하여 Lee et al. (2020)은 Fig. 1과 같이 수리‧수문 및 해양공학 분야에서 사용되는 물리 기반 모형의 연계를 통해 조위, 월파, 강우를 고려한 침수 분석 방법을 제시하였고, 이 연구에서는 해당 방법을 이용하였다.

/media/sites/kwra/2021-054-07/N0200540702/images/kwra_54_07_02_F1.jpg
Fig. 1.

Connection among the models for inundation analysis in coastal areas (Lee et al., 2020)

우선, 태풍에 의해 발생되는 폭풍 해일의 영향을 분석하기 위해서는 태풍에 의해 발생되는 기압 강하, 해상풍, 진행 속도 등을 고려하여 해수면의 변화 양상 및 조석-해일-파랑을 충분히 재현 가능해야 한다. 이 연구에서는 국내․외에서 검증 및 공인된 폭풍 해일 모형인 ADCIRC 모형과 파랑 모형인 UnSWAN이 결합된 ADCSWAN (coupled model of ADCIRC and UnSWAN)을 이용하였다. 정수압 가정의 ADCSWAN은 월파량 산정에 단순 경험식을 적용하는 단점이 있지만 넓은 영역을 모의할 수 있고, FLOW-3D는 해안선의 경계를 고해상도로 재현이 가능하다. 이에 연구에서는 먼 바다 영역에 대해서는 ADCSWAN을 이용하여 분석하였고, 연안 주변의 바다 영역과 월파량 산정에 대해서는 FLOW-3D 모형을 이용하였다. 한편, 연안 지역의 침수 모의를 위해서는 유역에서 발생하는 강우-유출 현상과 우수 관거 등의 배수 체계에 대한 분석이 가능해야 한다. 또한, 배수 체계로부터 범람한 물이 지표면을 따라 흘러가는 현상을 해석할 수 있어야 하고, 바다의 조위 및 월파량을 경계조건으로 반영할 수 있어야 한다. 이 연구에서는 이러한 현상을 모의할 수 있고, 도시 침수 모의에 활용도가 높은 XP-SWMM을 이용하였다.

2.3 침수 분석 대상지역

연구의 대상지역은 조위 및 월파에 의한 침수와 강우에 의한 내수 침수의 영향이 복합적으로 발생할 수 있는 남해안과 서해안에 위치한 4개 지역이다. Table 2는 침수 분석 대상지역을 정리하여 나타낸 표이고, Fig. 2는 각 지역의 유역 경계를 나타낸 그림이다.

Table 2.

Target region for inundation analysis

ClassificationAdministrative districtTarget regionArea
(km2)
Main cause of inundationPump
facility
Number of
major outfall
The south
coast
Haundae-gu, BusanMarine City area0.53Wave overtopping9
Haundae-gu, BusanCentum City area4.76Poor interior drainage at high tide level12
The west
coast
GunsanJungang-dong area0.79Poor interior drainage at high tide level23
BoryeongOcheon Port area0.41High tide level5

/media/sites/kwra/2021-054-07/N0200540702/images/kwra_54_07_02_F2.jpg
Fig. 2.

Watershed area

남해안의 분석 대상지역 중 부산시 해운대구의 마린시티는 바다 조망을 중심으로 조성된 주거지 및 상업시설 중심의 개발지역이다. 마린시티는 2016년 태풍 차바 및 2018년 태풍 콩레이 등 태풍 내습 시 월파에 의한 해수 월류로 인해 도로 및 상가 일부가 침수를 겪은 지역이다. 부산시 해운대구의 센텀시티는 과거 수영만 매립지였던 곳에 조성된 주거지 및 상업시설 중심의 신도시 지역이다. 센텀시티 유역의 북쪽은 해발고도 El. 634 m의 장산이 위치하는 등 산지 특성도 가지고 있어 상대적으로 유역 면적이 넓고, 배수시설의 규모도 크고 복잡하다. 하지만 수영강 하구의 저지대 지역에 위치함에 따라 강우 시 내수 배제가 불량하고, 특히 만조 시 침수가 잦은 지역이다.

서해안 분석 대상지역 중 전라북도 군산시의 중앙동 일원은 군산시 내항 내측에 조성된 구도시로서, 금강 및 경포천 하구에 위치하는 저지대이다. 이에 따라 군산시 풍수해저감종합계획에서는 해당 지역을 3개의 영역으로 구분하여 내수재해 위험지구(영동지구, 중동지구, 경암지구)로 지정하였고, 이 연구에서는 해당 지역을 모두 고려하였다. 한편, 군산시 중앙동 일원은 특히, 만조 시 내수 배제가 매우 불량하여 2개의 펌프시설이 운영되고 있다. 충청남도 보령시의 오천면에 위치한 오천항은 배후의 산지를 포함한 소규모 유역에 위치한다. 서해안의 특성에 따라 조석 간만의 차가 크고, 특히 태풍 내습 시 폭풍 해일에 의한 침수가 잦은 지역이다. 산지의 강우-유출수는 복개된 2개의 수로를 통해 바다로 배제되고, 상가들이 위치한 연안 주변 지역에는 강우-유출수 배제를 위한 3개의 배수 체계가 구성되어 있다.

3. 연구 결과

3.1 침수 모의 모형 구축

XP-SWMM을 이용하여 분석 대상지역별 침수 모의 모형을 구축하였다. 적절한 침수 분석 수행을 위해 지역별 수치지형도, 도시 공간 정보 시스템(urban information system, UIS), 하수 관망도 등의 수치 자료와 현장 조사를 통해 유역의 배수 체계를 구성하였다. 그리고 2차원 침수 분석을 위해 무인 드론 및 육상 라이다(LiDAR) 측량을 수행하여 평면해상도가 1 m 이하인 고해상도 수치지형모형(digital terrain model, DTM)을 구성하였고, 침수 모의 격자를 생성하였다.

Fig. 3은 XP-SWMM의 상세 구축 사례로서 부산시 마린시티 배수 유역에 대한 소유역 및 관거 분할 등을 통해 구성한 배수 체계와 고해상도 측량 결과를 이용하여 구성한 수치표면모형(digital surface model, DSM)을 나타낸다. Fig. 4는 각 대상지역에 대해 XP-SWMM을 이용하여 구축한 침수 모의 모형을 나타낸다. 침수 분석을 위해서는 침수 모의 영역에 대한 설정이 필요한데, 다수의 사전 모의를 통해 유역 내에서 침수가 발생되는 지역을 검토하여 결정하였다.

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Fig. 3.

Analysis of watershed drainage system and high-resolution survey for Marine City

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Fig. 4.

Simulation model for inundation analysis by target region using XP-SWMM

한편, 이 연구에서는 월파량 및 조위의 산정 과정과 침수 모의 모형의 보정에 관한 내용 등은 다루지 않았다. 관련된 내용은 선행 연구인 Kang et al. (2019b)와 Lee et al. (2020)을 참조할 수 있다.

3.2 침수 모의 설정

3.2.1 분석 방법

복합 외력에 의한 침수 영향을 검토하기 위해서는 외력 조건에 대한 빈도와 지속기간의 설정이 필요하다. 이 연구에서는 재해 현상이 충분히 나타날 수 있도록 강우와 조위 및 월파의 빈도를 모두 100년으로 설정하였다. 이때, 조위와 월파량의 산정에는 만조(약최고고조위) 시, 100년 빈도에 해당하는 태풍 내습에 따른 폭풍 해일의 발생 조건을 고려하였다.

지역별 강우 발생 특성과 유역 특성을 고려하기 위해 MOIS (2017)의 방재성능목표 기준에 따라 임계 지속기간을 결정하여 대상지역별 강우의 지속기간으로 설정하였다. 이때, 강우의 시간 분포는 MLTM (2011)의 Huff 3분위를 이용하였다. 그리고 조위와 월파의 경우, 일반적인 폭풍 해일의 지속기간을 고려하여 5시간으로 결정하였다. 한편, 침수 모의를 위한 계산 시간 간격, 2차원 모의 격자 등의 입력자료는 분석 대상지역의 유역 규모와 침수 분석 대상 영역을 고려하여 결정하였다. 참고로 침수 분석에 사용된 수치지형모형은 1 m 급의 고해상도로 구성되었지만, 2차원 침수 모의 격자의 크기는 지역별로 3 ~ 4 m이다. 이는 연구에서 사용된 XP-SWMM의 격자 수(100,000개) 제약에 따른 설정이나, Sun (2021)은 민감도 분석을 통해 2차원 침수 분석을 위한 적정 격자 크기를 3 ~ 4.5 m로 제시한 바 있다.

Table 3은 이 연구에서 설정한 침수 모의 조건과 분석 방법을 정리하여 나타낸 표이다.

Table 3.

Simulation condition and method

ClassificationTarget regionSimulation conditionSimulation method
RainfallStorm surgeSimulation time interval2D
grid size
Return
period
DurationTemporal
distribution
Return
period
DurationWatershed
routing
Channel
routing
2D
inundation
The south coastMarine City area100 yr1 hr3rd quartile
of Huff’s
method
1005 hr5 min10 sec1 sec3 m
Centum City area1 hr1005 min10 sec1 sec4 m
The west coastJungang-dong area2 hr1005 min10 sec1 sec3.5 m
Ocheon Port area1 hr1001 min10 sec1 sec3 m

3.2.2 복합 재해의 동시 고려

이 연구의 대상지역들은 모두 소규모의 해안가 도시지역이고, 이러한 지역에 대한 강우의 임계지속기간은 1시간 ~ 2시간이나, 이 연구에서 분석한 폭풍 해일의 지속기간은 5시간으로 강우의 지속기간과 폭풍 해일의 지속기간이 상이하다. 이에 이 연구에서는 서로 다른 지속기간을 가진 강우와 폭풍 해일 또는 조위를 고려하기 위해 강우의 중심과 폭풍 해일의 중심이 동일한 시간에 위치하도록 설정하였다(Fig. 5).

XP-SWMM은 폭풍 해일이 지속되는 5시간 전체를 모의하도록 설정하였고, 폭풍 해일이 가장 큰 시점에 강우의 중심이 위치하도록 강우 발생 시기를 결정하였다. 다만, 부산 마린시티의 경우, 폭풍 해일에 의한 피해가 주로 월파에 의해 발생되므로 강우의 중심과 월파의 중심을 일치시켰고(Fig. 5(a)), 상대적으로 조위의 영향이 큰 3개 지역은 강우의 중심과 조위의 중심을 맞추었다. Fig. 5(b)는 군산시 중앙동 지역의 복합 외력에 의한 침수 분석에 사용된 강우와 조위의 조합이다.

한편, 100년 빈도의 확률강우량만을 고려한 침수 분석에서는 유역 유출부의 경계조건으로 우수 관거의 설계 조건을 고려하여 약최고고조위가 일정하게 유지되도록 설정하였다.

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Fig. 5.

Consideration of external force conditions with different durations

3.2.3 XP-SWMM의 월파량 고려

XP-SWMM에 ADCSWAN 및 FLOW-3D 모형에 의해 산정된 월파량을 입력하기 위해 해안가 지역에 절점을 생성하여 월파 현상을 구현하였다. XP-SWMM에서 월파량을 입력하기 위한 절점의 위치는 FLOW-3D 모형에서 월파량을 산정한 격자의 중심 위치이다.

Fig. 6(a)는 마린시티 지역에 대한 월파량 입력 지점을 나타낸 것으로서, 유역 경계 주변에 동일 간격으로 원으로 표시한 지점들이 해당된다. Fig. 6(b)는 XP-SWMM에 월파량 입력 지점들을 반영하고, 하나의 절점에 월파량 시계열을 입력한 화면을 나타낸다.

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Fig. 6.

Considering wave overtopping on XP-SWMM

3.3 침수 모의 결과

3.3.1 단일 외력에 의한 침수 모의 결과

Fig. 7은 단일 외력을 고려한 지역별 침수 모의 결과이다. 즉, Fig. 7의 왼쪽 그림들은 지역별로 100년 빈도 강우에 의한 침수 모의 결과를 나타내고, Fig. 7의 오른쪽 그림들은 만조 시 100년 빈도 폭풍 해일에 의한 침수 모의 결과이다. 대체로 강우에 의한 침수 영역은 유역 중․상류 지역의 유역 전반에 걸쳐 발생하였고, 폭풍 해일에 의한 침수 영역은 해안가 전면부에 위치하는 것을 볼 수 있다. 이는 폭풍 해일에 의한 조위 상승과 월파의 영향이 상류로 갈수록 감소하기 때문이다.

한편, 4개 지역 모두에서 공통적으로 강우에 비해 폭풍 해일에 의한 침수 영향이 상대적으로 크게 분석되었다. 이러한 결과는 연안 지역의 경우, 폭풍 해일에 대비한 침수 피해 저감 노력이 보다 중요함을 의미한다.

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Fig. 7.

Simulation results by single external force (left: rainfall, right: storm surge)

3.3.2 복합 외력에 의한 침수 모의 결과

Fig. 8은 복합 외력을 고려한 지역별 침수 모의 결과이다. 즉, 강우 및 폭풍 해일을 동시에 고려함에 따라 발생된 침수 영역을 나타낸다. 복합 외력을 고려하는 경우, 단일 외력만을 고려한 분석 결과(Fig. 7)보다 침수 영역은 넓어졌고, 침수심은 깊어졌다.

복합 외력에 의한 침수 분석 결과는 대체로 단일 외력에 의한 침수 모의 결과를 중첩시켜 나타낸 결과와 유사하였고, 이는 일반적으로 예상할 수 있는 결과이다. 주목할만한 결과는 군산시 중앙동의 침수 분석에서 나타났다. 즉, 군산시 중앙동의 경우, 단일 외력만을 고려한 침수 모의 결과에서 나타나지 않았던 새로운 침수 영역이 발생하였다(Fig. 8(c)). 이와 관련된 상세 내용은 3.4절의 고찰에서 기술하였다.

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Fig. 8.

Simulation results by compound external forces

3.4 결과 고찰

외력 조건별 침수의 영향을 정량적으로 비교하기 위해 침수 면적을 이용하였다. 이 연구에서는 강우만에 의해 유발된 침수 면적을 기준(기준값: 1)으로 하고, 폭풍 해일(조위+월파량)에 의한 침수 면적과 복합 외력에 의한 침수 면적의 상대적 비율로 분석하였다(Table 4).

Table 4.

Impact evaluation for inundation area by external force

ConditionMarine City, BusanCentum City, BusanJungang-dong area,
Gunsan
Ocheon Port area,
Boryeong
Inundation area
(km2)
RateInundation area
(km2)
RateInundation area
(km2)
RateInundation area
(km2)
Rate
Single
external force
Rainfall (①)0.01641.00.07591.00.04571.00.01751.0
Storm surge (②)0.03632.210.06850.900.14633.200.04122.35
Compound
external forces
Combination
(①+②)
0.05243.190.15051.980.26325.760.04732.70

분석 결과, 부산 센텀시티를 제외한 3개 지역은 모두 폭풍 해일에 의한 침수 면적이 강우에 의한 침수 면적에 비해 2.2 ~ 3.2배 넓은 것으로 분석되었다. 한편, 복합 외력에 의한 침수 면적은 마린시티와 센텀시티의 경우, 각각의 외력에 의한 침수 면적의 합과 유사하게 나타났다. 이는 각각의 외력에 의한 침수 영역이 상이하여 거의 중복되지 않음을 의미한다. 반면에, 오천항에서는 각각의 외력에 의한 침수 면적의 합이 복합 외력에 의한 면적보다 크게 나타났다. 이는 오천항의 경우, 유역면적이 작고 배수 체계가 비교적 단순하여 강우와 폭풍 해일에 의한 침수 영역이 중복되기 때문인 것으로 분석되었다(Fig. 7(d)).

군산시 중앙동 일대의 경우, 복합 외력에 의한 침수 면적이 각각의 독립적인 외력 조건에 의한 침수 면적의 합에 비해 37.1% 크게 나타났다. 이러한 현상의 원인을 분석하기 위해 복합 외력 조건에서만 나타난 우수 관거(Fig. 8(c)의 A 구간)에 대하여 종단을 검토하였다(Fig. 9). Fig. 9(a)는 강우만에 의해 분석된 우수 관거 내 흐름 종단을 나타내고, Fig. 9(b)는 폭풍 해일만에 의한 우수 관거의 종단이다. 그림을 통해 각각의 독립적인 외력 조건 하에서는 해당 구간에서 침수가 발생되지 않은 것을 볼 수 있다. 다만, 강우만을 고려하더라도 우수 관거는 만관이 된 상태를 확인할 수 있다(Fig. 9(a)). 반면에, 만관 상태에서 폭풍 해일이 함께 고려됨에 따라 해수 범람과 조위 상승에 의해 우수 배제가 불량하게 되었고, 이로 인해 침수가 유발된 것으로 분석되었다(Fig. 9(c)). 따라서 이러한 지역은 복합 외력에 대한 취약지구로 판단할 수 있고, 단일 외력의 고려만으로는 침수를 예상하기 어려운 지역임을 알 수 있다.

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Fig. 9.

A part of drainage profiles by external force in Jungang-dong area, Gunsan

4. 결 론

이 연구에서는 외력 조건에 따른 연안 지역의 침수 특성을 분석하였다. 연구에서 고려된 외력 조건은 두 가지로서 강우와 폭풍 해일(조위와 월파)이다. 분석 대상 연안 지역으로는 남해안에 위치하는 2개 지역(부산시 해운대구의 마린시티와 센텀시티)과 서해안의 2개 지역(군산시 중앙동 일원 및 보령시 오천항)이 선정되었다.

복합 외력을 고려한 연안 지역의 침수 모의를 위해서는 유역의 강우-유출 현상과 바다의 조위 및 월파량을 경계조건으로 반영할 수 있는 침수 모의 모형이 요구되는데, 이 연구에서는 XP-SWMM을 이용하였다. 한편, 조위 및 월파량 산정에는 ADCSWAN (ADCIRC와 UnSWAN) 및 FLOW-3D 모형이 이용되었다.

연안 지역별 침수 모의는 100년 빈도의 강우와 폭풍 해일을 독립적으로 고려한 경우와 복합적으로 고려한 경우를 구분하여 수행되었다. 우선, 외력을 독립적으로 고려한 결과, 대체로 폭풍 해일만 고려한 경우가 강우만 고려한 경우에 비해 침수 영향이 크게 나타났다. 따라서 연안 지역의 경우, 폭풍 해일에 의한 침수 피해 방지 계획이 상대적으로 중요한 것으로 분석되었다. 두 번째, 복합 외력에 의한 침수 분석 결과는 대체로 단일 외력에 의한 침수 모의 결과를 중첩시켜 나타낸 결과와 유사하였다. 다만, 특정 지역에서는 복합 외력을 고려함에 따라 단일 외력만을 고려한 침수 모의에서 나타나지 않았던 새로운 침수 영역이 발생하기도 하였다. 이러한 결과는 독립적인 외력 조건에서는 우수 관거가 만관 또는 그 이하의 상태가 되지만, 두 가지의 외력이 동시에 고려됨에 따라 우수 관거의 통수능 한계를 초과하여 나타났다. 이러한 지역은 복합 외력에 대한 취약지구로 판단되었고, 해당 지역의 적절한 침수 방지 대책 수립을 위해서는 복합적인 외력 조건이 고려되어야 함을 시사하였다.

현행, 자연재해저감종합계획에서는 침수와 관련된 재해 원인 지역을 내수재해, 해안재해, 하천재해 등으로 구분하고 있다. 하지만 이 연구에서 검토된 바와 같이, 연안 지역의 침수 원인은 복합적으로 나타날 뿐만 아니라, 복합 외력을 고려함에 따라 추가적으로 나타날 수 있는 침수 위험 지역도 존재한다. 따라서 기존의 획일적인 재해 원인의 구분보다는 지역의 특성에 맞는 복합적인 재해 원인을 검토할 필요가 있음을 제안한다.

Acknowledgements

본 논문은 행정안전부 극한 재난대응 기반기술 개발사업의 일환인 “해안가 복합재난 위험지역 피해저감 기술개발(연구과제번호: 2018-MOIS31-008)”의 지원으로 수행되었습니다.

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Fig. 1. (a) Dimensions of the casting with runners (unit: mm), (b) a melt flow simulation using Flow-3D software together with Reilly's model[44], predicted that a large amount of bifilms (denoted by the black particles) would be contained in the final casting. (c) A solidification simulation using Pro-cast software showed that no shrinkage defect was contained in the final casting.

AZ91 합금 주물 내 연행 결함에 대한 캐리어 가스의 영향

Effect of carrier gases on the entrainment defects within AZ91 alloy castings

Tian Liab J.M.T.Daviesa Xiangzhen Zhuc
aUniversity of Birmingham, Birmingham B15 2TT, United Kingdom
bGrainger and Worrall Ltd, Bridgnorth WV15 5HP, United Kingdom
cBrunel Centre for Advanced Solidification Technology, Brunel University London, Kingston Ln, London, Uxbridge UB8 3PH, United Kingdom

Abstract

An entrainment defect (also known as a double oxide film defect or bifilm) acts a void containing an entrapped gas when submerged into a light-alloy melt, thus reducing the quality and reproducibility of the final castings. Previous publications, carried out with Al-alloy castings, reported that this trapped gas could be subsequently consumed by the reaction with the surrounding melt, thus reducing the void volume and negative effect of entrainment defects. Compared with Al-alloys, the entrapped gas within Mg-alloy might be more efficiently consumed due to the relatively high reactivity of magnesium. However, research into the entrainment defects within Mg alloys has been significantly limited. In the present work, AZ91 alloy castings were produced under different carrier gas atmospheres (i.e., SF6/CO2, SF6/air). The evolution processes of the entrainment defects contained in AZ91 alloy were suggested according to the microstructure inspections and thermodynamic calculations. The defects formed in the different atmospheres have a similar sandwich-like structure, but their oxide films contained different combinations of compounds. The use of carrier gases, which were associated with different entrained-gas consumption rates, affected the reproducibility of AZ91 castings.

Keywords

Magnesium alloyCastingOxide film, Bifilm, Entrainment defect, Reproducibility

연행 결함(이중 산화막 결함 또는 이중막 결함이라고도 함)은 경합금 용융물에 잠길 때 갇힌 가스를 포함하는 공극으로 작용하여 최종 주물의 품질과 재현성을 저하시킵니다. Al-합금 주조로 수행된 이전 간행물에서는 이 갇힌 가스가 주변 용융물과의 반응에 의해 후속적으로 소모되어 공극 부피와 연행 결함의 부정적인 영향을 줄일 수 있다고 보고했습니다. Al-합금에 비해 마그네슘의 상대적으로 높은 반응성으로 인해 Mg-합금 내에 포집된 가스가 더 효율적으로 소모될 수 있습니다. 그러나 Mg 합금 내 연행 결함에 대한 연구는 상당히 제한적이었습니다. 현재 작업에서 AZ91 합금 주물은 다양한 캐리어 가스 분위기(즉, SF 6 /CO2 , SF 6 / 공기). AZ91 합금에 포함된 엔트레인먼트 결함의 진화 과정은 미세조직 검사 및 열역학적 계산에 따라 제안되었습니다. 서로 다른 분위기에서 형성된 결함은 유사한 샌드위치 구조를 갖지만 산화막에는 서로 다른 화합물 조합이 포함되어 있습니다. 다른 동반 가스 소비율과 관련된 운반 가스의 사용은 AZ91 주물의 재현성에 영향을 미쳤습니다.

키워드

마그네슘 합금주조Oxide film, Bifilm, Entrainment 불량, 재현성

1 . 소개

지구상에서 가장 가벼운 구조용 금속인 마그네슘은 지난 수십 년 동안 가장 매력적인 경금속 중 하나가 되었습니다. 결과적으로 마그네슘 산업은 지난 20년 동안 급속한 발전을 경험했으며 [1 , 2] , 이는 전 세계적으로 Mg 합금에 대한 수요가 크게 증가했음을 나타냅니다. 오늘날 Mg 합금의 사용은 자동차, 항공 우주, 전자 등의 분야에서 볼 수 있습니다. [3 , 4] . Mg 금속의 전 세계 소비는 특히 자동차 산업에서 앞으로 더욱 증가할 것으로 예측되었습니다. 기존 자동차와 전기 자동차 모두의 에너지 효율성 요구 사항이 설계를 경량화하도록 더욱 밀어붙이기 때문입니다 [3 , 56] .

Mg 합금에 대한 수요의 지속적인 성장은 Mg 합금 주조의 품질 및 기계적 특성 개선에 대한 광범위한 관심을 불러일으켰습니다. Mg 합금 주조 공정 동안 용융물의 표면 난류는 소량의 주변 대기를 포함하는 이중 표면 필름의 포획으로 이어질 수 있으므로 동반 결함(이중 산화막 결함 또는 이중막 결함이라고도 함)을 형성합니다. ) [7] , [8] , [9] , [10] . 무작위 크기, 수량, 방향 및 연행 결함의 배치는 주조 특성의 변화와 관련된 중요한 요인으로 널리 받아들여지고 있습니다 [7] . 또한 Peng et al. [11]AZ91 합금 용융물에 동반된 산화물 필름이 Al 8 Mn 5 입자에 대한 필터 역할을 하여 침전될 때 가두는 것을 발견했습니다 . Mackie et al. [12]는 또한 동반된 산화막이 금속간 입자를 트롤(trawl)하는 작용을 하여 입자가 클러스터링되어 매우 큰 결함을 형성할 수 있다고 제안했습니다. 금속간 화합물의 클러스터링은 비말동반 결함을 주조 특성에 더 해롭게 만들었습니다.

연행 결함에 관한 이전 연구의 대부분은 Al-합금에 대해 수행되었으며 [7 , [13] , [14] , [15] , [16] , [17] , [18] 몇 가지 잠재적인 방법이 제안되었습니다. 알루미늄 합금 주물의 품질에 대한 부정적인 영향을 줄이기 위해. Nyahumwa et al., [16] 은 연행 결함 내의 공극 체적이 열간 등방압 압축(HIP) 공정에 의해 감소될 수 있음을 보여줍니다. Campbell [7] 은 결함 내부의 동반된 가스가 주변 용융물과의 반응으로 인해 소모될 수 있다고 제안했으며, 이는 Raiszedeh와 Griffiths [19]에 의해 추가로 확인되었습니다 ..혼입 가스 소비가 Al-합금 주물의 기계적 특성에 미치는 영향은 [8 , 9]에 의해 조사되었으며 , 이는 혼입 가스의 소비가 주조 재현성의 개선을 촉진함을 시사합니다.

Al-합금 내 결함에 대한 조사와 비교하여 Mg-합금 내 연행 결함에 대한 연구는 상당히 제한적입니다. 연행 결함의 존재는 Mg 합금 주물 [20 , 21] 에서 입증 되었지만 그 거동, 진화 및 연행 가스 소비는 여전히 명확하지 않습니다.

Mg 합금 주조 공정에서 용융물은 일반적으로 마그네슘 점화를 피하기 위해 커버 가스로 보호됩니다. 따라서 모래 또는 매몰 몰드의 공동은 용융물을 붓기 전에 커버 가스로 세척해야 합니다 [22] . 따라서, Mg 합금 주물 내의 연행 가스는 공기만이 아니라 주조 공정에 사용되는 커버 가스를 포함해야 하며, 이는 구조 및 해당 연행 결함의 전개를 복잡하게 만들 수 있습니다.

SF 6 은 Mg 합금 주조 공정에 널리 사용되는 대표적인 커버 가스입니다 [23] , [24] , [25] . 이 커버 가스는 유럽의 마그네슘 합금 주조 공장에서 사용하도록 제한되었지만 상업 보고서에 따르면 이 커버는 전 세계 마그네슘 합금 산업, 특히 다음과 같은 글로벌 마그네슘 합금 생산을 지배한 국가에서 여전히 인기가 있습니다. 중국, 브라질, 인도 등 [26] . 또한, 최근 학술지 조사에서도 이 커버가스가 최근 마그네슘 합금 연구에서 널리 사용된 것으로 나타났다 [27] . SF 6 커버 가스 의 보호 메커니즘 (즉, 액체 Mg 합금과 SF 6 사이의 반응Cover gas)에 대한 연구는 여러 선행연구자들에 의해 이루어졌으나 표면 산화막의 형성과정이 아직 명확하게 밝혀지지 않았으며, 일부 발표된 결과들도 상충되고 있다. 1970년대 초 Fruehling [28] 은 SF 6 아래에 형성된 표면 피막이 주로 미량의 불화물과 함께 MgO 임을 발견 하고 SF 6 이 Mg 합금 표면 피막에 흡수 된다고 제안했습니다 . Couling [29] 은 흡수된 SF 6 이 Mg 합금 용융물과 반응하여 MgF 2 를 형성함을 추가로 확인했습니다 . 지난 20년 동안 아래에 자세히 설명된 것처럼 Mg 합금 표면 필름의 다양한 구조가 보고되었습니다.(1)

단층 필름 . Cashion [30 , 31] 은 X선 광전자 분광법(XPS)과 오제 분광법(AES)을 사용하여 표면 필름을 MgO 및 MgF 2 로 식별했습니다 . 그는 또한 필름의 구성이 두께와 전체 실험 유지 시간에 걸쳐 일정하다는 것을 발견했습니다. Cashion이 관찰한 필름은 10분에서 100분의 유지 시간으로 생성된 단층 구조를 가졌다.(2)

이중층 필름 . Aarstad et. al [32] 은 2003년에 이중층 표면 산화막을 보고했습니다. 그들은 예비 MgO 막에 부착된 잘 분포된 여러 MgF 2 입자를 관찰 하고 전체 표면적의 25-50%를 덮을 때까지 성장했습니다. 외부 MgO 필름을 통한 F의 내부 확산은 진화 과정의 원동력이었습니다. 이 이중층 구조는 Xiong의 그룹 [25 , 33] 과 Shih et al. 도 지지했습니다 . [34] .(삼)

트리플 레이어 필름 . 3층 필름과 그 진화 과정은 Pettersen [35]에 의해 2002년에 보고되었습니다 . Pettersen은 초기 표면 필름이 MgO 상이었고 F의 내부 확산에 의해 점차적으로 안정적인 MgF 2 상 으로 진화한다는 것을 발견했습니다 . 두꺼운 상부 및 하부 MgF 2 층.(4)

산화물 필름은 개별 입자로 구성 됩니다. Wang et al [36] 은 Mg-alloy 표면 필름을 SF 6 커버 가스 하에서 용융물에 교반 한 다음 응고 후 동반된 표면 필름을 검사했습니다. 그들은 동반된 표면 필름이 다른 연구자들이 보고한 보호 표면 필름처럼 계속되지 않고 개별 입자로 구성된다는 것을 발견했습니다. 젊은 산화막은 MgO 나노 크기의 산화물 입자로 구성되어 있는 반면, 오래된 산화막은 한쪽 면에 불화물과 질화물이 포함된 거친 입자(평균 크기 약 1μm)로 구성되어 있습니다.

Mg 합금 용융 표면의 산화막 또는 동반 가스는 모두 액체 Mg 합금과 커버 가스 사이의 반응으로 인해 형성되므로 Mg 합금 표면막에 대한 위에서 언급한 연구는 진화에 대한 귀중한 통찰력을 제공합니다. 연행 결함. 따라서 SF 6 커버 가스 의 보호 메커니즘 (즉, Mg-합금 표면 필름의 형성)은 해당 동반 결함의 잠재적인 복잡한 진화 과정을 나타냅니다.

그러나 Mg 합금 용융물에 표면 필름을 형성하는 것은 용융물에 잠긴 동반된 가스의 소비와 다른 상황에 있다는 점에 유의해야 합니다. 예를 들어, 앞서 언급한 연구에서 표면 성막 동안 충분한 양의 커버 가스가 담지되어 커버 가스의 고갈을 억제했습니다. 대조적으로, Mg 합금 용융물 내의 동반된 가스의 양은 유한하며, 동반된 가스는 완전히 고갈될 수 있습니다. Mirak [37] 은 3.5% SF 6 /기포를 특별히 설계된 영구 금형에서 응고되는 순수한 Mg 합금 용융물에 도입했습니다. 기포가 완전히 소모되었으며, 해당 산화막은 MgO와 MgF 2 의 혼합물임을 알 수 있었다.. 그러나 Aarstad [32] 및 Xiong [25 , 33]에 의해 관찰된 MgF 2 스팟 과 같은 핵 생성 사이트 는 관찰되지 않았습니다. Mirak은 또한 조성 분석을 기반으로 산화막에서 MgO 이전에 MgF 2 가 형성 되었다고 추측했는데 , 이는 이전 문헌에서 보고된 표면 필름 형성 과정(즉, MgF 2 이전에 형성된 MgO)과 반대 입니다. Mirak의 연구는 동반된 가스의 산화막 형성이 표면막의 산화막 형성과 상당히 다를 수 있음을 나타내었지만 산화막의 구조와 진화에 대해서는 밝히지 않았습니다.

또한 커버 가스에 캐리어 가스를 사용하는 것도 커버 가스와 액체 Mg 합금 사이의 반응에 영향을 미쳤습니다. SF 6 /air 는 용융 마그네슘의 점화를 피하기 위해 SF 6 /CO 2 운반 가스 [38] 보다 더 높은 함량의 SF 6을 필요로 하여 다른 가스 소비율을 나타냅니다. Liang et.al [39] 은 CO 2 가 캐리어 가스로 사용될 때 표면 필름에 탄소가 형성된다고 제안했는데 , 이는 SF 6 /air 에서 형성된 필름과 다릅니다 . Mg 연소 [40]에 대한 조사 에서 Mg 2 C 3 검출이 보고되었습니다.CO 2 연소 후 Mg 합금 샘플 에서 이는 Liang의 결과를 뒷받침할 뿐만 아니라 이중 산화막 결함에서 Mg 탄화물의 잠재적 형성을 나타냅니다.

여기에 보고된 작업은 다양한 커버 가스(즉, SF 6 /air 및 SF 6 /CO 2 )로 보호되는 AZ91 Mg 합금 주물에서 형성된 연행 결함의 거동과 진화에 대한 조사 입니다. 이러한 캐리어 가스는 액체 Mg 합금에 대해 다른 보호성을 가지며, 따라서 상응하는 동반 가스의 다른 소비율 및 발생 프로세스와 관련될 수 있습니다. AZ91 주물의 재현성에 대한 동반 가스 소비의 영향도 연구되었습니다.

2 . 실험

2.1 . 용융 및 주조

3kg의 AZ91 합금을 700 ± 5 °C의 연강 도가니에서 녹였습니다. AZ91 합금의 조성은 표 1 에 나타내었다 . 가열하기 전에 잉곳 표면의 모든 산화물 스케일을 기계가공으로 제거했습니다. 사용 된 커버 가스는 0.5 %이었다 SF 6 / 공기 또는 0.5 % SF 6 / CO 2 (부피. %) 다른 주물 6L / 분의 유량. 용융물은 15분 동안 0.3L/min의 유속으로 아르곤으로 가스를 제거한 다음 [41 , 42] , 모래 주형에 부었습니다. 붓기 전에 샌드 몰드 캐비티를 20분 동안 커버 가스로 플러싱했습니다 [22] . 잔류 용융물(약 1kg)이 도가니에서 응고되었습니다.

표 1 . 본 연구에 사용된 AZ91 합금의 조성(wt%).

아연미네소타마그네슘
9.40.610.150.020.0050.0017잔여

그림 1 (a)는 러너가 있는 주물의 치수를 보여줍니다. 탑 필링 시스템은 최종 주물에서 연행 결함을 생성하기 위해 의도적으로 사용되었습니다. Green과 Campbell [7 , 43] 은 탑 필링 시스템이 바텀 필링 시스템에 비해 주조 과정에서 더 많은 연행 현상(즉, 이중 필름)을 유발한다고 제안했습니다. 이 금형의 용융 흐름 시뮬레이션(Flow-3D 소프트웨어)은 연행 현상에 관한 Reilly의 모델 [44] 을 사용하여 최종 주조에 많은 양의 이중막이 포함될 것이라고 예측했습니다( 그림 1 에서 검은색 입자로 표시됨) . NS).

그림 1

수축 결함은 또한 주물의 기계적 특성과 재현성에 영향을 미칩니다. 이 연구는 주조 품질에 대한 이중 필름의 영향에 초점을 맞추었기 때문에 수축 결함이 발생하지 않도록 금형을 의도적으로 설계했습니다. ProCAST 소프트웨어를 사용한 응고 시뮬레이션은 그림 1c 와 같이 최종 주조에 수축 결함이 포함되지 않음을 보여주었습니다 . 캐스팅 건전함도 테스트바 가공 전 실시간 X-ray를 통해 확인했다.

모래 주형은 1wt를 함유한 수지 결합된 규사로 만들어졌습니다. % PEPSET 5230 수지 및 1wt. % PEPSET 5112 촉매. 모래는 또한 억제제로 작용하기 위해 2중량%의 Na 2 SiF 6 을 함유했습니다 .. 주입 온도는 700 ± 5 °C였습니다. 응고 후 러너바의 단면을 Sci-Lab Analytical Ltd로 보내 H 함량 분석(LECO 분석)을 하였고, 모든 H 함량 측정은 주조 공정 후 5일째에 실시하였다. 각각의 주물은 인장 강도 시험을 위해 클립 신장계가 있는 Zwick 1484 인장 시험기를 사용하여 40개의 시험 막대로 가공되었습니다. 파손된 시험봉의 파단면을 주사전자현미경(SEM, Philips JEOL7000)을 이용하여 가속전압 5~15kV로 조사하였다. 파손된 시험 막대, 도가니에서 응고된 잔류 Mg 합금 및 주조 러너를 동일한 SEM을 사용하여 단면화하고 연마하고 검사했습니다. CFEI Quanta 3D FEG FIB-SEM을 사용하여 FIB(집속 이온 빔 밀링 기술)에 의해 테스트 막대 파괴 표면에서 발견된 산화막의 단면을 노출했습니다. 분석에 필요한 산화막은 백금층으로 코팅하였다. 그런 다음 30kV로 가속된 갈륨 이온 빔이 산화막의 단면을 노출시키기 위해 백금 코팅 영역을 둘러싼 재료 기판을 밀링했습니다. 산화막 단면의 EDS 분석은 30kV의 가속 전압에서 FIB 장비를 사용하여 수행되었습니다.

2.2 . 산화 세포

전술 한 바와 같이, 몇몇 최근 연구자들은 마그네슘 합금의 용탕 표면에 형성된 보호막 조사 [38 , 39 , [46] , [47] , [48] , [49] , [50] , [51] , [52 ] . 이 실험 동안 사용된 커버 가스의 양이 충분하여 커버 가스에서 불화물의 고갈을 억제했습니다. 이 섹션에서 설명하는 실험은 엔트레인먼트 결함의 산화막의 진화를 연구하기 위해 커버 가스의 공급을 제한하는 밀봉된 산화 셀을 사용했습니다. 산화 셀에 포함된 커버 가스는 큰 크기의 “동반된 기포”로 간주되었습니다.

도 2에 도시된 바와 같이 , 산화셀의 본체는 내부 길이가 400mm, 내경이 32mm인 폐쇄형 연강관이었다. 수냉식 동관을 전지의 상부에 감았습니다. 튜브가 가열될 때 냉각 시스템은 상부와 하부 사이에 온도 차이를 만들어 내부 가스가 튜브 내에서 대류하도록 했습니다. 온도는 도가니 상단에 위치한 K형 열전대로 모니터링했습니다. Nieet al. [53] 은 Mg 합금 용융물의 표면 피막을 조사할 때 SF 6 커버 가스가 유지로의 강철 벽과 반응할 것이라고 제안했습니다 . 이 반응을 피하기 위해 강철 산화 전지의 내부 표면(그림 2 참조)) 및 열전대의 상반부는 질화붕소로 코팅되었습니다(Mg 합금은 질화붕소와 ​​접촉하지 않았습니다).

그림 2

실험 중에 고체 AZ91 합금 블록을 산화 셀 바닥에 위치한 마그네시아 도가니에 넣었습니다. 전지는 1L/min의 가스 유속으로 전기 저항로에서 100℃로 가열되었다. 원래의 갇힌 대기(즉, 공기)를 대체하기 위해 셀을 이 온도에서 20분 동안 유지했습니다. 그런 다음, 산화 셀을 700°C로 더 가열하여 AZ91 샘플을 녹였습니다. 그런 다음 가스 입구 및 출구 밸브가 닫혀 제한된 커버 가스 공급 하에서 산화를 위한 밀폐된 환경이 생성되었습니다. 그런 다음 산화 전지를 5분 간격으로 5분에서 30분 동안 700 ± 10°C에서 유지했습니다. 각 유지 시간이 끝날 때 세포를 물로 켄칭했습니다. 실온으로 냉각한 후 산화된 샘플을 절단하고 연마한 다음 SEM으로 검사했습니다.

3 . 결과

3.1 . SF 6 /air 에서 형성된 엔트레인먼트 결함의 구조 및 구성

0.5 % SF의 커버 가스 하에서 AZ91 주물에 형성된 유입 결함의 구조 및 조성 6 / 공기는 SEM 및 EDS에 의해 관찰되었다. 결과는 그림 3에 스케치된 엔트레인먼트 결함의 두 가지 유형이 있음을 나타냅니다 . (1) 산화막이 전통적인 단층 구조를 갖는 유형 A 결함 및 (2) 산화막이 2개 층을 갖는 유형 B 결함. 이러한 결함의 세부 사항은 다음에 소개되었습니다. 여기에서 비말동반 결함은 생물막 또는 이중 산화막으로도 알려져 있기 때문에 B형 결함의 산화막은 본 연구에서 “다층 산화막” 또는 “다층 구조”로 언급되었습니다. “이중 산화막 결함의 이중층 산화막”과 같은 혼란스러운 설명을 피하기 위해.

그림 3

그림 4 (ab)는 약 0.4μm 두께의 조밀한 단일층 산화막을 갖는 Type A 결함을 보여줍니다. 이 필름에서 산소, 불소, 마그네슘 및 알루미늄이 검출되었습니다( 그림 4c). 산화막은 마그네슘과 알루미늄의 산화물과 불화물의 혼합물로 추측됩니다. 불소의 검출은 동반된 커버 가스가 이 결함의 형성에 포함되어 있음을 보여주었습니다. 즉, Fig. 4 (a)에 나타난 기공 은 수축결함이나 수소기공도가 아니라 연행결함이었다. 알루미늄의 검출은 Xiong과 Wang의 이전 연구 [47 , 48] 와 다르며 , SF 6으로 보호된 AZ91 용융물의 표면 필름에 알루미늄이 포함되어 있지 않음을 보여주었습니다.커버 가스. 유황은 원소 맵에서 명확하게 인식할 수 없었지만 해당 ESD 스펙트럼에서 S-피크가 있었습니다.

그림 4

도 5 (ab)는 다층 산화막을 갖는 Type B 엔트레인먼트 결함을 나타낸다. 산화막의 조밀한 외부 층은 불소와 산소가 풍부하지만( 그림 5c) 상대적으로 다공성인 내부 층은 산소만 풍부하고(즉, 불소가 부족) 부분적으로 함께 성장하여 샌드위치 모양을 형성합니다. 구조. 따라서 외층은 불화물과 산화물의 혼합물이며 내층은 주로 산화물로 추정된다. 황은 EDX 스펙트럼에서만 인식될 수 있었고 요소 맵에서 명확하게 식별할 수 없었습니다. 이는 커버 가스의 작은 S 함량(즉, SF 6 의 0.5% 부피 함량 때문일 수 있음)커버 가스). 이 산화막에서는 이 산화막의 외층에 알루미늄이 포함되어 있지만 내층에서는 명확하게 검출할 수 없었다. 또한 Al의 분포가 고르지 않은 것으로 보입니다. 결함의 우측에는 필름에 알루미늄이 존재하지만 그 농도는 매트릭스보다 높은 것으로 식별할 수 없음을 알 수 있다. 그러나 결함의 왼쪽에는 알루미늄 농도가 훨씬 높은 작은 영역이 있습니다. 이러한 알루미늄의 불균일한 분포는 다른 결함(아래 참조)에서도 관찰되었으며, 이는 필름 내부 또는 아래에 일부 산화물 입자가 형성된 결과입니다.

그림 5

무화과 도 4 및 5 는 SF 6 /air 의 커버 가스 하에 주조된 AZ91 합금 샘플에서 형성된 연행 결함의 횡단면 관찰을 나타낸다 . 2차원 단면에서 관찰된 수치만으로 연행 결함을 특성화하는 것만으로는 충분하지 않습니다. 더 많은 이해를 돕기 위해 테스트 바의 파단면을 관찰하여 엔트레인먼트 결함(즉, 산화막)의 표면을 더 연구했습니다.

Fig. 6 (a)는 SF 6 /air 에서 생산된 AZ91 합금 인장시험봉의 파단면을 보여준다 . 파단면의 양쪽에서 대칭적인 어두운 영역을 볼 수 있습니다. 그림 6 (b)는 어두운 영역과 밝은 영역 사이의 경계를 보여줍니다. 밝은 영역은 들쭉날쭉하고 부서진 특징으로 구성되어 있는 반면, 어두운 영역의 표면은 비교적 매끄럽고 평평했습니다. 또한 EDS 결과( Fig. 6 c-d 및 Table 2) 불소, 산소, 황 및 질소는 어두운 영역에서만 검출되었으며, 이는 어두운 영역이 용융물에 동반된 표면 보호 필름임을 나타냅니다. 따라서 어두운 영역은 대칭적인 특성을 고려할 때 연행 결함이라고 제안할 수 있습니다. Al-합금 주조물의 파단면에서 유사한 결함이 이전에 보고되었습니다 [7] . 질화물은 테스트 바 파단면의 산화막에서만 발견되었지만 그림 1과 그림 4에 표시된 단면 샘플에서는 검출되지 않았습니다 4 및 5 . 근본적인 이유는 이러한 샘플에 포함된 질화물이 샘플 연마 과정에서 가수분해되었을 수 있기 때문입니다 [54] .

그림 6

표 2 . EDS 결과(wt.%)는 그림 6에 표시된 영역에 해당합니다 (커버 가스: SF 6 /공기).

영형마그네슘NS아연NSNS
그림 6 (b)의 어두운 영역3.481.3279.130.4713.630.570.080.73
그림 6 (b)의 밝은 영역3.5884.4811.250.68

도 1 및 도 2에 도시된 결함의 단면 관찰과 함께 도 4 및 도 5 를 참조하면, 인장 시험봉에 포함된 연행 결함의 구조를 도 6 (e) 와 같이 스케치하였다 . 결함에는 산화막으로 둘러싸인 동반된 가스가 포함되어 있어 테스트 바 내부에 보이드 섹션이 생성되었습니다. 파괴 과정에서 결함에 인장력이 가해지면 균열이 가장 약한 경로를 따라 전파되기 때문에 보이드 섹션에서 균열이 시작되어 연행 결함을 따라 전파됩니다 [55] . 따라서 최종적으로 시험봉이 파단되었을 때 Fig. 6 (a) 와 같이 시험봉의 양 파단면에 연행결함의 산화피막이 나타났다 .

3.2 . SF 6 /CO 2 에 형성된 연행 결함의 구조 및 조성

SF 6 /air 에서 형성된 엔트레인먼트 결함과 유사하게, 0.5% SF 6 /CO 2 의 커버 가스 아래에서 형성된 결함 도 두 가지 유형의 산화막(즉, 단층 및 다층 유형)을 가졌다. 도 7 (a)는 다층 산화막을 포함하는 엔트레인먼트 결함의 예를 도시한다. 결함에 대한 확대 관찰( 그림 7b )은 산화막의 내부 층이 함께 성장하여 SF 6 /air 의 분위기에서 형성된 결함과 유사한 샌드위치 같은 구조를 나타냄을 보여줍니다 ( 그림 7b). 5 나 ). EDS 스펙트럼( 그림 7c) 이 샌드위치형 구조의 접합부(내층)는 주로 산화마그네슘을 함유하고 있음을 보여주었다. 이 EDS 스펙트럼에서는 불소, 황, 알루미늄의 피크가 확인되었으나 그 양은 상대적으로 적었다. 대조적으로, 산화막의 외부 층은 조밀하고 불화물과 산화물의 혼합물로 구성되어 있습니다( 그림 7d-e).

그림 7

Fig. 8 (a)는 0.5%SF 6 /CO 2 분위기에서 제작된 AZ91 합금 인장시험봉의 파단면의 연행결함을 보여준다 . 상응하는 EDS 결과(표 3)는 산화막이 불화물과 산화물을 함유함을 보여주었다. 황과 질소는 검출되지 않았습니다. 게다가, 확대 관찰(  8b)은 산화막 표면에 반점을 나타내었다. 반점의 직경은 수백 나노미터에서 수 마이크론 미터까지 다양했습니다.

그림 8

산화막의 구조와 조성을 보다 명확하게 나타내기 위해 테스트 바 파단면의 산화막 단면을 FIB 기법을 사용하여 현장에서 노출시켰다( 그림 9 ). 도 9a에 도시된 바와 같이 , 백금 코팅층과 Mg-Al 합금 기재 사이에 연속적인 산화피막이 발견되었다. 그림 9 (bc)는 다층 구조( 그림 9c 에서 빨간색 상자로 표시)를 나타내는 산화막에 대한 확대 관찰을 보여줍니다 . 바닥층은 불소와 산소가 풍부하고 불소와 산화물의 혼합물이어야 합니다 . 5 와 7, 유일한 산소가 풍부한 최상층은 도 1 및 도 2에 도시 된 “내층”과 유사하였다 5 및 7 .

그림 9

연속 필름을 제외하고 도 9 에 도시된 바와 같이 연속 필름 내부 또는 하부에서도 일부 개별 입자가 관찰되었다 . 그림 9( b) 의 산화막 좌측에서 Al이 풍부한 입자가 검출되었으며, 마그네슘과 산소 원소도 풍부하게 함유하고 있어 스피넬 Mg 2 AlO 4 로 추측할 수 있다 . 이러한 Mg 2 AlO 4 입자의 존재는 Fig. 5 와 같이 관찰된 필름의 작은 영역에 높은 알루미늄 농도와 알루미늄의 불균일한 분포의 원인이 된다 .(씨). 여기서 강조되어야 할 것은 연속 산화막의 바닥층의 다른 부분이 이 Al이 풍부한 입자보다 적은 양의 알루미늄을 함유하고 있지만, 그림 9c는 이 바닥층의 알루미늄 양이 여전히 무시할 수 없는 수준임을 나타냅니다 . , 특히 필름의 외층과 비교할 때. 도 9b에 도시된 산화막의 우측 아래에서 입자가 검출되어 Mg와 O가 풍부하여 MgO인 것으로 추측되었다. Wang의 결과에 따르면 [56], Mg 용융물과 Mg 증기의 산화에 의해 Mg 용융물의 표면에 많은 이산 MgO 입자가 형성될 수 있다. 우리의 현재 연구에서 관찰된 MgO 입자는 같은 이유로 인해 형성될 수 있습니다. 실험 조건의 차이로 인해 더 적은 Mg 용융물이 기화되거나 O2와 반응할 수 있으므로 우리 작업에서 형성되는 MgO 입자는 소수에 불과합니다. 또한 필름에서 풍부한 탄소가 발견되어 CO 2 가 용융물과 반응하여 탄소 또는 탄화물을 형성할 수 있음을 보여줍니다 . 이 탄소 농도는 표 3에 나타낸 산화막의 상대적으로 높은 탄소 함량 (즉, 어두운 영역) 과 일치하였다 . 산화막 옆 영역.

표 3 . 도 8에 도시된 영역에 상응하는 EDS 결과(wt.%) (커버 가스: SF 6 / CO 2 ).

영형마그네슘NS아연NSNS
그림 8 (a)의 어두운 영역7.253.6469.823.827.030.86
그림 8 (a)의 밝은 영역2.100.4482.8313.261.36

테스트 바 파단면( 도 9 ) 에서 산화막의 이 단면 관찰은 도 6 (e)에 도시된 엔트레인먼트 결함의 개략도를 추가로 확인했다 . SF 6 /CO 2 와 SF 6 /air 의 서로 다른 분위기에서 형성된 엔트레인먼트 결함 은 유사한 구조를 가졌지만 그 조성은 달랐다.

3.3 . 산화 전지에서 산화막의 진화

섹션 3.1 및 3.2 의 결과 는 SF 6 /air 및 SF 6 /CO 2 의 커버 가스 아래에서 AZ91 주조에서 형성된 연행 결함의 구조 및 구성을 보여줍니다 . 산화 반응의 다른 단계는 연행 결함의 다른 구조와 조성으로 이어질 수 있습니다. Campbell은 동반된 가스가 주변 용융물과 반응할 수 있다고 추측했지만 Mg 합금 용융물과 포획된 커버 가스 사이에 반응이 발생했다는 보고는 거의 없습니다. 이전 연구자들은 일반적으로 개방된 환경에서 Mg 합금 용융물과 커버 가스 사이의 반응에 초점을 맞췄습니다 [38 , 39 , [46] , [47][48] , [49] , [50] , [51] , [52] , 이는 용융물에 갇힌 커버 가스의 상황과 다릅니다. AZ91 합금에서 엔트레인먼트 결함의 형성을 더 이해하기 위해 엔트레인먼트 결함의 산화막의 진화 과정을 산화 셀을 사용하여 추가로 연구했습니다.

.도 10 (a 및 d) 0.5 % 방송 SF 보호 산화 셀에서 5 분 동안 유지 된 표면 막 (6) / 공기. 불화물과 산화물(MgF 2 와 MgO) 로 이루어진 단 하나의 층이 있었습니다 . 이 표면 필름에서. 황은 EDS 스펙트럼에서 검출되었지만 그 양이 너무 적어 원소 맵에서 인식되지 않았습니다. 이 산화막의 구조 및 조성은 도 4 에 나타낸 엔트레인먼트 결함의 단층막과 유사하였다 .

그림 10

10분의 유지 시간 후, 얇은 (O,S)가 풍부한 상부층(약 700nm)이 예비 F-농축 필름에 나타나 그림 10 (b 및 e) 에서와 같이 다층 구조를 형성했습니다 . ). (O, S)가 풍부한 최상층의 두께는 유지 시간이 증가함에 따라 증가했습니다. Fig. 10 (c, f) 에서 보는 바와 같이 30분간 유지한 산화막도 다층구조를 가지고 있으나 (O,S)가 풍부한 최상층(약 2.5μm)의 두께가 10분 산화막의 그것. 도 10 (bc) 에 도시 된 다층 산화막 은 도 5에 도시된 샌드위치형 결함의 막과 유사한 외관을 나타냈다 .

도 10에 도시된 산화막의 상이한 구조는 커버 가스의 불화물이 AZ91 합금 용융물과의 반응으로 인해 우선적으로 소모될 것임을 나타내었다. 불화물이 고갈된 후, 잔류 커버 가스는 액체 AZ91 합금과 추가로 반응하여 산화막에 상부 (O, S)가 풍부한 층을 형성했습니다. 따라서 도 1 및 도 3에 도시된 연행 결함의 상이한 구조 및 조성 4 와 5 는 용융물과 갇힌 커버 가스 사이의 진행 중인 산화 반응 때문일 수 있습니다.

이 다층 구조는 Mg 합금 용융물에 형성된 보호 표면 필름에 관한 이전 간행물 [38 , [46] , [47] , [48] , [49] , [50] , [51] 에서 보고되지 않았습니다 . . 이는 이전 연구원들이 무제한의 커버 가스로 실험을 수행했기 때문에 커버 가스의 불화물이 고갈되지 않는 상황을 만들었기 때문일 수 있습니다. 따라서 엔트레인먼트 결함의 산화피막은 도 10에 도시된 산화피막과 유사한 거동특성을 가지나 [38 ,[46] , [47] , [48] , [49] , [50] , [51] .

SF 유지 산화막와 마찬가지로 6 / 공기, SF에 형성된 산화물 막 (6) / CO 2는 또한 세포 산화 다른 유지 시간과 다른 구조를 가지고 있었다. .도 11 (a)는 AZ91 개최 산화막, 0.5 %의 커버 가스 하에서 SF 표면 용융 도시 6 / CO 2, 5 분. 이 필름은 MgF 2 로 이루어진 단층 구조를 가졌다 . 이 영화에서는 MgO의 존재를 확인할 수 없었다. 30분의 유지 시간 후, 필름은 다층 구조를 가졌다; 내부 층은 조밀하고 균일한 외관을 가지며 MgF 2 로 구성 되고 외부 층은 MgF 2 혼합물및 MgO. 0.5%SF 6 /air 에서 형성된 표면막과 다른 이 막에서는 황이 검출되지 않았다 . 따라서, 0.5%SF 6 /CO 2 의 커버 가스 내의 불화물 도 막 성장 과정의 초기 단계에서 우선적으로 소모되었다. SF 6 /air 에서 형성된 막과 비교하여 SF 6 /CO 2 에서 형성된 막에서 MgO 는 나중에 나타났고 황화물은 30분 이내에 나타나지 않았다. 이는 SF 6 /air 에서 필름의 형성과 진화 가 SF 6 /CO 2 보다 빠르다 는 것을 의미할 수 있습니다 . CO 2 후속적으로 용융물과 반응하여 MgO를 형성하는 반면, 황 함유 화합물은 커버 가스에 축적되어 반응하여 매우 늦은 단계에서 황화물을 형성할 수 있습니다(산화 셀에서 30분 후).

그림 11

4 . 논의

4.1 . SF 6 /air 에서 형성된 연행 결함의 진화

Outokumpu HSC Chemistry for Windows( http://www.hsc-chemistry.net/ )의 HSC 소프트웨어를 사용하여 갇힌 기체와 액체 AZ91 합금 사이에서 발생할 수 있는 반응을 탐색하는 데 필요한 열역학 계산을 수행했습니다. 계산에 대한 솔루션은 소량의 커버 가스(즉, 갇힌 기포 내의 양)와 AZ91 합금 용융물 사이의 반응 과정에서 어떤 생성물이 가장 형성될 가능성이 있는지 제안합니다.

실험에서 압력은 1기압으로, 온도는 700°C로 설정했습니다. 커버 가스의 사용량은 7 × 10으로 가정 하였다 -7  약 0.57 cm의 양으로 kg 3 (3.14 × 10 -6  0.5 % SF위한 kmol) 6 / 공기, 0.35 cm (3) (3.12 × 10 – 8  kmol) 0.5%SF 6 /CO 2 . 포획된 가스와 접촉하는 AZ91 합금 용융물의 양은 모든 반응을 완료하기에 충분한 것으로 가정되었습니다. SF 6 의 분해 생성물 은 SF 5 , SF 4 , SF 3 , SF 2 , F 2 , S(g), S 2(g) 및 F(g) [57] , [58] , [59] , [60] .

그림 12 는 AZ91 합금과 0.5%SF 6 /air 사이의 반응에 대한 열역학적 계산의 평형 다이어그램을 보여줍니다 . 다이어그램에서 10 -15  kmol 미만의 반응물 및 생성물은 표시되지 않았습니다. 이는 존재 하는 SF 6 의 양 (≈ 1.57 × 10 -10  kmol) 보다 5배 적 으므로 영향을 미치지 않습니다. 실제적인 방법으로 과정을 관찰했습니다.

그림 12

이 반응 과정은 3단계로 나눌 수 있다.

1단계 : 불화물의 형성. AZ91 용융물은 SF 6 및 그 분해 생성물과 우선적으로 반응하여 MgF 2 , AlF 3 및 ZnF 2 를 생성 합니다. 그러나 ZnF 2 의 양 이 너무 적어서 실제적으로 검출되지  않았을 수 있습니다(  MgF 2 의 3 × 10 -10 kmol에 비해 ZnF 2 1.25 × 10 -12 kmol ). 섹션 3.1 – 3.3에 표시된 모든 산화막 . 한편, 잔류 가스에 황이 SO 2 로 축적되었다 .

2단계 : 산화물의 형성. 액체 AZ91 합금이 포획된 가스에서 사용 가능한 모든 불화물을 고갈시킨 후, Mg와의 반응으로 인해 AlF 3 및 ZnF 2 의 양이 빠르게 감소했습니다. O 2 (g) 및 SO 2 는 AZ91 용융물과 반응하여 MgO, Al 2 O 3 , MgAl 2 O 4 , ZnO, ZnSO 4 및 MgSO 4 를 형성 합니다. 그러나 ZnO 및 ZnSO 4 의 양은 EDS에 의해 실제로 발견되기에는 너무 적었을 것입니다(예: 9.5 × 10 -12  kmol의 ZnO, 1.38 × 10 -14  kmol의 ZnSO 4 , 대조적으로 4.68 × 10−10  kmol의 MgF 2 , X 축의 AZ91 양 이 2.5 × 10 -9  kmol일 때). 실험 사례에서 커버 가스의 F 농도는 매우 낮고 전체 농도 f O는 훨씬 높습니다. 따라서 1단계와 2단계, 즉 불화물과 산화물의 형성은 반응 초기에 동시에 일어나 그림 1과 2와 같이 불화물과 산화물의 가수층 혼합물이 형성될 수 있다 . 4 및 10 (a). 내부 층은 산화물로 구성되어 있지만 불화물은 커버 가스에서 F 원소가 완전히 고갈된 후에 형성될 수 있습니다.

단계 1-2는 도 10 에 도시 된 다층 구조의 형성 과정을 이론적으로 검증하였다 .

산화막 내의 MgAl 2 O 4 및 Al 2 O 3 의 양은 도 4에 도시된 산화막과 일치하는 검출하기에 충분한 양이었다 . 그러나, 도 10 에 도시된 바와 같이, 산화셀에서 성장된 산화막에서는 알루미늄의 존재를 인식할 수 없었다 . 이러한 Al의 부재는 표면 필름과 AZ91 합금 용융물 사이의 다음 반응으로 인한 것일 수 있습니다.(1)

Al 2 O 3  + 3Mg + = 3MgO + 2Al, △G(700°C) = -119.82 kJ/mol(2)

Mg + MgAl 2 O 4  = MgO + Al, △G(700°C) = -106.34 kJ/mol이는 반응물이 서로 완전히 접촉한다는 가정 하에 열역학적 계산이 수행되었기 때문에 HSC 소프트웨어로 시뮬레이션할 수 없었습니다. 그러나 실제 공정에서 AZ91 용융물과 커버 가스는 보호 표면 필름의 존재로 인해 서로 완전히 접촉할 수 없습니다.

3단계 : 황화물과 질화물의 형성. 30분의 유지 시간 후, 산화 셀의 기상 불화물 및 산화물이 고갈되어 잔류 가스와 용융 반응을 허용하여 초기 F-농축 또는 (F, O )이 풍부한 표면 필름, 따라서 그림 10 (b 및 c)에 표시된 관찰된 다층 구조를 생성합니다 . 게다가, 질소는 모든 반응이 완료될 때까지 AZ91 용융물과 반응했습니다. 도 6 에 도시 된 산화막 은 질화물 함량으로 인해 이 반응 단계에 해당할 수 있다. 그러나, 그 결과는 도 1 및 도 5에 도시 된 연마된 샘플에서 질화물이 검출되지 않음을 보여준다. 4 와 5, 그러나 테스트 바 파단면에서만 발견됩니다. 질화물은 다음과 같이 샘플 준비 과정에서 가수분해될 수 있습니다 [54] .(삼)

Mg 3 N 2  + 6H 2 O = 3Mg(OH) 2  + 2NH 3 ↑(4)

AlN+ 3H 2 O = Al(OH) 3  + NH 3 ↑

또한 Schmidt et al. [61] 은 Mg 3 N 2 와 AlN이 반응하여 3원 질화물(Mg 3 Al n N n+2, n=1, 2, 3…) 을 형성할 수 있음을 발견했습니다 . HSC 소프트웨어에는 삼원 질화물 데이터베이스가 포함되어 있지 않아 계산에 추가할 수 없습니다. 이 단계의 산화막은 또한 삼원 질화물을 포함할 수 있습니다.

4.2 . SF 6 /CO 2 에서 형성된 연행 결함의 진화

도 13 은 AZ91 합금과 0.5%SF 6 /CO 2 사이의 열역학적 계산 결과를 보여준다 . 이 반응 과정도 세 단계로 나눌 수 있습니다.

그림 13

1단계 : 불화물의 형성. SF 6 및 그 분해 생성물은 AZ91 용융물에 의해 소비되어 MgF 2 , AlF 3 및 ZnF 2 를 형성했습니다 . 0.5% SF 6 /air 에서 AZ91의 반응에서와 같이 ZnF 2 의 양 이 너무 작아서 실제적으로 감지되지  않았습니다( 2.67 x 10 -10  kmol의 MgF 2 에 비해 ZnF 2 1.51 x 10 -13 kmol ). S와 같은 잔류 가스 트랩에 축적 유황 2 (g) 및 (S)의 일부분 (2) (g)가 CO와 반응하여 2 SO 형성하는 2및 CO. 이 반응 단계의 생성물은 도 11 (a)에 도시된 필름과 일치하며 , 이는 불화물만을 함유하는 단일 층 구조를 갖는다.

2단계 : 산화물의 형성. ALF 3 및 ZnF 2 MgF로 형성 용융 AZ91 마그네슘의 반응 2 , Al 및 Zn으로한다. SO 2 는 소모되기 시작하여 표면 필름에 산화물을 생성 하고 커버 가스에 S 2 (g)를 생성했습니다. 한편, CO 2 는 AZ91 용융물과 직접 반응하여 CO, MgO, ZnO 및 Al 2 O 3 를 형성 합니다. 도 1에 도시 된 산화막 9 및 11 (b)는 산소가 풍부한 층과 다층 구조로 인해 이 반응 단계에 해당할 수 있습니다.

커버 가스의 CO는 AZ91 용융물과 추가로 반응하여 C를 생성할 수 있습니다. 이 탄소는 온도가 감소할 때(응고 기간 동안) Mg와 추가로 반응하여 Mg 탄화물을 형성할 수 있습니다 [62] . 이것은 도 4에 도시된 산화막의 탄소 함량이 높은 이유일 수 있다 8 – 9 . Liang et al. [39] 또한 SO 2 /CO 2 로 보호된 AZ91 합금 표면 필름에서 탄소 검출을 보고했습니다 . 생성된 Al 2 O 3 는 MgO와 더 결합하여 MgAl 2 O [63]를 형성할 수 있습니다 . 섹션 4.1 에서 논의된 바와 같이, 알루미나 및 스피넬은 도 11 에 도시된 바와 같이 표면 필름에 알루미늄 부재를 야기하는 Mg와 반응할 수 있다 .

3단계 : 황화물의 형성. AZ91은 용융물 S 소비하기 시작 2 인 ZnS와 MGS 형성 갇힌 잔류 가스 (g)를. 이러한 반응은 반응 과정의 마지막 단계까지 일어나지 않았으며, 이는 Fig. 7 (c)에 나타난 결함의 S-함량 이 적은 이유일 수 있다 .

요약하면, 열역학적 계산은 AZ91 용융물이 커버 가스와 반응하여 먼저 불화물을 형성한 다음 마지막에 산화물과 황화물을 형성할 것임을 나타냅니다. 다른 반응 단계에서 산화막은 다른 구조와 조성을 가질 것입니다.

4.3 . 운반 가스가 동반 가스 소비 및 AZ91 주물의 재현성에 미치는 영향

SF 6 /air 및 SF 6 /CO 2 에서 형성된 연행 결함의 진화 과정은 4.1절 과 4.2  에서 제안되었습니다 . 이론적인 계산은 실제 샘플에서 발견되는 해당 산화막과 관련하여 검증되었습니다. 연행 결함 내의 대기는 Al-합금 시스템과 다른 시나리오에서 액체 Mg-합금과의 반응으로 인해 효율적으로 소모될 수 있습니다(즉, 연행된 기포의 질소가 Al-합금 용융물과 효율적으로 반응하지 않을 것입니다 [64 , 65] 그러나 일반적으로 “질소 연소”라고 하는 액체 Mg 합금에서 질소가 더 쉽게 소모될 것입니다 [66] ).

동반된 가스와 주변 액체 Mg-합금 사이의 반응은 동반된 가스를 산화막 내에서 고체 화합물(예: MgO)로 전환하여 동반 결함의 공극 부피를 감소시켜 결함(예: 공기의 동반된 가스가 주변의 액체 Mg 합금에 의해 고갈되면 용융 온도가 700 °C이고 액체 Mg 합금의 깊이가 10 cm라고 가정할 때 최종 고체 제품의 총 부피는 0.044가 됩니다. 갇힌 공기가 취한 초기 부피의 %).

연행 결함의 보이드 부피 감소와 해당 주조 특성 사이의 관계는 알루미늄 합금 주조에서 널리 연구되었습니다. Nyahumwa와 Campbell [16] 은 HIP(Hot Isostatic Pressing) 공정이 Al-합금 주물의 연행 결함이 붕괴되고 산화물 표면이 접촉하게 되었다고 보고했습니다. 주물의 피로 수명은 HIP 이후 개선되었습니다. Nyahumwa와 Campbell [16] 도 서로 접촉하고 있는 이중 산화막의 잠재적인 결합을 제안했지만 이를 뒷받침하는 직접적인 증거는 없었습니다. 이 결합 현상은 Aryafar et.al에 의해 추가로 조사되었습니다. [8], 그는 강철 튜브에서 산화물 스킨이 있는 두 개의 Al-합금 막대를 다시 녹인 다음 응고된 샘플에 대해 인장 강도 테스트를 수행했습니다. 그들은 Al-합금 봉의 산화물 스킨이 서로 강하게 결합되어 용융 유지 시간이 연장됨에 따라 더욱 강해짐을 발견했으며, 이는 이중 산화막 내 동반된 가스의 소비로 인한 잠재적인 “치유” 현상을 나타냅니다. 구조. 또한 Raidszadeh와 Griffiths [9 , 19] 는 연행 가스가 반응하는 데 더 긴 시간을 갖도록 함으로써 응고 전 용융 유지 시간을 연장함으로써 Al-합금 주물의 재현성에 대한 연행 결함의 부정적인 영향을 성공적으로 줄였습니다. 주변이 녹습니다.

앞서 언급한 연구를 고려할 때, Mg 합금 주물에서 혼입 가스의 소비는 다음 두 가지 방식으로 혼입 결함의 부정적인 영향을 감소시킬 수 있습니다.

(1) 이중 산화막의 결합 현상 . 도 5 및 도 7 에 도시 된 샌드위치형 구조 는 이중 산화막 구조의 잠재적인 결합을 나타내었다. 그러나 산화막의 결합으로 인한 강도 증가를 정량화하기 위해서는 더 많은 증거가 필요합니다.

(2) 연행 결함의 보이드 체적 감소 . 주조품의 품질에 대한 보이드 부피 감소의 긍정적인 효과는 HIP 프로세스 [67]에 의해 널리 입증되었습니다 . 섹션 4.1 – 4.2 에서 논의된 진화 과정과 같이 , 동반된 가스와 주변 AZ91 합금 용융물 사이의 지속적인 반응으로 인해 동반 결함의 산화막이 함께 성장할 수 있습니다. 최종 고체 생성물의 부피는 동반된 기체에 비해 상당히 작았다(즉, 이전에 언급된 바와 같이 0.044%).

따라서, 혼입 가스의 소모율(즉, 산화막의 성장 속도)은 AZ91 합금 주물의 품질을 향상시키는 중요한 매개변수가 될 수 있습니다. 이에 따라 산화 셀의 산화막 성장 속도를 추가로 조사했습니다.

도 14 는 상이한 커버 가스(즉, 0.5%SF 6 /air 및 0.5%SF 6 /CO 2 ) 에서의 표면 필름 성장 속도의 비교를 보여준다 . 필름 두께 측정을 위해 각 샘플의 15개의 임의 지점을 선택했습니다. 95% 신뢰구간(95%CI)은 막두께의 변화가 가우시안 분포를 따른다는 가정하에 계산하였다. 0.5%SF 6 /air 에서 형성된 모든 표면막이 0.5%SF 6 /CO 2 에서 형성된 것보다 빠르게 성장함을 알 수 있다 . 다른 성장률은 0.5%SF 6 /air 의 연행 가스 소비율 이 0.5%SF 6 /CO 2 보다 더 높음 을 시사했습니다., 이는 동반된 가스의 소비에 더 유리했습니다.

그림 14

산화 셀에서 액체 AZ91 합금과 커버 가스의 접촉 면적(즉, 도가니의 크기)은 많은 양의 용융물과 가스를 고려할 때 상대적으로 작았다는 점에 유의해야 합니다. 결과적으로, 산화 셀 내에서 산화막 성장을 위한 유지 시간은 비교적 길었다(즉, 5-30분). 하지만, 실제 주조에 함유 된 혼입 결함은 (상대적으로 매우 적은, 즉, 수 미크론의 크기에 도시 된 바와 같이 ,도 3. – 6 및 [7]), 동반된 가스는 주변 용융물로 완전히 둘러싸여 상대적으로 큰 접촉 영역을 생성합니다. 따라서 커버 가스와 AZ91 합금 용융물의 반응 시간은 비교적 짧을 수 있습니다. 또한 실제 Mg 합금 모래 주조의 응고 시간은 몇 분일 수 있습니다(예: Guo [68] 은 직경 60mm의 Mg 합금 모래 주조가 응고되는 데 4분이 필요하다고 보고했습니다). 따라서 Mg-합금 용융주조 과정에서 포획된 동반된 가스는 특히 응고 시간이 긴 모래 주물 및 대형 주물의 경우 주변 용융물에 의해 쉽게 소모될 것으로 예상할 수 있습니다.

따라서, 동반 가스의 다른 소비율과 관련된 다른 커버 가스(0.5%SF 6 /air 및 0.5%SF 6 /CO 2 )가 최종 주물의 재현성에 영향을 미칠 수 있습니다. 이 가정을 검증하기 위해 0.5%SF 6 /air 및 0.5%SF 6 /CO 2 에서 생산된 AZ91 주물 을 기계적 평가를 위해 테스트 막대로 가공했습니다. Weibull 분석은 선형 최소 자승(LLS) 방법과 비선형 최소 자승(비 LLS) 방법을 모두 사용하여 수행되었습니다 [69] .

그림 15 (ab)는 LLS 방법으로 얻은 UTS 및 AZ91 합금 주물의 연신율의 전통적인 2-p 선형 Weibull 플롯을 보여줍니다. 사용된 추정기는 P= (i-0.5)/N이며, 이는 모든 인기 있는 추정기 중 가장 낮은 편향을 유발하는 것으로 제안되었습니다 [69 , 70] . SF 6 /air 에서 생산된 주물 은 UTS Weibull 계수가 16.9이고 연신율 Weibull 계수가 5.0입니다. 대조적으로, SF 6 /CO 2 에서 생산된 주물의 UTS 및 연신 Weibull 계수는 각각 7.7과 2.7로, SF 6 /CO 2 에 의해 보호된 주물의 재현성이 SF 6 /air 에서 생산된 것보다 훨씬 낮음을 시사합니다. .

그림 15

또한 저자의 이전 출판물 [69] 은 선형화된 Weibull 플롯의 단점을 보여주었으며, 이는 Weibull 추정 의 더 높은 편향과 잘못된 2 중단을 유발할 수 있습니다 . 따라서 그림 15 (cd) 와 같이 Non-LLS Weibull 추정이 수행되었습니다 . SF 6 /공기주조물 의 UTS Weibull 계수 는 20.8인 반면, SF 6 /CO 2 하에서 생산된 주조물의 UTS Weibull 계수는 11.4로 낮아 재현성에서 분명한 차이를 보였다. 또한 SF 6 /air elongation(El%) 데이터 세트는 SF 6 /CO 2 의 elongation 데이터 세트보다 더 높은 Weibull 계수(모양 = 5.8)를 가졌습니다.(모양 = 3.1). 따라서 LLS 및 Non-LLS 추정 모두 SF 6 /공기 주조가 SF 6 /CO 2 주조 보다 더 높은 재현성을 갖는다고 제안했습니다 . CO 2 대신 공기를 사용 하면 혼입된 가스의 더 빠른 소비에 기여하여 결함 내의 공극 부피를 줄일 수 있다는 방법을 지원합니다 . 따라서 0.5%SF 6 /CO 2 대신 0.5%SF 6 /air를 사용 하면(동반된 가스의 소비율이 증가함) AZ91 주물의 재현성이 향상되었습니다.

그러나 모든 Mg 합금 주조 공장이 현재 작업에서 사용되는 주조 공정을 따랐던 것은 아니라는 점에 유의해야 합니다. Mg의 합금 용탕 본 작업은 탈기에 따라서, 동반 가스의 소비에 수소의 영향을 감소 (즉, 수소 잠재적 동반 가스의 고갈 억제, 동반 된 기체로 확산 될 수있다 [7 , 71 , 72] ). 대조적으로, 마그네슘 합금 주조 공장에서는 마그네슘을 주조할 때 ‘가스 문제’가 없고 따라서 인장 특성에 큰 변화가 없다고 널리 믿어지기 때문에 마그네슘 합금 용융물은 일반적으로 탈기되지 않습니다 [73] . 연구에 따르면 Mg 합금 주물의 기계적 특성에 대한 수소의 부정적인 영향 [41 ,42 , 73] , 탈기 공정은 마그네슘 합금 주조 공장에서 여전히 인기가 없습니다.

또한 현재 작업에서 모래 주형 공동은 붓기 전에 SF 6 커버 가스 로 플러싱되었습니다 [22] . 그러나 모든 Mg 합금 주조 공장이 이러한 방식으로 금형 캐비티를 플러싱한 것은 아닙니다. 예를 들어, Stone Foundry Ltd(영국)는 커버 가스 플러싱 대신 유황 분말을 사용했습니다. 그들의 주물 내의 동반된 가스 는 보호 가스라기 보다는 SO 2 /공기일 수 있습니다 .

따라서 본 연구의 결과는 CO 2 대신 공기를 사용 하는 것이 최종 주조의 재현성을 향상시키는 것으로 나타났지만 다른 산업용 Mg 합금 주조 공정과 관련하여 캐리어 가스의 영향을 확인하기 위해서는 여전히 추가 조사가 필요합니다.

7 . 결론

1.

AZ91 합금에 형성된 연행 결함이 관찰되었습니다. 그들의 산화막은 단층과 다층의 두 가지 유형의 구조를 가지고 있습니다. 다층 산화막은 함께 성장하여 최종 주조에서 샌드위치 같은 구조를 형성할 수 있습니다.2.

실험 결과와 이론적인 열역학적 계산은 모두 갇힌 가스의 불화물이 황을 소비하기 전에 고갈되었음을 보여주었습니다. 이중 산화막 결함의 3단계 진화 과정이 제안되었습니다. 산화막은 진화 단계에 따라 다양한 화합물 조합을 포함했습니다. SF 6 /air 에서 형성된 결함 은 SF 6 /CO 2 에서 형성된 것과 유사한 구조를 갖지만 산화막의 조성은 달랐다. 엔트레인먼트 결함의 산화막 형성 및 진화 과정은 이전에 보고된 Mg 합금 표면막(즉, MgF 2 이전에 형성된 MgO)의 것과 달랐다 .삼.

산화막의 성장 속도는 SF하에 큰 것으로 입증되었다 (6) / SF보다 공기 6 / CO 2 손상 봉입 가스의 빠른 소비에 기여한다. AZ91 합금 주물의 재현성은 SF 6 /CO 2 대신 SF 6 /air를 사용할 때 향상되었습니다 .

감사의 말

저자는 EPSRC LiME 보조금 EP/H026177/1의 자금 지원 과 WD Griffiths 박사와 Adrian Carden(버밍엄 대학교)의 도움을 인정합니다. 주조 작업은 University of Birmingham에서 수행되었습니다.

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Fig. 5 Comparison of experimental SEM image and CtFD simulated melt pool with beam diameters of(a)700 μm,(b)1000 μm, and(c)1300 μm and an absorption rate of 0.3. Electron beam power and scan speed are 900 W and 100 mm s-1, respectively

추가 생산용 전자빔 조사에 의한 316L 스테인리스 용융 · 응고 거동

Melting and Solidification Behavior of 316L Steel Induced by Electron-Beam Irradiation for Additive Manufacturing

付加製造用電子ビーム照射による 316L ステンレス鋼の溶融・凝固挙動

奥 川 将 行*・宮 田 雄一朗*・王     雷*・能 勢 和 史*
小 泉 雄一郎*・中 野 貴 由*
Masayuki OKUGAWA, Yuichiro MIYATA, Lei WANG, Kazufumi NOSE,
Yuichiro KOIZUMI and Takayoshi NAKANO

Abstract

적층 제조(AM) 기술은 복잡한 형상의 3D 부품을 쉽게 만들고 미세 구조 제어를 통해 재료 특성을 크게 제어할 수 있기 때문에 많은 관심을 받았습니다. PBF(Powderbed fusion) 방식의 AM 공정에서는 금속 분말을 레이저나 전자빔으로 녹이고 응고시키는 과정을 반복하여 3D 부품을 제작합니다.

일반적으로 응고 미세구조는 Hunt[Mater. 과학. 영어 65, 75(1984)]. 그러나 CET 이론이 일반 316L 스테인리스강에서도 높은 G와 R로 인해 PBF형 AM 공정에 적용될 수 있을지는 불확실하다.

본 연구에서는 미세구조와 응고 조건 간의 관계를 밝히기 위해 전자빔 조사에 의해 유도된 316L 강의 응고 미세구조를 분석하고 CtFD(Computational Thermal-Fluid Dynamics) 방법을 사용하여 고체/액체 계면에서의 응고 조건을 평가했습니다.

CET 이론과 반대로 높은 G 조건에서 등축 결정립이 종종 형성되는 것으로 밝혀졌다. CtFD 시뮬레이션은 약 400 mm s-1의 속도까지 유체 흐름이 있음을 보여 주며 수상 돌기의 파편 및 이동의 영향으로 등축 결정립이 형성됨을 시사했습니다.

Additive manufacturing(AM)technologies have attracted much attention because it enables us to build 3D parts with complicated geometry easily and control material properties significantly via the control of microstructures. In the powderbed fusion(PBF)type AM process, 3D parts are fabricated by repeating a process of melting and solidifying metal powders by laser or electron beams. In general, the solidification microstructures can be predicted from solidification conditions defined by the combination of temperature gradient G and solidification rate R on the basis of columnar-equiaxed transition(CET)theory proposed by Hunt [Mater. Sci. Eng. 65, 75(1984)]. However, it is unclear whether the CET theory can be applied to the PBF type AM process because of the high G and R, even for general 316L stainless steel. In this study, to reveal relationships between microstructures and solidification conditions, we have analyzed solidification microstructures of 316L steel induced by electronbeam irradiation and evaluated solidification conditions at the solid/liquid interface using a computational thermal-fluid dynamics (CtFD)method. It was found that equiaxed grains were often formed under high G conditions contrary to the CET theory. CtFD simulation revealed that there is a fluid flow up to a velocity of about 400 mm s-1, and suggested that equiaxed grains are formed owing to the effect of fragmentations and migrations of dendrites.

Keywords

Additive Manufacturing, 316L Stainless Steel, Powder Bed Fusion, Electron Beam Melting, Computational Thermal
Fluid Dynamics Simulation

Fig. 1 Width, height, and height differences calculated from laser microscope analysis of melt tracks formed by scanning electron beam. Fig. 2(a)Scanning electron microscope(SEM)image and(b) corresponding electron back-scattering diffraction(EBSD) IPF-map taken from the electron-beam irradiated region in P900-V100 sample. Fig. 3 Average grain size and their aspect ratio calculated from EBSD IPF-map taken from the electron-beam irradiated region.
Fig. 1 Width, height, and height differences calculated from laser microscope analysis of melt tracks formed by scanning electron beam. Fig. 2(a)Scanning electron microscope(SEM)image and(b) corresponding electron back-scattering diffraction(EBSD) IPF-map taken from the electron-beam irradiated region in P900-V100 sample. Fig. 3 Average grain size and their aspect ratio calculated from EBSD IPF-map taken from the electron-beam irradiated region.
Fig. 4 Comparison of experimental SEM image and computational thermal fluid dynamics(CtFD)simulated melt pool with a beam diameter of 700 μm and absorption rates of(a)0.3,(b)0.5, and (c)0.7. Electron beam power and scan speed are 900 W and 100 mm s-1, respectively.
Fig. 4 Comparison of experimental SEM image and computational thermal fluid dynamics(CtFD)simulated melt pool with a beam diameter of 700 μm and absorption rates of(a)0.3,(b)0.5, and (c)0.7. Electron beam power and scan speed are 900 W and 100 mm s-1, respectively.
Fig. 5 Comparison of experimental SEM image and CtFD simulated melt pool with beam diameters of(a)700 μm,(b)1000 μm, and(c)1300 μm and an absorption rate of 0.3. Electron beam power and scan speed are 900 W and 100 mm s-1, respectively
Fig. 5 Comparison of experimental SEM image and CtFD simulated melt pool with beam diameters of(a)700 μm,(b)1000 μm, and(c)1300 μm and an absorption rate of 0.3. Electron beam power and scan speed are 900 W and 100 mm s-1, respectively
Fig. 6 Depth of melt tracks calculated from experimental SEM image and CtFD simulation results.
Fig. 6 Depth of melt tracks calculated from experimental SEM image and CtFD simulation results.
Fig. 7 G-R plots of 316L steel colored by(a)aspect ratio of crystalline grains and(b)fluid velocity.
Fig. 7 G-R plots of 316L steel colored by(a)aspect ratio of crystalline grains and(b)fluid velocity.
Fig. 8 Comparison of solidification microstructure(EBSD IPF-map)of melt region formed by scanning electron beam and corresponding snap shot of CtFD simulation colored by fluid velocity
Fig. 8 Comparison of solidification microstructure(EBSD IPF-map)of melt region formed by scanning electron beam and corresponding snap shot of CtFD simulation colored by fluid velocity

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The Optimal Operation on Auxiliary Spillway to Minimize the Flood Damage in Downstream River with Various Outflow Conditions

류하천의 영향 최소화를 위한 보조 여수로 최적 활용방안 검토

Hyung Ju Yoo1 Sung Sik Joo2 Beom Jae Kwon3 Seung Oh Lee4*
유 형주1 주 성식2 권 범재3 이 승오4*
1Ph.D Student, Dept. of Civil & Environmental Engineering, Hongik University2Director, Water Resources & Environment Department, HECOREA3Director, Water Resources Department, ISAN4Professor, Dept. of Civil & Environmental Engineering, Hongik University
1홍익대학교 건설환경공학과 박사과정
2㈜헥코리아 수자원환경사업부 이사
3㈜이산 수자원부 이사
4홍익대학교 건설환경공학과 교수*Corresponding Author

ABSTRACT

최근 기후변화로 인해 강우강도 및 빈도의 증가에 따른 집중호우의 영향 및 기존 여수로의 노후화에 대비하여 홍수 시 하류 하천의 영향을 최소화할 수 있는 보조 여수로 활용방안 구축이 필요한 실정이다. 이를 위해, 수리모형 실험 및 수치모형 실험을 통하여 보조 여수로 운영에 따른 흐름특성 변화 검토에 관한 연구가 많이 진행되어 왔다.

그러나 대부분의 연구는 여수로에서의 흐름특성 및 기능성에 대한 검토를 수행하였을 뿐 보조 여수로의 활용방안에 따른 하류하천 영향 검토 및 호안 안정성 검토에 관한 연구는 미비한 실정이다.

이에 본 연구에서는 기존 여수로 및 보조 여수로 방류 조건에 따른 하류영향 분석 및 호안 안정성 측면에서 최적 방류 시나리오 검토를 3차원 수치모형인 FLOW-3D를 사용하여 검토하였다. 또한 FLOW-3D 수치모의 수행을 통한 유속, 수위 결과와 소류력 산정 결과를 호안 설계허용 기준과 비교하였다.

수문 완전 개도 조건으로 가정하고 계획홍수량 유입 시 다양한 보조 여수로 활용방안에 대하여 수치모의를 수행한 결과, 보조 여수로 단독 운영 시 기존 여수로 단독운영에 비하여 최대유속 및 최대 수위의 감소효과를 확인하였다. 다만 계획홍수량의 45% 이하 방류 조건에서 대안부의 호안 안정성을 확보하였고 해당 방류량 초과 경우에는 처오름 현상이 발생하여 월류에 대한 위험성 증가를 확인하였다.

따라서 기존 여수로와의 동시 운영 방안 도출이 중요하다고 판단하였다. 여수로의 배분 비율 및 총 허용 방류량에 대하여 검토한 결과 보조 여수로의 방류량이 기존 여수로의 방류량보다 큰 경우 하류하천의 흐름이 중심으로 집중되어 대안부의 유속 저감 및 수위 감소를 확인하였고, 계획 홍수량의 77% 이하의 조건에서 호안의 허용 유속 및 허용 소류력 조건을 만족하였다.

이를 통하여 본 연구에서 제안한 보조 여수로 활용방안으로는 기존 여수로와 동시 운영 시 총 방류량에 대하여 보조 여수로의 배분량이 기존 여수로의 배분량보다 크게 설정하는 것이 하류하천의 영향을 최소화 할 수 있는 것으로 나타났다.

그러나 본 연구는 여수로 방류에 따른 대안부에서의 영향에 대해서만 검토하였고 수문 전면 개도 조건에서 검토하였다는 한계점은 분명히 있다. 이에 향후에는 다양한 수문 개도 조건 및 방류 시나리오를 적용 및 검토한다면 보다 효율적이고, 효과적인 보조 여수로 활용방안을 도출이 가능할 것으로 기대 된다.

키워드

보조 여수로, FLOW-3D, 수치모의, 호안 안정성, 소류력

Recently, as the occurrence frequency of sudden floods due to climate change increased and the aging of the existing spillway, it is necessary to establish a plan to utilize an auxiliary spillway to minimize the flood damage of downstream rivers. Most studies have been conducted on the review of flow characteristics according to the operation of auxiliary spillway through the hydraulic experiments and numerical modeling. However, the studies on examination of flood damage in the downstream rivers and the stability of the revetment according to the operation of the auxiliary spillway were relatively insufficient in the literature. In this study, the stability of the revetment on the downstream river according to the outflow conditions of the existing and auxiliary spillway was examined by using 3D numerical model, FLOW-3D. The velocity, water surface elevation and shear stress results of FLOW-3D were compared with the permissible velocity and shear stress of design criteria. It was assumed the sluice gate was fully opened. As a result of numerical simulations of various auxiliary spillway operations during flood season, the single operation of the auxiliary spillway showed the reduction effect of maximum velocity and the water surface elevation compared with the single operation of the existing spillway. The stability of the revetment on downstream was satisfied under the condition of outflow less than 45% of the design flood discharge. However, the potential overtopping damage was confirmed in the case of exceeding the 45% of the design flood discharge. Therefore, the simultaneous operation with the existing spillway was important to ensure the stability on design flood discharge condition. As a result of examining the allocation ratio and the total allowable outflow, the reduction effect of maximum velocity was confirmed on the condition, where the amount of outflow on auxiliary spillway was more than that on existing spillway. It is because the flow of downstream rivers was concentrated in the center due to the outflow of existing spillway. The permissible velocity and shear stress were satisfied under the condition of less than 77% of the design flood discharge with simultaneous operation. It was found that the flood damage of downstream rivers can be minimized by setting the amount allocated to the auxiliary spillway to be larger than the amount allocated to the existing spillway for the total outflow with simultaneous operation condition. However, this study only reviewed the flow characteristics around the revetment according to the outflow of spillway under the full opening of the sluice gate condition. Therefore, the various sluice opening conditions and outflow scenarios will be asked to derive more efficient utilization of the auxiliary spillway in th future.KeywordsAuxiliary spillway FLOW-3D Numerical simulation Revetment stability Shear stress

1. 서 론

최근 기후변화로 인한 집중호우의 영향으로 홍수 시 댐으로 유입되는 홍수량이 설계 홍수량보다 증가하여 댐 안정성 확보가 필요한 실정이다(Office for Government Policy Coordination, 2003). MOLIT & K-water(2004)에서는 기존댐의 수문학적 안정성 검토를 수행하였으며 이상홍수 발생 시 24개 댐에서 월류 등으로 인한 붕괴위험으로 댐 하류지역의 극심한 피해를 예상하여 보조여수로 신설 및 기존여수로 확장 등 치수능력 증대 기본계획을 수립하였고 이를 통하여 극한홍수 발생 시 홍수량 배제능력을 증대하여 기존댐의 안전성 확보 및 하류지역의 피해를 방지하고자 하였다. 여기서 보조 여수로는 기존 여수로와 동시 또는 별도 운영하는 여수로로써 비상상황 시 방류 기능을 포함하고 있고(K-water, 2021), 최근에는 기존 여수로의 노후화에 따라 보조여수로의 활용방안에 대한 관심이 증가하고 있다. 따라서 본 연구에서는 3차원 수치해석을 수행하여 기존 및 보조 여수로의 방류량 조합에 따른 하류 영향을 분석하고 하류 호안 안정성 측면에서 최적 방류 시나리오를 검토하고자 한다.

기존의 댐 여수로 검토에 관한 연구는 주로 수리실험을 통하여 방류조건 별 흐름특성을 검토하였으나 최근에는 수치모형 실험결과가 수리모형실험과 비교하여 근사한 것을 확인하는 등 점차 수치모형실험을 수리모형실험의 대안으로 활용하고 있다(Jeon et al., 2006Kim, 2007Kim et al., 2008). 국내의 경우, Jeon et al.(2006)은 수리모형 실험과 수치모의를 이용하여 임하댐 바상여수로의 기본설계안을 도출하였고, Kim et al.(2008)은 가능최대홍수량 유입 시 비상여수로 방류에 따른 수리학적 안정성과 기능성을 3차원 수치모형인 FLOW-3D를 활용하여 검토하였다. 또한 Kim and Kim(2013)은 충주댐의 홍수조절 효과 검토 및 방류량 변화에 따른 상·하류의 수위 변화를 수치모형을 통하여 검토하였다. 국외의 경우 Zeng et al.(2017)은 3차원 수치모형인 Fluent를 활용한 여수로 방류에 따른 흐름특성 결과와 측정결과를 비교하여 수치모형 결과의 신뢰성을 검토하였다. Li et al.(2011)은 가능 최대 홍수량(Probable Maximum Flood, PMF)조건에서 기존 여수로와 신규 보조 여수로 유입부 주변의 흐름특성에 대하여 3차원 수치모형 Fluent를 활용하여 검토하였고, Lee et al.(2019)는 서로 근접해있는 기존 여수로와 보조여수로 동시 운영 시 방류능 검토를 수리모형 실험 및 수치모형 실험(FLOW-3D)을 통하여 수행하였으며 기존 여수로와 보조 여수로를 동시운영하게 되면 배수로 간섭으로 인하여 총 방류량이 7.6%까지 감소되어 댐의 방류능력이 감소하였음을 확인하였다.

그러나 대부분의 여수로 검토에 대한 연구는 여수로 내에서의 흐름특성 및 기능성에 대한 검토를 수행하였고. 이에 기존 여수로와 보조 여수로 방류운영에 따른 하류하천의 흐름특성 변화 및 호안 안정성 평가에 관한 추가적인 검토가 필요한 실정이다. 따라서 본 연구에서는 기존 여수로 및 보조 여수로 방류 조건에 따른 하류하천의 흐름특성 및 호안 안정성분석을 3차원 수치모형인 FLOW-3D를 이용하여 검토하였다. 또한 다양한 방류 배분 비율 및 허용 방류량 조건 변화에 따른 하류하천의 흐름특성 및 소류력 분석결과를 호안 설계 허용유속 및 허용 소류력 기준과 비교하여 하류하천의 영향을 최소화 할 수 있는 최적의 보조 여수로 활용방안을 도출하고자 한다.

2. 본 론

2.1 이론적 배경

2.1.1 3차원 수치모형의 기본이론

FLOW-3D는 미국 Flow Science, Inc에서 개발한 범용 유체역학 프로그램(CFD, Computational Fluid Dynamics)으로 자유 수면을 갖는 흐름모의에 사용되는 3차원 수치해석 모형이다. 난류모형을 통해 난류 해석이 가능하고, 댐 방류에 따른 하류 하천의 흐름 해석에도 많이 사용되어 왔다(Flow Science, 2011). 본 연구에서는 FLOW-3D(version 12.0)을 이용하여 홍수 시 기존 여수로의 노후화에 대비하여 보조 여수로의 활용방안에 대한 검토를 하류하천의 호안 안정성 측면에서 검토하였다.

2.1.2 유동해석의 지배방정식

1) 연속 방정식(Continuity Equation)

FLOW-3D는 비압축성 유체에 대하여 연속방정식을 사용하며, 밀도는 상수항으로 적용된다. 연속 방정식은 Eqs. (1)(2)와 같다.

(1)

∇·v=0

(2)

∂∂x(uAx)+∂∂y(vAy)+∂∂z(wAz)=RSORρ

여기서, ρ는 유체 밀도(kg/m3), u, v, w는 x, y, z방향의 유속(m/s), Ax, Ay, Az는 각 방향의 요소면적(m2), RSOR는 질량 생성/소멸(mass source/sink)항을 의미한다.

2) 운동량 방정식(Momentum Equation)

각 방향 속도성분 u, v, w에 대한 운동방정식은 Navier-Stokes 방정식으로 다음 Eqs. (3)(4)(5)와 같다.

(3)

∂u∂t+1VF(uAx∂u∂x+vAy∂v∂y+wAz∂w∂z)=-1ρ∂p∂x+Gx+fx-bx-RSORρVFu

(4)

∂v∂t+1VF(uAx∂u∂x+vAy∂v∂y+wAz∂w∂z)=-1ρ∂p∂y+Gy+fy-by-RSORρVFv

(5)

∂w∂t+1VF(uAx∂u∂x+vAy∂v∂y+wAz∂w∂z)=-1ρ∂p∂z+Gz+fz-bz-RSORρVFw

여기서, Gx, Gy, Gz는 체적력에 의한 가속항, fx, fy, fz는 점성에 의한 가속항, bx, by, bz는 다공성 매체에서의 흐름손실을 의미한다.

2.1.3 소류력 산정

호안설계 시 제방사면 호안의 안정성 확보를 위해서는 하천의 흐름에 의하여 호안에 작용하는 소류력에 저항할 수 있는 재료 및 공법 선택이 필요하다. 국내의 경우 하천공사설계실무요령(MOLIT, 2016)에서 계획홍수량 유하 시 소류력 산정 방법을 제시하고 있다. 소류력은 하천의 평균유속을 이용하여 산정할 수 있으며, 소류력 산정식은 Eqs. (6)(7)과 같다.

1) Schoklitsch 공식

Schoklitsch(1934)는 Chezy 유속계수를 적용하여 소류력을 산정하였다.

(6)

τ=γRI=γC2V2

여기서, τ는 소류력(N/m2), R은 동수반경(m), γ는 물의 단위중량(10.0 kN/m3), I는 에너지경사, C는 Chezy 유속계수, V는 평균유속(m/s)을 의미한다.

2) Manning 조도계수를 고려한 공식

Chezy 유속계수를 대신하여 Manning의 조도계수를 고려하여 소류력을 산정할 수 있다.

(7)

τ=γn2V2R1/3

여기서, τ는 소류력(N/m2), R은 동수반경(m), γ는 물의 단위중량(10.0 kN/m3), n은 Manning의 조도계수, V는 평균유속(m/s)을 의미한다.

FLOW-3D 수치모의 수행을 통하여 하천의 바닥 유속을 도출할 수 있으며, 본 연구에서는 Maning 조도계수롤 고려하여 소류력을 산정하고자 한다. 소류력을 산정하기 위해서 여수로 방류에 따른 대안부의 바닥유속 변화를 검토하여 최대 유속 값을 이용하였다. 최종적으로 산정한 소류력과 호안의 재료 및 공법에 따른 허용 소류력과 비교하여 제방사면 호안의 안정성 검토를 수행하게 된다.

2.2 하천호안 설계기준

하천 호안은 계획홍수위 이하의 유수작용에 대하여 안정성이 확보되도록 계획하여야 하며, 호안의 설계 시에는 사용재료의 확보용이성, 시공상의 용이성, 세굴에 대한 굴요성(flexibility) 등을 고려하여 호안의 형태, 시공방법 등을 결정한다(MOLIT, 2019). 국내의 경우, 하천공사설계실무요령(MOLIT, 2016)에서는 다양한 호안공법에 대하여 비탈경사에 따라 설계 유속을 비교하거나, 허용 소류력을 비교함으로써 호안의 안정성을 평가한다. 호안에 대한 국외의 설계기준으로 미국의 경우, ASTM(미국재료시험학회)에서 호안블록 및 식생매트 시험방법을 제시하였고 제품별로 ASTM 시험에 의한 허용유속 및 허용 소류력을 제시하였다. 일본의 경우, 호안 블록에 대한 축소실험을 통하여 항력을 측정하고 이를 통해서 호안 블록에 대한 항력계수를 제시하고 있다. 설계 시에는 항력계수에 의한 블록의 안정성을 평가하고 있으나, 최근에는 세굴의 영향을 고려할 수 있는 호안 안정성 평가의 필요성을 제기하고 있다(MOLIT, 2019). 관련된 국내·외의 하천호안 설계기준은 Table 1에 정리하여 제시하였고, 본 연구에서 하천 호안 안정성 평가 시 하천공사설계실무요령(MOLIT, 2016)과 ASTM 시험에서 제시한 허용소류력 및 허용유속 기준을 비교하여 각각 0.28 kN/m2, 5.0 m/s 미만일 경우 호안 안정성을 확보하였다고 판단하였다.

Table 1.

Standard of Permissible Velocity and Shear on Revetment

Country (Reference)MaterialPermissible velocity (Vp, m/s)Permissible Shear (τp, kN/m2)
KoreaRiver Construction Design Practice Guidelines
(MOLIT, 2016)
Vegetated5.00.50
Stone5.00.80
USAASTM D’6460Vegetated6.10.81
Unvegetated5.00.28
JAPANDynamic Design Method of Revetment5.0

2.3. 보조여수로 운영에 따른 하류하천 영향 분석

2.3.1 모형의 구축 및 경계조건

본 연구에서는 기존 여수로의 노후화에 대비하여 홍수 시 보조여수로의 활용방안에 따른 하류하천의 흐름특성 및 호안안정성 평가를 수행하기 위해 FLOW-3D 모형을 이용하였다. 기존 여수로 및 보조 여수로는 치수능력 증대사업(MOLIT & K-water, 2004)을 통하여 완공된 ○○댐의 제원을 이용하여 구축하였다. ○○댐은 설계빈도(100년) 및 200년빈도 까지는 계획홍수위 이내로 기존 여수로를 통하여 운영이 가능하나 그 이상 홍수조절은 보조여수로를 통하여 조절해야 하며, 또한 2011년 기존 여수로 정밀안전진단 결과 사면의 표층 유실 및 옹벽 밀림현상 등이 확인되어 노후화에 따른 보수·보강이 필요한 상태이다. 이에 보조여수로의 활용방안 검토가 필요한 것으로 판단하여 본 연구의 대상댐으로 선정하였다. 하류 하천의 흐름특성을 예측하기 위하여 격자간격을 0.99 ~ 8.16 m의 크기로 하여 총 격자수는 49,102,500개로 구성하였으며, 여수로 방류에 따른 하류하천의 흐름해석을 위한 경계조건으로 상류는 유입유량(inflow), 바닥은 벽면(wall), 하류는 수위(water surface elevation)조건으로 적용하도록 하였다(Table 2Fig. 1 참조). FLOW-3D 난류모형에는 혼합길이 모형, 난류에너지 모형, k-ϵ모형, RNG(Renormalized Group Theory) k-ϵ모형, LES 모형 등이 있으며, 본 연구에서는 여수로 방류에 따른 복잡한 난류 흐름 및 높은 전단흐름을 정확하게 모의(Flow Science, 2011)할 수 있는 RNG k-ϵ모형을 사용하였고, 하류하천 호안의 안정성 측면에서 보조여수로의 활용방안을 검토하기 위하여 방류시나리오는 Table 3에 제시된 것 같이 설정하였다. Case 1 및 Case 2를 통하여 계획홍수량에 대하여 기존 여수로와 보조 여수로의 단독 운영이 하류하천에 미치는 영향을 확인하였고 보조 여수로의 방류량 조절을 통하여 호안 안정성 측면에서 보조 여수로 방류능 검토를 수행하였다(Case 3 ~ Case 6). 또한 기존 여수로와 보조 여수로의 방류량 배분에 따른 하류하천의 영향 검토(Case 7 ~ Case 10) 및 방류 배분에 따른 허용 방류량을 호안 안정성 측면에서 검토를 수행하였다(Case 11 ~ Case 14).

수문은 완전개도 조건으로 가정하였으며 하류하천의 계획홍수량에 대한 기존 여수로와 보조여수로의 배분량을 조절하여 모의를 수행하였다. 여수로는 콘크리트의 조도계수 값(Chow, 1959)을 채택하였고, 댐 하류하천의 조도계수는 하천기본계획(Busan Construction and Management Administration, 2009) 제시된 조도계수 값을 채택하였으며 FLOW-3D의 적용을 위하여 Manning-Strickler 공식(Vanoni, 2006)을 이용하여 조도계수를 조고값으로 변환하여 사용하였다. Manning-Strickler 공식은 Eq. (8)과 같으며, FLOW-3D에 적용한 조도계수 및 조고는 Table 4와 같다.

(8)

n=ks1/68.1g1/2

여기서, kS는 조고 (m), n은 Manning의 조도계수, g는 중력가속도(m/s2)를 의미한다.

시간에 따라 동일한 유량이 일정하게 유입되도록 모의를 수행하였으며, 시간간격(Time Step)은 0.0001초로 설정(CFL number < 1.0) 하였다. 또한 여수로 수문을 통한 유량의 변동 값이 1.0%이내일 경우는 연속방정식을 만족하고 있다고 가정하였다. 이는, 유량의 변동 값이 1.0%이내일 경우 유속의 변동 값 역시 1.0%이내이며, 수치모의 결과 1.0%의 유속변동은 호안의 유속설계기준에 크게 영향을 미치지 않는다고 판단하였다. 그 결과 모든 수치모의 Case에서 2400초 이내에 결과 값이 수렴하는 것을 확인하였다.

Table 2.

Mesh sizes and numerical conditions

MeshNumbers49,102,500 EA
Increment (m)DirectionExisting SpillwayAuxiliary Spillway
∆X0.99 ~ 4.301.00 ~ 4.30
∆Y0.99 ~ 8.161.00 ~ 5.90
∆Z0.50 ~ 1.220.50 ~ 2.00
Boundary ConditionsXmin / YmaxInflow / Water Surface Elevation
Xmax, Ymin, Zmin / ZmaxWall / Symmetry
Turbulence ModelRNG model
Table 3.

Case of numerical simulation (Qp : Design flood discharge)

CaseExisting Spillway (Qe, m3/s)Auxiliary Spillway (Qa, m3/s)Remarks
1Qp0Reference case
20Qp
300.58QpReview of discharge capacity on
auxiliary spillway
400.48Qp
500.45Qp
600.32Qp
70.50Qp0.50QpDetermination of optimal division
ratio on Spillways
80.61Qp0.39Qp
90.39Qp0.61Qp
100.42Qp0.58Qp
110.32Qp0.45QpDetermination of permissible
division on Spillways
120.35Qp0.48Qp
130.38Qp0.53Qp
140.41Qp0.56Qp
Table 4.

Roughness coefficient and roughness height

CriteriaRoughness coefficient (n)Roughness height (ks, m)
Structure (Concrete)0.0140.00061
River0.0330.10496
/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F1.jpg
Fig. 1

Layout of spillway and river in this study

2.3.2 보조 여수로의 방류능 검토

본 연구에서는 기존 여수로와 보조 여수로의 방류량 배분에 따른 하류하천 대안부의 유속분포 및 수위분포를 검토하기 위해 수치모의 Case 별 다음과 같이 관심구역을 설정하였다(Fig. 2 참조). 관심구역(대안부)의 길이(L)는 총 1.3 km로 10 m 등 간격으로 나누어 검토하였으며, Section 1(0 < X/L < 0.27)은 기존 여수로 방류에 따른 영향이 지배적인 구간, Section 2(0.27 < X/L < 1.00)는 보조 여수로 방류에 따른 영향이 지배적인 구간으로 각 구간에서의 수위, 유속, 수심결과를 확인하였다. 기존 여수로의 노후화에 따른 보조 여수로의 방류능 검토를 위하여 Case 1 – Case 6까지의 결과를 비교하였다.

보조 여수로의 단독 운영 시 기존 여수로 운영 시 보다 하류하천의 대안부의 최대 유속(Vmax)은 약 3% 감소하였으며, 이는 보조 여수로의 하천 유입각이 기존 여수로 보다 7°작으며 유입하천의 폭이 증가하여 유속이 감소한 것으로 판단된다. 대안부의 최대 유속 발생위치는 하류 쪽으로 이동하였으며 교량으로 인한 단면의 축소로 최대유속이 발생하는 것으로 판단된다. 또한 보조 여수로의 배분량(Qa)이 증가함에 따라 하류하천 대안부의 최대 유속이 증가하였다. 하천호안 설계기준에서 제시하고 있는 허용유속(Vp)과 비교한 결과, 계획홍수량(Qp)의 45% 이하(Case 5 & 6)를 보조 여수로에서 방류하게 되면 허용 유속(5.0 m/s)조건을 만족하여 호안안정성을 확보하였다(Fig. 3 참조). 허용유속 외에도 대안부에서의 소류력을 산정하여 하천호안 설계기준에서 제시한 허용 소류력(τp)과 비교한 결과, 유속과 동일하게 보조 여수로의 방류량이 계획홍수량의 45% 이하일 경우 허용소류력(0.28 kN/m2) 조건을 만족하였다(Fig. 4 참조). 각 Case 별 호안설계조건과 비교한 결과는 Table 5에 제시하였다.

하류하천의 수위도 기존 여수로 운영 시 보다 보조 여수로 단독 운영 시 최대 수위(ηmax)가 약 2% 감소하는 효과를 보였으며 최대 수위 발생위치는 수충부로 여수로 방류시 처오름에 의한 수위 상승으로 판단된다. 기존 여수로의 단독운영(Case 1)의 수위(ηref)를 기준으로 보조 여수로의 방류량이 증가함에 따라 수위는 증가하였으나 계획홍수량의 58%까지 방류할 경우 월류에 대한 안정성(ηmax/ηref<0.97(=기설제방고))은 확보되었다(Fig. 5 참조). 그러나 계획홍수량 조건에서는 월류에 대한 위험성이 존재하기 때문에 기존여수로와 보조여수로의 적절한 방류량 배분 조합을 도출하는 것이 중요하다고 판단되어 진다.

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F2.jpg
Fig. 2

Region of interest in this study

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F3.jpg
Fig. 3

Maximum velocity and location of Vmax according to Qa

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F4.jpg
Fig. 4

Maximum shear according to Qa

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F5.jpg
Fig. 5

Maximum water surface elevation and location of ηmax according to Qa

Table 5.

Numerical results for each cases (Case 1 ~ Case 6)

CaseMaximum Velocity
(Vmax, m/s)
Maximum Shear
(τmax, kN/m2)
Evaluation
in terms of Vp
Evaluation
in terms of τp
1
(Qa = 0)
9.150.54No GoodNo Good
2
(Qa = Qp)
8.870.56No GoodNo Good
3
(Qa = 0.58Qp)
6.530.40No GoodNo Good
4
(Qa = 0.48Qp)
6.220.36No GoodNo Good
5
(Qa = 0.45Qp)
4.220.12AccpetAccpet
6
(Qa = 0.32Qp)
4.040.14AccpetAccpet

2.3.3 기존 여수로와 보조 여수로 방류량 배분 검토

기존 여수로 및 보조 여수로 단독운영에 따른 하류하천 및 호안의 안정성 평가를 수행한 결과 계획홍수량 방류 시 하류하천 대안부에서 호안 설계 조건(허용유속 및 허용 소류력)을 초과하였으며, 처오름에 의한 수위 상승으로 월류에 대한 위험성 증가를 확인하였다. 따라서 계획 홍수량 조건에서 기존 여수로와 보조 여수로의 방류량 배분을 통하여 호안 안정성을 확보하고 하류하천에 방류로 인한 피해를 최소화할 수 있는 배분조합(Case 7 ~ Case 10)을 검토하였다. Case 7은 기존 여수로와 보조여수로의 배분 비율을 균등하게 적용한 경우이고, Case 8은 기존 여수로의 배분량이 보조 여수로에 비하여 많은 경우, Case 9는 보조 여수로의 배분량이 기존 여수로에 비하여 많은 경우를 의미한다. 최대유속을 비교한 결과 보조 여수로의 배분 비율이 큰 경우 기존 여수로의 배분량에 의하여 흐름이 하천 중심에 집중되어 대안부의 유속을 저감하는 효과를 확인하였다. 보조여수로의 방류량 배분 비율이 증가할수록 기존 여수로 대안부 측(0.00<X/L<0.27, Section 1) 유속 분포는 감소하였으나, 신규여수로 대안부 측(0.27<X/L<1.00, Section 2) 유속은 증가하는 것을 확인하였다(Fig. 6 참조). 그러나 유속 저감 효과에도 대안부 전구간에서 설계 허용유속 조건을 초과하여 제방의 안정성을 확보하지는 못하였다. 소류력 산정 결과 유속과 동일하게 보조 여수로의 방류량이 기존 여수로의 방류량 보다 크면 감소하는 것을 확인하였고 일부 구간에서는 허용 소류력 조건을 만족하는 것을 확인하였다(Fig. 7 참조).

따라서 유속 저감효과가 있는 배분 비율 조건(Qa>Qe)에서 Section 2에 유속 저감에 영향을 미치는 기존 여수로 방류량 배분 비율을 증가시켜 추가 검토(Case 10)를 수행하였다. 단독운영과 비교 시 하류하천에 유입되는 유량은 증가하였음에도 불구하고 기존 여수로 방류량에 의해 흐름이 하천 중심으로 집중되는 현상에 따라 대안부의 유속은 단독 운영에 비하여 감소하는 것을 확인하였고(Fig. 8 참조), 호안 설계 허용유속 및 허용 소류력 조건을 만족하는 구간이 발생하여 호안 안정성도 확보한 것으로 판단되었다. 최종적으로 각 Case 별 수위 결과의 경우 여수로 동시 운영을 수행하게 되면 대안부 전 구간에서 월류에 대한 안정성(ηmax/ηref<0.97(=기설제방고))은 확보하였다(Fig. 9 참조). 각 Case 별 대안부에서 최대 유속결과 및 산정한 소류력은 Table 6에 제시하였다.

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F6.jpg
Fig. 6

Maximum velocity on section 1 & 2 according to Qa

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F7.jpg
Fig. 7

Maximum shear on section 1 & 2 according to Qa

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F8.jpg
Fig. 8

Velocity results of FLOW-3D (a: auxiliary spillway operation only , b : simultaneous operation of spillways)

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F9.jpg
Fig. 9

Maximum water surface elevation on section 1 & 2 according to Qa

Table 6.

Numerical results for each cases (Case 7 ~ Case 10)

Case (Qe &amp; Qa)Maximum Velocity (Vmax, m/s)Maximum Shear
(τmax, kN/m2)
Evaluation in terms of VpEvaluation in terms of τp
Section 1Section 2Section 1Section 2Section 1Section 2Section 1Section 2
7
Qe : 0.50QpQa : 0.50Qp
8.106.230.640.30No GoodNo GoodNo GoodNo Good
8
Qe : 0.61QpQa : 0.39Qp
8.886.410.610.34No GoodNo GoodNo GoodNo Good
9
Qe : 0.39QpQa : 0.61Qp
6.227.330.240.35No GoodNo GoodAcceptNo Good
10
Qe : 0.42QpQa : 0.58Qp
6.394.790.300.19No GoodAcceptNo GoodAccept

2.3.4 방류량 배분 비율의 허용 방류량 검토

계획 홍수량 방류 시 기존 여수로와 보조 여수로의 배분 비율 검토 결과 Case 10(Qe = 0.42Qp, Qa = 0.58Qp)에서 방류에 따른 하류 하천의 피해를 최소화시킬 수 있는 것을 확인하였다. 그러나 대안부 전 구간에 대하여 호안 설계조건을 만족하지 못하였다. 따라서 기존 여수로와 보조 여수로의 방류 배분 비율을 고정시킨 후 총 방류량을 조절하여 허용 방류량을 검토하였다(Case 11 ~ Case 14).

호안 안정성 측면에서 검토한 결과 계획홍수량 대비 총 방류량이 감소하면 최대 유속 및 최대 소류력이 감소하고 최종적으로 계획 홍수량의 77%를 방류할 경우 하류하천의 대안부에서 호안 설계조건을 모두 만족하는 것을 확인하였다(Fig. 10Fig. 11 참조). 각 Case 별 대안부에서 최대 유속결과 및 산정한 소류력은 Table 7에 제시하였다. 또한 Case 별 수위 검토 결과 처오름으로 인한 대안부 전 구간에서 월류에 대한 안정성(ηmax/ηref<0.97(=기설제방고))은 확보하였다(Fig. 12 참조).

Table 7.

Numerical results for each cases (Case 11 ~ Case 14)

Case (Qe &amp; Qa)Maximum Velocity
(Vmax, m/s)
Maximum Shear
(τmax, kN/m2)
Evaluation in terms of VpEvaluation in terms of τp
Section 1Section 2Section 1Section 2Section 1Section 2Section 1Section 2
11
Qe : 0.32QpQa : 0.45Qp
3.634.530.090.26AcceptAcceptAcceptAccept
12
Qe : 0.35QpQa : 0.48Qp
5.745.180.230.22No GoodNo GoodAcceptAccept
13
Qe : 0.38QpQa : 0.53Qp
6.704.210.280.11No GoodAcceptAcceptAccept
14
Qe : 0.41QpQa : 0.56Qp
6.545.240.280.24No GoodNo GoodAcceptAccept
/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F10.jpg
Fig. 10

Maximum velocity on section 1 & 2 according to total outflow

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F11.jpg
Fig. 11

Maximum shear on section 1 & 2 according to total outflow

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F12.jpg
Fig. 12

Maximum water surface elevation on section 1 & 2 according to total outflow

3. 결 론

본 연구에서는 홍수 시 기존 여수로의 노후화로 인한 보조 여수로의 활용방안에 대하여 하류하천의 호안 안정성 측면에서 검토하였다. 여수로 방류로 인한 하류하천의 흐름특성을 검토하기 위하여 3차원 수치모형인 FLOW-3D를 활용하였고, 여수로 지형은 치수능력 증대사업을 통하여 완공된 ○○댐의 제원을 이용하였다. 하류하천 조도 계수 및 여수로 방류량은 하천기본계획을 참고하여 적용하였다. 최종적으로 여수로 방류로 인한 하류하천의 피해를 최소화 시킬 수 있는 적절한 보조 여수로의 활용방안을 도출하기 위하여 보조 여수로 단독 운영과 기존 여수로와의 동시 운영에 따른 하류 하천의 흐름특성 및 소류력의 변화를 검토하였다.

수문은 완전 개도 상태에서 방류한다는 가정으로 계획 홍수량 조건에서 보조 여수로 단독 운영 시 하류하천 대안부의 유속 및 수위를 검토한 결과 기존 여수로 단독운영에 비하여 최대 유속 및 최대 수위가 감소하는 것을 확인할 수 있었으며, 이는 보조 여수로 단독 운영 시 하류하천으로 유입각도가 작아지고, 유입되는 하천의 폭이 증가되기 때문이다. 그러나 계획 홍수량 조건에서 하천호안 설계기준에서 제시한 허용 유속(5.0 m/s)과 허용 소류력(0.28 kN/m2)과 비교하였을 때 호안 안정성을 확보하지 못하였으며, 계획홍수량의 45% 이하 방류 시에 대안부의 호안 안정성을 확보하였다. 수위의 경우 여수로 방류에 따른 대안부에서 처오름 현상이 발생하여 월류에 대한 위험성을 확인하였고 이를 통하여 기존 여수로와의 동시 운영 방안을 도출하는 것이 중요하다고 판단된다. 따라서 기존 여수로와의 동시 운영 측면에서 기존 여수로와 보조 여수로의 배분 비율 및 총 방류량을 변화시켜가며 하류 하천의 흐름특성 및 소류력의 변화를 검토하였다. 배분 비율의 경우 기존 여수로와 보조 여수로의 균등 배분(Case 7) 및 편중 배분(Case 8 & Case 9)을 검토하여 보조 여수로의 방류량이 기존 여수로의 방류량보다 큰 경우 하류하천의 중심부로 집중되어 대안부의 최대유속, 최대소류력 및 최대수위가 감소하는 것을 확인하였다. 이를 근거로 기존 여수로의 방류 비율을 증가(Qe=0.42Qp, Qa=0.58Qp)시켜 검토한 결과 대안부 일부 구간에서 허용 유속 및 허용소류력 조건을 만족하는 것을 확인하였다. 이를 통하여 기존 여수로와 보조 여수로의 동시 운영을 통하여 적절한 방류량 배분 비율을 도출하는 것이 방류로 인한 하류하천의 피해를 저감하는데 효과적인 것으로 판단된다. 그러나 설계홍수량 방류 시 전 구간에서 허용 유속 및 소류력 조건을 만족하지 못하였다. 최종적으로 전체 방류량에서 기존 여수로의 방류 비율을 42%, 보조 여수로의 방류 비율을 58%로 설정하여 허용방류량을 검토한 결과, 계획홍수량의 77%이하로 방류 시 대안부의 최대유속은 기존여수로 방류의 지배영향구간(section 1)에서 3.63 m/s, 기존 여수로와 보조 여수로 방류의 영향구간(section 2)에서 4.53 m/s로 허용유속 조건을 만족하였고, 산정한 소류력도 각각 0.09 kN/m2 및 0.26 kN/m2로 허용 소류력 조건을 만족하여 대안부 호안의 안정성을 확보하였다고 판단된다.

본 연구 결과는 기후변화 및 기존여수로의 노후화로 인하여 홍수 시 기존여수로의 단독운영으로 하류하천의 피해가 발생할 수 있는 현시점에서 치수증대 사업으로 완공된 보조 여수로의 활용방안에 대한 기초자료로 활용될 수 있고, 향후 계획 홍수량 유입 시 최적의 배분 비율 및 허용 방류량 도출에 이용할 수 있다. 다만 본 연구는 여수로 방류에 따른 제방에 작용하는 수충력은 검토하지 못하고, 허용 유속 및 허용소류력은 제방과 유수의 방향이 일정한 구간에 대하여 검토하였다. 또한 여수로 방류에 따른 대안부에서의 영향에 대해서만 검토하였고 수문 전면 개도 조건에서 검토하였다는 한계점은 분명히 있다. 이에 향후에는 다양한 수문 개도 조건 및 방류 시나리오를 적용 및 검토하여 보다 효율적이고, 효과적인 보조 여수로 활용방안을 도출하고자 한다.

Acknowledgements

본 결과물은 K-water에서 수행한 기존 및 신규 여수로 효율적 연계운영 방안 마련(2021-WR-GP-76-149)의 지원을 받아 연구되었습니다.

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Fig. 1. Schematic of (a) geometry of the simulation model, (b) A-A cross-section presenting the locations of point probes for recording temperature history (unit: µm).

Laser powder bed fusion of 17-4 PH stainless steel: a comparative study on the effect of heat treatment on the microstructure evolution and mechanical properties

17-4 PH 스테인리스강의 레이저 분말 베드 융합: 열처리가 미세조직의 진화 및 기계적 특성에 미치는 영향에 대한 비교 연구

panelS.Saboonia, A.Chaboka, S.Fenga,e, H.Blaauwb, T.C.Pijperb,c, H.J.Yangd, Y.T.Peia
aDepartment of Advanced Production Engineering, Engineering and Technology Institute Groningen, University of Groningen, Nijenborgh 4, 9747 AG, Groningen, The Netherlands
bPhilips Personal Care, Oliemolenstraat 5, 9203 ZN, Drachten, The Netherlands
cInnovation Cluster Drachten, Nipkowlaan 5, 9207 JA, Drachten, The Netherlands
dShi-changxu Innovation Center for Advanced Materials, Institute of Metal Research, Chinese Academy of Sciences, 72 Wenhua Road, Shenyang 110016, P. R. China
eSchool of Mechanical Engineering, University of Science and Technology Beijing, Beijing, 100083, P.R. China

Abstract

17-4 PH (precipitation hardening) stainless steel is commonly used for the fabrication of complicated molds with conformal cooling channels using laser powder bed fusion process (L-PBF). However, their microstructure in the as-printed condition varies notably with the chemical composition of the feedstock powder, resulting in different age-hardening behavior. In the present investigation, 17-4 PH stainless steel components were fabricated by L-PBF from two different feedstock powders, and subsequently subjected to different combinations of post-process heat treatments. It was observed that the microstructure in as-printed conditions could be almost fully martensitic or ferritic, depending on the ratio of Creq/Nieq of the feedstock powder. Aging treatment at 480 °C improved the yield and ultimate tensile strengths of the as-printed components. However, specimens with martensitic structures exhibited accelerated age-hardening response compared with the ferritic specimens due to the higher lattice distortion and dislocation accumulation, resulting in the “dislocation pipe diffusion mechanism”. It was also found that the martensitic structures were highly susceptible to the formation of reverted austenite during direct aging treatment, where 19.5% of austenite phase appeared in the microstructure after 15 h of direct aging. Higher fractions of reverted austenite activates the transformation induced plasticity and improves the ductility of heat treated specimens. The results of the present study can be used to tailor the microstructure of the L-PBF printed 17-4 PH stainless steel by post-process heat treatments to achieve a good combination of mechanical properties.

17-4 PH(석출 경화) 스테인리스강은 레이저 분말 베드 융합 공정(L-PBF)을 사용하여 등각 냉각 채널이 있는 복잡한 금형 제작에 일반적으로 사용됩니다. 그러나 인쇄된 상태의 미세 구조는 공급원료 분말의 화학적 조성에 따라 크게 달라지므로 시효 경화 거동이 다릅니다.

현재 조사에서 17-4 PH 스테인리스강 구성요소는 L-PBF에 의해 두 가지 다른 공급원료 분말로 제조되었으며, 이후에 다양한 조합의 후처리 열처리를 거쳤습니다. 인쇄된 상태의 미세구조는 공급원료 분말의 Creq/Nieq 비율에 따라 거의 완전히 마르텐사이트 또는 페라이트인 것으로 관찰되었습니다.

480 °C에서 노화 처리는 인쇄된 구성 요소의 수율과 극한 인장 강도를 개선했습니다. 그러나 마텐자이트 구조의 시편은 격자 변형 및 전위 축적이 높아 페라이트 시편에 비해 시효 경화 반응이 가속화되어 “전위 파이프 확산 메커니즘”이 발생합니다.

또한 마르텐사이트 구조는 직접 시효 처리 중에 복귀된 오스테나이트의 형성에 매우 민감한 것으로 밝혀졌으며, 여기서 15시간의 직접 시효 후 미세 조직에 19.5%의 오스테나이트 상이 나타났습니다.

복귀된 오스테나이트의 비율이 높을수록 변형 유도 가소성이 활성화되고 열처리된 시편의 연성이 향상됩니다. 본 연구의 결과는 기계적 특성의 우수한 조합을 달성하기 위해 후처리 열처리를 통해 L-PBF로 인쇄된 17-4 PH 스테인리스강의 미세 구조를 조정하는 데 사용할 수 있습니다.

Keywords

Laser powder bed fusion17-4 PH stainless steelPost-process heat treatmentAge hardeningReverted austenite

Fig. 1. Schematic of (a) geometry of the simulation model, (b) A-A cross-section presenting the locations of point probes for recording temperature history (unit: µm).
Fig. 1. Schematic of (a) geometry of the simulation model, (b) A-A cross-section presenting the locations of point probes for recording temperature history (unit: µm).
Fig. 2. Optical (a, b) and TEM (c) micrographs of the wrought 17-4 PH stainless steel.
Fig. 2. Optical (a, b) and TEM (c) micrographs of the wrought 17-4 PH stainless steel.
Fig. 3. EBSD micrographs of the as-printed 17-4 PH steel fabricated with “powder A” (a, b) and “powder B” (c, d) on two different cross sections: (a, c) perpendicular to the building direction, and (b, d) parallel to the building direction.
Fig. 3. EBSD micrographs of the as-printed 17-4 PH steel fabricated with “powder A” (a, b) and “powder B” (c, d) on two different cross sections: (a, c) perpendicular to the building direction, and (b, d) parallel to the building direction.
Fig. 4. Microstructure of the as-printed 17-4 PH stainless steel fabricated with “powder A” (a) and “powder B” (b).
Fig. 4. Microstructure of the as-printed 17-4 PH stainless steel fabricated with “powder A” (a) and “powder B” (b).
Fig. 5. Simulated temperature history of the probes located at the cross section of the L-PBF 17-4 PH steel sample.
Fig. 5. Simulated temperature history of the probes located at the cross section of the L-PBF 17-4 PH steel sample.
Fig. 6. Dependency of the volume fraction of delta ferrite in the final microstructure of L-PBF printed 17-4 PH steel as a function of Creq/Nieq.
Fig. 6. Dependency of the volume fraction of delta ferrite in the final microstructure of L-PBF printed 17-4 PH steel as a function of Creq/Nieq.
Fig. 7. IQ + IPF (left column), parent austenite grain maps (middle column) and phase maps (right column, green color = martensite, red color = austenite) of the post-process heat treated 17-4 PH stainless steel: (a-c) direct aged, (d-f) HIP + aging, (g-i) SA + Aging, and (j-l) HIP + SA + aging (all sample were printed with “powder A”).
Fig. 7. IQ + IPF (left column), parent austenite grain maps (middle column) and phase maps (right column, green color = martensite, red color = austenite) of the post-process heat treated 17-4 PH stainless steel: (a-c) direct aged, (d-f) HIP + aging, (g-i) SA + Aging, and (j-l) HIP + SA + aging (all sample were printed with “powder A”).
Fig. 8. TEM micrographs of the post process heat treated 17-4 PH stainless steel: (a) direct aging and (b) HIP + aging (printed with “powder A”).
Fig. 8. TEM micrographs of the post process heat treated 17-4 PH stainless steel: (a) direct aging and (b) HIP + aging (printed with “powder A”).
Fig. 9. XRD patterns of the post-process heat treated 17-4 PH stainless steel printed with “powder A”.
Fig. 9. XRD patterns of the post-process heat treated 17-4 PH stainless steel printed with “powder A”.
Fig. 10. (a) Volume fraction of reverted austenite as a function of aging time for “direct aging” condition, (b) phase map (green color = martensite, red color = austenite) of the 15 h direct aged specimen printed with “powder A”.
Fig. 10. (a) Volume fraction of reverted austenite as a function of aging time for “direct aging” condition, (b) phase map (green color = martensite, red color = austenite) of the 15 h direct aged specimen printed with “powder A”.
Fig. 11. Microhardness variations of the “direct aged” specimens as a function of aging time at 480 °C.
Fig. 11. Microhardness variations of the “direct aged” specimens as a function of aging time at 480 °C.
Fig. 12. Kernel average misorientation graphs of the as-printed 17-4 PH steel with (a) martensitic structure (printed with “powder A”) and (b) ferritic structure (printed with “powder b”).
Fig. 12. Kernel average misorientation graphs of the as-printed 17-4 PH steel with (a) martensitic structure (printed with “powder A”) and (b) ferritic structure (printed with “powder b”).
Fig. 13. Typical stress-strain curves (a) along with the yield and ultimate tensile strengths (b) and elongation (c) of the as-printed and post-process heat treated 17-4 PH stainless steel (all sample are fabricated with “powder A”).
Fig. 13. Typical stress-strain curves (a) along with the yield and ultimate tensile strengths (b) and elongation (c) of the as-printed and post-process heat treated 17-4 PH stainless steel (all sample are fabricated with “powder A”).
Fig. 14. (a) IQ + IPF and (b) phase map (green color = martensite, red color = austenite) of the “direct aged” specimen after tensile test at a location nearby the rupture point (tension direction from left to right).
Fig. 14. (a) IQ + IPF and (b) phase map (green color = martensite, red color = austenite) of the “direct aged” specimen after tensile test at a location nearby the rupture point (tension direction from left to right).

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Flow on the inclined drop with bat-shaped elements: (a) Non-submerged flow

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토목공학의 수치해석법

Abstract

The main purpose of this study is to provide a method to increase energy dissipation on an inclined drop. Therefore, three types of rough elements with cylindrical, triangular and batshaped geometries are used on the inclined slope in the relative critical depth range of 0.128 to 0.36 and the effect of the geometry of these elements is examined using Flow 3D software. The results showed demonstrate that the downstream relative depth obtained from the numerical analysis is in good agreement with the laboratory results. The application of rough elements on the inclined drop increased the downstream relative depth and also the relative energy dissipation. The application of rough elements on the sloping surface of the drop significantly reduced the downstream Froude number, so that the Froude number in all models ranging from 4.7~7.5 to 1.45~3.36 also decreased compared to the plain drop. Bat-shaped elements are structurally smaller in size, so the use of these elements, in addition to dissipating more energy, is also economically viable.

이 연구의 주요 목적은 경사진 낙하에서 에너지 소산을 증가시키는 방법을 제공하는 것입니다. 따라서 0.128 ~ 0.36의 상대 임계 깊이 범위에서 경사면에 원통형, 삼각형 및 박쥐 모양의 형상을 가진 세 가지 유형의 거친 요소가 사용되며 이러한 요소의 형상의 영향은 Flow 3D 소프트웨어를 사용하여 조사됩니다. 결과는 수치 분석에서 얻은 하류 상대 깊이가 실험실 결과와 잘 일치함을 보여줍니다. 경 사진 낙하에 거친 요소를 적용하면 하류 상대 깊이와 상대 에너지 소산이 증가했습니다. 낙차 경사면에 거친 요소를 적용하면 하류의 Froude 수를 크게 감소시켜 4.7~7.5에서 1.45~3.36 범위의 모든 모델에서 Froude 수도 일반 낙차에 비해 감소했습니다. 박쥐 모양의 요소는 구조적으로 크기가 더 작기 때문에 더 많은 에너지를 분산시키는 것 외에도 이러한 요소를 사용하는 것이 경제적으로도 가능합니다.

Keywords: Downstream depth, Energy dissipation, Froude number, Inclined drop, Roughness elements

Introduction

급수 네트워크 시스템, 침식 수로, 수처리 시스템 및 경사가 큰 경우 흐름 에너지를 더 잘 제어하기 위해 경사 방울을 사용할 수 있습니다. 낙하 구조는 지반의 자연 경사를 설계 경사로 변환하여 에너지 소산, 유속 감소 및 수심 증가를 유발합니다. 따라서 흐름의 하류 에너지를 분산 시키기 위해 에너지 분산 구조를 사용할 수 있습니다. 난기류와 혼합된 물과 공기의 형성은 에너지 소비를 증가 시키는 효과적인 방법입니다. 흐름 경로에서 거칠기 요소를 사용하는 것은 에너지 소산을 위한 알려진 방법입니다. 이러한 요소는 흐름 경로에 배치됩니다. 그들은 종종 에너지 소산을 증가시키기 위해 다른 기하학적 구조와 배열을 가지고 있습니다. 이 연구의 목적은 직사각형 경사 방울에 대한 거칠기 요소의 영향을 조사하는 것입니다.

Fig. 1: Model made in Ardabil, Iran
Fig. 1: Model made in Ardabil, Iran
Fig. 2: Geometric and hydraulic parameters of an inclined drop equipped with roughness elements
Fig. 2: Geometric and hydraulic parameters of an inclined drop equipped with roughness elements
Fig. 3: Views of the incline with (a) Bat-shaped, (b) Cylindrical, (c) Triangular roughness elements
Fig. 3: Views of the incline with (a) Bat-shaped, (b) Cylindrical, (c) Triangular roughness elements
Fig. 4: Geometric profile of inclined drop and boundary conditions with the bat-shape roughness element
Fig. 4: Geometric profile of inclined drop and boundary conditions with the bat-shape roughness element
Fig. 5: Variation of the RMSE varying cell size
Fig. 5: Variation of the RMSE varying cell size
Fig. 6: Numerical and laboratory comparison of the downstream relative depth
Fig. 6: Numerical and laboratory comparison of the downstream relative depth
Fig. 7: Flow profile on inclined drop in discharge of 5 L/s: (a) Without roughness elements; (b) Bat-shaped roughness element; (c) Cylindrical roughness element; (d) Triangular roughness element
Fig. 7: Flow profile on inclined drop in discharge of 5 L/s: (a) Without roughness elements; (b) Bat-shaped roughness element; (c) Cylindrical roughness element; (d) Triangular roughness element
Fig. 8: Relative edge depth versus the relative critical depth
Fig. 8: Relative edge depth versus the relative critical depth
Flow on the inclined drop with bat-shaped elements: (a) Non-submerged flow
Flow on the inclined drop with bat-shaped elements: (a) Non-submerged flow
Fig. 9: Flow on the inclined drop with bat-shaped elements: (b) Submerged flow
Fig. 9: Flow on the inclined drop with bat-shaped elements: (b) Submerged flow
Fig. 10: Relative downstream depth versus the relative critical depth
Fig. 10: Relative downstream depth versus the relative critical depth
Fig. 11: Relative downstream depth versus the relative critical depth
Fig. 11: Relative downstream depth versus the relative critical depth

Conclusions

현재 연구에서 FLOW-3D 소프트웨어를 사용하여 한 높이, 한 각도, 밀도 15% 및 지그재그 배열에서 삼각형, 원통형 및 박쥐 모양의 형상을 가진 세 가지 유형의 거칠기 요소를 사용하여 경사 낙하 수리학적 매개변수에 대한 거칠기 요소 형상의 영향 평가되었다. VOF 방법을 사용하여 자유 표면 흐름을 시뮬레이션하고 초기에 3개의 난류 모델 RNG, k-ɛ 및 kω를 검증에 사용하고 이를 검토한 후 RNG 방법을 사용하여 다른 모델을 시뮬레이션했습니다. 1- 수치 결과에서 얻은 부드러운 경사 방울의 하류 상대 깊이는 실험실 데이터와 매우 좋은 상관 관계가 있으며 원통형 요소가 장착 된 경사 방울의 상대 에지 깊이 값이 가장 높았습니다. 2- 하류 상대깊이는 임계상대깊이가 증가함에 따라 상승하는 경향을 나타내어 박쥐형 요소를 구비한 경사낙하와 완만한 경사낙하가 각각 하류상대깊이가 가장 높고 가장 낮았다. 3- 하류 깊이의 증가로 인해 상대적 임계 깊이가 증가함에 따라 상대적 에너지 소산이 감소합니다. 한편, 가장 높은 에너지 소산은 박쥐 모양의 요소가 장착된 경사 낙하와 관련이 있으며 가장 낮은 에너지 소산은 부드러운 낙하와 관련이 있습니다. 삼각형, 원통형 및 박쥐 모양의 거친 요소가 장착된 드롭은 부드러운 드롭보다 각각 65%, 76% 및 85% 더 많은 흐름 에너지를 소산합니다. 4- 낙차의 경사면에 거친 요소를 적용하여 다운 스트림 Froude 수를 크게 줄여 4.7 ~ 7.5에서 1.45 ~ 3.36까지의 모든 모델에서 Froude 수가 부드러운 낙하에 비해 감소했습니다. 또한, 다른 원소보다 부피가 작은 박쥐 모양의 거칠기의 부피로 인해 이러한 유형의 거칠기를 사용하는 것이 경제적입니다.

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electromagnetic metal casting computation designs Fig1

A survey of electromagnetic metal casting computation designs, present approaches, future possibilities, and practical issues

The European Physical Journal Plus volume 136, Article number: 704 (2021) Cite this article

Abstract

Electromagnetic metal casting (EMC) is a casting technique that uses electromagnetic energy to heat metal powders. It is a faster, cleaner, and less time-consuming operation. Solid metals create issues in electromagnetics since they reflect the electromagnetic radiation rather than consume it—electromagnetic energy processing results in sounded pieces with higher-ranking material properties and a more excellent microstructure solution. For the physical production of the electromagnetic casting process, knowledge of electromagnetic material interaction is critical. Even where the heated material is an excellent electromagnetic absorber, the total heating quality is sometimes insufficient. Numerical modelling works on finding the proper coupled effects between properties to bring out the most effective operation. The main parameters influencing the quality of output of the EMC process are: power dissipated per unit volume into the material, penetration depth of electromagnetics, complex magnetic permeability and complex dielectric permittivity. The contact mechanism and interference pattern also, in turn, determines the quality of the process. Only a few parameters, such as the environment’s temperature, the interference pattern, and the rate of metal solidification, can be controlled by AI models. Neural networks are used to achieve exact outcomes by stimulating the neurons in the human brain. Additive manufacturing (AM) is used to design mold and cores for metal casting. The models outperformed the traditional DFA optimization approach, which is susceptible to local minima. The system works only offline, so real-time analysis and corrections are not yet possible.

Korea Abstract

전자기 금속 주조 (EMC)는 전자기 에너지를 사용하여 금속 분말을 가열하는 주조 기술입니다. 더 빠르고 깨끗하며 시간이 덜 소요되는 작업입니다.

고체 금속은 전자기 복사를 소비하는 대신 반사하기 때문에 전자기학에서 문제를 일으킵니다. 전자기 에너지 처리는 더 높은 등급의 재료 특성과 더 우수한 미세 구조 솔루션을 가진 사운드 조각을 만듭니다.

전자기 주조 공정의 물리적 생산을 위해서는 전자기 물질 상호 작용에 대한 지식이 중요합니다. 가열된 물질이 우수한 전자기 흡수재인 경우에도 전체 가열 품질이 때때로 불충분합니다. 수치 모델링은 가장 효과적인 작업을 이끌어 내기 위해 속성 간의 적절한 결합 효과를 찾는데 사용됩니다.

EMC 공정의 출력 품질에 영향을 미치는 주요 매개 변수는 단위 부피당 재료로 분산되는 전력, 전자기의 침투 깊이, 복합 자기 투과성 및 복합 유전율입니다. 접촉 메커니즘과 간섭 패턴 또한 공정의 품질을 결정합니다. 환경 온도, 간섭 패턴 및 금속 응고 속도와 같은 몇 가지 매개 변수 만 AI 모델로 제어 할 수 있습니다.

신경망은 인간 뇌의 뉴런을 자극하여 정확한 결과를 얻기 위해 사용됩니다. 적층 제조 (AM)는 금속 주조용 몰드 및 코어를 설계하는 데 사용됩니다. 모델은 로컬 최소값에 영향을 받기 쉬운 기존 DFA 최적화 접근 방식을 능가했습니다. 이 시스템은 오프라인에서만 작동하므로 실시간 분석 및 수정은 아직 불가능합니다.

electromagnetic metal casting computation designs Fig1
electromagnetic metal casting computation designs Fig1
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