Figure 9-15: Load-extension graphs obtained for welds carried out with industrial approach and continuous welding

로봇 TIG 용접의 미래: 지능형 3D 심 트래킹 및 적응형 공정 제어 기술

이 기술 요약은 Prasad Manorathna가 2015년 Loughborough University에 제출한 박사 학위 논문 “Intelligent 3D Seam Tracking and Adaptable Weld Process Control for Robotic TIG Welding”을 기반으로 하며, STI C&D의 기술 전문가에 의해 분석 및 요약되었습니다.

키워드

  • Primary Keyword: 로봇 TIG 용접
  • Secondary Keywords: 적응형 용접, 3D 심 트래킹, 용접 자동화, 용접 공정 제어, 항공우주 용접, 지능형 로봇

Executive Summary

  • 과제: 숙련된 용접사의 기술에 크게 의존하는 항공우주 부품의 복잡하고 정밀한 TIG 용접을 자동화하는 데에는 기존 로봇 기술의 한계가 있었습니다.
  • 방법: 6축 산업용 로봇, 레이저 삼각 측량 센서, 용접 시스템을 통합하고, 실시간으로 용접 조인트 형상을 분석하여 용접 파라미터를 조절하는 지능형 알고리즘 기반의 폐쇄 루프 시스템을 개발했습니다.
  • 핵심 돌파구: 개발된 로봇 시스템은 가변적인 용접 갭을 실시간으로 감지하고, 이에 맞춰 용접 전류, 듀티 사이클, 와이어 공급 속도를 자동으로 조절하여 숙련된 용접사와 유사한 수준의 고품질 용접을 성공적으로 수행했습니다.
  • 핵심: 본 연구는 복잡한 형상과 변수가 많은 고부가가치 TIG 용접 공정에 지능형 자동화를 적용할 수 있는 실질적인 프레임워크를 제시합니다.

과제: 왜 이 연구가 CFD 전문가에게 중요한가

TIG(Tungsten Inert Gas) 용접은 다른 아크 용접에 비해 월등히 높은 품질의 결과물을 제공하여 항공우주 산업에서 광범위하게 사용됩니다. 그러나 항공우주 부품 용접은 엄격한 공차, 복잡한 3D 형상, 부품 간의 미세한 부정합(fit-up) 등 다양한 변수로 인해 자동화가 매우 어려운 분야로 남아있습니다.

현재 산업에서 사용되는 대부분의 용접 로봇은 사전 프로그래밍된 경로와 설정값에 따라 움직이는 ‘블라인드(Blind)’ 로봇입니다. 이러한 로봇은 예기치 않은 형상 변화나 갭 변동에 적응할 수 없어 항공우주 분야에서 요구하는 정밀도와 품질을 만족시키기 어렵습니다. 결국, 고가의 항공우주 부품 용접은 여전히 비용이 많이 들고 수급이 어려운 숙련된 용접사의 수작업에 의존하고 있는 실정입니다. 이러한 산업적 난제를 해결하기 위해, 용접 조인트의 형상을 실시간으로 감지하고 숙련된 용접사처럼 지능적으로 판단하여 용접 공정을 제어하는 ‘적응형 로봇 TIG 용접‘ 기술의 필요성이 절실히 요구되었습니다.

접근 방식: 연구 방법론 분석

본 연구는 지능형 적응형 로봇 TIG 용접 시스템을 구축하기 위해 하드웨어와 소프트웨어를 통합한 포괄적인 접근 방식을 채택했습니다.

  • 핵심 장비 구성:
    • 모션 제어: 6축 산업용 로봇(KUKA KR 16)을 사용하여 용접 토치와 센서의 정밀한 3D 움직임을 구현했습니다.
    • 용접 시스템: 자동화 모드 제어가 가능한 Fronius Magicwave 4000 TIG 용접기와 푸시-풀(push-pull) 방식의 와이어 공급 장치를 사용했습니다.
    • 3D 비전 센서: Micro-Epsilon의 레이저 삼각 측량 기반 스캐너(Scan control 2900-25)를 사용하여 용접 전 조인트의 3D 형상 데이터를 실시간으로 수집했습니다.
    • 데이터 수집 및 제어: National Instruments (NI) DAQ 시스템과 HKS 용접 센서를 통해 용접 전류, 전압 등 핵심 공정 데이터를 모니터링했습니다.
  • 시스템 통합 및 제어: 모든 하드웨어는 단일 워크스테이션(PC)에 연결되었으며, LabVIEW를 사용하여 개발된 중앙 제어 소프트웨어를 통해 통합적으로 제어되었습니다. 이 소프트웨어는 로봇 제어, 레이저 스캐너 데이터 수집, 실시간 형상 특징 추출, 용접기 파라미터 설정 등 모든 프로세스를 자동화하는 역할을 수행합니다.
  • 2단계 접근법 (Two-Pass Approach): 항공우주 산업의 높은 품질 요구사항을 충족시키기 위해 ‘스캔 후 용접’ 방식을 채택했습니다.
    1. 스캔 패스(Scan Pass): 로봇이 용접 경로를 따라 이동하며 레이저 스캐너로 조인트의 3D 형상(갭 변화, 정렬 상태 등)을 정밀하게 측정합니다.
    2. 용접 패스(Weld Pass): 스캔 단계에서 얻은 형상 데이터를 기반으로, 개발된 알고리즘이 각 위치에 최적화된 용접 파라미터를 계산하고 이를 적용하여 로봇이 용접을 수행합니다.

이러한 접근법은 용접 시작 전에 조인트의 상태를 완벽하게 파악하고 지능적인 결정을 내릴 수 있게 하여, 고가의 부품을 폐기할 위험을 최소화합니다.

돌파구: 주요 연구 결과 및 데이터

본 연구는 숙련된 용접사의 기술을 정량화하고, 이를 기반으로 한 적응형 로봇 시스템의 우수성을 데이터로 입증했습니다.

결과 1: 숙련된 용접사의 기술 정량화 및 제어 전략 도출

자동화의 기반을 마련하기 위해, 연구진은 초보, 중급, 숙련된 용접사의 수동 TIG 용접 과정을 정밀하게 분석했습니다. 그 결과, 숙련된 용접사는 복잡한 용접 환경을 단순화하는 독특한 제어 전략을 사용한다는 사실을 발견했습니다.

  • 핵심 파라미터 집중: 숙련된 용접사는 용접 전류와 와이어 공급 속도를 가장 중요한 변수로 삼아 적극적으로 제어했으며, 용접 속도나 토치 높이(전압)는 비교적 일정하게 유지했습니다 (그림 4-10, 4-17 참조).
  • 시각적 피드백 의존: 용접 풀(weld pool)의 형태와 크기를 시각적으로 관찰하는 것이 파라미터를 조절하는 가장 중요한 피드백 메커니즘이었습니다 (그림 4-28 참조).

이러한 발견은 로봇 제어 알고리즘을 개발할 때 모든 변수를 동시에 제어하려는 복잡한 접근 대신, 가장 영향력 있는 핵심 파라미터(용접 전류, 와이어 공급 속도, 듀티 사이클)에 집중하는 것이 더 효율적이라는 중요한 단서를 제공했습니다.

Figure 6-34: extracted points at vertical offset orientation
Figure 6-34: extracted points at vertical offset orientation

결과 2: 적응형 로봇 용접 시스템의 성능 입증

연구진은 0.25mm에서 2.5mm까지 갭이 변하는 까다로운 맞대기 용접(butt joint) 시편을 사용하여 네 가지 다른 용접 접근법의 성능을 비교했습니다.

  1. 일정 파라미터 접근법: 용접 품질이 불균일하고 일부 구간에서 용접이 제대로 형성되지 않았습니다 (그림 9-14(a)).
  2. 구간별 파라미터 접근법 (산업 방식): 품질은 개선되었으나, 파라미터가 변경되는 구간에서 과도한 열 입력으로 인한 결함이 관찰되었습니다 (그림 9-14(b)).
  3. 숙련된 용접사 접근법: 만족스러운 용접 품질을 보였으나, 갭 변화에 따라 용접 비드 폭이 다소 불균일했습니다 (그림 9-14(c)).
  4. 적응형 제어 접근법 (본 연구): 개발된 시스템은 갭 변화를 실시간으로 반영하여 파라미터를 연속적으로 조절함으로써, 전체 용접 길이에 걸쳐 가장 일관된 비드 폭과 열영향부(HAZ)를 형성했습니다 (그림 9-14(d)).

인장 강도 테스트 결과, 적응형 제어 접근법으로 제작된 시편은 숙련된 용접사가 제작한 시편과 유사한 높은 기계적 강도와 연신율을 보였으며, 다른 두 접근법에 비해 월등히 우수한 성능을 나타냈습니다 (그림 9-15 참조). 이는 본 연구에서 개발한 시스템이 단순한 경로 추종을 넘어, 기계적 특성까지 고려한 고품질 용접을 수행할 수 있음을 증명합니다.

R&D 및 운영을 위한 실질적 시사점

  • 공정 엔지니어: 본 연구의 경험적 모델(Chapter 8)은 가변 갭 용접 시 듀티 사이클, 용접 전류, 와이어 공급 속도가 품질을 결정하는 가장 중요한 제어 변수임을 보여줍니다. 이는 복잡한 용접 공정의 최적화 변수를 단순화하여 더 빠르고 효과적인 공정 개발을 가능하게 합니다.
  • 품질 관리팀: 그림 9-15의 하중-연신율 그래프는 개발된 적응형 접근법이 숙련된 용접사와 동등한 수준의 반복 가능한 기계적 강도를 달성함을 보여줍니다. 이는 자동화된 용접 공정에 대한 새로운 품질 검사 기준을 수립하는 데 중요한 데이터가 될 수 있습니다.
  • 설계 엔지니어: 이 시스템은 롤(roll), 피치(pitch), 요(yaw)와 같은 다양한 조인트 부정합을 정량화하고 이에 적응할 수 있습니다 (Chapter 7). 이는 설계 단계에서 제조 공차에 더 유연하게 대응할 수 있는 설계를 가능하게 하여 생산 수율을 높이는 데 기여할 수 있습니다.

논문 정보


Intelligent 3D Seam Tracking and Adaptable Weld Process Control for Robotic TIG Welding

1. 개요:

  • 제목: Intelligent 3D Seam Tracking and Adaptable Weld Process Control for Robotic TIG Welding
  • 저자: Prasad Manorathna
  • 발행 연도: 2015
  • 학술지/학회: Loughborough University (박사 학위 논문)
  • 키워드: Robotic TIG welding, 3D seam tracking, adaptable weld process control, intelligent automation, human skill capture, empirical modelling

2. 초록:

텅스텐 불활성 가스(TIG) 용접은 다른 차폐 아크 용접 유형에 비해 고품질의 용접부를 생산하는 독특한 능력으로 인해 항공우주 분야에서 광범위하게 사용됩니다. 그러나 대부분의 TIG 용접은 수동으로 수행되며 다른 용접 기술만큼 자동화 수준을 달성하지 못했습니다. 이는 주로 공정 지식의 부족과 부품 조립 시 발생하는 불일치와 같은 복잡성에 대한 적응력 부족 때문입니다. 최근 자동화의 발전으로 센서를 통해 지능적인 의사결정이 필요한 복잡한 작업에 산업용 로봇을 사용할 수 있게 되었습니다. 항공우주 부품의 TIG 용접과 같은 응용 분야는 엄격한 공차를 요구하며, 예상치 못한 변화에 대응하고 복잡한 형상의 용접을 수행하기 위한 지능적인 의사결정 능력이 필요합니다. 이러한 의사결정 절차는 용접 프로파일 형상에 대한 피드백을 기반으로 해야 합니다.

본 논문에서는 6축 산업용 로봇(KUKA KR 16)과 레이저 삼각 측량 기반 센서(Micro-Epsilon Scan control 2900-25)를 사용하여 실시간 위치 기반 폐쇄 루프 시스템을 개발했습니다. National Instruments 데이터 수집 시스템(NI DAQ)을 사용하여 입출력 제어를 수행했습니다. 용접은 푸시-풀 와이어 공급 시스템이 장착된 Fronius Magicwave 용접 시스템을 사용하여 수행되었습니다. 프로젝트 계획, 장비 선정, 구매, 설계, 시스템 통합 및 전체 로봇 TIG 용접 셀 설정이 박사 과정 연구 작업에 포함됩니다. 본 연구에서는 3차원(3D) 용접 조인트의 조인트 프로파일을 찾고 경로를 추적하기 위한 새로운 알고리즘을 개발했습니다. 또한 실시간으로 조인트 특징을 추출하는 알고리즘도 개발되었습니다. 중요한 용접 품질 특성을 예측하고 용접 조인트 형상을 기반으로 용접 기계 설정을 추정하기 위한 경험적 모델이 개발되었습니다. 개발된 로봇 TIG 용접 시스템은 지능형 알고리즘과 함께 가변 갭 용접 조인트의 용접을 만족스러운 결과로 수행할 수 있었으며, 이는 시각적 외관, 용접 비드 치수 및 기계적 강도 면에서 숙련된 수동 용접사와 밀접하게 관련되었습니다.

이 연구는 TIG 용접의 맥락에서 제시되었지만, 이 개념은 모든 아크 용접 공정 및 로봇 실란트 적용, 스프레이 페인팅과 같은 다른 응용 분야에도 적용 가능합니다.

3. 서론:

대부분의 현대 고부가가치 제조 시스템은 여전히 수동 작업의 기술과 유연성에 크게 의존하고 있습니다. 그러나 많은 경우, 지능형 자동화는 운영 효율성을 개선하고 사람들이 비위생적이거나 어렵고 위험한 작업 환경에서 일할 필요를 없애줌으로써 인간의 작업을 대체하는 더 유리한 대안이 될 수 있습니다. 용접은 가장 역동적이고 복잡한 제조 공정 중 하나이므로 자동화하기 어렵습니다. 산업 기반 응용 분야에서의 용접 자동화는 엔지니어들이 특정 용접 공정, 재료, 크기, 두께 및 용접 형상을 고려해야 하므로 더욱 어렵습니다. 이러한 추가 제약 조건은 자동화를 더 어렵게 만들 수 있습니다.

TIG 용접은 다른 용접 공정보다 더 많은 공정 변수를 포함하므로 자동화하기 매우 어려운 것으로 간주됩니다. TIG 용접은 우수한 용접 품질 때문에 다른 용접 공정으로 대체되기도 어렵습니다. 따라서 더 높은 정밀도와 품질이 요구되는 항공우주 부품 용접과 같은 응용 분야에서는 계속해서 TIG 용접을 사용합니다. 그러나 TIG 용접 로봇은 아직 수동 TIG 용접만큼의 높은 정밀도와 품질을 충족할 수 있는 능력이 없기 때문에, 숙련된 수동 용접사들이 여전히 고급 항공우주 부품 용접에서 주도적인 역할을 하고 있습니다. 선진국에서는 숙련 노동력이 비싸고, 이는 저임금 지역과의 지속적인 경쟁에 직면해 있어 산업계가 TIG 용접 자동화를 지속적으로 모색하게 만들었습니다.

현재 산업에서 사용되는 로봇은 형상 변화에 적응할 수 없기 때문에 “블라인드(Blind)” 용접 로봇이라고 불립니다. 센서가 광범위하게 사용되었지만, 센서 피드백은 적응성을 달성하기 위해 만족스러운 수준으로 사용되지 않았습니다. 속도, 크기, 비용 및 계산 능력과 같은 요소들이 성공적인 자동화를 달성하지 못한 주요 제한 요인이었습니다. 이는 또한 완전 자동화된 용접 로봇의 산업적 실현을 상당히 어려운 과제로 만들었습니다. 따라서 현재 용접 궤적과 용접 공정 변수는 작업자에 의해 사전 프로그래밍됩니다. 이 방법은 항공우주 부품 용접에 필요한 품질을 제공하지 못했습니다.

4. 연구 요약:

연구 주제의 배경:

TIG 용접은 항공우주 산업에서 고품질이 요구되는 핵심 공정이지만, 공정의 복잡성과 변수(부품 부정합 등)로 인해 자동화가 더디게 진행되어 왔습니다. 현재의 ‘블라인드’ 로봇 용접 시스템은 이러한 변수에 대응할 수 없어, 생산성과 품질 향상을 위해 센서 기반의 지능형 적응형 자동화 기술이 필요합니다.

이전 연구 현황:

과거 용접 자동화 연구는 주로 MIG 용접에 집중되었으며, TIG 용접 자동화에 대한 연구는 매우 제한적이었습니다. 기존 연구들은 주로 용접 공정 변수가 용접 품질에 미치는 영향을 이해하는 데 초점을 맞추었으나, 이를 실제 로봇 시스템에 적용하여 조인트 형상 변화에 실시간으로 적응하는 완전한 솔루션을 제시한 사례는 거의 없었습니다. 특히, 실제 용접 조건이 아닌 비드-온-플레이트(bead-on-plate) 기법을 사용한 연구가 많아 산업 적용에 한계가 있었습니다.

연구 목적:

본 연구의 주된 목적은 숙련된 수동 용접사와 유사한 품질로 까다로운 용접 작업을 수행할 수 있는 완전한 적응형 지능형 TIG 용접 로봇 시스템(MCRL 3 수준)을 개발하는 것입니다. 이를 위해 다음 세부 목표를 설정했습니다: 1. 수동 TIG 용접에서 인간의 기술과 지식을 정량적으로 분석. 2. 3D 레이저 스캐너의 성능을 평가하고 데이터 품질을 최적화. 3. 3D 용접 조인트 형상을 실시간으로 추출하고 정량화하는 알고리즘 개발. 4. 용접 공정 변수와 용접 품질(비드 형상, 강도) 간의 관계를 설명하는 경험적 모델 구축. 5. 조인트 형상 피드백을 기반으로 용접 파라미터를 지능적으로 선택하는 적응형 제어 전략 개발 및 검증.

핵심 연구:

본 연구의 핵심은 6축 로봇, 3D 레이저 스캐너, TIG 용접기를 통합한 폐쇄 루프 제어 시스템을 구축하고, 이를 제어하는 지능형 소프트웨어를 개발하는 것입니다. 소프트웨어는 (1) 레이저 스캔을 통해 용접 조인트의 3D 형상과 부정합(fit-up)을 정밀하게 측정하고, (2) 개발된 특징 추출 알고리즘으로 갭, 각도 등 주요 특징을 실시간으로 분석하며, (3) 사전 구축된 경험적 모델을 사용하여 각 위치의 형상에 최적화된 용접 파라미터(전류, 듀티 사이클, 와이어 공급 속도)를 지능적으로 계산하고, (4) 계산된 파라미터를 용접기에 실시간으로 전송하여 용접 품질을 제어하는 일련의 과정을 자동으로 수행합니다.

5. 연구 방법론

연구 설계:

본 연구는 세 단계로 구성된 실험적 설계를 따랐습니다. 1. 1단계 (인간 기술 분석): 수동 TIG 용접 실험을 통해 숙련도(초보, 중급, 숙련)에 따른 용접사의 공정 파라미터 제어 방식을 정량적으로 분석하고, 자동화를 위한 핵심 제어 전략을 도출했습니다. 2. 2단계 (시스템 구축 및 2D 트래킹): KUKA 로봇, Fronius 용접기, NI DAQ, 센서 등을 통합하여 기본 시스템을 구축하고, 2D 카메라를 이용한 초기 심 트래킹 기술을 개발했습니다. 3. 3단계 (3D 트래킹 및 적응형 제어): 3D 레이저 스캐너를 통합하고, 3D 특징 추출 및 심 트래킹 알고리즘을 개발했습니다. 또한, 용접 품질 예측을 위한 경험적 모델을 구축하고, 이를 기반으로 가변 갭에 대응하는 완전한 적응형 공정 제어 시스템을 완성했습니다.

데이터 수집 및 분석 방법:

  • 데이터 수집: HKS 용접 센서와 NI DAQ 시스템을 사용하여 용접 전류 및 전압 데이터를 1kHz 샘플링 속도로 수집했습니다. Micro-Epsilon 3D 레이저 스캐너를 사용하여 용접 조인트의 3D 프로파일 데이터를 획득했습니다. 또한, 카메라를 통해 용접 과정과 토치 각도를 영상으로 기록했습니다. 용접 후 시편은 인장 시험기(INSTRON 8801)를 사용하여 기계적 강도를 측정했습니다.
  • 데이터 분석: 수집된 데이터는 LabVIEW와 Matlab을 사용하여 분석되었습니다. 노이즈 제거를 위해 저역 통과 필터(low-pass filter)가 적용되었습니다. 용접사의 기술 분석과 용접 품질에 미치는 파라미터의 영향을 정량화하기 위해 분산 분석(ANOVA)과 같은 통계적 기법이 사용되었습니다. 타구치(Taguchi) 방법을 적용하여 최소한의 실험으로 공정 변수 간의 관계를 모델링하는 경험적 모델을 개발했습니다.

연구 주제 및 범위:

본 연구는 316L 스테인리스강 박판(1.5mm 두께)의 맞대기(butt), 겹치기(lap), 필렛(fillet) 조인트에 대한 로봇 TIG 용접을 다룹니다. 특히, 용접 갭이 0.25mm에서 2.5mm까지 변하는 가변 갭 맞대기 조인트에 대한 적응형 용접에 중점을 둡니다. 제어 대상이 되는 주요 공정 변수는 용접 전류, 배경 전류, 펄스 주파수, 듀티 사이클, 와이어 공급 속도입니다. 용접 속도, 아크 갭 등 다른 변수들은 일정하게 유지되었습니다. 연구의 핵심은 조인트 형상(특히 갭)의 변화를 감지하여 이들 핵심 변수를 실시간으로 최적화하는 것입니다.

6. 주요 결과:

주요 결과:

  • 본 연구를 통해 개발된 지능형 로봇 TIG 용접 시스템은 가변 갭 맞대기 조인트 용접에서 숙련된 용접사와 유사하거나 더 일관된 용접 품질을 달성했습니다.
  • 분산 분석(ANOVA) 결과, 용접 비드 형상과 강도에 가장 큰 영향을 미치는 파라미터는 듀티 사이클, 용접 전류, 와이어 공급 속도 순이었으며, 배경 전류와 펄스 주파수의 영향은 미미했습니다. 이는 제어 문제의 복잡성을 줄이는 데 중요한 단서를 제공했습니다.
  • 타구치 방법을 사용하여 개발된 상호작용(interaction) 다항식 모델은 용접 비드 폭, 높이, 용입 및 인장 강도를 높은 정확도(R² 값 0.83~0.99)로 예측할 수 있었습니다.
  • 3D 레이저 스캐너 성능 평가를 통해, 최적의 데이터 품질을 얻기 위한 조건(스탠드오프 거리 67-68mm, 노출 시간 1-2ms, 임계 입사각 15°-25° 회피 등)을 확립했습니다.
  • 개발된 3D 특징 추출 알고리즘은 노이즈나 데이터 손실이 있는 상황에서도 V, U, I 형상의 용접 조인트 특징을 x축에서 ±38µm, z축에서 ±127µm의 최대 평균 제곱 오차(MSE)로 정확하게 추출했습니다.
  • 4가지 용접 접근법(일정 파라미터, 산업(구간별), 숙련 용접사, 적응형 제어) 비교 결과, 본 연구에서 제안한 적응형 제어 방식이 가장 균일한 비드 형상과 열영향부를 보였으며, 기계적 강도 또한 숙련 용접사와 동등한 수준으로 가장 우수했습니다.
Figure 9-15: Load-extension graphs obtained for welds carried out with industrial approach and continuous welding
Figure 9-15: Load-extension graphs obtained for welds carried out with industrial approach and continuous welding

Figure List:

  • Figure 1-1: An image of an aero-engine section showing important parts
  • Figure 1-2: Manufacturing capability readiness levels
  • Figure 1-3: Intelligent and adaptable robotic TIG welding system developed by the author
  • Figure 1-4: Project plan
  • Figure 2-1: Robot work volume
  • Figure 2-2: Stereo vision principle
  • Figure 2-3: Laser scanner principle
  • Figure 2-4: TIG welding principle
  • Figure 2-5: First welding robot developed by ABB (IRB 6)
  • Figure 2-6: Collaborative robotic welding
  • Figure 2-7: Underwater welding
  • Figure 2-8: human-robot collaboration in welding
  • Figure 2-9: Stereo vision system correcting for path
  • Figure 2-10: Laser scanner inspecting prior to welding
  • Figure 3-1: Summarized system integration diagram
  • Figure 3-2: CAD design of the welding cell
  • Figure 3-3: Photographic view of the welding equipment (a) Fronius Magicwave 4000 welding machine (b) Wire feeder unit
  • Figure 3-4: Different welding torches used for different phases of the project (a) Manual welding torch, (b) Robocta TTW 4500 robotic torch
  • Figure 3-5: NI DAQ card and PXIe chassis system
  • Figure 3-6: Hall effect current sensor (a) Hall effect principle, (b) HKS process sensor
  • Figure 3-7: Principal of welding voltage sensing
  • Figure 3-8: Block diagram for NI DAQ system integration with the PC
  • Figure 3-9: Signal channels without noise filtering at dwell state (a) Welding current signal in frequency domain, (b) Welding voltage channel in frequency domain
  • Figure 3-10: process parameters at dwell state
  • Figure 3-11: process parameters during welding
  • Figure 3-12: Current and voltage signals in frequency domain (a) welding current during welding, (b) welding voltage during welding
  • Figure 3-13: Acquired signals after applying filtering
  • Figure 3-14: Welding spectrum
  • Figure 3-15: (a)Band-pass filter, (b) lens and camera
  • Figure 3-16: Camera with illumination source for weld area viewing
  • Figure 3-17: The triangulation principle of laser scanners
  • Figure 3-18: The triangle shape of the scanning beam
  • Figure 3-19: KUKA KR16 robot and robot coordinate systems
  • Figure 3-20: Network connection diagram
  • Figure 3-21: System integration diagram
  • Figure 3-22: Control diagram of the system
  • Figure 3-23: Welding fixture
  • Figure 3-24: Software integration diagram
  • Figure 3-25: 3D Seam tracking software module
  • Figure 3-26: Sensor feedback software module
  • Figure 3-27: 3D Feature extraction software module
  • Figure 3-28: Weld process control software module
  • Figure 4-1: Output of manual and robotic welding
  • Figure 4-2: System diagram of the experimental setup (a) block diagram, (b) image of the physical set-up
  • Figure 4-3: Three weld joint selected for testing (a) Butt joint, (b) Lap joint, (c) Fillet joint
  • Figure 4-4: An image of the camera setup for testing a welder
  • Figure 4-5: Torch and filler wire position definition
  • Figure 4-6: Typical welding diagram
  • Figure 4-7: Butt weld completed by a novice welder (a) welding current and voltage variation against time, (b) top view of the weld, (c) bottom view of the weld
  • Figure 4-8: Butt weld completed by a semi-skilled welder (a) welding current and voltage variation against time, (b) top view of the weld, (c) bottom view of the weld
  • Figure 4-9: Butt weld completed by a skilled welder (a) welding current and voltage variation against time, (b) top view of the weld, (c) bottom view of the weld
  • Figure 4-10: Average welding current used by different welders
  • Figure 4-11: Standard deviation in welding current for different welders
  • Figure 4-12: Different manual welding techniques (a) pulse created by the manual welder from the foot pedal, (b) normal welding technique used by welders
  • Figure 4-13: Pictures of bottom side for different weld techniques (a) pulsed current, (b) constant current
  • Figure 4-14: Indirect effect of pulsing on the voltage signal
  • Figure 4-15: Average voltage measured for different skill levels
  • Figure 4-16: Standard deviation in voltage for different skill levels
  • Figure 4-17: Average welding speed maintained by different welders
  • Figure 4-18: Effect of welding speed on weld finish (a) Higher speed (b) average speed used by a skilled welder
  • Figure 4-19: Filler wire feed frequency and consumption rate for different welders (a) filler wire feed frequency, (b) filler wire consumption rate
  • Figure 4-20: (a) Globular droplets from melting the wire from the arc (b) a weld performed by feeding the wire in to the melt pool
  • Figure 4-21: Torch stand-off distance for different welders
  • Figure 4-22: Images taken for different skill levels (a) novice welder, (b) semi-skilled welder, (c) skilled welder
  • Figure 4-23: Torch/filler wire orientation
  • Figure 4-24: Average current variation against joint type
  • Figure 4-25: Average voltage against joint type for different welders
  • Figure 4-26: Filler wire consumption rate for different weld joints
  • Figure 4-27: Welding speeds used for different weld joint types
  • Figure 4-28: Decision making criteria for critical tasks identified in TIG welding
  • Figure 4-29: Sample weld joint to check human adaptability
  • Figure 4-30: Experimental results of welding corners (a) welded sample, (b) trial-1, (c) trial-2, (d) trial-3
  • Figure 5-1: Photographic view of the experimental set-up
  • Figure 5-2: Photographic view of the Scan-control software
  • Figure 5-3: Calibration samples (a) feeler gauge set, (b) slip gauge set
  • Figure 5-4: Specified and measured working ranges of the laser scanner (a) specified laser scanner span, (b) actual span
  • Figure 5-5: Setup for vertical resolution measurement
  • Figure 5-6: Percentage error in measurements along z-axis
  • Figure 5-7: Setup measuring a metric feeler gauge and percentage error in measurements
  • Figure 5-8: Percentage error along the x-axis of the laser scanner
  • Figure 5-9: Percentage error against exposure time
  • Figure 5-10: Percentage error in measurements for checking repeatability
  • Figure 5-11: Measurement error at different illumination conditions
  • Figure 5-12: Inappropriate data from a laser scanner
  • Figure 5-13: Number of missing data points against stand-off distance
  • Figure 5-14: Arrangement for measurements at different steepness angles
  • Figure 5-15: Results of number of missing data points measured against steepness angle
  • Figure 5-16: Data at various steepness angles
  • Figure 5-17: Arrangement for measurements at different incidences angles
  • Figure 5-18: Raw images obtained from the laser scanner at different incidence angles
  • Figure 5-19: Effect of incidence angle on data acquisition
  • Figure 5-20: Effect of incidence angle on data acquisition (a) number of noisy data points (b)noisy data percentage
  • Figure 5-21: Different surface finished samples
  • Figure 5-22: Results obtained for different surface finish
  • Figure 5-23: Raw images captured at different exposure levels
  • Figure 5-24: Effect of exposure time on data acquisition (a) number of noisy data points (b) noisy data percentage
  • Figure 5-25: U-groove for finding optimum exposure time
  • Figure 5-26: Missing and noisy data percentage against exposure time
  • Figure 5-27: Data acquisition performance against specified threshold value (a) number of noisy data points (b) noisy data percentage
  • Figure 6-1: Experimental setup used for joint feature extraction
  • Figure 6-2: Photographic view of the experimental setup
  • Figure 6-3: Sequence of operations for robotic scanning and feature extraction
  • Figure 6-4: Sample weld groove types used for feature extraction (a) I groove, (b) V groove, (c) U groove
  • Figure 6-5: Features to be extracted from a weld joint
  • Figure 6-6: Data cropping process for outlier removal (a) data cropping process (b) resulting data
  • Figure 6-7: Gradient values along the 2D point cloud (dy/dx)
  • Figure 6-8: horizontal offsets between two consecutive laser points (dx)
  • Figure 6-9: Extracted feature points (.)
  • Figure 6-10: Feature extraction steps for the U-groove (a) raw data, (b) cropped data, (c) gradient (dy/dx), (d) Offset between consecutive laser points (dx), (e) extracted feature points (.)
  • Figure 6-11: Feature extraction of a I-butt joint (a)raw data, (b) dx, (c) Detected points (*)
  • Figure 6-12: Continuous weld groove edge and detected noisy data point
  • Figure 6-13: Filtering applied in both x and z axis separately (a) x-y raw data, (b) x-y data after filtering, (c) x-y data after fitting, (d) y-z raw data, (e) y-z data after outlier removal, (f) y-z data after fitting
  • Figure 6-14: Extracted feature points (a) raw data, (b) fitted data
  • Figure 6-15: Possible joint configurations
  • Figure 6-16: Roll angle measurement (a) physical set-up, (b) roll angle
  • Figure 6-17: Roll angle measurement along the weld joint
  • Figure 6-18: Pitch angle measurement (a) physical set-up, (b)pitch angle
  • Figure 6-19: Line fitting for pitch angle measurement
  • Figure 6-20: Yaw angle measurement (a) physical set-up, (b) yaw angle
  • Figure 6-21: Line fitting for yaw angle measurement
  • Figure 6-22: Vertical offset measurement (a) physical set-up, (b) vertical offset
  • Figure 6-23: Vertical offset measurement along the weld joint
  • Figure 6-24: Extracted features of selected weld joint type (a) I-groove, (b) V-groove, (c) U-groove
  • Figure 6-25: Mean square error in detected points for different groove types
  • Figure 6-26: Gap measurements (a) physical setup (b) gap measured between top edges, (c) gap measured between bottom edges (b)
  • Figure 6-27: Gap measurements using feature detection algorithms
  • Figure 6-28: extracted points at roll orientation
  • Figure 6-29: Average roll angle measurement accuracy (a) absolute error, (b) percentage error
  • Figure 6-30: extracted points at pitch orientation
  • Figure 6-31: Pitch angle measurement accuracy (a) absolute error, (b) percentage error
  • Figure 6-32: extracted points at yaw orientation
  • Figure 6-33: yaw angle measurement accuracy (a) absolute error, (b) percentage error
  • Figure 6-34: extracted points at vertical offset orientation
  • Figure 6-35: vertical offset measurement accuracy (a) absolute error, (b) percentage error
  • Figure 6-36: Feature extraction in I and U grooves at various joint fit-ups
  • Figure 7-1: Coordinate systems in the robotic welding system
  • Figure 7-2: 2D seam tracking setup
  • Figure 7-3: 2D seam tracking sequence
  • Figure 7-4: 2D image processing for seam tracking (a) image processing sequence, (b) detected edges
  • Figure 7-5: 2D seam tracking results
  • Figure 7-6: Mean square error in x-y coordinates in 2D seam tracking
  • Figure 7-7: Setup for checking gap sensing performance
  • Figure 7-8: Results of 2D gap sensing
  • Figure 7-9: Seam tracking methodology in x-axis
  • Figure 7-10: Diagram showing the point used for seam tracking
  • Figure 7-11: Software operating sequence for 3D seam tracking
  • Figure 7-12: Look-ahead distance
  • Figure 7-13: Torch placement during seam tracking for robotic welding
  • Figure 7-14: Points used for guiding the welding torch (a) I-groove, (b) V-groove, (c) U-groove
  • Figure 7-15: Seam tracking performed at various joint fit-ups (a) roll, (b) pitch, (c) yaw, (d) vertical offset, (e) horizontal offset
  • Figure 7-16: Seam tracking performance check for possible joint fit-ups (a) horizontal offset, (b) vertical offset, (c) roll, (d) pitch, (e) yaw
  • Figure 7-17: Seam tracking performed on some complex paths (a) complex 2D, (b) 3D curve, (c) sinusoidal
  • Figure 7-18: Robotic welding procedure
  • Figure 7-19: Robotic welding system with fixture
  • Figure 7-20: Robotic welding results for all possible joint fit-ups (a) roll angle of 0.5˚, (b) pitch angle of 0.5˚, (c) yaw angle of 0.5˚, (d) vertical offset of 0.5mm, (e) horizontal offset of 0.5mm
  • Figure 8-1: Weld input out parameters
  • Figure 8-2: Weld bead parameters
  • Figure 8-3: Pulsing parameters
  • Figure 8-4: Method of measuring weld bead parameters (a) measurement of bead parameters from Scan-control software, (b) method of obtaining average value
  • Figure 8-5: Tensile testing machine
  • Figure 8-6: Specimen preparation for tensile testing
  • Figure 8-7: Load-extension graph and important parameters extracted
  • Figure 8-8: Weld bead measurements against welding current
  • Figure 8-9: Weld bead measurements against background current
  • Figure 8-10: Weld bead measurements against pulse frequency
  • Figure 8-11: Weld bead measurements against duty cycle
  • Figure 8-12: Weld bead measurements against wire feed rate
  • Figure 8-13: Mathematical model development procedure
  • Figure 8-14: Results from ANOVA test for two L8 table for weld bead dimensions (a) Bead width : Y1, (b) Penetration : Y2, (c) Bead height : Y3
  • Figure 8-15: F-value obtained from L8 Table
  • Figure 8-16: Results from ANOVA for L25 table for weld bead dimensions (a) bead width : Y1, (b) penetration : Y2, (c) bead height : Y3
  • Figure 8-17: F-values obtained from L25 table
  • Figure 8-18: Results from ANOVA for weld strength (a) load at maximum tensile extension: Y4, (b) maximum load:Y5, (c) load at break:Y6
  • Figure 8-19: F-values obtained for tensile strength
  • Figure 8-20: Actual and predicted results of weld bead dimensions using interaction model (a) Actual () and predicted () results of weld bead width, (b) Actual () and predicted () results of weld bead height, (c) Actual () and predicted () results of weld penetration
  • Figure 8-21: Actual () and predicted () results of tensile strength using interaction model
  • Figure 8-22: Results of bead width prediction from validation experiments
  • Figure 8-23: Results of bead height prediction from the validation experiments
  • Figure 8-24: Results of penetration prediction from the validation experiments
  • Figure 8-25: Results of tensile strength prediction from the validation experiments
  • Figure 9-1: Robotic welding system setup to carry out welding on a variable butt gap joint
  • Figure 9-2: Effect of process parameters on bead width
  • Figure 9-3: Cross-sectional profile of an irregular profile weld joint
  • Figure 9-4: Adjacent cross sectional profiles showing respective cross sectional area
  • Figure 9-5: Important parameters in the weld pool used for control
  • Figure 9-6: Methodology for adaptive welding
  • Figure 9-7: Best process parameters obtained against set gap
  • Figure 9-8: Adaptive weld process parameter control (a) welding current, (b) duty cycle, (c) wire feed rate
  • Figure 9-9: Selection of regions for robotic welding
  • Figure 9-10: Methodology of finding weld process parameters
  • Figure 9-11: Welding current variation along variable gap
  • Figure 9-12: Wire feed rate variation along variable gap
  • Figure 9-13: Welding speed variation along variable gap
  • Figure 9-14: Photographic views of the representative welds carried out using different approaches (a) Constant process parameter approach, (b) Segmented parameter (industrial) approach, (c) Skilled welder’s approach, (d) Adaptive control approach
  • Figure 9-15: Load-extension graphs obtained for welds carried out with industrial approach and continuous welding
  • Figure 10-1: Developed robotic TIG welding system as part of the work carried out for the PhD

7. 결론:

본 논문에서는 지능형 심 트래킹과 적응형 용접 공정 제어 기능을 갖춘 새로운 TIG 용접 로봇을 성공적으로 개발했습니다. MCRL 3 수준의 이 시스템은 산업계의 요구를 충족시키기 위한 연구 결과를 실제 적용 가능한 수준으로 끌어올렸습니다.

  • 인간 행동 분석: 숙련된 용접사는 용접 전류와 와이어 공급 속도를 우선적으로 제어하여 공정을 단순화한다는 것을 발견했으며, 이는 지능형 자동화의 제어 로직을 단순화하고 효율화하는 데 중요한 통찰을 제공했습니다.
  • 3D 비전 및 알고리즘: 3D 레이저 스캐너의 성능을 최적화하고, 개발된 3D 특징 추출 알고리즘을 통해 다양한 조인트 형상과 부정합을 µm 수준의 정밀도로 실시간 정량화하는 데 성공했습니다.
  • 수학적 모델 및 적응형 제어: 용접 공정 변수와 품질 특성 간의 관계를 규명하는 경험적 모델을 구축했으며, 이를 기반으로 한 역전파 알고리즘은 가변 갭 용접에서 용접 파라미터를 지능적으로 선택하고 제어할 수 있음을 입증했습니다.
  • 성능 검증: 제안된 적응형 용접 접근법은 기존의 일정 파라미터 방식이나 산업에서 사용하는 구간별 제어 방식보다 월등히 우수한 용접 품질을 보였으며, 그 결과는 숙련된 용접사의 결과와 동등하거나 일부 측면(일관성)에서는 더 나은 성능을 보였습니다.

결론적으로, 본 연구는 가변적인 갭을 가진 맞대기 용접을 자동으로 수행하는 것이 가능함을 보여주었으며, 지능적이고 적응적인 로봇 TIG 용접을 위한 방법론과 잠재력을 성공적으로 시연했습니다.

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전문가 Q&A: 주요 질문과 답변

Q1: 왜 실시간 단일 패스(single-pass) 방식이 아닌, ‘스캔 후 용접’의 2단계(two-pass) 접근법을 선택했습니까?

A1: 항공우주 산업에서는 고가의 재료를 사용하므로 용접 실패로 인한 부품 폐기는 막대한 비용 손실을 초래합니다. 본 연구에서 채택한 2단계 접근법은 용접을 시작하기 전에 레이저 스캐너로 전체 용접 조인트의 형상을 정밀하게 분석할 수 있게 해줍니다. 이를 통해 시스템은 갭 변화, 부정합 등 모든 변수를 사전에 파악하고 지능적인 판단을 내릴 수 있어 용접 실패 위험을 최소화하고 최고 품질의 용접을 보장할 수 있습니다. (Chapter 7 참조)

Q2: 연구 결과, 배경 전류와 펄스 주파수가 용접 비드 형상에 미치는 영향이 미미하다고 나왔습니다. 그렇다면 이 파라미터들은 중요하지 않은 것인가요?

A2: 비드 형상에 대한 영향은 상대적으로 적었지만, 용접 강도에 대한 분산 분석(ANOVA) 결과(Figure 8-19)에서는 이 두 파라미터가 주 용접 전류나 듀티 사이클보다는 낮지만 무시할 수 없는 영향을 미치는 것으로 나타났습니다. 이는 용접 품질이 단순히 기하학적 형상뿐만 아니라 기계적 특성까지 고려해야 하는 복합적인 문제임을 보여주며, 최적화 목표에 따라 각 파라미터의 중요도가 달라질 수 있음을 시사합니다.

Q3: 특히 반짝이는 표면에서 레이저 스캐너의 노이즈나 데이터 손실 문제는 어떻게 처리했습니까?

A3: 두 가지 방식으로 접근했습니다. 첫째, 사전 실험(Chapter 5)을 통해 반짝이는 스테인리스강 표면에서 최적의 데이터 품질을 얻을 수 있는 레이저 스캐너 설정값(예: 노출 시간 1-2ms, 스탠드오프 거리 67-68mm, 임계 입사각 회피)을 찾아냈습니다. 둘째, 그럼에도 불구하고 발생하는 노이즈 데이터는 3D 포인트 클라우드를 처리하는 후처리 필터링 알고리즘(Chapter 6)을 통해 제거했습니다. 이 알고리즘은 연속된 포인트 간의 예상 변위 임계값을 초과하는 이상치(outlier)를 효과적으로 걸러냅니다.

Q4: 숙련된 용접사의 작업을 분석하여 얻은 가장 핵심적인 교훈은 무엇이었습니까?

A4: 가장 큰 교훈은 숙련된 용접사가 복잡한 TIG 용접 공정을 ‘단순화’하여 제어한다는 점입니다. 그들은 모든 파라미터를 동시에 미세 조정하는 대신, 용접 품질에 가장 큰 영향을 미치는 핵심 파라미터(주로 용접 전류와 와이어 공급 속도)를 우선적으로 제어하고 나머지 변수(용접 속도 등)는 비교적 일정하게 유지했습니다. 이 원칙은 로봇의 적응형 제어 알고리즘 개발에 직접적으로 적용되어, 제어 변수의 수를 줄이고 알고리즘의 안정성과 효율성을 높이는 데 결정적인 역할을 했습니다. (Chapter 4 참조)

Q5: 가변 갭에 대응하기 위해 용접 파라미터를 조절하는 적응형 모델(수식 9.12-9.14)은 어떻게 도출되었습니까?

A5: 이 모델은 실험 데이터 기반의 역전파(back-propagation) 방식으로 도출되었습니다. 먼저, 다양한 크기의 알려진 갭(0.25mm ~ 2.5mm)을 설정하고 각 갭에서 최상의 용접 결과를 내는 용접 전류, 듀티 사이클, 와이어 공급 속도의 조합을 실험적으로 찾았습니다. 이 데이터들을 그래프로 나타내자 갭 크기와 각 파라미터 값 사이에 뚜렷한 선형 관계가 나타났습니다(Figure 9-7). 이 선형 추세선을 분석하여 갭 크기를 입력하면 최적의 파라미터 값을 예측하는 간단하면서도 강력한 선형 방정식을 유도할 수 있었습니다.


결론: 더 높은 품질과 생산성을 향한 길

본 연구는 숙련된 용접사의 노하우와 첨단 센서 기술을 결합하여 고부가가치 산업의 오랜 난제였던 로봇 TIG 용접 자동화의 새로운 가능성을 열었습니다. 용접 조인트의 3D 형상을 실시간으로 분석하고, 경험적 모델을 통해 최적의 파라미터를 지능적으로 도출하는 이 적응형 시스템은 기존의 경직된 로봇 용접 방식의 한계를 극복하는 청사진을 제시합니다. 이는 단순히 사람의 작업을 모방하는 것을 넘어, 데이터에 기반한 일관성과 정밀도를 통해 수동 용접보다 더 안정적인 품질을 달성할 수 있는 잠재력을 보여주었습니다.

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

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

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저작권 정보

  • 이 콘텐츠는 Prasad Manorathna의 논문 “Intelligent 3D Seam Tracking and Adaptable Weld Process Control for Robotic TIG Welding”을 기반으로 한 요약 및 분석 자료입니다.
  • 출처: Loughborough University Institutional Repository (https://repository.lboro.ac.uk/articles/thesis/Intelligent_3D_seam_tracking_and_adaptable_weld_process_control_for_robotic_TIG_welding/9585041)

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

Figure 2. The predicted shrinkage porosity of test castings: (a) mold temperature of 25 °C and gravity casting (short for 25 °C, 0 rpm); (b) 800 °C, 0 rpm; (c) 25 °C, 200 rpm; (d) 800 °C, 200 rpm; (e) 25 °C, 400 rpm; (f) 800 °C, 400 rpm; (g) 25 °C, 600 rpm; (h) 800 °C, 600 rpm.

결함 없는 TiAl 합금 주조: 수치 해석을 통한 인베스트먼트 캐스팅 최적화

이 기술 요약은 Yi Jia 외 저자가 2015년 Metals 저널에 발표한 “Modeling of TiAl Alloy Grating by Investment Casting” 논문을 기반으로 하며, STI C&D에서 기술 전문가를 위해 분석 및 요약했습니다.

키워드

  • Primary Keyword: TiAl 합금 인베스트먼트 캐스팅
  • Secondary Keywords: 수축 다공성, 수치 해석, ProCAST, 원심 주조, TiAl 합금, 주조 결함

Executive Summary

  • 도전 과제: TiAl 합금은 높은 화학 반응성, 고융점, 낮은 연성 및 가공성으로 인해 복잡한 형상의 부품을 결함 없이 제조하기 어렵습니다.
  • 해결 방법: ProCAST 수치 해석 소프트웨어를 사용하여 TiAl 합금 격자(Grating)의 인베스트먼트 캐스팅 공정을 모델링하고 최적화한 후, 실험을 통해 검증했습니다.
  • 핵심 돌파구: 수치 해석을 통해 수축 다공성 및 기공 결함을 최소화하는 최적의 주조 조건(주형 온도, 회전 속도)을 성공적으로 식별했습니다.
  • 핵심 결론: 수치 해석은 TiAl 합금 인베스트먼트 캐스팅에서 발생하는 결함을 예측하고 제어하여 고품질 부품을 생산하는 데 매우 효과적이고 비용 효율적인 방법입니다.

도전 과제: 이 연구가 CFD 전문가에게 중요한 이유

에너지 및 환경 문제는 경량 소재의 개발을 촉진하고 있습니다. 특히 TiAl 합금은 항공우주 및 자동차 산업에서 기존의 Ni기 초합금을 대체할 유망한 소재로 주목받고 있습니다. 600°C 이상의 고온에서도 우수한 기계적, 내산화성, 내식성 특성을 보이기 때문입니다.

하지만 TiAl 합금은 높은 화학 반응성, 고융점, 낮은 연성 및 가공성 때문에 양산에 어려움이 있습니다. 이러한 문제를 해결하기 위해 복잡한 형상의 부품을 정밀하게 제작할 수 있는 인베스트먼트 캐스팅(Investment Casting)이 주목받고 있습니다. 그러나 주조 공정은 육안으로 관찰할 수 없으며, 전통적인 방식은 경험에 의존하기 때문에 높은 비용과 긴 개발 주기를 요구합니다. 따라서 주조 공정을 사전에 예측하고 최적화할 수 있는 수치 해석 기술의 중요성이 그 어느 때보다 커지고 있습니다.

접근 방식: 연구 방법론 분석

본 연구는 TiAl 합금 격자 부품의 인베스트먼트 캐스팅 공정을 최적화하기 위해 수치 해석과 실험적 검증을 병행했습니다.

  • 수치 해석: 유한 요소 해석(FEM) 소프트웨어인 ProCAST를 사용하여 주형 충전 및 응고 거동을 시뮬레이션했습니다. 해석에 사용된 TiAl 합금(Ti–47Al–2.5V–1Cr at. %)과 ZrO2 주형의 열물성 데이터는 Sung의 연구[13, 14]와 ProCAST에서 제공된 값을 사용했습니다. 시뮬레이션의 주요 변수는 주입 온도(1700°C), 충전 시간(3초), 주형 예열 온도, 회전 속도였습니다.
  • 주조품 제작: “로스트 왁스(lost wax)” 공정을 통해 세라믹 쉘 주형을 제작했습니다. 진공 스컬 용해로(Vacuum Skull Furnace)를 사용하여 TiAl 합금을 용해한 후, 예열된 주형에 주입하여 주조품을 제작했습니다. 테스트용 주조품(직경 400mm)과 최종 풀사이즈 주조품(직경 580mm) 두 가지를 제작했습니다.
  • 특성 분석: 제작된 테스트 주조품에서 시편을 채취하여 미세조직을 광학 현미경으로 관찰하고, 상온 인장 시험을 통해 기계적 특성을 평가했습니다. 파단면은 주사전자현미경(SEM)으로 분석했으며, 풀사이즈 주조품은 X-ray 비파괴 검사를 통해 내부 결함을 확인했습니다.

돌파구: 주요 연구 결과 및 데이터

결과 1: 테스트 주조 공정 변수 최적화

연구팀은 먼저 직경 400mm의 테스트 주조품에 대한 시뮬레이션을 수행하여 최적의 공정 조건을 탐색했습니다. 주형 온도와 회전 속도를 변경하며 수축 다공성(Shrinkage Porosity)과 기공(Voids) 발생 가능성을 예측했습니다.

  • 시뮬레이션 결과, 주형 온도 25°C의 중력 주조(Figure 2a)에서는 주조품 전체에 걸쳐 심각한 수축 다공성이 예측되었습니다.
  • 주형 온도를 800°C로 높이고 400rpm의 원심 주조를 적용했을 때, 수축 다공성(Figure 2f)과 기공(Figure 3f)이 모두 가장 효과적으로 억제되는 것을 확인했습니다. ProCAST에서 예측하는 기공은 가스나 산화물층을 의미하며, 이는 미세 다공성보다 더 심각한 결함으로 간주됩니다. 따라서 주형 온도 800°C, 회전 속도 400rpm이 테스트 주조에 가장 적합한 조건으로 선정되었습니다.

결과 2: 풀사이즈 주조 설계 개선 및 실험적 검증

테스트 주조 결과를 바탕으로 직경 580mm의 풀사이즈 주조품에 대한 시뮬레이션을 진행했습니다. 이때, 용탕의 안정적인 흐름을 위해 게이트 크기를 확장하는 등 러너 시스템을 개선했습니다.

Figure 1. Three-dimensional drawing of runner system for test casting.
Figure 1. Three-dimensional drawing of runner system for test casting.
  • 개선된 설계를 통해 원심력의 효과가 극대화되어, 더 낮은 주형 온도에서도 우수한 결과를 얻을 수 있었습니다. 시뮬레이션 결과, 주형 온도 600°C, 회전 속도 200rpm 조건(Figure 10d, 11d)이 수축 다공성과 기공을 최소화하는 최적의 조건으로 나타났습니다.
  • 이 조건으로 실제 주조품을 제작하여 X-ray 비파괴 검사를 수행한 결과(Figure 12), 시뮬레이션 예측과 유사하게 대부분의 영역에서 결함이 없었으나, 일부 리브(rib)와 디스크 접합부에서 블로우홀(blowhole)과 수축 결함이 관찰되었습니다. 이는 실제 주형의 가스 투과성이 시뮬레이션의 이상적인 조건과 달랐기 때문으로 분석됩니다.
  • 최종적으로 제작된 주조품의 상온 인장 강도는 약 675 MPa, 연신율은 1.7%로 측정되어 양호한 기계적 특성을 보였습니다.
Figure 2. The predicted shrinkage porosity of test castings: (a) mold temperature of 25 °C and gravity casting (short for 25 °C, 0 rpm); (b) 800 °C, 0 rpm; (c) 25 °C, 200 rpm; (d) 800 °C, 200 rpm; (e) 25 °C, 400 rpm; (f) 800 °C, 400 rpm; (g) 25 °C, 600 rpm; (h) 800 °C, 600 rpm.
Figure 2. The predicted shrinkage porosity of test castings: (a) mold temperature of 25 °C and gravity casting (short for 25 °C, 0 rpm); (b) 800 °C, 0 rpm; (c) 25 °C, 200 rpm; (d) 800 °C, 200 rpm; (e) 25 °C, 400 rpm; (f) 800 °C, 400 rpm; (g) 25 °C, 600 rpm; (h) 800 °C, 600 rpm.

R&D 및 운영을 위한 실질적 시사점

  • 공정 엔지니어: 본 연구는 주형 예열 온도와 회전 속도 조절이 TiAl 합금 인베스트먼트 캐스팅의 수축 다공성 및 기공 결함 제어에 결정적임을 보여줍니다. 풀사이즈 부품에 대해 제시된 최적 조건(주형 온도 600°C, 회전 속도 200rpm)은 실제 공정 설정에 중요한 기준점을 제공할 수 있습니다.
  • 품질 관리팀: 논문의 Figure 12(X-ray 이미지)와 Figure 5(미세조직 사진)는 최적화된 조건에서도 발생할 수 있는 결함(미세 다공성, 블로우홀)의 유형과 위치를 명확히 보여줍니다. 이는 비파괴 검사(NDT) 시 중점적으로 확인할 부분을 특정하는 데 도움이 될 수 있습니다.
  • 설계 엔지니어: 테스트 주조에서 풀사이즈 주조로 넘어가면서 러너 시스템을 개선한 사례는, 특히 격자와 같이 얇고 복잡한 부품에서 게이트 설계가 안정적인 용탕 충전과 결함 형성에 얼마나 중요한지를 시사합니다. 이는 초기 설계 단계에서 반드시 고려해야 할 중요한 요소입니다.

논문 상세 정보


Modeling of TiAl Alloy Grating by Investment Casting

1. 개요:

  • 제목: Modeling of TiAl Alloy Grating by Investment Casting
  • 저자: Yi Jia, Shulong Xiao, Jing Tian, Lijuan Xu and Yuyong Chen
  • 발행 연도: 2015
  • 발행 저널/학회: Metals
  • 키워드: numerical simulation; TiAl alloys; investment casting; shrinkage porosity

2. 초록:

TiAl 합금의 인베스트먼트 캐스팅은 TiAl 부품 제조를 위한 가장 유망하고 비용 효율적인 기술이 되었습니다. 본 연구는 TiAl 합금의 인베스트먼트 캐스팅과 관련된 일련의 문제들을 조사하는 것을 목표로 했습니다. 이 주조 모델의 주형 충전 및 응고 과정은 ProCAST를 사용하여 수치적으로 시뮬레이션되었습니다. 수축 다공성은 내장된 공급 기준에 의해 정량적으로 예측되었습니다. 수치 시뮬레이션에서 얻은 결과는 인베스트먼트 블록 주형을 사용하여 진공 스컬 용해로에서 수행된 실험과 비교되었습니다. TiAl 격자의 인베스트먼트 캐스팅은 제안된 방법의 정확성과 타당성을 검증하기 위해 수행되었습니다. 인장 시험 결과, 상온에서 인장 강도와 연신율은 각각 약 675 MPa와 1.7%였습니다. 인베스트먼트 캐스팅된 TiAl 합금의 미세구조와 기계적 특성에 대해 논의했습니다.

3. 서론:

에너지 및 환경 문제는 사회 경제적 발전을 지속하기 위한 주요 장애물이 되었습니다. 경량 소재로 무거운 소재를 대체하는 것은 이 문제를 해결하는 데 효과적입니다. 항공 및 우주항공 소재는 경량, 고강도 소재 개발에 중점을 두고 개발되고 있습니다. TiAl 합금은 고온(600°C 이상)에서 우수한 기계적, 내산화성 및 내식성 특성을 보여 항공기 및 자동차 산업에서 기존의 Ni기 초합금 부품을 대체할 가능성이 있습니다. 그러나 TiAl 합금의 화학적 이질성과 물리적 특성 때문에 시장 도입 노력은 제한적이었습니다. TiAl 기반 부품의 대량 생산에 대한 한계는 TiAl이 매우 높은 화학 반응성, 높은 용융 온도, 낮은 연성 및 불량한 가공성을 보인다는 점입니다. 반면, 주조는 터빈 블레이드, 터보차저 회전자 및 배기 밸브와 같은 복잡한 형상의 부품에 대해 상당한 이점을 보입니다. 이러한 문제들 때문에, 좋은 표면 마감과 낮은 생산 비용으로 거의 최종 형상에 가까운 부품을 직접 생산할 수 있는 인베스트먼트 캐스팅이 점점 더 많은 관심을 받고 있습니다.

4. 연구 요약:

연구 주제의 배경:

TiAl 합금은 항공우주 및 자동차 산업에서 고온 성능이 요구되는 부품의 경량화를 위한 핵심 소재이지만, 제조 공정이 까다로워 상용화에 어려움을 겪고 있습니다. 인베스트먼트 캐스팅은 복잡한 형상을 정밀하게 제작할 수 있는 효과적인 방법입니다.

이전 연구 현황:

이전 연구들은 주로 CaO, Al2O3, ZrO2, Y2O3와 같은 내화물과 용융 TiAl 합금 간의 열역학적 안정성 및 상호작용 메커니즘에 초점을 맞추어 왔습니다. 그러나 경험에 기반한 주조 공정은 비용이 많이 들고 주기가 길다는 단점이 있습니다.

연구 목적:

본 연구의 목적은 Ti–47Al–2.5V–1Cr (at. %) 합금을 사용하여 인베스트먼트 캐스팅으로 격자(Grating) 부품을 제작하고, 수치 해석을 통해 공정을 최적화하며, 그 과정에서 나타나는 미세구조와 기계적 특성을 분석하는 것입니다.

핵심 연구:

ProCAST 소프트웨어를 이용한 수치 해석을 통해 주형 충전 및 응고 과정을 시뮬레이션하여 수축 다공성을 예측하고, 이를 바탕으로 최적의 주조 공정 변수(주형 온도, 회전 속도)를 도출했습니다. 이후 실제 주조 실험을 통해 시뮬레이션 결과의 타당성을 검증하고, 제작된 주조품의 품질과 기계적 특성을 평가했습니다.

5. 연구 방법론

연구 설계:

본 연구는 수치 해석(시뮬레이션)과 실험적 검증을 결합한 방식으로 설계되었습니다. 먼저 테스트용 소형 주조품(직경 400mm)에 대한 시뮬레이션을 통해 공정 변수의 영향을 분석하고 최적 조건을 찾은 후, 이를 바탕으로 러너 시스템을 개선하여 풀사이즈 주조품(직경 580mm)을 제작하고 평가했습니다.

데이터 수집 및 분석 방법:

  • 수치 해석: ProCAST 소프트웨어를 사용하여 주형 충전, 온도장, 응고 파라미터를 계산하고, 이를 통해 수축 다공성과 기공 발생을 예측했습니다.
  • 주조품 제작: 로스트 왁스 공법으로 ZrO2 기반의 세라믹 주형을 제작하고, VAM-150 진공 스컬 용해로를 사용하여 TiAl 합금을 용해 및 주입했습니다.
  • 특성 분석: 광학 현미경 및 SEM을 사용하여 미세구조와 파단면을 분석했으며, 만능시험기를 이용해 상온 인장 특성을 측정했습니다. 풀사이즈 주조품은 X-ray 비파괴 검사를 통해 내부 결함을 확인했습니다.

연구 주제 및 범위:

이 연구는 TiAl 합금 격자 부품의 인베스트먼트 캐스팅 공정에 초점을 맞춥니다. 주요 연구 범위는 수치 해석을 통한 공정 최적화, 수축 다공성 예측, 실험적 검증, 그리고 최종 주조품의 미세구조 및 기계적 특성 평가를 포함합니다.

6. 주요 결과:

주요 결과:

  • 직경 400mm와 580mm의 TiAl 합금 격자 부품을 성공적으로 제작했습니다.
  • 테스트 주조품의 최적 주조 조건은 주입 온도 1700°C, 주형 예열 온도 800°C, 회전 속도 400rpm으로 확인되었습니다.
  • 풀사이즈 주조품의 최적 주조 조건은 주입 온도 1700°C, 주형 예열 온도 600°C, 회전 속도 200rpm으로 도출되었습니다.
  • 제작된 시편은 미세하게 분리된 γ-입자를 포함하는 전형적인 완전 층상(fully lamellar) 미세구조를 보였으며, 상온에서 인장 강도 약 675 MPa, 연신율 1.7%의 준수한 기계적 특성을 나타냈습니다.
Figure 7. Slice view at a mold temperature of 800 °C and rotation speed of 400 rpm, (a) disk and (b) rib.
Figure 7. Slice view at a mold temperature of 800 °C and rotation speed of 400 rpm, (a) disk and (b) rib.

Figure 목록:

  • Figure 1. Three-dimensional drawing of runner system for test casting.
  • Figure 2. The predicted shrinkage porosity of test castings: (a) mold temperature of 25 C and gravity casting (short for 25 C, 0 rpm); (b) 800 C, 0 rpm; (c) 25 C, 200 rpm; (d) 800 C, 200 rpm; (e) 25 C, 400 rpm; (f) 800 C, 400 rpm; (g) 25 C, 600 rpm; (h) 800 C, 600 rpm.
  • Figure 3. Predicted voids of test castings, (a–h), the same as the Figure 2.
  • Figure 4. Test casting (a,b) showed the specimen locations: I, II, III, IV, and V, for Figure 5a–e, respectively; VI for Figure 6a; Tensile for the tensile test.
  • Figure 5. Optical microstructure of test casting (a–e) were from the center hole to the outer edge, and the interval between the two samples measured 20 mm.
  • Figure 6. Micro-defects of test casting, (a) pore and (b–d) shrinkage.
  • Figure 7. Slice view at a mold temperature of 800 C and rotation speed of 400 rpm, (a) disk and (b) rib.
  • Figure 8. Tensile test stress-strain curve obtained at room temperature (a) and fracture surface (b) of as-cast TiAl specimen, transgranular (TG) and translamellar (TL).
  • Figure 9. Three-dimensional drawing of runner system for full-size casting.
  • Figure 10. The predicted shrinkage porosity of full-size castings, (a) mold temperature of 600 C and gravity casting (short for 600 C, 0 rpm); (b) 200 C, 200 rpm; (c) 400 C, 200 rpm; (d) 600 C, 200 rpm; (e) 600 C, 400 rpm.
  • Figure 11. Predicted voids of full-size castings, (a–e) the same as the Figure 10.
  • Figure 12. X-ray nondestructive inspection results of full-size casting, (a) the grating casting and (b–d) correspond to b, c and d areas on (a), respectively.

7. 결론:

원심 인베스트먼트 캐스팅에 의한 TiAl 격자의 주형 충전 및 응고 과정이 시뮬레이션되었습니다. 본 연구로부터 다음과 같은 주요 결론을 도출했습니다:

  1. 직경 400mm와 580mm의 격자 부품이 성공적으로 생산되었습니다.
  2. 테스트 주조의 주조 파라미터는 주입 온도 1700°C, 주형 예열 온도 800°C, 회전 속도 400rpm이었습니다.
  3. 풀사이즈 주조의 최적 주조 파라미터는 주입 온도 1700°C, 주형 예열 온도 600°C, 회전 속도 200rpm이었습니다.
  4. 시편은 미세하게 분리된 γ-입자를 나타내는 전형적인 완전 층상 미세구조를 보였습니다. 주조된 TiAl 시편은 적절한 기계적 특성을 보였습니다. 상온에서 인장 강도와 연신율은 각각 약 675 MPa와 1.7%였습니다.

8. 참고 문헌:

  1. Kim, Y.W. Gamma-titanium aluminides: Their status and future. J. Miner. 1995, 47, 39–41.
  2. Yamaguchi, M.; Inui, H.; Ito, K. High-temperature structural intermetallics. Acta Mater. 2000, 48, 307–322.
  3. Varin, R.A.; Gao, Q. The effect of chromium on the microstructure and micromechanical properties of TiAl-base alloys. Mater. Manuf. Process. 1996, 11, 381–410.
  4. Kuang, J.P.; Harding, R.A.; Campbell, J. Microstructures and properties of investment castings of y-titanium aluminide. Mater. Sci. Eng. A 2002, 329, 31–37.
  5. Gomes, F.; Barbosa, J.; Ribeiro, C.S. Induction melting of y-TiAl in CaO crucibles. Intermetallics 2008, 16, 1292–1297.
  6. Tsukihashi, F.; Tawara, E.; Hatta, T. Thermodynamics of calcium and oxygen in molten titanium and titanium-aluminum alloy. Metall. Mater. Trans. B 1996, 27, 967–972.
  7. Barbosa, J.; Ribeiro, C.S.; Monteiro, A.C. Influence of superheating on casting of y-TiAl. Intermetallics 2007, 15, 945–955.
  8. Kuang, J.P.; Harding, R.A.; Campbell, J. Investigation into refractories as crucible and mould materials for melting and casting y-TiAl alloys. Mater. Sci. Technol. 2000, 16, 1007–1016.
  9. Jia, Q.; Cui, Y.Y.; Yang, R. Intensified interfacial reactions between y-titanium aluminide and CaO stabilised ZrO2. Int. J. Cast Met. Res. 2004, 17, 23–27.
  10. Nowak, R.; Lanata, T.; Sobczak, N.; Ricci, E.; Giuranno, D.; Novakovic, R.; Holland-Moritz, D.; Egry, I. Surface tension of y-TiAl-based alloys. J. Mater. Sci. 2010, 45, 1993–2001.
  11. Cui, R.J.; Gao, M.; Zhang, H.; Gong, S.K. Interactions between TiAl alloys and yttria refractory material in casting process. J. Mater. Process. Technol. 2010, 210, 1190–1196.
  12. Teodoro, O.; Barbosa, J.; Naia, M.D.; Moutinho, A.M.C. Effect of low level contamination on TiAl alloys studied by SIMS. Appl. Surf. Sci. 2004, 231, 854–858.
  13. Sung, S.Y.; Kim, Y.J. Modeling of titanium aluminides turbo-charger casting. Intermetallics 2007, 15, 468–474.
  14. Fu, P.X.; Kang, X.H.; Ma, Y.C.; Liu, K.; Li, D.Z.; Li, Y.Y. Centrifugal casting of TiAl exhaust valves. Intermetallics 2008, 16, 130–138.
  15. Yang, R.; Cui, Y.Y.; Dong, L.M.; Jia, Q. Alloy development and shell mould casting of y-TiAl. J. Mater. Process. Technol. 2003, 135, 179–188.

전문가 Q&A: 자주 묻는 질문

Q1: 시뮬레이션과 실험에서 주입 온도를 1700°C로 설정한 이유는 무엇인가요?

A1: 논문에 따르면, TiAl 합금은 밀도가 낮고 응고 구간이 좁아 유동성이 좋지 않기 때문에 가능한 한 높은 온도로 주입하는 것이 주조 품질 향상에 유리합니다. 1700°C는 실험에 사용된 장비(Vacuum Skull Furnace)가 도달할 수 있는 최고 용해 온도였기 때문에 이 온도를 주입 온도로 선택했습니다.

Q2: Figure 2를 보면, 회전 속도를 400rpm에서 600rpm으로 높였을 때 오히려 수축 다공성이 증가했습니다. 그 이유는 무엇인가요?

A2: 논문에서는 초기 테스트 주조의 러너 시스템 설계 때문이라고 설명합니다. 과도한 원심력은 용탕의 흐름을 깨뜨려 오히려 충전 불량을 유발할 수 있습니다. 즉, 해당 러너 설계에서는 600rpm의 회전 속도가 너무 높아 용탕이 안정적으로 주형을 채우지 못하고 결함이 악화된 것입니다.

Q3: 테스트 주조의 최적 조건은 800°C, 400rpm이었지만, 풀사이즈 주조에서는 600°C, 200rpm으로 변경되었습니다. 어떤 이유로 조건이 바뀌었나요?

A3: 풀사이즈 주조에서는 테스트 주조의 시뮬레이션 결과를 바탕으로 러너 시스템(특히 게이트)을 개선했습니다. 개선된 설계 덕분에 용탕이 더 안정적으로 공급되고 원심력의 효과가 향상되어, 더 낮은 주형 예열 온도와 회전 속도로도 충분한 충전성을 확보할 수 있었습니다. 주형 온도를 낮추면 주형과 용탕 간의 계면 반응을 줄일 수 있는 장점도 있습니다.

Q4: ProCAST 시뮬레이션에서 예측한 “수축 다공성(shrinkage porosity)”과 “기공(voids)”은 어떤 차이가 있나요?

A4: 논문에 따르면, ProCAST에서 예측하는 “기공(voids)”은 갇힌 가스(air bubbles)나 산화물층(oxide layers)을 의미합니다. 이는 미세한 “수축 다공성(shrinkage porosity)”보다 더 심각한 결함으로 간주됩니다. 왜냐하면 고온 등방압 가압법(HIP) 공정으로 기공은 제거할 수 있지만, 미세 다공성은 제거하기 어렵기 때문입니다. 따라서 연구팀은 기공이 없는 조건(Figure 3f)을 우선적으로 고려했습니다.

Q5: Figure 12의 실험 결과(X-ray)에서는 시뮬레이션에서 예측하지 못한 블로우홀(blowhole) 같은 결함이 관찰되었습니다. 논문에서 그 원인을 어떻게 추정하나요?

A5: 논문에서는 이러한 결함이 실제 실험에 사용된 주형의 가스 투과성(permeability)이 충분하지 않았기 때문일 수 있다고 추정합니다. 시뮬레이션은 이상적인 조건을 가정하지만, 실제 주조에서는 주형의 가스 배출 능력이 부족하면 용탕 내 가스가 빠져나가지 못하고 블로우홀과 같은 결함을 형성할 수 있습니다.


결론: 더 높은 품질과 생산성을 향한 길

TiAl 합금의 복잡한 특성으로 인한 주조의 어려움은 고부가가치 산업에서 큰 도전 과제였습니다. 본 연구는 TiAl 합금 인베스트먼트 캐스팅 공정에서 수치 해석이 어떻게 결함을 예측하고 최적의 공정 조건을 찾아낼 수 있는지를 명확하게 보여주었습니다. 시뮬레이션을 통해 주형 온도와 회전 속도 같은 핵심 변수를 최적화함으로써, 양호한 기계적 특성을 가진 고품질의 격자 부품을 성공적으로 생산할 수 있었습니다. 이는 경험에 의존하던 기존 방식에서 벗어나, 데이터 기반의 예측을 통해 개발 시간과 비용을 획기적으로 줄일 수 있음을 의미합니다.

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

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

저작권 정보

  • 이 콘텐츠는 “Yi Jia” 외 저자의 논문 “Modeling of TiAl Alloy Grating by Investment Casting”을 기반으로 한 요약 및 분석 자료입니다.
  • 출처: https://doi.org/10.3390/met5042328

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

Figure 21: Dye penetrant testing. a) WD-40 and flaw detector cleaner b) weld plates sprayed with penetrant c) developer for exposing the defects d) result of dye penetrant test

AI 기반 용접 순서 최적화: 자동차 및 항공우주 산업의 용접 변형 최소화

이 기술 요약은 Jeyaganesh Devaraj가 2021년 United Arab Emirates University에 제출한 석사 학위 논문 “MINIMIZATION OF THE WELD DISTORTION BY WELD SEQUENCE OPTIMIZATION USING ARTIFICIAL INTELLIGENCE”를 기반으로 하며, STI C&D의 기술 전문가에 의해 분석 및 요약되었습니다.

키워드

  • Primary Keyword: 용접 변형 최소화
  • Secondary Keywords: 용접 순서 최적화, 인공지능 용접, 유한요소해석(FEA), 이종 금속 용접, GMAW

Executive Summary

  • 도전 과제: 자동차, 항공우주 등에서 경량화를 위해 필수적인 이종 금속 용접 시 발생하는 심각한 변형은 추가 공정, 비용 증가, 품질 저하의 주된 원인이 됩니다.
  • 해결 방법: 유한요소해석(FEA) 시뮬레이션으로 다양한 용접 순서에 따른 변형 데이터를 생성하고, 이를 인공신경망(ANN)에 학습시킨 후 유전 알고리즘(GA)을 결합하여 최적의 용접 순서를 도출했습니다.
  • 핵심 성과: 개발된 AI 통합 모델(GANN)을 통해 최적의 용접 순서를 적용한 결과, 5개 용접부 조인트의 변형은 74.7%, 8개 용접부 조인트의 변형은 73.8%까지 획기적으로 감소했습니다.
  • 핵심 결론: AI 기반 용접 순서 최적화는 시간과 비용이 많이 드는 시행착오를 줄이고, 용접 구조물의 품질과 생산성을 극대화할 수 있는 강력하고 실용적인 솔루션입니다.

도전 과제: 왜 이 연구가 CFD 전문가에게 중요한가?

자동차, 항공우주, 해양 산업에서 무게 감소와 성능 향상을 위해 강철과 알루미늄 같은 이종 금속의 접합 수요가 급증하고 있습니다. 가스 메탈 아크 용접(GMAW)과 같은 융합 용접은 효율적인 접합 방법이지만, 용접부의 비균일한 가열 및 냉각 사이클로 인해 심각한 변형(Distortion)과 잔류 응력을 피할 수 없습니다.

이러한 변형은 부품의 정밀도를 떨어뜨려 조립 공정을 어렵게 만들고, 이는 곧 재작업 비용 증가와 전체 생산성 저하로 이어집니다. 기존에는 숙련된 용접사의 경험에 의존하거나, 시간과 비용이 많이 드는 반복적인 실험을 통해 최적의 용접 순서를 찾아야 했습니다. 하지만 용접 경로가 복잡해질수록 경우의 수는 기하급수적으로 늘어나기 때문에, 전통적인 방식으로는 진정한 최적해를 찾기 어렵다는 기술적 한계가 있었습니다. 본 연구는 이러한 산업 현장의 고질적인 문제를 해결하기 위해 인공지능을 활용한 새로운 접근법을 제시합니다.

Figure 2: Wire extension, CTWD and arc length diagram
Figure 2: Wire extension, CTWD and arc length diagram

접근 방식: 연구 방법론 분석

본 연구는 이종 금속(SS304 스테인리스강, AISI 1008 연강)의 맞대기 용접에서 발생하는 변형을 최소화하기 위해 체계적인 다단계 접근법을 사용했습니다.

  1. 용접 공정 파라미터 최적화: 먼저, 용접 품질 자체를 높이기 위해 다구치 기법(Taguchi Method)과 그레이 관계 분석(Grey Relational Analysis)을 사용하여 전류, 와이어 공급 속도, 용접 속도 등 핵심 GMAW 공정 변수들을 최적화했습니다. 이를 통해 인장 강도, 경도 등 기계적 특성이 우수한 용접 조인트를 확보하는 기반을 마련했습니다.
  2. FEA 시뮬레이션을 통한 데이터 생성: 최적화된 공정 파라미터를 적용하여 MSC Simufact 용접 소프트웨어로 유한요소해석(FEA)을 수행했습니다. 용접 비드를 여러 세그먼트로 나누고, 수백 가지의 다양한 용접 순서(Weld Sequence) 조합에 따른 최종 변형 값을 시뮬레이션을 통해 예측하고 데이터를 축적했습니다.
  3. 인공신경망(ANN) 모델 개발 및 학습: FEA로 확보한 방대한 ‘용접 순서-변형 값’ 데이터를 인공신경망(ANN) 모델에 학습시켰습니다. 이때, 순서 데이터는 ANN이 인식할 수 있도록 ‘원-핫 인코딩(One-hot encoding)’ 기법을 통해 이진 배열로 변환되었습니다. 이 과정을 통해 ANN은 특정 용접 순서가 주어지면 최종 변형을 빠르고 정확하게 예측하는 ‘대리 모델(Surrogate Model)’의 역할을 수행하게 됩니다.
  4. 유전 알고리즘(GA)을 통한 최적 순서 탐색: 마지막으로, 잘 훈련된 ANN 모델을 유전 알고리즘(GA)과 통합(GANN)했습니다. GA는 수천, 수만 가지의 가능한 용접 순서 조합을 효율적으로 탐색하며, 각 조합에 대한 변형 예측은 시간이 오래 걸리는 FEA 대신 빠른 ANN 모델을 통해 수행됩니다. 이 과정을 반복하여 변형을 최소화하는 최적의 용접 순서를 도출했습니다.
Figure 9: Bead geometry configuration
Figure 9: Bead geometry configuration

핵심 성과: 주요 발견 및 데이터

본 연구는 AI 기반 최적화 모델이 용접 변형을 극적으로 줄일 수 있음을 구체적인 데이터로 입증했습니다.

Figure 21: Dye penetrant testing. a) WD-40 and flaw detector cleaner b) weld plates sprayed with penetrant c) developer for exposing the defects d) result of dye penetrant test
Figure 21: Dye penetrant testing. a) WD-40 and flaw detector cleaner b) weld plates sprayed with penetrant c) developer for exposing the defects d) result of dye penetrant test

성과 1: GANN 모델을 통한 용접 변형의 획기적인 감소

개발된 GANN(Genetic Algorithm-Artificial Neural Network) 모델을 통해 도출된 최적 용접 순서를 실제 실험 및 시뮬레이션에 적용한 결과, 변형이 크게 감소했습니다.

  • 5개 용접부 설계: 초기 설계(순차 용접)에서 9.48mm에 달했던 최대 변형은 최적 순서(Sequence 34251)를 적용한 후 2.45mm(실험값)로 감소하여, 약 74.7%의 변형 감소 효과를 보였습니다 (Table 33 참조).
  • 7개 용접부 설계: 최대 변형이 16.25mm였던 조인트는 최적 순서(Sequence 5231467) 적용 후 8.31mm로 줄어들어 약 45.7%의 변형이 감소했습니다 (Table 33 참조).
  • 8개 용접부 설계: 최대 변형이 15.67mm였던 복잡한 조인트 역시 최적 순서(Sequence 65237148)를 통해 4.2mm로 변형이 줄어, 무려 73.8%의 감소율을 기록했습니다 (Table 33 참조).

이는 AI 모델이 단순히 변형을 예측하는 것을 넘어, 복잡한 문제에서 실질적인 최적해를 찾아 생산 품질을 극적으로 향상시킬 수 있음을 보여주는 강력한 증거입니다.

성과 2: 높은 정확도의 ANN 예측 모델 검증

GANN의 핵심인 ANN 예측 모델은 실험 및 FEA 결과와 비교하여 높은 신뢰도를 보였습니다. 개발된 ANN 모델의 평균 상대 오차(Mean Relative Error, MRE)는 다음과 같이 측정되었습니다.

  • 5개 용접부 모델: MRE 10.5% (Table 27)
  • 7개 용접부 모델: MRE 7.3% (Table 25)
  • 8개 용접부 모델: MRE 13.95% (Table 29)

모든 모델에서 오차율이 20% 허용 범위 이내로 나타났으며, 특히 R-value(상관계수)가 0.93 이상으로 매우 높아(Figure 38, Figure 39, Figure 41 참조) ANN 모델이 용접 순서에 따른 변형을 매우 정확하게 예측함을 입증했습니다. 이는 비용과 시간이 많이 소요되는 물리적 실험이나 FEA 시뮬레이션 횟수를 줄이고, 개발 초기 단계에서 빠르고 신뢰성 있는 의사결정을 내리는 데 ANN이 효과적인 도구가 될 수 있음을 시사합니다.

R&D 및 운영을 위한 실질적 시사점

  • 공정 엔지니어: 이 연구는 용접 순서가 최종 변형에 미치는 막대한 영향을 정량적으로 보여줍니다. 제안된 GANN 접근법을 활용하면, 생산 시작 전에 변형을 최소화하는 용접 순서를 사전에 설계하여 재작업률을 낮추고 공정 안정성을 높일 수 있습니다.
  • 품질 관리팀: 논문의 Table 30, 31, 32 데이터는 최악의 순서와 최적의 순서 간의 변형 차이를 명확히 보여줍니다. 이를 통해 용접 순서가 핵심 관리 포인트임을 인식하고, 새로운 품질 검사 기준을 수립하거나 공정 모니터링의 근거로 활용할 수 있습니다.
  • 설계 엔지니어: 연구 결과는 용접부의 위치와 순서가 구조물의 최종 형상에 결정적인 영향을 미친다는 것을 보여줍니다. 초기 설계 단계에서부터 용접 순서의 영향을 고려하여 변형에 강한 구조를 설계하는 데 중요한 통찰을 제공합니다.

논문 정보


MINIMIZATION OF THE WELD DISTORTION BY WELD SEQUENCE OPTIMIZATION USING ARTIFICIAL INTELLIGENCE

1. 개요:

  • 제목: MINIMIZATION OF THE WELD DISTORTION BY WELD SEQUENCE OPTIMIZATION USING ARTIFICIAL INTELLIGENCE
  • 저자: Jeyaganesh Devaraj
  • 발행 연도: 2021
  • 발행 기관: United Arab Emirates University
  • 키워드: Dissimilar Metal Welding, Gas Metal Arc Welding, Grey-based Taguchi Optimization, Weld Sequence Optimization, Artificial Neural Network (ANN), Genetic algorithm integrated ANN (GANN).

2. 초록:

이종 금속 용접 공정의 적용은 자동차, 항공우주, 해양 산업에서 증가하고 있으며, 이는 다른 금속의 접합뿐만 아니라 수리 및 재작업을 단순화하는 데도 도움이 됩니다. 용접 파라미터를 최적화하여 구조물을 용접하는 연구는 변형, 질량 증착, 인장 강도 등을 제어하는 데 중요합니다. 본 연구는 핫-인코딩 기법을 사용하여 이종 금속 접합의 변형을 줄이기 위한 유전 알고리즘 통합 인공신경망(GANN) 기반 용접 순서 최적화의 개발 및 구현을 보고합니다. 강철과 알루미늄의 이종 금속 용접에는 가스 메탈 아크 용접(GMAW)이 사용됩니다. 용접 비드를 여러 세그먼트로 나누어 다양한 용접 순서를 형성하는 것이 계획입니다. MSC MARC Simufact에서 제공하는 FEA 소프트웨어를 사용하여 용접 조인트의 변형 패턴을 시뮬레이션하고 분석합니다. 시뮬레이션 결과는 실험을 통해 검증되며, 변형 패턴 연구의 정확성을 달성하기 위해 20% 미만의 오차율로 검증될 것입니다. 다양한 순서의 훈련 세트를 사용하여 신경망을 훈련시켜 최적에 가까운 순서를 얻습니다. 이 연구의 결과는 인장 강도, 경도, 비드 형상 등 더 나은 조인트 특성을 위한 최적화된 공정 파라미터의 선택입니다. 이 최적화된 공정 파라미터는 순서대로 수행되는 조인트 용접에 사용됩니다. 마지막으로, GANN을 사용하여 순서를 최적화하여 변형을 줄이고 용접물의 효율성을 향상시킵니다. 얻어진 순서는 GMAW와 Simufact 용접 소프트웨어를 모두 사용하여 최소 변형 기준에 대해 테스트됩니다. 결과는 제안된 최적화 모델이 모든 종류의 용접 설계 및 최적화 문제에 적합함을 예시합니다.

3. 서론:

이종 금속 용접은 에너지 생산, 전자, 원자력 발전소, 석유 및 제조 부문에서 무게 감소, 고가 금속 대체 및 우수한 특성 결합을 위해 널리 사용됩니다. 그러나 공통된 용접 조건 하에서 용접될 재료의 야금학적 및 화학적 특성 차이로 인해 다른 금속의 효과적인 접합은 중요한 도전 과제였습니다. 용접 변형은 용접 구조물, 특히 금속 특성 및 구조적 무결성에 부정적인 영향을 미치는 것으로 알려져 있습니다. 변형을 적절히 제어하여 불완전한 형상과 균열의 발생을 피하는 것이 필수적입니다. 이 문제를 해결하는 가능한 방법 중 하나는 용접 공정의 공정 파라미터와 용접 순서를 최적화하는 것입니다. 본 연구는 GMAW의 공정 파라미터를 최적화하여 필러 금속 소비, 인장 강도, 경도 및 최적의 용접 비드 형상에 대한 역할을 예시하고, 나아가 용접 순서 최적화를 통해 변형을 최소화하는 것을 목표로 합니다.

4. 연구 요약:

연구 주제의 배경:

이종 금속 용접은 경량화 및 비용 효율성을 위해 여러 산업에서 중요성이 커지고 있습니다. 그러나 재료 간의 열팽창 계수, 열전도율 등의 차이로 인해 용접 후 심각한 변형이 발생하여 제품의 정밀도와 성능을 저하시키는 문제가 있습니다.

이전 연구 현황:

과거 연구들은 용접 공정 파라미터(전류, 전압 등) 최적화나 용접 순서 최적화에 개별적으로 초점을 맞추었습니다. 특히 용접 순서 최적화는 경우의 수가 방대하여 유전 알고리즘(GA)이나 대리 모델(Surrogate Model)을 사용하는 접근법이 있었지만, ANN과 GA를 통합하여 이종 금속 용접 변형 최소화에 적용한 연구는 드물었습니다.

연구 목적:

본 연구의 핵심 목적은 다음과 같습니다. 1. 이종 금속 용접의 용접성을 향상시킨다. 2. 다구치 기법 및 그레이 관계 분석을 통해 인장 강도, 경도, 비드 형상 등 기계적 특성을 극대화하는 최적의 용접 공정 파라미터를 도출한다. 3. 유한요소해석(FEA) 데이터를 기반으로 높은 예측 성능을 가진 인공신경망(ANN) 모델을 개발하고 검증한다. 4. ANN과 유전 알고리즘(GA)을 통합한 GANN 모델을 사용하여 용접 변형을 최소화하는 최적의 용접 순서를 찾는다.

핵심 연구:

연구의 핵심은 두 단계로 구성됩니다. 첫째, 통계적 기법(다구치, GRA)을 사용하여 GMAW 공정 자체의 품질을 보장하는 최적의 파라미터를 결정합니다. 둘째, 이 최적의 파라미터 조건 하에서, 복잡한 ‘용접 순서’ 문제를 해결하기 위해 FEA, ANN, GA를 결합한 AI 기반 최적화 프레임워크를 구축하고 그 효과를 검증합니다. 특히, ANN이 FEA 시뮬레이션을 대체하는 빠른 대리 모델 역할을 하고 GA가 광범위한 해결책 공간을 효율적으로 탐색하는 통합 모델(GANN)의 개발 및 적용이 본 연구의 핵심입니다.

5. 연구 방법론

연구 설계:

본 연구는 실험적 설계, 수치 시뮬레이션, 인공지능 모델링을 결합한 통합적 연구 설계를 따릅니다. 1. 실험 설계: 1.5mm 두께의 SS304와 AISI 1008 강판을 맞대기 용접하기 위해 L9 직교 배열을 사용한 다구치 실험 설계를 적용했습니다. 제어 변수는 용접 전류, 와이어 공급 속도, 용접 속도였습니다. 2. 수치 시뮬레이션: 3D CAD 모델을 생성하고 MSC Apex를 사용하여 헥사헤드럴 메시로 분할했습니다. 이후 MSC Simufact 용접 전문 소프트웨어를 사용하여 열-기계 연성 해석을 수행했습니다. 열원 모델로는 Goldak의 이중 타원체 모델을 사용했습니다. 3. AI 모델링: FEA로부터 얻은 용접 순서와 변형 데이터를 사용하여 다층 순방향 역전파 신경망(BPNN)을 구축했습니다. 입력 데이터는 원-핫 인코딩으로 처리되었고, MATLAB R2020 환경에서 Levenberg-Marquardt 알고리즘으로 네트워크를 훈련시켰습니다. 훈련된 ANN은 유전 알고리즘(GA)과 통합되어 최적화(GANN)에 사용되었습니다.

데이터 수집 및 분석 방법:

  • 기계적 특성 측정: 용접된 시편에 대해 만능시험기(UTM)를 사용하여 인장 강도(ASTM E8/E8M)를, 비커스 경도 시험기(ASTM A370)를 사용하여 경도를 측정했습니다.
  • 형상 및 결함 분석: 용접 비드의 형상(폭, 높이, 용입 깊이)을 측정하고, 육안 검사 및 염료 침투 탐상 시험(Dye Penetrant Test)을 통해 표면 결함을 확인했습니다. 주사전자현미경(SEM)을 사용하여 미세조직 및 파단면을 분석했습니다.
  • 변형 측정: 용접 후 평평한 표면에 시편을 놓고 다이얼 게이지를 사용하여 Z축 방향의 변형을 여러 지점에서 측정했습니다.
  • 데이터 분석: 다구치 기법의 신호 대 잡음비(S/N ratio)와 분산 분석(ANOVA)을 사용하여 공정 파라미터의 영향을 분석했습니다. 다중 목표 최적화를 위해 그레이 관계 분석(GRA)을 적용했습니다. ANN 모델의 성능은 평균 상대 오차(MRE)와 상관계수(R-value)로 평가했습니다.

연구 주제 및 범위:

본 연구는 1.5mm 두께의 SS304와 AISI 1008 강판의 GMAW 맞대기 용접에 국한됩니다. 주요 연구 주제는 용접 공정 파라미터 최적화를 통한 기계적 특성 향상과, AI 기반 용접 순서 최적화를 통한 Z축 방향의 변형 최소화입니다. 5개, 7개, 8개의 용접 세그먼트로 구성된 세 가지 다른 복잡도의 용접 설계에 대해 최적화 모델을 개발하고 검증했습니다.

6. 주요 결과:

주요 결과:

  • 그레이 관계 분석을 통한 다중 목표 최적화 결과, 최적의 공정 파라미터 조합은 전류 90A, 와이어 공급 속도 3.1 m/min, 용접 속도 380 mm/min (I3F1S2)으로 도출되었습니다. 이 조건으로 제작된 시편(C1)은 초기 설계(DM5) 대비 인장 강도 15.7%, 경도 12.7%, 용입 깊이 5.9%가 향상되었고, 질량 증착은 21.4% 감소했습니다.
  • 개발된 ANN 예측 모델은 5, 7, 8개 용접 순서 모델에 대해 각각 10.5%, 7.3%, 13.95%의 낮은 평균 상대 오차(MRE)를 보여 높은 예측 정확도를 입증했습니다.
  • ANN과 GA를 통합한 GANN 최적화 모델은 각 용접 설계에서 변형을 최소화하는 최적의 순서를 성공적으로 찾아냈습니다.
  • 5개 용접부 설계의 경우, 최적 순서(34251) 적용 시 변형이 9.48mm에서 2.45mm로 74.7% 감소했습니다.
  • 7개 용접부 설계의 경우, 최적 순서(5231467) 적용 시 변형이 16.25mm에서 8.31mm로 45.7% 감소했습니다.
  • 8개 용접부 설계의 경우, 최적 순서(65237148) 적용 시 변형이 15.67mm에서 4.2mm로 73.8% 감소했습니다.
  • 미세구조 분석 결과, 최적화된 파라미터로 용접된 시편(C1)은 초기 설계 시편(DM9)에 비해 더 미세한 등축 페라이트 조직을 가졌으며, 이는 기계적 특성 향상과 일치하는 결과입니다.

Figure 목록:

  • Figure 1: Structure of the thesis
  • Figure 2: Wire extension, CTWD and arc length diagram
  • Figure 3: Crossover process
  • Figure 4: Mutation of a chromosome
  • Figure 5: Anatomy of experimental setup
  • Figure 6: Top view of table CNC and fixture of weld sample
  • Figure 7: Welding apparatus – self-build table CNC coupled with weld machine
  • Figure 8: Schematic diagram of weld sample
  • Figure 9: Bead geometry configuration
  • Figure 10: Schematic representation of tensile strength, yield point and respective deformation phase in stress-strain curve
  • Figure 11: Tensile test specimen of standard ASTM E8/E8M
  • Figure 12: Schematic representation of hardness testing
  • Figure 13: Layout of grey relational analysis
  • Figure 14: FE model for the weld design used in the present investigation
  • Figure 15: Layout of numerical simulation
  • Figure 16: Meshing with hexagonal elements for the welded plates
  • Figure 17: Double ellipsoidal heat source model. Where, af -front length of molten pool; ar – rear length of molten pool; b- half width; d- depth of penetration
  • Figure 18: Boundary conditions for FEM provided by clamping on the weld design.
  • Figure 19: Model of a classical artificial neural network
  • Figure 20: Proposed optimization model –GANN
  • Figure 21: Dye penetrant testing
  • Figure 22: SN ratio plots of parametric effect on MD and bead geometry
  • Figure 23: Stress-strain curve for sample DM-9
  • Figure 24: Load vs strain curve for sample DM-9
  • Figure 25: SN ratio and mean effect plots for larger the better.
  • Figure 26: Optimization and experimental results for hardness.
  • Figure 27: The dissimilar weld in cross – sectional area (38 μm – magnification of ×200). Optical microscopy images after double etching (A-austenite, D- columnar structure, P- pearlite, F- ferrite)
  • Figure 28: SEM microstructure images MS-FZ region at ×500 (C1 sample)
  • Figure 29: Comparison of SEM microstructure images
  • Figure 30: Dimpled structure observed in the fracture zone
  • Figure 31: Distortion measurement
  • Figure 32: 3D model of work piece nomenclature
  • Figure 33: Displacement results of continuous weld bead from FEM analysis
  • Figure 34: Distortion for the weld sequence 1357246
  • Figure 35: Distortion for the weld sequence 1427365
  • Figure 36: Distortion for the weld sequence 5673214
  • Figure 37: Distortion for the weld sequence 7162354
  • Figure 38: Performance of BPNN
  • Figure 39: Performance of BPNN for 8 sequence model
  • Figure 40: Macroscopic image of the weld bead
  • Figure 41: Performance of BPNN for 7 sequence model
  • Figure 42: Optimal distortion after 200 iteration runs
  • Figure 43: Best solution history from GANN
  • Figure 44: Minimum distortion obtained after 200 iterations in 5 sequences weld design.
  • Figure 45: Minimum distortion obtained after 200 iterations for 8 sequences weld design
  • Figure 46: Best solution history from GANN for 8 sequence weld design
  • Figure 47: Fixture and clamping design used during welding process.
  • Figure 48: Assembly of Z-axis of CNC
  • Figure 49: Assembly of X, Y, and Z-axis of CNC
  • Figure 50: Assembly of complete CNC
  • Figure 51: Experimental setup used in the current investigation
  • Figure 52: Top-view of the weld torch mounted with CNC
  • Figure 53: Top-view of the weld torch mounted with CNC
  • Figure 54: Varying speed at current- 140 A and WFR- 4.5 m/min
  • Figure 55: Varying speed at current- 140 A and WFR- 5 m/min

7. 결론:

본 연구는 다구치 기반 그레이 관계 분석을 통해 이종 금속 GMAW 공정의 기계적 특성을 최적화했으며, 나아가 AI(ANN+GA)를 활용하여 용접 순서 최적화를 통한 변형 최소화 문제를 성공적으로 해결했습니다. 개발된 GANN 모델은 5, 7, 8개 용접 순서를 갖는 다양한 설계에서 최대 74.7%의 변형 감소 효과를 보이며 그 우수성을 입증했습니다. ANN 예측 모델은 실험 데이터와 높은 일치도를 보여, 시간과 비용이 많이 드는 시뮬레이션 및 실험을 대체할 수 있는 가능성을 제시했습니다. 이 연구에서 제안된 독창적인 최적화 접근법은 제한된 수의 순서뿐만 아니라 모든 정의된 순서 및 모든 종류의 조인트 구조에 적용될 수 있습니다. 결론적으로, 본 연구는 용접 변형 예측 및 최소화를 위한 강력한 AI 기반 프레임워크를 제공하며, 이는 자동차, 조선, 철강 구조물 등 다양한 산업 분야의 생산성과 품질 향상에 크게 기여할 수 있습니다.

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전문가 Q&A: 주요 질문과 답변

Q1: 왜 단순한 최적화 기법 대신 GANN(유전 알고리즘 + 인공신경망)이라는 복잡한 모델을 선택했나요?

A1: 용접 순서 최적화 문제는 용접 세그먼트 수가 늘어날수록 가능한 조합의 수가 폭발적으로 증가하는 ‘조합 최적화’ 문제입니다. 예를 들어, 8개의 용접 순서는 4만 가지가 넘는 경우의 수를 가집니다. 이 모든 경우를 FEA로 시뮬레이션하는 것은 현실적으로 불가능합니다. 따라서, 시간이 오래 걸리는 FEA 시뮬레이션을 빠르고 정확하게 모사하는 ANN ‘대리 모델’을 만들고, 방대한 탐색 공간을 효율적으로 탐색하는 GA를 결합하여 현실적인 시간 내에 최적해를 찾기 위해 GANN 모델을 사용했습니다.

Q2: 논문의 Table 33을 보면 5개 용접부에서 74.7%의 변형 감소를 달성했는데, 이는 기존 연구와 비교했을 때 어느 정도 수준의 성과인가요?

A2: 본 논문은 Asadi와 Goldak이 대리 모델을 사용하여 약 35%의 변형 감소를 달성한 선행 연구를 언급하고 있습니다(p.128). 이와 비교할 때, 본 연구에서 제안한 GANN 모델이 달성한 74.7%(5개 용접부) 및 73.8%(8개 용접부)의 변형 감소율은 기존 연구 대비 월등히 높은 성과입니다. 이는 ANN과 GA의 통합이 용접 변형 문제 해결에 매우 효과적임을 보여주는 결과입니다.

Q3: 연구에서 ‘원-핫 인코딩(one-hot encoding)’ 기법이 왜 필요했나요?

A3: 인공신경망(ANN)은 숫자 데이터를 입력으로 받지만, ‘1-2-3-4-5’와 같은 용접 순서는 단순한 크기 관계가 아닌 범주형 데이터입니다. 예를 들어, 순서 ‘2’가 ‘1’보다 두 배의 의미를 갖는 것이 아닙니다. 원-핫 인코딩은 ‘3’이라는 순서를 ‘[0,0,1,0,0…]’과 같은 이진 벡터로 변환하여 각 순서가 독립적인 범주임을 명확히 해줍니다. 이를 통해 ANN이 순서 간의 복잡한 비선형 관계를 효과적으로 학습하고 변형을 정확하게 예측할 수 있게 됩니다.

Q4: 연구 초반에 용접 공정 파라미터(전류, 속도 등)를 최적화한 이유는 무엇이며, 이것이 최종 목표인 순서 최적화와 어떻게 연결되나요?

A4: 최종 목표는 용접 ‘순서’가 변형에 미치는 영향을 분석하고 최적화하는 것입니다. 만약 용접 공정 ‘파라미터’가 최적이 아니라면, 변형의 원인이 순서 때문인지, 아니면 불안정한 용접 공정 자체 때문인지 명확히 구분하기 어렵습니다. 따라서 연구 초반에 다구치 기법 등으로 인장 강도와 경도가 우수한 최적의 공정 파라미터를 먼저 확립함으로써, 이후의 순서 최적화 단계에서는 변형에 대한 ‘순서’의 영향을 순수하게 평가하고 극대화할 수 있었습니다.

Q5: 이 연구 결과는 다른 종류의 재료나 더 두꺼운 판재 용접에도 동일하게 적용될 수 있을까요?

A5: 본 연구에서 개발한 GANN 방법론 자체는 범용성이 있습니다. 즉, 다른 재료(예: 알루미늄-구리)나 다른 두께의 판재에도 동일한 프레임워크(FEA 데이터 생성 → ANN 학습 → GA 최적화)를 적용할 수 있습니다. 다만, 재료의 물성치와 두께가 달라지면 열전달 및 기계적 거동이 변하므로, 해당 조건에 맞는 새로운 FEA 시뮬레이션 데이터를 생성하고 ANN 모델을 다시 훈련시키는 과정이 필요합니다. 도출된 최적 순서는 달라지겠지만, 최적 순서를 찾아가는 과정과 그 효과는 유사할 것으로 기대됩니다.


결론: 더 높은 품질과 생산성을 향한 길

이종 금속 용접에서 발생하는 변형은 오랫동안 제조 현장의 품질과 비용을 저해하는 고질적인 문제였습니다. 본 연구는 인공지능과 유한요소해석을 결합하여 용접 변형 최소화를 위한 강력한 해법을 제시했습니다. ANN과 GA를 통합한 GANN 모델은 수만 가지의 가능성 속에서 최적의 용접 순서를 효율적으로 찾아내고, 변형을 최대 74.7%까지 획기적으로 줄일 수 있음을 입증했습니다.

이러한 접근법은 더 이상 값비싼 시행착오나 숙련공의 감에 의존하지 않고, 데이터 기반의 과학적인 방법으로 용접 공정을 사전에 설계할 수 있음을 의미합니다. 이는 자동차, 항공우주, 조선 등 고정밀 용접이 요구되는 모든 산업 분야에서 품질 향상과 생산성 증대를 위한 중요한 전환점이 될 수 있습니다.

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

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

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

저작권 정보

  • 이 콘텐츠는 “Jeyaganesh Devaraj”의 논문 “MINIMIZATION OF THE WELD DISTORTION BY WELD SEQUENCE OPTIMIZATION USING ARTIFICIAL INTELLIGENCE”를 기반으로 한 요약 및 분석 자료입니다.
  • 출처: https://scholarworks.uaeu.ac.ae/all_theses/1013/

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

Рис. 13. Распределение никеля в сварном шве в отраженных электронах: a — продольное; б — поперечное сечение бугра

고속 용접의 한계 돌파: 비진공 전자빔 용접(NV-EBW)의 험핑 결함, CFD로 원인 규명 및 해결

이 기술 요약은 U. Reisgen 외 저자가 2012년 ‘Автоматическая сварка (Automatic Welding)’에 발표한 논문 “Исследование факторов, влияющих на образование дефектов сварного шва при электронно-лучевой сварке в открытой атмосфере (비진공 전자빔 용접 시 용접 비드 결함 형성에 영향을 미치는 요인 연구)”를 기반으로 STI C&D의 기술 전문가에 의해 분석 및 요약되었습니다.

Keywords

  • Primary Keyword: 비진공 전자빔 용접 (Non-Vacuum Electron Beam Welding, NV-EBW)
  • Secondary Keywords: 용접 결함, 험핑(Humping), 언더컷(Undercutting), 마랑고니 효과(Marangoni Effect), CFD 시뮬레이션

Executive Summary

  • The Challenge: 비진공 전자빔 용접(NV-EBW)은 높은 생산성을 자랑하지만, 고속 용접 시 발생하는 험핑(humping) 및 언더컷(undercutting)과 같은 표면 결함으로 인해 그 잠재력을 완전히 활용하지 못하는 문제가 있었습니다.
  • The Method: 연구팀은 실험적 연구(고속 비디오 촬영, 트레이서 물질 사용)와 나비에-스토크스 방정식 기반의 이론적 모델링을 결합하여 고속 용접 중 용융 풀의 동적 거동을 분석했습니다.
  • The Key Breakthrough: 용접 결함의 주된 원인이 용융 풀 내부의 대류가 아닌, 표면 장력 구배로 인한 열모세관 흐름(마랑고니 효과)의 불안정성 때문임을 실험적으로 규명했습니다.
  • The Bottom Line: 보호 가스에 산소를 첨가하거나 표면 활성 물질을 도포하여 표면 장력을 제어함으로써 험핑 결함을 억제하고, 결함 없는 고속 용접이 가능한 공정 윈도우를 크게 확장할 수 있습니다.

The Challenge: Why This Research Matters for CFD Professionals

비진공 전자빔 용접(NV-EBW)은 진공 챔버가 필요 없어 작업 사이클이 짧고, 높은 용접 속도를 구현할 수 있어 자동차 산업의 배기 시스템, 변속기 부품 등 대량 생산 공정에 널리 사용되는 혁신적인 기술입니다. 이론적으로는 매우 높은 용접 속도를 달성할 수 있지만, 실제 현장에서는 강재의 경우 8 m/min, 알루미늄 합금의 경우 15 m/min 이상의 속도에서 용접 비드 표면이 주기적으로 솟아오르는 험핑(humping)이나 비드 가장자리가 움푹 파이는 언더컷(undercutting)과 같은 심각한 결함이 발생합니다.

이러한 동적 결함은 용접부의 품질을 저하시키고 후속 공정을 어렵게 만들어, NV-EBW 기술이 가진 높은 생산성의 잠재력을 제한하는 핵심적인 기술적 병목 현상이었습니다. 따라서 결함 발생의 근본적인 물리적 메커니즘을 이해하고 이를 제어하는 것은 공정 효율성과 제품 신뢰성을 극대화하기 위해 반드시 해결해야 할 과제입니다.

The Approach: Unpacking the Methodology

본 연구는 결함 형성 메커니즘을 규명하기 위해 실험적 접근과 이론적 모델링을 병행했습니다.

  • 실험 장비: 최대 출력 25kW, 가속 전압 175kV 사양의 PTR-Precision technology社 NV-EBW 25-175 TU 장비와 최대 출력 30kW, 가속 전압 150kV의 Steigerwald社 장비를 사용하여 다양한 재료와 조건에서 용접 실험을 수행했습니다.
  • 이론적 모델링: 용융 풀의 동적 거동을 설명하기 위해 나비에-스토크스 방정식을 기반으로 한 유체 역학 모델을 개발했습니다. 이 모델은 용융 풀 표면의 안정성을 분석하여 험핑과 같은 파동이 발생하는 조건을 예측하는 데 사용되었습니다.
  • 핵심 변수 분석: 용접 속도, 빔 전류, 작동 거리, 보호 가스 종류, 소재 종류(DC05 강, TRIP 700 강, AlMg3, Pb 등) 및 두께 등 다양한 공정 변수가 결함 형성에 미치는 영향을 체계적으로 평가했습니다.
  • 유동 가시화: 고속 비디오 촬영을 통해 용융 풀의 동적 거동과 개별 험프의 성장 과정을 실시간으로 관찰했으며, 니켈(Ni)을 트레이서(tracer) 물질로 사용하여 용융 풀 내부의 유체 흐름 패턴을 명확히 시각화했습니다.
Рис. 1. Динамические дефекты сварных швов: a — бугристость (vw = 10 м/мин); б — подрез (vw = 12 м/мин)
Рис. 1. Динамические дефекты сварных швов: a — бугристость (vw = 10 м/мин); б — подрез (vw = 12 м/мин)

The Breakthrough: Key Findings & Data

Finding 1: 험핑 결함의 주범은 표면 장력 구배(마랑고니 효과)

기존에는 용융 풀 깊은 곳에서 표면으로 올라오는 강한 수직 대류가 험핑의 원인으로 추정되었습니다. 하지만 본 연구에서는 얇은 니켈 포일을 강판 사이에 삽입하여 용접한 후 단면을 분석하는 독창적인 트레이서 실험을 수행했습니다. 그 결과, 니켈은 용융 풀 하단에서 수직으로 상승하지 않고, 용융 풀 후방으로 향하는 수평적 흐름을 명확하게 보여주었습니다 (그림 13). 이는 박판 용접 시 험핑을 유발하는 주된 구동력은 표면 장력의 온도 구배에 따른 열모세관 유동, 즉 마랑고니 효과(Marangoni Effect)임을 직접적으로 증명한 것입니다.

Finding 2: 재료 물성과 두께에 따른 임계 용접 속도 규명

실험을 통해 다양한 재료에서 험핑이 발생하기 시작하는 임계 용접 속도를 정량적으로 확인했습니다. – 재료의 영향: 표면 장력(σ)이 높은 DC05 강(1800 mN/m)은 12 m/min에서 험핑이 시작된 반면, 표면 장력이 낮은 AlMg3(865 mN/m)는 20 m/min의 고속에서도 험핑이 발생하지 않았습니다 (표 1). 이는 표면 장력이 험핑 발생에 결정적인 역할을 한다는 것을 보여줍니다. – 두께의 영향:* 동일한 DC05 강에서도 두께가 0.7mm에서 3.5mm로 증가함에 따라 험핑 발생 임계 속도가 20 m/min에서 6 m/min으로 크게 감소했습니다 (표 2). 이는 열전달 메커니즘이 2차원에서 3차원으로 바뀌면서 용융 풀의 동역학이 변하기 때문입니다.

Finding 3: 표면 활성 원소를 이용한 험핑 제어 가능성 입증

마랑고니 효과가 주된 원인이라는 발견에 기초하여, 연구팀은 용융 풀의 표면 장력을 인위적으로 제어하여 험핑을 억제하는 방법을 제시했습니다. – 활성 보호 가스: 순수 Ar 가스 대신 4%의 산소(O2)가 포함된 Ar 혼합 가스를 보호 가스로 사용했을 때, 험핑 발생 없이 용접 가능한 속도가 약 2 m/min 증가했습니다 (그림 9). 산소는 강철의 표면 장력을 낮추는 표면 활성 원소로 작용하여 마랑고니 흐름을 안정화시킵니다. – 표면 코팅: 용접 라인의 일부에 흑연(graphite)을 도포한 후 용접을 진행한 결과, 흑연이 도포되지 않은 영역에서는 험핑이 발생했지만 흑연이 도포된 영역에서는 매끄러운 비드가 형성되었습니다 (그림 10). 이는 흑연의 주성분인 탄소 역시 표면 활성 원소로 작용했기 때문입니다.

Practical Implications for R&D and Operations

  • For Process Engineers: 이 연구는 보호 가스 성분을 미세 조정(예: 소량의 산소 추가)하는 것만으로도 고속 용접 공정의 안정성을 크게 향상시킬 수 있음을 시사합니다. 이는 생산 속도를 높이고 결함률을 줄이는 데 직접적으로 기여할 수 있습니다.
  • For Quality Control Teams: 논문의 데이터(표 1, 표 2)는 특정 재료와 두께에서 결함이 발생할 수 있는 임계 속도에 대한 명확한 기준을 제공합니다. 이는 새로운 품질 검사 기준을 수립하거나 공정 모니터링 시스템을 개발하는 데 중요한 기초 자료가 될 수 있습니다.
  • For Design Engineers: 이 연구 결과는 재료 선택 단계에서 표면 장력과 같은 물리적 특성이 용접성에 미치는 영향을 고려하는 것이 중요함을 보여줍니다. 특히 고속 용접이 요구되는 부품 설계 시, 표면 활성 원소 함량이 높은 재료를 선택하는 것이 초기 설계 단계에서부터 용접 결함을 예방하는 효과적인 전략이 될 수 있습니다.

Paper Details


비진공 전자빔 용접 시 용접 비드 결함 형성에 영향을 미치는 요인 연구 (Investigation of Factors Affecting the Formation of Weld Defects in Non-Vacuum Electron Beam Welding)

1. Overview:

  • Title: Исследование факторов, влияющих на образование дефектов сварного шва при электронно-лучевой сварке в открытой атмосфере
  • Author: У. Райзген (U. Reisgen), М. Шлезер (M. Schleser), А. Абдурахманов (A. Abdurakhmanov), Г. Туричин (G. Turichin), Е. Валдайцева (E. Valdaytseva), Ф.-В. Бах (F.-W. Bach), Т. Хассель (T. Hassel), А. Беньяш (A. Beniyash)
  • Year of publication: 2012
  • Journal/academic society of publication: Автоматическая сварка (Automatic Welding), 2/2012
  • Keywords: 비진공 전자빔 용접, 용접 속도, 출력 밀도, 보호 가스, 용접 비드 결함, 험핑, 언더컷

2. Abstract:

본 논문은 비진공 전자빔 용접 시 험핑 및 언더컷과 같은 결함 형성에 영향을 미치는 용접 공정 변수와 재료 특성의 영향을 연구했다. 용접 품질에 대한 개별 변수들의 영향을 규명하였다.

3. Introduction:

비진공 전자빔 용접(NV-EBW)은 진공 챔버 없이 높은 용접 속도와 효율을 제공하여 자동차 산업 등에서 널리 사용된다. 그러나 강재에서 8 m/min, 알루미늄 합금에서 15 m/min 이상의 고속 용접 시, 험핑과 언더컷 같은 표면 결함이 발생하여 기술의 잠재력을 제한한다. 본 연구는 이러한 결함 형성의 원인을 규명하는 것을 목표로 한다.

4. Summary of the study:

Background of the research topic:

NV-EBW는 높은 생산성을 가진 기술이지만 고속에서 발생하는 동적 결함(험핑, 언더컷)이 문제점으로 지적되어 왔다.

Status of previous research:

이전 연구들에서 고속 용접 시 결함이 관찰되었으나, 특히 박판 NV-EBW에서 결함을 유발하는 지배적인 물리적 메커니즘에 대한 명확한 규명이 부족했다.

Purpose of the study:

NV-EBW 공정에서 험핑과 언더컷 결함이 형성되는 근본적인 원인을 규명하고, 용접 변수, 재료 특성, 표면 활성 원소 등이 결함 발생에 미치는 영향을 정량적으로 분석하여 결함을 제어할 수 있는 방안을 제시하고자 한다.

Core study:

실험과 이론적 모델링을 통해 용융 풀의 동역학을 분석했다. 특히 고속 비디오 촬영과 니켈 트레이서 실험을 통해 용융 풀 내부 유동을 가시화하여, 결함 발생의 주된 원인이 표면 장력 구배에 의한 마랑고니 효과임을 입증했다. 또한, 보호 가스 및 표면 코팅을 통해 표면 장력을 제어하여 험핑을 억제할 수 있음을 보였다.

5. Research Methodology

Research Design:

실험적 연구와 이론적 모델링을 결합한 통합적 접근 방식을 사용했다. 다양한 재료와 공정 조건에서 용접 실험을 수행하고, 그 결과를 유체 역학 모델의 예측과 비교 분석했다.

Data Collection and Analysis Methods:

용접된 시편의 표면 및 단면을 금속학적으로 분석했으며, 고속 비디오 카메라로 용융 풀의 동적 거동을 촬영했다. 니켈 트레이서가 포함된 시편은 전자현미경(SEM)과 에너지 분산형 분광법(EDS)을 사용하여 성분 분포를 분석했다.

Research Topics and Scope:

연구는 NV-EBW 공정에 국한되며, 주요 분석 대상 결함은 험핑과 언더컷이다. 연구 대상 재료는 저탄소강(DC05), TRIP강, 알루미늄 합금(AlMg3), 구리(Cu), 납(Pb) 등이며, 주로 박판 소재에 초점을 맞추었다.

6. Key Results:

Key Results:

  • 박판 NV-EBW에서 험핑 결함의 주된 구동력은 용융 풀 내부의 체적 대류가 아닌, 표면 장력 구배에 의한 마랑고니 효과(열모세관 유동)의 불안정성이다.
  • 재료의 표면 장력은 험핑 발생 임계 속도에 결정적인 영향을 미치며, 표면 장력이 낮을수록 고속 용접에 유리하다.
  • 재료 두께가 증가할수록 험핑 발생 임계 속도는 감소한다.
  • 보호 가스에 산소(O2)를 첨가하거나 용접부에 흑연을 도포하는 등 표면 활성 원소를 활용하면 마랑고니 흐름을 안정시켜 험핑을 효과적으로 억제하고, 결함 없는 용접 속도 범위를 넓힐 수 있다.
  • 고속 비디오 분석 결과, 험프는 초기에는 빠르게 성장하다가 크기가 커짐에 따라 성장 속도가 급격히 감소하는 경향을 보였다.

Figure List:

  • Рис. 1. Динамические дефекты сварных швов: а – бугристость (vw = 10 м/мин); б – подрез (vw = 12 м/мин)
  • Рис. 2. Экспериментальные установки для ЭЛС в открытой атмосфере: а – Anlage Typ IGM G 150 K фирмы «Steigerwald»; б – 25-175 TU компании «PTR-Precision technology»
  • Рис. 3. Обозначение параметров сечения сварочной ванны
  • Рис. 4. Поверхность сварного шва при скорости сварки до появления бугров (DC05 толщиной 1,5 мм, ѵw = 10 м/мин, Іb = 70 мА, А = 15 мм)
  • Рис. 5. Обозначения параметров к модели бугристости шва
  • Рис. 6. Зависимость инкремента нарастания волн от волнового числа (описание см. в тексте)
  • Рис. 7. Зависимость образования бугров от скорости сварки (соответственно от длины сварочной ванны) (А = 10 мм): а – vw = 12 м/мин, Іb = 65 мА; б – vw = 15 м/мин, Іb = 5 мА
  • Рис. 8. Образование бугров и подрезов при разных скоростях сварки (сталь DC05, Uacc = 150 кВ, Іb = 100 мА, А = 10 мм): а – vw = 14; б – 16; в – 18 м/мин
  • Рис. 9. Влияние защитного газа в нахлесточном соединении на образование бугров (сталь S420MC толщиной 2 мм, ѵw = 10 м/мин, кадры позади процесса сварки): а, б – без защитного газа; в, г – с защитным газом Ar + O2
  • Рис. 10. Влияние поверхностно-активного вещества на динамику сварочной ванны (DC05 толщиной 1,5 мм, vw = 14 м/мин) с графитом (а) и без графита (б)
  • Рис. 11. Динамика роста бугров (высокоскоростная видеосъемка сварочной ванны)
  • Рис. 12. Динамика роста бугров сварочной ванны (видиосъемка в процессе сварки)
  • Рис. 13. Распределение никеля в сварном шве в отраженных электронах: а – продольное; б – поперечное сечение бугра
  • Рис. 14. Распределение никеля в бугре по горизонтали (а) и вертикали (б)
Рис. 13. Распределение никеля в сварном шве в отраженных электронах: a — продольное; б — поперечное сечение бугра
Рис. 13. Распределение никеля в сварном шве в отраженных электронах: a — продольное; б — поперечное сечение бугра

7. Conclusion:

  1. 험핑 발생의 원인은 용융 풀 내 열모세관 유동의 불안정성 발달이며, 언더컷은 표면 현상과 관련이 있다.
  2. 빔 전류와 작동 거리에 따른 험핑 및 언더컷 발생 속도 임계값을 확인했다.
  3. 다양한 재료에 대한 험핑 발생 임계 속도를 실험적으로 결정했으며, 재료 두께가 증가하면 임계 속도가 감소함을 확인했다. 주된 역할은 마랑고니 효과가 한다.
  4. 표면 활성 물질을 사용하면 표면 장력 계수를 변화시켜 험핑 발생을 억제할 수 있다.
  5. 고속 비디오 촬영을 통해 용융 풀의 유동 속도와 개별 험프의 성장 동역학 및 크기를 평가했다.
  6. 니켈 트레이서 실험을 통해 용융 풀 내 수평적 유동을 확인하고 수직적 유동은 없음을 밝혀, 표면 효과가 지배적임을 재확인했다.

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  8. Dynamic processes at high speed laser and electron beam treatment of materials / G. Turichin, E. Valdaytseva, Fr.-W. Bach, A. Beniyash // 25th Anniversary of cooperation, transactions of saint-petersburg state polytechnic university and Leibniz University of Hannover. — St. Petersburg-Hannover, 2010. — P. 91–101.
  9. Messung der Strahlqualitaet einer Elektronenstrahlanlage in Umgebungsatmosphaere / U. Reisgen, M. Schleser, A. Abdurakhmanov, H. Masny // Materialwissenschaft und Werkstofftechnik. — 2010. — 41, № 1. — S. 45–52.
  10. Rayleigh J. The theory of sound. — New York: Dover publ., 1945.
  11. Czerner St. Schmelzbaddynamik beim Laserstrahl-Waermeleitungsschweißen von eisenwerkstoffen. — Diss.: Hannover, 2005.
  12. Sievers E-R. Schmelzbadinstabilitaeten beim Elektronstrahlschweißen von Grobblechen // Schweißen und Schneiden. — 2006. — 58, № 6. — P. 288–295.

Expert Q&A: Your Top Questions Answered

Q1: 왜 니켈(Nickel)을 트레이서 물질로 사용했으며, 이를 통해 다른 방법으로는 알 수 없었던 무엇을 밝혀냈나요?

A1: 니켈은 용접 대상인 강철과 용융점이 비슷하면서도 성분 분석(EDS)을 통해 명확히 구별되기 때문에 트레이서로 선택되었습니다. 이 실험을 통해 용융 풀 내부의 물질 이동 경로를 직접 시각화할 수 있었습니다. 그 결과, 니켈이 용융 풀 바닥에서 표면으로 솟구치는 수직 대류가 아닌, 용융 풀 후방으로 이동하는 수평 흐름을 보인다는 것을 명확히 밝혀냈습니다(그림 13). 이는 험핑의 주된 구동력이 깊이 방향의 대류가 아닌 표면에서의 마랑고니 효과임을 증명하는 결정적인 증거가 되었습니다.

Q2: 보호 가스에 산소를 첨가하는 것이 어떻게 험핑을 억제하는 물리적 메커니즘은 무엇인가요?

A2: 산소는 강철에 대한 대표적인 표면 활성 원소입니다. 용융된 강철 표면에 산소가 흡착되면 표면 장력이 크게 감소합니다. 마랑고니 효과는 표면 장력의 온도 구배에 의해 발생하는데, 산소는 이 구배의 방향과 크기를 변화시켜 용융 풀의 흐름을 안정화시키는 역할을 합니다. 결과적으로 용융 풀의 불안정성이 억제되어 험핑이 발생하기 어려워지고, 더 높은 속도에서도 안정적인 용접이 가능해집니다.

Q3: 표 1을 보면 강철과 AlMg3 합금의 험핑 발생 임계 속도에 큰 차이가 있습니다. 이러한 차이를 유발하는 가장 중요한 물리적 특성은 무엇인가요?

A3: 가장 중요한 물리적 특성은 표면 장력(surface tension)입니다. 논문에 따르면, 강철(Fe)의 표면 장력은 약 1800 mN/m인 반면, 알루미늄(Al)은 865 mN/m로 훨씬 낮습니다. 험핑은 표면 장력 구배로 인한 유동 불안정성에 기인하므로, 절대적인 표면 장력 값이 낮은 AlMg3 합금은 강철에 비해 동일한 온도 구배에서도 마랑고니 효과가 약하게 나타나 험핑에 대한 저항성이 훨씬 높습니다.

Q4: 이 연구는 주로 박판(thin sheet)에 초점을 맞추었습니다. 두꺼운 후판(thick plate) 용접에서도 마랑고니 효과가 험핑의 지배적인 원인이라고 동일하게 결론 내릴 수 있을까요?

A4: 꼭 그렇다고 단정하기는 어렵습니다. 본 연구의 트레이서 실험 결과는 수평적 흐름이 지배적인 박판 용접에 특화된 결론입니다. 참고문헌 [12]에서 언급된 바와 같이, 두꺼운 후판 용접에서는 용융 풀의 깊이가 깊어지면서 부력 등에 의한 수직 대류의 영향이 상대적으로 더 커질 수 있습니다. 따라서 후판 용접의 경우, 마랑고니 효과와 함께 체적 대류 현상도 험핑 발생에 복합적으로 기여할 가능성이 있습니다.

Q5: 흑연을 도포하는 것이 험핑 방지에 효과가 있다는 점이 흥미롭습니다. 실제 산업 현장에서 적용할 수 있는 실용적인 방법일까요?

A5: 흑연 도포는 험핑의 원인이 표면 현상임을 증명하는 매우 효과적인 실험 방법이었습니다. 하지만 실제 대량 생산 라인에 적용하기에는 몇 가지 현실적인 어려움이 있을 수 있습니다. 예를 들어, 용접 전에 흑연을 균일하게 도포하는 추가 공정이 필요하고, 용접 후 잔류물이 남을 수 있으며, 용접부의 기계적 특성에 미칠 영향도 검토해야 합니다. 따라서 산업적으로는 흑연 도포보다는 보호 가스 성분을 최적화하거나, 재료 자체에 표면 활성 원소(황, 산소 등) 함량을 제어하는 방식이 더 실용적인 해결책이 될 수 있습니다.


Conclusion: Paving the Way for Higher Quality and Productivity

본 연구는 비진공 전자빔 용접(NV-EBW) 시 고속에서 발생하는 험핑 결함의 근본 원인이 표면 장력 구배로 인한 마랑고니 효과의 불안정성임을 명확히 규명했습니다. 더 나아가, 보호 가스에 산소를 첨가하거나 표면 활성 물질을 사용하는 간단한 방법으로 표면 장력을 제어하여 결함을 억제하고 생산성을 획기적으로 높일 수 있는 길을 열었습니다. 이는 복잡한 유체 역학 현상이 실제 제조 공정의 품질과 효율에 얼마나 직접적인 영향을 미치는지를 보여주는 훌륭한 사례입니다.

STI C&D에서는 FLOW-3D를 활용하여 마랑고니 효과, 자유 표면 유동, 열전달 등 비진공 전자빔 용접 공정에서 발생하는 복잡한 물리 현상을 정밀하게 시뮬레이션합니다. 이 연구에서 논의된 문제들이 귀사의 운영 목표와 관련이 있다면, 저희 엔지니어링 팀에 연락하여 이러한 원리들을 귀사의 부품에 어떻게 적용할 수 있는지 논의해 보십시오.

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

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

Copyright Information

  • This content is a summary and analysis based on the paper “Исследование факторов, влияющих на образование дефектов сварного шва при электронно-лучевой сварке в открытой атмосфере” by “U. Reisgen, et al.”.
  • Source: Avtomaticheskaya Svarka, no. 2, pp. 13-20, 2012.

This material is for informational purposes only. Unauthorized commercial use is prohibited. Copyright © 2025 STI C&D. All rights reserved.

Weir

2D-3D Modeling of Flow Over Sharp-Crested Weirs

샤프 크레스트 위어(Sharp-Crested Weir) 위 유동의 2D 및 3D 모델링

연구 배경

  • 문제 정의: 샤프 크레스트 위어는 수로에서 유량 측정과 조절을 위해 가장 널리 사용되는 구조물이다.
  • 목표: CFD(Computational Fluid Dynamics) 기법을 활용하여 샤프 크레스트 위어 위의 유동 특성을 분석하고 방출 계수(Discharge Coefficient)를 예측.
  • 접근법: FLOW-3D를 사용하여 수치 해석을 수행하고 실험 데이터와 비교.

연구 방법

  1. 위어 특성 및 방출 계수(Cd) 분석
    • 기존 실험 연구를 기반으로 방출 계수 CdCdCd 추정식을 개발.
    • 다양한 유량 및 위어 높이 조합을 사용하여 최적의 방출 계수 관계식 도출.
  2. FLOW-3D 기반 수치 모델링
    • VOF(Volume of Fluid) 기법을 적용하여 자유 수면을 해석.
    • RNG k−ϵk-\epsilonk−ϵ 난류 모델을 사용하여 난류 흐름을 해석.
    • FAVOR(Fractional Area-Volume Obstacle Representation) 기법을 활용하여 격자 내 장애물 표현.
  3. 격자 수렴 분석
    • 다양한 해상도의 격자를 비교하여 최적의 계산 비용과 정확도를 확보.

주요 결과

  1. 수치 모델링 vs 실험 데이터 비교
    • 방출 계수(Cd) 예측값과 기존 실험값 간의 오차 범위가 ±3% 이내로 매우 높은 정확도를 보임.
    • Cd는 Ht/tw(총 수두 대비 위어 높이)와 강한 상관관계를 가짐.
  2. 유동 특성 분석
    • 유량 변화에 따른 방출 계수:
      • 유량이 증가할수록 방출 계수가 점진적으로 감소하는 경향 확인.
    • 위어 주변의 속도 및 압력 분포 분석:
      • 위어 크레스트에서 유동이 가속되면서 속도 증가 및 압력 감소 현상 관찰.
      • 위어 하류에서 수압이 낮아지며 유동 패턴이 변화.
  3. FLOW-3D의 유용성
    • FLOW-3D는 실험 대비 비용이 낮고 신속한 설계 검토 가능.
    • 다양한 위어 형상 및 유량 조건에서 적용 가능성이 높음.

결론 및 향후 연구

  • FLOW-3D 기반 CFD 시뮬레이션이 샤프 크레스트 위어의 방출 계수 예측 및 유동 분석에 효과적임을 입증.
  • 실험 결과와 비교했을 때 높은 정확도(오차 ±3%)를 나타내며, 초기 설계 검토에 유용함.
  • 향후 연구에서는 다양한 위어 형상 및 추가적인 난류 모델 적용(k-ω, LES 등)을 통해 더욱 정밀한 해석이 필요.

연구의 의의

이 연구는 샤프 크레스트 위어의 유동 특성을 CFD 기반으로 해석하여 설계 최적화 및 방출 계수 예측의 신뢰성을 향상시켰다는 점에서 의미가 크다.

Reference

  1. Bhallamudi, S.M. and M.H. Chaudhry, 1994. Computation of Flows in Open Channel Transitions. Journal of Hydraulic. Research, 30(1): 77-93.
  2. Fritz, H.M. and H.W. Hager, 1998. Hydraulics of Embankment Weirs. Journal of Hydraulic Engineering,
  3. ASCE., 124(9): 963-971.
  4. Hargreaves, D.M., H.P. Morvan, N.G. Wright, 2007. Validation of the Volume of Fluid Method for Free
  5. Surface Calculation. Engineering Applications of Computational Fluid mechanics, 1(2): 136-147.
  6. Kindsvater, C.E., R.W. Carter, 1957. Discharge Characteristics of Rectangular Thin-Plate Weirs. Journal of Hydraulic Engineering, ASCE., 14: 1-36.
  7. King, H.W. and E.F. Brater, 1963. Handbook of Hydraulics, 5th Edition, McGraw-Hill Book Company, New York.
  8. Patankar, S.V., 1980. Numerical Heat Transfer and Fluid Flow. McGraw-Hill Book Company, New York.
  9. Raju, K.G.R., G.L. Asawa, 1977. Viscosity and Surface Tension Effects on Weir Flow. Journal of Hydraulic Engineering, ASCE., 103: 1227-1231.
  10. Rouse, H., 1950. Engineering Hydraulics. Proceedings of the Fourth Hydraulics Conference, Iowa Institute of Hydraulic Research, John Wiley and Sons, Inc., New York.
  11. Sarginson, E.J., 1972. The Iinfluence of Surface Tension on Weir Flow. Journal of Hydraulic Research, 10:431-446.
Fig. 5 Fluid behavior in liquid propellant dischargesimulation

FLOW-3D를 이용한 표면장력 탱크용 메시 스크린 모델링

본 소개 자료는 한국추진공학회 2017년도 춘계학술대회 논문집 에 게재된 논문 “Flow-3d를 이용한 표면장력 탱크용메시스크린모델링”의 소개 내용입니다.

Fig. 5 Fluid behavior in liquid propellant dischargesimulation
Fig. 5 Fluid behavior in liquid propellant discharge simulation

1. 서론

  • 우주비행체의 미소 중력 환경에서 추진제 관리가 필수적이며, 이를 위해 표면장력 탱크(Surface Tension Tank, STT)가 사용됨.
  • STT 내 주요 구성 요소인 메시 스크린(Mesh Screen)은 추진제와 가압 기체를 분리하여 액상 추진제의 안정적인 배출을 돕는 핵심 장치임.
  • 본 연구는 FLOW-3D를 이용하여 메시 스크린을 모델링하고, 기포점(bubble point) 시뮬레이션을 수행하여 수치 모델의 정확성을 평가하는 것을 목표로 함.

2. 연구 방법

FLOW-3D 기반 CFD 모델링

  • VOF(Volume of Fluid) 기법을 사용하여 자유 수면을 추적.
  • 거시적 다공성 매체 모델(Macroscopic Porous Media Model)을 적용하여 메시 스크린의 공극률, 모세관압, 항력 계수를 설정.
  • 경계 조건 설정:
    • 유입부: 초기 추진제(NTO) 유입 설정.
    • 유출부: 배출구에서 자유 배출(Outflow) 조건 적용.
    • 벽면: No-slip 조건 적용.

3. 연구 결과

기포점 측정 시뮬레이션

  • 350 × 2600, 400 × 3000, 510 × 3600 DTW 메시 스크린 모델을 사용하여 기포점 측정을 수행.
  • FLOW-3D 시뮬레이션 결과와 실험 결과 비교 시, 최대 오차율 1.6% 이내로 높은 신뢰도 확인.
  • 스크린 모델의 차압은 초기 270 Pa에서 점진적으로 증가하여 약 630 Pa에 도달 시 배출 중단, 이는 예상된 기포점과 유사.

PMD(Propellant Management Device) 내 추진제 배출 해석

  • 스크린을 포함한 STT 시스템의 추진제 배출 시뮬레이션 수행.
  • 출구 스크린에서 기포점 도달 전까지 추진제 배출이 지속되며, 기포점 도달 후 배출이 중단됨을 확인.
  • 베인(Vane) 구조를 통한 추진제의 균등 분포 확인, 표면장력 효과로 인해 추진제가 특정 경로를 따라 흐름.

4. 결론 및 제안

결론

  • FLOW-3D를 이용한 메시 스크린 모델링이 실험 결과와 높은 신뢰도를 보이며, 표면장력 탱크 내 추진제 배출 특성을 효과적으로 분석할 수 있음.
  • 기포점 특성을 정확히 반영하여 추진제 관리 장치(PMD)의 설계 최적화 가능성을 제시.

향후 연구 방향

  • 추진제 종류 및 다양한 미소 중력 조건에서 추가 연구 필요.
  • LES(Large Eddy Simulation) 모델을 적용하여 난류 효과 정밀 분석.
  • 현장 데이터를 활용한 추가 검증 연구 수행.

5. 연구의 의의

본 연구는 FLOW-3D를 활용하여 표면장력 탱크용 메시 스크린의 모델링 및 추진제 배출 해석을 수행하였으며, 향후 우주비행체의 추진제 관리 시스템 설계 최적화에 기여할 수 있는 실질적인 데이터 및 분석 방법을 제공한다.

Fig. 1 Real geometry-based mesh screen model (left)
and mesh screen model based on macroscopic
porous media model in Flow-3d (right
Fig. 1 Real geometry-based mesh screen model (left)
and mesh screen model based on macroscopic
porous media model in Flow-3d (right)
Fig. 4 Fluid behavior in bubble point test simulation
(350 × 2600 DTW mesh screen)
Fig. 4 Fluid behavior in bubble point test simulation (350 × 2600 DTW mesh screen)
Fig. 5 Fluid behavior in liquid propellant dischargesimulation
Fig. 5 Fluid behavior in liquid propellant discharge simulation

6. 참고 문헌

  1. David J. C and Maureen T. K, “Screen Channel Liquid Acquisition Devices for Cryogenic Propellants” NASA-TM-2005-213638, 2005.
  2. Hartwig, J., Mann, J. A. Jr., Darr, S. R., “Parametric Analysis of the Liquid Hydrogen and Nitrogen Bubble Point Pressure for Cryogenic Liquid Acquisition Devices”, Cryogenics, Vol. 63, 2014, pp. 25-36.
  3. Jurns, J. M., McQuillen, J. B., “Bubble Point Measurement with Liquid Methane of a Screen Capillary Liquid Acquisition Device”, NASA-TM-2009-215496, 2009.
  4. Jaekle, D. E. Jr., “Propellant Management Device: Conceptual Design and Analysis: Galleries”, AIAA 29th Joint Propulsion Conference, AIAA-97-2811, 1997.
  5. Jaekle, D. E. Jr., “Propellant Management Device: Conceptual Design and Analysis: Traps and Troughs”, AIAA 31st Joint Propulsion Conference, AIAA-95-2531, 1995.
  6. Yu, A., Ji, B., Zhuang, B. T., Hu, Q., Luo, X. W., Xu, H. Y., “Flow Analysis in a Vane-type Surface Tension Propellant Tank”, IOP Conference Series: Materials Science and Engineering, Vol. 52, No. 7, 2013, Article number: 072018.
  7. Chato, D. J., McQuillen, J. B., Motil, B. J., Chao, D. F., Zhang, N., “CFD simulation of Pressure Drops in Liquid Acquisition Device Channel with Sub-Cooled Oxygen”, World Academy of Science, Engineering and Technology, Vol. 3, 2009, pp. 144-149.
  8. McQuillen, J. B., Chao, D. F., Hall, N. R., Motil, B. J., Zhang, N., “CFD simulation of Flow in Capillary Flow Liquid Acquisition Device Channel”, World Academy of Science, Engineering and Technology, Vol. 6, 2012, pp. 640-646.
  9. Hartwig, J., Chato, D., McQuillen, J., “Screen Channel LAD Bubble Point Tests in Liquid Hydrogen”, International Journal of Hydrogen Energy, Vol. 39, No. 2, 2014, pp. 853-861.
  10. Fischer, A., Gerstmann, J., “Flow Resistance of Metallic Screens in Liquid, Gaseous and Cryogenic Flow”, 5th European Conference for Aeronautics and Space Sciences, Munich, Germany, 2013.
  11. Fries, N., Odic, K., Dreyer, M., “Wicking of Perfectly Wetting Liquids into a Metallic Mesh”, 2nd International Conference on Porous Media and its Applications in Science and Engineering, 2007.
  12. Seo, M. K., Kim, D. H., Seo, C. W., Lee, S. Y., Jang, S. P., Koo, J., “Experimental Study of Pressure Drop in Compressible Fluid through Porous Media”, Transactions of the Korean Society of Mechanical Engineers – B, Vol. 37, No. 8, pp. 759-765, 2013.
  13. Hartwig, J., Mann, J. A., “Bubble Point Pressures of Binary Methanol/Water Mixtures in Fine-Mesh Screens”, AlChE Journal, Vol. 60, No. 2, 2014, pp. 730-739.
Cladding

Influence of Fluid Convection on Weld Pool Formation in Laser Cladding

레이저 클래딩(Laser Cladding)에서 유체 대류(Fluid Convection)가 용융풀(Weld Pool) 형성에 미치는 영향

연구 배경 및 목적

  • 문제 정의: 레이저 클래딩(Laser Cladding)은 금속 표면에 보호 코팅을 입히거나 마모된 부품을 복구하는 데 사용되는 정밀 금속 적층 기술이다.
    • Inconel® 718 초합금을 사용한 제트 엔진 터빈 블레이드 팁 재생 및 부품 보호에 적용된다.
    • 그러나 복잡한 물리적 현상정확하게 예측할 수 있는 모델의 부족으로 인해 경제적인 응용 개발에 어려움이 존재한다.
  • 연구 목적:
    • FLOW-3D 소프트웨어를 활용하여 Inconel® 718 레이저 클래딩용융풀 형성, 유체 대류, 응고(Solidification) 현상 분석.
    • 마랑고니(Marangoni) 대류에 의한 온도 프로파일 변화유동 패턴을 평가.
    • 모델 예측 결과를 실험 데이터와 비교하여 시뮬레이션의 신뢰성 검증.

연구 방법

  1. 수치 모델링 및 시뮬레이션 설정
    • FLOW-3D 소프트웨어VOF(Volume of Fluid) 기법을 사용하여 유체 흐름 및 용융풀 형상 예측.
    • 질량, 에너지 및 운동량 보존 방정식을 기반으로 용융풀 및 기판 모델링.
    • 열전달, 질량 및 운동량 추가를 통한 정확한 공정 모델링 구현.
    • 마랑고니 대류(Marangoni Convection) 모델링:
      • 표면 장력 변화용융풀 내 유체 흐름에 미치는 영향 분석.
      • 표면 활성 원소(Surface-Active Elements)인 황(S)의 농도에 따른 표면 장력 기울기 변화 반영.
  2. 실험 설정 및 시뮬레이션 조건
    • 재료 및 장비:
      • IN718 초합금 분말(100–325 메쉬)을 사용.
      • 350~550 W의 균일한 강도(Fiber Laser)를 사용하여 아르곤 분위기에서 실험 수행.
      • 빔 스폿 직경 1.0 mm, 빔 이동 속도 1.016 cm/s.
    • Boundary Condition:
      • 입출구 및 벽면 경계 조건:
        • 입구(Inlet): 유량 일정 조건.
        • 출구(Outlet): 자유 유출 조건.
        • 벽면(Wall): 비투과성 경계 조건.
      • 레이저 에너지 흡수율 계산:
        • Hagen-Rubens 관계식을 이용하여 온도 변화에 따른 흡수율(A(T)) 평가.

주요 결과

  1. 용융풀 형상 및 유동 패턴
    • 예측된 용융풀 형상실험 데이터 간 높은 일치도 확인.
    • 350, 450, 550 W 레이저 출력 조건에서의 용융풀 폭, 높이, 침투 깊이 비교.
    • 레이저 출력 증가 시:
      • 용접 폭 및 침투 깊이 증가.
      • 클래딩 높이는 상대적으로 일정하게 유지.
  2. 마랑고니 대류 및 온도 분포 분석
    • 마랑고니 흐름에 의해 용융풀 후방(Back)에서 가장 깊은 침투 영역 형성.
    • 표면 장력 기울기 전환 지점(Ti)에서 상대적으로 평탄한 온도 프로파일 형성.
    • 온도 구배(G) 및 응고 속도(R)를 통해 응고 모드(Columnar Dendritic Solidification) 예측.
    • 표면 장력 변화유체 흐름을 저온에서 고온 영역으로 유도하여 혼합 및 침투 증가를 촉진.
  3. 시뮬레이션 신뢰성 및 유효성 검증
    • 시뮬레이션 예측 결과실험 측정치의 일치도 평가.
    • 예측된 용융풀 형상, 폭, 깊이실험 데이터와 평균 5% 이내의 오차율을 보임.
    • FLOW-3D 모델이 복잡한 용융풀 대류 현상 및 응고 메커니즘을 정확히 설명할 수 있음을 증명.

결론 및 향후 연구

  • 결론:
    • FLOW-3D를 사용한 레이저 클래딩 공정 시뮬레이션용융풀 형성 및 응고 조건을 정확하게 예측할 수 있음.
    • 마랑고니 대류에 의해 용융풀 내 온도 분포 및 유동 패턴이 결정되며, 이는 응고 모드와 기계적 특성에 중요한 영향을 미침.
    • 시뮬레이션 결과를 통해 용접 풀의 중심선 온도 구배(G) 및 응고 속도(R)를 이용해 응고 형태(기둥형 수지상 조직) 예측 가능.
  • 향후 연구 방향:
    • 다층(Multi-Layer) 클래딩 공정으로 연구 확장.
    • 실험적 검증을 통한 시뮬레이션 예측 유동 패턴 및 침투 형상 확인.
    • AI 및 머신러닝을 활용한 레이저 클래딩 공정 최적화 모델 개발.

연구의 의의

이 연구는 FLOW-3D를 활용하여 레이저 클래딩 공정의 복잡한 물리적 현상을 정량적으로 평가하고, 부품 보호 및 재생 공정의 생산성 향상 및 비용 절감에 기여할 수 있는 실질적인 데이터를 제공한다​.

Reference

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Weir

Discharge Formula and Hydraulics of Rectangular Side Weirs in the Small Channel and Field Inlet

소규모 수로 및 유입구에서의 직사각형 측면 위어의 유량 공식 및 수리학

Yingying Wang, Mouchao Lv, Wen’e Wang, Ming Meng

Abstract


In this study, experimental investigations were conducted on rectangular side weirs with different widths and heights. Corresponding simulations were also performed to analyze hydraulic characteristics including the water surface profile, flow velocity, and pressure. The relationship between the discharge coefficient and the Froude number, as well as the ratios of the side weir height and width to upstream water depth, was determined. A discharge formula was derived based on a dimensional analysis. The results demonstrated good agreement between simulated and experimental data, indicating the reliability of numerical simulations using FLOW-3D software (version 11.1). Notably, significant fluctuations in water surface profiles near the side weir were observed compared to those along the center line or away from the side weir in the main channel, suggesting that the entrance effect of the side weir did not propagate towards the center line of the main channel. The proposed discharge formula exhibited relative errors within 10%, thereby satisfying the flow measurement requirements for small channels and field inlets.

1. Introduction


Sharp crested weirs are used to obtain discharge in open channels by solely measuring the water head upstream of the water. Side weirs, as a kind of sharp-crested weir, are extensively used for flow measurement, flow diversion, and flow regulation in open channels. Side weirs can be placed directly in the channel direction or field inlet, without changing the original structure of the channel. Thus, side weirs have certain advantages in the promotion and application of flow measurement facilities in small channels and field inlets. The rectangular sharp-crested weir is the most commonly available, and many scholars have conducted research on it.
Research on side weirs started in 1934. De Marchi studied the side weir in the rectangular channel and derived the theoretical formula based on the assumption that the specific energy of the main flow section of the rectangular channel in the side weir section was constant [1]. Ackers discussed the existing formulas for the prediction of the side weir discharge coefficient [2]. Chen concluded that the momentum theorem was more suitable for the analytical calculation of the side weir based on the experimental data [3]. Based on previous theoretical research, more and more scholars began to carry out experimental research on side weirs. Uyumaz and Muslu conducted experiments under subcritical and supercritical flow regimes and derived expressions for the side weir discharge and water surface profiles for these regimes by comparing them with experimental results [4]. Borghei et al. developed a discharge coefficient equation for rectangular side weirs in subcritical flow [5]. Ghodsian [6] and Durga and Pillai [7] developed a discharge coefficient equation of rectangular side weirs in supercritical flow. Mohamed proposed a new approach based on the video monitoring concept to measure the free surface of flow over rectangular side weirs [8]. Durga conducted experiments on rectangular side weirs of different lengths and sill heights and discussed the application of momentum and energy principles to the analysis of spatially varied flow under supercritical conditions. The results showed that the momentum principle was fitting better [7]. Omer et al. obtained sharp-crested rectangular side weirs discharge coefficients in the straight channel by using an artificial neural network model for a total of 843 experiments [9]. Emiroglu et al. studied water surface profile and surface velocity streamlines, and developed a discharge coefficient formula of the upstream Froude number, the ratios of weir length to channel width, weir length to flow depth, and weir height to flow depth [10]. Other investigators [11,12,13,14] have conducted experiments to study flow over rectangular side weirs in different flow conditions.
Numerous studies have been conducted in laboratories to this day. Compared to experimental methods, the numerical simulation method has many attractive advantages. We can easily obtain a wide range of hydraulic parameters of side weirs using numerical simulation methods, without investing a lot of manpower and resources. In addition, we can conduct small changes in inlet condition, outlet condition, and geometric parameters, and study their impact on the flow characteristics of side weirs. Therefore, with the development and improvement of computational fluid dynamics, the numerical simulation method has begun to be widely applied on side weirs. Salimi et al. studied the free surface changes and the velocity field along a side weir located on a circular channel in the supercritical regime by numerical simulation [15]. Samadi et al. conducted a three-dimensional simulation on rectangular sharp-crested weirs with side contraction and without side contraction and verified the accuracy of numerical simulation compared with the experimental results [16]. Aydin investigated the effect of the sill on rectangular side weir flow by using a three-dimensional computational fluid dynamics model [17]. Azimi et al. studied the discharge coefficient of rectangular side weirs on circular channels in a supercritical flow regime using numerical simulation and experiments [18]. The discharge coefficient over the two compound side weirs (Rectangular and Semi-Circle) was modeled by using the FLOW-3D software to describe the flow characteristics in subcritical flow conditions [19]. Safarzadeh and Noroozi compared the hydraulics and 3D flow features of the ordinary rectangular and trapezoidal plan view piano key weirs (PKWs) using two-phase RANS numerical simulations [20]. Tarek et al. investigated the discharge performance, flow characteristics, and energy dissipation over PK and TL weirs under free-flow conditions using the FLOW-3D software [21].
As evident from the aforementioned, the majority of studies have primarily focused on determining the discharge coefficient, while comparatively less attention has been devoted to investigating the hydraulic characteristics of rectangular side weirs. Numerical simulations were conducted on different types of side weirs, including compound side weirs and piano key weirs, in different cross-section channels under different flow regimes. It is imperative to derive the discharge formula and investigate other crucial flow parameters such as depth, velocity, and pressure near side weirs for their effective implementation in water measurement. In this study, a combination of experimental and numerical simulation methods was employed to examine the relationship between the discharge coefficient and its influencing factors; furthermore, a dimensionless analysis was utilized to derive the discharge formula. Additionally, water surface profiles near side weirs and pressure distribution at the bottom of the side channel were analyzed to assess safety operation issues associated with installing side weirs.

2. Principle of Flow Measurement


Flow discharge over side weirs is a function of different dominant physical and geometrical quantities, which is defined as

where Q is flow discharge over the side weir, b is the side weir width, B is the channel width, P is the side weir height, v is the mean velocity, h1 is water depth upstream the side weir in the main channel, g is the gravitational acceleration, μ is the dynamic viscosity of fluid, ρ is fluid density, and i is the channel slope (Figure 1).

Figure 1. Definition sketch of parameters of rectangular side weir under subcritical flow. Note: h1 and h2 represent water depth upstream and downstream of the side weir in the main channel, respectively; y1 and y2 represent weir head upstream and downstream of the side weir in the main channel, respectively.

In experiments when the upstream weir head was over 30 mm, the effects of surface tension on discharge were found to be minor [22]. The viscosity effect was far less than the gravity effect in a turbulent flow. Hence μ and σ were excluded from the analysis [23,24]. In addition, the channel width, the channel slope, and the fluid density were all constant, so the discharge formula can be simplified as:

According to the Buckingham π theorem, the following relationship among the dimensionless parameters is established:

Selected h1 and g as basic fundamental quantities, and the remaining physical quantities were represented in terms of these fundamental quantities as follows:

In which

Based on dimensional analysis, the following equations were derived.

Namely

So the discharge formula can be simplified as:

In a sharp-crested weir, discharge over the weir is proportional to 𝐻1.51H11.5 (H1 is the upstream total head above the crest, namely H1 = y1 + v2/2 g), so Equation (6) can be transformed as follows:

Consequently, the discharge formula over rectangular side weirs is defined as follows, in which 𝑚=𝑓(𝑏ℎ1m=f(bh1,𝑃ℎ1,𝐹𝑟1)Ph1,Fr1). Parameter m represents the dimensionless discharge coefficient. Parameter Fr1 represents the Froude number at the upstream end of the side weir in the main channel.

3. Experiment Setup


The experimental setup contained a storage reservoir, a pumping station, an electromagnetic flow meter, a control valve, a stabilization pond, rectangular channels, a side weir, and a sluice gate. The layout of the experimental setup is shown in Figure 2. Water was supplied from the storage reservoir using a pump. The flow discharge was measured with an electromagnetic flow meter with precision of ±3‰. Water depth was measured with a point gauge with an accuracy of ±0.1 mm. The flow velocity was measured with a 3D Acoustic Doppler Velocimeter (Nortek Vectrino, manufactured by Nortek AS in Rud, Norway). In order to eliminate accidental and human error, multiple measurements of the water depth and flow velocity at the same point were performed and the average values were used as the actual water depth and flow velocity of the point. The main and side channels were both rectangular open channels measuring 47 cm in width and 60 cm in height. The geometrical parameters of rectangular side weirs are shown in Table 1.

Figure 2. Layout of the test system.
Table 1. The geometrical parameters of rectangular side weirs.

When water passes through a side weir, its quality point is affected not only by gravity but also by centrifugal inertia force, leading to an inclined water surface within that particular cross-section before reaching the weir. In order to examine water profiles adjacent to side weirs, cross-sectional measurements were conducted at regular intervals of 12 cm both upstream and downstream of each side weir, denoted as sections ① to ⑩, respectively. Measuring points were positioned near the side weir (referred to as “Side I”), along the center line of the main channel (referred to as “Side II”), and far away from the side weir (referred to as “Side III”) for each cross-section. The schematic diagram illustrating these measuring points is presented in Figure 3.

Figure 3. Schematic diagram of measurement points.

4. Numerical Simulation Settings

4.1. Mathematical Model

4.1.1. Governing Equations

Establishing the controlling equations is a prerequisite for solving any problem. For the flow analysis problem of water flowing over a side weir in a rectangular channel, assuming that no heat exchange occurs, the continuity equation (Equation (9)) and momentum equation (Equation (10)) can be used as the controlling equations as follows:

The continuity equation:

Momentum equation:

where: ρ is the fluid density, kg/m3t is time, s; uiuj are average flow velocities, u1u2u3 represent average flow velocity components in Cartesian coordinates x, y, and z, respectively, m/s; μ is dynamic viscosity of fluid, N·s/m2p is the pressure, pa; Si is the body force, S1 = 0, S2 = 0, S3 = −ρg, N [24].

4.1.2. RNG k-ε Model

The water flow in the main channel is subcritical flow. When the water flows through the side weir, the flow line deviates sharply, the cross section suddenly decreases, and due to the blocking effect of the side weir, the water reflects and diffracts, resulting in strong changes in the water surface and obvious three-dimensional characteristics of the water flow [25]. Therefore the RNG kε model is selected. The model can better handle flows with greater streamline curvature, and its corresponding k and ε equation is, respectively, as follows:

where: k is the turbulent kinetic energy, m2/s2μeff is the effective hydrodynamic viscous coefficient; Gk is the generation item of turbulent kinetic energy k due to gradient of the average flow velocity; C∗1εC1ε*, C are empirical constants of 1.42 and 1.68, respectively; ε is turbulence dissipation rate, kg·m2/s2.

4.1.3. TruVOF Model

Because the shape of the free surface is very complex and the overall position is constantly changing, the fluid flow phenomenon with a free surface is a typical flow phenomenon that is difficult to simulate. The current methods used to simulate free surfaces mainly include elevation function method, the MAC method [26] and the VOF (Volume of Fluid) method [27]. The VOF method is a method proposed by Hirt and Nichols to deal with the complex motion of the free surface of a fluid, which can describe all the complexities of the free surface with only one function. The basic idea of the method is to define functions αw and αa, which represent the volume percentage of the calculation area occupied by water and air, respectively. In each unit cell, the sum of the volume fractions of water and air is equal to 1, i.e.,

The TruVOF calculation method can accurately track the change of free liquid level and accurately simulate the flow problems with free interface. Its equation is:

where: u_¯m is the average velocity of the mixture; t is the time; F is the volume fraction of the required fluid.

4.2. Parameter Setting and Boundary Conditions

To streamline the iterative calculation and minimize simulation time, we selected a main channel measuring 7.5 m in length and a side channel measuring 2.5 m in length for simulation. Three-dimensional geometrical models were developed using the software AutoCAD (version 2016-Simplified Chinese). The spatial domain was meshed using a constructed rectangular hexahedral mesh and each cell size was 2 cm. A volume flow rate was set in the channel inlet with an auto-adjusted fluid height. An outflow–outlet condition was positioned at the end of the side channel. A symmetry boundary condition was set in the air inlet at the top of the model, which represented that no fluid flows through the boundary. The lower Z (Zmin) and both of the side boundaries were treated as a rigid wall (W). No-slip conditions were applied at the wall boundaries. Figure 4 illustrates these boundary conditions.

Figure 4. Diagram of boundary conditions.

5. Results

5.1. Water Surface Profiles

Water surface profiles were crucial parameters for selecting water-measuring devices. Upon analyzing the consistent patterns observed in different conditions, one specific condition was chosen for further analysis. To validate the reliability of numerical simulation, measured and simulated water depths of rectangular side weirs with different widths and heights at a discharge rate of 25 L/s were extracted for comparison (Table 2 and Figure 5). The results in Table 2 and Figure 5 indicate a maximum absolute relative error value of 9.97% and all absolute relative error values within 10%, demonstrating satisfactory agreement between experimental and simulated results.

Figure 5. Comparison between measured and simulated flow depth.
P/cmSection Positionb = 20 cmb = 30 cmb = 40 cmb = 47 cm
hm/cmhs/cmR/%hm/cmhs/cmR/%hm/cmhs/cmR/%hm/cmhs/cmR/%
721.4919.49.7317.7416.94.7416.0714.519.7113.7912.509.35
④′20.4819.056.9817.7816.149.2215.6914.318.80
20.7119.028.1617.8216.318.4715.9214.538.7315.2313.809.39
⑧′22.0020.228.0918.2716.748.3716.5914.969.83
22.3720.179.8317.7316.805.2516.2715.087.3115.3614.366.51
1024.1522.66.4219.9618.845.6119.0318.582.3616.8315.855.82
④′24.2122.058.9219.4918.196.6718.7518.352.13
24.0121.789.2919.6518.346.6718.9518.631.6917.5216.098.16
⑧′24.8822.49.9720.6519.216.9720.1219.294.13
24.0322.964.4521.1619.348.6019.7119.431.4218.3917.365.60
1528.8527.564.4725.8624.096.8424.0521.898.9822.7320.808.49
④′28.4926.975.3425.1923.845.3623.4221.468.37
28.8526.986.4825.7223.996.7323.2321.826.0723.1021.058.87
⑧′28.9627.305.7326.3824.198.3024.1822.277.90
29.1827.964.1826.5724.547.6424.5722.339.1223.2021.109.05
2033.2932.342.8530.6329.025.2628.4926.875.6926.9925.814.37
④′33.1431.953.5929.7528.623.8028.1126.794.70
33.3231.794.5930.0428.455.2928.9926.867.3527.4226.722.55
⑧′34.0232.394.7930.6928.955.6729.5927.257.91
34.6232.845.1431.4429.296.8429.5127.317.4628.2127.004.29
Table 2. Comparison of measured and simulated water depths on Side I of each side weir at a discharge of 25 L/s

Due to the diversion caused by the side weir, there was a rapid variation in flow near the side weir in the main channel. In order to investigate the impact of the side weir on water flow in the main channel, water surface profiles on Side I, Side II, and Side III were plotted with a side weir width and height both set at 20 cm at a discharge rate of 25 L/s (Figure 6). As depicted in Figure 6, within a certain range of the upstream end of the main channel, water depths on Side I, Side II, and Side III were nearly equal with almost horizontal profiles. As the distance between the location of water flow and the upstream end of the weir crest decreased gradually, there was a gradual decrease in water depth on Side I along with an inclined trend in its corresponding profile; however, both Side II and Side III still maintained almost horizontal profiles. When approaching closer to the side weir area with flowing water, there was an evident reduction in water depth on Side I accompanied by a significant downward trend visible across an expanded decline range. The minimum point occurred near the upstream end of the weir crest before gradually increasing again towards downstream sections. At the crest section of the side weir, there is an upward trend observed in the water surface. The water surface tended to stabilize downstream of the main channel within a certain range from the downstream end of the weir crest. There was no significant change in the water surface profiles of Side Ⅱ and Side Ⅲ in the crest section. It can be inferred that the side weir entrance effect occurred only between Side Ⅰ and Side Ⅱ. M. Emin reported the same pattern [10].

Figure 6. Water surface profiles on Side I, Side II, and Side III with a side weir width of 20 cm and height of 15 cm at a discharge of 25 L/s.

For a more accurate study on the entrance effect of the side weir on the Water Surface Profile (WSP) for Side I; a comparative analysis conducted using different widths but the same height (15 cm) at a discharge rate of 25 L/s is presented through Figure 7, Figure 8, Figure 9 and Figure 10.

Figure 7. Water surface profile on Side Ⅰ with a side weir width of 20 cm and height of 15 cm at a discharge of 25 L/s.
Figure 8. Water surface profile on Side Ⅰ with a side weir width of 30 cm and height of 15 cm at a discharge of 25 L/s.
Figure 9. Water surface profile on Side Ⅰ with a side weir width of 40 cm and height of 15 cm at a discharge of 25 L/s.
Figure 10. Water surface profile on Side Ⅰ with a side weir width of 47 cm and height of 15 cm at a discharge of 25 L/s.

According to Figure 7, Figure 8, Figure 9 and Figure 10, the water depth upstream of the main channel started to decrease as it approached the upstream end of the weir crest and then gradually increased at the weir crest section. In other words, the water surface profile exhibited a backwater curve along the length of the weir crest. The water depth remained relatively stable downstream of the main channel within a certain range from the downstream end of the weir crest. Additionally, there was a higher water depth downstream of the main channel compared to that upstream of the main channel. Furthermore, an increase in the width of the side weir led to a gradual reduction in fluctuations on its water surface.

5.2. Velocity Distribution

The law of flow velocity distribution near the side weir is the focus of research and analysis, so the simulated and measured values of flow velocity near the side weir were compared and analyzed. Take the discharge of 25 L/s, the height of 15 cm, and the width of 30 cm of the side weir as an example to illustrate. Figure 11 shows the measured and simulated velocity distribution in the x-direction of cross-section ④. As can be seen from Figure 11, the diagrams of the measured and simulated velocity distribution were relatively consistent, and the maximum absolute relative error between the measured and simulated values at the same measurement point was 9.37%, and the average absolute relative error was 3.97%, which indicated a satisfactory agreement between the experimental and simulated results.

Figure 11. Velocity distribution in the x-direction of section ④: when the discharge is 25 L/s, the height of the side weir is 15 cm and the width of the side weir is 30 cm. (a) Measured velocity distribution; (b) Simulated velocity distribution.

From Figure 11, it can be seen that the flow velocity gradually increased from the bottom of the channel towards the water surface in the Z-direction, and the flow velocity gradually increased from Side Ⅲ to Side Ⅰ in the Y-direction. The maximum flow velocity occurred near the weir crest.

Figure 12 shows the distribution of flow velocity at different depths (z/P = 0.3, z/P = 0.8, z/P = 1.6) with a side weir width of 30 cm and height of 15 cm at a discharge of 25 L/s. The water flow line began to bend at a certain point upstream of the main channel, and the closer it was to the upstream end of the weir crest, the greater the curvature. The maximum curvature occurred at the downstream end of the weir crest. The flow patterns at the bottom, near the side weir crest, and above the side weir crest were significantly different. There was a reverse flow at the bottom of the main channel, where the forward and reverse flows intersect, resulting in a detention zone. The maximum flow velocity at the bottom layer occurred at the upstream end of the side weir crest. When the location of water flow approached the weir crest, the maximum flow velocity occurred at the upstream end of the weir crest. The maximum flow velocity on the water surface occurred at the downstream end of the weir crest. As the water depth decreased, the position of the maximum flow velocity gradually moved from the upstream end of the side weir to the downstream end of the side weir.

Figure 12. Distribution of flow velocity at different depths with a side weir width of 30 cm and height of 15 cm at a discharge of 25 L/s. (a) z/P = 0.3; (b) z/P = 0.8; (c) z/P = 1.6.

5.3. Side Channel Pressure Distribution

When water flowed through the side weir, an upstream water level was formed, resulting in a pressure zone at the junction with the side channel. This pressure zone led to increased water pressure on the floor of the side channel, which affected its stability and durability. In small channels or fields where erosion resistance is weak, excessive pressure can cause scour holes. Therefore, analyzing the pressure distribution in the side channel is necessary to select an appropriate height and width for the side weir that effectively reduces its impact on the bottom plate.

To investigate the impact of side weir width on hydraulic characteristics, pressure data was collected at a discharge rate of 25 L/s for side weirs with heights of 20 cm and widths ranging from 20 cm to 47 cm. The pressure distribution map was drawn, as shown in Figure 13.

Figure 13. Comparison of pressure distribution on the bottom plate of the side channel with different widths of side weirs when the discharge is 25 L/s and the height of side weirs is 20 cm. (aP = 20 cm, b = 20 cm; (bP = 20 cm, b = 30 cm; (cP = 20 cm, b = 40 cm; (dP = 20 cm, b = 47 cm.

As can be seen from Figure 13, the pressure at the bottom of the side channel decreased as the width of the side weir increased. This uneven distribution of water flow on the weir was caused by the sharp bending of water flow lines and the influence of centrifugal inertia force over a short period. After passing through the side weir, the water flow became symmetrically distributed with respect to the axis of the side channel, leaning towards the right bank at a certain distance. As we increased the width of the side weir, we noticed that its position gradually approached the side weir and maximum pressure decreased at this location where the water tongue formed due to flowing through it (Figure 13). For a constant height (20 cm) but varying widths (20 cm, 30 cm, 40 cm, and 47 cm), we measured maximum pressures at these positions as follows: 103,713 Pa, 103,558 Pa, 103,324 Pa, and 103,280 Pa, respectively. Consequently, increasing width reduced the impact on the side channel from water flowing through it while changing pressure distribution from concentration to dispersion in a vertical direction. In the practical application of side weirs, appropriate height should be selected based on the bottom plate’s capacity to withstand the pressure exerted by flowing water within channels.

To investigate how height affects the hydraulic characteristics of rectangular side weirs further (Figure 14), we extracted pressures on bottom plates when discharge was fixed at 25 L/s while varying heights were set as follows: 7 cm, 10 cm, 15 cm, and 20 cm, respectively.

Figure 14. Comparison of pressure distribution on the bottom plate of the side channel with different heights of side weirs when discharge is 25 L/s and the width of side weirs is 20 cm. (aP = 7 cm, b = 20 cm; (bP = 10 cm, b = 20 cm; (cP = 15 cm, b = 20 cm; (dP = 20 cm, b = 20 cm.

As shown in Figure 14, when the width of the side weir was constant, the pressure at the bottom of the side channel increased with the height of the side weir. As the height of the side weir increased, the water tongue formed by flow through the side weir gradually moved away from it in a downstream direction. In terms of vertical water flow, as the height of the side weir increased, the position of maximum pressure at which the water tongue falls shifted closer to the axis of the side channel from its right bank. Moreover, an increase in height resulted in higher maximum pressure at this falling point. For a constant width (20 cm) and varying heights (7 cm, 10 cm, 15 cm, and 20 cm), corresponding maximum pressures at this landing point were measured as 102,422 Pa, 102,700 Pa, 103,375 Pa, and 103,766 Pa, respectively. Consequently, increasing width led to a greater impact on both flow through and pressure distribution within the side channel; transforming it from scattered to concentrated along its lengthwise direction. Therefore, when applying such weirs practically one should select an appropriate width based on what pressure can be sustained by their respective channel bottom plates.

5.4. Discharge Coefficient

Based on dimensionless analysis, the influencing parameters of the discharge coefficient were obtained. To study the effect of parameters Fr1b/h1, and P/h1, discharge coefficient values were plotted against Fr1b/h1, and P/h1, shown in Figure 15, Figure 16 and Figure 17. The discharge coefficient decreased as parameters Fr1 and b/h1 increased. The discharge coefficient increased as parameter P/h1 increased. As Uyumaz and Muslu reported in a previous study, the variation of the discharge coefficient with respect to the Froude number showed a second-degree curve for a subcritical regime [4].

Figure 15. Variation of discharge coefficient values against Froude number.
Figure 16. Variation of discharge coefficient values against the percentage of the side weir width to the upstream flow depth over the side weir.
Figure 17. Variation of discharge coefficient values against the percentage of the side weir height to the upstream flow depth over the side weir.

Quantitative analysis between discharge coefficient values and parameters Fr1b/h1, and P/h1 was conducted using data analysis software (IBM SPSS Statistics 19). The various coefficients obtained are shown in Table 3.

ModelUnstandardized CoefficientsStandardized CoefficientstSig
BStd. ErrorBeta (β)
Constant−1.2940.155−8.3690.000
Fr13.4300.2863.40112.0130.000
b/h1−0.0040.004−0.045−0.9440.348
P/h12.4010.1674.06414.3940.000
Table 3. Coefficient.

The value of t and Sig are the significance results of the independent variable, and the value of Sig corresponding to the value of t is less than 0.05, indicating that the independent variable has a significant impact on the dependent variable. Therefore, the values of Sig corresponding to the parameters Fr1 and P/h1 were less than 0.05, indicating that the parameters Fr1 and P/h1 have a significant impact on the discharge coefficient. On the contrary, the parameter b/h1 has less impact on the discharge coefficient. Therefore, quantitative analysis between discharge coefficient values and parameters Fr1, and P/h1 was conducted using data analysis software by removing factor b/h1. The model summary, ANOVA, and coefficient obtained are shown respectively in Table 4, Table 5 and Table 6. R and adjusted R square in Table 4 were approaching 1, which indicated the goodness of fit of the regression model was high. The value of Sig corresponding to the value of F in Table 5 was less than 0.05, which indicated that the regression equation was useful. The values of Sig corresponding to the parameters Fr1 and P/h1 in Table 6 were less than 0.05, indicating that the parameters Fr1 and P/h1 have a significant impact on the discharge coefficient.

ModelRR SquareAdjusted R SquareStd. Error of the Estimate
10.913 a0.8330.8290.03232
Table 4. Model Summary b. Note: a. Predictors:(Constant), Fr1P/h1b. Discharge coefficient.
ModelSum of SquaresdfMean SquareFSig
1Regression0.40220.201192.5450.000 a
Residual0.080770.001
Total0.48379
Table 5. ANOVA b. Note: a. Predictors:(Constant), Fr1P/h1b. Discharge coefficient.
ModelUnstandardized CoefficientsStandardized CoefficientstSig
BStd. ErrorBeta (β)
Constant−1.3260.151−8.7960.000
Fr13.4790.2813.44912.3960.000
P/h12.4270.1644.10814.7650.000
Table 6. Coefficient a. Note: a. Predictors:(Constant), Fr1P/h1.

Based on the above analysis, the flow coefficient formula has been obtained, shown as follows:

Discharge formula were obtained by substituting Equation (15) into Equation (12), as shown in Equation (16).

where Q ∈ [0.006, 0.030], m3/s; b ∈ [0.20, 0.47], m; P ∈ [0.07, 0.20], m.

Figure 18 showed the measured discharge coefficient values with those calculated from discharge formulas in Table 3. The scatter of the data with respect to perfect line was limited to ±10%.

Figure 18. Comparison of the measured discharge coefficient values with those calculated from discharge formulas in Table 3.

6. Discussions

Determining water surface profile near the side weir in the main channel is one of the tasks of hydraulic calculation for side weirs. As the water flows through the side weir, discharge in the main channel is gradually decreasing, namely dQ/ds<0. According to the Equation (17) derived from Qimo Chen [3], it can be inferred that the value of 𝑑ℎ/𝑑𝑠 is greater than zero in subcritical flow (Fr < 1), that is, the water surface profile near the side weir in the main channel is a backwater curve. Due to the side weir entrance effect at the upstream end, water surface profiles drop slightly at the upstream end of the side weir crest, as EI-Khashab [28] and Emiroglu et al. [29] reported in previous experimental studies.

In this study, the water surface profile exhibited a backwater curve along the length of the weir crest. Therefore, during side weir application, it is crucial to ensure that downstream water levels do not exceed the highest water level of the channel.

The head on the weir is one of the important factors that flow over side weirs depends on. At the same time, the head depends on the water surface profile near the side weir in the main channel. Therefore, further research on the quantitative analysis of water surface profile needs to be conducted. Mohamed Khorchani proposed a new approach based on the video monitoring concept to measure the free surface of flow over side weirs. It points out a new direction for future research [8].

The maximum flow velocity, a key parameter in assessing the efficiency of a weir, occurs at the upstream end of the weir crest, typically near the crest. This is attributed to the convergence of the flow as it approaches the crest, resulting in a significant increase in velocity. It was found that in this study the minimum flow velocity occurred at the bottom of the main channel away from the side weir. Under such conditions, the accumulation of sediments could lead to siltation, which in turn can affect the accuracy of flow measurement through side weirs. This is because the presence of sediments can alter the flow patterns and cause errors in the measurement. Therefore, it becomes crucial to explore methods to optimize the selection of side weirs in order to minimize or eliminate the effects of sedimentation on flow measurement.

Pressure distribution plays a crucial role in ensuring structural safety for side weirs since small channels and field inlets have relatively limited pressure-bearing capacities. Therefore, it is important to select an appropriate geometrical parameter of rectangular side weirs based on their ability to withstand the pressure exerted on their bottom combined with pressure distribution data at the bottom of the side channel we have obtained in this study.

The discharge coefficient formula (Equation (15)), which incorporates Fr1 and P/h1, was derived based on dimensional analysis. However, it is worth noting that previous research has contradicted this formula by suggesting that the discharge coefficient solely depends on the Froude number. This conclusion can be observed in this study such as in Equations (18)–(23) in Table 7 of the manuscript [30,31,32,33,34,35], which clearly demonstrate the dependency of the discharge coefficient on the Froude number. In contrast, our derived discharge coefficient formula (Equation (15)) offers a more streamlined and simplified approach compared to Equation (25) [36] and Equation (29) [10]—making it easier to comprehend and apply—an advantageous feature particularly valuable in fluid dynamics where intricate calculations can be time-consuming. Furthermore, our derived discharge coefficient formula (Equation (15)) exhibits a broader application scope than that of Equation (24) [37] as shown in Table 8. Equation (26) [38] and Equation (27) [5] are specifically applicable under high flow discharge conditions. Conversely, our derived discharge coefficient formula (Equation (15)) is better suited for low-flow discharge conditions.

Table 7. Discharge coefficient formulas of rectangular side weirs presented in previous studies.
Discharge/(L·s−1)Width of Side Weir/cmHeight of Side Weir/cmNumber of Formula
10~1410~206~12(24)
35–10020~751~19(26), (27)
6~3020~477~20(15)
Table 8. Application scope of discharge coefficient formulas.

In addition to the factors studied in the paper, factors such as the sediment content in the flow, the bottom slope, and the cross-section shape of the channel also have a certain impact on the hydraulic characteristics of the side weir. Further numerical simulation methods can be used to study the hydraulic characteristics and the influencing factors of the side weir. Water measurement facilities generally require high accuracy of water measurement, the flow of sharp-crested side weirs is complex, and the water surface fluctuates greatly. While conducting numerical simulations, experimental research on prototype channels is necessary to ensure the reliability of the results and provide reference for the body design and optimization of side weirs in small channels and field inlets.

7. Conclusions

This paper presents a comprehensive study that encompasses both experimental and numerical simulation research on rectangular side weirs of varying heights and widths within rectangular channels. A thorough analysis of the experimental and numerical simulation results has been conducted, leading to the derivation of several notable conclusions:

  1. A comparative analysis was conducted on the measured and simulated values of water depth and flow velocity. Both of the maximum absolute relative errors were within 10%, which indicated that the numerical simulation of the side weir was feasible and effective.
  2. The water surface profile exhibited a backwater curve along the length of the weir crest. The side weir entrance effect occurred only between Side Ⅰ and Side Ⅱ. This indicates that flow patterns and associated hydraulic forces at the weir entrance play a crucial role in determining water level distribution along the weir crest.
  3. The maximum flow velocity of the cross-section at the upstream end of the weir crest occurred near the weir crest, while the minimum flow velocity occurred at the bottom of the main channel away from the side weir. As the water depth decreased, the position of the maximum flow velocity gradually moved from the upstream end of the side weir to the downstream end of the side weir.
  4. When the height of the side weir remains constant, an increase in the width of the side weir leads to a decrease in pressure at the bottom of the side channel. Conversely, when the width of the side weir is kept constant, an increase in its height results in an increase in pressure at the bottom of the side channel. Therefore, during practical applications involving side weirs, it is crucial to select an appropriate weir width based on the maximum pressure that can be sustained by the channel’s bottom plate.
  5. The discharge coefficient was found to depend on the upstream Froude number Fr1 and the percentage of the side weir height to the upstream flow depth over the side weir P/h1. The relationship between the discharge coefficient and parameters Fr1 and P/h1 was obtained using multiple regression analysis, which was of linear form and provided an easy means to estimate the discharge coefficient. The discharge formula is of high accuracy with relative errors within 10%, which met the water measurement accuracy requirements of small channels in irrigation areas.

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  27. Hirt, C.W.; Nichols, B.D. Volume of fluid (VOF) method for dynamics of free boundaries. Phys. Fluids 1981, 39, 201–221.
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  29. Emiroglu, M.E.; Kaya, N.; Agaccioglu, H. Discharge capacity of labyrinth side-weir located on a straight channel. ASCE J. Irrig. Drain. Eng. 2010, 136, 37–46.
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stencil

Experimental and numerical investigation of the squeegee process during stencil printing of thick adhesive sealings

두꺼운 접착제 실링의 스텐실 인쇄 중 스퀴지 프로세스에 대한 실험적 및 수치적 조사

 Fabiano I. Indicatti, Bo Cheng, Michael Rädler, Elisabeth Stammen, Klaus Dilger

ABSTRACT

To reliably compensate fuel cell stack tolerances, sealings with a layer thickness of at least 500 µm are necessary. Additionally, threads positioned at the upper region of the stencil apertures need to be integrated to print closed-loop designs under cycle times of as low as 3 seconds. All these requirements can intensify the occurrence of print defects and diminish the process stability. This paper addresses the issues of incomplete regions and air bubbles emerging during the squeegee process. It was detected that the cleanliness state of the stencil directly impacts the formation of incomplete regions by affecting venting conditions inside the aperture. Moreover, it was identified that bubbles are either transferred from the adhesive roll into the aperture or created due to interactions between the moving adhesive and stencil threads. Further, it was shown that bubbles cannot be completely eliminated using a stencil with threads but their size can remain smaller than 300 µm when printing with a new adhesive roll. Finally, distinct strategies were derived and verified experimentally to successfully print a basic sealing design. By introducing a small local gap between substrate and stencil, the entire sealing aperture was reliably filled without the need of a cleaning step.

1. Introduction


The structure of a single low temperature proton exchange membrane fuel cell (LT-PEMFC) fundamentally consists of a membrane electrode assembly (MEA) sandwiched between bipolar plates (BPPs) with sealings between these elements.[Citation1] Up to hundreds of cells can be combined into a stack to provide the required power output, which demands highly reliable manufacturing processes since a single defective cell can compromise the entire stack safety and performance.[Citation2] In light of this, the sealing is one specific component that has been receiving increased attention in the last years. Besides impeding gas and coolant leakages, the sealing is a crucial element in the overall stack concept for compensating assembly tolerances, which can reach up to 300 µm.[Citation3]

To achieve projected market volumes, stencil printing was identified as an attractive technique to meet cycle time requirements for the sealing production, which should be as low as 3 seconds.[Citation4–6] Despite that simple deposit structures achieving heights of up to 500 µm have been reported using solder pastes and conductive adhesives,[Citation7,Citation8] stencil printing is typically not adopted to apply layer thicknesses higher than 200 µm. In comparison, fuel cell sealing concepts demand a minimum layer thickness of 500 µm to safely offset the mentioned stack tolerances under compression ratios of up to 40%.[Citation9–12] Additionally, the sealings are characterized by significantly more complex contour designs to effectively seal ports, flow field and distribution channels of BPPs.

To print closed-loop designs, a so-called double-layer stencil can be adopted to apply the desired structure using a single print cycle.[Citation12–15] As shown in Figure 1, it consists of an upper layer with patterned threads that link different regions of the stencil and provide sufficient mechanical stability. These threads also support the second lower layer, which delineates the print design. This same stencil concept was previously tested using distinct configurations for the threads to print sealings for fuel cells.[Citation5,Citation6] These studies were mainly focused on investigating phenomena and print inconsistencies occurring during the separation process, such as the formation of air bubbles, filaments and excessive spreading. In contrast, print defects emerging during the squeegee process have not been thoroughly explored using this stencil concept.

Figure 1. Schematic of the stencil printing process consisting of a squeegee process (a) and a separation process (b). Perspective view of an aperture segment of a double-layer stencil made from stainless steel, based on.[Citation5,Citation6]

In this paper, a basic sealing design was used to identify relevant printing problems during the squeegee process, as shown in Figure 2. It presents approximate dimensions of 60 mm x 60 mm that should resemble the sealing design in the ports region of typical fuel cells. The squeegee direction corresponds to the indicated x-direction and the three sealing lines perpendicular to the squeegee direction were marked with the letters A, B and C for the sake of better differentiation. With this design, potential printing difficulties closer to the real application can be identified and evaluated more effectively. Based on preliminary experiments, two main print defects during the squeegee process were identified: incomplete regions and bubble formation.

Figure 2. Representative specimen of the basic sealing design with highlighted print defects (printed at 160 mm/s using condition SS–R1). The used squeegee direction corresponds to the indicated positive x-direction.

Incomplete regions are a known issue in stencil printing.[Citation16–20] Typically, small aperture dimensions and an insufficient pressure inside the print material are the main reported reasons for the emergence of this defect. In contrast, the formation of bubbles during the squeegee process is a less recognized phenomenon in stencil printing but can considerably impact the process reproducibility. In the field of screen printing, the presence of bubbles inside specimens was already reported by several studies.[Citation20–27] The mechanical agitation of the print material before the squeegee process and inherent interactions with the mesh were indicated as driving mechanisms for bubbles to appear.[Citation24–28] Yet, there is still very little consensus and a general lack of correlation with experimental data on describing how these bubbles are produced. Several computational fluid dynamics (CFD) simulations were developed to estimate the pressure distribution within the print material in front of the moving squeegee[Citation29–32] and the filling completeness of a given aperture volume,[Citation17,Citation18,Citation33,Citation34] where the latter has the additional advantage of being experimentally measurable. However, more comprehensive simulative approaches demonstrating the print material motion are still missing in the literature, which could provide valuable information to optimize the aperture filling behaviour and avoid print defects.

Based on this scenario, comprehensive print experiments were conducted to determine how print and stencil parameters influence the formation of incomplete regions and bubbles during the squeegee process. Characterisation methods using microscope images and micro-CT scans were applied to quantify and analyse these defects. Here, a stencil containing a lines design with and without threads was adopted, which allows to isolate the impact of threads in the print results. In addition, a new CFD model of the squeegee process was developed in FLOW–3D[Citation35] to visualize how these print defects emerge. The squeegee process was recorded in slow motion to analyse the adhesive roll behaviour and provide additional validation for the simulations. Based upon the combined experimental and simulation results, potential approaches to avoid these printing problems using the basic sealing design were derived and tested. Ultimately, the collected findings in this paper should enhance the understanding on decisive process and stencil parameters during the squeegee step, increasing the attractiveness of this technique for the application of sealings and adhesives in the industry.

2. Materials and methods


All preparation steps and experiments were conducted in laboratory conditions, at 23°C.

2.1. Stencil design

Two different stencils made from stainless steel (Christian Koenen GmbH, Ottobrunn, Germany) were used for the experiments. As illustrated in Figure 3, both stencils presented apertures with a 680 µm thick step and 120 µm thick threads, resulting in a stencil thickness of 800 µm. Here, a thicker stencil than the minimum layer thickness of 500 µm is required since a certain degree of spreading (height loss) of the applied material over the substrate always occurs. A very similar configuration was previously used to reliably reach the same layer thickness using several distinct adhesives as print material.[Citation6] The first stencil (a) corresponds to the one used to print the mentioned sealing design, and the second stencil (b) consists of 80 mm length lines with two different widths: 1.52 and 2.34 mm, which correspond to aperture aspect ratios (AR = width/height) of 1.90 and 2.93, respectively. A second pair of lines without threads was included in this stencil to separately examine how the addition of threads influences the print results. The line orientation relative to the squeegee direction was primarily adjusted at 0°. This considerably reduces the modelling and computational effort for the numerical simulations but still allows to capture the basic formation mechanisms of desired print defects.

Figure 3. Schematic of used stencils and detailed views of the aperture threads design.

2.2. Adhesive selection and print parameters

An ultraviolet (UV) curable acrylic was selected for all experiments, and it corresponds to adhesive B3, which was thoroughly characterized and tested previously by Indicatti et al.[Citation6] It exhibited very good printability, and its transparency facilitates the characterisation of bubbles inside the specimen. Moreover, this adhesive presented a reduced filament-stretching tendency, which avoided the formation of bubbles during the separation process.

The rheological properties of this adhesive required for the simulation model are reported in Table 1. The viscosity values were obtained with a stepped flow approach using a rheometer (MCR 500, Anton-Paar GmbH, Ostfildern, Germany) equipped with a plate-plate setup (25 mm diameter) and a 0.4 mm gap. The adhesive surface tension was measured with the Wilhelmy plate method (K100 Force Tensiometer, KRÜSS GmbH, Hamburg, Germany) using a platin-iridium Wilhelmy-plate (10 × 20 x 0.2 mm). These measurements were carried out at a constant speed of 0.01 mm/s and an immersion depth of 2 mm. An optical contact angle measurement system (DSA 10, KRÜSS GmbH, Hamburg, Germany) was used to determine the adhesive equilibrium contact angle with the stencil surface. The surface tension and contact angle measurements were conducted with adhesive B3 without fumed silica since the filled one used for the print experiments exhibited an apparent yield stress that prevented wetting and thereby reliable measurements with these methods. For additional information about this adhesive and rheological characterisations, see reference.[Citation6]

Equilibrium surface tension [mN/m]28.6 ± 0.1
Equilibrium contact angle of the adhesive on the stencil surface (smooth untreated stainless steel) [°]20.0 ± 1.5
Density [g/cm3]0.970
Shear rate [1/s]Steady-state viscosity [Pa∙s]
1021.1
15.615.4
25.111.5
39.88.9
63.17.1
1005.8
Table 1. Average and corresponding standard deviation of the adhesive properties incorporated into the model. The contact angle and surface tension measurements were repeated five times. The viscosity standard deviation remained below 5%, based upon three measurements.

The print experiments were performed with a commercial stencil printer (EKRA STS E5, ASYS Group, Dornstadt, Germany). Squeegee speeds of 40 and 160 mm/s were tested, and the separation speed kept unchanged at 1 mm/s to minimize the risk of print defects emerging during separation. A squeegee pressure of 0.5 N/mm was adopted to leave the stencil topside completely free of adhesive remains after the squeegee process, which is a required condition to not affect the final layer thickness. The used squeegee (RKS Carbon S HQ/30 65 Shore, RK Siebdrucktechnik GmbH, Rösrath, Germany) presented a length of 120 mm and a 4 mm chamfer (45°) at the tip. A squeegee holder of 60° was adopted, resulting in a nominal squeegee angle of 15°. This squeegee configuration was selected based on previous experiments to enhance the aperture filling and process reproducibility.

An adhesive roll was manually dispensed over the stencil using an adhesive gun to ensure comparable initial conditions. Every new adhesive roll was completely free of bubbles and its height was always between 8 and 12 mm. Large adhesive residues on the squeegee after printing were also removed when a new roll was added to prevent any further sources of bubbles. Another additional parameter evaluated was the aperture state and cleanliness of the stencil underside before printing. Considering the adhesive roll state, four different print conditions were investigated, as illustrated in Figure 4
: cleaned aperture with cleaned stencil and a new adhesive roll (CA–R1), pre-wetted aperture with cleaned stencil and a new adhesive roll (CS–R1), pre-wetted aperture with smeared stencil and a new adhesive roll (SS–R1), and pre-wetted aperture with smeared stencil and a three-times used adhesive roll (SS–R3).

Figure 4. Simplified illustration of the aperture cross section describing the four tested print conditions considering the state of the aperture, stencil underside and adhesive roll.

With exception of condition CA–R1, these correspond to relevant operation modes that have direct impact on the production cycle time and process efficiency. The cleaning procedure of the stencil was conducted manually by hand using absorbent wipes. It is important to emphasize that the illustrated smearings in Figure 4 were not considered as a print defect since these remained roughly smaller than 0.2 mm throughout the performed experiments. Moreover, the extent of smearings observed did not cause instabilities during the separation process, nor did it significantly affect print resolution due to the relatively large dimensions of the printed structures.

2.3. Specimens characterisation

All specimens were scanned using a light microscope (VHX-2000, Keyence, Osaka, Japan) with a resolution of 5.2 µm/pixel. To analyse the bubbles inside the specimens, ImageJ[Citation36,Citation37] was used for image processing and extracting the quantity and area of bubbles, as depicted in Figure 5
. Since the majority of the bubbles exhibited a circular shape, the measured bubble area was converted to an equivalent bubble diameter, which is a more convenient indicator. Frequency distribution histograms of the bubble diameter were derived from this data by combining the quantity of bubbles of three different specimens printed at identical conditions. Furthermore, micro-CT measurements (voxel-size: 10 µm) were conducted with a few representative specimens to obtain the precise position of the bubbles along the specimen height, which could not be assessed using the microscope.

Figure 5. Developed approach using ImageJ to characterize bubbles formed during the squeegee process.

3. Experimental results and discussion


3.1. Incomplete regions

The gap between stencil and substrate was measured and set to zero in order to keep the smearings at a minimum. Prominent smearings were not observed during all experiments. However, it was identified that the cleanliness state of the stencil before printing was associated with the emergence of incomplete regions, as reported in Figure 6. When the stencil was not cleaned before printing (conditions SS–R1 and SS–R3), 95.8% of the specimens exhibited incomplete regions. In contrast, only 6.3% of the specimens printed with a cleaned stencil (conditions CA–R1 and CS–R1) presented this defect. The incomplete regions were located exclusively at the line extremity that was last filled by the squeegee and appeared either as a large bubble that extends almost throughout the entire line width (Figure 7(a)) or as an empty space (Figure 7(b)).

Figure 6. Number of specimens exhibiting incomplete regions printed at 40 and 160 mm/s.
Figure 7. Representative specimens with incomplete regions at the line extremity (last part to be filled by the squeegee).

The occurrence of this defect was attributed to the lack of air venting at the line extremity due to the smearings at the stencil underside. Despite being small, the smearings can act like an additional seal between the stencil and substrate that impedes air to be expelled from the aperture during the squeegee process. This deduction is supported by the fact that large air bubbles were transferred into the adhesive roll when printing with a smeared stencil whereas such bubbles were not observed when it was cleaned. Figure 8 displays this phenomenon with two image sequences from the squeegee process recorded at a frame rate of 120 fps using a cleaned (a) and a smeared stencil (b). As can be seen, both adhesive rolls are completely free of bubbles before reaching the line extremity. The gap between stencil and substrate is intended to be zero, however, it still allows air to escape when the stencil is cleaned, which most of the time is sufficient to avoid filling defects and the formation of bubbles inside the adhesive roll. This phenomenon was identified using all four print conditions and was consistently replicated using both squeegee speeds.

Figure 8. Image sequences of the squeegee process using a cleaned (a) and smeared stencil (b) to compare the formation of bubbles inside the adhesive roll when the squeegee (40 mm/s) passes through the line extremity.

The same effect was observed when printing the sealing design, where large bubbles formed inside the adhesive roll when it was passing by the T-intersections and the line C of the sealing. Here, the detection of these bubbles was correlated with the presence of incomplete regions as well. The T-intersections can be considered as a more critical part to be completely filled due to their geometry and larger volume compared to the lines. Thus, the aperture design and its orientation relative to the squeegee direction can be considered as an additional influencing parameter, which directly determine the available time for filling. For instance, a few small incomplete regions were also formed at lines A and B, as shown in Figure 2. In this case, large bubbles did not appear inside the adhesive roll when passing through these lines, and the formation of these incomplete regions can be further associated with an insufficient time for the adhesive to fill the aperture or air to be expelled from it. This is reinforced by the observation that lines A and B of sealing specimens printed at 40 mm/s exhibited a better or even complete filling of those lines. Therefore, additional approaches to provide sufficient venting and time for filling are required to reliably fill all critical regions, which will be discussed later in section 5.

Variations of the squeegee speed and aperture AR or the presence of stencil threads did not notably impact the formation of incomplete regions, see Figure 6. All specimens were printed with a nominal squeegee angle of 15°, and experiments performed with larger (30°) and shallower (5°) angles did not result in any significant improvement of the aperture filling completeness. Increasing the vertical squeegee pressure to minimize the extent of smearings at the stencil underside also did not avoid incomplete regions. Indeed, an excessive squeegee pressure (>1 N/mm) might even enhance the restriction on air flow between stencil and substrate, leading to the emergence of incomplete regions using a cleaned stencil as well. This description better indicates the ‘cleanliness state’ as the decisive parameter on the formation of the print defect.

3.2. Bubble formation

Figure 9 reports frequency distribution histograms of the bubble diameter from specimens printed at two different squeegee speeds and aperture ARs. The measured quantity of bubbles was normalized by the total considered length of three specimens (240 mm) to enhance comparability. The histograms of specimens printed without threads were included as well. Yet, the following explanations are only considered for the specimens printed with threads if not indicated.

Figure 9. Frequency histograms of the diameter of the bubbles produced during the squeegee process.

Overall, the diameter of the bubbles did not surpass 1000 µm and the majority of them remained below 300 µm. By increasing the squeegee speed from 40 to 160 mm/s, the quantity of bubbles more than doubled in average considering the four tested print conditions. When the aperture AR is increased from 1.90 to 2.93, the average quantity of bubbles increased about 44%. In all considered cases, the cleaned aperture (CA–R1) produced the smallest quantity of bubbles. The bubble formation drastically increased with a pre-wetted aperture, as represented by the profiles of the cleaned (CS–R1) and smeared stencil (SS–R1). Here, the quantity of bubbles stayed relatively constant independent of the cleanliness state of the stencil (CS–R1 or SS–R1), and the distribution of the bubble diameter maintained a similar range as well. In this case, the largest discrepancy was notable in bubbles of up to 50 µm in diameter. Specimens printed with a smeared stencil (SS–R1) presented about twice the quantity of bubbles of this size when compared to those printed with the cleaned stencil (CS–R1). When printing with the same adhesive roll for the third time (SS–R3), the quantity of bubbles kept in about the same level of specimens printed with a new adhesive roll (SS–R1). One exception here was observed using the larger aperture AR at 160 mm/s, which produced approximately 50% more bubbles with the three times used adhesive roll. In addition, SS–R3 specimens were the only ones that exhibited very large bubbles with more than 300 µm in diameter.

By combining the results from the diagrams with the recordings of the squeegee process and specimens characteristics, three main mechanisms for bubble formation were identified, as shown in Figure 10. The first mechanism corresponds to bubbles that are not created due to the stencil threads but transferred from the adhesive roll into the aperture during the squeegee process. These bubbles are in general smaller than 300 µm and they hardly interact with stencil threads due to their size. This was confirmed by the fact that lines printed with the aperture without threads still presented bubbles but in considerable smaller quantities. In this case, lines printed with a new adhesive roll did not exhibit a significant quantity of bubbles independent of the squeegee speed. However, if a new adhesive roll was not added, the quantity of bubbles increased with the number of print cycles. Figure 11 presents an adhesive roll free of air bubbles before the squeegee process (a) and the same adhesive roll after three print cycles (b). The visible bubbles in the roll correspond to the ones that can be transferred into the aperture during the squeegee process. These bubbles might be created by random local instabilities during filling, but the main sources appear to be the air entrapment due to the lack of venting at the aperture extremity, as mentioned earlier, and due to the first contact or recontact between the squeegee and the adhesive over the stencil.

Figure 10. Identified bubble formation mechanisms during the squeegee process. The shown specimen segments were printed with an aperture AR of 2.93.
Figure 11. Adhesive roll over the stencil free of air bubbles before printing (a) and after three print cycles (b). In this case, the aperture with threads was used but very similar bubble characteristics inside the adhesive roll were observed when printing with the aperture without threads.

The second mechanism is very similar to the first one, with the difference that the stencil threads interact with large bubbles from the adhesive roll (shown in Figure 11(b)) when these are entering the aperture. This was deduced considering the regular position of large bubbles coinciding with the threads pitch and by comparing specimens printed with and without threads. This mechanism was responsible for producing the largest bubbles identified (>300 µm), which solely emerged inside specimens printed with threads. Thus, it is plausible to say that the interactions with the threads might increase the final air volume of bubbles coming from the adhesive roll since the characteristics of bubbles produced inside the adhesive roll were very similar independent of the threads presence. Alternatively, the threads might also locally change flow conditions, which could facilitate the transfer of larger bubbles from the adhesive roll.

Finally, the third mechanism is exclusively related to the presence of stencil threads, as these bubbles presented a very uniform pattern correlated with the threads pitch. Here, bubbles having a broad size range between 50 and 300 µm appearing near the centreline were the main type responsible for increasing the quantity of bubbles when a higher squeegee speed was used. Moreover, bubbles typically smaller than 100 µm in diameter emerged very close to the aperture walls and mostly in pairs. These are the primary contributors to the increase of the bubbles quantity when printing with a pre-wetted aperture (CS–R1 and SS–R1) instead with a cleaned aperture (CA–R1). The formation mechanisms of these two types of bubbles could not be captured experimentally but were assessed by the numerical simulations.

During the experiments it was also observed that bubbles can disappear after the separation process, as shown in Figure 12. Bubbles close to the aperture walls and threads might stay in the aperture or break due to the separation process since filaments are stretched near these regions. However, this phenomenon happened only occasionally and has a considerable smaller impact than the mechanisms previously presented. Yet, this phenomenon should be still mentioned since these bubbles might remain inside the aperture after separation and reappear in the following printed specimen. Thus, considering this and the three bubble formation mechanisms shown in Figure 10, it can be stated that all bubbles inside specimens printed with condition CA–R1 emerge due to the presence of stencil threads (Mechanism 3). Specimens produced with conditions CS–R1 and SS–R1 present bubbles that are majorly originated from Mechanism 3 since a new adhesive roll is used for these two conditions as well. Finally, specimens printed with condition SS–R3 exhibit bubbles from all mechanisms described before. It is possible to infer that all bubbles larger than 300 µm emerge due to Mechanism 2. However, excepting the small bubbles (<100 µm) close to the lateral walls exhibiting a uniform relative distance (Mechanism 3), the remaining bubbles cannot be categorized into their corresponding formation mechanism with certainty.

Figure 12. Comparison of the aperture before the separation process (left) and the final specimen (right) demonstrating how bubbles can disappear when located near the aperture walls and threads. This specimen was printed using condition SS–R1.

4. Modelling approach


This numerical study is focused on reproducing the basic formation mechanisms of incomplete regions and bubbles during the squeegee process. The simulations were performed only at a constant squeegee speed of 40 mm/s since it was already sufficient for both print defects to emerge. As previously discussed, a higher squeegee speed solely increased the quantity of bubbles but did not drastically change other characteristics of these print defects. For validation, the position and relative size of these defects were assessed alongside real specimens using microscope images and micro-CT scans. In addition, recordings of the adhesive motion during the squeegee process were compared with the simulation results to identify possible similarities. The CFD model was implemented in the commercially available software FLOW–3D,[Citation35] which applies the finite volume method (FVM) to numerically solve the conservation equations for mass and momentum. By neglecting turbulence effects and mass generation, these two equations can be described by the following expressions, respectively:

∂𝜌∂t+∇⋅(𝜌⁢𝒖)=0 (1)

∂𝒖∂𝑡+(𝒖⋅∇)⁢𝒖=1𝜌∇𝑝+𝜈∇2𝒖+𝒇 (2)

where 𝜌 is the adhesive density, 𝑡 is the time, ∇ is the divergence, 𝒖 is the velocity vector, and 𝑝 is the static pressure. 𝜈 corresponds to the kinematic viscosity and 𝒇 to the external body forces, such as gravitational and surface tension forces. To describe the free interface between the two fluids (adhesive and air), the volume of fluid (VOF) method is used:

∂𝛼∂t+∇⋅(𝛼⁢𝒖)=0 (3)

The variable 𝛼 represents the proportion of the cell volume occupied by adhesive, with 𝛼=0 signifying a cell entirely filled with air and 𝛼=1 indicating a cell entirely filled with adhesive. Consequently, a partially filled cell is defined as 0<𝛼<1. At each step time, the interface between the fluids can be dynamically reconstructed based on this cell information and is iteratively recalculated considered the updated moving squeegee location. For further details about the model implementation, we refer here to the software’s user manual.[Citation38]

4.1. Model description and assumptions

The same squeegee and threads dimensions from the experiments were incorporated into the model. To reduce computational effort, the aperture with 2.34 mm width (AR = 2.93) was modelled using an axisymmetric geometry, and only a line segment with 9.96 mm length was considered, as shown in Figure 13. A 3D model was adopted since a 2D model is not able to capture the adhesive flow perpendicular to the squeegee direction, which is a decisive phenomenon inside the aperture during the filling process. In order to investigate the impact of venting on the formation of incomplete regions and bubbles, two different simulation cases were established. In the first case, a 50 µm gap between stencil and substrate was integrated to allow air to escape from the aperture during filling. This should be equivalent to condition CA–R1 tested experimentally. In the second case, the model did not include a gap and should correspond to condition SS–R1. Here, it is important to note that the simulation model did not contain pre-wetted aperture walls or threads, which has to be considered when comparing it with experimental results.

Figure 13. Model overview with relevant dimensions and mesh details.

The following assumptions have been further considered for the model:

  1. The simulation domain contains only two phases (adhesive and air) with constant volumes, where the adhesive motion is simulated as an incompressible and laminar fluid flow.
  2. The stencil and squeegee are modelled as rigid bodies and exhibit no-slip boundary conditions. A horizontal translational speed is given to the squeegee to simulate the filling process, and the stencil remains stationary. There is no gap between the squeegee tip and the stencil.
  3. The shear thinning viscosity of the adhesive was defined in a tabular form between the shear rates of 10 and 100 s−1, see Table 1.
  4. The measured adhesive surface tension and its equilibrium contact angle with the stencil surface were included in the material model. The same equilibrium contact angle was adopted for the squeegee surface in the simulation.

The entire simulation domain was meshed with regular block shaped cells adopting a commonly used meshing strategy, where the cells exhibit reducing dimensions towards the aperture region and remain unchanged throughout the entire simulation time, as shown in Figure 12. To minimize repeated calculations, the squeegee process was modelled using a two-step approach. In the first step, the adhesive over the stencil rolls for about 25 mm up to near the aperture, reproducing the initial conditions from the experiments. The rolling motion of the adhesive reduces the viscosity due its shear thinning properties, which can impact the filling behaviour. This step was identical in both simulation cases, and the adhesive roll remained free of air bubbles. A coarser mesh with cell sides of up to 750 µm was applied for this step resulting in a simulation domain with about 1.8 million cells. In the second step, the adhesive starts entering the aperture, which corresponds to the simulation stage of main interest. Inside the aperture, the cells exhibited equal sides of 40 µm, which was adopted as a balance between computational time and accuracy. Using this mesh approach, the second domain contained about 3 million cells. The time step was automatically adjusted and ranged from 1 × 103 to 1 × 104 s during the first step while in the second one it stayed between 1 × 10−4 and 1 × 10−5 s.

4.2. Simulation results and validation

Figure 14 shows two simultaneous views from the symmetry plane and aperture bottom over the simulation time during the aperture filling with (a) and without (b) a gap between stencil and substrate. As can be seen, the adhesive is able to completely fill the aperture when a gap for venting is available. When the gap is removed, the right aperture extremity remains unfilled due to the enclosed volume formed between substrate, aperture walls and adhesive (t = 1.44 s). In this case, the formation of an air bubble inside the adhesive roll (t = 1.53 s) was captured by the simulation as well, agreeing with the experiment results presented in Figure 8(b). Another important phenomenon observed in the experiments and replicated by the model was the adhesive infiltrating the gap between the stencil and substrate, resulting in the formation of smearings that remained smaller than 0.15 mm in the simulation.

Figure 14. Simultaneous views (∆t = 0.09 s) from the symmetry plane and aperture bottom of the simulated squeegee process with (a) and without (b) a gap between stencil and substrate.

The simulations were also able to reproduce the formation of bubbles due to the presence of threads, as previously described by the third mechanism shown in Figure 10
. In the simulation case without a gap, bubbles with size ranging between 50 and 100 µm formed at the aperture walls and substrate surface with their relative distance coinciding with the threads pitch. When entering the aperture, the adhesive front is split by the threads into two smaller fronts that entrap air when reencountering at the substrate surface (t = 1.35 s). As the squeegee advances, the air is pushed towards the lateral walls but remains inside the aperture due to lack of venting. From micro-CT scans, it was possible to verify that these bubbles are touching the substrate surface as well, see Figure 15(b)
. Thus, these simulation results correlate very well with real specimens printed using condition SS–R1. Here is important to stress that the bubbles in the simulation are directly touching the aperture walls and would disappear in a subsequent separation process. In the real specimens, these bubbles are not contacting the aperture walls before separation, as shown in Figure 12
. This difference can be explained by the fact that the aperture in the simulation is not pre-wetted with adhesive before being filled, which differs from real SS–R1 conditions. Hence, the formation of these bubbles near the aperture walls results from the interplay between the incoming adhesive pushed by the squeegee and the adhesive that is pre-wetting the aperture walls. For comparison, these bubbles near the aperture walls did not appear when venting was available in the simulation, which also correlates with real specimens printed with CA–R1 conditions.

Figure 15. Qualitative comparison of representative specimens (scanned with microscope and micro-CT) and corresponding simulation exhibiting the final state of the aperture after the squeegee process with (a) and without (b) a venting gap. Bubbles produced due to the presence of threads (Mechanism 3) are visible in both experimental and simulation results, as indicated by the arrows. Two additional views (perspective and symmetry plane showing mesh cell size) of the two last threads (aperture extremity) from the simulated cases were included with the adhesive showing transparent properties to better visualize the generated bubbles.

Bubbles along the aperture centreline were formed in both simulation cases as well, see Figure 15. These bubbles are located close to or on the threads and exhibited sizes in the range of 100 to 200 µm, which fairly correlates with the experimental results. In the model, these bubbles only remained at the two last threads of the aperture. However, it is possible to observe bubbles forming around the other threads during filling (t = 1.44 s) but are broken after the squeegee tip passes through them (t = 1.62 s). In the experiments, these bubbles were visible all along the line length using conditions CA–R1 and SS–R1. Hence, the formation of these bubbles is unaffected by whether the threads are pre-wetted with adhesive or not. This discrepancy can be related to the apparent higher difficulty for the bubbles to detach from the threads in the model, which might be associated with insufficient small cell elements or simplifications in the material model.

To better understand this behaviour, Figure 16 presents the resulting adhesive velocity during the aperture filling for the case with a venting gap. The bubbles around the threads are formed approximately 4 to 6 mm in front of the squeegee tip (t = 1.46 s) and remain attached up until the squeegee tip reaches them (t = 1.55 s). The generated adhesive flow around the bubbles is not sufficient to release these from the threads. About 1 mm in front of the squeegee tip, a region with practically zero velocity is formed due to the flow direction change inside the aperture (t = 1.46 s). Immediately below the squeegee tip, the adhesive flow follows the squeegee direction but is gradually reorientated towards the substrate surface up until reaching the opposite direction of the squeegee. This reorientation leads to the formation of a backflow behind the squeegee tip, which causes a local overfilling of the aperture and contributes to break the bubbles around the threads (t = 1.55 s). When approaching the aperture extremity, the backflow region is affected by the aperture wall, which can explain why these bubbles only formed near the last two threads in the simulation.

Figure 16. Detailed symmetry plane view (∆t = 0.03 s) showing the resulting adhesive velocity for the simulation case with a venting gap between the stencil and substrate. The velocity vectors and fields are represented for a stationary observer fixed on the stencil.

This backflow was also observed experimentally but not in the same intensity as in the simulations. This difference can be related to the reduced viscosity range adopted and calibrated for the model, which used the viscosity value at 10 s−1 for lower shear rates. In addition, the neglected thixotropic properties of the adhesive might also have an impact on this response. Simulations using a larger range for the shear thinning viscosity of up to 0.1 and 1 s−1 were carried out but the higher viscosity avoided the reliable filling of the aperture, preventing any assessment of bubble formation during this step. Thus, the model is sensitive to changes in the viscosity range and should be recalibrated when, for instance, the squeegee speed is considerably increased. Additional simulation cases were not conducted since the formation of incomplete regions and bubbles was already detected and an appropriate investigation of the mentioned models deviations would go beyond the scope of this paper.

5. Sealing design with optimized print conditions

In this section, new strategies based on the presented experimental and numerical results were assessed to enhance the print conditions of the sealing design. Primary focus was placed on minimizing the process cycle time and on reducing print defects. The exhibited findings indicate that bubbles cannot be completely eliminated when using a stencil with threads. However, when using a new adhesive roll, the bubble diameter generally did not surpass 300 µm independent of the squeegee speed. Therefore, for every new specimen, a new adhesive roll was used. Despite producing more bubbles, the higher squeegee speed of 160 mm/s was favoured since these marginally impacted the process reliability. Yet, it should be emphasized that the influence of such bubbles on other sealing characteristics still needs to be quantified experimentally. For instance, previous studies have shown that voids inside composite and polymeric materials can notably diminish gas permeability, which on the other hand might be also compensated by increasing the sealing width or altering material properties.[Citation39–43] Hence, systematic investigations should be conducted in the future to assess the real performance of sealings printed with stencil printing and determine how process parameters can be actively adjusted to control gas permeability.

It is possible to reduce the number of stencil threads and consequently the quantity of bubbles. However, the mechanical stability of the stencil must be re-evaluated when altering the threads design. In this case, the stencil was not changed but the orientation of the sealing design relative to the squeegee direction was rotated by 20°. This angle was selected based on previous experiments to shift the position of incomplete regions to the sealing edges highlighted in Figure 17. Yet, solely adjusting the sealing orientation was not sufficient to prevent all filling defects, which can be considered the major cause for print inconsistencies. For this reason, four different approaches were investigated to achieve a completely filled sealing, as reported in Table 2. Here, only approaches using the least amount of cleaning were considered since adding a cleaning step before printing every single specimen can substantially increase cycle time and production costs. Thus, all approaches were conducted using a pre-wetted aperture with a smeared stencil (SS–R1 condition), and three specimens were printed in sequence to confirm the observations. It is also important to note that, despite rotating the sealing design at 20° or adding a second squeegee stroke, the observed quantity and size of bubbles did not notably change compared to sealings printed at 0° with a single squeegee stroke. Thereby, further bubble characterisations were not conducted to analyse the influence of these parameters.

Figure 17. Illustration of the rotated stencil with the sealing design and indication of regions exhibiting filling problems.
Approach descriptionSnap-off distance [mm]Formation of incomplete regions
(a) Single squeegee stroke with snap-off distance0.2Yes
(b) Double squeegee stroke0Yes
(c) Double squeegee stroke with snap-off distance0.2Yes
(d) Single squeegee stroke with local tape pieces (0.2 mm)0.2No
Table 2. Overview of evaluated approaches to eliminate incomplete regions in the sealing design.

The first approach was based on introducing a gap of 0.2 mm between stencil and substrate, also sometimes referred as snap-off distance.[Citation44,Citation45] It was expected that this gap could provide sufficient venting to fill the aperture entirely. However, no significant improvement in avoiding incomplete regions was observed compared to sealings printed without a gap, see Figure 18(a)
. Here, the squeegee vertical pressure closes the gap when it advances towards the aperture, and the smearings at the stencil underside act, as previously described, as an additional seal that inhibit air being expelled through it. Additional tests including the cleaning of the stencil enhanced the filling completeness of the T-intersection, but the last sealing edge (at line C) still remained incomplete.

Figure 18. Representative specimens printed with four different approaches to avoid the formation of incomplete regions: (a) single squeegee stroke with snap-off distance, (b) double squeegee stroke, (c) double squeegee stroke with snap-off distance, and (d) single squeegee stroke with local tape pieces.

The second and third approaches relied on using two squeegee strokes moving forwards and backwards. The idea here was that a second squeegee stroke could eliminate the incomplete regions by pushing adhesive from the opposite direction. However, this approach was insufficient to completely prevent this print defect as well. Adding a gap of 0.2 mm between stencil and substrate also did not improve the filling completeness. Instead of an incomplete filling, large bubbles usually larger than 1000 µm formed at these regions, see cases (b) and (c) in Figure 18. The main disadvantage of this approach is that it requires at least twice the time for the squeegee process. Yet, an additional squeegee stroke can be considered to have a smaller impact on production efficiency compared to introducing a cleaning step before every single specimen.

For the fourth approach, local gaps of about 0.2 mm height were introduced between the stencil and substrate by adding a small piece of adhesive tape near the edges with filling problems. The main difference to the first approach is that the gap created by the piece of tape does not close due to the squeegee vertical pressure or due to smearings. Thus, a small venting channel is maintained during the squeegee process that allows air to escape the aperture at those edges, ensuring the complete filling of the entire sealing, see Figure 18(d)
. The use of a tape piece was solely a simple method to prove the effectiveness of a local gap and more sophisticated approaches can be used, such as integrating a local elevation or channel on the substrate or stencil.[Citation46–48]

6. Conclusions


The squeegee process to print a basic sealing including relevant design features close to real fuel cell applications was optimized using experimental and numerical approaches. First, incomplete regions and bubbles forming during the squeegee process were detected as the main print defects. An additional stencil containing only lines with and without threads was used to isolate the formation mechanisms of these two defects. It was shown that the stencil cleanliness state considerably impacts the venting conditions inside the aperture during filling and thereby is determinant on the emergence of incomplete regions. Moreover, three main formation mechanisms of bubbles were proposed, evidencing that pre-existing bubbles inside the adhesive roll might be transferred into the aperture by the squeegee movement or produced due to interactions between the adhesive and stencil threads. The developed numerical model presented an overall good agreement with experimental observations and was able to reproduce the formation of incomplete regions and bubbles as well.

By combining experiment and simulation results it was verified that bubbles cannot be completely avoided when using a stencil with threads. However, by adding a new adhesive roll for every new print cycle, the quantity of bubbles can be reduced, and their diameter remained generally smaller than 300 µm, which was considered to have a minor impact on the process reliability. Based on these findings, four different print strategies focused on minimizing the print cycle time were assessed to eliminate incomplete regions emerging in the sealing design. By reorienting the aperture relative to the squeegee direction and maintaining a local gap during the squeegee process, this printing issue was prevented and the reproducible filling of the entire sealing was successfully achieved.

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Velocity of pipe

Dynamic Performance of Suspended Pipelines with Permeable Wrappers under Solitary Waves

단일 파동 하에서 투과성 포장지가 있는 현수 파이프라인의 동적 성능

Youkou Dong, Enjin Zhao, Lan Cui, Yizhe Li, Yang Wang

Abstract


Submarine pipelines are widely adopted around the world for transporting oil and gas from offshore fields. They tend to be severely ruined by the extreme waves induced by the natural disaster, such as hurricanes and tsunamis. To maintain the safety and function integrity of the pipelines, porous media have been used to wrap them from the external loads by the submarine environment. The functions of the porous wrappers under the hydrodynamic impact remain to be uncovered before they are widely accepted by the industry. In this study, a numerical wave tank is established with the immersed boundary method as one of the computational fluid dynamics. The submarine pipelines and their porous wrappers are two-way-coupled in terms of displacement and pressure at their interfaces. The impact from the solitary waves, which approximately represent the extreme waves in the reality, on the pipelines with different configurations of the porous wrapper is investigated. The results present significant protective functions of the wrappers on the internal pipelines, transferring the impact forces from the pipelines to the wrappers. The protective effects tend to be enhanced by the porosity and thickness of the wrappers. The influence of the pipeline configurations and the marine environment are then analysed. As for the front pipeline, an increase in the gap leads to a slight increase in the horizontal forces on both the wrapper and the pipeline, but a significant increase in the vertical forces. As for the rear pipeline, because of the shield function of the front pipeline, the velocity within the gap space and the forces on the pipes are decreased with the decrease in the gap size. The complex flow fields around the pipelines with wrappers are also illuminated, implying that the protection function of the wrapper is enhanced by the wave height reduction.

Keywords


extreme wave; submarine pipeline; external wrapper; coupling analysis; computational fluid dynamics

1. Introduction


Pipelines that are laid on or below the seabed and continuously transport large amounts of oil (or gas) are collectively referred to as submarine pipelines. They constitute the main transporting structures and currently they are the most economical and reliable selections in the design of transportation tools. Pipelines are usually installed within the seabed sediments under the protection of rock berms [1]. However, the sediments around the pipelines may be scoured by contour currents and internal waves, which expose the pipelines to the threat of complex marine environments [2]. The scour mechanism and its evolution process around the in-position pipelines were investigated by many scholars, such as Reference [3]. Occasionally, segments of a pipeline may be suspended between high points through continental slopes due to an uneven seabed profile. For example, suspended pipelines were widely used in the Ormen Lange projects, with massive depressions and landslide blocks scattered along the 120-km-long route [4].
Natural disaster, such as hurricanes and tsunamis, may induce extreme waves that generate enormous impact loads on the pipelines and may cause serious ruins to the whole production and transportation system [5,6,7]. Tsunamis, one of the major marine disasters caused by earthquakes and submarine landslides [8,9], send surges of water with extremely long waves that are not especially steep [10]. The tsunami triggered by a 9.0-Mw earthquake in 2011 extensively destroyed 70% of the total 200,000 structures along the Miyagi coastline, including submarine pipelines, seawalls, and coastal bridges. A tsunami is typically composed of several transient waves with varying amplitudes, wave-lengths, and wave periods during propagation. Solitary waves were proposed to simulate the tsunami waves by decomposing them into N-waves through the Korteweg-de Vries equation [11,12,13,14]. Since then, the run-up process of the tsunami waves along the shoreline was investigated with the depth-averaged smooth particle hydrodynamics method [15,16]. References [17,18] quantified the impact loads over cylinders from a tsunami wave.
To protect the marine structures from potential damages due to extreme marine conditions, engineers have developed outer protections in terms of wrappers made of porous media. A porous medium enhances the buffering performance of the structures and dissipates part of the incoming wave energy [19]. For example, the turbulent intensities on a permeable breakwater were significantly attenuated in the numerical analysis by References [20,21,22]. Naturally, porous media are expected to be protective to submarine pipelines under extreme marine conditions, although thermal insulation and erosion prevention were mainly considered in designing pipeline coatings in the industry [23,24]. Reference [25] quantified the wave forces on pipelines buried in an impermeable bed with coverings of porous media. References [26,27] evaluated the protective performance of a porous polymer coating on subsea pipelines under sudden impacts. The drag reduction function of the porous coatings over cylinders were then quantified by Reference [28]. Two factors were considered to influence the stabilization effect of the porous coatings on pipelines: the production of an entrainment layer through the coating and the triggering of turbulent transition of the detaching shear layers. In engineering practice, applications of porous coatings on submarine pipelines are limited. Concrete wrappers, mainly designed to counteract the buoyancy forces of pipelines, can be considered as one kind of porous wrapper with medium permeability. In addition, porous wrappers made with woven carbon-fiber materials or polyurethane foam may be designed in future for pipeline protection.
The above literature review revealed that few studies were performed to examine the protective effect by the porous media on submarine pipelines, which is the main aim of this study. The porous wrapper and the submarine pipeline modules are simulated in a numerical wave tank (NWT) with the immersed boundary (IB) method. The numerical methods and equations will be provided in Section 2. Verification of the numerical model is provided in Section 3. The parametric simulations are in Section 4, in which the effects of different waves on various pipelines with porous wrappers are analysed. The conclusions are given in Section 5.

2. Numerical Methods


For simulating the interactions between pipelines and waves, the finite volume methods have been widely used. In this study, the commercial finite volume package FLOW-3D® (version 11.1.0; 2014; https://www.flow3d.com (accessed on 10 December 2022); Flow Science, Inc., Santa Fe, NM, USA). Flow-3D aims to solve the transient response of fluids under interactions with structures, internal and external loads and multi-physical processes. It features some advantages in terms of a high level of accuracy in solving the Navier-Stokes equation with the volume of fluid (VOF) method, efficient meshing techniques for complex geometries, and high efficiency level for large-scale problems. Also, Flow-3D provides the flexibility and utility for flowing through porous media. A two-dimensional numerical wave tank was constructed by using the immersed boundary (IB) method and an in-house subroutine termed as IFS_IB. A submarine pipeline and porous medium were two-way coupled at the interface described by the individual volume fractions [29]. The pipeline was wrapped with a layer of a porous medium. A solitary wave was generated at the inlet boundary of the tank to simulate an approaching tsunami. Non-slip wall conditions were assigned at the bottom of the tank and the pipe surface, which was also specified with a roughness coefficient. The top boundary was defined as a free boundary and configured with the atmospheric pressure. A Neumann-type absorbing boundary condition, a stable, local, and absorbing numerical boundary condition for discretized transport equations [30], was imposed on the outlet boundary to attenuate the reflections of the outgoing waves. A transition zone is set within a certain range from the boundary to reduce the horizontal gradient force of the elements near the boundary and suppress the calculation wave caused by this boundary condition. Through the relaxation coefficient, the predicted value on the inner boundary of the transition zone and the initial value on the outer boundary are continuously transitioned to achieve the purpose of reducing the reflection of propagating waves. The CUSTOMIZATION function of the software FLOW-3D was utilised to impose the Neumann-type absorbing boundary condition. The FLOW-3D distribution includes a variety of FORTRAN source subroutines that allow the user to customize FLOW-3D to meet their requirements. The FORTRAN subroutines provided allow the user to customize boundary conditions, include their own material property correlations, specify custom fluid forces (i.e., electromagnetic forces), add physical models to FLOW-3D, and have additional benefits. Several “dummy” variables have been provided in the input file namelists that users may use for custom options. A user definable namelist has also been provided for customization. Makefiles are provided for Linux and Windows distributions and Visual Studio solution files are provided for Windows distributions to allow users to recompile the FLOW-3D code with their customizations.

2.1. Governing Equations

The governing equations involved include the continuity equations and Reynolds-averaged Navier-Stokes equations. The mass and momentum are conserved in a two-dimensional zone [31]:

where U is the velocity vector, X is the Cartesian position vector, g denotes the gravitational acceleration vector, and ρ represents the weighted averaged density. The term μ is the viscosity. σκα identifies the surface tension effects with σ as the surface tension and α as the fluid volume fraction. Each cell in the fluid domain has a water volume fraction (α) ranging between 0 and 1, where 1 represents cells that are fully occupied with water, while 0 represents cells that fully occupied with air. Values between 1 and 0 represent free surface between air and water. The free surface elevation is defined by using the volume of fluid (VOF) function:

where VF is the volume of fluid fraction, FSOR is the source function, FDIF is the diffusion function; AxAy, and Az represent the fractional areas; and uv, and w are the velocity components in the xy, and z directions.

2.2. Porous Media Module

In FLOW-3D, the porous medium’s flow resistance is modelled by the inclusion of a drag term in the momentum equations (Equation (2)). Coarse granular material is used in most coastal engineering applications, in which case the Forchheimer model is suitable. Using this model, a drag term Fdui is added to the righthand-side of Equation (2):

where |U| is the norm of the velocity vector, n the porosity, and a and b are the factors.

2.3. Solitary Wave Boundary

The solitary wave is generated in terms of variations of the surface elevation η and velocities u and v by following McCowan’s theory [32]:

where h is the still water depth; Q is the reference value

where X = x − c0t; 𝑐0=√𝑔𝐻+ℎ; H is the wave height; and t is the elapsed time.

3. Validation

3.1. Propagation over a Porous Breakwater

An experimental test on the propagation process of a solitary wave over a permeable breakwater was performed by Reference [20], which was simulated in this study to validate the adopted two-way coupling model (Figure 1a). The length, width, and depth of the flume tank were 25, 0.5, and 0.6 m, respectively. A permeable breakwater was mounted at the bottom of the flume, which had dimensions of 13 cm and 6.5 cm in the length and height, respectively. The porous breakwater with an average porosity of 0.52 was configured by glass beads with a constant diameter of 1.5 cm. Two wave gauges were fixed before (WG1) and behind (WG2) the breakwater, respectively. The initial still water depth h was assumed to be 10.6 cm. Height of the solitary wave H was considered to be 4.77 cm. In the numerical model, the calculation zone had dimensions of 5 m in length and 0.25 m in height. The second order quadrilateral mesh elements were adopted. The grid around the breakwater was the finest of 0.001 m. The adopted time step size was 0.05 s. The numerical predictions of the water elevations at the locations WG1 and WG2 by the adopted numerical tool FLOW-3D are close to both the experimental measurements and the numerical predictions from another CFD FLUENT version 14.0.1 [33] (Figure 1). Figure 1b,c show the comparison of monitored water levels at the two water level monitoring points in Figure 1a. It can be seen that the experimental results of the two monitoring points are consistent with the numerical simulation results, indicating that the propagating solitary wave energy is basically completely dissipated and then flows out. If the propagating wave energy is not dissipated, the phenomenon of wave reflection will occur. The waves monitored at the two monitoring points will appear superposition of propagating waves and reflected waves. The numerical simulation results do not agree with the physical experiment results. The fluctuations of the water surface elevation after the bypass of the incoming wave are due to its residual reflection at the right absorbing boundary condition, which arrives at WG2 at an earlier time than WG1. Evolution of the wave surfaces was also compared between the experimental and the numerical models (Figure 2), which demonstrates that the numerical tool is sufficiently reliable. The velocity of the wave is reduced by the porous medium as it partially infiltrates into the breakwater, which is shown as in Figure 3 by comparing the horizontal velocity distributions between the experimental and numerical results at times of 1.5 s and 2 s. The numerical predictions of the flow velocities have slight discrepancies with the experimental measurements, which are attributed to the material assumptions made in the numerical model for the glass beads in the experimental setup.

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Figure 1. The diagrammatic sketch of the numerical setup (non–scaled) (a) and the temporal evolution comparison of water surface between experimental and numerical results (b,c).

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Figure 2. Water surface comparison between experimental and numerical results.

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Figure 3. Comparison of horizontal velocity distribution between experimental and numerical results.

3.2. Forces on Pipeline

Another experimental test of a solitary wave impacting a pipeline was performed by Reference [34], which was also reproduced in this study for validation purposes. The calculation zone had dimensions of 40 m in length and 0.6 m in height. The solitary wave had a height of 0.0555 m with the initial water depth of 0.192 m. The pipe had a diameter of 0.048 m, which had a distance of 0.136 m over the bottom boundary of the model. A dense mesh consisting of 413,411 cells was employed with a mesh size of 0.1 mm around the pipe, which proved to be sufficiently fine through convergence studies. History of the horizontal and vertical forces, normalized by ρgL(πD2/4) with L as the unit length of 1 m, is compared between the experimental and numerical results (Figure 4). Both the peak values and the transient variations of the forces predicted by the numerical analysis converge to the measured values in the experimental test. The slight discrepancy between the numerical and experimental results at 2.5 s and 3.1 s, which may be induced by the error of the numerical model simulating the complicated turbulence behaviour, is acceptable in relation to the requirements of this study as our concern is mainly the peak values of forces.

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Figure 4. Force comparison between the experimental and numerical results.

Therefore, the adopted numerical tool is sufficiently reliable to simulate the interactions between solitary waves and the permeable structure through the above validation cases.

4. Results and Discussion

Influence of the solitary waves on the performance of wrapped pipelines was investigated by considering different wave heights (H) and thicknesses (T) and wrapper porosities (n). The still water depth (h) was taken to be 6 m (Figure 5). The diameter of the porous medium was assumed to be 0.05 m. The pipeline diameter D was set at 1 m. In Figure 5 the variable G represents the gap between the permeable wrapper and the seabed. The scouring process had been completed before the simulation; therefore, the seabed boundary was taken as a rigid wall. The tandem pipelines had a distance of S between each other. The whole model had dimensions of 400 m in length and 12 m in height. The finest mesh around the pipeline was configured as 0.0025 m, which was verified to be sufficiently fine through trial calculations with finer meshes.

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Figure 5. Layout for solitary wave impinging on the submarine pipeline encased in porous media.

4.1. Effect of Porous Wrapper

4.1.1. Wrapper Porosity

The pipeline was put on the seabed. The gap (G) between the wrapper and the seabed was considered to be zero. The height (H) of the solitary wave was considered to be 2 m. The porosity (n) was taken to be 0.0, 0.4, 0.6, and 1.0. Note that n = 0.0 indicates the impervious condition, while n = 1.0 corresponds to the non-wrapping condition. The thickness of the permeable wrapper remained at 0.5 m. In calculation, the wave approaches the pipe at around 6.3 s and departs from it at 10.2 s. When the wave approaches, the kinematic performance over the pipe is enhanced (Figure 6). Due to the wave disturbance, a number of small vortices are generated around the pipe (Figure 7). At the departure of the wave, the disturbance to the flow field seems to be more intense than that at its arrival, which further generates vortices around the pipeline. Without a wrapper, the pipe is fully exposed to the disturbance of the incoming wave, which maximises the velocity and vorticity values around the pipe. When the pipeline is wrapped by a porous medium, some water seeps into the wrapper, and the velocity in the wrapper is reduced to a very low value, which implies that the porous medium is capable of absorbing the dynamic energy of the flowing fluid. With an external coverage (n < 1.0), the disturbance is generated mainly at the outer surface of the wrapper. As the wrapper porosity increases, the domain of the low-speed flow underneath the pipeline expands.

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Figure 6. The velocity contours of the flow fields under different porosities; (an = 0.0; (bn = 0.4; (cn = 0.6; (dn = 1.0; left to right: arrival, departure.

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Figure 7. The vorticity contours of the flow fields under different porosities; (an = 0.0; (bn = 0.4; (cn = 0.6; (dn = 1.0; left to right: arrival, departure.

The peak velocity around the pipeline without a wrapper (1.9 m/s) is larger than that with a wrapper (1.6 m/s) (Figure 8). For pipes with wrappers, the peak velocities around them are similar to one another. In contrast, the velocity profiles at x = 23 m are quite different. When the pipeline has no wrapper (i.e., n = 1.0), the change in velocity is fairly moderate. When the pipeline has a wrapper, the porous wrapper causes a secondary fluctuation in the rear water body after the primary fluctuation due to the peak of the wave passing through the pipeline. This generates a series of velocity peaks. The secondary velocity peaks for a porosity coefficient of 0.4 are higher than those for a porosity coefficient of 0.6. Accordingly, the turbulent kinetic energy (TKE) also changes with the porosities, as shown in Figure 9. The TKE is expressed as

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Figure 8. Comparison of horizontal and vertical velocities at front and rear of pipeline under different porosities.

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Figure 9. Comparison of turbulent kinetic energy at front and rear of wrapper under different porosities.

With the propagation of the wave, the TKE increases gradually in front of the pipeline. The TKE value under the pipeline without a wrapper (n = 1.0) (0.0008 kJ) is nearly half of that with a wrapper (0.0015 kJ). In comparison, the TKE values for the wrapped pipelines (n < 1.0) are very close to each other. After the wave leaves the pipeline, the TKE in front of the pipeline decreases for around 50%. Then, the TKE in the rear of the pipeline with a porous wrapper increases intensively because the porous media perturb the flow field. Compared with the pipeline without the wrapper, the interaction between the wrapped pipeline with the flow field is more severe. Furthermore, the solid wrapper can cause a strong disturbance to the flow, but the interference of the solid wrapper (n = 0.0) in the rear flow is still weaker than the wrapper with the porosity of 0.4.
The hydrodynamic forces (F), including the pressure and shear stress, are normalized by ρgL(πD2/4) (Figure 10). With a fully solid (i.e., n = 0.0) wrapper, the pipeline tends to be unaffected by the external flow. Hence, the hydrodynamic forces are zero while the forces on the wrapper reach their maximum. With porous wrappers, water seeps into the wrapper, buffering the impact of the incoming waves on the pipe. As the porosity coefficient increases, the induced forces on the pipeline increase while those on the wrapper decrease. When the porosity coefficient is 0.4, the forces on the external wrapper become higher than that on the internal pipeline. Therefore, the porous wrapper is capable of protecting the pipeline. The smaller the porosity coefficient the better protection the wrapper provides to the pipeline. The pressure gradient and shear stress forces are also shown in Figure 11.

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Figure 10. Comparisons of the maximum hydrodynamic forces on the pipeline and wrapper.

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Figure 11. Decomposed pressure gradient force (a) and shear stress (b) force on the pipeline.

4.1.2. Thickness of Wrapper

Seven wrapper thicknesses are considered: T = 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, and 0.5 m. The porosity coefficient is taken to be 0.6. At the moment that the wave goes through the pipe, the transient evolution of the vorticity contours around the pipeline with a wrapper thickness of 0.25 m is depicted in Figure 12. A couple of vortices emerge on the upper and lower vertices of the pipeline as the wave approaches the pipeline. As the wave propagates, many vortices flow along the wrapper and then shed off. Compared with the top vortices, the bottom vortices are shed off faster for two reasons. Firstly, as the friction at the seabed is small, the bottom flow velocity is higher than that on the top. Secondly, when the wave peak departs from the pipeline, a strong disturbance by the water body occurs behind the pipeline, followed by the irregular swing and fall off of the vortices. After the wave travels far away, the water flow near the pipeline becomes weak, and the vortices are scattered around the pipeline.

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Figure 12. Temporal evolutions of vorticity contours around pipeline with wrapper thickness of 0.25 m (a) 6.0 s (b) 6.6 s (c) 7.2 s (d) 7.8 s (e) 8.1 s (f) 8.7 s (g) 9.0 s (h) 10.2 s (i) 12.6 s.

Figure 13 shows a comparison of flow field stream traces and the velocity contours. When the fluid penetrates the wrapper, the streamline starts to diverge, which indicates that the free flow is hindered. Therefore, the flow becomes slower and the flow direction becomes non-uniform. For the fluid flows out of the wrapper, the stream traces are quite complex and chaotic. The reason is that the seeping fluid mixes with the bypass flows and causes strong interference in the water body behind the pipeline. The streamlines passing through the wrapper indicates frequent water exchange at the wrapper surface. Along with the small-attached vortices on the wrapper surface, more fluid passes over the wrapper and causes a large vortex behind the wrapper.

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Figure 13. Comparisons of flow field streamtraces and velocity contours under different wrapper thicknesses; (a) T = 0.2 m; (b) T = 0.3 m; (c) T = 0.4 m; (d) T = 0.5 m.

The highest free surface elevations and velocities at the front and at the rear of the pipeline with different wrapper thicknesses are depicted in Figure 14. As the wrapper thickness increases, the highest elevation at the front of the pipeline seems to be quite stable, although the peak velocity increases by around 6%. At the moment that the wave bypasses the pipeline, the maximum elevation reduces with an increase in the wrapper thickness. This is because the pipeline blocks the wave propagation. However, due to the strong mixing effect of the seepage and bypass water, the maximum velocity rises to be higher than that in front of the pipe. The maximum forces on the wrapper and the pipeline for different wrapper thicknesses are shown in Figure 15. With an increase in the wrapper thickness from 0.2 to 0.5 m, the normalized forces on the wrapper are doubled as a larger interaction area is involved. In contrast, the vertical forces on the pipeline decrease by 12.5%. Therefore, the larger the thickness of the wrapper the safer the pipeline.

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Figure 14. Comparisons of the maximum elevations and velocities in front and rear of the pipelines with different wrapper thicknesses; (a) free surface elevation (note: original water depth is 6 m); (b) velocity.

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Figure 15. Hydrodynamic forces on the pipeline and wrapper.

4.2. Effect of Pipeline Structure

The in-situ pipelines may be under various suspended conditions since the seabed topography is often uneven. Some pipelines are also laid in tandem for the sake of the transportation efficiency. In order to examine the effects of porous wrappers on pipelines under different conditions, a study was carried out considering two scenarios, namely, suspended pipelines and pipelines in tandem. In the numerical models, the porosity coefficient (n) remained at 0.6, the thickness (T) of the wrapper was kept at 0.5 m, and the wave height (H) was assumed to be 2.0 m.

4.2.1. Suspended Pipelines

Six gaps (G) between the wrapper and the seabed (0.0, 0.2, 0.4, 0.6, 0.8, and 1.0 m) were considered [35,36,37]. The representative flow field at three points in time (6.3, 7.2, and 10.2 s) are shown in Figure 16. At the arrival of the wave at the pipeline (at 6.3 s), the flow is accelerated and the velocities over and beneath the pipe reach the maximum values due to the bypass effect of the fluid. At the moment that the wave peak is above the pipe (at 7.2 s), all the velocities around the pipe reach their highest values. After the wave passes over the pipe (at 10.2 s), the velocity decreases and several vortices are formed behind the pipeline. With a tiny wrapper-seabed gap, the velocity within the gap is very high while the flux is relatively small. An increase in the gap will result in an increase in the flux and a decrease in the velocity. A symmetric velocity distribution similar to a fisheye is observed behind the pipeline, which becomes more obvious when the gap increases (Figure 16c).

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Figure 16. The velocity contours of the flow fields under different gaps; (a) G = 0.2 m; (b) G = 0.6 m; (c) G = 1.0 m. Left to right: 6.3 s, 7.2 s, and 10.2 s. Left to right: arrival, stay, departure.

With the bypass of the wave, the vortices generated around the pipeline become larger. The vorticity contours and the streamlines of the flow field are shown in Figure 17. As the solitary wave approaches, a pair of whirlpools shed off from the wrapper with a gap of 0.2 m. With an increase in the gap, the two whirlpools gradually disappear and are replaced with two smaller vortices. Due to the internal pores within the wrapper, the streamlines in the wrapper are dispersed, and it is hard for a vortex to be generated. With an increase in the gap, two anti-symmetric vortices shed off from the wrapper. Besides, some tiny vortices remain adhered to the wrapper due to the interaction by the seepage and the external flow. When the gap is very small, a few small vortices are generated between the wrapper and the seabed. In contrast to the interface of vortex from the flow around a solid cylinder, the vortex interface at the wrapper is not fully smooth. Because of the strong interactions of fluid over the wrapper surface, several small vortices mingle with the large shedding vortices. The flow direction also varies greatly according to the streamline mobilisation.

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Figure 17. The vorticity contours of the flow fields under different gaps; (a) G = 0.2 m; (b) G = 0.6 m; (c) G = 1.0 m. Left to right: 6.3 s, 7.2 s and 10.2 s.

The gap is normalized by the pipeline diameter as β = G/D. With a small gap (β < 0.2), the horizontal forces on both the wrapper and the pipeline are slightly smaller than those on the wrapper and pipeline without a gap (Figure 18). With a further rise of the gap width, the horizontal forces are accordingly enlarged due to higher velocity around the pipeline as shown in Figure 16.

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Figure 18. Comparisons of the maximum horizontal and vertical hydrodynamic forces on the pipeline and wrapper under different gaps.

In contrast, an increase in the gap width may inversely cause the reduction of vertical forces on both the wrapper and the pipeline. The vertical forces can be considered to consist of two parts. One is caused by the weight of the water body at the bypass of the wave from the pipeline, while the other can be caused by the velocity difference between the flow above and below the pipeline after the flow passes over. In summary, as the gap increases, the flow velocity within the gap initially increases when β < 0.2 and then decreases when β > 0.2. In contrast, the vertical forces caused by the wave’s weight always decrease with an increase in the gap.

4.2.2. Pipelines in Tandem

The hydrodynamic forces on pipelines in tandem are investigated considering five different distances (S) between the two pipeline centres (2.5, 3.0, 3.5, 4.0, and 4.5 m). The velocity and vorticity fields at 6.3, 7.2, and 10.2 s around the tandem pipelines with distances of 2.5, 3.5, and 4.5 m are depicted (Figure 19 and Figure 20). As the wave approaches the pipeline, the velocity within the pipeline gap is very small due to the blockage effect of the pipeline in front. As the distance increases, the velocity field within gap space is enhanced as more water flow is allowed. The velocity above the pipeline has its maximum value, and part of the high-speed fluid flows into the gap through the space underneath the pipeline. With a small distance, the vortices shedding off from the front pipeline impinge directly on the rear pipeline without any stretching. When the distance is increased, noticeable vortex shedding emerges in the middle space (Figure 20c). Similar vortex shedding behind the rear pipeline is observed for different distances. After the wave bypasses the pipeline, the increase in the distance between the pipelines will cause an increase in the velocity magnitudes in the space among the pipelines. As the distance increases, the flow becomes more chaotic due to the seepage from the wrapper and the limited flow space. In summary, influence of the distance between the pipelines over the whole kinematic field is not significant, although the local flow field around the pipelines is severely affected. When the wave bypasses the tandem pipelines, the largest forces on structures (i.e., the pipelines and wrappers) are shown in Figure 21, in which the distance ratio (θ) is calculated as θ = S/D.

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Figure 19. The velocity contours of the flow fields under different spacings; (a) S = 2.5 m; (b) S = 3.5 m; (c) S = 4.5 m. Left to right: 6.3 s, 7.2 s and 10.2 s.

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Figure 20. The vorticity contours of the flow fields under different porosities; (a) S = 2.5 m; (b) S = 3.5 m; (c) S = 4.5 m. Left to right: 6.3 s, 7.2 s and 10.2 s.

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Figure 21. The maximum forces on the pipeline and wrapper under different distances.

As for the pipeline in front, as the distance ratio increases, the horizontal loads on the wrapper and pipeline increase slightly, while the vertical forces are almost doubled. As for the rear pipeline, as the distance reduces, the velocity in the gap becomes smaller and the forces on the pipelines and wrappers are also reduced, which is mainly attributed to the shield effect from the front pipeline. With an increase in the distance, the forces increase due to the increase in the turbulence energy in the gap.
Different ratios of the forces on the front and rear pipelines are depicted in Figure 22. The difference ratio is defined as ΔFn = (ff,max−fr,max)/ff,max, where ff,max and fr,max are the maximum forces on the pipeline or wrapper. It is found that the horizontal loads on the rear pipe and wrapper tend to be always higher than their counterparts on the front pipe. This means that a turbulent flow in the horizontal direction on rear pipe is more intense than that on the front pipe. For different distances, deviations for the forces on the pipelines and wrappers are also different. The deviation is found to be maximized at a distance of 1 m and this indicates that the pipeline is not well protected and needs to be avoided in engineering practice.

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Figure 22. The deviation of the forces on the front and rear pipelines and wrappers under different distances.

4.3. Effect of Wave Height

Six groups of wave heights (H), i.e., 1.6, 1.8, 2.0, 2.2, 2.4, and 2.6 m, are selected to consider different marine environment. After bypassing the pipeline, the height of the wave decreases because of the blockage effect of the pipeline and the dissipation of the flow energy (Figure 23a). The deviation ratio of the wave heights before and after the wave passes over the pipeline is shown in Figure 23b and is defined as δ = (Hf,max − Hr,max)/Hf,max. The wave height attenuation becomes more significant as the wave height increases. This means that waves with larger heights are more easily affected by the pipelines.

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Figure 23. Waves with different wave heights; (a) temporal evolutions; (b) attenuation deviation.

At the bypass of the wave through the pipe, the loads are increased until they reach the maximum values at the moment that the wave peak appears above pipeline (Figure 24). The forces gradually decrease as the wave propagates. Because of some reflux after the wave bypasses the pipeline, the flow is in the opposite direction to that of the wave propagation, resulting in a negative force. The vibration of the water body by the wave propagation induces oscillations of the forces on the pipeline and wrapper. When the wave height is larger, the force oscillation becomes fiercer and the maximum loads on the pipeline and the wrapper increase (Figure 25). The vertical forces on the pipeline are the largest compared with other forces under the same conditions. Besides, as the wave height increases, the increased amplitude of vertical forces on the pipeline is the most significant change since the weight of the water above the pipeline increases. Therefore, given that the wave height is very high, the protective function of wrapper on the pipeline tends to be weakened compared with that of the wrapper for a low wave height.

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Figure 24. The temporal evolutions of forces on the pipeline and wrapper; (a) Horizontal maximum force on pipeline; (b) Vertical maximum force on pipeline; (c) Horizontal maximum force on wrapper; (d) Vertical maximum force on wrapper.

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Figure 25. Variation of hydrodynamic forces on the pipeline and wrapper under different distances.

5. Conclusions

The effect of porous media on the dynamic performance of submarine pipelines under solitary waves was investigated. The porosity of the wrapper, the seabed topography, the structure of the pipeline, and the marine environment were considered. The study had a limitation of the model sizes due to the limited computational resource and the simplification of the solitary wave due to its mathematical complication, which will be tackled in future works. The following main conclusions have been made.

(1) When a pipe is wrapped by a porous medium, the velocity in the wrapper is relatively small because the porous medium can consume the water energy and weaken the flow. With an increase in the porosity, the range of the low-speed flow at the bottom of the pipeline expands. This indicates that the porous wrapper can slow down the flow and affect a wider region of the surrounding water. After the bypass of the wave through the pipe, the number and volume of the vortices behind the porous wrapper are larger than those for a pipeline with a solid wrapper or without a wrapper. As the porosity coefficient increases, the impact forces on the pipe increase, while those on the wrapper decrease. This implies that the porous wrapper is capable of protecting the pipeline.

With an increase in the wrapper’s thickness, the hydrodynamic forces on the wrapper tend to increase. In particular, the horizontal forces on the pipeline decrease with an increase in the thickness due to the protection of the wrapper, while the vertical forces are increased because of variations in the fluid’s stagnation point.

(2) For a wave bypassing a pipe with different heights, a symmetric speed change similar to a fisheye appears behind the pipeline, along with two antisymmetric vortices shedding off from the wrapper.

As the internal seepage interacts with the external fluid flow, several small vortices are still attached to the wrapper. The hydrodynamic vertical forces on both the wrapper and the pipeline decrease with the pipeline distance. With an increase in the suspension of the pipe, the velocity and TKE within the gap space increase and both the vortex intensity and the number of vortices increase. Therefore, the flow pattern appears to be chaotic. As for the front pipeline, an increase in the gap leads to a slight increase in the horizontal forces on both the wrapper and the pipeline, but a significant increase in the vertical forces. As for the rear pipeline, because of the shield function of the front pipeline, the velocity within the gap space and the forces on the pipes decrease with a decrease in the gap size.

(3)When the waves with different heights pass over the pipeline, the height of the wave is reduced because of the blockage function from the pipeline and the dissipation characteristic of the flow energy. When the wave height is increased, the velocity around the pipeline increases, inducing an increase in the TKE. As the wave height increases, all the maximum forces on the pipeline and wrapper also increase. Note that an increase in the vertical forces on the pipeline is the most significant change because the weight of the water above the pipeline increases, which implies that the protection function of the wrapper is enhanced by the reduction in the wave height.

From the above investigation, the mechanism of load transfer from the pipeline to the external wrapper has been presented. This encourages industrial experts and academic scholars to arrange more investigations of the functions and cost-efficiency of porous wrappers, which could form a new branch of the pipeline design practice.

Author Contributions

Contributor Roles Taxonomy: E.Z.: Conceptualization, Methodology, Validation, Investigation and Writing—Original Draft; Y.D.: Data Curation, Formal analysis; Y.D.: Visualization, Project administration; Y.D., L.C., Y.W. and Y.L.: Writing—Review & Editing. All authors have read and agreed to the published version of the manuscript.

Funding

The paper was supported by the National Natural Science Foundations of China (Grants No. 52001286 and No. 42272328), GuangDong Basic and Applied Basic Research Foundation (Grant No. 2022A1515240002) and Comprehensive Survey of Natural Resources in Huizhou-Shanwei Coastal Zone (Grant No. DD20230415).

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflict of interest.

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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

Coupled CFD-DEM simulation of interfacial fluid–particle interaction during binder jet 3D printing

Coupled CFD-DEM simulation of interfacial fluid–particle interaction during binder jet 3D printing

바인더 제트 3D 프린팅 중 계면 유체-입자 상호 작용에 대한 CFD-DEM 결합 시뮬레이션

Joshua J. Wagner, C. Fred Higgs III

https://doi.org/10.1016/j.cma.2024.116747

Abstract

The coupled dynamics of interfacial fluid phases and unconstrained solid particles during the binder jet 3D printing process govern the final quality and performance of the resulting components. The present work proposes a computational fluid dynamics (CFD) and discrete element method (DEM) framework capable of simulating the complex interfacial fluid–particle interaction that occurs when binder microdroplets are deposited into a powder bed. The CFD solver uses a volume-of-fluid (VOF) method for capturing liquid–gas multifluid flows and relies on block-structured adaptive mesh refinement (AMR) to localize grid refinement around evolving fluid–fluid interfaces. The DEM module resolves six degrees of freedom particle motion and accounts for particle contact, cohesion, and rolling resistance. Fully-resolved CFD-DEM coupling is achieved through a fictitious domain immersed boundary (IB) approach. An improved method for enforcing three-phase contact lines with a VOF-IB extension technique is introduced. We present several simulations of binder jet primitive formation using realistic process parameters and material properties. The DEM particle systems are experimentally calibrated to reproduce the cohesion behavior of physical nickel alloy powder feedstocks. We demonstrate the proposed model’s ability to resolve the interdependent fluid and particle dynamics underlying the process by directly comparing simulated primitive granules with one-to-one experimental counterparts obtained from an in-house validation apparatus. This computational framework provides unprecedented insight into the fundamental mechanisms of binder jet 3D printing and presents a versatile new approach for process parameter optimization and defect mitigation that avoids the inherent challenges of experiments.

바인더 젯 3D 프린팅 공정 중 계면 유체 상과 구속되지 않은 고체 입자의 결합 역학이 결과 구성 요소의 최종 품질과 성능을 좌우합니다. 본 연구는 바인더 미세액적이 분말층에 증착될 때 발생하는 복잡한 계면 유체-입자 상호작용을 시뮬레이션할 수 있는 전산유체역학(CFD) 및 이산요소법(DEM) 프레임워크를 제안합니다.

CFD 솔버는 액체-가스 다중유체 흐름을 포착하기 위해 VOF(유체량) 방법을 사용하고 블록 구조 적응형 메쉬 세분화(AMR)를 사용하여 진화하는 유체-유체 인터페이스 주위의 그리드 세분화를 국지화합니다. DEM 모듈은 6개의 자유도 입자 운동을 해결하고 입자 접촉, 응집력 및 구름 저항을 설명합니다.

완전 분해된 CFD-DEM 결합은 가상 도메인 침지 경계(IB) 접근 방식을 통해 달성됩니다. VOF-IB 확장 기술을 사용하여 3상 접촉 라인을 강화하는 향상된 방법이 도입되었습니다. 현실적인 공정 매개변수와 재료 특성을 사용하여 바인더 제트 기본 형성에 대한 여러 시뮬레이션을 제시합니다.

DEM 입자 시스템은 물리적 니켈 합금 분말 공급원료의 응집 거동을 재현하기 위해 실험적으로 보정되었습니다. 우리는 시뮬레이션된 기본 과립과 내부 검증 장치에서 얻은 일대일 실험 대응물을 직접 비교하여 프로세스의 기본이 되는 상호 의존적인 유체 및 입자 역학을 해결하는 제안된 모델의 능력을 보여줍니다.

이 계산 프레임워크는 바인더 제트 3D 프린팅의 기본 메커니즘에 대한 전례 없는 통찰력을 제공하고 실험에 내재된 문제를 피하는 공정 매개변수 최적화 및 결함 완화를 위한 다용도의 새로운 접근 방식을 제시합니다.

Introduction

Binder jet 3D printing (BJ3DP) is a powder bed additive manufacturing (AM) technology capable of fabricating geometrically complex components from advanced engineering materials, such as metallic superalloys and ultra-high temperature ceramics [1], [2]. As illustrated in Fig. 1(a), the process is comprised of many repetitive print cycles, each contributing a new cross-sectional layer on top of a preceding one to form a 3D CAD-specified geometry. The feedstock material is first delivered from a hopper to a build plate and then spread into a thin layer by a counter-rotating roller. After powder spreading, a print head containing many individual inkjet nozzles traverses over the powder bed while precisely jetting binder microdroplets onto select regions of the spread layer. Following binder deposition, the build plate lowers by a specified layer thickness, leaving a thin void space at the top of the job box that the subsequent powder layer will occupy. This cycle repeats until the full geometries are formed layer by layer. Powder bed fusion (PBF) methods follow a similar procedure, except they instead use a laser or electron beam to selectively melt and fuse the powder material. Compared to PBF, binder jetting offers several distinct advantages, including faster build rates, enhanced scalability for large production volumes, reduced machine and operational costs, and a wider selection of suitable feedstock materials [2]. However, binder jetted parts generally possess inferior mechanical properties and reduced dimensional accuracy [3]. As a result, widescale adoption of BJ3DP to fabricate high-performance, mission-critical components, such as those common to the aerospace and defense sectors, is contingent on novel process improvements and innovations [4].

A major obstacle hindering the advancement of BJ3DP is our limited understanding of how various printing parameters and material properties collectively influence the underlying physical mechanisms of the process and their effect on the resulting components. To date, the vast majority of research efforts to uncover these relationships have relied mainly on experimental approaches [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], which are often expensive and time-consuming and have inherent physical restrictions on what can be measured and observed. For these reasons, there is a rapidly growing interest in using computational models to circumvent the challenges of experimental investigations and facilitate a deeper understanding of the process’s fundamental phenomena. While significant progress has been made in developing and deploying numerical frameworks aimed at powder spreading [20], [21], [22], [23], [24], [25], [26], [27] and sintering [28], [29], [30], [31], [32], simulating the interfacial fluid–particle interaction (IFPI) in the binder deposition stage is still in its infancy. In their exhaustive review, Mostafaei et al. [2] point out the lack of computational models capable of resolving the coupled fluid and particle dynamics associated with binder jetting and suggest that the development of such tools is critical to further improving the process and enhancing the quality of its end-use components.

We define IFPI as a multiphase flow regime characterized by immiscible fluid phases separated by dynamic interfaces that intersect the surfaces of moving solid particles. As illustrated in Fig. 1(b), an elaborate IFPI occurs when a binder droplet impacts the powder bed in BJ3DP. The momentum transferred from the impacting droplet may cause powder compaction, cratering, and particle ejection. These ballistic disturbances can have deleterious effects on surface texture and lead to the formation of large void spaces inside the part [5], [13]. After impact, the droplet spreads laterally on the bed surface and vertically into the pore network, driven initially by inertial impact forces and then solely by capillary action [33]. Attractive capillary forces exerted on mutually wetted particles tend to draw them inward towards each other, forming a packed cluster of bound particles referred to as a primitive [34]. A single-drop primitive is the most fundamental building element of a BJ3DP part, and the interaction leading to its formation has important implications on the final part characteristics, such as its mechanical properties, resolution, and dimensional accuracy. Generally, binder droplets are deposited successively as the print head traverses over the powder bed. The traversal speed and jetting frequency are set such that consecutive droplets coalesce in the bed, creating a multi-drop primitive line instead of a single-drop primitive granule. The binder must be jetted with sufficient velocity to penetrate the powder bed deep enough to provide adequate interlayer binding; however, a higher impact velocity leads to more pronounced ballistic effects.

A computational framework equipped to simulate the interdependent fluid and particle dynamics in BJ3DP would allow for unprecedented observational and measurement capability at temporal and spatial resolutions not currently achievable by state-of-the-art imaging technology, namely synchrotron X-ray imaging [13], [14], [18], [19]. Unfortunately, BJ3DP presents significant numerical challenges that have slowed the development of suitable modeling frameworks; the most significant of which are as follows:

  • 1.Incorporating dynamic fluid–fluid interfaces with complex topological features remains a nontrivial task for standard mesh-based CFD codes. There are two broad categories encompassing the methods used to handle interfacial flows: interface tracking and interface capturing [35]. Interface capturing techniques, such as the popular volume-of-fluid (VOF) [36] and level-set methods [37], [38], are better suited for problems with interfaces that become heavily distorted or when coalescence and fragmentation occur frequently; however, they are less accurate in resolving surface tension and boundary layer effects compared to interface tracking methods like front-tracking [39], arbitrary Lagrangian–Eulerian [40], and space–time finite element formulations [41]. Since interfacial forces become increasingly dominant at decreasing length scales, inaccurate surface tension calculations can significantly deteriorate the fidelity of IFPI simulations involving <100 μm droplets and particles.
  • 2.Dynamic powder systems are often modeled using the discrete element method (DEM) introduced by Cundall and Strack [42]. For IFPI problems, a CFD-DEM coupling scheme is required to exchange information between the fluid and particle solvers. Fully-resolved CFD-DEM coupling suggests that the flow field around individual particle surfaces is resolved on the CFD mesh [43], [44]. In contrast, unresolved coupling volume averages the effect of the dispersed solid phase on the continuous fluid phases [45], [46], [47], [48]. Comparatively, the former is computationally expensive but provides detailed information about the IFPI in question and is more appropriate when contact line dynamics are significant. However, since the pore structure of a powder bed is convoluted and evolves with time, resolving such solid–fluid interfaces on a computational mesh presents similar challenges as fluid–fluid interfaces discussed in the previous point. Although various algorithms have been developed to deform unstructured meshes to accommodate moving solid surfaces (see Bazilevs et al. [49] for an overview of such methods), they can be prohibitively expensive when frequent topology changes require mesh regeneration rather than just modification through nodal displacement. The pore network in a powder bed undergoes many topology changes as particles come in and out of contact with each other, constantly closing and opening new flow channels. Non-body-conforming structured grid approaches that rely on immersed boundary (IB) methods to embed the particles in the flow field can be better suited for such cases [50]. Nevertheless, accurately representing these complex pore geometries on Cartesian grids requires extremely high mesh resolutions, which can impose significant computational costs.
  • 3.Capillary effects depend on the contact angle at solid–liquid–gas intersections. Since mesh nodes do not coincide with a particle surface when using an IB method on structured grids, imposing contact angle boundary conditions at three-phase contact lines is not straightforward.

While these issues also pertain to PBF process modeling, resolving particle motion is generally less crucial for analyzing melt pool dynamics compared to primitive formation in BJ3DP. Therefore, at present, the vast majority of computational process models of PBF assume static powder beds and avoid many of the complications described above, see, e.g., [51], [52], [53], [54], [55], [56], [57], [58], [59]. Li et al. [60] presented the first 2D fully-resolved CFD-DEM simulations of the interaction between the melt pool, powder particles, surrounding gas, and metal vapor in PBF. Following this work, Yu and Zhao [61], [62] published similar melt pool IFPI simulations in 3D; however, contact line dynamics and capillary forces were not considered. Compared to PBF, relatively little work has been published regarding the computational modeling of binder deposition in BJ3DP. Employing the open-source VOF code Gerris [63], Tan [33] first simulated droplet impact on a powder bed with appropriate binder jet parameters, namely droplet size and impact velocity. However, similar to most PBF melt pool simulations described in the current literature, the powder bed was fixed in place and not allowed to respond to the interacting fluid phases. Furthermore, a simple face-centered cubic packing of non-contacting, monosized particles was considered, which does not provide a realistic pore structure for AM powder beds. Building upon this approach, we presented a framework to simulate droplet impact on static powder beds with more practical particle size distributions and packing arrangements [64]. In a study similar to [33], [64], Deng et al. [65] used the VOF capability in Ansys Fluent to examine the lateral and vertical spreading of a binder droplet impacting a fixed bimodal powder bed with body-centered packing. Li et al. [66] also adopted Fluent to conduct 2D simulations of a 100 μm diameter droplet impacting substrates with spherical roughness patterns meant to represent the surface of a simplified powder bed with monosized particles. The commercial VOF-based software FLOW-3D offers an AM module centered on process modeling of various AM technologies, including BJ3DP. However, like the above studies, particle motion is still not considered in this codebase. Ur Rehman et al. [67] employed FLOW-3D to examine microdroplet impact on a fixed stainless steel powder bed. Using OpenFOAM, Erhard et al. [68] presented simulations of different droplet impact spacings and patterns on static sand particles.

Recently, Fuchs et al. [69] introduced an impressive multipurpose smoothed particle hydrodynamics (SPH) framework capable of resolving IFPI in various AM methods, including both PBF and BJ3DP. In contrast to a combined CFD-DEM approach, this model relies entirely on SPH meshfree discretization of both the fluid and solid governing equations. The authors performed several prototype simulations demonstrating an 80 μm diameter droplet impacting an unconstrained powder bed at different speeds. While the powder bed responds to the hydrodynamic forces imparted by the impacting droplet, the particle motion is inconsistent with experimental time-resolved observations of the process [13]. Specifically, the ballistic effects, such as particle ejection and bed deformation, were drastically subdued, even in simulations using a droplet velocity ∼ 5× that of typical jetting conditions. This behavior could be caused by excessive damping in the inter-particle contact force computations within their SPH framework. Moreover, the wetted particles did not appear to be significantly influenced by the strong capillary forces exerted by the binder as no primitive agglomeration occurred. The authors mention that the objective of these simulations was to demonstrate their codebase’s broad capabilities and that some unrealistic process parameters were used to improve computational efficiency and stability, which could explain the deviations from experimental observations.

In the present paper, we develop a novel 3D CFD-DEM numerical framework for simulating fully-resolved IFPI during binder jetting with realistic material properties and process parameters. The CFD module is based on the VOF method for capturing binder–air interfaces. Surface tension effects are realized through the continuum surface force (CSF) method with height function calculations of interface curvature. Central to our fluid solver is a proprietary block-structured AMR library with hierarchical octree grid nesting to focus enhanced grid resolution near fluid–fluid interfaces. The GPU-accelerated DEM module considers six degrees of freedom particle motion and includes models based on Hertz-Mindlin contact, van der Waals cohesion, and viscoelastic rolling resistance. The CFD and DEM modules are coupled to achieve fully-resolved IFPI using an IB approach in which Lagrangian solid particles are mapped to the underlying Eulerian fluid mesh through a solid volume fraction field. An improved VOF-IB extension algorithm is introduced to enforce the contact angle at three-phase intersections. This provides robust capillary flow behavior and accurate computations of the fluid-induced forces and torques acting on individual wetted particles in densely packed powder beds.

We deploy our integrated codebase for direct numerical simulations of single-drop primitive formation with powder beds whose particle size distributions are generated from corresponding laboratory samples. These simulations use jetting parameters similar to those employed in current BJ3DP machines, fluid properties that match commonly used aqueous polymeric binders, and powder properties specific to nickel alloy feedstocks. The cohesion behavior of the DEM powder is calibrated based on the angle of repose of the laboratory powder systems. The resulting primitive granules are compared with those obtained from one-to-one experiments conducted using a dedicated in-house test apparatus. Finally, we demonstrate how the proposed framework can simulate more complex and realistic printing operations involving multi-drop primitive lines.

Section snippets

Mathematical description of interfacial fluid–particle interaction

This section briefly describes the governing equations of fluid and particle dynamics underlying the CFD and DEM solvers. Our unified framework follows an Eulerian–Lagrangian approach, wherein the Navier–Stokes equations of incompressible flow are discretized on an Eulerian grid to describe the motion of the binder liquid and surrounding gas, and the Newton–Euler equations account for the positions and orientations of the Lagrangian powder particles. The mathematical foundation for

CFD solver for incompressible flow with multifluid interfaces

This section details the numerical methodology used in our CFD module to solve the Navier–Stokes equations of incompressible flow. First, we introduce the VOF method for capturing the interfaces between the binder and air phases. This approach allows us to solve the fluid dynamics equations considering only a single continuum field with spatial and temporal variations in fluid properties. Next, we describe the time integration procedure using a fractional-step projection algorithm for

DEM solver for solid particle dynamics

This section covers the numerical procedure for tracking the motion of individual powder particles with DEM. The Newton–Euler equations (Eqs. (10), (11)) are ordinary differential equations (ODEs) for which many established numerical integrators are available. In general, the most challenging aspects of DEM involve processing particle collisions in a computationally efficient manner and dealing with small time step constraints that result from stiff materials, such as metallic AM powders. The

Unified CFD-DEM solver

The preceding sections have introduced the CFD and DEM solution algorithms separately. Here, we discuss the integrated CFD-DEM solution algorithm and related details.

Binder jet process modeling and validation experiments

In this section, we deploy our CFD-DEM framework to simulate the IFPI occurring during the binder droplet deposition stage of the BJ3DP process. The first simulations attempt to reproduce experimental single-drop primitive granules extracted from four nickel alloy powder samples with varying particle size distributions. The experiments are conducted with a dedicated in-house test apparatus that allows for the precision deposition of individual binder microdroplets into a powder bed sample. The

Conclusions

This paper introduces a coupled CFD-DEM framework capable of fully-resolved simulation of the interfacial fluid–particle interaction occurring in the binder jet 3D printing process. The interfacial flow of binder and surrounding air is captured with the VOF method and surface tension effects are incorporated using the CSF technique augmented by height function curvature calculations. Block-structured AMR is employed to provide localized grid refinement around the evolving liquid–gas interface.

CRediT authorship contribution statement

Joshua J. Wagner: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Visualization, Writing – original draft, Writing – review & editing. C. Fred Higgs III: Conceptualization, Funding acquisition, Investigation, Methodology, Project administration, Resources, Supervision, Writing – original draft, 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.

Acknowledgments

This work was supported by a NASA Space Technology Research Fellowship, United States of America, Grant No. 80NSSC19K1171. Partial support was also provided through an AIAA Foundation Orville, USA and Wilbur Wright Graduate Award, USA . The authors would like to gratefully acknowledge Dr. Craig Smith of NASA Glenn Research Center for the valuable input he provided on this project.

References (155)

Fig. 3. (a–c) Snapshots of the CtFD simulation of laser-beam irradiation: (a) Top, (b) longitudinal vertical cross-sectional, and (c) transversal vertical cross-sectional views. (d) z-position of the solid/liquid interface during melting and solidification.

Solute segregation in a rapidly solidified Hastelloy-X Ni-based superalloy during laser powder bed fusion investigated by phase-field simulations and computational thermal-fluid dynamics

Masayuki Okugawa ab, Kenji Saito a, Haruki Yoshima a, Katsuhiko Sawaizumi a, Sukeharu Nomoto c, Makoto Watanabe c, Takayoshi Nakano ab, Yuichiro Koizumi abShow moreAdd to MendeleyShareCite

https://doi.org/10.1016/j.addma.2024.104079

Get rights and content Under a Creative Commons license open access

Abstract

Solute segregation significantly affects material properties and is a critical issue in the laser powder-bed fusion (LPBF) additive manufacturing (AM) of Ni-based superalloys. To the best of our knowledge, this is the first study to demonstrate a computational thermal-fluid dynamics (CtFD) simulation coupled multi-phase-field (MPF) simulation with a multicomponent-composition model of Ni-based superalloy to predict solute segregation under solidification conditions in LPBF. The MPF simulation of the Hastelloy-X superalloy reproduced the experimentally observed submicron-sized cell structure. Significant solute segregations were formed within interdendritic regions during solidification at high cooling rates of up to 10K s-1, a characteristic feature of LPBF. Solute segregation caused a decrease in the solidus temperature (TS), with a reduction of up to 30.4 K, which increases the risk of liquation cracks during LPBF. In addition, the segregation triggers the formation of carbide phases, which increases the susceptibility to ductility dip cracking. Conversely, we found that the decrease in TS is suppressed at the melt-pool boundary regions, where re-remelting occurs during the stacking of the layer above. Controlling the re-remelting behavior is deemed to be crucial for designing crack-free alloys. Thus, we demonstrated that solute segregation at the various interfacial regions of Ni-based multicomponent alloys can be predicted by the conventional MPF simulation. The design of crack-free Ni-based superalloys can be expedited by MPF simulations of a broad range of element combinations and their concentrations in multicomponent Ni-based superalloys.

Graphical abstract

Keywords

Laser powder-bed fusion, Hastelloy-X Nickel-based superalloy, solute element segregation, computational thermal-fluid dynamics simulation, phase-field method

1. Introduction

Additive manufacturing (AM) technologies have attracted considerable attention as they allow us to easily build three-dimensional (3D) parts with complex geometries. Among the wide range of available AM techniques, laser powder-bed fusion (LPBF) has emerged as a preferred technique for metal AM [1][2][3][4][5]. In LPBF, metal products are built layer-by-layer by scanning laser, which fuse metal powder particles into bulk solids.

Significant attempts have been made to integrate LPBF techniques within the aerospace industry, with a particular focus on weldable Ni-based superalloys, such as IN718 [6][7][8], IN625 [9][10], and Hastelloy-X (HX) [11][12][13][14]. Non-weldable alloys, such as IN738LC [15][16] and CMSX-4 [1][17] are also suitable for their sufficient creep resistance under higher temperature conditions. However, non-weldable alloys are difficult to build using LPBF because of their susceptibility to cracking during the process. In general, a macro solute-segregation during solidification is suppressed by the rapid cooling conditions (up to 108 K s-1) unique to the LPBF process [18]. However, the solute segregation still occurs in the interdendritic regions that are smaller than the micrometer scale [5][19][20][21]; these regions are suggested to be related to the hot cracks in LPBF-fabricated parts. Therefore, an understanding of solute segregation is essential for the fabrication of reliable LPBF-fabricated parts while avoiding cracks.

The multiphase-field (MPF) method has gained popularity for modeling the microstructure evolution and solute segregation under rapid cooling conditions [5][20][21][22][23][24][25][26][27][28]. Moreover, quantifiable predictions have been achieved by combining the MPF method with temperature distribution analysis methods such as the finite-element method (FEM) [20] and computational thermal-fluid dynamics (CtFD) simulations [28]. These aforementioned studies have used binary-approximated multicomponent systems, such as Ni–Nb binary alloys, to simulate IN718 alloys. While MPF simulations using binary alloy systems can effectively reproduce microstructure formations and segregation behaviors, the binary approximation might be affected by the chemical interactions between the removed solute elements in the target multicomponent alloy. The limit of absolute stability predicted by the Mullins-Sekerka theory [29] is also crucial because the limit velocity is close to the solidification rate in the LPBF process and is different in multicomponent and binary-approximated systems. The difference between the solidus and liquidus temperatures, ΔT0, directly determines the absolute stability according to the Mullins-Sekerka theory. For example, the ΔT0 values of IN718 and its binary-approximated Ni–5 wt.%Nb alloy are 134 K [28] and 71 K [30], respectively. The solidification rate compared to the limit of absolute stability, i.e., the relative non-equilibrium of solidification, changes by simplification of the system. It is therefore important to use the composition of the actual multicomponent system in such simulations. However, to the best of our knowledge, there is no MPF simulation using a multicomponent model coupled with a temperature analysis simulation to predict solute segregation in a Ni-based superalloy.

In this study, we demonstrate that the conventional MPF model can reproduce experimentally observed dendritic structures by performing a phase-field simulation using the temperature distribution obtained by a CtFD simulation of a multicomponent Ni-based alloy (conventional solid-solution hardening-type HX). The MPF simulation revealed that the segregation behavior of solute elements largely depends on the regions of the melt pool, such as the cell boundary, the interior of the melt-pool boundary, and heat-affected regions. The sensitivities of the various interfaces to liquation and solidification cracks are compared based on the predicted concentration distributions. Moreover, the feasibility of using the conventional MPF model for LPBF is discussed in terms of the absolute stability limit.

2. Methods

2.1. Laser-beam irradiation experiments

Rolled and recrystallized HX ingots with dimensions of 20 × 50 × 10 mm were used as the specimens for laser-irradiation experiments. The specimens were irradiated with a laser beam scanned along straight lines of 10 mm in length using a laser AM machine (EOS 290 M, EOS) equipped with a 400 W Yb-fiber laser. Irradiation was performed with a beam power of P = 300 W and a scanning speed of V = 600 mm s-1, which are the conditions generally used in the LPBF fabrication of Ni-based superalloy [8]. The corresponding line energy was 0.5 J mm-1. The samples were cut perpendicular to the beam-scanning direction for cross-sectional observation using a field-emission scanning electron microscope (FE-SEM, JEOL JSM 6500). Crystal orientation analysis was performed by electron backscatter diffraction (EBSD). The sizes of each crystal grain and their aspect ratios were evaluated by analyzing the EBSD data.

2.2. CtFD simulation

CtFD simulations of the laser-beam irradiation of HX were performed using a 3D thermo-fluid analysis software (Flow Science FLOW-3D® with Flow-3D Weld module). A Gaussian heat source model was used, in which the irradiation intensity distribution of the beam is regarded as a symmetrical Gaussian distribution over the entire beam. The distribution of the beam irradiation intensity is expressed by the following equation.(1)q̇=2ηPπR2exp−2r2R2.

Here, P is the power, R is the effective beam radius, r is the actual beam radius, and η is the beam absorption rate of the substrate. To improve the accuracy of the model, η was calculated by assuming multiple reflections using the Fresnel equation:(2)�=1−121+1−�cos�21+1+�cos�2+�2−2�cos�+2cos2��2+2�cos�+2cos2�.

ε is the Fresnel coefficient and θ is the incident angle of the laser. A local laser melt causes the vaporization of the material and results in a high vapor pressure. This vapor pressure acts as a recoil pressure on the surface, pushing the weld pool down. The recoil pressure is reproduced using the following equation.(3)precoil=Ap0exp∆HLVRTV1−TVT.

Here, p0 is the atmospheric pressure, ∆HLV is the latent heat of vaporization, R is the gas constant, and TV is the boiling point at the saturated vapor pressure. A is a ratio coefficient that is generally assumed to be 0.54, indicating that the recoil pressure due to evaporation is 54% of the vapor pressure at equilibrium on the liquid surface.

Table 1 shows the parameters used in the simulations. Most parameters were evaluated using an alloy physical property calculation software (Sente software JMatPro v11). The values in a previously published study [31] were used for the emissivity and the Stefan–Boltzmann constant, and the values for pure Ni [32] were used for the heat of vaporization and vaporization temperatures. The Fresnel coefficient, which determines the beam absorption efficiency, was used as a fitting parameter to reproduce the morphology of the experimentally observed melt region, and a Fresnel coefficient of 0.12 was used in this study.

Table 1. Parameters used in the CtFD simulations.

ParameterSymbolValueReference
Density at 298.15 Kρ8.24 g cm-3[]
Liquidus temperatureTL1628.15 K[]
Solidus temperatureTS1533.15 K[]
Viscosity at TLη6.8 g m-1 s-1[]
Specific heat at 298.15 KCP0.439 J g-1 K-1[]
Thermal conductivity at 298.15 Kλ10.3 W m-1 K-1[]
Surface tension at TLγL1.85 J m-2[]
Temperature coefficient of surface tensiondγL/dT–2.5 × 10−4 J m-2 K-1[]
EmissivityΕ0.27[31]
Stefan–Boltzmann constantσ5.67 × 10-8 W m-2 K-4[31]
Heat of fusionΔHSL2.76 × 102 J g-1[32]
Heat of vaporizationΔHLV4.29 × 10J g-1[32]
Vaporization temperatureTV3110 K[32]

Calculated using JMatPro v11.

The dimensions of the computational domain of the numerical model were 4.0 mm in the beam-scanning direction, 0.4 mm in width, and 0.3 mm in height. A uniform mesh size of 10 μm was applied throughout the computational domain. The boundary condition of continuity was applied to all boundaries except for the top surface. The temperature was initially set to 300 K. P and V were set to their experimental values, i.e., 300 W and 600 mm s-1, respectively. Solidification conditions based on the temperature gradient, G, the solidification rate, R, and the cooling rate were evaluated, and the obtained temperature distribution was used in the MPF simulations.

2.3. MPF simulation

Two-dimensional MPF simulations weakly coupled with the CtFD simulation were performed using the Microstructure Evolution Simulation Software (MICRESS) [33][34][35][36][37] with the TQ-Interface for Thermo-Calc [38]. A simplified HX alloy composition of Ni-21.4Cr-17.6Fe-0.46Mn-8.80Mo-0.39Si-0.50W-1.10Co-0.08 C (mass %) was used in this study. The Gibbs free energy and diffusion coefficient of the system were calculated using the TCNI9 thermodynamic database [39] and the MOBNi5 mobility database [40]. Τhe equilibrium phase diagram calculated using Thermo-Calc indicates that the face-centered cubic (FCC) and σ phases appear as the equilibrium solid phases [19]. However, according to the time-temperature-transformation (TTT) diagram [41], the phases are formed after the sample is maintained for tens of hours in a temperature range of 1073 to 1173 K. Therefore, only the liquid and FCC phases were assumed to appear in the MPF simulations. The simulation domain was 5 × 100 μm, and the grid size Δx and interface width were set to 0.025 and 0.1 µm, respectively. The interfacial mobility between the solid and liquid phases was set to 1.0 × 10-8 m4 J-1 s-1. Initially, one crystalline nucleus with a [100] crystal orientation was placed at the left bottom of the simulation domain, with the liquid phase occupying the remainder of the domain. The model was solidified under the temperature field distribution obtained by the CtFD simulation. The concentration distribution and crystal orientation of the solidified model were examined. The primary dendrite arm space (PDAS) was compared to the experimental PDAS measured by the cross-sectional SEM observation.

In an actual LPBF process, solidified layers are remelted and resolidified during the stacking of the one layer above, thereby greatly affecting solute element distributions in those regions. Therefore, remelting and resolidification simulations were performed to examine the effect of remelting on solute segregation. The solidified model was remelted and resolidified by applying a time-dependent temperature field shifted by 60 μm in the height direction, assuming reheating during the stacking of the upper layer (i.e., the upper 40 μm region of the simulation box was remelted and resolidified). The changes in the composition distribution and formed microstructure were investigated.

3. Results

3.1. Experimental observation of melt pool

Fig. 1 shows a cross-sectional optical microscopy image and corresponding inverse pole figure (IPF) orientation maps obtained from the laser-melted region of HX. The dashed line indicates the fusion line. A deep melted region was formed by keyhole-mode melting due to the vaporization of the metal and resultant recoil pressure. Epitaxial growth from the unmelted region was observed. Columnar crystal grains with an average diameter of 5.46 ± 0.32 μm and an aspect ratio of 3.61 ± 0.13 appeared at the melt regions (Figs. 1b–1d). In addition, crystal grains growing in the z direction could be observed in the lower center.

Fig. 1

Fig. 2a shows a cross-sectional backscattering electron image (BEI) obtained from the laser-melted region indicated by the black square in Fig. 1a. The bright particles with a diameter of approximately 2 μm observed outside the melt pool. It is well known that M6C, M23C6, σ, and μ precipitate phases are formed in Hastelloy-X [41]. These precipitates mainly consisted of Mo, Cr, Fe, and Ni; The μ and M6C phases are rich in Mo, while the σ and M23C6 phases are rich in Cr. The SEM energy dispersive X-ray spectroscopy analysis suggested that the bright particles are the stable precipitates as shown in Fig. S2 and Table S1. Conversely, there are no carbides in the melt pool. This suggests that the cooling rate is extremely high during LPBF, which prevents the formation of a stable carbide during solidification. Figs. 2b–2f show magnified BEI images at different height positions indicated in Fig. 2a. Bright regions are observed between the cells, which become fragmentary at the center of the melt pool, as indicated by the yellow arrow heads in Figs. 2e and 2f.

Fig. 2

3.2. CtFD simulation

Figs. 3a–3c show snapshots of the CtFD simulation of HX at 2.72 ms, with the temperature indicated in color. A melt pool with an elongated teardrop shape formed and keyhole-mode melting was observed at the front of the melt region. The cooling rate, temperature gradient (G), and solidification rate (R) were evaluated from the temporal change in the temperature distribution of the CtFD simulation results. The z-position of the solid/liquid interface during the melting and solidification processes is shown in Fig. 3d. The interface goes down rapidly during melting and then rises during solidification. The MPF simulation of the microstructure formation during solidification was performed using the temperature distribution. Moreover, the microstructure formation process during the fabrication of the upper layer was investigated by remelting and resolidifying the solidified layer using the same temperature distribution with a 60 μm upward shift, corresponding to the layer thickness commonly used in the LPBF of Ni-based superalloys.

Fig. 3

Figs. 4a–4c show the changes in the cooling rate, temperature gradient, and solidification rate in the center line of the melt pool parallel to the z direction. To output the solidification conditions at the solid/liquid interface in the melt pool, only the data of the mesh where the solid phase ratio was close to 0.5 were plotted. Solidification occurred where the cooling rate was in the range of 2.1 × 105–1.6 × 10K s-1G was in the range of 3.6 × 105–1.9 × 10K m-1, and R was in the range of 8.2 × 10−2–6.3 × 10−1 m s-1. The cooling rate was the highest near the fusion line and decreased as the interface approached the center of the melt region (Fig. 4a). G also exhibited the highest value in the regions near the fusion line and decreased throughout the solid/liquid interface toward the center of the melt pool (Fig. 4b). R had the lowest value near the fusion line and increased as the interface approached the center of the melt region (Fig. 4c).

Fig. 4

3.3. MPF simulations coupled with CtFD simulation

MPF simulations of solidification, remelting, and resolidification were performed using the temperature-time distribution obtained by the CtFD simulation. Fig. 5 shows the MPF solidified models colored by phase and Mo concentration. All the computational domains show the FCC phase after the solidification (Fig. 5a). Dendrites grew parallel to the heat flow direction, and solute segregations were observed in the interdendritic regions. At the bottom of the melt pool (Fig. 5d), planar interface growth occurred before the formation of primary dendrites. The bottom of the melt pool is the turning point of the solid/liquid interface from the downward motion in melting to the upward motion in solidification. Thus, the solidification rate at the boundary is zero, and is extremely low immediately above the molt-pool boundary. Here, the lower limit of the solidification rate (R) for dendritic growth can be represented by the constitutional supercooling criterion [29]Vcs = (G × DL) / ΔT, and planar interface growth occurs at R < VcsDL and ΔT denote the diffusion coefficient in the liquid and the equilibrium freezing range, respectively. The results suggest that planar interface growth occurs at the bottom of the melt pool, resulting in a dark region with a different solute element distribution. Some of the primary dendrites were diminished by competition with other dendrites. In addition, secondary dendrite arms could be seen in the upper regions (Fig. 5c), where solidification occurred at a lower cooling rate. The fragmentation of the solute segregation near the secondary dendrite arms is similar to that observed in the experimental melt pool shown in Figs. 2e and 2f, and the secondary dendrite arms are suggested to have appeared at the center of the melt region. Fig. 6 shows the PDASs measured from the MPF simulation models, compared to the experimental PDASs measured by the cross-sectional SEM observation of the laser-melted regions (Fig. 2). The PDAS obtained by the MPF simulation become larger as the solidification progress. Ghosh et al. [21] evident by the phase-field method that the PDAS decreases as the cooling rate increases under the rapid cooling conditions obtained by the finite element analysis. In this study, the cooling rate was decreased as the interface approached the center of the melt region (Fig. 4a), and the trends in PDAS changes with respect to cooling rate is same as the reported trend [21]. The simulated trends of the PDAS with the position in the melt pool agreed well with the experimental trends. However, all PDASs in the simulation were larger than those observed in the experiment at the same positions. Ode et al. [42] reported that PDAS differences between 2D and 3D MPF simulations can be represented by PDAS2D = 1.12 × PDAS3D owing to differences in the effects of the interfacial energy and diffusivity. We also performed 2D and 3D MPF simulations under the solidification conditions of G = 1.94 × 10K m-1 and R = 0.82 m s-1 (Fig. S1), and found that the PDAS from the 2D MPF simulation was 1.26 times larger than that from the 3D simulation. Therefore, the cell structure obtained by the CtFD simulation coupled with the 2D MPF simulation agreed well with the experimental results over the entire melt pool region considering the dimensional effects.

Fig. 5
Fig. 6

Fig. 7b1 and 7c1 show the concentration profiles of the solidified model along the growth direction indicated by dashed lines in Fig. 7a. The differences in concentrations from the alloy composition are also shown in Fig. 7b2 and 7c2. Cr, Mo, C, Mn, and W were segregated to the interdendritic regions, while Si, Fe, and Co were depressed. The solute segregation behavior agrees with the experimentally observation [43] and the prediction by the Scheil-Gulliver simulation [19]. Segregation occurred to the highest degree in Mo, while the ratio of segregation to the alloy composition was remarkable in C. The concentration fluctuations correlated with the position in the melt pool and decreased at the center of the melt pool, which was suggested to correspond to the lower cooling rate in this region. Conversely, droplets that appeared between secondary dendrite arms in the upper regions of the simulation domain exhibited a locally high segregation of solute elements, with the same amount of segregation as that at the bottom of the melt pool.

Fig. 7

3.4. Remelting and resolidification simulation

The solidified model was subjected to remelting and resolidification conditions by shifting the temperature profile upward by 60 µm to reveal the effect of reheating on the solute segregation behavior. Figs. 8a and 8b shows the simulation domains of the HX model after resolidification, colored by phase and Mo concentration. The magnified MPF models during the resolidification of the regions indicated by rectangles in Figs. 8a and 8b are also shown as Figs. 8c and 8d. Dendrites grew from the bottom of the remelted region, with the segregation of solute elements occurring in the interdendritic regions. The entire domain become the FCC phase after the resolidification, as shown in Fig. 8a. The bottom of the remelted regions exhibited a different microstructure, and Mo was depressed at the remelted regions, rather than the interdendritic regions. The different solute segregation behavior [44] and the microstructure formation [45] at the melt pool boundary is also observed in LPBF manufactured 316 L stainless steel. We found that this microstructure was formed by further remelting during the resolidification process, which is shown in Fig. 9. Here, the solidified HX model was heated, and the interdendritic regions were preferentially melted while concentration fluctuations were maintained (Fig. 9a1 and 9a2). Subsequently, planer interface growth occurs near the melt pool boundary where the solidification rate is almost zero, and the dendrites outside of the boundary are grown epitaxially (Fig. 9b1 and 9b2). However, these remelted again because of the temperature rise (Fig. 9c1 and 9c2, and the temperature-time profile shown in Fig. 9e). The remelted regions then cooled and solidified with the abnormal solute segregations (Fig. 9d1 and 9d2). Then, dendrite grows from amplified fluctuations under the solidification rate larger than the criterion of constitutional supercooling (Fig. 9d1, 9d2, and Fig. 8d). It has been reported [46][47] that temperature rising owning to latent heat affects microstructure formation: phase-field simulations of a Ni–Al binary alloy suggest that the release of latent heat during solidification increases the average temperature of the system [46] and strongly influences the solidification conditions [47]. In this study, the release of latent heat during solidification is considered in CtFD simulations for calculating the temperature distribution, and the temperature increase is suggested to have also occurred due to the release of latent heat.

Fig. 8
Fig. 9

Fig. 10b1 and 10c1 show the solute element concentration line profiles of the resolidified model along the growth direction indicated by dashed lines in Fig. 10a. Fig. 10b2 and 10c2 show the corresponding differences in concentration from the alloy composition. The segregation behavior of solute elements at the interdendritic regions (Fig. 10b1 and 10b2) was the same as that in the solidified model (Figs. 7b1 and 7b2). Here, Cr, Mo, C, Mn, and W were segregated to the interdendritic regions, while Si, Fe, and Co were depressed. However, the concentration fluctuations at the interdendritic regions were larger than those in the solidified model. Moreover, the segregation of the outside of the melt pool, i.e., the heat-affected zone, was remarkable throughout remelting and resolidification. Different segregation behaviors were observed in the re-remelted region: Mo, Si, Mn, and W were segregated, while Ni, Fe, and Co were depressed. These solute segregations caused by remelting are expected to heavily influence the crack behavior.

Fig. 10

4. Discussion

4.1. Effect of segregation of solute elements on liquation cracking susceptibility

Strong solute segregation was observed between the interdendritic regions of the solidified alloy (Fig. 7). In addition, the solute segregation behavior was significantly affected by remelting and resolidification and varied across the alloy. Solute segregation can be categorized by the regions shown in Fig. 11a1–11a4, namely the cell boundary (Fig. 11a1), interior of the melt-pool boundary (Fig. 11a2), re-remelted regions (Fig. 11a3), and heat-affected regions (Fig. 11a4). The concentration profiles of these regions are shown in Fig. 11b1–11b4. Solute segregation was the highest in the cell boundary region. The solute segregation in the heat-affected region was almost the same as that in the cell boundary region, but seemed to have been attenuated by reheating during remelting and resolidification. The interior of the melt-pool boundary region also had the same tendency for solute segregation. However, the amount of Cr segregation was smaller than that of Mo. A decrease in the Cr concentration was also mitigated, and the concentration remained the same as that in the alloy composition. Fig. 11c1–11c4 show the chemical potentials of the solute elements for the FCC phase at 1073 K calculated using the compositions of those interfacial regions. All the interfacial regions showed non-constant chemical potentials for each element along the perpendicular direction, but the fluctuations of the chemical potentials differed by the type of interfaces. In particular, the fluctuation of the chemical potential of C at the cell boundary region was the largest, suggesting it can be relaxed easily by heat treatment. On the other hand, the fluctuations of the other elements in all the regions were small. The solute segregations are most likely to remain after the heat treatment and are supposed to affect the cracking susceptibilities.

Fig. 11

The solidus temperatures TS, the difference between the liquidus and solidus temperatures (i.e., the brittle temperature range (BTR)), and the fractions of the equilibrium precipitate phases at 1073 K of the interfacial regions were calculated as the liquation, solidification, and ductility dip cracking susceptibilities, respectively. At the cell boundary (Fig. 12a1), interior of the melt-pool boundary (Fig. 12a1), and heat-affected regions (Fig. 12a1), the internal and interfacial regions exhibited higher and lower TS compared to that of the alloy composition, respectively. The lowest Ts was obtained with the composition at the cell boundary region, which is the largest solute-segregated region. It has been suggested that strong segregations of solute elements in LPBF lead to liquation cracks [16]. This study also supports this suggestion, and liquation cracks are more likely to occur at the interfacial regions indicated by predicting the solute segregation behavior using the MPF model. Additionally, the BTRs of the cell boundary, interior of the melt-pool boundary, and heat-affected regions were wider at the interdendritic regions, and solidification cracks were also likely to occur in these regions. Moreover, within the solute segregation regions, the fraction of the precipitate phases in these interfacial regions was larger than that calculated using the alloy composition (Fig. 12c1, 12c2, and 12c4). This indicates that ductility dip cracking is also likely to occur at the cell boundary, interior of the melt-pool boundary, and in heat-affected regions. Contrarily, we found that the re-remelted region exhibited a higher TS and smaller BTR even in the interfacial region (Fig. 12a3 and 12b3), where the solute segregation behavior was different from that of the other regions. In addition, the re-remelting region exhibited less precipitation compared with the other segregated regions (Fig. 12c3). The re-remelting caused by the latent heat can attenuate solute segregation, prevent Ts from decreasing, decrease the BTR, and decrease the amount of precipitate phases. Alloys with a large amount of latent heat are expected to increase the re-remelting region, thereby decreasing the susceptibility to liquation and ductility dip cracks due to solute element segregation. This can be a guide for designing alloys for the LPBF process. As mentioned in Section 3.4, the microstructure [45] and the solute segregation behavior [44] at the melt pool boundary of LPBF-manufactured 316 L stainless steel are observed, and they are different from that of the interdendritic regions. Experimental observations of the solute segregation behavior in the LPBF-fabricated Ni-based alloys are currently underway.

Fig. 12

4.2. Applicability of the conventional MPF simulation to microstructure formation under LPBF

As the solidification growth rate increases, segregation coefficients approach 1, and the fluctuation of the solid/liquid interface is suppressed by the interfacial tension. The interface growth occurs in a flat fashion instead of having a cellular morphology at a velocity above the absolute stability limit, Ras, predicted by the Mullins-Sekerka theory [29]Ras = (ΔT0 DL) / (k Γ) where ΔT0DLk, and Γ are the difference between the liquidus and solidus temperatures, equilibrium segregation coefficient, the diffusivity of liquid, and the Gibbs-Thomson coefficient, respectively.

The Ras of HX was calculated using the equation and the thermodynamic parameters obtained by the TCNI9 thermodynamic database [39]. The calculated Ras of HX was 3.9 m s-1 and is ten times larger than that of the Ni–Nb alloy (approximately 0.4 m s-1[20]. The HX alloy was solidified under R values in the range of 8.2 × 10−2–6.3 × 10−1 m s-1. The theoretically calculated criterion is larger than the evaluated R, and is in agreement with the experiment in which dendritic growth is observed in the melt pool (Fig. 5). In contrast, Karayagiz et al. [20] reported that the R of the Ni–Nb binary alloy under LPBF was as high as approximately 2 m s-1, and planar interface growth was observed to be predominant under the high-growth-rate conditions. These experimentally observed microstructures agree well with the prediction by the Mullins-Sekerka theory about the relationship between the morphology and solidification rates.

In this study, the solidification microstructure formed by the laser-beam irradiation of an HX multicomponent Ni-based superalloy was reproduced by a conventional MPF simulation, in which the system was assumed to be in a quasi-equilibrium condition. Boussinot et al. [24] also suggested that the conventional phase-field model can be applied to simulate the microstructure of an IN718 multicomponent Ni-based superalloy in LPBF. In contrast, Kagayaski et al. [20] suggested that the conventional MPF simulation cannot be applied to the solidification of the Ni-Nb binary alloy system and that the finite interface dissipation model proposed by Steinbach et al. [48][49] is necessary to simulate the high solidification rates observed in LPBF. The difference in the applicability of the conventional MPF method to HX and Ni–Nb binary alloys is presumed to arise from the differences in the non-equilibrium degree of these systems under the high solidification rates of LPBF. The results suggest that Ras can be used as a simple index to apply the conventional MPF model for solidification in LPBF. Solidification becomes a non-equilibrium process as the solidification rate approaches the limit of absolute stability, Ras. In this study, the solidification of the HX multicomponent system occurred under a relatively low solidification rate compared to Ras, and the microstructure of the conventional MPF model was successfully reproduced in the physical experiment. However, note that the limit of absolute stability predicted by the Mullins-Sekerka theory was originally proposed for solidification in a binary alloy system, and further investigation is required to consider its applicability to multicomponent alloy systems. Moreover, the fast solidification, such as in the LPBF process, causes segregation coefficient approaching a value of 1 [20][21][25] corresponds to a diffusion length that is on the order of the atomic interface thickness. When the segregation coefficient approaches 1, solute undercooling disappears; hence, there is no driving force to amplify fluctuations regardless of whether interfacial tension is present. This phenomenon should be further investigated in future studies.

5. Conclusions

We simulated solute segregation in a multicomponent HX alloy under the LPBF process by an MPF simulation using the temperature distributions obtained by a CtFD simulation. We set the parameters of the CtFD simulation to match the melt pool shape formed in the laser-irradiation experiment and found that solidification occurred under high cooling rates of up to 1.6 × 10K s-1.

MPF simulations using the temperature distributions from CtFD simulation could reproduce the experimentally observed PDAS and revealed that significant solute segregation occurred at the interdendritic regions. Equilibrium thermodynamic calculations using the alloy compositions of the segregated regions when considering crack sensitivities suggested a decrease in the solidus temperature and an increase in the amount of carbide precipitation, thereby increasing the susceptibility to liquation and ductility dip cracks in these regions. Notably, these changes were suppressed at the melt-pool boundary region, where re-remelting occurred during the stacking of the layer above. This effect can be used to achieve a novel in-process segregation attenuation.

Our study revealed that a conventional MPF simulation weakly coupled with a CtFD simulation can be used to study the solidification of multicomponent alloys in LPBF, contrary to the cases of binary alloys investigated in previous studies. We discussed the applicability of the conventional MPF model to the LPBF process in terms of the limit of absolute stability, Ras, and suggested that alloys with a high limit velocity, i.e., multicomponent alloys, can be simulated using the conventional MPF model even under the high solidification velocity conditions of LPBF.

CRediT authorship contribution statement

Masayuki Okugawa: Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Takayoshi Nakano: Writing – review & editing, Validation, Supervision, Funding acquisition. Yuichiro Koizumi: Writing – review & editing, Visualization, Validation, Supervision, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. Sukeharu Nomoto: Writing – review & editing, Validation, Investigation. Makoto Watanabe: Writing – review & editing, Validation, Supervision, Funding acquisition. Katsuhiko Sawaizumi: Validation, Software, Investigation, Formal analysis, Data curation. Kenji Saito: Visualization, Validation, Software, Methodology, Investigation, Formal analysis, Data curation. Haruki Yoshima: Visualization, Validation, Software, Investigation, Formal analysis, Data curation.

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 work was partly supported by the Cabinet Office, Government of Japan, Cross-ministerial Strategic Innovation Promotion Program (SIP), “Materials Integration for Revolutionary Design System of Structural Materials,” (funding agency: The Japan Science and Technology Agency), by JSPS KAKENHI Grant Numbers 21H05018 and 21H05193, and by CREST Nanomechanics: Elucidation of macroscale mechanical properties based on understanding nanoscale dynamics for innovative mechanical materials (Grant Number: JPMJCR2194) from the Japan Science and Technology Agency (JST). The authors would like to thank Mr. H. Kawabata and Mr. K. Kimura for their technical support with the sample preparations and laser beam irradiation experiments.

Appendix A. Supplementary material

Download : Download Word document (654KB)

Supplementary material.

Data availability

Data will be made available on request.

References

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 transfer, Nonequilibrium thermodynamics, Solidification process, Computer simulation, Discrete element method, Lasers, Mass transfer, Fluid mechanics, Computational fluid dynamics, Multiphase 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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Effects of ramp slope and discharge on hydraulic performance of submerged hump weirs

Effects of ramp slope and discharge on hydraulic performance of submerged hump weirs

Arash Ahmadi a, Amir H. Azimi b

Abstract

험프 웨어는 수위 제어 및 배출 측정을 위한 기존의 수력 구조물 중 하나입니다. 상류 및 하류 경사로의 경사는 자유 및 침수 흐름 조건 모두에서 험프 웨어의 성능에 영향을 미치는 설계 매개변수입니다.

침수된 험프보의 유출 특성 및 수위 변화에 대한 램프 경사 및 유출의 영향을 조사하기 위해 일련의 수치 시뮬레이션이 수행되었습니다. 1V:1H에서 1V:5H까지의 5개 램프 경사를 다양한 업스트림 방전에서 테스트했습니다.

수치모델의 검증을 위해 수치결과를 실험실 데이터와 비교하였다. 수면수위 예측과 유출계수의 시뮬레이션 불일치는 각각 전체 범위의 ±10%와 ±5% 이내였습니다.

모듈 한계 및 방전 감소 계수의 변화에 대한 램프 경사의 영향을 연구했습니다. 험프보의 경사로 경사가 증가함에 따라 상대적으로 높은 침수율에서 모듈러 한계가 발생함을 알 수 있었다.

침수 시작은 방류 수위를 작은 증분으로 조심스럽게 증가시켜 모델링되었으며 그 결과는 모듈 한계의 고전적인 정의와 비교되었습니다. 램프 경사와 방전이 증가함에 따라 모듈러 한계가 증가하는 것으로 밝혀졌지만, 모듈러 한계의 고전적인 정의는 모듈러 한계가 방전과 무관하다는 것을 나타냅니다.

Hump weir 하류의 속도와 와류장은 램프 경사에 의해 제어되는 와류 구조 형성을 나타냅니다. 에너지 손실은 수치 출력으로부터 계산되었으며 정규화된 에너지 손실은 침수에 따라 선형적으로 감소하는 것으로 나타났습니다.

Hump weirs are amongst conventional hydraulic structures for water level control and discharge measurement. The slope in the upstream and downstream ramps is a design parameter that affects the performance of Hump weirs in both free and submerged flow conditions. A series of numerical simulations was performed to investigate the effects of ramp slope and discharge on discharge characteristics and water level variations of submerged Hump weirs. Five ramp slopes ranging from 1V:1H to 1V:5H were tested at different upstream discharges. The numerical results were compared with the laboratory data for verifications of the numerical model. The simulation discrepancies in prediction of water surface level and discharge coefficient were within ±10 % and ±5 % of the full range, respectively. The effects of ramp slope on variations of modular limit and discharge reduction factor were studied. It was found that the modular limit occurred at relatively higher submergence ratios as the ramp slope in Hump weirs increased. The onset of submergence was modeled by carefully increasing tailwater level with small increments and the results were compared with the classic definition of modular limit. It was found that the modular limit increases with increasing the ramp slope and discharge while the classic definition of modular limit indicated that the modular limit is independent of the discharge. The velocity and vortex fields in the downstream of Hump weirs indicated the formation vortex structure, which is controlled by the ramp slope. The energy losses were calculated from the numerical outputs, and it was found that the normalized energy losses decreased linearly with submergence.

Introduction

Weirs have been utilized predominantly for discharge measurement, flow diversion, and water level control in open channels, irrigation canal, and natural streams due to their simplicity of operation and accuracy. Several research studies have been conducted to determine the head-discharge relationship in weirs as one of the most common hydraulic structures for flow measurement (Rajaratnam and Muralidhar, 1969 [[1], [2], [3]]; Vatankhah, 2010, [[4], [5], [6]]; b [[7], [8], [9]]; Azimi and Seyed Hakim, 2019; Salehi et al., 2019; Salehi and Azimi, 2019, [10]. Weirs in general are classified into two major categories named as sharp-crested weirs and weirs of finite-crest length (Rajaratnam and Muralidhar, 1969; [11]. Sharp-crested weirs are typically used for flow measurement in small irrigation canals and laboratory flumes. In contrast, weirs of finite crest length are more suitable for water level control and flow diversion in rivers and natural streams [7,[12], [13], [14]].

The head-discharge relationship in sharp-crested weirs is developed by employing energy equation between two sections in the upstream and downstream of the weir and integration of the velocity profile at the crest of the weir as:

where Qf is the free flow discharge, B is the channel width, g is the acceleration due to gravity, ho is the water head in free-flow condition, and Cd is the discharge coefficient. Rehbock [15] proposed a linear correlation between discharge coefficient and the ratio of water head, ho, and the weir height, P as Cd = 0.605 + 0.08 (ho/P).

Upstream and/or downstream ramp(s) can be added to sharp-crested weirs to enhance the structural stability of the weir. A sharp-crested weir with upstream and/or downstream ramp(s) are known as triangular weirs in the literature. Triangular weirs with both upstream and downstream ramps are also known as Hump weirs and are first introduced in the experimental study of Bazin [16]. The ramps are constructed upstream and downstream of sharp-crested weirs to enhance the weir’s structural integrity and improve the hydraulic performance of the weir. In free-flow condition, the discharge coefficient of Hump weirs increases with increasing downstream ramp slope but decreases as upstream ramp slope increases (Azimi et al., 2013).

The hydraulic performance of weirs is evaluated in both free and submerged flow conditions. In free flow condition, water freely flows over weirs since the downstream water level is lower than that of the crest level of the weir. Channel blockage or flood in the downstream of weirs can raise the tailwater level, t. As tailwater passes the crest elevation in sharp-crested weirs, the upstream flow decelerates due to the excess pressure force in the downstream and the upstream water level increases. The onset of water level raise due to tailwater raise is called the modular limit. Once the tailwater level passes the modular limit, the weir is submerged. In sharp-crested weirs, the submerged flow regime may occur even before the tailwater reaches the crest elevation [8,14], whereas, in weirs of finite crest length, the upstream water level remains unchanged even if the tailwater raises above the crest elevation and it normally causes submergence once the tailwater level passes the critical depth at the crest of the weir [7,17]. The degree of submergence can be estimated by careful observation of the water surface profile. Observations of water surface at different submergence levels indicated two distinct flow patterns in submerged sharp-crested weirs that was initially classified as impinging jet and surface flow regimes [14]. [8] analyzed the variations of water surface profiles over submerged sharp-crested weirs with different submergence ratios and defined four distinct regimes of impinging jet, surface jump, surface wave, and surface jet.

[18] characterized the onset of submergence by defining the modular limit as a stage when the free flow head increases by +1 mm due to tailwater rise. The definition of modular limit is somewhat arbitrary, and it is difficult to identify for large discharges because the upstream water surface begins to fluctuate. This definition did not consider the effects of channel and weir geometries. The experimental data in triangular weirs and weirs finite-crest length with upstream and downstream ramp(s) revealed that the modular limit varied with the ratio of the free-flow head to the total streamwise length of the weir [17]. Weirs of finite crest length with upstream and downstream ramps are known as embankment weirs in literature [1,19,20] and Azimi et al., 2013) [19]. conducted two series of laboratory experiments to study the hydraulics of submerged embankment weirs with the upstream and downstream ramps of 1V:1H and 1V:2H. Empirical correlations were proposed to directly estimate the flow discharge in submerged embankment weirs for t/h > 0.7 where h is the water head in submerged flow condition. He found that the free flow discharge is a function of upstream water head, but the submerged discharge is a function of submergence level, t/h [21]. studied the hydraulics of four embankment weirs with different weir heights ranging from 0.09 m to 0.36 m. It was found that submerged embankments with a higher ho/P, where P is the height of the weir, have a smaller discharge reduction due to submergence. Effects of crest length in embankment weirs with both upstream and downstream ramps of 1V:2H was studied in both free and submerged flow conditions [1]. It was found that the modular limit in submerged embankment weirs decreased linearly with the relative crest length, Ho/(Ho + L), where Ho is the total head and L is the crest length.

In submerged flow condition, the performance of weirs is quantified by the discharge reduction factor, ψ, which is a ratio of the submerged discharge, Qs, to the corresponding free-flow discharge, Qf, based on the upstream head, h [12]. In submerged-flow conditions, flow discharge can be estimated as:��=���

[1] proposed a formula to predict ψ that could be used for embankment weirs with different crest lengths ranging from 0 to 0.3 m as:�=(1−��)�where n is an exponent varying from 4 to 7 and Yt is the normalized submergence defined as:��=�ℎ−[0.85−(0.5��+�)]1−[0.85−(0.5��+�)]where H is the total upstream head in submerged-flow conditions [7]. proposed a simpler formula to predict ψ for weirs of finite-crest length as:�=[1−(�ℎ)�]�where m and n are exponents varying for different types of weirs. Hakim and Azimi (2017) employed regression analysis to propose values of n = 0.25 and m = 0.28 (ho/L)−2.425 for triangular weirs.

The discharge capacity of weirs decreases in submerged flow condition and the onset of submergence occurs at the modular limit. Therefore, the determination of modular limit in weirs with different geometries is critical to understanding the sensitivity of a particular weir model with tailwater level variations. The available definition of modular limit as when head water raises by +1 mm due to tailwater rise does not consider the effects of channel and weir geometries. Therefore, a new and more accurate definition of modular limit is proposed in this study to consider the effect of other geometry and approaching flow parameters. The second objective of this study is to evaluate the effects of upstream and downstream ramps and ramps slopes on the hydraulic performance of submerged Hump weirs. The flow patterns, velocity distributions, and energy dissipation rates were extracted from validated numerical data to better understand the discharge reduction mechanism in Hump weirs in both free and submerged flow conditions.

Section snippets

Governing equations

Numerical simulation has been employed as an efficient and effective method to analyze free surface flow problems and in particular investigating on the hydraulics of flow over weirs [22]. The weir models were developed in numerical domain and the water pressure and velocity field were simulated by employing the FLOW-3D solver (Flow Science, Inc., Santa Fe, USA). The numerical results were validated with the laboratory measurements and the effects of ramps slopes on the performance of Hump

Verification of numerical model

The experimental observations of Bazin [16,17] were used for model validation in free and submerged flow conditions, respectively. The weir height in the study of Bazin was P = 0.5 m and two ramp slopes of 1V:1H and 1V:2H were tested. The bed and sides of the channel were made of glass, and the roughness distribution of the bed and walls were uniform. The Hump weir models in the study of Seyed Hakim and Azimi (2017) had a weir height of 0.076 m and ramp slopes of 1V:2H in both upstream and

Conclusions

A series of numerical simulations was performed to study the hydraulics and velocity pattern downstream of a Hump weir with symmetrical ramp slopes. Effects of ramp slope and discharge on formation of modular limit and in submerged flow condition were tested by conducting a series of numerical simulations on Hump weirs with ramp slopes varying from 1V:1H to 1V:5H. A comparison between numerical results and experimental data indicated that the proposed numerical model is accurate with a mean

Author contributions

Arash Ahmadi: Software, Validation, Visualization, Writing – original draft. Amir Azimi: Conceptualization, Funding acquisition, Investigation, Project administration, Supervision, Writing – review & editing

Uncited References

[30]; [31]; [32]; [33].

Declaration of competing interest

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

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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

Jump To


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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Thermo-fluid modeling of influence of attenuated laser beam intensity profile on melt pool behavior in laser-assisted powder-based direct energy deposition

레이저 보조 분말 기반 직접 에너지 증착에서 용융 풀 거동에 대한 감쇠 레이저 빔 강도 프로파일의 영향에 대한 열유체 모델링

Thermo-fluid modeling of influence of attenuated laser beam intensity profile on melt pool behavior in laser-assisted powder-based direct energy deposition

Mohammad Sattari, Amin Ebrahimi, Martin Luckabauer, Gert-willem R.B.E. Römer

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Professional

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Abstract

A numerical framework based on computational fluid dynamics (CFD), using the finite volume method (FVM) and volume of fluid (VOF) technique is presented to investigate the effect of the laser beam intensity profile on melt pool behavior in laser-assisted powder-based directed energy deposition (L-DED). L-DED is an additive manufacturing (AM) process that utilizes a laser beam to fuse metal powder particles. To assure high-fidelity modeling, it was found that it is crucial to accurately model the interaction between the powder stream and the laser beam in the gas region above the substrate. The proposed model considers various phenomena including laser energy attenuation and absorption, multiple reflections of the laser rays, powder particle stream, particle-fluid interaction, temperature-dependent properties, buoyancy effects, thermal expansion, solidification shrinkage and drag, and Marangoni flow. The latter is induced by temperature and element-dependent surface tension. The model is validated using experimental results and highlights the importance of considering laser energy attenuation. Furthermore, the study investigates how the laser beam intensity profile affects melt pool size and shape, influencing the solidification microstructure and mechanical properties of the deposited material. The proposed model has the potential to optimize the L-DED process for a variety of materials and provides insights into the capability of numerical modeling for additive manufacturing optimization.

Original languageEnglish
Title of host publicationFlow-3D World Users Conference
Publication statusPublished – 2023
EventFlow-3D World User Conference – Strasbourg, France
Duration: 5 Jun 2023 → 7 Jun 2023

Conference

ConferenceFlow-3D World User Conference
Country/TerritoryFrance
CityStrasbourg
Period5/06/23 → 7/06/23
Fig. 1 Oscillation of a free surface due to the step reduction of gravity acceleration from kzi ≈ 9.81 to kz ≈ 0

Reorientation of Cryogenic Fluids Upon Step Reduction of Gravity

단계적 중력 감소 시 극저온 유체의 방향 전환

Malte Stief∗, Jens Gerstmann∗∗, and Michael E. Dreyer∗∗∗
ZARM, Center of Applied Space Technology and Microgravity, University of Bremen, Am Fallturm, D-28359 Bremen
Experiments to observe the surface oscillation of cryogenic liquids have been performed with liquid nitrogen inside a 50 mm
diameter right circular cylinder. The surface oscillation is driven by the capillary force that becomes dominant after a sudden
reduction of the gravity acceleration acting on the liquid. The experiments show differences from the speculated behavior and
enables one to observe new features.

Introduction and motivation

최근 몇 년 동안 Bremen의 낙하탑에서 중력의 단계적 감소 시 방향 재지향 거동과 표면 진동을 조사하기 위해 수많은 실험이 수행되었습니다[1]. 이 실험의 원리는 그림 1에 나와 있습니다.

그림 1의 왼쪽에 표시된 것처럼 오른쪽 원형 원통형 용기에 테스트 액체를 레벨 h0까지 채웁니다. 처음에 액체는 정지 상태이며 중앙에서 평평한 인터페이스를 형성합니다.

초기 중력 가속도 kzi ≈ 9.81 [m/s2]와 결과적으로 높은 BOND 수(Bo = ρkziR2/σ)로 인해 실린더의 대칭축에서. 낙하탑에서 실험 캡슐의 방출에 의해 확립된 μ-중력 환경 kz ≈ 0 [m/s2]로의 갑작스러운 전환과 함께 자유 표면은 진동 운동으로 새로운 평형 구성을 찾기 시작합니다(그림의 오른쪽) 1). 이러한 움직임은 그림 1의 중앙에 스케치되어 있습니다.

표면 진동의 구동력은 접착력과 결합된 표면 장력이며, 댐핑은 액체의 점도에 의해 제어됩니다. 위치가 zw인 벽에서 접촉선의 이동은 접촉각 γ에 의해 제어됩니다. 접촉각이 작은 액체용 γ ≈ 0◦

In recent years numerous experiments have been carried out to investigate the reorientation behavior and surface oscillations upon step reduction of gravity at the drop tower in Bremen [1]. The principals of these experiments are shown in figure 1. A right circular cylindrical container is filled up to the level h0 with the test liquid, as shown on the left of figure 1. Initially the liquid is quiescent and forms a flat interface at the center, in the symmetry axis of the cylinder, due to the initial gravity acceleration kzi ≈ 9.81 [m/s2] and the resulting high BOND number (Bo = ρkziR2/σ). With the sudden transition to the µ-gravity environment kz ≈ 0 [m/s2], which is established by the release of the experiment capsular in the drop tower, the free surface is initiated to search its new equilibrium configuration (right side of figure 1) with an oscillatory motion. These movements are sketched in the center of figure 1. The driving force for the surface oscillation is the surface tension in combination with the adhesion force where the damping is controlled by the viscosity of the liquid. The movement of the contact line at the wall, with its position zw, is governed by the contact angle γ. For liquids with small contact angle γ ≈ 0◦

Fig. 1 Oscillation of a free surface due to the step reduction of gravity acceleration from kzi ≈ 9.81 to kz ≈ 0
Fig. 1 Oscillation of a free surface due to the step reduction of gravity acceleration from kzi ≈ 9.81 to kz ≈ 0
Fig. 2 Experiment picture-series showing the oscillation of the free surface at different times for a 50 mm diameter cylinder.
Fig. 2 Experiment picture-series showing the oscillation of the free surface at different times for a 50 mm diameter cylinder.

References

[1] M. Michaelis, Kapillarinduzierte Schwingungen freier Fl¨ussigkeitsoberfl¨achen, Dissertation Universit¨at Bremen, Fortschritt-Berichte
Nr. 454 (VDI Verlag, D¨usseldorf, 2003).

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.

References

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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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Object name is materials-15-05273-g010.jpg

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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Fig. 6 LH2 isotherms at 1020 s.

액체-수소 탱크를 위한 결합된 열역학-유체-역학 솔루션

Coupled thermodynamic-fluid-dynamic solution for a liquid-hydrogen tank

G. D. Grayson

Published Online:23 May 2012 https://doi.org/10.2514/3.26706

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Introduction

ROPELLANT 열 성층화 및 외부 교란에 대한 유체 역학적 반응은 발사체와 우주선 모두에서 중요합니다. 과거에는 결합된 솔루션을 제공할 수 있는 충분한 계산 기술이 부족하여 이러한 문제를 개별적으로 해결했습니다.1

이로 인해 모델링 기술의 불확실성을 허용하기 위해 큰 안전 계수를 가진 시스템이 과도하게 설계되었습니다. 고중력 환경과 저중력 환경 모두에서 작동하도록 설계된 미래 시스템은 기술적으로나 재정적으로 실현 가능하도록 과잉 설계 및 안전 요소가 덜 필요합니다.

이러한 유체 시스템은 열역학 및 유체 역학이 모두 중요한 환경에서 모델의 기능을 광범위하게 검증한 후에만 고충실도 수치 모델을 기반으로 할 수 있습니다. 상용 컴퓨터 코드 FLOW-3D2는 유체 역학 및 열 모델링 모두에서 가능성을 보여주었으며,1 따라서 열역학-유체-역학 엔지니어링 문제에서 결합된 질량, 운동량 및 에너지 방정식을 푸는 데 적합함을 시사합니다.

발사체의 복잡한 액체 가스 시스템에 대한 포괄적인 솔루션을 달성하기 위한 첫 번째 단계로 액체 유체 역학과 열역학을 통합하는 제안된 상단 단계 액체-수소(Lit) 탱크의 간단한 모델이 여기에 제시됩니다. FLOW-3D FLOW-3D 프로그램은 Los Alamos Scientific Laboratory에서 시작되었으며 마커 및 셀 방법에서 파생된 것입니다.3 현재 상태로 가져오기 위해 수년에 걸쳐 광범위한 코드 수정이 이루어졌습니다.2

프로그램은 다음과 같습니다. 일반 Navier-Stokes 방정식을 풀기 위해 수치 근사의 중앙 유한 차분 방법을 사용하는 3차원 유체 역학 솔버입니다. 모멘텀 및 에너지 방정식의 섹션은 특정 응용 프로그램에 따라 활성화 또는 비활성화할 수 있습니다.

코드는 1994년 9월 13일 접수를 인용하기 위해 무액체 표면, 복잡한 용기 기하학, 여러 점성 모델, 표면 장력, 다공성 매체를 통한 흐름 및 응고와 함께 압축성 또는 비압축성 유동 가정을 제공합니다. 1995년 1월 15일에 받은 개정; 1995년 2월 17일 출판 승인.

ROPELLANT thermal stratification and fluid-dynamic response to external disturbances are of concern in both launch vehicles and spacecraft. In the past these problems have been addressed separately for want of sufficient computational technology to provide for coupled solutions.1 This has resulted in overdesigned systems with large safety factors to allow for the uncertainty in modeling techniques. Future systems designed to perform in both highand low-gravity environments will require less overdesign and safety factors to be technically and financially feasible. Such fluid systems can be based on high-fidelity numerical models only after extensive validation of the models’ capabilities in environments where both the thermodynamics and the fluid dynamics are important. The commercial computer code FLOW-3D2 has shown promise in both fluid-dynamic and thermal modeling,1 thus suggesting suitability for solving the coupled mass, momentum, and energy equations in thermodynamic-fluid-dynamic engineering problems. As a first step to achieving a comprehensive solution for complex liquidgas systems in a launch vehicle, a simple model of a proposed upper-stage liquid-hydrogen (Lit) tank incorporating the liquid fluid dynamics and thermodynamics is presented here. FLOW-3D The FLOW-3D program originated at the Los Alamos Scientific Laboratory and is a derivative of the marker-and-cell method.3 Extensive code modifications have been made over the years to bring it to its present state.2 The program is a three-dimensional fluiddynamic solver that uses a central finite-difference method of numerical approximation to solve the general Navier-Stokes equations. Sections of the momentum and energy equations can be enabled or disabled depending on the particular application. The code provides compressible or incompressible flow assumptions with liquid free surfaces, complex container geometries, several viscosity models, surface tension, flow though porous media, and solidification, to cite Received Sept. 13, 1994; revision received Jan. 15, 1995; accepted for publication Feb. 17, 1995. Copyright © 1995 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. *Engineer/Scientist, Propulsion Analysis and Hydraulics, Space Transportation Division, MS 13-3, 5301 Bolsa Avenue. Member AIAA. a few of the possibilities. Further information on FLOW-3D’s capabilities and details of the numerical algorithms can be found in Ref. 2

Fig. 1 Axial-acceleration history.
Fig. 1 Axial-acceleration history.
Fig. 2 Heat flux histories.
Fig. 2 Heat flux histories.
Fig. 3 LHi isotherms at 50 s.
Fig. 3 LHi isotherms at 50 s.
Fig. 4 LH2 isotherms at 300 s
Fig. 4 LH2 isotherms at 300 s
Fig. 5 LH2 isotherms at 880 s.
Fig. 5 LH2 isotherms at 880 s.
Fig. 6 LH2 isotherms at 1020 s.
Fig. 6 LH2 isotherms at 1020 s.
Fig. 7 Tank-outlet temperature history.
Fig. 7 Tank-outlet temperature history.
Fig. 2 Modeling of bubble point test apparatus (left) and computational grid (righ

Flow-3d를 이용한 표면장력 탱크용메시스크린모델링

Modeling of Mesh Screen for Use in Surface TensionTankUsing Flow-3d Software

Hyuntak Kim․ Sang Hyuk Lim․Hosung Yoon․Jeong-Bae Park*․Sejin Kwon

ABSTRACT

Mesh screen modeling and liquid propellant discharge simulation of surface tension tank wereperformed using commercial CFD software Flow-3d. 350 × 2600, 400 × 3000 and 510 × 3600 DTW mesh screen were modeled using macroscopic porous media model. Porosity, capillary pressure, and drag
coefficient were assigned for each mesh screen model, and bubble point simulations were performed. The
mesh screen model was validated with the experimental data. Based on the screen modeling, liquidpropellant discharge simulation from PMD tank was performed. NTO was assigned as the liquidpropellant, and void was set to flow into the tank inlet to achieve an initial volume flowrate of
liquid propellant in 3 × 10-3 g acceleration condition. The intial flow pressure drop through the meshscreen was approximately 270 Pa, and the pressure drop increased with time. Liquid propellant
discharge was sustained until the flow pressure drop reached approximately 630 Pa, which was near
the estimated bubble point value of the screen model.

초 록

상용 CFD 프로그램 Flow-3d를 활용하여, 표면 장력 탱크 적용을 위한 메시 스크린의 모델링 및 추진제 배출 해석을 수행하였다. Flow-3d 내 거시적 다공성 매체 모델을 사용하였으며, 350 × 2600, 400× 3000, 510 × 3600 DTW 메시 스크린에 대한 공극률, 모세관압, 항력계수를 스크린 모델에 대입 후, 기포점 측정 시뮬레이션을 수행하였다.

시뮬레이션 결과를 실험 데이터와 비교하였으며, 메시 스크린 모델링의 적절성을 검증하였다. 이를 기반으로 스크린 모델을 포함한 PMD 구조체에 대한 추진제 배출 해석을 수행하였다. 추진제는 액상의 NTO를 가정하였으며, 3 × 10-3 g 가속 조건에서 초기 유량을만족하도록 void를 유입시켰다. 메시 스크린을 통한 차압은 초기 약 270 Pa에서 시간에 따라 증가하였으며, 스크린 모델의 예상 기포점과 유사한 630 Pa에 이르기까지 액상 추진제 배출을 지속하였다.

Key Words

Surface Tension Tank(표면장력 탱크), Propellant Management Device(추진제 관리 장치),
Mesh Screen(메시 스크린), Porous Media Model(다공성 매체 모델), Bubble Point(기포점)

서론

    우주비행체를 미소 중력 조건 내에서 운용하 는 경우, 가압 기체가 액상의 추진제와 혼합되어 엔진으로 공급될 우려가 있으므로 이를 방지하 기 위한 탱크의 설계가 필요하다.

    다이어프램 (Diaphragm), 피스톤(Piston) 등 다양한 장치들 이 활용되고 있으며, 이 중 표면 장력 탱크는 내 부의 메시 스크린(Mesh screen), 베인(Vane) 등 의 구조체에서 추진제의 표면장력을 활용함으로 써 액상 추진제의 이송 및 배출을 유도하는 방 식이다.

    표면 장력 탱크는 구동부가 없는 구조로 신뢰성이 높고, 전 부분을 티타늄 등의 금속 재 질로 구성함으로써 부식성 추진제의 사용 조건 에서도 장기 운용이 가능한 장점이 있다. 위에서 언급한 메시 스크린(Mesh screen)은 수 십 마이크로미터 두께의 금속 와이어를 직조한 다공성 재질로 표면 장력 탱크의 핵심 구성 요소 중 하나이다.

    미세 공극 상 추진제의 표면장력에 의해 기체와 액체 간 계면을 일정 차압 내에서 유지시킬 수 있다. 이러한 성질로 인해 일정 조 건에서 가압 기체가 메시 스크린을 통과하지 못 하게 되고, 스크린을 탱크 유로에 설치함으로써 액상의 추진제 배출을 유도할 수 있다.

    메시 스크린이 가압 기체를 통과시키기 직전 의 기체-액체 계면에 형성되는 최대 차압을 기포 점 (Bubble point) 이라 칭하며, 메시 스크린의 주 요 성능 지표 중 하나이다. IPA, 물, LH2, LCH4 등 다양한 기준 유체 및 추진제, 다양한 메시 스 크린 사양에 대해 기포점 측정 관련 실험적 연 구가 이루어져 왔다 [1-3].

    위 메시 스크린을 포함하여 표면 장력 탱크 내 액상의 추진제 배출을 유도하는 구조물 일체 를 PMD(Propellant management device)라 칭하 며, 갤러리(Gallery), 베인(Vane), 스펀지(Sponge), 트랩(Trap) 등 여러 종류의 구조물에 대해 각종 형상 변수를 내포한다[4, 5].

    따라서 다양한 파라미터를 고려한 실험적 연구는 제약이 따를 수 있으며, 베인 등 상대적으로 작은 미소 중력 조건에서 개방형 유로를 활용하는 경우 지상 추진제 배출 실험이 불가능하다[6]. 그러므로 CFD를 통한 표면장력 탱크 추진제 배출 해석은 다양한 작동 조건 및 PMD 형상 변수에 따른 추진제 거동을 이해하고, 탱크를 설계하는 데 유용하게 활용될 수 있다.

    상기 추진제 배출 해석을 수행하기 위해서는 핵심 요소 중 하나인 메시 스크린에 대한 모델링이 필수적이다. Chato, McQuillen 등은 상용 CFD 프로그램인 Fluent를 통해, 갤러리 내 유동 시뮬레이션을 수행하였으며, 이 때 메시 스크린에 ‘porous jump’ 경계 조건을 적용함으로써 액상의 추진제가 스크린을 통과할 때 생기는 압력 강하를 모델링하였다[7, 8].

    그러나 앞서 언급한 메시 스크린의 기포점 특성을 모델링한 사례는 찾아보기 힘들다. 이는 스크린을 활용하는 표면 장력 탱크 내 액상 추진제 배출 현상을 해석적으로 구현하기 위해 반드시 필요한 부분이다. 본 연구에서는 자유표면 해석에 상대적으로 강점을 지닌 상용 CFD 프로그램 Flow-3d를 사용하여, 메시 스크린을 모델링하였다.

    거시적 다공성 매체 모델(Macroscopic porous mediamodel)을 활용하여 메시 스크린 모델 영역에 공극률(Porosity), 모세관압(Capillary pressure), 항력 계수(Drag coefficient)를 지정하고, 이를 기반으로 기포점 측정 시뮬레이션을 수행, 해석 결과와 실험 데이터 간 비교 및 검증을 수행하였다.

    이를 기반으로 메시 스크린 및 PMD구조체를 포함한 탱크의 추진제 배출 해석을 수행하고, 기포점 특성의 반영 여부를 확인하였다.

    Fig. 1 Real geometry-based mesh screen model (left)
and mesh screen model based on macroscopic
porous media model in Flow-3d (righ
    Fig. 1 Real geometry-based mesh screen model (left) and mesh screen model based on macroscopic porous media model in Flow-3d (righ
    Fig. 2 Modeling of bubble point test apparatus (left)
and computational grid (righ
    Fig. 2 Modeling of bubble point test apparatus (left) and computational grid (righ)
    Fig. 3 Modeling of sump in a tank (left) and lower part
of the sump structure (right)
    Fig. 3 Modeling of sump in a tank (left) and lower part of the sump structure (right)

    참 고 문 헌

    1. David J. C and Maureen T. K, ScreenChannel Liquid Aquisition Devices for Cryogenic Propellants” NASA-TM-2005- 213638, 2005
    2. Hartwig, J., Mann, J. A. Jr., Darr, S. R., “Parametric Analysis of the LiquidHydrogen and Nitrogen Bubble Point Pressure for Cryogenic Liquid AcquisitionDevices”, Cryogenics, Vol. 63, 2014, pp. 25-36
    3. Jurns, J. M., McQuillen, J. B.,BubblePoint Measurement with Liquid Methane of a Screen Capillary Liquid AcquisitionDevice”, NASA-TM-2009-215496, 2009
    4. Jaekle, D. E. Jr., “Propellant Management Device: Conceptual Design and Analysis: Galleries”, AIAA 29th Joint PropulsionConference, AIAA-97-2811, 1997
    5. Jaekle, D. E. Jr., “Propellant Management Device: Conceptual Design and Analysis: Traps and Troughs”, AIAA 31th Joint Propulsion Conference, AIAA-95-2531, 1995
    6. Yu, A., Ji, B., Zhuang, B. T., Hu, Q., Luo, X. W., Xu, H. Y., “Flow Analysis inaVane-type Surface Tension Propellant Tank”, IOP Conference Series: MaterialsScience and Engineering, Vol. 52, No. 7, – 990 – 2013, Article number: 072018
    7. Chato, D. J., McQuillen, J. B., Motil, B. J., Chao, D. F., Zhang, N., CFD simulation of Pressure Drops in Liquid Acquisition Device Channel with Sub-Cooled Oxygen”, World Academy of Science, Engineering and Technology, Vol. 3, 2009, pp. 144-149
    8. McQuillen, J. B., Chao, D. F., Hall, N. R., Motil, B. J., Zhang, N., CFD simulation of Flow in Capillary Flow Liquid Acquisition Device Channel”, World Academy of Science, Engineering and Technology, Vol. 6, 2012, pp. 640-646
    9. Hartwig, J., Chato, D., McQuillen, J.,  Screen Channel LAD Bubble Point Tests in Liquid Hydrogen”, International Journal of Hydrogen Energy, Vol. 39, No. 2, 2014, pp. 853-861
    10. Fischer, A., Gerstmann, J., “Flow Resistance of Metallic Screens in Liquid, Gaseous and Cryogenic Flow”, 5th European Conferencefor Aeronautics and Space Sciences, Munich, Germany, 2013
    11. Fries, N., Odic, K., Dreyer, M., Wickingof Perfectly Wetting Liquids into a MetallicMesh”, 2nd International Conference onPorous Media and its Applications inScience and Engineering, 2007
    12. Seo, M, K., Kim, D, H., Seo, C, W., Lee, S, Y., Jang, S, P., Koo, J., “Experimental Study of Pressure Drop in CompressibleFluid through Porous Media”, Transactionsof the Korean Society of Mechanical Engineers – B, Vol. 37, No. 8, pp. 759-765, 2013.
    13. Hartwig, J., Mann, J. A., “Bubble Point Pressures of Binary Methanol/Water Mixtures in Fine-Mesh Screens”, AlChEJournal, Vol. 60, No. 2, 2014, pp. 730-739

    이종 금속 인터커넥트의 펄스 레이저 용접을 위한 가공 매개변수 최적화

    Optimization of processing parameters for pulsed laser welding of dissimilar metal interconnects

    본 논문은 독자의 편의를 위해 기계번역된 내용이어서 자세한 내용은 원문을 참고하시기 바랍니다.

    NguyenThi TienaYu-LungLoabM.Mohsin RazaaCheng-YenChencChi-PinChiuc

    aNational Cheng Kung University, Department of Mechanical Engineering, Tainan, Taiwan

    bNational Cheng Kung University, Academy of Innovative Semiconductor and Sustainable Manufacturing, Tainan, Taiwan

    cJum-bo Co., Ltd, Xinshi District, Tainan, Taiwan

    Abstract

    워블 전략이 포함된 펄스 레이저 용접(PLW) 방법을 사용하여 알루미늄 및 구리 이종 랩 조인트의 제조를 위한 최적의 가공 매개변수에 대해 실험 및 수치 조사가 수행됩니다. 피크 레이저 출력과 접선 용접 속도의 대표적인 조합 43개를 선택하기 위해 원형 패킹 설계 알고리즘이 먼저 사용됩니다.

    선택한 매개변수는 PLW 프로세스의 전산유체역학(CFD) 모델에 제공되어 용융 풀 형상(즉, 인터페이스 폭 및 침투 깊이) 및 구리 농도를 예측합니다. 시뮬레이션 결과는 설계 공간 내에서 PLW 매개변수의 모든 조합에 대한 용융 풀 형상 및 구리 농도를 예측하기 위해 3개의 대리 모델을 교육하는 데 사용됩니다.

    마지막으로, 대체 모델을 사용하여 구성된 처리 맵은 용융 영역에 균열이나 기공이 없고 향상된 기계적 및 전기적 특성이 있는 이종 조인트를 생성하는 PLW 매개변수를 결정하기 위해 세 가지 품질 기준에 따라 필터링됩니다.

    제안된 최적화 접근법의 타당성은 최적의 용접 매개변수를 사용하여 생성된 실험 샘플의 전단 강도, 금속간 화합물(IMC) 형성 및 전기 접촉 저항을 평가하여 입증됩니다.

    결과는 최적의 매개변수가 1209N의 높은 전단 강도와 86µΩ의 낮은 전기 접촉 저항을 생성함을 확인합니다. 또한 용융 영역에는 균열 및 기공과 같은 결함이 없습니다.

    An experimental and numerical investigation is performed into the optimal processing parameters for the fabrication of aluminum and copper dissimilar lap joints using a pulsed laser welding (PLW) method with a wobble strategy. A circle packing design algorithm is first employed to select 43 representative combinations of the peak laser power and tangential welding speed. The selected parameters are then supplied to a computational fluidic dynamics (CFD) model of the PLW process to predict the melt pool geometry (i.e., interface width and penetration depth) and copper concentration. The simulation results are used to train three surrogate models to predict the melt pool geometry and copper concentration for any combination of the PLW parameters within the design space. Finally, the processing maps constructed using the surrogate models are filtered in accordance with three quality criteria to determine the PLW parameters that produce dissimilar joints with no cracks or pores in the fusion zone and enhanced mechanical and electrical properties. The validity of the proposed optimization approach is demonstrated by evaluating the shear strength, intermetallic compound (IMC) formation, and electrical contact resistance of experimental samples produced using the optimal welding parameters. The results confirm that the optimal parameters yield a high shear strength of 1209 N and a low electrical contact resistance of 86 µΩ. Moreover, the fusion zone is free of defects, such as cracks and pores.

    Fig. 1. Schematic illustration of Al-Cu lap-joint arrangement
    Fig. 1. Schematic illustration of Al-Cu lap-joint arrangement
    Fig. 2. Machine setup (MFQS-150W_1500W
    Fig. 2. Machine setup (MFQS-150W_1500W
    Fig. 5. Lap-shear mechanical tests: (a) experimental setup and specimen dimensions, and (b) two different failures of lap-joint welding.
N. Thi Tien et al.
    Fig. 5. Lap-shear mechanical tests: (a) experimental setup and specimen dimensions, and (b) two different failures of lap-joint welding. N. Thi Tien et al.
    Fig. 9. Simulation and experimental results for melt pool profile. (a) Simulation results for melt pool cross-section, and (b) OM image of melt pool cross-section.
(Note that laser processing parameter of 830 W and 565 mm/s is chosen.).
    Fig. 9. Simulation and experimental results for melt pool profile. (a) Simulation results for melt pool cross-section, and (b) OM image of melt pool cross-section. (Note that laser processing parameter of 830 W and 565 mm/s is chosen.).

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    Fig. 1. Schematic figure showing the PREP with additional gas flowing on the end face of electrode.

    플라즈마 회전 전극 공정 중 분말 형성에 대한 공정 매개변수 및 냉각 가스의 영향

    Effects of process parameters and cooling gas on powder formation during the plasma rotating electrode process

    Yujie Cuia Yufan Zhaoa1 Haruko Numatab Kenta Yamanakaa Huakang Biana Kenta Aoyagia AkihikoChibaa
    aInstitute for Materials Research, Tohoku University, Sendai 980-8577, JapanbDepartment of Materials Processing, Graduate School of Engineering, Tohoku University, Sendai 980-8577, Japan

    Highlights

    •The limitation of increasing the rotational speed in decreasing powder size was clarified.

    •Cooling and disturbance effects varied with the gas flowing rate.

    •Inclined angle of the residual electrode end face affected powder formation.

    •Additional cooling gas flowing could be applied to control powder size.

    Abstract

    The plasma rotating electrode process (PREP) is rapidly becoming an important powder fabrication method in additive manufacturing. However, the low production rate of fine PREP powder limits the development of PREP. Herein, we investigated different factors affecting powder formation during PREP by combining experimental methods and numerical simulations. The limitation of increasing the rotation electrode speed in decreasing powder size is attributed to the increased probability of adjacent droplets recombining and the decreased tendency of granulation. The effects of additional Ar/He gas flowing on the rotational electrode on powder formation is determined through the cooling effect, the disturbance effect, and the inclined effect of the residual electrode end face simultaneously. A smaller-sized powder was obtained in the He atmosphere owing to the larger inclined angle of the residual electrode end face compared to the Ar atmosphere. Our research highlights the route for the fabrication of smaller-sized powders using PREP.

    플라즈마 회전 전극 공정(PREP)은 적층 제조 에서 중요한 분말 제조 방법으로 빠르게 자리잡고 있습니다. 그러나 미세한 PREP 분말의 낮은 생산율은 PREP의 개발을 제한합니다. 여기에서 우리는 실험 방법과 수치 시뮬레이션을 결합하여 PREP 동안 분말 형성에 영향을 미치는 다양한 요인을 조사했습니다. 분말 크기 감소에서 회전 전극 속도 증가의 한계는 인접한 액적 재결합 확률 증가 및 과립화 경향 감소에 기인합니다.. 회전 전극에 흐르는 추가 Ar/He 가스가 분말 형성에 미치는 영향은 냉각 효과, 외란 효과 및 잔류 전극 단면의 경사 효과를 통해 동시에 결정됩니다. He 분위기에서는 Ar 분위기에 비해 잔류 전극 단면의 경사각이 크기 때문에 더 작은 크기의 분말이 얻어졌다. 우리의 연구는 PREP를 사용하여 더 작은 크기의 분말을 제조하는 경로를 강조합니다.

    Keywords

    Plasma rotating electrode process

    Ti-6Al-4 V alloy, Rotating speed, Numerical simulation, Gas flowing, Powder size

    Introduction

    With the development of additive manufacturing, there has been a significant increase in high-quality powder production demand [1,2]. The initial powder characteristics are closely related to the uniform powder spreading [3,4], packing density [5], and layer thickness observed during additive manufacturing [6], thus determining the mechanical properties of the additive manufactured parts [7,8]. Gas atomization (GA) [9–11], centrifugal atomization (CA) [12–15], and the plasma rotating electrode process (PREP) are three important powder fabrication methods.

    Currently, GA is the dominant powder fabrication method used in additive manufacturing [16] for the fabrication of a wide range of alloys [11]. GA produces powders by impinging a liquid metal stream to droplets through a high-speed gas flow of nitrogen, argon, or helium. With relatively low energy consumption and a high fraction of fine powders, GA has become the most popular powder manufacturing technology for AM.

    The entrapped gas pores are generally formed in the powder after solidification during GA, in which the molten metal is impacted by a high-speed atomization gas jet. In addition, satellites are formed in GA powder when fine particles adhere to partially molten particles.

    The gas pores of GA powder result in porosity generation in the additive manufactured parts, which in turn deteriorates its mechanical properties because pores can become crack initiation sites [17]. In CA, a molten metal stream is poured directly onto an atomizer disc spinning at a high rotational speed. A thin film is formed on the surface of the disc, which breaks into small droplets due to the centrifugal force. Metal powder is obtained when these droplets solidify.

    Compared with GA powder, CA powder exhibits higher sphericity, lower impurity content, fewer satellites, and narrower particle size distribution [12]. However, very high speed is required to obtain fine powder by CA. In PREP, the molten metal, melted using the plasma arc, is ejected from the rotating rod through centrifugal force. Compared with GA powder, PREP-produced powders also have higher sphericity and fewer pores and satellites [18].

    For instance, PREP-fabricated Ti6Al-4 V alloy powder with a powder size below 150 μm exhibits lower porosity than gas-atomized powder [19], which decreases the porosity of additive manufactured parts. Furthermore, the process window during electron beam melting was broadened using PREP powder compared to GA powder in Inconel 718 alloy [20] owing to the higher sphericity of the PREP powder.

    In summary, PREP powder exhibits many advantages and is highly recommended for powder-based additive manufacturing and direct energy deposition-type additive manufacturing. However, the low production rate of fine PREP powder limits the widespread application of PREP powder in additive manufacturing.

    Although increasing the rotating speed is an effective method to decrease the powder size [21,22], the reduction in powder size becomes smaller with the increased rotating speed [23]. The occurrence of limiting effects has not been fully clarified yet.

    Moreover, the powder size can be decreased by increasing the rotating electrode diameter [24]. However, these methods are quite demanding for the PREP equipment. For instance, it is costly to revise the PREP equipment to meet the demand of further increasing the rotating speed or electrode diameter.

    Accordingly, more feasible methods should be developed to further decrease the PREP powder size. Another factor that influences powder formation is the melting rate [25]. It has been reported that increasing the melting rate decreases the powder size of Inconel 718 alloy [26].

    In contrast, the powder size of SUS316 alloy was decreased by decreasing the plasma current within certain ranges. This was ascribed to the formation of larger-sized droplets from fluid strips with increased thickness and spatial density at higher plasma currents [27]. The powder size of NiTi alloy also decreases at lower melting rates [28]. Consequently, altering the melting rate, varied with the plasma current, is expected to regulate the PREP powder size.

    Furthermore, gas flowing has a significant influence on powder formation [27,29–31]. On one hand, the disturbance effect of gas flowing promotes fluid granulation, which in turn contributes to the formation of smaller-sized powder [27]. On the other hand, the cooling effect of gas flowing facilitates the formation of large-sized powder due to increased viscosity and surface tension. However, there is a lack of systematic research on the effect of different gas flowing on powder formation during PREP.

    Herein, the authors systematically studied the effects of rotating speed, electrode diameter, plasma current, and gas flowing on the formation of Ti-6Al-4 V alloy powder during PREP as additive manufactured Ti-6Al-4 V alloy exhibits great application potential [32]. Numerical simulations were conducted to explain why increasing the rotating speed is not effective in decreasing powder size when the rotation speed reaches a certain level. In addition, the different factors incited by the Ar/He gas flowing on powder formation were clarified.

    Fig. 1. Schematic figure showing the PREP with additional gas flowing on the end face of electrode.
    Fig. 1. Schematic figure showing the PREP with additional gas flowing on the end face of electrode.

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    Liquid-solid co-printing of multi-material 3D fluidic devices via material jetting

    재료 분사를 통한 다중 재료 3D 유체 장치의 액체-고체 공동 인쇄

    Liquid-solid co-printing of multi-material 3D fluidic devices via material jetting

    BrandonHayes,Travis Hainsworth, Robert MacCurdy
    University of Colorado Boulder, Department of Mechanical Engineering, Boulder, 80309, CO, USA

    Abstract

    다중 재료 재료 분사 적층 제조 공정은 3차원(3D) 부품을 레이어별로 구축하기 위해 다양한 모델 및 지지 재료의 미세 액적을 증착합니다.

    최근의 노력은 액체가 마이크로/밀리 채널에서 쉽게 퍼지할 수 있는 지지 재료로 작용할 수 있고 구조에 영구적으로 남아 있는 작동 유체로 작용할 수 있음을 보여주었지만 인쇄 프로세스 및 메커니즘에 대한 자세한 이해가 부족합니다.

    액체 인쇄의 제한된 광범위한 적용. 이 연구에서 광경화성 및 광경화성 액체 방울이 동시에 증착되는 액체-고체 공동 인쇄라고 하는 “한 번에 모두 가능한” 다중 재료 인쇄 프로세스가 광범위하게 특성화됩니다. 액체-고체 공동 인쇄의 메커니즘은 실험적인 고속 이미징 및 CFD(전산 유체 역학) 연구를 통해 설명됩니다.

    이 연구는 액체의 표면 장력이 액체 표면에서 광중합하여 재료의 단단한 층을 형성하는 분사된 광중합체 미세 방울을 지지할 수 있음을 보여줍니다.

    마이크로/밀리 유체 소자의 액체-고체 공동 인쇄를 위한 설계 규칙은 믹서, 액적 발생기, 고도로 분기되는 구조 및 통합된 단방향 플랩 밸브와 같은 평면, 3D 및 복합 재료 마이크로/메조 유체 구조에 대한 사례 연구뿐만 아니라 제시됩니다.

    우리는 액체-고체 공동 인쇄 과정을 마이크로/메조플루이딕 회로, 전기화학 트랜지스터, 칩 장치 및 로봇을 포함한 응용 프로그램을 사용하여 3D, 통합된 복합 재료 유체 회로 및 유압 구조의 단순하고 빠른 제작을 가능하게 하는 적층 제조의 핵심 새로운 기능으로 구상합니다.

    Multi-material material jetting additive manufacturing processes deposit micro-scale droplets of different model and support materials to build three-dimensional (3D) parts layer by layer. Recent efforts have demonstrated that liquids can act as support materials, which can be easily purged from micro/milli-channels, and as working fluids, which permanently remain in a structure, yet the lack of a detailed understanding of the print process and mechanism has limited widespread applications of liquid printing. In this study, an “all in one go” multi-material print process, herein termed liquid–solid co-printing in which non photo-curable and photo-curable liquid droplets are simultaneous deposited, is extensively characterized. The mechanism of liquid–solid co-printing is explained via experimental high speed imaging and computational fluid dynamic (CFD) studies. This work shows that a liquid’s surface tension can support jetted photopolymer micro-droplets which photo-polymerize on the liquid surface to form a solid layer of material. Design rules for liquid–solid co-printing of micro/milli-fluidic devices are presented as well as case studies of planar, 3D, and multi-material micro/mesofluidic structures such as mixers, droplet generators, highly branching structures, and an integrated one-way flap valve. We envision the liquid–solid co-printing process as a key new capability in additive manufacturing to enable simple and rapid fabrication of 3D, integrated print-in-place multi-material fluidic circuits and hydraulic structures with applications including micro/mesofluidic circuits, electrochemical transistors, lab-on-a-chip devices, and robotics.

    Liquid-solid co-printing of multi-material 3D fluidic devices via material jetting
    Liquid-solid co-printing of multi-material 3D fluidic devices via material jetting

    Keywords

    Additive manufacturing; Mesofluidics; Modeling and simulation; Multi-material; Material jetting

    Figure 3: 3D temperature contours and 2D melt pool cross-sections where the melt pool is stabilized at x=500 µm from the start of the laser initial location for cases where (a) absorptivity = 0.1, Recoil pressure coefficient B = 1 and laser beam radius = 12 µm, (b) absorptivity = 0.1, Recoil pressure coefficient B = 20 and laser beam radius = 12 µm, (c) absorptivity = 0.1, Recoil pressure coefficient B = 1 and laser beam radius = 18 µm, (d) absorptivity = 0.45, Recoil pressure coefficient B = 1 and laser beam radius = 18 µm, (e) absorptivity = 0.45, Recoil pressure coefficient B = 20 and laser beam radius = 12 µm, (f) absorptivity = 0.45, Recoil pressure coefficient B = 20 and laser beam radius = 18 µm.

    MULTI-PHYSICS NUMERICAL MODELLING OF 316L AUSTENITIC STAINLESS STEEL IN LASER POWDER BED FUSION PROCESS AT MESO-SCALE

    W.E. Alphonso1, M.Bayat1,*, M. Baier 2, S. Carmignato2, J.H. Hattel1
    1Department of Mechanical Engineering, Technical University of Denmark (DTU), Lyngby, Denmark
    2Department of Management and Engineering – University of Padova, Padova, Italy

    ABSTRACT

    L-PBF(Laser Powder Bed Fusion)는 레이저 열원을 사용하여 선택적으로 통합되는 분말 층으로 복잡한 3D 금속 부품을 만드는 금속 적층 제조(MAM) 기술입니다. 처리 영역은 수십 마이크로미터 정도이므로 L-PBF를 다중 규모 제조 공정으로 만듭니다.

    기체 기공의 형성 및 성장 및 용융되지 않은 분말 영역의 생성은 다중물리 모델에 의해 예측할 수 있습니다. 또한 이러한 모델을 사용하여 용융 풀 모양 및 크기, 온도 분포, 용융 풀 유체 흐름 및 입자 크기 및 형태와 같은 미세 구조 특성을 계산할 수 있습니다.

    이 작업에서는 용융, 응고, 유체 흐름, 표면 장력, 열 모세관, 증발 및 광선 추적을 통한 다중 반사를 포함하는 스테인리스 스틸 316-L에 대한 충실도 다중 물리학 중간 규모 수치 모델이 개발되었습니다. 완전한 실험 설계(DoE) 방법을 사용하는 통계 연구가 수행되었으며, 여기서 불확실한 재료 특성 및 공정 매개변수, 즉 흡수율, 반동 압력(기화) 및 레이저 빔 크기가 용융수지 모양 및 크기에 미치는 영향을 분석했습니다.

    또한 용융 풀 역학에 대한 위에서 언급한 불확실한 입력 매개변수의 중요성을 강조하기 위해 흡수율이 가장 큰 영향을 미치고 레이저 빔 크기가 그 뒤를 잇는 주요 효과 플롯이 생성되었습니다. 용융 풀 크기에 대한 반동 압력의 중요성은 흡수율에 따라 달라지는 용융 풀 부피와 함께 증가합니다.

    모델의 예측 정확도는 유사한 공정 매개변수로 생성된 단일 트랙 실험과 시뮬레이션의 용융 풀 모양 및 크기를 비교하여 검증됩니다.

    더욱이, 열 렌즈 효과는 레이저 빔 크기를 증가시켜 수치 모델에서 고려되었으며 나중에 결과적인 용융 풀 프로파일은 모델의 견고성을 보여주기 위한 실험과 비교되었습니다.

    Laser Powder Bed Fusion (L-PBF) is a Metal Additive Manufacturing (MAM) technology where a complex 3D metal part is built from powder layers, which are selectively consolidated using a laser heat source. The processing zone is in the order of a few tenths of micrometer, making L-PBF a multi-scale manufacturing process. The formation and growth of gas pores and the creation of un-melted powder zones can be predicted by multiphysics models. Also, with these models, the melt pool shape and size, temperature distribution, melt pool fluid flow and its microstructural features like grain size and morphology can be calculated. In this work, a high fidelity multi-physics meso-scale numerical model is developed for stainless steel 316-L which includes melting, solidification, fluid flow, surface tension, thermo-capillarity, evaporation and multiple reflection with ray-tracing. A statistical study using a full Design of Experiments (DoE) method was conducted, wherein the impact of uncertain material properties and process parameters namely absorptivity, recoil pressure (vaporization) and laser beam size on the melt pool shape and size was analysed. Furthermore, to emphasize on the significance of the above mentioned uncertain input parameters on the melt pool dynamics, a main effects plot was created which showed that absorptivity had the highest impact followed by laser beam size. The significance of recoil pressure on the melt pool size increases with melt pool volume which is dependent on absorptivity. The prediction accuracy of the model is validated by comparing the melt pool shape and size from the simulation with single track experiments that were produced with similar process parameters. Moreover, the effect of thermal lensing was considered in the numerical model by increasing the laser beam size and later on the resultant melt pool profile was compared with experiments to show the robustness of the model.

    Figure 1: a) Computational domain for single track L-PBF which includes a 200 μm thick substrate and 45 μm powder layer thickness b) 3D temperature contour plot after scanning a single track with melt pool contours at two locations along the scanning direction where the green region indicates the melted regions.
    Figure 1: a) Computational domain for single track L-PBF which includes a 200 μm thick substrate and 45 μm powder layer thickness b) 3D temperature contour plot after scanning a single track with melt pool contours at two locations along the scanning direction where the green region indicates the melted regions.
    Figure 2: Main effects plot of uncertain parameters: absorptivity, recoil pressure coefficient and laser beam radius on the melt pool dimensions (width and depth)
    Figure 2: Main effects plot of uncertain parameters: absorptivity, recoil pressure coefficient and laser beam radius on the melt pool dimensions (width and depth)
    Figure 3: 3D temperature contours and 2D melt pool cross-sections where the melt pool is stabilized at x=500 µm from the start of the laser initial location for cases where (a) absorptivity = 0.1, Recoil pressure coefficient B = 1 and laser beam radius = 12 µm, (b) absorptivity = 0.1, Recoil pressure coefficient B = 20 and laser beam radius = 12 µm, (c) absorptivity = 0.1, Recoil pressure coefficient B = 1 and laser beam radius = 18 µm, (d) absorptivity = 0.45, Recoil pressure coefficient B = 1 and laser beam radius = 18 µm, (e) absorptivity = 0.45, Recoil pressure coefficient B = 20 and laser beam radius = 12 µm, (f) absorptivity = 0.45, Recoil pressure coefficient B = 20 and laser beam radius = 18 µm.
    Figure 3: 3D temperature contours and 2D melt pool cross-sections where the melt pool is stabilized at x=500 µm from the start of the laser initial location for cases where (a) absorptivity = 0.1, Recoil pressure coefficient B = 1 and laser beam radius = 12 µm, (b) absorptivity = 0.1, Recoil pressure coefficient B = 20 and laser beam radius = 12 µm, (c) absorptivity = 0.1, Recoil pressure coefficient B = 1 and laser beam radius = 18 µm, (d) absorptivity = 0.45, Recoil pressure coefficient B = 1 and laser beam radius = 18 µm, (e) absorptivity = 0.45, Recoil pressure coefficient B = 20 and laser beam radius = 12 µm, (f) absorptivity = 0.45, Recoil pressure coefficient B = 20 and laser beam radius = 18 µm.
    Figure 4: Validation of Numerical model with Recoil pressure coefficient B= 20, absorptivity = 0.45 and a) laser beam radius = 15 µm b) laser beam radius = 20 µm
    Figure 4: Validation of Numerical model with Recoil pressure coefficient B= 20, absorptivity = 0.45 and a) laser beam radius = 15 µm b) laser beam radius = 20 µm

    CONCLUSION

    In this work, a high-fidelity multi-physics numerical model was developed for L-PBF using the FVM method in Flow-3D. The impact of uncertainty in the input parameters including absorptivity, recoil pressure and laser beam size on the melt pool is addressed using a DoE method. The DoE analysis shows that absorptivity has the highest impact on the melt pool. The recoil pressure and laser beam size only become significant once absorptivity is 0.45. Furthermore, the numerical model is validated by comparing the predicted melt pool shape and size with experiments conducted with similar process parameters wherein a high prediction accuracy is achieved by the model. In addition, the impact of thermal lensing on the melt pool dimensions by increasing the laser beam spot size is considered in the validated numerical model and the resultant melt pool is compared with experiments.

    REFERENCES

    [1] T. Bonhoff, M. Schniedenharn, J. Stollenwerk, P. Loosen, Experimental and theoretical analysis of thermooptical effects in protective window for selective laser melting, Proc. Int. Conf. Lasers Manuf. LiM. (2017)
    26–29. https://www.wlt.de/lim/Proceedings2017/Data/PDF/Contribution31_final.pdf.
    [2] L.R. Goossens, Y. Kinds, J.P. Kruth, B. van Hooreweder, On the influence of thermal lensing during selective
    laser melting, Solid Free. Fabr. 2018 Proc. 29th Annu. Int. Solid Free. Fabr. Symp. – An Addit. Manuf. Conf.
    SFF 2018. (2020) 2267–2274.
    [3] J. Shinjo, C. Panwisawas, Digital materials design by thermal-fluid science for multi-metal additive
    manufacturing, Acta Mater. 210 (2021) 116825. https://doi.org/10.1016/j.actamat.2021.116825.
    [4] Z. Zhang, Y. Huang, A. Rani Kasinathan, S. Imani Shahabad, U. Ali, Y. Mahmoodkhani, E. Toyserkani, 3-
    Dimensional heat transfer modeling for laser powder-bed fusion additive manufacturing with volumetric heat
    sources based on varied thermal conductivity and absorptivity, Opt. Laser Technol. 109 (2019) 297–312.
    https://doi.org/10.1016/j.optlastec.2018.08.012.
    [5] M. Bayat, A. Thanki, S. Mohanty, A. Witvrouw, S. Yang, J. Thorborg, N.S. Tiedje, J.H. Hattel, Keyholeinduced porosities in Laser-based Powder Bed Fusion (L-PBF) of Ti6Al4V: High-fidelity modelling and
    experimental validation, Addit. Manuf. 30 (2019) 100835. https://doi.org/10.1016/j.addma.2019.100835.
    [6] M. Bayat, S. Mohanty, J.H. Hattel, Multiphysics modelling of lack-of-fusion voids formation and evolution
    in IN718 made by multi-track/multi-layer L-PBF, Int. J. Heat Mass Transf. 139 (2019) 95–114.
    https://doi.org/10.1016/j.ijheatmasstransfer.2019.05.003.
    [7] J. Metelkova, Y. Kinds, K. Kempen, C. de Formanoir, A. Witvrouw, B. Van Hooreweder, On the influence
    of laser defocusing in Selective Laser Melting of 316L, Addit. Manuf. 23 (2018) 161–169.
    https://doi.org/10.1016/j.addma.2018.08.006.

    Effect of roughness on separation zone dimensions.

    Experimental and numerical study of flow at a 90 degree lateral turnout with enhanced roughness coefficient and invert level changes

    조도 계수 및 역전 수준 변화가 개선된 90도 측면 분출구에서의 유동에 대한 실험적 및 수치적 연구

    Maryam BagheriSeyed M. Ali ZomorodianMasih ZolghadrH. Md. AzamathullaC. Venkata Siva Rama Prasad

    Abstract

    측면 분기기(흡입구)의 상류 측에서 흐름 분리는 분기기 입구에서 와류를 일으키는 중요한 문제입니다. 이는 흐름의 유효 폭, 출력 용량 및 효율성을 감소시킵니다. 따라서 분리지대의 크기를 파악하고 크기를 줄이기 위한 방안을 제시하는 것이 필수적이다. 본 연구에서는 분리 구역의 치수를 줄이기 위한 방법으로 7가지 유형의 거칠기 요소를 분기구 입구에 설치하고 4가지 다른 배출(총 84번의 실험을 수행)과 함께 3개의 서로 다른 베드 반전 레벨을 조사했습니다. 또한 3D CFD(Computational Fluid Dynamics) 모델을 사용하여 분리 영역의 흐름 패턴과 치수를 평가했습니다. 결과는 거칠기 계수를 향상시키면 분리 영역 치수를 최대 38%까지 줄일 수 있는 반면, 드롭 구현 효과는 사용된 거칠기 계수를 기반으로 이 영역을 다르게 축소할 수 있음을 보여주었습니다. 두 가지 방법을 결합하면 분리 영역 치수를 최대 63%까지 줄일 수 있습니다.

    Flow separation at the upstream side of lateral turnouts (intakes) is a critical issue causing eddy currents at the turnout entrance. It reduces the effective width of flow, turnout capacity and efficiency. Therefore, it is essential to identify the dimensions of the separation zone and propose remedies to reduce its dimensions. Installation of 7 types of roughening elements at the turnout entrance and 3 different bed invert levels, with 4 different discharges (making a total of 84 experiments) were examined in this study as a method to reduce the dimensions of the separation zone. Additionally, a 3-D Computational Fluid Dynamic (CFD) model was utilized to evaluate the flow pattern and dimensions of the separation zone. Results showed that enhancing the roughness coefficient can reduce the separation zone dimensions up to 38% while the drop implementation effect can scale down this area differently based on the roughness coefficient used. Combining both methods can reduce the separation zone dimensions up to 63%.

    HIGHLIGHTS

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    • Flow separation at the upstream side of lateral turnouts (intakes) is a critical issue causing eddy currents at the turnout entrance.
    • Installation of 7 types of roughening elements at the turnout entrance and 3 different bed level inverts were investigated.
    • Additionally, a 3-D Computational Fluid Dynamic (CFD) model was utilized to evaluate the flow.
    • Combining both methods can reduce the separation zone dimensions by up to 63%.
    Experimental and numerical study of flow at a 90 degree lateral turnout with enhanced roughness coefficient and invert level changes
    Experimental and numerical study of flow at a 90 degree lateral turnout with enhanced roughness coefficient and invert level changes

    Keywords

    discharge ratioflow separation zoneintakethree dimensional simulation

    INTRODUCTION

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    Turnouts or intakes are amongst the oldest and most widely used hydraulic structures in irrigation networks. Turnouts are also used in water distribution, transmission networks, power generation facilities, and waste water treatment plants etc. The flows that enter a turnout have a strong momentum in the direction of the main waterway and that is why flow separation occurs inside the turnout. The horizontal vortex formed in the separation area is a suitable place for accumulation and deposition of sediments. The separation zone is a vulnerable area for sedimentation and for reduction of effective flow due to a contracted flow region in the lateral channel. Sedimentaion in the entrance of the intake can gradually be transfered into the lateral channel and decrease the capacity of the higher order channels over time (Jalili et al. 2011). On the other hand, the existence of coarse-grained materials causes erosion and destruction of the waterway side walls and bottom. In addition, sedimentation creates conditions for vegetation to take root and damage the waterway cover, which causes water to leak from its perimeter. Therefore, it is important to investigate the pattern of the flow separation area in turnouts and provide solutions to reduce the dimensions of this area.

    The three-dimensional flow structure at turnouts is quite complex. In an experimental study by Neary & Odgaard (1993) in a 90-degree water turnout it was found that the secondary currents and separation zone varies from the bed to the water surface. They also found that at a 90-degree water turnout, the bed roughness and discharge ratio play a critical role in flow structure. They asserted that an explanation of sediment behavior at a diversion entrance requires a comprehensive understanding of 3D flow patterns around the lateral-channel entrance. In addition, they suggested that there is a strong similarity between flow in a channel bend and a diversion channel, and that this similarity can rationalize the use of bend flow models for estimation of 3D flow structures in diversion channels.

    Some of the distinctive characteristics of dividing flow in a turnout include a zone of separation immediately near the entrance of the lateral turnout (separation zone), a contracted flow region in the branch channel (contracted flow), and a stagnation point near the downstream corner of the junction (stagnation zone). In the region downstream of the junction, along the continuous far wall, separation due to flow expansion may occur (Ramamurthy et al. 2007), that is, a separation zone. This can both reduce the turnout efficiency and the effective width of flow while increasing the sediment deposition in the turnout entrance (Jalili et al. 2011). Installation of submerged vanes in the turnout entrance is a method which is already applied to reduce the size of flow separation zones. The separation zone draws sediments and floating materials into themselves. This reduces effective cross-section area and reduces transmission capacity. These results have also been obtained in past studies, including by Ramamurthy et al. (2007) and in Jalili et al. (2011). Submerged vanes (Iowa vanes) are designed in order to modify the near-bed flow pattern and bed-sediment motion in the transverse direction of the river. The vanes are installed vertically on the channel bed, at an angle of attack which is usually oriented at 10–25 degrees to the local primary flow direction. Vane height is typically 0.2–0.5 times the local water depth during design flow conditions and vane length is 2–3 times its height (Odgaard & Wang 1991). They are vortex-generating devices that generate secondary circulation, thereby redistributing sediment within the channel cross section. Several factors affect the flow separation zone such as the ratio of lateral turnout discharge to main channel discharge, angle of lateral channel with respect to the main channel flow direction and size of applied submerged vanes. Nakato et al. (1990) found that sediment management using submerged vanes in the turnout entrance to Station 3 of the Council Bluffs plant, located on the Missouri River, is applicable and efficient. The results show submerged vanes are an appropriate solution for reduction of sediment deposition in a turnout entrance. The flow was treated as 3D and tests results were obtained for the flow characteristics of dividing flows in a 90-degree sharp-edged, junction. The main and lateral channel were rectangular with the same dimensions (Ramamurthy et al., 2007).

    Keshavarzi & Habibi (2005) carried out experiments on intake with angles of 45, 67, 79 and 90 degrees in different discharge ratios and reported the optimum angle for inlet flow with the lowest flow separation area to be about 55 degrees. The predicted flow characteristics were validated using experimental data. The results indicated that the width and length of the separation zone increases with the increase in the discharge ratio Qr (ratio of outflow per unit width in the turnout to inflow per unit width in the main channel).

    Abbasi et al. (2004) performed experiments to investigate the dimensions of the flow separation zone at a lateral turnout entrance. They demonstrated that the length and width of the separation zone decreases with the increasing ratio of lateral turn-out discharge. They also found that with a reducing angle of lateral turnout, the length of the separation zone scales up and width of separation zone reduces. Then they compared their observations with results of Kasthuri & Pundarikanthan (1987) who conducted some experiments in an open-channel junction formed by channels of equal width and an angle of lateral 90 degree turnout, which showed the dimensions of the separation zone in their experiments to be smaller than in previous studies. Kasthuri & Pundarikanthan (1987) studied vortex and flow separation dimensions at the entrance of a 90 degree channel. Results showed that increasing the diversion discharge ratio can reduce the length and width of the vortex area. They also showed that the length and width of the vortex area remain constant at diversion ratios greater than 0.7. Karami Moghaddam & Keshavarzi (2007) analyzed the flow characteristics in turnouts with angles of 55 and 90 degrees. They reported that the dimensions of the separation zone decrease by increasing the discharge ratio and reducing the turnout angle with respect to the main channel. Studies about flow separation zone can be found in Jalili et al. (2011)Nikbin & Borghei (2011)Seyedian et al. (2008).

    Jamshidi et al. (2016) measured the dimensions of a flow separation zone in the presence of submerged vanes with five arrangements (parallel, stagger, compound, piney and butterflies). Results showed that the ratio of the width to the length of the separation zone (shape index) was between 0.2 and 0.28 for all arrangements.

    Karami et al. (2017) developed a 3D computational fluid dynamic (CFD) code which was calibrated by measured data. They used the model to evaluate flow pattern, diversion ratio of discharge, strength of the secondary flow, and dimensions of the vortex inside the channel in various dikes and submerged vane installation scenarios. Results showed that the diversion ratio of discharge in the diversion channel is dependent on the width of the flow separation area in the main channel. A dike, perpendicular to the flow, doubles the ratio of diverted discharge and reduces the suspended sediment load compared with the base-line situation by creating outer arch conditions. In addition, increasing the longitudinal distance between vanes increases the velocity gradient between the vanes and leads to a more severe erosion of the bed near the vanes.Figure 1VIEW LARGEDOWNLOAD SLIDE

    Laboratory channel dimensions.

    Al-Zubaidy & Hilo (2021) used the Navier–Stokes equation to study the flow of incompressible fluids. Using the CFD software ANSYS Fluent 19.2, 3D flow patterns were simulated at a diversion channel. Their results showed good agreement using the comparison between the experimental and numerical results when the k-omega turbulence viscous model was employed. Simulation of the flow pattern was then done at the lateral channel junction using a variety of geometry designs. These improvements included changing the intake’s inclination angle and chamfering and rounding the inner corner of the intake mouth instead of the sharp edge. Flow parameters at the diversion including velocity streamlines, bed shear stress, and separation zone dimensions were computed in their study. The findings demonstrated that changing the 90° lateral intake geometry can improve the flow pattern and bed shear stress at the intake junction. Consequently, sedimentation and erosion problems are reduced. According to the conclusions of their study, a branching angle of 30° to 45° is the best configuration for increasing branching channel discharge, lowering branching channel sediment concentration.

    The review of the literature shows that most of the studies deal with turnout angle, discharge ratio and implementation of vanes as techniques to reduce the area of the separation zone. This study examines the effect of roughness coefficient and drop implementation at the entrance of a 90-degree lateral turnout on the dimensions of the separation zone. As far as the authors are aware, these two variables have never been studied as a remedy to decrease the separation zone dimensions whilst enhancing turnout efficiency. Additionally, a three-dimensional numerical model is applied to simulate the flow pattern around the turnout. The numerical results are verified against experimental data.

    METHOD

    Experimental setup

    Listen

    The experiments were conducted in a 90 degree dividing flow laboratory channel. The main channel is 15 m long, 0.5 m wide and 0.4 m high and the branch channel is 3 m long, 0.35 m wide and 0.4 m high, as shown in Figure 1. The tests were carried out at 9.65 m from the beginning of the flume and were far enough from the inlet, so we were sure that the flow was fully developed. According to Kirkgöz & Ardiçlioğlu (1997) the length of the developing region would be approximantly 65 and 72 times the flow depth. In this study, the depth is 9 cm, which makes this condition.

    Both the main and lateral channel had a slope of 0.0003 with side walls of concrete. A 100 hp pump discharged the water into a stilling basin at the entrance of the main flume. The discharge was measured using an ultrasonic discharge meter around the discharge pipe. Eighty-four experiments in total were carried out at range of 0.1<Fr<0.4 (Froude numbers in main channel and upstream of turnout). The depth of water in the main channel in the experiments was 9 cm, in which case the effect of surface tension can be considered; according to research by Zolghadr & Shafai Bejestan (2020) and Zolghadr et al. (2021), when the water depth is more than 6 cm, the effect of surface tension is reduced and can be ignored given that the separation phenomenon occurs in the boundary layer, the height of the roughness creates disturbances in growth and development of the boundary layer and, as a result, separation growth is also faced with disruption and its dimensions grow less compared to smooth surfaces. Similar conditions occur in case of drop implementation. A disturbance occurs in the growth of the boundary layer and as a result the separation zone dimensions decrease. In order to investigate the effect of roughness coefficient and drop implementation on the separation zone dimensions, four different discharges (16, 18, 21, 23 l/s) in subcritical conditions, seven Manning (Strickler) roughness coefficients (0.009, 0.011, 0.017, 0.023, 0.028, 0.030, 0.032) as shown in Figure 2 and three invert elevation differences between the main channel and lateral turnout invert (0, 5 and 10 cm) at the entrance of the turnout were considered. The Manning roughness coefficient values were selected based on available and feasible values for real conditions, so that 0.009 is equivalent to galvanized sheet roughness and selected for the baseline tests. 0.011 is for concrete with neat surface, 0.017 and 0.023 are for unfinished and gunite concrete respectively. 0.030 and 0.032 values are for concrete on irregular excavated rock (Chow 1959). The roughness coefficients were created by gluing sediment particles on a thin galvanized sheet which was installed at the upstream side of the lateral turnout. The values of roughness coefficients were calculated based on the Manning-Strickler formula. For this purpose, some uniformly graded sediment samples were prepared and the Manning roughness coefficient of each sample was determined with respect to the median size (D50) value pasted into the Manning-Strickler formula. Some KMnO4 was sifted in the main channel upstream to visualize and measure the dimensions of the separation zone. Consequently, when KMnO4 approached the lateral turnout a photo of the separation zone was taken from a top view. All the experiments were recorded and several photos were taken during the experiment after stablishment of steady flow conditions. The photos were then imported to AutoCAD to measure the separation zone dimensions. Because all the shooting was done with a high-definition camera and it was possible to zoom in, the results are very accurate.Figure 2VIEW LARGEDOWNLOAD SLIDE

    Roughness plates.

    The velocity values were also recorded by a one-dimensional velocity meter at 15 cm distance from the turnout entrance and in transverse direction (perpendicular to the flow direction).

    The water level was also measured by depth gauges with a accuracy of 0.1 mm, and velocity in one direction with a single-dimensional KENEK LP 1100 with an accuracy of ±0.02 m/s (0–1 m/s), ± 0.04 m/s (1–2 m/s), ± 0.08 m/s (2–4 m/s), ±0.10 m/s (4–5 m/s).

    Numerical simulation

    ListenA FLOW-3D numerical model was utilized as a solver of the Navier-Stokes equation to simulate the three-dimensional flow field at the entrance of the turnout. The governing equations included continuity momentum equations. The continuity equation, regardless of the density of the fluid in the form of Cartesian coordinates x, y, and z, is as follows:

    formula

    (1)where uv, and w represent the velocity components in the x, y, and z directions, respectively; AxAy, and Az are the surface flow fractions in the xy, and z directions, respectively; VF denotes flow volume fraction; r is the density of the fluid; t is time; and Rsor refers to the source of the mass. Equations (2)–(4) show momentum equations in xy and z dimensions respectively :

    formula

    (2)

    formula

    (3)

    formula

    (4)where GxGy, and Gz are the accelerations caused by gravity in the xy, and z directions, respectively; and fxfy, and fz are the accelerations caused by viscosity in the xy, and z directions, respectively.

    The turbulence models used in this study were the renormalized group (RNG) models. Evaluation of the concordance of the mentioned models with experimental studies showed that the RNG model provides more accurate results.

    Two blocks of mesh were used to simulate the main channels and lateral turnout. The meshes were denser in the vicinity of the entrance of the turnout in order to increase the accuracy of computations. Boundary conditions for the main mesh block included inflow for the channel entrance (volumetric flow rate), outflow for the channel exit, ‘wall’ for the bed and the right boundary and ‘symmetry’ for the top (free surface) and left boundaries (turnout). The side wall roughness coefficient was given to the software as the Manning number in surface roughness of any component. Considering the restrictions in the available processor, a main mesh block with appropriate mesh size was defined to simulate the main flow field in the channel, while the nested mesh-block technique was utilized to create a very dense solution field near the roughness plate in order to provide accurate results around the plates and near the entrance of the lateral turnout. This technique reduced the number of required mesh elements by up to 60% in comparison with the method in which the mesh size of the main solution field was decreased to the required extent.

    The numerical outputs are verified against experimental data. The hydraulic characteristics of the experiment are shown in Table 1.Table 1

    Hydraulic conditions of the flow

    Q(L/s)FrY1 (m)Q2/Q1
    16 0.449 0.09 0.22 
    18 0.335 0.09 0.61 
    21 0.242 0.09 0.71 
    23 0.180 0.09 1.04 

    RESULTS AND DISCUSSION

    Experimental results

    Listen

    During the experiments, the dimensions of the separation zone were recorded with an HD camera. Some photos were imported to AutoCad software. Then, the separation zones dimensions were measured and compared in different scenarios.

    At the beginning, the flow pattern in the separation zone for four different hydraulic conditions was studied for seven different Manning roughness coefficients from 0.009 to 0.032. To compare the obtained results, roughness of 0.009 was considered as the base line. The percentage of reduction in separation zone area in different roughness coefficients is shown in Figure 3. According to this figure, by increasing the roughness of the turnout side wall, the separation zone area ratio reduces (ratio of separation zone area to turnout area). In other words, in any desired Froud number, the highest dimensions of the separation zone area are related to the lowest roughness coefficients. In Figure 3, ‘A’ is the area of the separation zone and ‘Ai’ represents the total area of the turnout.Figure 3VIEW LARGEDOWNLOAD SLIDE

    Effect of roughness on separation zone dimensions.Figure 4VIEW LARGEDOWNLOAD SLIDE

    Effect of roughness on separation zone dimensions.

    It should be mentioned that the separation zone dimensions change with depth, so that the area is larger at the surface than near the bed. This study measured the dimensions of this area at the surface. Figure 4 show exactly where the roughness elements were located.Figure 5VIEW LARGEDOWNLOAD SLIDE

    Comparison of separation zone for n=0.023 and n=0.032.

    Figure 5 shows images of the separation zone at n=0.023 and n=0.032 as examples, and show that the separation area at n=0.032 is smaller than that of n=0.023.

    The difference between the effect of the two 0.032 and 0.030 roughnesses is minor. In other words, the dimensions of the separation zone decreased by increasing roughness up to 0.030 and then remained with negligable changes.

    In the next step, the effect of intake invert relative to the main stream (drop) on the dimensions of the separation zone was investigated. To do this, three different invert levels were considered: (1) without drop; (2) a 5 cm drop between the main canal and intake canal; and (3) a 10 cm drop between the main canal and intake canal. The without drop mode was considered as the control state. Figure 6 shows the effect of drop implementation on separation zone dimensions. Tables 2 and 3 show the reduced percentage of separation zone areas in 5 and 10 cm drop compared to no drop conditions as the base line. It was found that the best results were obtained when a 10 cm drop was implemented.Table 2

    Decrease percentage of separation zone area in 5 cm drop

    Frn=0.011n=0.017n=0.023n=0.028n=0.030n=0.032
    0.08 10.56 11.06 25.27 33.03 35.57 36.5 
    0.121 7.66 11.14 11.88 15.93 34.59 36.25 
    0.353 1.38 2.63 8.17 14.39 31.20 31.29 
    0.362 11.54 19.56 25.73 37.89 38.31 

    Table 3

    Decrease percentage of separation zone area in 10 cm drop

    Frn=0.011n=0.017n=0.023n=0.028n=0.030n=0.032
    0.047 4.30 8.75 23.47 31.22 34.96 35.13 
    0.119 11.01 13.16 15.02 21.48 39.45 40.68 
    0.348 3.89 5.71 9.82 16.09 29 30.96 
    0.354 2.84 10.44 18.42 25.45 35.68 35.76 

    Figure 6VIEW LARGEDOWNLOAD SLIDE

    Effect of drop implementation on separation zone dimensions.

    The combined effect of drop and roughness is shown in Figure 7. According to this figure, by installing a drop structure at the entrance of the intake, the dimensions of the separation zone scales down in any desired roughness coefficient. Results indicated that by increasing the roughness coefficient or drop implementation individually, the separation zone area decreases up to 38 and 25% respectively. However, employing both techniques simultaneously can reduce the separation zone area up to 63% (Table 4). The reason for the reduction of the dimensions of the separation zone area by drop implementation can be attributed to the increase of discharge ratio. This reduces the dimensions of the separation zone area.Table 4

    Reduction in percentage of combined effect of roughness and 10 cm drop

    Qin=0.011n=0.017n=0.023n=0.028n=0.030n=0.032
    16 32.3 35.07 37.2 45.7 58.01 59.1 
    18 44.5 34.15 36.18 48.13 54.2 56.18 
    21 43.18 32.33 42.30 37.79 57.16 63.2 
    23 40.56 34.5 34.09 46.25 50.12 57.2 

    Figure 7VIEW LARGEDOWNLOAD SLIDE

    Combined effect of roughness and drop on separation zone dimensions.

    This method increases the discharge ratio (ratio of turnout to main channel discharge). The results are compatible with the literature. Some other researchers reported that increasing the discharge ratio can scale down the separation zone dimensions (Karami Moghaddam & Keshavarzi 2007Ramamurthy et al. 2007). However, these researchers employed other methods to enhance the discharge ratio. Drop implementation is simple and applicable in practice, since there is normally an elevation difference between the main and lateral canal in irrigation networks to ensure gravity flow occurance.

    Table 4 depicts the decrease in percentage of the separation zone compared to base line conditions in different arrangements of the combined tests.Figure 8VIEW LARGEDOWNLOAD SLIDE

    Velocity profiles for various roughness coefficients along turnout width.

    A comparison between the proposed methods introduced in this paper and traditional methods such as installation of submerged vanes, and changing the inlet geometry (angle, radius) was performed. Figure 8 shows the comparison of the results. The comparison shows that the new techniques can be highly influential and still practical. In this research, with no change in structural geometry (enhancement of roughness coefficient) or minor changes with respect to drop implementation, the dimensions of the separation zone are decreased noticeably. The velocity values were also recorded by a one-dimensional velocity meter at 15 cm distance from the turnout entrance and in a transverse direction (perpendicular to the flow direction). The results are shown in Figure 9.Figure 9VIEW LARGEDOWNLOAD SLIDE

    Effect of roughness on separation zone dimensions in numerical study.

    Numerical results

    Listen

    This study examined the flow patterns around the entrance of a diversion channel due to various wall roughnesses in the diversion channel. Results indicated that increasing the discharge ratio in the main channel and diversion channel reduces the area of the separation zone in the diversion channel.Figure 10VIEW LARGEDOWNLOAD SLIDE

    Comparision of the vortex area (software output) for three roughnesses (0.009, 0.023 and 0.032).A laboratory and numerical error rate of 0.2605 was calculated from the following formula,

    formula

    where Uexp is the experimental result, Unum is the numerical result, and N is the number of data.

    Figure 9 shows the effect of roughness on separation zone dimensions in numerical study. Figure 10 compares the vortex area (software output) for three roughnesses, 0.009, 0.023 and 0.032 and Figure 11 shows the flow lines (tecplot output) that indicate the effect of roughness on flow in the separation zone. Numerical analysis shows that by increasing the roughness coefficient, the dimensions of the separation zone area decrease, as shown in Figure 10 where the separation zone area at n=0.032 is less than the separation zone area at n=0.009.Figure 11VIEW LARGEDOWNLOAD SLIDE

    Comparison of vortex area in 3D mode (tecplot output) with two roughnesses (a) 0.009 and (b) 0.032.Figure 12VIEW LARGEDOWNLOAD SLIDE

    Velocity vector for flow condition Q1/422 l/s, near surface.

    The velocities intensified moving midway toward the turnout showing that the effective area is scaled down. The velocity values were almost equal to zero near the side walls as expected. As shown in Figure 12 the approach vortex area velocity decreases. Experimental and numerical measured velocity at x=0.15 m of the diversion channel compared in Figure 13 shows that away from the separation zone area, the velocity increases. All longitudinal velocity contours near the vortex area are distinctly different between different roughnesses. The separation zone is larger at less roughness both in length and width.Figure 13VIEW LARGEDOWNLOAD SLIDE

    Exprimental and numerical measured velocity.

    CONCLUSION

    Listen

    This study introduces practical and feasible methods for enhancing turnout efficiency by reducing the separation zone dimensions. Increasing the roughness coefficient and implementation of inlet drop were considered as remedies for reduction of separation zone dimensions. A data set has been compiled that fully describes the complex, 3D flow conditions present in a 90 degree turnout channel for selected flow conditions. The aim of this numerical model was to compare the results of a laboratory model in the area of the separation zone and velocity. Results showed that enhancing roughness coefficient reduce the separation zone dimensions up to 38% while the drop implementation effect can scale down this area differently based on roughness coefficient used. Combining both methods can reduce the separation zone dimensions up to 63%. Further research is proposed to investigate the effect of roughness and drop implementation on sedimentation pattern at lateral turnouts. The dimensions of the separation zone decreases with the increase of the non-dimensional parameter, due to the reduction ratio of turnout discharge increasing in all the experiments.

    This method increases the discharge ratio (ratio of turnout to main channel discharge). The results are compatible with the literature. Other researchers have reported that intensifying the discharge ratio can scale down the separation zone dimensions (Karami Moghaddam & Keshavarzi 2007Ramamurthy et al. 2007). However, they employed other methods to enhance the discharge ratio. Employing both techniques simultaneously can decrease the separation zone dimensions up to 63%. A comparison between the new methods introduced in this paper and traditional methods such as installation of submerged vanes, and changing the inlet geometry (angle, radius) was performed. The comparison shows that the new techniques can be highly influential and still practical. The numerical and laboratory models are in good agreement and show that the method used in this study has been effective in reducing the separation area. This method is simple, economical and can prevent sediment deposition in the intake canal. Results show that CFD prediction of the fluid through the separation zone at the canal intake can be predicted reasonably well and the RNG model offers the best results in terms of predictability.

    DATA AVAILABILITY STATEMENT

    Listen

    All relevant data are included in the paper or its Supplementary Information.

    REFERENCES

    Abbasi A., Ghodsian M., Habibi M. & Salehi Neishabouri S. A. 2004 Experimental investigation on dimensions of flow separation zone at lateral intakeentrance. Research & Construction; Pajouhesh va Sazandegi 62, 38–44. (In Persian).Google Scholar Al-Zubaidy R. & Hilo A. 2021 Numerical investigation of flow behavior at the lateral intake using Computational Fluid Dynamics (CFD). Materials Today: Proceedings. https://doi.org/10.1016/j.matpr.2021.11.172.Google Scholar Chow V. T. 1959 Open Channel Hydraulics. McGraw-Hill, New York.Jalili H., Hosseinzadeh Dalir A. & Farsadizadeh D. 2011 Effect of intake geometry on the sediment transport and lateral flow pattern. Iranian Water Research Journal 5 (9), 1–10. (In Persian).Google Scholar Jamshidi A., Farsadizadeh D. & Hosseinzadeh Dalir A. 2016 Variations of flow separation zone at lateral intake entrance using submerged vanes. Journal of Civil Engineering Urban 6 (3), 54–63. Journal homepage. Available from: www.ojceu.ir/main.Google Scholar Karami Moghaddam K. & Keshavarzi A. 2007 Investigation of flow structure in lateral intakes of 55° and 90° with rounded entrance edge. In: 03 National Congress on Civil Engineering University of Tabriz. Available from: https://civilica.com/doc/16317. (In Persian).Google Scholar Karami H., Farzin S., Sadrabadi M. T. & Moazeni H. 2017 Simulation of flow pattern at rectangular lateral intake with different dike and submerged vane scenarios. Journal of Water Science and Engineering 10 (3), 246–255. https://doi.org/10.1016/j.wse.2017.10.001.Google ScholarCrossref  Kasthuri B. & Pundarikanthan N. V. 1987 Discussion on separation zone at open- channel junction. Journal of Hydraulic Engineering 113 (4), 543–548.Google ScholarCrossref  Keshavarzi A. & Habibi L. 2005 Optimizing water intake angle by flow separation analysis. Journal of Irrigation and Drain 54, 543–552. https://doi.org/10.1002/ird.207.Google ScholarCrossref  Kirkgöz M. S. & Ardiçlioğlu M. 1997 Velocity profiles of developing and developed open channel flow. Journal of Hydraulic Engineering 1099–1105. 10.1061/(ASCE)0733-9429(1997)123:12(1099).Google Scholar Nakato T., Kennedy J. F. & Bauerly D. 1990 Pumpstation intake-shoaling control with submerge vanes. Journal of Hydraulic Engineering. https://doi.org/10.1061/(ASCE)0733-9429(1990)116:1(119).Google Scholar Neary V. S. & Odgaard J. A. 1993 Three-dimensional flow structure at open channel diversions. Journal of Hydraulic Engineering. ASCE 119 (11), 1224–1230. https://doi.org/10.1061/(ASCE)0733-9429(1993)119:11(1223).Google ScholarCrossref  Nikbin S. & Borghei S. M. 2011 Experimental investigation of submerged vanes effect on dimensions of flow separation zone at a 90° openchannel junction. In: 06rd National Congress on Civil Engineering University of Semnan. (In Persian). Available from: https://civilica.com/doc/120494.Google Scholar Odgaard J. A. & Wang Y. 1991 Sediment management with submerged vanes, I: theory. Journal of Hydraulic Engineering 117 (3), 267–283.Google ScholarCrossref  Ramamurthy A. S., Junying Q. & Diep V. 2007 Numerical and experimental study of dividing open-channel flows. Journal of Hydraulic Engineering. See: https://doi.org/10.1061/(ASCE)0733-9429(2007)133:10(1135).Google Scholar Seyedian S., Karami Moghaddam K. & Shafai Begestan M. 2008 Determining the optimal radius in lateral intakes of 55° and 90° using variation of flow velocity. In: 07th Iranian Hydraulic Conference. Power & Water University of Technology (PWUT). (In Persian). Available from: https://civilica.com/doc/56251.Google Scholar Zolghadr M. & Shafai Bejestan M. 2020 Six legged concrete (SLC) elements as scour countermeasures at wing wall bridge abutments. International Journal of River Basin Management. doi: 10.1080/15715124.2020.1726357.Google Scholar Zolghadr M., Zomorodian S. M. A., Shabani R. & Azamatulla H.Md. 2021 Migration of sand mining pit in rivers: an experimental, numerical and case study. Measurement. https://doi.org/10.1016/j.measurement.2020.108944.Google Scholar © 2022 The AuthorsThis is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY-NC-ND 4.0), which permits copying and redistribution for non-commercial purposes with no derivatives, provided the original work is properly cited (http://creativecommons.org/licenses/by-nc-nd/4.0/).

    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 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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    Fig. 1. Hydraulic jump flow structure.

    Performance assessment of OpenFOAM and FLOW-3D in the numerical modeling of a low Reynolds number hydraulic jump

    낮은 레이놀즈 수 유압 점프의 수치 모델링에서 OpenFOAM 및 FLOW-3D의 성능 평가

    ArnauBayona DanielValerob RafaelGarcía-Bartuala Francisco ​JoséVallés-Morána P. AmparoLópez-Jiméneza

    Abstract

    A comparative performance analysis of the CFD platforms OpenFOAM and FLOW-3D is presented, focusing on a 3D swirling turbulent flow: a steady hydraulic jump at low Reynolds number. Turbulence is treated using RANS approach RNG k-ε. A Volume Of Fluid (VOF) method is used to track the air–water interface, consequently aeration is modeled using an Eulerian–Eulerian approach. Structured meshes of cubic elements are used to discretize the channel geometry. The numerical model accuracy is assessed comparing representative hydraulic jump variables (sequent depth ratio, roller length, mean velocity profiles, velocity decay or free surface profile) to experimental data. The model results are also compared to previous studies to broaden the result validation. Both codes reproduced the phenomenon under study concurring with experimental data, although special care must be taken when swirling flows occur. Both models can be used to reproduce the hydraulic performance of energy dissipation structures at low Reynolds numbers.

    CFD 플랫폼 OpenFOAM 및 FLOW-3D의 비교 성능 분석이 3D 소용돌이치는 난류인 낮은 레이놀즈 수에서 안정적인 유압 점프에 초점을 맞춰 제시됩니다. 난류는 RANS 접근법 RNG k-ε을 사용하여 처리됩니다.

    VOF(Volume Of Fluid) 방법은 공기-물 계면을 추적하는 데 사용되며 결과적으로 Eulerian-Eulerian 접근 방식을 사용하여 폭기가 모델링됩니다. 입방체 요소의 구조화된 메쉬는 채널 형상을 이산화하는 데 사용됩니다. 수치 모델 정확도는 대표적인 유압 점프 변수(연속 깊이 비율, 롤러 길이, 평균 속도 프로파일, 속도 감쇠 또는 자유 표면 프로파일)를 실험 데이터와 비교하여 평가됩니다.

    모델 결과는 또한 결과 검증을 확장하기 위해 이전 연구와 비교됩니다. 소용돌이 흐름이 발생할 때 특별한 주의가 필요하지만 두 코드 모두 실험 데이터와 일치하는 연구 중인 현상을 재현했습니다. 두 모델 모두 낮은 레이놀즈 수에서 에너지 소산 구조의 수리 성능을 재현하는 데 사용할 수 있습니다.

    Keywords

    CFDRANS, OpenFOAM, FLOW-3D ,Hydraulic jump, Air–water flow, Low Reynolds number

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    Numerical simulation of slag movement from Marangoni flow for GMAW with computational fluid dynamics

    전산 유체 역학을 사용하여 GMAW에 대한 Marangoni 흐름에서 슬래그 이동의 수치 시뮬레이션

    Dae-WonChoaYeong-DoParkbMuralimohanCheepucaBusan Machinery Research Center, Korea Institute of Machinery and Materials, 48, Mieumsandan 5-ro 41beon-gil, Gangseo-gu, Busan 46744, Republic of KoreabDepartment of Advanced Materials Engineering, Dong-Eui University, Busan, Republic of KoreacSuper-TIG Welding Co., Limited, Busan, Republic of Korea

    Keywords : Marangoni flowMolten slag movementMolten pool behavorSurface tension gradient

    Abstract

    이 연구는 전산 유체 역학을 이용하여 스프레이 모드 가스 금속 아크 용접에서 생성되는 산화물인 용융 슬래그의 거동을 분석했습니다. 주로 규산염 (SiO2)으로 구성된 용융 슬래그는 용융 풀 표면에 있습니다. 일반적으로 용융 슬래그는 아크 플라즈마 경계 주변에서 생성된다고 가정합니다.

    따라서 이 연구의 수치 시뮬레이션에서 슬래그는 특정 밀도와 크기를 가진 구형 입자로 모델링됩니다. Marangoni 유동 효과를 비교하기 위해 이 연구는 표면 장력 구배가 다른 두 가지 사례 (양수 및 음수)를 조사했습니다. 수치 시뮬레이션과 실험 결과 모두 음의 표면 장력 구배가 비드 가장자리에 갇힌 슬래그를 형성하는 반면 양의 표면 장력 구배는 상단 표면의 중앙에 갇힌 슬래그를 형성하는 것으로 나타났습니다.

    This study analyzed the behavior of molten slag, which is an oxide generated during spray mode gas metal arc welding, with computational fluid dynamics. The molten slag, composed mainly of silicate (SiO2), is located on the molten pool surface. It is generally assumed that the molten slag is generated around the arc plasma boundary. Therefore, in the numerical simulation in this study the slag is modeled as a spherical particle, which has a specific density and size. To compare the Marangoni flow effect, this study investigated two different cases where the surface tension gradients were different (positive and negative). In both the numerical simulation and experimental results it was found that negative surface tension gradient formed trapped slag on the bead edge while the positive surface tension gradient formed trapped slag on the center of the top surface.

    Numerical simulation of slag movement from Marangoni flow for GMAW with computational fluid dynamics Figures
    Numerical simulation of slag movement from Marangoni flow for GMAW with computational fluid dynamics Figures
    Weld bead surface images showing the slag formation location for (a) wire 1 and (b) wire 2.

    The effect of alloying elements of gas metal arc welding (GMAW) wire on weld pool flow and slag formation location in cold metal transfer (CMT)

    가스 금속 아크 용접 (GMAW) 와이어의 합금 원소가 CMT (Cold Metal Transfer)에서 용접 풀 흐름 및 슬래그 형성 위치에 미치는 영향

    Md. R. U. Ahsan1,3, Muralimohan. Cheepu2, Yeong-Do Park* 2,3
    1Department of Mechanical Engineering, International University of Business, Agriculture and Technology,
    Dhaka 1230, Bangladesh.
    r.ahsan06me@gmail.com
    2Department of Advanced Materials and Industrial Management Engineering, Dong-Eui University, Busan
    47340, Republic of Korea.
    muralicheepu@gmail.com
    3Department of Advanced Materials Engineering, Dong-Eui University, B

    Abstract

    용접시 표면 장력 구동 흐름 또는 마랑고니 흐름은 용접 비드 모양을 제어하는데 중요한 역할을 하므로 용접 접합 품질에 영향을 미칩니다. 용해된 금속의 표면 장력은 보통 음의 온도 계수를 가지므로 용접 풀이 중심에서 토우 방향으로 흐르게 됩니다.

    표면 장력의 이 온도 계수는 황(S), 산소(O), 셀레늄(Se) 및 텔루륨(Te)과 같은 표면 활성 요소가 있는 경우 양의 계수로 변경할 수 있습니다. 소모품에 존재하는 탈산화 원소의 양이 용접 금속에 존재하는 산소량을 결정합니다. 탈산화제 양이 적으면 용접 금속에 산소 농도가 높아집니다.

    적절한 양의 산소가 있으면 용융지에 표면 장력 구배의 양의 온도 계수가 발생할 수 있습니다. 이 경우 용접 풀은 토우에서 중앙 방향으로 흐릅니다. 그 결과, 아크와 용융지에 있는 화농성 반응의 경우, 합금 요소의 다양한 산화물이 슬래그(slag)라고 합니다. 슬래그는 용융지 표면에 떠서 용융지 흐름 패턴에 따라 누적됩니다.

    그 결과, 슬래그는 용융지 흐름 패턴에 따라 용접 비드 중심 또는 토우 중심을 따라 형성됩니다. 슬래그는 용접 비드의 외관과 도장 접착력을 저하시키므로 제거해야 합니다. 쉽게 분리할 수 있기 때문에 용접 비드 중심 부근에서 슬래그가 형성되는 것이 좋습니다.

    용접 풀의 현장 고속 비디오 촬영, 용접 금속 화학 성분 분석, 소모품 합금 요소가 용접 풀 흐름 패턴 및 슬래그 형성 위치에 미치는 영향이 공개되어 CMT-GMAW의 생산성 향상을 위해 용접 소모품 선택을 용이하게 할 수 있습니다.

    The surface tension driven flow or Marangoni flow in welding plays an important role in governing weld bead shape hence affecting the weld joint quality. The surface tension of molten metal usually has a negative temperature coefficient causing the weld pool to flow from the center towards the toe.

    This temperature coefficient of the surface tension can be altered to be a positive one in the presence of surface-active elements like sulfur (S), oxygen (O), selenium (Se) and tellurium (Te). The amount of deoxidizing elements present in the consumables governs the amount of oxygen present in the weld metal. The presence of a lower amount of deoxidizers results in higher concentration of oxygen in the weld metal.

    The presence of adequate amount of oxygen can result in a positive temperature coefficient of surface tension gradient in the weld pool. In such situation, the weld pool flows from the toe towards the direction of the center. As a result, of pyrometallurgical reactions in the arc and the weld pool various oxides of the alloying elements are former which are referred as slag.

    The slags float on the weld pool surface and accumulate following the weld pool flow pattern. As a result, slags form either along the center of the weld bead or the toe depending on the weld pool flow pattern. The slags need to be removed as they degrade the weld bead appearance and paint adhesiveness.

    Due to easy detachability, slag formation near the center of the weld bead is desired. From in-situ high-speed videography of weld pool, weld metal chemical composition analysis, the effect of consumables alloying elements on weld pool flow pattern and slag formation location are disclosed, which can facilitate the selection of the welding consumables for better productivity in CMT-GMAW.

    Weld bead surface images showing the slag formation location for (a) wire 1 and (b) wire 2.
    Weld bead surface images showing the slag formation location for (a) wire 1 and (b) wire 2.
    Fig. 2: High-speed movie frames and schematic showing the weld pool flow pattern and the slag formation location for wire 1 and wire 2.
    Fig. 2: High-speed movie frames and schematic showing the weld pool flow pattern and the slag formation location for wire 1 and wire 2.
    Fig. 3: Quantitative analysis data on slag formation for different wire.
    Fig. 3: Quantitative analysis data on slag formation for different wire.

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    Figure 2. Experimental setups for the (a) Al/Cu overlap joint and (b) laser welding process.

    Investigation on Laser Welding of Al Ribbon to Cu Sheet: Weldability, Microstructure, and Mechanical and Electrical Properties

    알루미늄 리본과 구리 시트의 레이저 용접에 대한 조사 : 용접성, 미세 구조, 기계적 및 전기적 특성

    Won‐Sang Shin 1,†, Dae‐Won Cho 2,†, Donghyuck Jung 1, Heeshin Kang 3, Jeng O Kim 3, Yoon‐Jun Kim 1,*
    and Changkyoo Park 3,*

    Al 리본과 Cu 시트의 펄스 레이저 용접은 전력 전자 모듈의 전기적 상호 연결에 대해 조사되었습니다. 결함 없는 Al / Cu 조인트를 얻기 위해 레이저 출력, 스캔 속도 및 열 입력이 서로 다른 다양한 실험 조건이 사용되었습니다. Al / Cu 레이저 용접 중에 금속 간 화합물이 용접 영역에 형성되었습니다. 전자 탐침 마이크로 분석기와 투과 전자 현미경으로 Al4Cu9, Al2Cu, AlCu 등으로 밝혀진 금속 간 화합물의 상을 확인했습니다. 전산 유체 역학 시뮬레이션은 Marangoni 효과가 용융 풀의 순환을 유도하여 혼합물을 생성하는 것으로 나타났습니다. Al과 Cu의 결합과 Al / Cu 조인트에서 소용돌이 모양의 구조 형성. Al / Cu 접합부의 인장 전단강도와 전기 저항을 측정하였으며 용접 면적과 강한 상관 관계를 보였다. Al / Cu 접합부의 용접 면적이 증가함에 따라 기계적 강도의 감소와 전기 저항의 증가가 측정 되었습니다. 또한 무결점 Al / Cu 접합을 위한 공정 창을 개발하고 Al / Cu 레이저 브레이즈 용접을 위한 실험 조건을 조사하여 Al / Cu 접합에서 금속 간 화합물 형성을 최소화했습니다.

    Introduction

    전기 상호 연결은 전력 전자 모듈을 패키징하는 데 중요합니다. 우수한 기계적 및 전기적 특성을 가진 견고한 전기적 상호 연결은 전력 전자 모듈의 전기적 고장을 방지하는 데 필수적입니다. 저항 스폿 용접, 브레이징, 납땜 및 초음파 용접 (USW)이 전기 상호 연결에 사용되었습니다.

    납땜과 납땜 모두 저온 공정으로 인해 접합부에서 한계 변형과 잔류 응력이 발생합니다 [1]. 필러 합금은 두 공정 모두 견고한 전기 접촉을 달성하는 데 필수적입니다. 따라서 조인트는 서로 접촉하는 서로 다른 금속으로 구성됩니다.

    결과적으로 조인트는 부식 환경에서 갈바닉 부식에 취약 할 수 있습니다 [2,3]. 더욱이, 비금속과 충전재 사이의 친화도를 고려해야 하기 때문에 제한된 충전재 만 특정 조인트에 사용할 수 있습니다 [1]. USW는 용접 온도가 낮고 용접 시간이 짧기 때문에 접합부의 변형이 비교적 적습니다.

    따라서 이는 특히 연질 재료 (예 : Al, Cu, Ag, Au 및 Ni)의 경우 기존 접합 방법을 대체하고 있습니다 [4–6]. 그러나 Cu를위한 USW 공정의 경우, 표면 산화물이 강해 용접성이 저하되는 것을 방지하기 위해 Cu 표면에 Sn 또는 Ni 코팅이 필요하며, 이는 공정 속도를 늦추고 산업적 응용을위한 경제적 측면을 악화시킨다 [7 , 8].

    레이저 용접은 쉬운 제어, 고정밀 및 원격 처리의 특성으로 인해 전력 전자 모듈의 전기 연결에 대한 유망한 후보입니다. 열의 영향을 받는 작은 영역과 변형은 전기 접점의 손상을 최소화 할 것으로 예상됩니다 [9-11]. 또한 레이저 용접을 위해 추가 표면 준비가 필요하지 않습니다.

    이종 재료의 용접은 산업 응용 분야에서 중요했습니다. 더욱이 그림 1 [12,13]에서 볼 수 있듯이 전기 연결을위한 와이어 또는 리본 본딩에 여러 다른 조인트가 필요하기 때문에 전력 전자 모듈에서 필수적인 기술이되고 있습니다.

    전기 접점의 다양한 조합 중에서 Al과 Cu는 높은 전기 전도성으로 인해 전기 연결에 중요한 재료로 종종 간주됩니다 [14]. 그러나 Al과 Cu의 서로 다른 용접은 금속 간 화합물 (IMC)의 형성을 촉진하고 동시에 Al / Cu 조인트의 기계적 및 전기적 특성에 영향을 줍니다. 일반적으로 Al / Cu 조인트 내부에 IMC가 있으면 연성 및 전기 저항에 해를 끼치므로 균열이 쉽게 발생하고 용접을 통한 전기 전도도를 방해합니다 [15,16].

    따라서 견고한 Al / Cu 조인트를 얻으려면 IMC의 형성을 피해야합니다. 여러 연구에서 Al 및 Cu 시트의 레이저 빔 용접을 조사했습니다. 연속파 (CW) 레이저가 Al / Cu 조인트에 사용되었습니다 [17-23]. 큰 열 입력과 상당한 IMC 형성으로 인해 용접 영역에서 많은 균열이 관찰되었습니다 [18,19].

    CW 레이저 빔의 공간 진동은 Al / Cu 조인트의 용접 품질을 향상시키는 것으로 나타났습니다. 직선 CW 레이저 빔 [18-20]과 비교하여 용접 영역에서 IMC 크기가 더 작은 기공과 균열이 더 적습니다.

    Al과 Cu 시트의 겹침 접합에는 CW 단일 모드 파이버 레이저를 사용했으며, IMC 형성을 억제하여 높은 용접 속도 (즉, 50m / min)에서 견고한 Al / Cu 접합을 얻었습니다 [22]. Mai et al. [23]은 다른 Al / Cu 용접을 달성하기 위해 펄스 레이저를 사용했습니다.

    그들은 Al / Cu 용접성이 레이저 공정 매개 변수에 크게 의존한다는 것을 밝혔으며 100mm / min 미만의 스캔 속도에서 균열없는 Al / Cu 접합을 달성하는 데 성공했습니다.

    본문 내용 생략 : 문서 하단부의 원문보기를 참고하시기 바랍니다.

    Figure 1. Schematic diagram of the insulated gate bipolar transistors (IGBT) power module. Red‐dotted box indicated the electrical connections
    Figure 1. Schematic diagram of the insulated gate bipolar transistors (IGBT) power module. Red‐dotted box indicated the electrical connections
    Figure 2. Experimental setups for the (a) Al/Cu overlap joint and (b) laser welding process.
    Figure 2. Experimental setups for the (a) Al/Cu overlap joint and (b) laser welding process.
    Figure 3. Schematic diagram of the numerical simulation domain and boundary conditions.
    Figure 3. Schematic diagram of the numerical simulation domain and boundary conditions.
    Figure 4. Experimental setup for the four‐point electrical resistance measurement.
    Figure 4. Experimental setup for the four‐point electrical resistance measurement.
    Figure 5. Cross‐sectional OM image of the Al/Cu joints in parallel to the laser welding direction. The laser power and scan speed were set at 2300 W and 20 mm/s, respectively.
    Figure 5. Cross‐sectional OM image of the Al/Cu joints in parallel to the laser welding direction. The laser power and scan speed were set at 2300 W and 20 mm/s, respectively.
    Figure 6 shows the cross‐sectional SEM images of the Al/Cu joints, and corresponding EPMA element mapping of Al and Cu for the (a) 23/20, (b) 25/28.6, (c) 25/15.4, and (d) 27/20.
    Figure 6 shows the cross‐sectional SEM images of the Al/Cu joints, and corresponding EPMA element mapping of Al and Cu for the (a) 23/20,
    Figure 6. Cross‐sectional SEM image and elemental distribution mapping of Al and Cu elements for the (a) 23/20, (b) 25/28.6, (c) 25/15.4, and (d) 27/20.
    Figure 6. Cross‐sectional SEM image and elemental distribution mapping of Al and Cu elements for the (d) 27/20.
    Figure 7. EPMA line scan analysis and identification of the IMCs for the (a) 23/20 and (b) 25/15.4.
    Figure 7. EPMA line scan analysis and identification of the IMCs for the (a) 23/20 and (b) 25/15.4.
    Figure 8. TEM analysis for the 25/28.6. (a) Indicating the location of TEM analysis in SEM image of the welding zone. (b) TEM bright‐field image and SAED pattern insets, examined at the location (1) in figure (a), confirmed Al‐rich phase (white globular shape) and Al2Cu eutectic phase (gray region), and (c) TEM bright‐field image and SAED pattern inset of Al4Cu9, examined at the location (2) in figure (a).
    Figure 8. TEM analysis for the 25/28.6. (a) Indicating the location of TEM analysis in SEM image of the welding zone. (b) TEM bright‐field image and SAED pattern insets, examined at the location (1) in figure (a), confirmed Al‐rich phase (white globular shape) and Al2Cu eutectic phase (gray region), and (c) TEM bright‐field image and SAED pattern inset of Al4Cu9, examined at the location (2) in figure (a).
    Figure 9. Temperature profiles and molten pool flow on transverse cross‐section (y–z plane at x = 1.23 cm): (a) Negative surface tension gradient for the 23/20 (Case 1), (b) negative surface tension gradient for the 25/15.4 (Case 2), (c) positive surface tension gradient for the 25/15.4 (Case 3), and (d) without surface tension for the 25/15.4 (Case 4).
    Figure 9. Temperature profiles and molten pool flow on transverse cross‐section (y–z plane at x = 1.23 cm): (a) Negative surface tension gradient for the 23/20 (Case 1), (b) negative surface tension gradient for the 25/15.4 (Case 2), (c) positive surface tension gradient for the 25/15.4 (Case 3), and (d) without surface tension for the 25/15.4 (Case 4).
    Figure 12. Results of the tensile shear tests for the (a) 23/20: fracture at the Al ribbon and (b) 25/15.4: fracture at the weld
    Figure 12. Results of the tensile shear tests for the (a) 23/20: fracture at the Al ribbon and (b) 25/15.4: fracture at the weld
    Figure 13. Stress–strain curves obtained by the tensile shear tests.
    Figure 13. Stress–strain curves obtained by the tensile shear tests.

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    Figure 2. Ink fraction contours for mesh 1 through 4 (left to right) at the following four time steps: (a) 6 µs, (b) 12 µs, (c) 18 µs, and (d) 24 µs.

    Coupled CFD-Response Surface Method (RSM) Methodology for Optimizing Jettability Operating Conditions

    분사성 작동 조건을 최적화하기 위한 결합된 CFD-Response Surface Method(RSM)

    Nuno Couto 1, Valter Silva 1,2,* , João Cardoso 2, Leo M. González-Gutiérrez 3 and Antonio Souto-Iglesias 41
    INEGI-FEUP, Faculty of Engineering, Porto University, 4200-465 Porto, Portugal;
    nunodiniscouto@hotmail.com
    2 VALORIZA, Polytechnic Institute of Portalegre, 7300-110 Portalegre, Portugal; jps.cardoso@ipportalegre.pt
    3 CEHINAV, DMFPA, ETSIN, Universidad Politécnica de Madrid, 28040 Madrid, Spain; leo.gonzalez@upm.es
    4 CEHINAV, DACSON, ETSIN, Universidad Politécnica de Madrid, 28040 Madrid, Spain;
    antonio.souto@upm.es

    • Correspondence: valter.silva@ipportalegre.pt; Tel.: +351-245-301-592

    소개

    물방울 생성에 대한 이해는 여러 산업 응용 분야에서 매우 중요합니다 [ 1 ]. 잉크젯 프린팅 프로세스는 일반적으로 10 ~ 100 μm [ 1 ] 범위의 독특하고 작은 액적 크기를 특징으로 하며 연속적 또는 충동적 흐름을 사용하여 얻을 수 있습니다 (마지막 방식은 주문형 드롭 (DoD)이라고도 함). 잉크젯).

    여러 장점 덕분에 DoD 방법은 산업 환경에서 상당한 수용을 얻고 있습니다 [ 2 ].DoD는 복잡한 프로세스이며 유체 속성, 노즐 형상 및 구동 파형 [ 1 , 3 ]의 세 가지 주요 범주로 분류되는 여러 매개 변수에 따라 달라집니다 .그러나 길이와 시간 척도가 모두 마이크로 오더 [ 4 ] 이기 때문에 실험을하기가 어렵습니다 .

    결과적으로 실험 설정은 항상 비용이 많이 들고 복잡하며 CFD (전산 유체 역학)와 같은 고급 수치 접근 방식이 엄격한 요구 사항입니다 [ 5 , 6 ]. VOF (volume-of-fluid) 접근 방식은 액체 분해 및 액적 생성에 대한 다상 공정을 시뮬레이션하기위한 적절한 대안으로 밝혀졌으며 과거 연구에서 그대로 사용되었습니다 [ 7 , 8], 인쇄 프로세스의 맥락에서 전자는 여전히 현재 연구의 주제입니다. 

    또한 VOF 체계를 사용하면 단일 운동량 방정식 세트를 해결하고 도메인 전체에 걸쳐 각 유체의 체적 분율을 추적하여 명확하게 정의된 인터페이스로 둘 이상의 혼합 불가능한 유체를 효과적으로 시뮬레이션 할 수 있습니다. Feng [ 9 ]는 VOF 접근 방식을 사용하여 일시적인 유체 인터페이스 변형 및 중단을 효과적으로 추적하는 패키지 FLOW-3D를 사용하여 낙하 배출 중 복잡한 유체 역학 프로세스를 시뮬레이션하는 선구자 작업 중 하나를 수행했습니다.

    주요 목표는 볼륨 및 속도와 같은 민감한 변수를 더 잘 이해하면서 장치 개발에서 일반적인 설계 규칙을 구현하는 것이 었습니다. 이러한 종류의 공정과 관련된 주요 질문 중 하나는 안정적인 액적 형성을 위한 작동 범위의 정의입니다.

    Fromm [ 10 ]은 Reynolds 수와 Weber 수의 제곱근 비율이 2보다 작으면 안정적인 방울을 생성 할 수 없다는 것을 확인했습니다. 이 무차원 값은 나중에 Z 번호로 알려졌으며 분사 가능성 범위 [ 11 ]를 정의합니다 . 문헌에서 분사 가능성을 위한 Z 간격은 1 ~ 10 [ 12 ], 4 ~ 14 [ 13 ] 또는 0.67 ~ 50 [ 14]을 찾을 수 있습니다. 

    이것은 Z 값 만으로는 분사 가능성 조건을 나타낼 수 없음을 분명히 의미합니다. 실제로, 다른 속성을 가진 유체는 다른 인쇄 품질을 나타내면서 동일한 Z 값을 나타낼 수 있습니다. 액적 생성 공정과 해당 분사 성은 주로 전체 공정 품질에 큰 영향을 미치는 매개 변수 세트에 의해 결정됩니다. 

    토대 메커니즘을 더 잘 이해하려면 확장 된 작동 조건 및 매개 변수 세트를 고려하여 여러 실험 또는 수치 실행을 수행해야 합니다. DoE (design-of-experiment) 접근 방식과 같은 체계적인 접근 방식이 없으면 이것은 달성하기 매우 어려운 작업이 될 수 있습니다. 최적화 문제를 해결하기 위해 반응 표면 방법을 사용하여 처음으로 체계화된 접근 방식이 개발된 Box and Wilson [ 15 ] 의 선구자 기사 이후 ,이 입증된 방법론은 많은 화학 및 산업 공정[ 16 ] 및 기타 관련 학계에 성공적으로 적용되었습니다.

    예를 들어 Silva와 Rouboa [ 17 ]는 직접 메탄올 연료 전지의 출력 밀도에 영향을 미치는 관련 매개 변수를 식별하기 위해 반응 표면 방법론 (RSM)을 사용했습니다. 많은 실제 산업 응용 분야에서 실험 연구는 작동 매개 변수를 조절하기 어렵 기 때문에 제한적이지만 주로 설정을 개발하거나 실험을 실행하는 데 드는 비용이 높기 때문입니다. 

    따라서 솔루션은 주요 시스템 응답을 시뮬레이션하고 예측할 수 있는 효과적인 수학적 모델의 개발에 의존합니다. DoE와 같은 최적화 방법론을 수치 모델과 결합하면 비용이 많이 들고 시간이 많이 걸리는 실험을 피하고 다양한 입력 조합을 사용하여 최적의 조건을 얻을 수 있습니다 [ 16 ]. 

    실바와 루 보아 [ 18] CFD 프레임 워크 하에서 개발 된 2D Eulerian-Eulerian 바이오 매스 가스화 모델에서 얻은 결과를 RSM과 결합하여 다양한 응용 분야에서 합성 가스를 생성하기 위한 최적의 작동 조건을 찾습니다. 

    저자는 입력 요인으로 인한 최상의 응답과 최소한의 변동을 모두 보장하는 작동 조건을 찾을 수 있었습니다. Frawley et al. [ 19 ] CFD 및 DoE 기술 (특히 RSM)을 결합하여 파이프의 팔꿈치에서 고체 입자 침식에 대한 다양한 주요 요인의 영향을 조사하여 침식 예측 모델을 개발할 수 있습니다.우리가 아는 한, DoD 잉크젯 프로세스의 개선 및 더 나은 이해에 적용되는 DoE 접근법 (실험적으로 또는 모든 종류의 수치 모델과 결합)을 구현하는 연구는 없습니다. 선도 기업이 이러한 접근 방식을 적용 할 가능성이 있지만 관련 결과는 민감할 수 있으므로 더 넓은 커뮤니티에서 사용할 수 없습니다. 이 사실은 DoD 잉크젯 공정에서 액적 생성에 대한 여러 매개 변수의 영향을 평가하기 위한 이러한 종류의 연구로서 현재 논문의 영향을 증가 시킬 수 있습니다.

    CFD 프레임 워크 내에서 VOF 접근 방식을 사용하여 여러 컴퓨터 실험의 설계를 개발하고 RSM을 분석 도구로 사용했습니다. 충분한 수치 정확도와 수용 가능한 시간 계산 시뮬레이션의 균형을 맞추기 위해 메쉬 수렴 연구가 수행되었습니다. 설계 목적을 위해 점도, 표면 장력, 입구 속도 및 노즐 직경이 입력 요인으로 선택되었습니다. 응답은 break-up 시간과 break-up 길이였습니다.

    Figure 1. Schematic of the computational domain
    Figure 1. Schematic of the computational domain
    Figure 2. Ink fraction contours for mesh 1 through 4 (left to right) at the following four time steps: (a) 6 µs, (b) 12 µs, (c) 18 µs, and (d) 24 µs.
    Figure 2. Ink fraction contours for mesh 1 through 4 (left to right) at the following four time steps: (a) 6 µs, (b) 12 µs, (c) 18 µs, and (d) 24 µs.
    Figure 3. Comparison between surface tensions at the following four time steps: (a) 6 µs, (b) 12 µs, (c) 18 µs, and (d) 24 µs
    Figure 3. Comparison between surface tensions at the following four time steps: (a) 6 µs, (b) 12 µs, (c) 18 µs, and (d) 24 µs
    Figure 4. Comparison between viscosity values at the following four time steps: (a) 6 μs, (b) 12 μs, (c) 18 μs, and (d) 24 μs.
    Figure 4. Comparison between viscosity values at the following four time steps: (a) 6 μs, (b) 12 μs, (c) 18 μs, and (d) 24 μs.
    Figure 5. Comparison between different nozzle diameters at the following four time steps: (a) 6 µs, (b) 12 µs, (c) 18 µs, and (d) 24 µs
    Figure 5. Comparison between different nozzle diameters at the following four time steps: (a) 6 µs, (b) 12 µs, (c) 18 µs, and (d) 24 µs
    Figure 6. Comparison between different inlet velocities at the following four time steps: (a) 6 µs, (b) 12 µs, (c) 18 µs, and (d) 24 µs
    Figure 6. Comparison between different inlet velocities at the following four time steps: (a) 6 µs, (b) 12 µs, (c) 18 µs, and (d) 24 µs
    Figure 8. Contour response plots for break-up time as a function of (a) surface tension and viscosity, (b) nozzle diameter and viscosity, (c) inlet velocity and viscosity, (d) nozzle diameter and surface tension, (e) inlet velocity and surface tension, and (f) inlet velocity and nozzle diameter.
    Figure 8. Contour response plots for break-up time as a function of (a) surface tension and viscosity, (b) nozzle diameter and viscosity, (c) inlet velocity and viscosity, (d) nozzle diameter and surface tension, (e) inlet velocity and surface tension, and (f) inlet velocity and nozzle diameter.
    Figure 12. Break-up length as a function of the We–Ca space (obtained from the 25 runs).
    Figure 12. Break-up length as a function of the We–Ca space (obtained from the 25 runs).

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    Figure 1.1: A water droplet with a radius of 1 mm resting on a glass substrate. The surface of the droplet takes on a spherical cap shape. The contact angle θ is defined by the balance of the interfacial forces.

    Effect of substrate cooling and droplet shape and composition on the droplet evaporation and the deposition of particles

    기판 냉각 및 액적 모양 및 조성이 액적 증발 및 입자 증착에 미치는 영향

    by Vahid Bazargan
    M.A.Sc., Mechanical Engineering, The University of British Columbia, 2008
    B.Sc., Mechanical Engineering, Sharif University of Technology, 2006
    B.Sc., Chemical & Petroleum Engineering, Sharif University of Technology, 2006

    고착 방울은 평평한 기판에 놓인 액체 방울입니다. 작은 고정 액적이 증발하는 동안 액적의 접촉선은 고정된 접촉 영역이 있는 고정된 단계와 고정된 접촉각이 있는 고정 해제된 단계의 두 가지 단계를 거칩니다. 고정된 접촉 라인이 있는 증발은 액적 내부에서 접촉 라인을 향한 흐름을 생성합니다.

    이 흐름은 입자를 운반하고 접촉 선 근처에 침전시킵니다. 이로 인해 일반적으로 관찰되는 “커피 링”현상이 발생합니다. 이 논문은 증발 과정과 고착성 액적의 증발 유도 흐름에 대한 연구를 제공하고 콜로이드 현탁액에서 입자의 침착에 대한 통찰력을 제공합니다. 여기서 우리는 먼저 작은 고착 방울의 증발을 연구하고 증발 과정에서 기판의 열전도도의 중요성에 대해 논의합니다.

    현재 증발 모델이 500µm 미만의 액적 크기에 대해 심각한 오류를 생성하는 방법을 보여줍니다. 우리의 모델에는 열 효과가 포함되어 있으며, 특히 증발 잠열의 균형을 맞추기 위해 액적에 열을 제공하는 기판의 열전도도를 포함합니다. 실험 결과를 바탕으로 접촉각의 진화와 관련된 접촉 선의 가상 움직임을 정의하여 고정 및 고정 해제 단계의 전체 증발 시간을 고려합니다.

    우리의 모델은 2 % 미만의 오차로 500 µm보다 작은 물방울에 대한 실험 결과와 일치합니다. 또한 유한한 크기의 라인 액적의 증발을 연구하고 증발 중 접촉 라인의 복잡한 동작에 대해 논의합니다. 에너지 공식을 적용하고 접촉 선이 구형 방울의 후퇴 접촉각보다 높은 접촉각을 가진 선 방울의 두 끝에서 후퇴하기 시작 함을 보여줍니다. 그리고 라인 방울 내부의 증발 유도 흐름을 보여줍니다.

    마지막으로, 계면 활성제 존재 하에서 접촉 라인의 거동을 논의하고 입자 증착에 대한 Marangoni 흐름 효과에 대해 논의합니다. 열 Marangoni 효과는 접촉 선 근처에 증착 된 입자의 양에 영향을 미치며, 기판 온도가 낮을수록 접촉 선 근처에 증착되는 입자의 양이 많다는 것을 알 수 있습니다.

    Figure 1.1: A water droplet with a radius of 1 mm resting on a glass substrate. The surface of the droplet takes on a spherical cap shape. The contact angle θ is defined by the balance of the interfacial forces.
    Figure 1.1: A water droplet with a radius of 1 mm resting on a glass substrate. The surface of the droplet takes on a spherical cap shape. The contact angle θ is defined by the balance of the interfacial forces.
    Figure 2.1: Evaporation modes of sessile droplets on a substrate: (a) evaporation at constant contact angle (de-pinned stage) and (b) evaporation at constant contact area (pinned stage)
    Figure 2.1: Evaporation modes of sessile droplets on a substrate: (a) evaporation at constant contact angle (de-pinned stage) and (b) evaporation at constant contact area (pinned stage)
    Figure 2.2: A sessil droplet with its image can be profiled as the equiconvex lens formed by two intersecting spheres with radius of a.
    Figure 2.2: A sessil droplet with its image can be profiled as the equiconvex lens formed by two intersecting spheres with radius of a.
    Figure 2.3: The droplet life time for both evaporation modes derived from Equation 2.2.
    Figure 2.3: The droplet life time for both evaporation modes derived from Equation 2.2.
    Figure 2.4: A probability of escape for vapor molecules at two different sites of the surface of the droplet for diffusion controlled evaporation. The random walk path initiated from a vapor molecule is more likely to result in a return to the surface if the starting point is further away from the edge of the droplet.
    Figure 2.4: A probability of escape for vapor molecules at two different sites of the surface of the droplet for diffusion controlled evaporation. The random walk path initiated from a vapor molecule is more likely to result in a return to the surface if the starting point is further away from the edge of the droplet.
    Figure 2.5: Schematic of the sessile droplet on a substrate
    Figure 2.5: Schematic of the sessile droplet on a substrate. The evaporation rate at the surface of the droplet is enhanced toward the edge of the droplet.
    Figure 2.6: The domain mesh (a) and the solution of the Laplace equation for diffusion of the water vapor molecule with the concentration of Cv = 1.9×10−8 g/mm3 at the surface of the droplet into the ambient air with the relative humidity of 55%, i.e. φ = 0.55 (b).
    Figure 2.6: The domain mesh (a) and the solution of the Laplace equation for diffusion of the water vapor molecule with the concentration of Cv = 1.9×10−8 g/mm3 at the surface of the droplet into the ambient air with the relative humidity of 55%, i.e. φ = 0.55 (b).
    Figure 3.1: The portable micro printing setup. A motorized linear stage from Zaber Technologies Inc. was used to control the place and speed of the micro nozzle.
    Figure 3.1: The portable micro printing setup. A motorized linear stage from Zaber Technologies Inc. was used to control the place and speed of the micro nozzle.
    Figure 4.6: Temperature contours inside the substrate adjacent to the droplet
    Figure 4.6: Temperature contours inside the substrate adjacent to the droplet
    Figure 4.7: The effect of substrate cooling on the evaporation rate, the basic model shows the same value for all substrates.
    Figure 4.7: The effect of substrate cooling on the evaporation rate, the basic model shows the same value for all substrates.

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    Result of simulation by changing surface tension

    잉크젯 프린팅에서 해상력에 관한 컴퓨터 시뮬레이션 연구

    A Study on the Simulation of the Resolution for Ink-Jet Printing

    • Lee, Ji-Eun (Dept. of Graphic Arts Engineering, Graduate School, Pukyong National University) ;
    • Youn, Jong-Tae (Dept. of Graphic Arts Information, College of Engineering, Pukyong National University) ;
    • Koo, Chul-Whoi (Dept. of Graphic Arts Information, College of Engineering, Pukyong National University)
    • 이지은 (부경대학교 대학원 인쇄공학과) ;
    • 윤종태 (부경대학교 공과대학 인쇄정보공학과) ;
    • 구철회 (부경대학교 공과대학 인쇄정보공학과)

    초록

    Ink-jet is part of the non impact printing that shooting the ink drop from the nozzle to paper. It is very silence and express good color. There are two types of printing that continuous and drop on demand. But drop on demand process is becoming the mainstream. these days, LCD, PDP is passed more than semiconductor industry. And we expect organic EL, FED as a next display. But product equipment, main component and technology have a gap between an advanced country and us nevertheless physical development. Expecially, previous process part is depended on imports. Ink-jet printing technology that there isn’t complicated photo lithography process is attracted, so ink-jet printing resolution is more embossed. But there were not many of ink-jet resolution thesis but ink-jet head or nozzle. Because, to out of the ink from the nozzle is unseeable and hard to experiment. Therefore this thesis was experimented and simulated how can ink-jet printer improved resolution by flow-3d simulation package program.

    잉크젯은 노즐에서 종이로 잉크 방울을 분사하는 비 충격 인쇄의 일부입니다. 매우 조용하고 좋은 색상을 표현합니다. 연속 및 요청시 드롭되는 두 가지 유형의 인쇄가 있습니다. 그러나 주문형 드롭 프로세스가 주류가되고 있습니다. 요즘 LCD, PDP는 반도체 산업을 넘어서고 있습니다. 그리고 우리는 유기 EL, FED를 다음 디스플레이로 기대합니다. 그러나 제품 장비, 주요 부품 및 기술은 선진국과 우리의 물리적 발달 사이에 격차가 있습니다. 특히 이전 공정 부분은 수입품에 의존합니다. 복잡한 포토 리소그래피 공정이없는 잉크젯 프린팅 기술이 매료되어 잉크젯 프린팅 해상도가 더욱 강조됩니다. 하지만 잉크젯 해상도 논문은 많지 않고 잉크젯 헤드 나 노즐이 많았습니다. 왜냐하면 노즐에서 잉크가 빠져 나가는 것은 보이지 않고 실험하기 어렵 기 때문입니다. 따라서이 논문은 flow-3d 시뮬레이션 패키지 프로그램을 통해 잉크젯 프린터가 해상도를 향상시킬 수있는 방법을 실험하고 시뮬레이션했습니다.

    국내 및 해외에 다양한 인쇄 기술이 보급되어 있는 상황에서 잉크젯 기술은 1990년대 후반부터 궤도에 올랐다. 잉크젯은 비접촉성 인쇄 기술의 하나로 인쇄 표면에 잉크 방울 들을 투사해 전자적으로 조정하기 때문에 여러 가지 장점들이 있다. 원하는 양을 원하는 때 제작 가능하고 2,400dpi이상의 높은 해상도를 가지며 잉크 방울의 크기를 조절하여 보다 정확한 이미지인 그레이 스케일 이미지를 얻을 수 있다. 따라서 사진과 같은 이미 지를 만들 수 있다. 또한 기존의 붓을 이용한 디자인에 비해 높은 해상도의 이미지를 손 쉽게 만들 수 있으므로 그래픽 디자인에 대한 적용 범위를 확장할 수 있다. 그리고 카트 리지에 저장되어 있는 잉크를 이미지에 필요한 양만큼 소비하기 때문에 생산비 절감에 유리하다. 이는 코팅 기술이 가지고 있는 원료의 소모를 획기적으로 개선할 수 있다.또 한 코팅 방법과는 달리 기판에 영향을 주지 않는다. 거칠거나 민감한 모든 종류의 표면 위에 인쇄가 가능하며, 1분당 100,000라인의 인쇄 속도로 고속 처리에 적합하다. 현재 잉 크젯 프린터의 성능을 평가하는 방법 중에 가장 기본적인 것은 해상도이다. 그렇기 때문 에 인쇄물의 해상도에서는 dpi가 무척 중요하다. dpi는 dot per inch의 약자로 1인치당 찍은 점의 수이다. dpi는 인쇄물의 해상력을 결정하는 단위이다. 예를 들어 300dpi는 1인 치에 300개의 점을 찍는 밀도로 잉크 점을 찍어 인쇄를 한다는 뜻이다. 당연히 dpi는 숫 자가 클수록 인쇄물이 더 정교해진다. 그러나 제조업체에 따라 출력 dpi 수가 다르며 요 구되는 최적의 해상도도 프린터 엔진의 특성에 따라 다르다. 일반적인 인쇄물은 200dpi 면 좋은 품질이며, 300dpi를 넘으면 매우 우수한 품질이 된다. 우리가 일상생활에서 보 는 대부분의 인쇄물은 100~300dpi 정도롤 사용한다. 잉크젯 프린터에 1,440dpi라고 쓰여 있는 것은 dot의 실질적인 것을 말하는 것이 아니라, 이상적인 종이에 잉크 방울을 려 구현할 수 있는 이론상의 수치이다. 종이에 작은 잉크 입자돌을 뿌려 번지게 하는 방법 으로 인해, 표시된 해상력만큼 재현하지 못하는 경우가 많다. 따라서 실제로는 600dpi 잉크젯 프린터라고 해도 인쇄소에서 300dpi로 출력한 것보다 품질이 떨어지기도 한다. 그러므로 좋은 품질을 얻기 위해서는 목표로 한 해상력 보다 높게 인쇄해야 하는데 그 러기 위해서는 잉크젯의 해상력에 관한 연구가 필수적이다. 잉크에서는 주로 헤드와 노즐에 관한 연구들이 많이 있지만,~9 본 논문에서는 잉크젯의 해상력에 관한 연구를 하고자 한다. 본 연구의 목적은 FLOW-3D 시뮬레이션 프로그램을 이용하여 액적의 비산 모양을 시뮬레이션 함으로서 해상력에 대한 예측을 하기 위한 것이다. 잉크 방울의 크기가 해상 력에 미친다는 것을 알고, 잉크의 물성을 변화시켜가며 액적을 줄이기 위한 시뮬레이션 을 하였다.

    Simulation of the bubble jet printing by FLOW-3D
    ZSimulation of the bubble jet printing by FLOW-3D
    Result of simulation by changing surface tension
    Result of simulation by changing surface tension

    자유 표면 모델링 방법

    본 자료는 국내 사용자들의 편의를 위해 원문 번역을 해서 제공하기 때문에 일부 오역이 있을 수 있어서 원문과 함께 수록합니다. 자료를 이용하실 때 참고하시기 바랍니다.

    Free Surface Modeling Methods

    An interface between a gas and liquid is often referred to as a free surface. The reason for the “free” designation arises from the large difference in the densities of the gas and liquid (e.g., the ratio of density for water to air is 1000). A low gas density means that its inertia can generally be ignored compared to that of the liquid. In this sense the liquid moves independently, or freely, with respect to the gas. The only influence of the gas is the pressure it exerts on the liquid surface. In other words, the gas-liquid surface is not constrained, but free.

    자유 표면 모델링 방법

    기체와 액체 사이의 계면은 종종 자유 표면이라고합니다.  ‘자유’라는 호칭이 된 것은 기체와 액체의 밀도가 크게 다르기 때문입니다 (예를 들어, 물 공기에 대한 밀도 비는 1000입니다).  기체의 밀도가 낮다는 것은 액체의 관성에 비해 기체의 관성은 일반적으로 무시할 수 있다는 것을 의미합니다.  이러한 의미에서, 액체는 기체에 대해 독립적으로, 즉 자유롭게 움직입니다.  기체의 유일한 효과는 액체의 표면에 대한 압력입니다.  즉, 기체와 액체의 표면은 제약되어있는 것이 아니라 자유롭다는 것입니다.

    In heat-transfer texts the term ‘Stephen Problem’ is often used to describe free boundary problems. In this case, however, the boundaries are phase boundaries, e.g., the boundary between ice and water that changes in response to the heat supplied from convective fluid currents.

    열전달에 관한 문서는 자유 경계 문제를 묘사할 때 “Stephen Problem’”라는 용어가 자주 사용됩니다.  그러나 여기에서 경계는 상(phase) 경계, 즉 대류적인 유체의 흐름에 의해 공급된 열에 반응하여 변화하는 얼음과 물 사이의 경계 등을 말합니다.

    Whatever the name, it should be obvious that the presence of a free or moving boundary introduces serious complications for any type of analysis. For all but the simplest of problems, it is necessary to resort to numerical solutions. Even then, free surfaces require the introduction of special methods to define their location, their movement, and their influence on a flow.

    이름이 무엇이든, 자유 또는 이동 경계가 존재한다는 것은 어떤 유형의 분석에도 복잡한 문제를 야기한다는 것은 분명합니다. 가장 간단한 문제를 제외한 모든 문제에 대해서는 수치 해석에 의존할 필요가 있습니다. 그 경우에도 자유 표면은 위치, 이동 및 흐름에 미치는 영향을 정의하기 위한 특별한 방법이 필요합니다.

    In the following discussion we will briefly review the types of numerical approaches that have been used to model free surfaces, indicating the advantages and disadvantages of each method. Regardless of the method employed, there are three essential features needed to properly model free surfaces:

    1. A scheme is needed to describe the shape and location of a surface,
    2. An algorithm is required to evolve the shape and location with time, and
    3. Free-surface boundary conditions must be applied at the surface.

    다음 설명에서는 자유 표면 모델링에 사용되어 온 다양한 유형의 수치적 접근에 대해 간략하게 검토하고 각 방법의 장단점을 설명합니다. 어떤 방법을 사용하는지에 관계없이 자유롭게 표면을 적절히 모델화하는 다음의 3 가지 기능이 필요합니다.

    1. 표면의 형상과 위치를 설명하는 방식
    2. 시간에 따라 모양과 위치를 업데이트 하는 알고리즘
    3. 표면에 적용할 자유 표면 경계 조건

    Lagrangian Grid Methods

    Conceptually, the simplest means of defining and tracking a free surface is to construct a Lagrangian grid that is imbedded in and moves with the fluid. Many finite-element methods use this approach. Because the grid and fluid move together, the grid automatically tracks free surfaces.

    라그랑주 격자 법

    개념적으로 자유 표면을 정의하고 추적하는 가장 간단한 방법은 유체와 함께 이동하는 라그랑주 격자를 구성하는 것입니다. 많은 유한 요소 방법이 이 접근 방식을 사용합니다. 격자와 유체가 함께 움직이기 때문에 격자는 자동으로 자유 표면을 추적합니다.

    At a surface it is necessary to modify the approximating equations to include the proper boundary conditions and to account for the fact that fluid exists only on one side of the boundary. If this is not done, asymmetries develop that eventually destroy the accuracy of a simulation.

    표면에서 적절한 경계 조건을 포함하고 유체가 경계의 한면에만 존재한다는 사실을 설명하기 위해 근사 방정식을 수정해야합니다. 이것이 수행되지 않으면 결국 시뮬레이션의 정확도를 훼손하는 비대칭이 발생합니다.

    The principal limitation of Lagrangian methods is that they cannot track surfaces that break apart or intersect. Even large amplitude surface motions can be difficult to track without introducing regridding techniques such as the Arbitrary-Lagrangian-Eulerian (ALE) method. References 1970 and 1974 may be consulted for early examples of these approaches.

    라그랑지안 방법의 주요 제한은 분리되거나 교차하는 표면을 추적 할 수 없다는 것입니다. ALE (Arbitrary-Lagrangian-Eulerian) 방법과 같은 격자 재생성 기법을 도입하지 않으면 진폭이 큰 표면 움직임도 추적하기 어려울 수 있습니다. 이러한 접근법의 초기 예를 보려면 참고 문헌 1970 및 1974를 참조하십시오.

    The remaining free-surface methods discussed here use a fixed, Eulerian grid as the basis for computations so that more complicated surface motions may be treated.

    여기에서 논의된 나머지 자유 표면 방법은 보다 복잡한 표면 움직임을 처리할 수 있도록 고정된 오일러 그리드를 계산의 기준으로 사용합니다.

    Surface Height Method

    Low amplitude sloshing, shallow water waves, and other free-surface motions in which the surface does not deviate too far from horizontal, can be described by the height, H, of the surface relative to some reference elevation. Time evolution of the height is governed by the kinematic equation, where (u,v,w) are fluid velocities in the (x,y,z) directions. This equation is a mathematical expression of the fact that the surface must move with the fluid:

    표면 높이 법

    낮은 진폭의 슬로 싱, 얕은 물결 및 표면이 수평에서 너무 멀리 벗어나지 않는 기타 자유 표면 운동은 일부 기준 고도에 대한 표면의 높이 H로 설명 할 수 있습니다. 높이의 시간 진화는 운동학 방정식에 의해 제어되며, 여기서 (u, v, w)는 (x, y, z) 방향의 유체 속도입니다. 이 방정식은 표면이 유체와 함께 움직여야한다는 사실을 수학적으로 표현한 것입니다.

    Finite-difference approximations to this equation are easy to implement. Further, only the height values at a set of horizontal locations must be recorded so the memory requirements for a three-dimensional numerical solution are extremely small. Finally, the application of free-surface boundary conditions is also simplified by the condition on the surface that it remains nearly horizontal. Examples of this technique can be found in References 1971 and 1975.

    이 방정식의 유한 차분 근사를 쉽게 실행할 수 있습니다.  또한 3 차원 수치 해법의 메모리 요구 사항이 극도로 작아지도록 같은 높이의 위치 값만을 기록해야합니다.  마지막으로 자유 표면 경계 조건의 적용도 거의 수평을 유지하는 표면의 조건에 의해 간소화됩니다.  이 방법의 예는 참고 문헌의 1971 및 1975을 참조하십시오.

    Marker-and-Cell (MAC) Method

    The earliest numerical method devised for time-dependent, free-surface, flow problems was the Marker-and-Cell (MAC) method (see Ref. 1965). This scheme is based on a fixed, Eulerian grid of control volumes. The location of fluid within the grid is determined by a set of marker particles that move with the fluid, but otherwise have no volume, mass or other properties.

    MAC 방법

    시간 의존성을 가지는 자유 표면 흐름의 문제에 대해 처음 고안된 수치 법이 MAC (Marker-and-Cell) 법입니다 (참고 문헌 1965 참조).  이 구조는 컨트롤 볼륨 고정 오일러 격자를 기반으로합니다.  격자 내의 유체의 위치는 유체와 함께 움직이고, 그 이외는 부피, 질량, 기타 특성을 갖지 않는 일련의 마커 입자에 의해 결정됩니다.

    Grid cells containing markers are considered occupied by fluid, while those without markers are empty (or void). A free surface is defined to exist in any grid cell that contains particles and that also has at least one neighboring grid cell that is void. The location and orientation of the surface within the cell was not part of the original MAC method.

    마커를 포함한 격자 셀은 유체로 채워져있는 것으로 간주되며 마커가 없는 격자 셀은 빈(무효)것입니다.  입자를 포함하고, 적어도 하나의 인접 격자 셀이 무효인 격자의 자유 표면은 존재하는 것으로 정의됩니다.  셀 표면의 위치와 방향은 원래의 MAC 법에 포함되지 않았습니다.

    Evolution of surfaces was computed by moving the markers with locally interpolated fluid velocities. Some special treatments were required to define the fluid properties in newly filled grid cells and to cancel values in cells that are emptied.

    표면의 발전(개선)은 국소적으로 보간된 유체 속도로 마커를 이동하여 계산되었습니다.  새롭게 충전된 격자 셀의 유체 특성을 정의하거나 비어있는 셀의 값을 취소하거나 하려면 특별한 처리가 필요했습니다.

    The application of free-surface boundary conditions consisted of assigning the gas pressure to all surface cells. Also, velocity components were assigned to all locations on or immediately outside the surface in such a way as to approximate conditions of incompressibility and zero-surface shear stress.

    자유 표면 경계 조건의 적용은 모든 표면 셀에 가스 압력을 할당하는 것으로 구성되었습니다. 또한 속도 성분은 비압축성 및 제로 표면 전단 응력의 조건을 근사화하는 방식으로 표면 위 또는 외부의 모든 위치에 할당되었습니다.

    The extraordinary success of the MAC method in solving a wide range of complicated free-surface flow problems is well documented in numerous publications. One reason for this success is that the markers do not track surfaces directly, but instead track fluid volumes. Surfaces are simply the boundaries of the volumes, and in this sense surfaces may appear, merge or disappear as volumes break apart or coalesce.

    폭넓게 복잡한 자유 표면 흐름 문제 해결에 MAC 법이 놀라운 성공을 거두고 있는 것은 수많은 문헌에서 충분히 입증되고 있습니다.  이 성공 이유 중 하나는 마커가 표면을 직접 추적하는 것이 아니라 유체의 체적을 추적하는 것입니다.  표면은 체적의 경계에 불과하며, 그러한 의미에서 표면은 분할 또는 합체된 부피로 출현(appear), 병합, 소멸 할 가능성이 있습니다.

    A variety of improvements have contributed to an increase in the accuracy and applicability of the original MAC method. For example, applying gas pressures at interpolated surface locations within cells improves the accuracy in problems driven by hydrostatic forces, while the inclusion of surface tension forces extends the method to a wider class of problems (see Refs. 1969, 1975).

    다양한 개선으로 인해 원래 MAC 방법의 정확성과 적용 가능성이 증가했습니다. 예를 들어, 셀 내 보간 된 표면 위치에 가스 압력을 적용하면 정 수력으로 인한 문제의 정확도가 향상되는 반면 표면 장력의 포함은 방법을 더 광범위한 문제로 확장합니다 (참조 문헌. 1969, 1975).

    In spite of its successes, the MAC method has been used primarily for two-dimensional simulations because it requires considerable memory and CPU time to accommodate the necessary number of marker particles. Typically, an average of about 16 markers in each grid cell is needed to ensure an accurate tracking of surfaces undergoing large deformations.

    수많은 성공에도 불구하고 MAC 방법은 필요한 수의 마커 입자를 수용하기 위해 상당한 메모리와 CPU 시간이 필요하기 때문에 주로 2 차원 시뮬레이션에 사용되었습니다. 일반적으로 큰 변형을 겪는 표면의 정확한 추적을 보장하려면 각 그리드 셀에 평균 약 16 개의 마커가 필요합니다.

    Another limitation of marker particles is that they don’t do a very good job of following flow processes in regions involving converging/diverging flows. Markers are usually interpreted as tracking the centroids of small fluid elements. However, when those fluid elements get pulled into long convoluted strands, the markers may no longer be good indicators of the fluid configuration. This can be seen, for example, at flow stagnation points where markers pile up in one direction, but are drawn apart in a perpendicular direction. If they are pulled apart enough (i.e., further than one grid cell width) unphysical voids may develop in the flow.

    마커 입자의 또 다른 한계는 수렴 / 발산 흐름이 포함된 영역에서 흐름 프로세스를 따라가는 작업을 잘 수행하지 못한다는 것입니다. 마커는 일반적으로 작은 유체 요소의 중심을 추적하는 것으로 해석됩니다. 그러나 이러한 유체 요소가 길고 복잡한 가닥으로 당겨지면 마커가 더 이상 유체 구성의 좋은 지표가 될 수 없습니다. 예를 들어 마커가 한 방향으로 쌓여 있지만 수직 방향으로 떨어져 있는 흐름 정체 지점에서 볼 수 있습니다. 충분히 분리되면 (즉, 하나의 그리드 셀 너비 이상) 비 물리적 공극이 흐름에서 발생할 수 있습니다.

    Surface Marker Method

    One way to limit the memory and CPU time consumption of markers is to keep marker particles only on surfaces and not in the interior of fluid regions. Of course, this removes the volume tracking property of the MAC method and requires additional logic to determine when and how surfaces break apart or coalesce.

    표면 마커 법

    마커의 메모리 및 CPU 시간의 소비를 제한하는 방법 중 하나는 마커 입자를 유체 영역의 내부가 아니라 표면에만 보존하는 것입니다.  물론 이는 MAC 법의 체적 추적 특성이 배제되기 때문에 표면이 분할 또는 합체하는 방식과 시기를 특정하기위한 논리를 추가해야합니다.

    In two dimensions the marker particles on a surface can be arranged in a linear order along the surface. This arrangement introduces several advantages, such as being able to maintain a uniform particle spacing and simplifying the computation of intersections between different surfaces. Surface markers also provide a convenient way to locate the surface within a grid cell for the application of boundary conditions.

    2 차원의 경우 표면 마커 입자는 표면을 따라 선형으로 배치 할 수 있습니다.  이 배열은 입자의 간격을 균일하게 유지할 수있는 별도의 표면이 교차하는 부분의 계산이 쉽다는 등 몇 가지 장점이 있습니다.  또한 표면 마커를 사용하여 경계 조건을 적용하면 격자 셀의 표면을 간단한 방법으로 찾을 수 있습니다.

    Unfortunately, in three-dimensions there is no simple way to order particles on surfaces, and this leads to a major failing of the surface marker technique. Regions may exist where surfaces are expanding and no markers fill the space. Without markers the configuration of the surface is unknown, consequently there is no way to add markers. Reference 1975 contains examples that show the advantages and limitations of this method.

    불행히도 3 차원에서는 표면에 입자를 정렬하는 간단한 방법이 없으며 이로 인해 표면 마커 기술이 크게 실패합니다. 표면이 확장되고 마커가 공간을 채우지 않는 영역이 존재할 수 있습니다. 마커가 없으면 표면의 구성을 알 수 없으므로 마커를 추가 할 방법이 없습니다.
    참고 문헌 1975이 방법의 장점과 한계를 보여주는 예제가 포함되어 있습니다.

    Volume-of-Fluid (VOF) Method

    The last method to be discussed is based on the concept of a fluid volume fraction. The idea for this approach originated as a way to have the powerful volume-tracking feature of the MAC method without its large memory and CPU costs.

    VOF (Volume-of-Fluid) 법

    마지막으로 설명하는 방법은 유체 부피 분율의 개념을 기반으로합니다. 이 접근 방식에 대한 아이디어는 대용량 메모리 및 CPU 비용없이 MAC 방식의 강력한 볼륨 추적 기능을 갖는 방법에서 시작되었습니다.

    Within each grid cell (control volume) it is customary to retain only one value for each flow quantity (e.g., pressure, velocity, temperature, etc.) For this reason it makes little sense to retain more information for locating a free surface. Following this reasoning, the use of a single quantity, the fluid volume fraction in each grid cell, is consistent with the resolution of the other flow quantities.

    각 격자 셀 (제어 체적) 내에서 각 유량 (예 : 압력, 속도, 온도 등)에 대해 하나의 값만 유지하는 것이 일반적입니다. 이러한 이유로 자유 표면을 찾기 위해 더 많은 정보를 유지하는 것은 거의 의미가 없습니다. 이러한 추론에 따라 각 격자 셀의 유체 부피 분율인 단일 수량의 사용은 다른 유량의 해상도와 일치합니다.

    If we know the amount of fluid in each cell it is possible to locate surfaces, as well as determine surface slopes and surface curvatures. Surfaces are easy to locate because they lie in cells partially filled with fluid or between cells full of fluid and cells that have no fluid.

    각 셀 내의 유체의 양을 알고 있는 경우, 표면의 위치 뿐만 아니라  표면 경사와 표면 곡률을 결정하는 것이 가능합니다.  표면은 유체 가 부분 충전 된 셀 또는 유체가 전체에 충전 된 셀과 유체가 전혀없는 셀 사이에 존재하기 때문에 쉽게 찾을 수 있습니다.

    Slopes and curvatures are computed by using the fluid volume fractions in neighboring cells. It is essential to remember that the volume fraction should be a step function, i.e., having a value of either one or zero. Knowing this, the volume fractions in neighboring cells can then be used to locate the position of fluid (and its slope and curvature) within a particular cell.

    경사와 곡률은 인접 셀의 유체 체적 점유율을 사용하여 계산됩니다.  체적 점유율은 계단 함수(step function)이어야 합니다, 즉, 값이 1 또는 0 인 것을 기억하는 것이 중요합니다.  이 것을 안다면, 인접 셀의 부피 점유율을 사용하여 특정 셀 내의 유체의 위치 (및 그 경사와 곡률)을 찾을 수 있습니다.

    Free-surface boundary conditions must be applied as in the MAC method, i.e., assigning the proper gas pressure (plus equivalent surface tension pressure) as well as determining what velocity components outside the surface should be used to satisfy a zero shear-stress condition at the surface. In practice, it is sometimes simpler to assign velocity gradients instead of velocity components at surfaces.

    자유 표면 경계 조건을 MAC 법과 동일하게 적용해야 합니다.  즉, 적절한 기체 압력 (및 대응하는 표면 장력)을 할당하고, 또한 표면에서 제로 전단 응력을 충족 시키려면 표면 외부의 어떤 속도 성분을 사용할 필요가 있는지를 확인합니다.  사실, 표면에서의 속도 성분 대신 속도 구배를 지정하는 것이보다 쉬울 수 있습니다.

    Finally, to compute the time evolution of surfaces, a technique is needed to move volume fractions through a grid in such a way that the step-function nature of the distribution is retained. The basic kinematic equation for fluid fractions is similar to that for the height-function method, where F is the fraction of fluid function:

    마지막으로, 표면의 시간 변화를 계산하려면 분포의 계단 함수의 성질이 유지되는 방법으로 격자를 통과하고 부피 점유율을 이동하는 방법이 필요합니다.  유체 점유율의 기본적인 운동학방정식은 높이 함수(height-function) 법과 유사합니다.  F는 유체 점유율 함수입니다.

    A straightforward numerical approximation cannot be used to model this equation because numerical diffusion and dispersion errors destroy the sharp, step-function nature of the F distribution.

    이 방정식을 모델링 할 때 간단한 수치 근사는 사용할 수 없습니다.  수치의 확산과 분산 오류는 F 분포의 명확한 계단 함수(step-function)의 성질이 손상되기 때문입니다.

    It is easy to accurately model the solution to this equation in one dimension such that the F distribution retains its zero or one values. Imagine fluid is filling a column of cells from bottom to top. At some instant the fluid interface is in the middle region of a cell whose neighbor below is filled and whose neighbor above is empty. The fluid orientation in the neighboring cells means the interface must be located above the bottom of the cell by an amount equal to the fluid fraction in the cell. Then the computation of how much fluid to move into the empty cell above can be modified to first allow the empty region of the surface-containing cell to fill before transmitting fluid on to the next cell.

    F 분포가 0 또는 1의 값을 유지하는 같은 1 차원에서이 방정식의 해를 정확하게 모델링하는 것은 간단합니다.  1 열의 셀에 위에서 아래까지 유체가 충전되는 경우를 상상해보십시오.  어느 순간에 액체 계면은 셀의 중간 영역에 있고, 그 아래쪽의 인접 셀은 충전되어 있고, 상단 인접 셀은 비어 있습니다.  인접 셀 내의 유체의 방향은 계면과 셀의 하단과의 거리가 셀 내의 유체 점유율과 같아야 한다는 것을 의미합니다.  그 다음 먼저 표면을 포함하는 셀의 빈 공간을 충전 한 후 다음 셀로 유체를 보내도록 위쪽의 빈 셀에 이동하는 유체의 양의 계산을 변경할 수 있습니다.

    In two or three dimensions a similar procedure of using information from neighboring cells can be used, but it is not possible to be as accurate as in the one-dimensional case. The problem with more than one dimension is that an exact determination of the shape and location of the surface cannot be made. Nevertheless, this technique can be made to work well as evidenced by the large number of successful applications that have been completed using the VOF method. References 1975, 1980, and 1981 should be consulted for the original work on this technique.

    2 차원과 3 차원에서 인접 셀의 정보를 사용하는 유사한 절차를 사용할 수 있지만, 1 차원의 경우만큼 정확하게 하는 것은 불가능합니다.  2 차원 이상의 경우의 문제는 표면의 모양과 위치를 정확히 알 수없는 것입니다.  그래도 VOF 법을 사용하여 달성 된 다수의 성공 사례에서 알 수 있듯이 이 방법을 잘 작동시킬 수 있습니다.  이 기법에 관한 초기의 연구 내용은 참고 문헌 1975,1980,1981를 참조하십시오.

    The VOF method has lived up to its goal of providing a method that is as powerful as the MAC method without the overhead of that method. Its use of volume tracking as opposed to surface-tracking function means that it is robust enough to handle the breakup and coalescence of fluid masses. Further, because it uses a continuous function it does not suffer from the lack of divisibility that discrete particles exhibit.

    VOF 법은 MAC 법만큼 강력한 기술을 오버 헤드없이 제공한다는 목표를 달성 해 왔습니다.  표면 추적이 아닌 부피 추적 기능을 사용하는 것은 유체 질량의 분할과 합체를 처리하는 데 충분한 내구성을 가지고 있다는 것을 의미합니다.  또한 연속 함수를 사용하기 때문에 이산된 입자에서 발생하는 숫자를 나눌 수 없는 문제를 겪지 않게 됩니다.

    Variable-Density Approximation to the VOF Method

    One feature of the VOF method that requires special treatment is the application of boundary conditions. As a surface moves through a grid, the cells containing fluid continually change, which means that the solution region is also changing. At the free boundaries of this changing region the proper free surface stress conditions must also be applied.

    VOF 법의 가변 밀도 근사

    VOF 법의 특수 처리가 필요한 기능 중 하나는 경계 조건의 적용입니다.  표면이 격자를 통과하여 이동할 때 유체를 포함하는 셀은 끊임없이 변화합니다.  즉, 계산 영역도 변화하고 있다는 것입니다.  이 변화하고있는 영역의 자유 경계에는 적절한 자유 표면 응력 조건도 적용해야합니다.

    Updating the flow region and applying boundary conditions is not a trivial task. For this reason some approximations to the VOF method have been used in which flow is computed in both liquid and gas regions. Typically, this is done by treating the flow as a single fluid having a variable density. The F function is used to define the density. An argument is then made that because the flow equations are solved in both liquid and gas regions there is no need to set interfacial boundary conditions.

    유체 영역의 업데이트 및 경계 조건의 적용은 중요한 작업입니다.  따라서 액체와 기체의 두 영역에서 흐름이 계산되는 VOF 법에 약간의 근사가 사용되어 왔습니다.  일반적으로 가변 밀도를 가진 단일 유체로 흐름을 처리함으로써 이루어집니다.  밀도를 정의하려면 F 함수를 사용합니다.  그리고, 흐름 방정식은 액체와 기체의 두 영역에서 계산되기 때문에 계면의 경계 조건을 설정할 필요가 없다는 논증이 이루어집니다.

    Unfortunately, this approach does not work very well in practice for two reasons. First, the sensitivity of a gas region to pressure changes is generally much greater than that in liquid regions. This makes it difficult to achieve convergence in the coupled pressure-velocity solution. Sometimes very large CPU times are required with this technique.

    공교롭게도 이 방법은 두 가지 이유로 인해 실제로는 그다지 잘 작동하지 않습니다.  하나는 압력의 변화에 대한 기체 영역의 감도가 일반적으로 액체 영역보다 훨씬 큰 것입니다.  따라서 압력 – 속도 결합 해법 수렴을 달성하는 것은 어렵습니다.  이 기술은 필요한 CPU 시간이 매우 커질 수 있습니다.

    The second, and more significant, reason is associated with the possibility of a tangential velocity discontinuity at interfaces. Because of their different responses to pressure, gas and liquid velocities at an interface are usually quite different. In the Variable-Density model interfaces are moved with an average velocity, but this often leads to unrealistic movement of the interfaces.

    두 번째 더 중요한 이유는 계면에서 접선 속도가 불연속이되는 가능성에 관련이 있습니다.  압력에 대한 반응이 다르기 때문에 계면에서 기체와 액체의 속도는 일반적으로 크게 다릅니다.  가변 밀도 모델은 계면은 평균 속도로 동작하지만, 이는 계면의 움직임이 비현실적으로 되는 경우가 많습니다.

    Even though the Variable-Density method is sometimes referred to as a VOF method, because is uses a fraction-of-fluid function, this designation is incorrect. For accurately tracking sharp liquid-gas interfaces it is necessary to actually treat the interface as a discontinuity. This means it is necessary to have a technique to define an interface discontinuity, as well as a way to impose the proper boundary conditions at that interface. It is also necessary to use a special numerical method to track interface motions though a grid without destroying its character as a discontinuity.

    가변 밀도 방법은 유체 분율 함수를 사용하기 때문에 VOF 방법이라고도하지만 이것은 올바르지 않습니다. 날카로운 액체-가스 인터페이스를 정확하게 추적하려면 인터페이스를 실제로 불연속으로 처리해야합니다. 즉, 인터페이스 불연속성을 정의하는 기술과 해당 인터페이스에서 적절한 경계 조건을 적용하는 방법이 필요합니다. 또한 불연속성으로 특성을 훼손하지 않고 격자를 통해 인터페이스 동작을 추적하기 위해 특수한 수치 방법을 사용해야합니다.

    Summary

    A brief discussion of the various techniques used to numerically model free surfaces has been given here with some comments about their relative advantages and disadvantages. Readers should not be surprised to learn that there have been numerous variations of these basic techniques proposed over the years. Probably the most successful of the methods is the VOF technique because of its simplicity and robustness. It is this method, with some refinement, that is used in the FLOW-3D program.

    여기에서는 자유 표면을 수치적으로 모델링 할 때 사용하는 다양한 방법에 대해 상대적인 장점과 단점에 대한 설명을 포함하여 쉽게 설명하였습니다.  오랜 세월에 걸쳐 이러한 기본적인 방법이 많이 제안되어 온 것을 알고도 독자 여러분은 놀라지 않을 것입니다.  아마도 가장 성과를 거둔 방법은 간결하고 강력한 VOF 법 입니다.  이 방법에 일부 개량을 더한 것이 현재 FLOW-3D 프로그램에서 사용되고 있습니다.

    Attempts to improve the VOF method have centered on better, more accurate, ways to move fluid fractions through a grid. Other developments have attempted to apply the method in connection with body-fitted grids and to employ more than one fluid fraction function in order to model more than one fluid component. A discussion of these developments is beyond the scope of this introduction.

    VOF 법의 개선은 더 나은, 더 정확한 방법으로 유체 점유율을 격자를 통과하여 이동하는 것에 중점을 두어 왔습니다.  기타 개발은 물체 적합 격자(body-fitted grids) 관련 기법을 적용하거나 여러 유체 성분을 모델링하기 위해 여러 유체 점유율 함수를 채용하기도 했습니다.  이러한 개발에 대한 논의는 여기에서의 설명 범위를 벗어납니다.

    References

    1965 Harlow, F.H. and Welch, J.E., Numerical Calculation of Time-Dependent Viscous Incompressible Flow, Phys. Fluids 8, 2182.

    1969 Daly, B.J., Numerical Study of the Effect of Surface Tension on Interface Instability, Phys. Fluids 12, 1340.

    1970 Hirt, C.W., Cook, J.L. and Butler, T.D., A Lagrangian Method for Calculating the Dynamics of an Incompressible Fluid with Free Surface, J. Comp. Phys. 5, 103.

    1971 Nichols, B.D. and Hirt, C.W.,Calculating Three-Dimensional Free Surface Flows in the Vicinity of Submerged and Exposed Structures, J. Comp. Phys. 12, 234.

    1974 Hirt, C.W., Amsden, A.A., and Cook, J.L.,An Arbitrary Lagrangian-Eulerian Computing Method for all Flow Speeds, J. Comp. Phys., 14, 227.

    1975 Nichols, B.D. and Hirt, C.W., Methods for Calculating Multidimensional, Transient Free Surface Flows Past Bodies, Proc. of the First International Conf. On Num. Ship Hydrodynamics, Gaithersburg, ML, Oct. 20-23.

    1980 Nichols, B.D. and Hirt, C.W., Numerical Simulation of BWR Vent-Clearing Hydrodynamics, Nucl. Sci. Eng. 73, 196.

    1981 Hirt, C.W. and Nichols, B.D., Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries, J. Comp. Phys. 39, 201.

    Thermocapillary Actuation

    Thermocapillary Actuation

    표면 장력의 온도 의존성은 유체 방울을 패턴 있는 표면 위로 전달하는 데 사용될 수 있습니다. 표면은 유체 방울이 친수성-수소성 인터페이스에 의해 형성된 채널을 따르도록 제한되도록 친수성 또는 친수성 접촉 각도로 패턴화됩니다. 또한 프로그램 가능한 방식으로 가열된 마이크로 히터의 배열은 열전압 작동을 유발하여 유체 방울을 뜨거운 영역에서 차가운 지역으로 유도합니다. 아래 이미지는 문제 설정의 상단 및 단면 뷰(Anton A)를 보여줍니다. Darhuber 외.) 다음에 Flow-3D를 설정합니다.

    Liquid droplet moving along hydrophilic microstripe
    Top-view of a liquid droplet moving along a hydrophilic microstripe. The array of Ti-resistors (shown in light gray) beneath the hydrophilic stripes locally heat the droplet thereby modifying the surface tension and propelling the liquid toward the colder regions of the device surface. The dark gray stripes represent the leads and contacts (Au) for the heating resistors.
    Cross sectional view of device
    Cross-sectional view of a portion of the device containing two micro-heaters and an overlying droplet.

    더 차가운 표면 온도 영역은 인접한 따뜻한 지점보다 더 높은 표면 장력을 유지하여 액체를 당기는 접선 표면 힘을가합니다. 부분적 습윤 (접촉각> 0) 표면은 전체 습윤 표면 (접촉각 = 0)에 비해 부피 손실이 적은 유체 수송을 허용하기 때문에 바람직한 옵션입니다.

    FLOW-3D setup of three microheaters

    Top view of the setup in FLOW-3D showing three microheaters in pink, yellow and blue respectively. The central hydrophilic strip is shown in black with a fluid (water) droplet in sky blue.

    아래 애니메이션은 완전히 젖은 표면과 부분적으로 젖은 표면의 비교를 보여줍니다. 예상대로 완전히 젖은 표면은 부분적으로 젖은 표면보다 액적을 더 평평하게 (그리고 더 많이 퍼지게) 만듭니다. 히터가 한 번에 하나씩 활성화되면 물방울이 더 차가운 영역으로 이동됩니다. 더 많은 유체가 남겨질수록 시뮬레이션이 끝날 때까지 완전히 젖은 표면은 더 많은 유체 볼륨을 잃는 것을 볼 수 있습니다. 따라서 부분적으로 젖은 표면은 유체 손실을 줄이기위한 더 바람직한 옵션입니다. 두 경우 모두 소수성 표면으로 둘러싸인 중앙 친수성 스트립으로 인해 물방울이 중앙에 머물러야합니다.

    Animation of the results post-processed in FlowSight.

    References

    Anton A. Darhuber, Joseph P. Valentino, Sandra M. Trian and Sigurd Wagner, Thermocapillary Actuation of Droplets on Chemically Patterned Surfaces by Programmable Microheater Arrays, Journal of Microelectrochemical Systems, Vol. 12, No. 6, December 2003

    Coating Application/코팅분야 응용

    해석 조건

    • Viscosity(점도) = 0.204 Pa-s
    • Density(밀도) = 965 kg/m^3
    • Surface tension(표면 장력) = 0.035N/m
    • Roll coating

    물리 모델

    • Surface tension(표면 장력) 모델
    • Viscosity(점도)
    • Moving Objects(운동)

    Classic Inlet Flooded Regime

    Revers Operating Regime

    Inlet Starved Operating Regime

    • 2D 시뮬레이션은 작동 코팅 윈도우의 빠른 평가를 제공
    • 계단식, 공기 유입, 기아 및 런백을 식별
    • 리빙(Ribbing)은 3D 분석이 필요

    해석 결과

    Additive Manufacturing & Welding Bibliography

    Additive Manufacturing & Welding Bibliography

    다음은 적층 제조 및 용접 참고 문헌의 기술 문서 모음입니다. 이 모든 논문에는 FLOW-3D AM 결과가 나와 있습니다. FLOW-3D AM을 사용하여 적층 제조, 레이저 용접 및 기타 용접 기술에서 발견되는 프로세스를 성공적으로 시뮬레이션하는 방법에 대해 자세히 알아보십시오.

    2024년 11월 20일 update

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    111-24 Ruijie Liu, Melt pool dynamic modelling for the titanium-based metal additive manufacturing process, Thesis, The University of Auckland, 2024.

    104-24 Ju Wang, Meng Li, Huarong Zhang, Zhe Liu, Xiaodan Li, Dengzhi Yao, Yuhang Wu, Qiong Wu, Xizhong An, Shujun Li, Jian Wang, Xing Zhang , Cumulative effects of powder beds and melted areas on pore defects in electron beam powder bed fusion of tungsten, Powder Technology, 443; 119971, 2024. doi.org/10.1016/j.powtec.2024.119971

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    68-24 Jialu Wang, Shuaicheng Zhu, Miaojin Jiang, Yunwei Gui, Huadong Fu, Jianxin Xie, Solidification track morphology, residual stress behavior, and microstructure evolution mechanism of FGH96-R nickel-based superalloys during laser powder bed fusion process, Journal of Materials Engineering and Performance, 2024. doi.org/10.1007/s11665-024-09326-5

    66-24 Erik Holmen Olofsson, Ashley Dan, Michael Roland, Ninna Halberg Jokil, Rohit Ramachandran, Jesper Henri Hattel, Numerical modeling of fill-level and residence time in starve-fed single-screw extrusion: a dimensionality reduction study from a 3D CFD model to a 2D convection-diffusion model, The International Journal of Advanced Manufacturing Technology, 132; pp. 1111-1125, 2024. doi.org/10.1007/s00170-024-13378-1

    64-24 Feipeng An, Linjie Zhang, Wei Ma, Suck Joo Na, Influences of the powder size and process parameters on the quasi-stability of molten pool shape in powder bed fusion-laser beam of molybdenum, Journal of Materials Engineering and Performance, 2024. doi.org/10.1007/s11665-024-09328-3

    63-24 Haodong Chen, Xin Lin, Yajing Sun, Shuhao Wang, Kunpeng Zhu, Binbin Dan, Revealing formation mechanism of end of process depression in laser powder bed fusion by multi-physics meso-scale simulation, Virtual and Physical Prototyping, 19.1; e2326599, 2024. doi.org/10.1080/17452759.2024.2326599

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    50-24 James Lamb, Ruben Ochoa, Adriana Eres-Castellanos, Jonah Klemm-Toole, McLean P. Echlin, Tao Sun, Kamel Fezzaa, Amy Clarke, Tresa M. Pollack, Quantification of melt pool dynamics and microstructure during simulated additive manufacturing, Scripta Materialia, 245; 116036, 2024. doi.org/10.1016/j.scriptamat.2024.116036

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    27-24 Zehui Liu, Yiyang Hu, Mingyang Zhang, Wei Zhang, Jun Wang, Wenbo Lei, Chunming Wang, Surface morphology evolution mechanisms of pulse laser polishing mold steel, International Journal of Mechanical Sciences, 269; 109039, 2024. doi.org/10.1016/j.ijmecsci.2024.109039

    25-24 Muhammad Arif Mahmood, Kashif Ishfaq, Marwan Khraisheh, Inconel-718 processing windows by directed energy deposition: a framework combining computational fluid dynamics and machine learning models with experimental validation, The International Journal of Advanced Manufacturing Technology, 130; pp. 3997-4011, 2024. doi.org/10.1007/s00170-024-12980-7

    24-24   Jinsheng Ning, Lida Zhu, Shuhao Wang, Zhichao Yang, Peihua Xu, Pengsheng Xue, Hao Lu, Miao Yu, Yunhang Zhao, Jiachen Li, Susmita Bose, Amit Bandyopadhyay, Printability disparities in heterogeneous material combinations via laser directed energy deposition: a comparative study, International Journal of Extreme Manufacturing, 6; 025001, 2024. doi.org/10.1088/2631-7990/ad172f

    18-24   Delong Jia, Dong Zhou, Peng Yi, Chuanwei Zhang, Junru Li, Yankuo Guo, Shengyue Zhang, Yanhui Li, Splat deposition stress formation mechanism of droplets impacting onto texture, International Journal of Mechanical Sciences, 266; 109002, 2024. doi.org/10.1016/j.ijmecsci.2024.109002

    11-24   Dae Gune Jung, Ji Young Park, Choong Mo Ryu, Jong Jin Hwang, Seung Jae Moon, Numerical study of laser welding of 270 μm thick silicon-steel sheets for electrical motors, Metals, 14.1; 24, 2024. doi.org/10.3390/met14010024

    8-24   Zhifu Yao, Longke Bao, Mujin Yang, Yuechao Chen, Minglin He, Jiang Yi, Xintong Yang, Tao Yang, Yilu Zhao, Cuiping Wang, Zheng Zhong, Shuai Wang, Xingjun Liu, Thermally stabe strong <101> texture in additively manufactured cobalt-based superalloys, Scripta Materialia, 242; 115942, 2024. doi.org/10.1016/j.scriptamat.2023.115942

    5-24   Xi Shu, Chunyu Wang, Guoqing Chen, Chunju Wang, Lining Sun, Pre-melted electron beam freeform fabrication additive manufacturing: modeling and numerical simulation, Welding in the World, 68; pp. 163-176, 2024. doi.org/10.1007/s40194-023-01647-8

    4-24   Lin Gao, Andrew C. Chuang, Peter Kenesei, Zhongshu Ren, Lilly Balderson, Tao Sun, An operando synchrotron study on the effect of wire melting state on solidification microstructures of Inconel 718 in wire-laser directed energy deposition, International Journal of Machine Tools and Manufacture, 194; 104089, 2024. doi.org/10.1016/j.ijmachtools.2023.104089

    3-24 Kunjie Dai, Xing He, Decheng Kong, Chaofang Dong, Multi-physical field simulation to yield defect-free IN718 alloy fabricated by laser powder bed fusion, Materials Letters, 355; 135437, 2024. doi.org/10.1016/j.matlet.2023.135437

    2-24 You Wang, Yinkai Xie, Huaixue Li, Caiyou Zeng, Ming Xu, Hongqiang Zhang, In-situ monitoring plume, spattering behavior and revealing their relationship with melt flow in laser powder bed fusion of nickel-based superalloy, Journal of Materials Science & Technology, 177; pp. 44-58, 2024. doi.org/10.1016/j.jmst.2023.07.068

    1-24 Yukai Chen, Hongtu Xu, Yu Lu, Yin Wang, Shuangyuzhou Wang, Ke Huang, Qi Zhang, Prediction of microstructure for Inconel 718 laser welding process using multi-scale model, Proceedings of the 14th International Conference on the Technology of Plasticity – Current Trends in the Technology of Plasticity, pp. 713-722, 2024. doi.org/10.1007/978-3-031-41341-4_75

    211-23 Giovanni Chianese, Qamar Hayat, Sharhid Jabar, Pasquale Franciosa, Darek Ceglarek, Stanislao Patalano, A multi-physics CFD study to investigate the impact of laser beam shaping on metal mixing and molten pool dynamics during laser welding of copper to steel for battery terminal-to-casing connections, Journal of Materials Processing Technology, 322; 118202, 2023. doi.org/10.1016/j.jmatprotec.2023.118202

    207-23 Dong Liu, Jiaqi Pei, Hua Hou, Xiaofeng Niu, Yuhong Zhao, Optimizing solidification dendrites and process parameters for laser powder bed fusion additive manufacturing of GH3536 superalloy by finite volume and phase-field method, Journal of Materials Research and Technology, 27; pp. 3323-3338, 2023. doi.org/10.1016/j.jmrt.2023.10.188

    206-23 Houshang Yin, Jingfan Yang, Ralf D. Fischer, Zilong Zhang, Bart Prorok, Lang Yuan, Xiaoyuan Lou, Pulsed laser additive manufacturing for 316L stainless steel: a new approach to control subgrain cellular structure, JOM, 75; pp. 5027-5036, 2023. doi.org/10.1007/s11837-023-06177-8

    205-23 Francis Ogoke, William Lee, Ning-Yu Kao, Alexander Myers, Jack Beuth, Jonathan Malen, Amir Barati Farimani, Convolutional neural networks for melt depth prediction and visualization in laser powder bed fusion, The International Journal of Advanced Manufacturing Technology, 129; pp. 3047-3062, 2023. doi.org/10.1007/s00170-023-12384-z

    202-23 Habib Hamed Zargari, Kazuhiro Ito, Abhay Sharma, Effect of workpiece vibration frequency on heat distribution and material flow in the molten pool in tandem-pulsed gas metal arc welding, The International Journal of Advanced Manufacturing Technology, 129; pp. 2507-2522, 2023. doi.org/10.1007/s00170-023-12424-8

    199-23 Yukai Chen, Yin Wang, Hao Li, Yu Lu, Bin Han, Qi Zhang, Effects of process parameters on the microstructure of Inconel 718 during powder bed fusion based on cellular automata approach, Virtual and Physical Prototyping, 18.1; e2251032, 2023. doi.org/10.1080/17452759.2023.2251032

    197-23 Qiong Wu, Chuang Qiao, Yuhang Wu, Zhe Liu, Xiaodan Li, Ju Wang, Xizhong An, Aijun Huang, Chao Voon Samuel Lim, Numerical investigation on the reuse of recycled powders in powder bed fusion additive manufacturing, Additive Manufacturing, 77; 103821, 2023. doi.org/10.1016/j.addma.2023.103821

    196-23 Daicong Zhang, Chunhui Jing, Wei Guo, Yuan Xiao, Jun Luo, Lehua Qi, Microchannels formed using metal microdroplets, Micromachines, 14.10; 1922, 2023. doi.org/10.3390/mi14101922

    195-23 Trong-Nhan Le, Santosh Rauniyar, V.H. Nismath, Kevin Chou, An investigation into the effects of contouring process parameters on the up-skin surface characteristics in laser powder-bed fusion process, Manufacturing Letters, 35; Supplement, pp. 707-716, 2023. doi.org/10.1016/j.mfglet.2023.08.085

    194-23 Kyubok Lee, Teresa J. Rinker, Masoud M. Pour, Wayne Cai, Wenkang Huang, Wenda Tan, Jennifer Bracey, Jingjing Li, A study on cracks and IMCs in laser welding of Al and Cu, Manufacturing Letters, 35; Supplement, pp. 221-231, 2023. doi.org/10.1016/j.mfglet.2023.08.026

    192-23 Kunjie Dai, Xing He, Wei Zhang, Decheng Kong, Rong Guo, Minlei Hu, Ketai He, Chaofang Dong, Tailoring the microstructure and mechanical properties for Hastelloy X alloy by laser powder bed fusion via scanning strategy, Materials & Design, 235; 112386, 2023. doi.org/10.1016/j.matdes.2023.112386

    191-23 Jun Du, Daqing Wang, Jimiao He, Yongheng Zhang, Zhike Peng, Influence of droplet size and ejection frequency on molten pool dynamics and deposition morphology in TIG-aided droplet deposition manufacturing, International Communications in Heat and Mass Transfer, 148; 107075, 2023. doi.org/10.1016/j.icheatmasstransfer.2023.107075

    188-23 Jin-Hyeong Park, Du-Song Kim, Dae-Won Cho, Jaewoong Kim, Changmin Pyo, Influence of thermal flow and predicting phase transformation on various welding positions, Heat and Mass Transfer, 2023. doi.org/10.1007/s00231-023-03429-w

    184-23 Lin Gao, Jishnu Bhattacharyya, Wenhao Lin, Zhongshu Ren, Andrew C. Chuang, Pavel D. Shevchenko, Viktor Nikitin, Ji Ma, Sean R. Agnew, Tao Sun, Tailoring material microstructure and property in wire-laser directed energy deposition through a wiggle deposition strategy, Additive Manufacturing, 77; 103801, 2023. doi.org/10.1016/j.addma.2023.103801

    182-23 Liping Guo, Hanjie Liu, Hongze Wang, Qianglong Wei, Jiahui Zhang, Yingyan Chen, Chu Lun Alex Leung, Qing Lian, Yi Wu, Yu Zou, Haowei Wang, A high-fidelity comprehensive framework for the additive manufacturing printability assessment, Journal of Manufacturing Processes, 105; pp. 219-231, 2023. doi.org/10.1016/j.jmapro.2023.09.041

    172-23 Liping Guo, Hanjie Liu, Hongze Wang, Qianglong Wei, Yakai Xiao, Zijue Tang, Yi Wu, Haowei Wang, Identifying the keyhole stability and pore formation mechanisms in laser powder bed fusion additive manufacturing, Journal of Materials Processing Technology, 321; 118153, 2023. doi.org/10.1016/j.jmatprotec.2023.118153

    171-23 Yuhang Wu, Qiong Wu, Meng Li, Ju Wang, Dengzhi Yao, Hao Luo, Xizhong An, Haitao Fu, Hao Zhang, Xiaohong Yang, Qingchuan Zou, Shujun Li, Haibin Ji, Xing Zhang, Numerical investigation on effects of operating conditions and final dimension predictions in laser powder bed fusion of molybdenum, Additive Manufacturing, 76; 103783, 2023. doi.org/10.1016/j.addma.2023.103783

    158-23 K. El Abbaoui, I. Al Korachi, M.T. Mollah, J. Spangenberg, Numerical modelling of planned corner deposition in 3D concrete printing, Archives of Materials Science and Engineering, 121.2; pp. 71-79, 2023. doi.org/10.5604/01.3001.0053.8488

    156-23 Liping Guo, Hanjie Liu, Hongze Wang, Valentino A.M. Cristino, C.T. Kwok, Qianglong Wei, Zijue Tang, Yi Wu, Haowei Wang, Deepening the scientific understanding of different phenomenology in laser powder bed fusion by an integrated framework, International Journal of Heat and Mass Transfer, 216; 124596, 2023. doi.org/10.1016/j.ijheatmasstransfer.2023.124596

    154-23 Zhiyong Li, Xiuli He, Shaoxia Li, Xinfeng Kan, Yanjun Yin, Gang Yu, Sulfur-induced transitions of thermal behavior and flow dynamics in laser powder bed fusion of 316L powders, Thermal Science and Engineering Progress, 45; 102072, 2023. doi.org/10.1016/j.tsep.2023.102072

    149-23 Shardul Kamat, Wayne Cai, Teresa J. Rinker, Jennifer Bracey, Liang Xi, Wenda Tan, A novel integrated process-performance model for laser welding of multi-layer battery foils and tabs, Journal of Materials Processing Technology, 320; 118121, 2023. doi.org/10.1016/j.jmatprotec.2023.118121

    148-23 Reza Ghomashchi, Shahrooz Nafisi, Solidification of Al12Si melt pool in laser powder bed fusion, Journal of Materials En gineering and Performance, 2023. doi.org/10.1007/s11665-023-08502-3

    133-23 Hesam Moghadasi, Md Tusher Mollah, Deepak Marla, Hamid Saffari, Jon Spangenberg, Computational fluid dynamics modeling of top-down digital light processing additive manufacturing, Polymers, 15.11; 2459, 2023. doi.org/10.3390/polym15112459

    131-23 Luca Santoro, Raffaella Sesana, Rosario Molica Nardo, Francesca Curà, In line defect detection in steel welding process by means of thermography, Experimental Mechanics in Engineering and Biomechanics – Proceedings ICEM20, 19981, 2023.

    128-23 Md Tusher Mollah, Raphaël Comminal, Wilson Ricardo Leal da Silva, Berin Šeta, Jon Spangenberg, Computational fluid dynamics modelling and experimental analysis of reinforcement bar integration in 3D concrete printing, Cement and Concrete Research, 173; 107263, 2023. doi.org/10.1016/j.cemconres.2023.107263

    123-23 Arash Samaei, Zhongsheng Sang, Jennifer A. Glerum, Jon-Erik Mogonye, Gregory J. Wagner, Multiphysics modeling of mixing and material transport in additive manufacturing with multicomponent powder beds, Additive Manufacturing, 67; 103481, 2023. doi.org/10.1016/j.addma.2023.103481

    122-23 Chu Han, Ping Jiang, Shaoning Geng, Lingyu Guo, Kun Liu, Inhomogeneous microstructure distribution and its formation mechanism in deep penetration laser welding of medium-thick aluminum-lithium alloy plates, Optics & Laser Technology, 167; 109783, 2023. doi.org/10.1016/j.optlastec.2023.109783

    111-23 Alexander J. Myers, Guadalupe Quirarte, Francis Ogoke, Brandon M. Lane, Syed Zia Uddin, Amir Barati Farimani, Jack L. Beuth, Jonathan A. Malen, High-resolution melt pool thermal imaging for metals additive manufacturing using the two-color method with a color camera, Additive Manufacturing, 73; 103663, 2023. doi.org/10.1016/j.addma.2023.103663

    107-23 M. Mohsin Raza, Yu-Lung Lo, Hua-Bin Lee, Chang Yu-Tsung, Computational modeling of laser welding for aluminum–copper joints using a circular strategy, Journal of Materials Research and Technology, 25; pp. 3350-3364, 2023. doi.org/10.1016/j.jmrt.2023.06.122

    106-23 H.Z. Lu, L.H. Liu, X. Luo, H.W. Ma, W.S. Cai, R. Lupoi, S. Yin, C. Yang, Formation mechanism of heterogeneous microstructures and shape memory effect in NiTi shape memory alloy fabricated via laser powder bed fusion, Materials & Design, 232; 112107, 2023. doi.org/10.1016/j.matdes.2023.112107

    105-23 Harun Kahya, Hakan Gurun, Gokhan Kucukturk, Experimental and analytical investigation of the re-melting effect in the manufacturing of 316L by direct energy deposition (DED) method, Metals, 13.6; 1144, 2023. doi.org/10.3390/met13061144

    100-23 Dongju Chen, Gang Li, Peng Wang, Zhiqiang Zeng, Yuhang Tang, Numerical simulation of melt pool size and flow evolution for laser powder bed fusion of powder grade Ti6Al4V, Finite Elements in Analysis and Design, 223; 103971, 2023. doi.org/10.1016/j.finel.2023.103971

    97-23 Mahyar Khorasani, Martin Leary, David Downing, Jason Rogers, Amirhossein Ghasemi, Ian Gibson, Simon Brudler, Bernard Rolfe, Milan Brandt, Stuart Bateman, Numerical and experimental investigations on manufacturability of Al–Si–10Mg thin wall structures made by LB-PBF, Thin-Walled Structures, 188; 110814, 2023. doi.org/10.1016/j.tws.2023.110814

    95-23 M.S. Serdeczny, Laser welding of dissimilar materials – simulation driven optimization of process parameters, IOP Conference Series: Materials Science and Engineering, 1281; 012018, 2023. doi.org/10.1088/1757-899X/1281/1/012018

    90-23 Lin Liu, Tubin Liu, Xi Dong, Min Huang, Fusheng Cao, Mingli Qin, Numerical simulation of thermal dynamic behavior and morphology evolution of the molten pool of selective laser melting BN/316L stainless steel composite, Journal of Materials Engineering and Performance, 2023. doi.org/10.1007/s11665-023-08210-y

    89-23 M. P. Serdeczny, A. Jackman, High fidelity modelling of bead geometry in directed energy deposition – simulation driven optimization, Journal of Physics: Conference Series, NOLAMP19, 2023.

    88-23 Lu Wang, Shuhao Wang, Yanming Zhang, Wentao Yan, Multi-phase flow simulation of powder streaming in laser-based directed energy deposition, International Journal of Heat and Mass Transfer, 212; 124240, 2023. doi.org/10.1016/j.ijheatmasstransfer.2023.124240

    80-23 Mahyar Khorasani, AmirHossein Ghasemi, Martin Leary, David Downing, Ian Gibson, Elmira G. Sharabian, Jithin Kozuthala Veetil, Milan Brandt, Stuart Batement, Bernard Rolfe, Benchmark models for conduction and keyhole modes in laser-based powder bed fusion of Inconel 718, Optics & Laser Technology, 164; 109509, 2023. doi.org/10.1016/j.optlastec.2023.109509

    78-23   Md. Tusher Mollah, Raphaël Comminal, Marcin P. Serdeczny, Berin Šeta, Jon Spangenberg, Computational analysis of yield stress buildup and stability of deposited layers in material extrusion additive manufacturing, Additive Manufacturing, 71; 103605, 2023. doi.org/10.1016/j.addma.2023.103605

    76-23   Asif Ur Rehman, Kashif Azher, Abid Ullah, Celal Sami Tüfekci, Metin Uymaz Salamci, Binder jetting of SS316L: a computational approach for droplet-powder interaction, Rapid Prototyping Journal, 2023. doi.org/10.1108/RPJ-08-2022-0264

    75-23   Dengzhi Yao, Ju Wang, Hao Luo, Yuhang Wu, Xizhong An, Thermal behavior and control during multi-track laser powder bed fusion of 316 L stainless steel, Additive Manufacturing, 70; 103562, 2023. doi.org/10.1016/j.addma.2023.103562

    61-23   Yaqing Hou, Hang Su, Hao Zhang, Fafa Li, Xuandong Wang, Yazhou He, Dupeng He, An integrated simulation model towards laser powder bed fusion in-situ alloying technology, Materials & Design, 228; 111795, 2023. doi.org/10.1016/j.matdes.2023.111795

    56-23   Maohong Yang, Guiyi Wu, Xiangwei Li, Shuyan Zhang, Honghong Wang, Jiankang Huang, Influence of heat source model on the behavior of laser cladding pool, Journal of Laser Applications, 35.2; 2023. doi.org/10.2351/7.0000963

    45-23   Daniel Martinez, Philip King, Santosh Reddy Sama, Jay Sim, Hakan Toykoc, Guha Manogharan, Effect of freezing range on reducing casting defects through 3D sand-printed mold designs, The International Journal of Advanced Manufacturing Technology, 2023. doi.org/10.1007/s00170-023-11112-x

    39-23   Peter S. Cook, David J. Ritchie, Determining the laser absorptivity of Ti-6Al-4V during laser powder bed fusion by calibrated melt pool simulation, Optics & Laser Technology, 162; 109247. 2023. doi.org/10.1016/j.optlastec.2023.109247

    36-23   Yixuan Chen, Weihao Wang, Yao Ou, Yingna Wu, Zirong Zhai, Rui Yang, Impact of laser power and scanning velocity on microstructure and mechanical properties of Inconel 738LC alloys fabricated by laser powder bed fusion, TMS 2023 152nd Annual Meeting & Exhibition Supplemental Proceedings, pp. 138-149, 2023. doi.org/10.1007/978-3-031-22524-6_15

    34-23   Chao Kang, Ikki Ikeda, Motoki Sakaguchi, Recoil and solidification of a paraffin droplet impacted on a metal substrate: Numerical study and experimental verification, Journal of Fluids and Structures, 118; 103839, 2023. doi.org/10.1016/j.jfluidstructs.2023.103839

    30-23   Fei Wang, Tiechui Yuan, Ruidi Li, Shiqi Lin, Zhonghao Xie, Lanbo Li, Valentino Cristino, Rong Xu, Bing liu, Comparative study on microstructures and mechanical properties of ultra ductility single-phase Nb40Ti40Ta20 refractory medium entropy alloy by selective laser melting and vacuum arc melting, Journal of Alloys and Compounds, 942; 169065, 2023. doi.org/10.1016/j.jallcom.2023.169065

    29-23   Haejin Lee, Yeonghwan Song, Seungkyun Yim, Kenta Aoyagi, Akihiko Chiba, Byoungsoo Lee, Influence of linear energy on side surface roughness in powder bed fusion electron beam melting process: Coupled experimental and simulation study, Powder Technology, 418; 118292, 2023.

    27-23   Yinan Chen, Bo Li, Double-phase refractory medium entropy alloy NbMoTi via selective laser melting (SLM) additive manufacturing, Journal of Physics: Conference Series, 2419; 012074, 2023. doi.org/10.1088/1742-6596/2419/1/012074

    23-23   Yunwei Gui, Kenta Aoyagi, Akihiko Chiba, 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, Materials Science and Engineering: A, 864; 144595, 2023. doi.org/10.1016/j.msea.2023.144595

    21-23   Tatsuhiko Sakai, Yasuhiro Okamoto, Nozomi Taura, Riku Saito, Akira Okada, Effect of scanning speed on molten metal behaviour under angled irradiation with a continuous-wave laser, Journal of Materials Processing Technology, 313; 117866, 2023. doi.org/10.1016/j.jmatprotec.2023.117866

    19-23   Gianna M. Valentino, Arunima Banerjee, Alexander lark, Christopher M. Barr, Seth H. Myers, Ian D. McCue, Influence of laser processing parameters on the density-ductility tradeoff in additively manufactured pure tantalum, Additive Manufacturing Letters, 4; 100117, 2023. doi.org/10.1016/j.addlet.2022.100117

    15-23   Runbo Jiang, Zhongshu Ren, Joseph Aroh, Amir Mostafaei, Benjamin Gould, Tao Sun, Anthony D. Rollett, Quantifying equiaxed vs epitaxial solidification in laser melting of CMSX-4 single crystal superalloy, Metallurgical and Materials Transactions A, 54; pp. 808-822, 2023. doi.org/10.1007/s11661-022-06929-2

    14-23   Nguyen Thi Tien, Yu-Lung Lo, M. Mohsin Raza, Cheng-Yen Chen, Chi-Pin Chiu, Optimization of processing parameters for pulsed laser welding of dissimilar metal interconnects, Optics & Laser Technology, 159; 109022, 2023. doi.org/10.1016/j.optlastec.2022.109022

    9-23 Hou Yi Chia, Wentao Yan, High-fidelity modeling of metal additive manufacturing, Additive Manufacturing Technology: Design, Optimization, and Modeling, Ed. Kun Zhou, 2023.

    8-23 Akash Aggarwal, Yung C. Shin, Arvind Kumar, Investigation of the transient coupling between the dynamic laser beam absorptance and the melt pool – vapor depression morphology in laser powder bed fusion process, International Journal of Heat and Mass Transfer, 201.2; 123663, 2023. doi.org/10.1016/j.ijheatmasstransfer.2022.123663

    199-22 Md. Tusher Mollah, Raphaël Comminal, Marcin P. Serdeczny, David B. Pedersen, Jon Spangenberg, Numerical predictions of bottom layer stability in material extrusion additive manufacturing, JOM, 74; pp. 1096-1101, 2022. doi.org/10.1007/s11837-021-05035-9

    198-22 Md. Tusher Mollah, Amirpasha Moetazedian, Andy Gleadall, Jiongyi Yan, Wayne Edgar Alphonso, Raphael Comminal, Berin Seta, Tony Lock, Jon Spangenberg, Investigation on corner precision at different corner angles in material extrusion additive manufacturing: An experimental and computational fluid dynamics analysis, Proceedings of the 33rd Annual Solid Freeform Fabrication Symposium, 2022.

    197-22 Md. Tusher Mollah, Marcin P. Serdeczny, Raphaël Comminal, Berin Šeta, Marco Brander, David B. Pedersen, Jon Spangenberg, A numerical investigation of the inter-layer bond and surface roughness during the yield stress buildup in wet-on-wet material extrusion additive manufacturing, ASPE and euspen Summer Topical Meeting, 77, 2022.

    182-22   Chan Kyu Kim, Dae-Won Cho, Seok Kim, Sang Woo Song, Kang Myung Seo, Young Tae Cho, High-throughput metal 3D printing pen enabled by a continuous molten droplet transfer, Advanced Science, 2205085, 2022. doi.org/10.1002/advs.202205085

    180-22 Xu Kaikai, Gong Yadong, Zhang Qiang, Numerical simulation of dynamic analysis of molten pool in the process of direct energy deposition, The International Journal of Advanced Manufacturing Technology, 2022. doi.org/10.1007/s00170-022-10271-7

    179-22 Yasuhiro Okamoto, Nozomi Taura, Akira Okada, Study on laser drilling process of solid metal on its liquid, International Journal of Electrical Machining, 27; 2022. doi.org/10.2526/ijem.27.35

    175-22 Lu Min, Xhi Xiaojie, Lu Peipei, Wu Meiping, Forming quality and wettability of surface texture on CuSn10 fabricated by laser powder bed fusion, AIP Advances, 12.12; 125114, 2022. doi.org/10.1063/5.0122076

    174-22 Thinus Van Rhijn, Willie Du Preez, Maina Maringa, Dean Kouprianoff, An investigation into the optimization of the selective laser melting process parameters for Ti6Al4V through numerical modelling, JOM, 2022. doi.org/10.1007/s11837-022-05608-2

    171-22 Jonathan Yoshioka, Mohsen Eshraghi, Temporal evolution of temperature gradient and solidification rate in laser powder bed fusion additive manufacturing, Heat and Mass Transfer, 2022. doi.org/10.1007/s00231-022-03318-8

    170-22 Subin Shrestha and Kevin Chou, Residual heat effect on the melt pool geometry during the laser powder bed fusion process, Journal of Manufacturing and Materials Processing, 6.6; 153, 2022. doi.org/10.3390/jmmp6060153

    169-22 Aryan Aryan, Obinna Chukwubuzo, Desmond Bourgeois, Wei Zhang, Hardness prediction by incorporating heat transfer and molten pool fluid flow in a mult-pass, multi-layer weld for onsite repair of Grade 91 steel, U.S. Department of Energy Office of Scientific and Technical Information, DOE-OSU-0032067, 2022. doi.org/10.2172/1898594

    158-22 Dafan Du, Lu Wang, Anping Dong, Wentao Yan, Guoliang Zhu, Baode Sun, Promoting the densification and grain refinement with assistance of static magnetic field in laser powder bed fusion, International Journal of Machine Tools and Manufacture, 183; 103965, 2022. doi.org/10.1016/j.ijmachtools.2022.103965

    157-22 Han Chu, Jiang Ping, Geng Shaoning, Liu Kun, Nucleation mechanism in oscillating laser welds of 2024 aluminium alloy: A combined experimental and numerical study, Optics & Laser Technology, 158.A; 108812, 2022. doi.org/10.1016/j.optlastec.2022.108812

    153-22 Zixiang Li, Yinan Cui, Baohua Chang, Guan Liu, Ze Pu, Haoyu Zhang, Zhiyue Liang, Changmeng Liu, Li Wang, Dong Du, Manipulating molten pool in in-situ additive manufacturing of Ti-22Al-25 Nb through alternating dual-electron beams, Additive Manufacturing, 60.A; 103230, 2022. doi.org/10.1016/j.addma.2022.103230

    149-22   Qian Chen, Yao Fu, Albert C. To, Multiphysics modeling of particle spattering and induced defect formation mechanism in Inconel 718 laser powder bed fusion, The International Journal of Advanced Manufacturing Technology, 123; pp. 783-791, 2022. doi.org/10.1007/s00170-022-10201-7

    146-22   Zixuan Wan, Hui-ping Wang, Jingjing Li, Baixuan Yang, Joshua Solomon, Blair Carlson, Effect of welding mode on remote laser stitch welding of zinc-coated steel with different sheet thickness combinations, Journal of Manufacturing Science and Engineering, MANU-21-1598, 2022. doi.org/10.1115/1.4055792

    143-22   Du-Rim Eo, Seong-Gyu Chung, JeongHo Yang, Won Tae Cho, Sun-Hong Park, Jung-Wook Cho, Surface modification of high-Mn steel via laser-DED: Microstructural characterization and hot crack susceptibility of clad layer, Materials & Design, 223; 111188, 2022. doi.org/10.1016/j.matdes.2022.111188

    142-22   Zichuan Fu, Xiangman Zhou, Bin Luo, Qihua Tian, Numerical simulation study of the effect of weld current on WAAM welding pool dynamic and weld bead morphology, International Conference on Mechanical Design and Simulation, Proceedings, 12261; 122614G, 2022. doi.org/10.1117/12.2639074

    132-22   Yiyu Huang, Zhonghao Xie, Wenshu Li, Haoyu Chen, Bin Liu, Bingfeng Wang, Dynamic mechanical properties of the selective laser melting NiCrFeCoMo0.2 high entropy alloy and the microstructure of molten pool, Journal of Alloys and Compounds, 927; 167011, 2022. doi.org/10.1016/j.jallcom.2022.167011

    126-22   Jingqi Zhang, Yingang Liu, Gang Sha, Shenbao Jin, Ziyong Hou, Mohamad Bayat, Nan Yang, Qiyang Tan, Yu Yin, Shiyang Liu, Jesper Henri Hattel, Matthew Dargusch, Xiaoxu Huang, Ming-Xing Zhang, Designing against phase and property heterogeneities in additively manufactured titanium alloys, Nature Communications, 13; 4660, 2022. doi.org/10.1038/s41467-022-32446-2

    119-22   Xu Kaikai, Gong Yadong, Zhao Qiang, Numerical simulation on molten pool flow of Inconel718 alloy based on VOF during additive manufacturing, Materials Today Communications, 33; 104147, 2022. doi.org/10.1016/j.mtcomm.2022.104147

    118-22   AmirPouya Hemmasian, Francis Ogoke, Parand Akbari, Jonathan Malen, Jack Beuth, Amir Barati Farimani, Surrogate modeling of melt pool thermal field using deep learning, SSRN, 2022. doi.org/10.2139/ssrn.4190835

    117-22   Chiara Ransenigo, Marialaura Tocci, Filippo Palo, Paola Ginestra, Elisabetta Ceretti, Marcello Gelfi, Annalisa Pola, Evolution of melt pool and porosity during laser powder bed fusion of Ti6Al4V alloy: Numerical modelling and experimental validation, Lasers in Manufacturing and Materials Processing, 2022. doi.org/10.1007/s40516-022-00185-3

    112-22   Chris Jasien, Alec Saville, Chandler Gus Becker, Jonah Klemm-Toole, Kamel Fezzaa, Tao Sun, Tresa Pollock, Amy J. Clarke, In situ x-ray radiography and computational modeling to predict grain morphology in β-titanium during simulated additive manufacturing, Metals, 12.7; 1217, 2022. doi.org/10.3390/met12071217

    110-22   Haotian Zhou, Haijun Su, Yinuo Guo, Peixin Yang, Yuan Liu, Zhonglin Shen, Di Zhao, Haifang Liu, Taiwen Huang, Min Guo, Jun Zhang, Lin Liu, Hengzhi Fu, Formation and evolution mechanisms of pores in Inconel 718 during selective laser melting: Meso-scale modeling and experimental investigations, Journal of Manufacturing Processes, 81; pp. 202-213, 2022. doi.org/10.1016/j.jmapro.2022.06.072

    109-22   Yufan Zhao, Huakang Bian, Hao Wang, Aoyagi Kenta, Yamanaka Kenta, Akihiko Chiba, Non-equilibrium solidification behavior associated with powder characteristics during electron beam additive manufacturing, Materials & Design, 221; 110915, 2022. doi.org/10.1016/j.matdes.2022.110915

    107-22   Dan Lönn, David Spångberg, Study of process parameters in laser beam welding of copper hairpins, Thesis, University of Skövde, 2022.

    106-22   Liping Guo, Hongze Wang, Qianglong Wei, Hanjie Liu, An Wang, Yi Wu, Haowei Wang, A comprehensive model to quantify the effects of additional nano-particles on the printability in laser powder bed fusion of aluminum alloy and composite, Additive Manufacturing, 58; 103011, 2022. doi.org/10.1016/j.addma.2022.103011

    104-22   Hongjiang Pan, Thomas Dahmen, Mohamad Bayat, Kang Lin, Xiaodan Zhang, Independent effects of laser power and scanning speed on IN718’s precipitation and mechanical properties produced by LBPF plus heat treatment, Materials Science and Engineering: A, 849; 143530, 2022. doi.org/10.1016/j.msea.2022.143530

    101-22   Yufan Zhao, Kenta Aoyagi, Kenta Yamanaka, Akihiko Chiba, A survey on basic influencing factors of solidified grain morphology during electron beam melting, Materials & Design, 221; 110927, 2022. doi.org/10.1016/j.matdes.2022.110927

    98-22   Jon Spangenberg, Wilson Ricardo Leal da Silva, Md. Tusher Mollah, Raphaël Comminal, Thomas Juul Andersen, Henrik Stang, Integrating reinforcement with 3D concrete printing: Experiments and numerical modelling, Third RILEM International Conference on Concrete and Digital Fabrication, Eds. Ana Blanco, Peter Kinnell, Richard Buswell, Sergio Cavalaro, pp. 379-384, 2022.

    93-22   Minglei Qu, Qilin Guo, Luis I. Escano, Samuel J. Clark Kamel Fezzaa, Lianyi Chen, Mitigating keyhole pore formation by nanoparticles during laser powder bed fusion additive manufacturing, Additive Manufacturing Letters, 100068, 2022. doi.org/10.1016/j.addlet.2022.100068

    86-22   Patiparn Ninpetch, Prasert Chalermkarnnon, Pruet Kowitwarangkul, Multiphysics simulation of thermal-fluid behavior in laser powder bed fusion of H13 steel: Influence of layer thickness and energy input, Metals and Materials International, 2022. doi.org/10.1007/s12540-022-01239-z

    85-22   Merve Biyikli, Taner Karagoz, Metin Calli, Talha Muslim, A. Alper Ozalp, Ali Bayram, Single track geometry prediction of laser metal deposited 316L-Si via multi-physics modelling and regression analysis with experimental validation, Metals and Materials International, 2022. doi.org/10.1007/s12540-022-01243-3

    76-22   Zhichao Yang, Shuhao Wang, Lida Zhu, Jinsheng Ning, Bo Xin, Yichao Dun, Wentao Yan, Manipulating molten pool dynamics during metal 3D printing by ultrasound, Applied Physics Reviews, 9; 021416, 2022. doi.org/10.1063/5.0082461

    73-22   Yu Sun, Liqun Li, Yu Hao, Sanbao Lin, Xinhua Tang, Fenggui Lu, Numerical modeling on formation of periodic chain-like pores in high power laser welding of thick steel plate, Journal of Materials Processing Technology, 306; 117638, 2022. doi.org/10.1016/j.jmatprotec.2022.117638

    67-22   Yu Hao, Hiu-Ping Wang, Yu Sun, Liqun Li, Yihan Wu, Fenggui Lu, The evaporation behavior of zince and its effect on spattering in laser overlap welding of galvanized steels, Journal of Materials Processing Technology, 306; 117625, 2022. doi.org/10.1016/j.jmatprotec.2022.117625

    65-22   Yanhua Zhao, Chuanbin Du, Peifu Wang, Wei Meng, Changming Li, The mechanism of in-situ laser polishing and its effect on the surface quality of nickel-based alloy fabricated by selective laser melting, Metals, 12.5; 778, 2022. doi.org/10.3390/met12050778

    58-22   W.E. Alphonso, M. Bayat, M. Baier, S. Carmignato, J.H. Hattel, Multi-physics numerical modelling of 316L Austenitic stainless steel in laser powder bed fusion process at meso-scale, 17th UK Heat Transfer Conference (UKHTC2021), Manchester, UK, April 4-6, 2022.

    57-22   Brandon Hayes, Travis Hainsworth, Robert MacCurdy, Liquid-solid co-printing of multi-material 3D fluidic devices via material jetting, Additive Manufacturing, in press, 102785, 2022. doi.org/10.1016/j.addma.2022.102785

    55-22   Xiang Wang, Lin-Jie Zhang, Jie Ning, Suck-joo Na, Fluid thermodynamic simulation of Ti-6Al-4V alloy in laser wire deposition, 3D Printing and Additive Manufacturing, 2022. doi.org/10.1089/3dp.2021.0159

    54-22   Junhao Zhao, Binbin Wang, Tong Liu, Liangshu Luo, Yanan Wang, Xiaonan Zheng, Liang Wang, Yanqing Su, Jingjie Guo, Hengzhi Fu, Dayong Chen, Study of in situ formed quasicrystals in Al-Mn based alloys fabricated by SLM, Journal of Alloys and Compounds, 909; 164847, 2022. doi.org/10.1016/j.jallcom.2022.164847

    48-22   Yueming Sun, Jianxing Ma, Fei Peng, Konstantin G. Kornev, Making droplets from highly viscous liquids by pushing a wire through a tube, Physics of Fluids, 34; 032119, 2022. doi.org/10.1063/5.0082003

    46-22   H.Z. Lu, T. Chen, H. Liu, H. Wang, X. Luo, C.H. Song, Constructing function domains in NiTi shape memory alloys by additive manufacturing, Virtual and Physical Prototyping, 17.3; 2022. doi.org/10.1080/17452759.2022.2053821

    42-22   Islam Hassan, P. Ravi Selvaganapathy, Microfluidic printheads for highly switchable multimaterial 3D printing of soft materials, Advanced Materials Technologies, 2101709, 2022. doi.org/10.1002/admt.202101709

    41-22   Nan Yang, Youping Gong, Honghao Chen, Wenxin Li, Chuanping Zhou, Rougang Zhou, Huifeng Shao, Personalized artificial tibia bone structure design and processing based on laser powder bed fusion, Machines, 10.3; 205, 2022. doi.org/10.3390/machines10030205

    31-22   Bo Shen, Raghav Gnanasambandam, Rongxuan Wang, Zhenyu (James) Kong, Multi-Task Gaussian process upper confidence bound for hyperparameter tuning and its application for simulation studies of additive manufacturing, IISE Transactions, 2022. doi.org/10.1080/24725854.2022.2039813

    27-22   Lida Zhu, Shuhao Wang, Hao Lu, Dongxing Qi, Dan Wang, Zhichao Yang, Investigation on synergism between additive and subtractive manufacturing for curved thin-walled structure, Virtual and Physical Prototyping, 17.2; 2022. doi.org/10.1080/17452759.2022.2029009

    24-22   Hoon Sohn, Peipei Liu, Hansol Yoon, Kiyoon Yi, Liu Yang, Sangjun Kim, Real-time porosity reduction during metal directed energy deposition using a pulse laser, Journal of Materials Science & Technology, 116; pp. 214-223. doi.org/10.1016/j.jmst.2021.12.013

    18-22   Yaohong Xiao, Zixuan Wan, Pengwei Liu, Zhuo Wang, Jingjing Li, Lei Chen, Quantitative simulations of grain nucleation and growth at additively manufactured bimetallic interfaces of SS316L and IN625, Journal of Materials Processing Technology, 302; 117506, 2022. doi.org/10.1016/j.jmatprotec.2022.117506

    06-22   Amal Charles, Mohamad Bayat, Ahmed Elkaseer, Lore Thijs, Jesper Henri Hattel, Steffen Scholz, Elucidation of dross formation in laser powder bed fusion at down-facing surfaces: Phenomenon-oriented multiphysics simulation and experimental validation, Additive Manufacturing, 50; 102551, 2022. doi.org/10.1016/j.addma.2021.102551

    05-22   Feilong Ji, Xunpeng Qin, Zeqi Hu, Xiaochen Xiong, Mao Ni, Mengwu Wu, Influence of ultrasonic vibration on molten pool behavior and deposition layer forming morphology for wire and arc additive manufacturing, International Communications in Heat and Mass Transfer, 130; 105789, 2022. doi.org/10.1016/j.icheatmasstransfer.2021.105789

    150-21   Daniel Knüttel, Stefano Baraldo, Anna Valente, Konrad Wegener, Emanuele Carpanzano, Model based learning for efficient modelling of heat transfer dynamics, Procedia CIRP, 102; pp. 252-257, 2021. doi.org/10.1016/j.procir.2021.09.043

    149-21   T. van Rhijn, W. du Preez, M. Maringa, D. Kouprianoff, Towards predicting process parameters for selective laser melting of titanium alloys through the modelling of melt pool characteristics, Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie, 40.1; 2021. 

    148-21   Qian Chen, Multiscale process modeling of residual deformation and defect formation for laser powder bed fusion additive manufacturing, Thesis, University of Pittsburgh, Pittsburgh, PA USA, 2021. 

    147-21   Pareekshith Allu, Developing process parameters through CFD simulations, Lasers in Manufacturing Conference, 2021.

    143-21   Asif Ur Rehman, Muhammad Arif Mahmood, Fatih Pitir, Metin Uymaz Salamci, Andrei C. Popescu, Ion N. Mihailescu, Spatter formation and splashing induced defects in laser-based powder bed fusion of AlSi10Mg alloy: A novel hydrodynamics modelling with empirical testing, Metals, 11.12; 2023, 2021. doi.org/10.3390/met11122023

    142-21   Islam Hassan, Ponnambalam Ravi Selvaganapathy, A microfluidic printhead with integrated hybrid mixing by sequential injection for multimaterial 3D printing, Additive Manufacturing, 102559, 2021. doi.org/10.1016/j.addma.2021.102559

    137-21   Ting-Yu Cheng, Ying-Chih Liao, Enhancing drop mixing in powder bed by alternative particle arrangements with contradictory hydrophilicity, Journal of the Taiwan Institute of Chemical Engineers, 104160, 2021. doi.org/10.1016/j.jtice.2021.104160

    134-21   Asif Ur Rehman, Muhammad Arif Mahmood, Fatih Pitir, Metin Uymaz Salamci, Andrei C. Popescu, Ion N. Mihailescu, 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, Nanomaterials, 11.2; 3284, 2021. doi.org/10.3390/nano11123284

    128-21   Sang-Woo Han, Won-Ik Cho, Lin-Jie Zhang, Suck-Joo Na, Coupled simulation of thermal-metallurgical-mechanical behavior in laser keyhole welding of AH36 steel, Materials & Design, 212; 110275, 2021. doi.org/10.1016/j.matdes.2021.110275

    127-21   Jiankang Huang, Zhuoxuan Li, Shurong Yu, Xiaoquan Yu, Ding Fan, Real-time observation and numerical simulation of the molten pool flow and mass transfer behavior during wire arc additive manufacturing, Welding in the World, 2021. doi.org/10.1007/s40194-021-01214-z

    123-21   Boxue Song, Tianbiao Yu, Xingyu Jiang, Wenchao Xi, Xiaoli Lin, Zhelun Ma, ZhaoWang, Development of the molten pool and solidification characterization in single bead multilayer direct energy deposition, Additive Manufacturing, 102479, 2021. doi.org/10.1016/j.addma.2021.102479

    112-21   Kathryn Small, Ian D. McCue, Katrina Johnston, Ian Donaldson, Mitra L. Taheri, Precision modification of microstructure and properties through laser engraving, JOM, 2021. doi.org/10.1007/s11837-021-04959-6

    111-21   Yongki Lee, Jason Cheon, Byung-Kwon Min, Cheolhee Kim, Modelling of fume particle behaviour and coupling glass contamination during vacuum laser beam welding, Science and Technology of Welding and Joining, 2021. doi.org/10.1080/13621718.2021.1990658

    110-21   Menglin Liu, Hao Yi, Huajun Cao, Rufeng Huang, Le Jia, Heat accumulation effect in metal droplet-based 3D printing: Evolution mechanism and elimination strategy, Additive Manufacturing, 48.A; 102413, 2021. doi.org/10.1016/j.addma.2021.102413

    108-21   Nozomi Taura, Akiya Mitsunobu, Tatsuhiko Sakai, Yasuhiro Okamoto, Akira Okada, Formation and its mechanism of high-speed micro-grooving on metal surface by angled CW laser irradiation, Journal of Laser Micro/Nanoengineering, 16.2, 2021. doi.org/10.2961/jlmn.2021.02.2006

    105-21   Jon Spangenberg, Wilson Ricardo Leal da Silva, Raphaël Comminal, Md. Tusher Mollah, Thomas Juul Andersen, Henrik Stang, Numerical simulation of multi-layer 3D concrete printing, RILEM Technical Letters, 6; pp. 119-123, 2021. doi.org/10.21809/rilemtechlett.2021.142

    104-21   Lin Chen, Chunming Wang, Gaoyang Mi, Xiong Zhang, Effects of laser oscillating frequency on energy distribution, molten pool morphology and grain structure of AA6061/AA5182 aluminum alloys lap welding, Journal of Materials Research and Technology, 15; pp. 3133-3148, 2021. doi.org/10.1016/j.jmrt.2021.09.141

    101-21   R.J.M. Wolfs, T.A.M. Salet, N. Roussel, Filament geometry control in extrusion-based additive manufacturing of concrete: The good, the bad and the ugly, Cement and Concrete Research, 150; 106615, 2021. doi.org/10.1016/j.cemconres.2021.106615

    89-21   Wenlin Ye, Jin Bao, Jie Lei, Yichang Huang, Zhihao Li, Peisheng Li, Ying Zhang, Multiphysics modeling of thermal behavior of commercial pure titanium powder during selective laser melting, Metals and Materials International, 2021. doi.org/10.1007/s12540-021-01019-1

    81-21   Lin Chen, Gaoyang Mi, Xiong Zhang, Chunming Wang, Effects of sinusoidal oscillating laser beam on weld formation, melt flow and grain structure during aluminum alloys lap welding, Journals of Materials Processing Technology, 298; 117314, 2021. doi.org/10.1016/j.jmatprotec.2021.117314

    77-21   Yujie Cui, Yufan Zhao, Haruko Numata, Kenta Yamanaka, Huakang Bian, Kenta Aoyagi, Akihiko Chiba, Effects of process parameters and cooling gas on powder formation during the plasma rotating electrode process, Powder Technology, 393; pp. 301-311, 2021. doi.org/10.1016/j.powtec.2021.07.062

    76-21   Md Tusher Mollah, Raphaël Comminal, Marcin P. Serdeczny, David B. Pedersen, Jon Spangenberg, Stability and deformations of deposited layers in material extrusion additive manufacturing, Additive Manufacturing, 46; 102193, 2021. doi.org/10.1016/j.addma.2021.102193

    72-21   S. Sabooni, A. Chabok, S.C. Feng, H. Blaauw, T.C. Pijper, H.J. Yang, Y.T. Pei, 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, Additive Manufacturing, 46; 102176, 2021. doi.org/10.1016/j.addma.2021.102176

    71-21   Yu Hao, Nannan Chena, Hui-Ping Wang, Blair E. Carlson, Fenggui Lu, Effect of zinc vapor forces on spattering in partial penetration laser welding of zinc-coated steels, Journal of Materials Processing Technology, 298; 117282, 2021. doi.org/10.1016/j.jmatprotec.2021.117282

    67-21   Lu Wang, Wentao Yan, Thermoelectric magnetohydrodynamic model for laser-based metal additive manufacturing, Physical Review Applied, 15.6; 064051, 2021. doi.org/10.1103/PhysRevApplied.15.064051

    61-21   Ian D. McCue, Gianna M. Valentino, Douglas B. Trigg, Andrew M. Lennon, Chuck E. Hebert, Drew P. Seker, Salahudin M. Nimer, James P. Mastrandrea, Morgana M. Trexler, Steven M. Storck, Controlled shape-morphing metallic components for deployable structures, Materials & Design, 208; 109935, 2021. doi.org/10.1016/j.matdes.2021.109935

    60-21   Mahyar Khorasani, AmirHossein Ghasemi, Martin Leary, William O’Neil, Ian Gibson, Laura Cordova, Bernard Rolfe, Numerical and analytical investigation on meltpool temperature of laser-based powder bed fusion of IN718, International Journal of Heat and Mass Transfer, 177; 121477, 2021. doi.org/10.1016/j.ijheatmasstransfer.2021.121477

    57-21   Dae-Won Cho, Yeong-Do Park, Muralimohan Cheepu, Numerical simulation of slag movement from Marangoni flow for GMAW with computational fluid dynamics, International Communications in Heat and Mass Transfer, 125; 105243, 2021. doi.org/10.1016/j.icheatmasstransfer.2021.105243

    55-21   Won-Sang Shin, Dae-Won Cho, Donghyuck Jung, Heeshin Kang, Jeng O Kim, Yoon-Jun Kim, Changkyoo Park, Investigation on laser welding of Al ribbon to Cu sheet: Weldability, microstructure and mechanical and electrical properties, Metals, 11.5; 831, 2021. doi.org/10.3390/met11050831

    50-21   Mohamad Bayat, Venkata K. Nadimpalli, Francesco G. Biondani, Sina Jafarzadeh, Jesper Thorborg, Niels S. Tiedje, Giuliano Bissacco, David B. Pedersen, Jesper H. Hattel, On the role of the powder stream on the heat and fluid flow conditions during directed energy deposition of maraging steel—Multiphysics modeling and experimental validation, Additive Manufacturing, 43;102021, 2021. doi.org/10.1016/j.addma.2021.102021

    47-21   Subin Shrestha, Kevin Chou, An investigation into melting modes in selective laser melting of Inconel 625 powder: single track geometry and porosity, The International Journal of Advanced Manufacturing Technology, 2021. doi.org/10.1007/s00170-021-07105-3

    34-21   Haokun Sun, Xin Chu, Cheng Luo, Haoxiu Chen, Zhiying Liu, Yansong Zhang, Yu Zou, Selective laser melting for joining dissimilar materials: Investigations ofiInterfacial characteristics and in situ alloying, Metallurgical and Materials Transactions A, 52; pp. 1540-1550, 2021. doi.org/10.1007/s11661-021-06178-9

    32-21   Shanshan Zhang, Subin Shrestha, Kevin Chou, On mesoscopic surface formation in metal laser powder-bed fusion process, Supplimental Proceedings, TMS 150th Annual Meeting & Exhibition (Virtual), pp. 149-161, 2021. doi.org/10.1007/978-3-030-65261-6_14

    22-21   Patiparn Ninpetch, Pruet Kowitwarangkul, Sitthipong Mahathanabodee, Prasert Chalermkarnnon, Phadungsak Rattanadecho, Computational investigation of thermal behavior and molten metal flow with moving laser heat source for selective laser melting process, Case Studies in Thermal Engineering, 24; 100860, 2021. doi.org/10.1016/j.csite.2021.100860

    19-21   M.B. Abrami, C. Ransenigo, M. Tocci, A. Pola, M. Obeidi, D. Brabazon, Numerical simulation of laser powder bed fusion processes, La Metallurgia Italiana, February; pp. 81-89, 2021.

    16-21   Wenjun Ge, Jerry Y.H. Fuh, Suck Joo Na, Numerical modelling of keyhole formation in selective laser melting of Ti6Al4V, Journal of Manufacturing Processes, 62; pp. 646-654, 2021. doi.org/10.1016/j.jmapro.2021.01.005

    11-21   Mohamad Bayat, Venkata K. Nadimpalli, David B. Pedersen, Jesper H. Hattel, A fundamental investigation of thermo-capillarity in laser powder bed fusion of metals and alloys, International Journal of Heat and Mass Transfer, 166; 120766, 2021. doi.org/10.1016/j.ijheatmasstransfer.2020.120766

    10-21   Yufan Zhao, Yuichiro Koizumi, Kenta Aoyagi, Kenta Yamanaka, Akihiko Chiba, Thermal properties of powder beds in energy absorption and heat transfer during additive manufacturing with electron beam, Powder Technology, 381; pp. 44-54, 2021. doi.org/10.1016/j.powtec.2020.11.082

    9-21   Subin Shrestha, Kevin Chou, A study of transient and steady-state regions from single-track deposition in laser powder bed fusion, Journal of Manufacturing Processes, 61; pp. 226-235, 2021. doi.org/10.1016/j.jmapro.2020.11.023

    6-21   Qian Chen, Yunhao Zhao, Seth Strayer, Yufan Zhao, Kenta Aoyagi, Yuichiro Koizumi, Akihiko Chiba, Wei Xiong, Albert C. To, Elucidating the effect of preheating temperature on melt pool morphology variation in Inconel 718 laser powder bed fusion via simulation and experiment, Additive Manufacturing, 37; 101642, 2021. doi.org/10.1016/j.addma.2020.101642

    04-21   Won-Ik Cho, Peer Woizeschke, Analysis of molten pool dynamics in laser welding with beam oscillation and filler wire feeding, International Journal of Heat and Mass Transfer, 164; 120623, 2021. doi.org/10.1016/j.ijheatmasstransfer.2020.120623

    128-20   Mahmood Al Bashir, Rajeev Nair, Martina M. Sanchez, Anil Mahapatro, Improving fluid retention properties of 316L stainless steel using nanosecond pulsed laser surface texturing, Journal of Laser Applications, 32.4, 2020. doi.org/10.2351/7.0000199

    127-20   Eric Riedel, Niklas Bergedieck, Stefan Scharf, CFD simulation based investigation of cavitation cynamics during high intensity ultrasonic treatment of A356, Metals, 10.11; 1529, 2020. doi.org/10.3390/met10111529

    126-20   Benjamin Himmel, Material jetting of aluminium: Analysis of a novel additive manufacturing process, Thesis, Technical University of Munich, Munich, Germany, 2020. 

    121-20   Yufan Zhao, Yujie Cui, Haruko Numata, Huakang Bian, Kimio Wako, Kenta Yamanaka, Kenta Aoyagi, Akihiko Chiba, Centrifugal granulation behavior in metallic powder fabrication by plasma rotating electrode process, Scientific Reports, 10; 18446, 2020. doi.org/10.1038/s41598-020-75503-w

    116-20   Raphael Comminal, Wilson Ricardo Leal da Silva, Thomas Juul Andersen, Henrik Stang, Jon Spangenberg, Modelling of 3D concrete printing based on computational fluid dynamics, Cement and Concrete Research, 138; 106256, 2020. doi.org/10.1016/j.cemconres.2020.106256

    112-20   Peng Liu, Lijin Huan, Yu Gan, Yuyu Lei, Effect of plate thickness on weld pool dynamics and keyhole-induced porosity formation in laser welding of Al alloy, The International Journal of Advanced Manufacturing Technology, 111; pp. 735-747, 2020. doi.org/10.1007/s00170-020-05818-5

    108-20   Fan Chen, Wentao Yan, High-fidelity modelling of thermal stress for additive manufacturing by linking thermal-fluid and mechanical models, Materials & Design, 196; 109185, 2020. doi.org/10.1016/j.matdes.2020.109185

    104-20   Yunfu Tian, Lijun Yang, Dejin Zhao, Yiming Huang, Jiajing Pan, Numerical analysis of powder bed generation and single track forming for selective laser melting of SS316L stainless steel, Journal of Manufacturing Processes, 58; pp. 964-974, 2020. doi.org/10.1016/j.jmapro.2020.09.002

    100-20   Raphaël Comminal, Sina Jafarzadeh, Marcin Serdeczny, Jon Spangenberg, Estimations of interlayer contacts in extrusion additive manufacturing using a CFD model, International Conference on Additive Manufacturing in Products and Applications (AMPA), Zurich, Switzerland, September 1-3: Industrializing Additive Manufacturing, pp. 241-250, 2020. doi.org/10.1007/978-3-030-54334-1_17

    97-20   Paree Allu, CFD simulation for metal Additive Manufacturing: Applications in laser- and sinter-based processes, Metal AM, 6.4; pp. 151-158, 2020.

    95-20   Yufan Zhao, Kenta Aoyagi, Kenta Yamanaka, Akihiko Chiba, Role of operating and environmental conditions in determining molten pool dynamics during electron beam melting and selective laser melting, Additive Manufacturing, 36; 101559, 2020. doi.org/10.1016/j.addma.2020.101559

    94-20   Yan Zeng, David Himmler, Peter Randelzhofer, Carolin Körner, Processing of in situ Al3Ti/Al composites by advanced high shear technology: influence of mixing speed, The International Journal of Advanced Manufacturing Technology, 110; pp. 1589-1599, 2020. doi.org/10.1007/s00170-020-05956-w

    93-20   H. Hamed Zargari, K. Ito, M. Kumar, A. Sharma, Visualizing the vibration effect on the tandem-pulsed gas metal arc welding in the presence of surface tension active elements, International Journal of Heat and Mass Transfer, 161; 120310, 2020. doi.org/10.1016/j.ijheatmasstransfer.2020.120310

    90-20   Guangxi Zhao, Jun Du, Zhengying Wei, Siyuan Xu, Ruwei Geng, Numerical analysis of aluminum alloy fused coating process, Journal of the Brazilian Society of Mechanical Science and Engineering, 42; 483, 2020. doi.org/10.1007/s40430-020-02569-y

    85-20   Wenkang Huang, Hongliang Wang, Teresa Rinker, Wenda Tan, Investigation of metal mixing in laser keyhold welding of dissimilar metals, Materials & Design, 195; 109056, 2020. doi.org/10.1016/j.matdes.2020.109056

    82-20   Pan Lu, Zhang Cheng-Lin, Wang Liang, Liu Tong, Liu Jiang-lin, Molten pool structure, temperature and velocity flow in selective laser melting AlCu5MnCdVA alloy, Materials Research Express, 7; 086516, 2020. doi.org/10.1088/2053-1591/abadcf

    80-20   Yujie Cui, Yufan Zhao, Haruko Numata, Huakang Bian, Kimio Wako, Kento Yamanaka, Kenta Aoyagi, Chen Zhang, Akihiko Chiba, Effects of plasma rotating electrode process parameters on the particle size distribution and microstructure of Ti-6Al-4 V alloy powder, Powder Technology, 376; pp. 363-372, 2020. doi.org/10.1016/j.powtec.2020.08.027

    78-20   F.Q. Liu, L. Wei, S.Q. Shi, H.L. Wei, On the varieties of build features during multi-layer laser directed energy deposition, Additive Manufacturing, 36; 101491, 2020. doi.org/10.1016/j.addma.2020.101491

    75-20   Nannan Chen, Zixuan Wan, Hui-Ping Wang, Jingjing Li, Joshua Solomon, Blair E. Carlson, Effect of Al single bond Si coating on laser spot welding of press hardened steel and process improvement with annular stirring, Materials & Design, 195; 108986, 2020. doi.org/10.1016/j.matdes.2020.108986

    72-20   Yujie Cui, Kenta Aoyagi, Yufan Zhao, Kenta Yamanaka, Yuichiro Hayasaka, Yuichiro Koizumi, Tadashi Fujieda, Akihiko Chiba, Manufacturing of a nanosized TiB strengthened Ti-based alloy via electron beam powder bed fusion, Additive Manufacturing, 36; 101472, 2020. doi.org/10.1016/j.addma.2020.101472

    64-20   Dong-Rong Liu, Shuhao Wang, Wentao Yan, Grain structure evolution in transition-mode melting in direct energy deposition, Materials & Design, 194; 108919, 2020. doi.org/10.1016/j.matdes.2020.108919

    61-20   Raphael Comminal, Wilson Ricardo Leal da Silva, Thomas Juul Andersen, Henrik Stang, Jon Spangenberg, Influence of processing parameters on the layer geometry in 3D concrete printing: Experiments and modelling, 2nd RILEM International Conference on Concrete and Digital Fabrication, RILEM Bookseries, 28; pp. 852-862, 2020. doi.org/10.1007/978-3-030-49916-7_83

    60-20   Marcin P. Serdeczny, Raphaël Comminal, Md. Tusher Mollah, David B. Pedersen, Jon Spangenberg, Numerical modeling of the polymer flow through the hot-end in filament-based material extrusion additive manufacturing, Additive Manufacturing, 36; 101454, 2020. doi.org/10.1016/j.addma.2020.101454

    58-20   H.L. Wei, T. Mukherjee, W. Zhang, J.S. Zuback, G.L. Knapp, A. De, T. DebRoy, Mechanistic models for additive manufacturing of metallic components, Progress in Materials Science, 116; 100703, 2020. doi.org/10.1016/j.pmatsci.2020.100703

    55-20   Masoud Mohammadpour, Experimental study and numerical simulation of heat transfer and fluid flow in laser welded and brazed joints, Thesis, Southern Methodist University, Dallas, TX, US; Available in Mechanical Engineering Research Theses and Dissertations, 24, 2020.

    48-20   Masoud Mohammadpour, Baixuan Yang, Hui-Ping Wang, John Forrest, Michael Poss, Blair Carlson, Radovan Kovacevica, Influence of laser beam inclination angle on galvanized steel laser braze quality, Optics and Laser Technology, 129; 106303, 2020. doi.org/10.1016/j.optlastec.2020.106303

    34-20   Binqi Liu, Gang Fang, Liping Lei, Wei Liu, A new ray tracing heat source model for mesoscale CFD simulation of selective laser melting (SLM), Applied Mathematical Modeling, 79; pp. 506-520, 2020. doi.org/10.1016/j.apm.2019.10.049

    27-20   Xuesong Gao, Guilherme Abreu Farira, Wei Zhang and Kevin Wheeler, Numerical analysis of non-spherical particle effect on molten pool dynamics in laser-powder bed fusion additive manufacturing, Computational Materials Science, 179, art. no. 109648, 2020. doi.org/10.1016/j.commatsci.2020.109648

    26-20   Yufan Zhao, Yuichiro Koizumi, Kenta Aoyagi, Kenta Yamanaka and Akihiko Chiba, Isothermal γ → ε phase transformation behavior in a Co-Cr-Mo alloy depending on thermal history during electron beam powder-bed additive manufacturing, Journal of Materials Science & Technology, 50, pp. 162-170, 2020. doi.org/10.1016/j.jmst.2019.11.040

    21-20   Won-Ik Cho and Peer Woizeschke, Analysis of molten pool behavior with buttonhole formation in laser keyhole welding of sheet metal, International Journal of Heat and Mass Transfer, 152, art. no. 119528, 2020. doi.org/10.1016/j.ijheatmasstransfer.2020.119528

    06-20  Wei Xing, Di Ouyang, Zhen Chen and Lin Liu, Effect of energy density on defect evolution in 3D printed Zr-based metallic glasses by selective laser melting, Science China Physics, Mechanics & Astronomy, 63, art. no. 226111, 2020. doi.org/10.1007/s11433-019-1485-8

    04-20   Santosh Reddy Sama, Tony Badamo, Paul Lynch and Guha Manogharan, Novel sprue designs in metal casting via 3D sand-printing, Additive Manufacturing, 25, pp. 563-578, 2019. doi.org/10.1016/j.addma.2018.12.009

    02-20   Dongsheng Wu, Shinichi Tashiro, Ziang Wu, Kazufumi Nomura, Xueming Hua, and Manabu Tanaka, Analysis of heat transfer and material flow in hybrid KPAW-GMAW process based on the novel three dimensional CFD simulation, International Journal of Heat and Mass Transfer, 147, art. no. 118921, 2020. doi.org/10.1016/j.ijheatmasstransfer.2019.118921

    01-20   Xiang Huang, Siying Lin, Zhenxiang Bu, Xiaolong Lin, Weijin Yi, Zhihong Lin, Peiqin Xie, and Lingyun Wang, Research on nozzle and needle combination for high frequency piezostack-driven dispenser, International Journal of Adhesion and Adhesives, 96, 2020. doi.org/10.1016/j.ijadhadh.2019.102453

    88-19   Bo Cheng and Charles Tuffile, Numerical study of porosity formation with implementation of laser multiple reflection in selective laser melting, Proceedings Volume 1: Additive Manufacturing; Manufacturing Equipment and Systems; Bio and Sustainable Manufacturing, ASME 2019 14th International Manufacturing Science and Engineering Conference, Erie, Pennsylvania, USA, June 10-14, 2019. doi.org/10.1115/MSEC2019-2891

    87-19   Shuhao Wang, Lida Zhu, Jerry Ying His Fuh, Haiquan Zhang, and Wentao Yan, Multi-physics modeling and Gaussian process regression analysis of cladding track geometry for direct energy deposition, Optics and Lasers in Engineering, 127:105950, 2019. doi.org/10.1016/j.optlaseng.2019.105950

    78-19   Bo Cheng, Lukas Loeber, Hannes Willeck, Udo Hartel, and Charles Tuffile, Computational investigation of melt pool process dynamics and pore formation in laser powder bed fusion, Journal of Materials Engineering and Performance, 28:11, 6565-6578, 2019. doi.org/10.1007/s11665-019-04435-y

    77-19   David Souders, Pareekshith Allu, Anurag Chandorkar, and Ruendy Castillo, Application of computational fluid dynamics in developing process parameters for additive manufacturing, Additive Manufacturing Journal, 9th International Conference on 3D Printing and Additive Manufacturing Technologies (AM 2019), Bangalore, India, September 7-9, 2019.

    75-19   Raphaël Comminal, Marcin Piotr Serdeczny, Navid Ranjbar, Mehdi Mehrali, David Bue Pedersen, Henrik Stang, Jon Spangenberg, Modelling of material deposition in big area additive manufacturing and 3D concrete printing, Proceedings, Advancing Precision in Additive Manufacturing, Nantes, France, September 16-18, 2019.

    73-19   Baohua Chang, Zhang Yuan, Hao Cheng, Haigang Li, Dong Du 1, and Jiguo Shan, A study on the influences of welding position on the keyhole and molten pool behavior in laser welding of a titanium alloy, Metals, 9:1082, 2019. doi.org/10.3390/met9101082

    57-19     Shengjie Deng, Hui-Ping Wang, Fenggui Lu, Joshua Solomon, and Blair E. Carlson, Investigation of spatter occurrence in remote laser spiral welding of zinc-coated steels, International Journal of Heat and Mass Transfer, Vol. 140, pp. 269-280, 2019. doi.org/10.1016/j.ijheatmasstransfer.2019.06.009

    53-19     Mohamad Bayat, Aditi Thanki, Sankhya Mohanty, Ann Witvrouw, Shoufeng Yang, Jesper Thorborg, Niels Skat Tieldje, and Jesper Henri Hattel, Keyhole-induced porosities in Laser-based Powder Bed Fusion (L-PBF) of Ti6Al4V: High-fidelity modelling and experimental validation, Additive Manufacturing, Vol. 30, 2019. doi.org/10.1016/j.addma.2019.100835

    51-19     P. Ninpetch, P. Kowitwarangkul, S. Mahathanabodee, R. Tongsri, and P. Ratanadecho, Thermal and melting track simulations of laser powder bed fusion (L-PBF), International Conference on Materials Research and Innovation (ICMARI), Bangkok, Thailand, December 17-21, 2018. IOP Conference Series: Materials Science and Engineering, Vol. 526, 2019. doi.org/10.1088/1757-899X/526/1/012030

    46-19     Hongze Wang and Yu Zou, Microscale interaction between laser and metal powder in powder-bed additive manufacturing: Conduction mode versus keyhole mode, International Journal of Heat and Mass Transfer, Vol. 142, 2019. doi.org/10.1016/j.ijheatmasstransfer.2019.118473

    45-19     Yufan Zhao, Yuichiro Koizumi, Kenta Aoyagi, Kenta Yamanaka, and Akihiko Chiba, Manipulating local heat accumulation towards controlled quality and microstructure of a Co-Cr-Mo alloy in powder bed fusion with electron beam, Materials Letters, Vol. 254, pp. 269-272, 2019. doi.org/10.1016/j.matlet.2019.07.078

    44-19     Guoxiang Xu, Lin Li, Houxiao Wang, Pengfei Li, Qinghu Guo, Qingxian Hu, and Baoshuai Du, Simulation and experimental studies of keyhole induced porosity in laser-MIG hybrid fillet welding of aluminum alloy in the horizontal position, Optics & Laser Technology, Vol. 119, 2019. doi.org/10.1016/j.optlastec.2019.105667

    38-19     Subin Shrestha and Y. Kevin Chou, A numerical study on the keyhole formation during laser powder bed fusion process, Journal of Manufacturing Science and Engineering, Vol. 141, No. 10, 2019. doi.org/10.1115/1.4044100

    34-19     Dae-Won Cho, Jin-Hyeong Park, and Hyeong-Soon Moon, A study on molten pool behavior in the one pulse one drop GMAW process using computational fluid dynamics, International Journal of Heat and Mass Transfer, Vol. 139, pp. 848-859, 2019. doi.org/10.1016/j.ijheatmasstransfer.2019.05.038

    30-19     Mohamad Bayat, Sankhya Mohanty, and Jesper Henri Hattel, Multiphysics modelling of lack-of-fusion voids formation and evolution in IN718 made by multi-track/multi-layer L-PBF, International Journal of Heat and Mass Transfer, Vol. 139, pp. 95-114, 2019. doi.org/10.1016/j.ijheatmasstransfer.2019.05.003

    29-19     Yufan Zhao, Yuichiro Koizumi, Kenta Aoyagi, Daixiu Wei, Kenta Yamanaka, and Akihiko Chiba, Comprehensive study on mechanisms for grain morphology evolution and texture development in powder bed fusion with electron beam of Co–Cr–Mo alloy, Materialia, Vol. 6, 2019. doi.org/10.1016/j.mtla.2019.100346

    28-19     Pareekshith Allu, Computational fluid dynamics modeling in additive manufacturing processes, The Minerals, Metals & Materials Society (TMS) 148th Annual Meeting & Exhibition, San Antonio, Texas, USA, March 10-14, 2019.

    24-19     Simulation Software: Use, Advantages & Limitations, The Additive Manufacturing and Welding Magazine, Vol. 2, No. 2, 2019

    22-19     Hunchul Jeong, Kyungbae Park, Sungjin Baek, and Jungho Cho, Thermal efficiency decision of variable polarity aluminum arc welding through molten pool analysis, International Journal of Heat and Mass Transfer, Vol. 138, pp. 729-737, 2019. doi.org/10.1016/j.ijheatmasstransfer.2019.04.089

    07-19   Guangxi Zhao, Jun Du, Zhengying Wei, Ruwei Geng and Siyuan Xu, Numerical analysis of arc driving forces and temperature distribution in pulsed TIG welding, Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 41, No. 60, 2019. doi.org/10.1007/s40430-018-1563-0

    04-19   Santosh Reddy Sama, Tony Badamo, Paul Lynch and Guha Manogharan, Novel sprue designs in metal casting via 3D sand-printing, Additive Manufacturing, Vol. 25, pp. 563-578, 2019. doi.org/10.1016/j.addma.2018.12.009

    03-19   Dongsheng Wu, Anh Van Nguyen, Shinichi Tashiro, Xueming Hua and Manabu Tanaka, Elucidation of the weld pool convection and keyhole formation mechanism in the keyhold plasma arc welding, International Journal of Heat and Mass Transfer, Vol. 131, pp. 920-931, 2019. doi.org/10.1016/j.ijheatmasstransfer.2018.11.108

    97-18   Wentao Yan, Ya Qian, Wenjun Ge, Stephen Lin, Wing Kam Liu, Feng Lin, Gregory J. Wagner, Meso-scale modeling of multiple-layer fabrication process in Selective Electron Beam Melting: Inter-layer/track voids formation, Materials & Design, 2018. doi.org/10.1016/j.matdes.2017.12.031

    84-18   Bo Cheng, Xiaobai Li, Charles Tuffile, Alexander Ilin, Hannes Willeck and Udo Hartel, Multi-physics modeling of single track scanning in selective laser melting: Powder compaction effect, Proceedings of the 29th Annual International Solid Freeform Fabrication Symposium, pp. 1887-1902, 2018.

    81-18 Yufan Zhao, Yuichiro Koizumi, Kenta Aoyagi, Daixiu Wei, Kenta Yamanaka and Akihiko Chiba, Molten pool behavior and effect of fluid flow on solidification conditions in selective electron beam melting (SEBM) of a biomedical Co-Cr-Mo alloy, Additive Manufacturing, Vol. 26, pp. 202-214, 2019. doi.org/10.1016/j.addma.2018.12.002

    77-18   Jun Du and Zhengying Wei, Numerical investigation of thermocapillary-induced deposited shape in fused-coating additive manufacturing process of aluminum alloy, Journal of Physics Communications, Vol. 2, No. 11, 2018. doi.org/10.1088/2399-6528/aaedc7

    76-18   Yu Xiang, Shuzhe Zhang, Zhengying We, Junfeng Li, Pei Wei, Zhen Chen, Lixiang Yang and Lihao Jiang, Forming and defect analysis for single track scanning in selective laser melting of Ti6Al4V, Applied Physics A, 124:685, 2018. doi.org/10.1007/s00339-018-2056-9

    74-18   Paree Allu, CFD simulations for laser welding of Al Alloys, Proceedings, Die Casting Congress & Exposition, Indianapolis, IN, October 15-17, 2018.

    72-18   Hunchul Jeong, Kyungbae Park, Sungjin Baek, Dong-Yoon Kim, Moon-Jin Kang and Jungho Cho, Three-dimensional numerical analysis of weld pool in GMAW with fillet joint, International Journal of Precision Engineering and Manufacturing, Vol. 19, No. 8, pp. 1171-1177, 2018. doi.org/10.1007/s12541-018-0138-4

    60-18   R.W. Geng, J. Du, Z.Y. Wei and G.X. Zhao, An adaptive-domain-growth method for phase field simulation of dendrite growth in arc preheated fused-coating additive manufacturing, IOP Conference Series: Journal of Physics: Conference Series 1063, 012077, 2018. doi.org/10.1088/1742-6596/1063/1/012077

    59-18   Guangxi Zhao, Jun Du, Zhengying Wei, Ruwei Geng and Siyuan Xu, Coupling analysis of molten pool during fused coating process with arc preheating, IOP Conference Series: Journal of Physics: Conference Series 1063, 012076, 2018. doi.org/10.1088/1742-6596/1063/1/012076 (Available at http://iopscience.iop.org/article/10.1088/1742-6596/1063/1/012076/pdf and in shared drive)

    58-18   Siyuan Xu, Zhengying Wei, Jun Du, Guangxi Zhao and Wei Liu, Numerical simulation and analysis of metal fused coating forming, IOP Conference Series: Journal of Physics: Conference Series 1063, 012075, 2018. doi.org/10.1088/1742-6596/1063/1/012075

    55-18   Jason Cheon, Jin-Young Yoon, Cheolhee Kim and Suck-Joo Na, A study on transient flow characteristic in friction stir welding with realtime interface tracking by direct surface calculation, Journal of Materials Processing Tech., vol. 255, pp. 621-634, 2018.

    54-18   V. Sukhotskiy, P. Vishnoi, I. H. Karampelas, S. Vader, Z. Vader, and E. P. Furlani, Magnetohydrodynamic drop-on-demand liquid metal additive manufacturing: System overview and modeling, Proceedings of the 5th International Conference of Fluid Flow, Heat and Mass Transfer, Niagara Falls, Canada, June 7 – 9, 2018; Paper no. 155, 2018. doi.org/10.11159/ffhmt18.155

    52-18   Michael Hilbinger, Claudia Stadelmann, Matthias List and Robert F. Singer, Temconex® – Kontinuierliche Pulverextrusion: Verbessertes Verständnis mit Hilfe der numerischen Simulation, Hochleistungsmetalle und Prozesse für den Leichtbau der Zukunft, Tagungsband 10. Ranshofener Leichtmetalltage, 13-14 Juni 2018, Linz, pp. 175-186, 2018.

    38-18   Zhen Chen, Yu Xiang, Zhengying Wei, Pei Wei, Bingheng Lu, Lijuan Zhang and Jun Du, Thermal dynamic behavior during selective laser melting of K418 superalloy: numerical simulation and experimental verification, Applied Physics A, vol. 124, pp. 313, 2018. doi.org/10.1007/s00339-018-1737-8

    19-18   Chenxiao Zhu, Jason Cheon, Xinhua Tang, Suck-Joo Na, and Haichao Cui, Molten pool behaviors and their influences on welding defects in narrow gap GMAW of 5083 Al-alloy, International Journal of Heat and Mass Transfer, vol. 126:A, pp.1206-1221, 2018. doi.org/10.1016/j.ijheatmasstransfer.2018.05.132

    16-18   P. Schneider, V. Sukhotskiy, T. Siskar, L. Christie and I.H. Karampelas, Additive Manufacturing of Microfluidic Components via Wax Extrusion, Biotech, Biomaterials and Biomedical TechConnect Briefs, vol. 3, pp. 162 – 165, 2018.

    09-18   The Furlani Research Group, Magnetohydrodynamic Liquid Metal 3D Printing, Department of Chemical and Biological Engineering, © University at Buffalo, May 2018.

    08-18   Benjamin Himmel, Dominik Rumschöttel and Wolfram Volk, Thermal process simulation of droplet based metal printing with aluminium, Production Engineering, March 2018 © German Academic Society for Production Engineering (WGP) 2018.

    07-18   Yu-Che Wu, Cheng-Hung San, Chih-Hsiang Chang, Huey-Jiuan Lin, Raed Marwan, Shuhei Baba and Weng-Sing Hwang, Numerical modeling of melt-pool behavior in selective laser melting with random powder distribution and experimental validation, Journal of Materials Processing Tech. 254 (2018) 72–78.

    60-17   Pei Wei, Zhengying Wei, Zhen Chen, Yuyang He and Jun Du, Thermal behavior in single track during selective laser melting of AlSi10Mg powder, Applied Physics A: Materials Science & Processing, 123:604, 2017. doi.org/10.1007/z00339-017-1194-9

    51-17   Koichi Ishizaka, Keijiro Saitoh, Eisaku Ito, Masanori Yuri, and Junichiro Masada, Key Technologies for 1700°C Class Ultra High Temperature Gas Turbine, Mitsubishi Heavy Industries Technical Review, vol. 54, no. 3, 2017.

    49-17   Yu-Che Wu, Weng-Sing Hwang, Cheng-Hung San, Chih-Hsiang Chang and Huey-Jiuan Lin, Parametric study of surface morphology for selective laser melting on Ti6Al4V powder bed with numerical and experimental methods, International Journal of Material Forming, © Springer-Verlag France SAS, part of Springer Nature 2017. doi.org/10.1007/s12289-017-1391-2.

    37-17   V. Sukhotskiy, I. H. Karampelas, G. Garg, A. Verma, M. Tong, S. Vader, Z. Vader, and E. P. Furlani, Magnetohydrodynamic Drop-on-Demand Liquid Metal 3D Printing, Solid Freeform Fabrication 2017: Proceedings of the 28th Annual International Solid Freeform Fabrication Symposium – An Additive Manufacturing Conference

    15-17   I.H. Karampelas, S. Vader, Z. Vader, V. Sukhotskiy, A. Verma, G. Garg, M. Tong and E.P. Furlani, Drop-on-Demand 3D Metal Printing, Informatics, Electronics and Microsystems TechConnect Briefs 2017, Vol. 4

    14-17   Jason Cheon and Suck-Joo Na, Prediction of welding residual stress with real-time phase transformation by CFD thermal analysis, International Journal of Mechanical Sciences 131–132 (2017) 37–51.

    91-16   Y. S. Lee and D. F. Farson, Surface tension-powered build dimension control in laser additive manufacturing process, Int J Adv Manuf Technol (2016) 85:1035–1044, doi.org/10.1007/s00170-015-7974-5.

    84-16   Runqi Lin, Hui-ping Wang, Fenggui Lu, Joshua Solomon, Blair E. Carlson, Numerical study of keyhole dynamics and keyhole-induced porosity formation in remote laser welding of Al alloys, International Journal of Heat and Mass Transfer 108 (2017) 244–256, Available online December 2016.

    68-16   Dongsheng Wu, Xueming Hua, Dingjian Ye and Fang Li, Understanding of humping formation and suppression mechanisms using the numerical simulation, International Journal of Heat and Mass Transfer, Volume 104, January 2017, Pages 634–643, Published online 2016.

    39-16   Chien-Hsun Wang, Ho-Lin Tsai, Yu-Che Wu and Weng-Sing Hwang, Investigation of molten metal droplet deposition and solidification for 3D printing techniques, IOP Publishing, J. Micromech. Microeng. 26 (2016) 095012 (14pp), doi: 10.1088/0960-1317/26/9/095012, July 8, 2016

    29-16   Scott Vader, Zachary Vader, Ioannis H. Karampelas and Edward P. Furlani, Advances in Magnetohydrodynamic Liquid Metal Jet Printing, Nanotech 2016 Conference & Expo, May 22-25, Washington, DC.

    26-16   Y.S. Lee and W. Zhang, Modeling of heat transfer, fluid flow and solidification microstructure of nickel-base superalloy fabricated by laser powder bed fusion, S2214-8604(16)30087-2, doi.org/10.1016/j.addma.2016.05.003, ADDMA 86.

    123-15   Koji Tsukimoto, Masashi Kitamura, Shuji Tanigawa, Sachio Shimohata, and Masahiko Mega, Laser welding repair for single crystal blades, Proceedings of International Gas Turbine Congress, pp. 1354-1358, 2015.

    122-15   Y.S. Lee, W. Zhang, Mesoscopic simulation of heat transfer and fluid flow in laser powder bed additive manufacturing, Proceedings, 26th Solid Freeform Fabrication Symposium, Austin, Texas, 2015. 

    116-15   Yousub Lee, Simulation of Laser Additive Manufacturing and its Applications, Ph.D. Thesis: Graduate Program in Welding Engineering, The Ohio State University, 2015, Copyright by Yousub Lee 2015

    103-15   Ligang Wu, Jason Cheon, Degala Venkata Kiran, and Suck-Joo Na, CFD Simulations of GMA Welding of Horizontal Fillet Joints based on Coordinate Rotation of Arc Models, Journal of Materials Processing Technology, Available online December 29, 2015

    96-15   Jason Cheon, Degala Venkata Kiran, and Suck-Joo Na, Thermal metallurgical analysis of GMA welded AH36 steel using CFD – FEM framework, Materials & Design, Volume 91, February 5 2016, Pages 230-241, published online November 2015

    86-15   Yousub Lee and Dave F. Farson, Simulation of transport phenomena and melt pool shape for multiple layer additive manufacturing, J. Laser Appl. 28, 012006 (2016). doi: 10.2351/1.4935711, published online 2015.

    63-15   Scott Vader, Zachary Vader, Ioannis H. Karampelas and Edward P. Furlani, Magnetohydrodynamic Liquid Metal Jet Printing, TechConnect World Innovation Conference & Expo, Washington, D.C., June 14-17, 2015

    46-15   Adwaith Gupta, 3D Printing Multi-Material, Single Printhead Simulation, Advanced Qualification of Additive Manufacturing Materials Workshop, July 20 – 21, 2015, Santa Fe, NM

    25-15   Dae-Won Cho and Suck-Joo Na, Molten pool behaviors for second pass V-groove GMAW, International Journal of Heat and Mass Transfer 88 (2015) 945–956.

    21-15   Jungho Cho, Dave F. Farson, Kendall J. Hollis and John O. Milewski, Numerical analysis of weld pool oscillation in laser welding, Journal of Mechanical Science and Technology 29 (4) (2015) 1715~1722, www.springerlink.com/content/1738-494x, doi.org/10.1007/s12206-015-0344-2.

    82-14  Yousub Lee, Mark Nordin, Sudarsanam Suresh Babu, and Dave F. Farson, Effect of Fluid Convection on Dendrite Arm Spacing in Laser Deposition, Metallurgical and Materials Transactions B, August 2014, Volume 45, Issue 4, pp 1520-1529

    59-14   Y.S. Lee, M. Nordin, S.S. Babu, and D.F. Farson, Influence of Fluid Convection on Weld Pool Formation in Laser Cladding, Welding Research/ August 2014, VOL. 93

    18-14  L.J. Zhang, J.X. Zhang, A. Gumenyuk, M. Rethmeier, and S.J. Na, Numerical simulation of full penetration laser welding of thick steel plate with high power high brightness laser, Journal of Materials Processing Technology (2014), doi.org/10.1016/j.jmatprotec.2014.03.016.

    36-13  Dae-Won Cho,Woo-Hyun Song, Min-Hyun Cho, and Suck-Joo Na, Analysis of Submerged Arc Welding Process by Three-Dimensional Computational Fluid Dynamics Simulations, Journal of Materials Processing Technology, 2013. doi.org/10.1016/j.jmatprotec.2013.06.017

    12-13 D.W. Cho, S.J. Na, M.H. Cho, J.S. Lee, A study on V-groove GMAW for various welding positions, Journal of Materials Processing Technology, April 2013, doi.org/10.1016/j.jmatprotec.2013.02.015.

    01-13  Dae-Won Cho & Suck-Joo Na & Min-Hyun Cho & Jong-Sub Lee, Simulations of weld pool dynamics in V-groove GTA and GMA welding, Weld World, doi.org/10.1007/s40194-012-0017-z, © International Institute of Welding 2013.

    63-12  D.W. Cho, S.H. Lee, S.J. Na, Characterization of welding arc and weld pool formation in vacuum gas hollow tungsten arc welding, Journal of Materials Processing Technology, doi.org/10.1016/j.jmatprotec.2012.09.024, September 2012.

    77-10  Lim, Y. C.; Yu, X.; Cho, J. H.; et al., Effect of magnetic stirring on grain structure refinement Part 1-Autogenous nickel alloy welds, Science and Technology of Welding and Joining, Volume: 15 Issue: 7, Pages: 583-589, doi.org/10.1179/136217110X12720264008277, October 2010

    18-10 K Saida, H Ohnishi, K Nishimoto, Fluxless laser brazing of aluminium alloy to galvanized steel using a tandem beam–dissimilar laser brazing of aluminium alloy and steels, Welding International, 2010

    58-09  Cho, Jung-Ho; Farson, Dave F.; Milewski, John O.; et al., Weld pool flows during initial stages of keyhole formation in laser welding, Journal of Physics D-Applied Physics, Volume: 42 Issue: 17 Article Number: 175502 ; doi.org/10.1088/0022-3727/42/17/175502, September 2009

    57-09  Lim, Y. C.; Farson, D. F.; Cho, M. H.; et al., Stationary GMAW-P weld metal deposit spreading, Science and Technology of Welding and Joining, Volume: 14 Issue: 7 ;Pages: 626-635, doi.org/10.1179/136217109X441173, October 2009

    1-09 J.-H. Cho and S.-J. Na, Three-Dimensional Analysis of Molten Pool in GMA-Laser Hybrid Welding, Welding Journal, February 2009, Vol. 88

    52-07   Huey-Jiuan Lin and Wei-Kuo Chang, Design of a sheet forming apparatus for overflow fusion process by numerical simulation, Journal of Non-Crystalline Solids 353 (2007) 2817–2825.

    50-07  Cho, Min Hyun; Farson, Dave F., Understanding bead hump formation in gas metal arc welding using a numerical simulation, Metallurgical and Mateials Transactions B-Process Metallurgy and Materials Processing Science, Volume: 38, Issue: 2, Pages: 305-319, doi.org/10.1007/s11663-007-9034-5, April 2007

    49-07  Cho, M. H.; Farson, D. F., Simulation study of a hybrid process for the prevention of weld bead hump formation, Welding Journal Volume: 86, Issue: 9, Pages: 253S-262S, September 2007

    48-07  Cho, M. H.; Farson, D. F.; Lim, Y. C.; et al., Hybrid laser/arc welding process for controlling bead profile, Science and Technology of Welding and Joining, Volume: 12 Issue: 8, Pages: 677-688, doi.org/10.1179/174329307X236878, November 2007

    47-07   Min Hyun Cho, Dave F. Farson, Understanding Bead Hump Formation in Gas Metal Arc Welding Using a Numerical Simulation, Metallurgical and Materials Transactions B, Volume 38, Issue 2, pp 305-319, April 2007

    36-06  Cho, M. H.; Lim, Y. C.; Farson, D. F., Simulation of weld pool dynamics in the stationary pulsed gas metal arc welding process and final weld shape, Welding Journal, Volume: 85 Issue: 12, Pages: 271S-283S, December 2006

    Aluminum Integral Foam Molding Process

    Aluminum Integral Foam Molding Process

    This application note was contributed by Johannes Hartmann and Vera Jüchter, Department of Materials Science, Chair of Metals Science and Technology, University of Erlangen-Nuremberg

     

    알루미늄 폼은 우수한 댐핑 및 높은 에너지 흡수율 및 굴곡 강성과 같은 예외적인 특성을 보여줍니다[1]. 강성은 특히 하중 지지 및 경량 구조에 사용하기에 특히 매력적입니다. 중량별 강성을 높이고 보다 우수한 하중 전달을 위해 알 Aluminum Foam Sandwiches (AFS)와 같은 컴팩트한 특성이 필요합니다 [2].

    Erlangen-Nuremberg 대학의 금속 공학과 기술 위원장은 알루미늄 발포 특성을 점차적으로 생산하기 위해 다이캐스팅 공정인 Integral Foam Molding 개발하였습니다(그림 1 참조). 이 공정은 폴리머의 사출 성형으로 개발되었으며 따라서 컴팩트한 층을 가진 복잡한 폼을 비용 효율적으로 대량 생산에 적합합니다. 이 노트에 설명 된 시뮬레이션 기법은 프로세스 매개 변수를 선택하는데 도움을 주기 위한 모델링프로세스를 확인할 수 있습니다.

    Figure 1. Cross section of an aluminum integral foam with a compact skin, a transition region with decreasing relative density and smaller pores, as well as a foamed core.

    Aluminum Integral Foam Molding Technology

    일정량의 발포제 (수소화 마그네슘, MgH2)가 러너 시스템에 배치되고 샷 챔버는 알루미늄 용융물로 채워진다 (공정은 그림 2에 묘사되어 있으며, 공정은 [3]에 자세히 설명되어있다). 피스톤이 진행됨에 따라, 분말은 난류 방식으로 주형에 이송된다. 기술 변형 “고압 일체형 폼 몰딩 (HP-IFM)”의 경우 표준 다이캐스팅 공정에서 알 수 있듯이 이 부품은 주변의 높은 압력에서 완전히 채워져 우수한 표면 품질을 보장합니다. 템퍼링된 금형 표면에서 시작하여 용융물은 일체형으로 고형화되기 시작합니다. 몇 밀리 초가 지나면 금형은 코어 풀러 시스템 위에 열리고 부피는 국부적으로 증가하고 압력은 감소하여 열분해 및 수소화 마그네슘 입자의 수소 방출로 인해 여전히 반고체 내부 영역에서 기공 성장을 시작합니다. 모든 발포제 입자는 이웃하는 공극의 역압에 의해 멈추어 질 때까지 공극의 성장을 지속합니다. 발포된 입자의 벽은 알루미늄 합금의 응고된 입자에 의해 안정화가 되며 이를 endogenous stabilization이라고 합니다[4].

    Figure 2. Schematic process cycle of “High Pressure Integral Foam Molding (HP-IFM)” of aluminum.

    주조 부품의 전체 부피에서 균일한 형태에 대한 전제조건은 분해 순간의 양호한 입자분포입니다. 또한, 발포제 유입시의 용융물의 온도는 수소화 마그네슘의 분해를 결정하며 (그림 3 참조), 게다가 발포시 solid phase의 양을 결정한다. 그러나 고상의 양이 너무 많으면 기공의 강성이 증가하고 현상 기공의 구형화를 방해하여 구조가 파괴된다 [2].

    Microcellular Aluminum Integral Foams – Approaching the Process Limits

    일체형 발포 성형 공정시뮬레이션은 새로운 부품 설계의 몰드 충진 특성을 조사하는 데 도움이 될 뿐만 아니라 입자 침투도 예측하고 비용을 절약할 수 있게 발포 공정 조건을 결정할 수 있는 강력한 도구입니다. 현재 연구의 목표는 다공성 수준을 일정하게 유지하면서 기공 크기를 줄이는 것입니다. 전산 유체 역학 (CFD) 시뮬레이션은 가능한 한 현재의 프로세스 한계에 가깝게 접근할 수 있습니다. 발포 형태의 개선은 기계적 물성에서 균질 한 구조를 유도 할뿐만 아니라 기계적 성질에 의해 더 얇은 부품의 생산이 가능할 것입니다. 이 목적은 용융물 내에서의 높은 입자 분포 밀도와 동시에 응집 현상의 감소와 함께 완전히 안정된 기공 성장에 의해서만 달성 될 수 있다.

    Figure 3. Schematic curves of decomposition of magnesium hydride as a function of the melt temperature, calculated by the Johnson-Mehl-Avrami approach [2]

    Figure 4. Adjustment of heat transfer by comparisons of a real solidification curve (black) to the growth rate of the solidified skin in simulation (red).

    Adapting the Simulation Parameters to Practical Integral Foam Molding Experiments

    입자 거동이나 온도장에 대한 신뢰성 있는 예측을 위한 CFD 시뮬레이션을 사용할 수 있으려면 실제 실험과 일치하도록 매개 변수를 결정해야 합니다. 이를 위해, 30-130 ms의 지연 시간을 갖는 일체형 발포 부품을 제작하였으며 성형 팽창 및 기공 성장 개시 순간에 고상분율 때문에 발포 형성이 불가능한 다른 밀도의 형상을 만들었습니다. 열 전달 계수 (완전한 액체 용융물과 완전 응고된 용융물)를 변화시켜 합금 AlSi9Cu3 (Fe)의 주조 사이클을 시뮬레이션하면 응고 곡선을 적용할 수 있습니다. 이러한 목표를 달성하기 위해 시뮬레이션을 피스톤 이동이 시작되기 전에 실제 온도분포를 묘사해야 합니다. 온도는 배치된 열에 의해 숏 챔버에서 국부적으로 측정되었으며 시뮬레이션 내 실제 데이터와 잘 일치하여 성공적으로 묘사 될 수 있었습니다. 금형 충진 중에 금형 표면에서 온도 측정을 참조 할 수도 있습니다. 시간 경과에 따른 그 변화는 시뮬레이션 결과와 잘 일치합니다.

    표면장력이나 응고 항력계수와 같은 용융의 유동을 정의하는 추가 매개 변수 단계에서는 다른 설정과 시뮬레이션을 비교하여 조정됩니다. 시뮬레이션 내에서 용융물의 흐름이 실제 시험과 일치하는 즉시 매개 변수가 설정됩니다

    Figure 5. Adjustment of melt flow defining parameters such as the surface tension by comparisons of real experiments (left) to simulations (right)

    냉각 및 용해 흐름 특성을 정의한 후 입자의 유입을 시뮬레이션 합니다. 입자 / 유체 의 상호 작용에 대한 시뮬레이션을 조정하기 위해 매개 변수계수의 X 선 샘플과 비교가 되며 구리선 입자에서는 수산화 마그네슘보다 높은 함량 입자가 적용됩니다. (그림 6 참조). 시뮬레이션 결과는 실험과 매우 잘 어울리므로 프로세스 매개 변수의 함수로서 입자 분포의 신뢰할 수 있습니다.

    Figure 6. Adjustment of parameters influencing particle/melt-interactions by comparisons of x-rayed samples left); produced by the entrainment of copper particles) to simulations (right)

    Conclusion

    전체적으로 FLOW-3D는 실제 생산 전에 새로운 부품 제조의 잠재적 결함을 조사하는 중요한 수단이 될 수 있다는 것을 증명할 수 있었습니다. 이러한 방식으로, 차가운 흐름 또는 데드 존이 없는 성공적인 충전 및 발포제 분포가 보장 될 수 있다. 또한, 예상되는 온도 필드의 정확한 묘사로, 수소화 마그네슘의 분해 특성 및 기공형성을 예측할 수 있습니다. 이는 일체형 폼 구조와 관련하여 고객의 요구를 충족시키기 위한 공정 변수를 정의 할 수 있는 가능성을 제공합니다

    1 Criterion is the solid phase fraction where the shear strength and therefore the resistance to pore evolution increases drastically.

    References

    [1] C. Körner, R. F. Singer, Adv. Eng. Mater. 20002 (4), pp. 159-165.
    [2] C. Körner, in Integral Foam Molding of Light Metals – Technology, Foam Physics and Foam Simulation, Springer, Berlin, Heidelberg, Germany 2008.
    [3] H. Wiehler, C. Körner, R. F. Singer, Adv. Eng. Mater. 200810 (3), pp. 171-178.
    [4] J. Hartmann, A. Trepper, C. Körner, Adv. Eng. Mater. 201113 (11), pp. 1050-1055.

    Learn more about the versatility and power of modeling metal casting processes with FLOW-3D Cast>

     

    CFD에 대해서

    What You Should Know About CFD Modeling when Selecting a CFD Package

    유체 흐름 및 열 전달 해석용 소프트웨어 패키지에는 여러 형태가 있습니다. 물리적 근사와 수치 해법의 기법이 패키지마다 크게 다르기 때문에 적절한 패키지를 선택하는 것은 매우 어렵습니다. 다음 설명에서는 열유동 시뮬레이션 소프트웨어를 선택할 때 고려해야 할 중요한 몇 가지를 소개합니다.

    Software packages for fluid flow and heat transfer analysis come in many forms. These packages differ greatly in their physical approximations and numerical solution techniques, which makes the selection of a suitable package a challenging proposition. The following discussion covers some important items to consider when choosing flow simulation software.

    Meshing and Geometry

    유한 요소 또는 “body-fitted coordinates”를 채용하고 있는 수치해석 방법은 유체 영역의 기하학적 형상에 적합한 격자를 생성해야 합니다. 정확한 수치 근사치를 얻기 위해 허용 할 수 있는 요소 크기 및 형상에서 이러한 격자를 생성하는 것은 매우 중요한 작업입니다.

    복잡한 경우에는 이와 같은 방법으로 격자를 생성하면 며칠 또는 몇 주가 걸릴 수 있습니다.  어떤 프로그램은 사각형의 격자 요소만을 사용함으로써 문제를 해결하려고 하지만, 그럴 경우에는 경계부분에 계단이 생기고 흐름과 열전달 특성이 달라지는 문제에 직면하게 됩니다.

    FLOW-3D는 FAVOR™(면적율 / 부피 비율)법 을 사용하여 지오메트리의 특성을 원활하게 포함하므로써, 간단한 사각형 격자만으로도 두 문제를 해결할 수 있습니다.  또한, 간단하고 강력한 솔리드 모델러가 FLOW-3D 패키지에 기본 포함되어 있으며, CAD 프로그램에서 생성한 기하형상 데이터를 가져올 수 있습니다.

    Solution methods that employ finite-element or “body-fitted coordinates” require the generation of a solution grid that conforms to the geometry of the flow region. It is a non-trivial task to generate these grids with acceptable element sizes and shapes for accurate numerical approximations. In complicated cases this type of grid generation may consume days or even weeks of effort. Some programs attemptto eliminate this generation problem by using only rectangular grid elements, but then they must contend with “stair-step” boundaries that alter flow and heat-transfer properties. FLOW-3D solves both problems by using easy-to-generate rectangular grids in which geometric features are smoothly embedded using the FAVOR™ (fractional area/volume) method. A simple and powerful solids modeler is packaged with FLOW-3D or users may import geometric data from a CAD program.

    Momentum Equation vs. Approximate Flow Models

    유체 운동량의 정확한 처리가 중요한 몇 가지 이유가 있습니다.  첫째, 이것은 복잡한 기하학적 형상에서 유체가 어떻게 흐르는지를 예측하는 유일한 방법입니다.  둘째, 액체에 의하여 걸린 동적인 힘(압력)은 운동량에서만 계산할 수 있습니다.  마지막으로, 열 에너지의 대류 수송을 계산하려면 다른 유체 입자 및 경계에 대한 개별 유체 입자의 상대적인 움직임을 정확하게 파악하는 것이 필요합니다. 이것은 운동량의 정확한 처리를 의미합니다.  운동량 보존을 대충 근사하기만 한 CFD 모델은 FLOW-3D에서는 사용되지 않습니다.  이러한 모델은 현실적인 유체 구성 및 온도 분포 예측에 사용할 수 없기 때문입니다.

    An accurate treatment of fluid momentum is important for several reasons. First, it is the only way to predict how fluid will flow through complicated geometry. Second, the dynamic forces (i.e., pressures) exerted by the fluid can only be computed from momentum considerations. Finally, to compute the convective transport of thermal energy, it is necessary to have an accurate picture of how individual fluid particles move in relation to other fluid particles and confining boundaries. This implies an accurate treatment of momentum. Simplified flow models that only crudely approximate the conservation of momentum are not used in FLOW-3D because they cannot be used to predict realistic fluid configurations and temperature distributions.

    Liquid-Solid Heat Transfer Area

    액체와 고체 사이 (금속 주형 등)의 열전달은 경계면 면적의 정확한 추정이 필요합니다.  경계가 계단 모양으로 되어 있는 경우, 보통 이 면적이 크게 추정됩니다.  예를 들어, 실린더의 표면적은 약 27 %정도 크게 추정됩니다.  FLOW-3D의 경우 정확한 경계면 면적은 FAVOR™법에 따라 FLOW-3D 전처리기에서 컨트롤 볼륨마다 자동으로 계산됩니다.

    Heat transfer between a liquid and a solid (e.g., metal-to-mold) requires an accurate estimate of the interfacial area. Stair-step boundaries over-estimate this area; for example, the surface area of a cylinder would be over-estimated by a factor of 27%. Accurate interfacial areas are automatically computed by the FAVOR™ method for each control volume in the FLOW-3D pre-processor.

    Control Volume Effects on Liquid-Solid Heat Transfer

    컨트롤 볼륨의 크기가 액체와 고체 사이에서 교환되는 열 비율과 양에 영향을 줄 수 있습니다.  이것은 열이 액체와 고체의 경계면을 포함하는 컨트롤 볼륨을 흐를 필요가 있기 때문입니다.  FLOW-3D는 액체와 고체의 경계면에 걸쳐 열 전달률을 계산할 때 컨트롤 볼륨의 크기와 전도율이 고려됩니다.

    The size of control volumes can influence the rate and amount of heat exchanged between a liquid and solid because heat must also flow in the control volumes containing the liquid/solid interface. In FLOW-3D control volume sizes and their conductivities are accounted for when computing heat transfer rates across liquid-solid interfaces.

    Implicitness and Accuracy

    비선형 방정식과 결합 방정식의 Implicit 방법은 반복 될 때마다 under-relaxation 특성을 갖는 반복적 해법이 필요합니다.  이 동작은 상황에 따라 심각한 오류 (또는 수렴 속도의 급격한 하락)가 발생할 수 있습니다.  예를 들어, 비율이 큰 컨트롤 볼륨을 사용하는 경우나, 실제로는 중요하지 않은 효과를 예상하고 암시적인 해법을 사용하는 경우 등입니다.  FLOW-3D는 가능한 명시적인 수치해법이 사용되고 있습니다.  이것은 필요한 계산량이 적고, 수치 안정성의 요구 사항이 요구된 정밀도에 상응하기 때문입니다.  자세한 내용은 “암시적인 수치해법과 명시적인 수치해법“을 참조하십시오.

    Implicit methods for nonlinear and coupled equations require iterative solution methods that have the character of an under-relaxation in each iteration. This behavior can cause significant errors (or very slow convergence) in some situations, for example, when using control volumes with large aspect ratios or when the implicitness is used in anticipation of an effect that is not actually significant. In FLOW-3D explicit numerical methods are used whenever possible because they require less computational effort, and their numerical stability requirements are equivalent to accuracy requirements. Read more in the Implicit vs. Explicit Numerical Methods article.

    Implicit Numerical Methods For Convective Transport

    모든 크기의 타임 스텝 크기를 계산에 사용할 수 있는 암시적인 수치 기법은 CPU 시간을 줄이기 위해 많이 사용되는 방법입니다.  불행하게도, 이 방법은 대류 현상 해석에 대해 정확하지 않습니다.  암시적인 해법은 근사 방정식에 확산 효과를 도입함으로써 시간 단계의 독립성을 획득합니다.  수치 확산을 물리적 확산 (열전도 등)에 추가해도 확산율이 변경될 뿐이므로 심각한 문제가 되지 않을 수 있습니다.  그러나 수치 확산(발산)을 대류 과정에 추가하면 모델링 대상의 물리 현상의 특성은 완전히 다르게 됩니다.  FLOW-3D는 시간의 정확한 근사치를 보장하기 위해 프로그램에 의해 time step이 자동으로 제어됩니다.

    Implicit numerical techniques that allow arbitrarily large time-step sizes to be used in calculations are a popular way to reduce CPU time requirements. Unfortunately, these methods are not accurate for convective processes. Implicit methods gain their time-step independence by introducing diffusive effects into the approximating equations. The addition of numerical diffusion to physical diffusion, e.g., to heat conduction, may not cause a serious problem as it only modifies the diffusion rate. However, adding numerical diffusion to convective processes completely changes the character of the physical phenomena being modeled. In FLOW-3D time steps are automatically controlled by the program to ensure time-accurate approximations.

    Relaxation and Convergence Parameters

    암시적으로 근사치를 사용하는 수치법은 하나 이상의 수렴 및 완화(이완)의 매개 변수를 선택해야 합니다.  이러한 매개 변수를 신중하게 선택하지 않으면 발산하거나 수렴에 시간이 걸리는 경우가 있습니다.  FLOW-3D를 융합하는 매개 변수와 완화(이완) 매개 변수를 하나씩만 사용하여 두 매개 변수는 프로그램에 의해 동적으로 선택됩니다.  수치 해법을 제어하는 매개 변수를 사용자가 설정할 필요는 없습니다.

    Numerical methods that use implicit approximations also require the selection of one or more convergence and relaxation parameters. Making poor choices for these parameters can lead to either divergences or slow convergence rates. Only one convergence and one relaxation parameter are used in FLOW-3D, and both parameters are dynamically selected by the program. Users are not required to set any parameters controlling the numerical solver.

    Free-Surface Tracking

    액체와 기체의 경계면 (자유 표면 등)의 모델링에 사용되는 방법은 두 가지가 있습니다.  하나는 액체, 기체 두 영역의 흐름을 계산하고 경계면을 유체 밀도의 급격한 변화로 처리하는 방법입니다.

    일반적으로 밀도의 불연속은 고차 수치 근사를 사용하여 모델링됩니다.  불행하게도 이 프로세스는 소수의 격자 셀에서 경계면이 평탄화되고, 이러한 경계면에 보통 존재하는 유체흐름의 접선 속도의 급격한 변화는 고려되지 않습니다.

    기체가 계산 영역에 들어가는 액체로 대체되는 경우에는 이 방법에는 기체의 출구 포트 또는 출구 싱크도 보충 할 필요가 있습니다.  또한 이러한 방법은 일반적으로 유체의 비압축성를 충족하기 위해 더 많은 노력이 필요합니다.  이것이 발생하는 기체 영역에 거의 균일 한 압력 조정이 필요하며, 이를 통해 계산 수렴 시간이 소요되기 때문입니다.

    FLOW-3D는 VOF (Volume-of-Fluid) 법 이라는 독창적인 방법이 사용되고 있습니다.  이것은 진정한 3 차원 경계면 추적 방식으로, 경계면을  3 차원 인터페이스로 추적하는 체계입니다.  또한 옵션의 표면 장력을 포함한 일반적인 접선 응력 경계 조건은 경계면에 적용됩니다.  기체 영역은 모델에 포함하도록 사용자가 요청하지 않는 한 계산되지 않습니다.

    There are two methods used to model liquid-gas interfaces (i.e., free surfaces). One of these is to compute flow in both the liquid and gas regions and to treat the interface as a sharp change in fluid density. Typically, the density discontinuity is modeled using higher-order numerical approximations. Unfortunately, this treatment allows the interface to smooth out over a few grid cells and does not account for a corresponding sharp change in tangential flow velocity that generally exists at such interfaces. This technique must also be supplemented with escape ports or sinks for the gas if it is to be replaced by liquid entering a computational region. Further, such methods must typically work harder to satisfy the incompressibility of the fluids. This happens because gas regions must have nearly uniform pressure adjustments which tend to slow down the solution convergence rate. A different technique, the Volume-of-Fluid (VOF) method, is used in FLOW-3D. This is a true three-dimensional interface tracking scheme in which the interface is closely maintained as a step discontinuity. Moreover, normal and tangential stress boundary conditions, including optional surface tension forces, are applied at the interface. Gas regions are not computed unless the user requests these regions to be included in the model.

    본 자료는 국내 사용자들의 편의를 위해 원문 번역을 해서 제공하기 때문에 일부 오역이 있을 수 있어서 원문과 함께 수록합니다. 자료를 이용하실 때 참고하시기 바랍니다.

    FLOW-3D CAST Suites

    FLOW-3D CAST Suites

    FLOW-3D CAST v5 comes in Suites of relevant casting processes: 

    HIGH PRESSURE DIE CASTING SUITE

    Process Workspace

    High Pressure Die Casting

    Features

    Thermal Die Cycling
    – Cooling/heating channels
    – Spray cooling
    Filling
    – Shot sleeve with Plunger
    – Shot motion
    – Ladles, stoppers
    – Venting efficiency
    – PQ^2 analysis
    – HPDC machine database
    Solidification
    – Squeeze pins
    Cooling


    PERMANENT MOLD CASTING SUITE

    Process Workspaces

    Permanent Mold Casting
    Low Pressure Die Casting
    Tilt Pour Casting

    Features

    Thermal Die Cycling
    – Cooling/heating channels
    Filling
    – Tilt pouring
    Solidification
    – Squeeze pins
    Cooling


    SAND CASTING SUITE

    Process Workspaces

    Sand Casting
    Low Pressure Sand Casting

    Features

    Filling
    – Permeable molds
    – Moisture evaporation in molds
    – Gas generation in cores
    – Ladle model
    Solidification
    – Exothermic sleeves
    – Chills
    – Cast iron solidification
    Cooling


    LOST FOAM CASTING SUITE

    Process Workspaces

    Lost Foam
    Sand Casting
    Low Pressure Sand Casting

    Features

    Filling
    – Permeable molds
    – Moisture evaporation in molds
    – Gas generation in cores
    – Ladle model
    – Lost foam pattern evaporation models (Fast model and Full model)
    – Lost foam defect prediction
    Solidification
    – Exothermic sleeves
    – Chills
    – Cast iron solidification
    Cooling

     


    ALL SUITES INCLUDE THESE CORE FEATURES:

    Solver Engine

    • TruVOF – The most accurate filling simulation tool in the industry
    • Heat transfer and solidification
    • Shrinkage – Rapid Shrinkage model and Shrinkage with flow model
    • Temperature dependent properties
    • Multi-block meshing including conforming meshes
    • Turbulence models
    • Non-Newtonian viscosity (shear thinning/thickening, thixotropic)
    • Flow tracers
    • Active Simulation Control with Global Conditions
    • Surface tension model
    • Thermal stress analysis with warpage
    • General moving geometry w/6 DOF

    FlowSight

    • Multi-case analysis
    • Porosity analysis tool

    Defect Prediction Tools

    • Gas entrainment model
    • Thermal Modulus output
    • Hot Spot identification
    • Micro and macro porosity prediction
    • Surface defect prediction
    • Shrinkage
    • Cavitation and Cavitation Potential
    • Particle models (Inclusion modeling, collapsed bubble tracking)

    User Conveniences

    • Process-oriented workspaces
    • Configurable Simulation Monitor
    • Metal and solid material databases
    • Heat transfer database
    • Filter database
    • Remote solving queues
    • Quick Analyze/Display tool

    Computational Analysis of Drop Formation and Detachment

    Computational Analysis of Drop Formation and Detachment

    Introduction and Problem Statement

    신속, 반복, 작은 물방울의 생성 및 증착, 작은 형상의 프린팅 또는 패터닝 (예 : l = 10-3-1 mm), 스프레이로  균일한 두께의 박막 형성은 다양한 산업에 매우 중요합니다(1-5). 액체 이동과 액적 형성 / 증착 공정은 복잡한 자유 표면 흐름, 자연적인 모세관운동 형성, thinning, pinch-off를 수반한다 (1-5). 단순한 뉴턴 및 비탄성 유체에 대해 액적 생성 및 액적 이동을 분석하기위한 실험적, 이론적 및 1 차원 시뮬레이션 연구가 진행되었지만 프린팅 또는 패터닝에 대한 기계론적인 이해는 여전히 과제로 남아 있습니다. 현재의 계산에 대한 주된 목표는 뉴턴 유체의 pinch-off에 대한 기계론적 이해를 얻기 위해 FLOW-3D에 내장된 VOF(volume-of-fluid) 접근법으로 시험하는 것입니다. 전산해석은 모세관, 관성, 점성 응력의 복잡한 상호 작용을 포착하여 자기유사 모세관의 thinning and pinch-off를 결정합니다. 뉴턴 유체의 물방울 형성 ​​및 분리현상은  전산해석으로부터 얻어진 자기유사 모세관현상 이론, 보편적인 축소화 기법인 1D 시뮬레이션 (1-7)과 실험 (1, 2, 8-12)을 이용하여 설명될 수 있음을 보여준다. 이러한 우리가 진행한 원형흐름 시뮬레이션은 유한한 시간의 비선형 역학, 위성 낙하현상, 복잡한 형상의 프린팅과 같이 어려운 전산해석의 기반이 될 것 입니다.

    방울 형성의 전산 분석
    그림 1 : FLOW-3D를 사용하여 시뮬레이션 한 저점도 유체의 드롭 형성 및 분리에 대한 전산해석 : (a) 5개의 저점도 유체에 대한 물방울의 necking에 대한 반경이 시간변화에 따라 표시됩니다. 물방울 necking의 반지름이 오른쪽에서 왼쪽으로 시간에 따른 전개를 보여줍니다. 마찬가지로 스냅 샷은 necking의 반경이 오른쪽에서 왼쪽으로 줄어듭니다. 속도의 크기 (단위 : cm/s) 와 화살표의 방향에 대한 컬러 맵을 사용하면 변형장을 결정할 수 있으며 Fluid 5 (표 1 참조)의 경우에는 순식간에 신장이됩니다. 이미지 II에 캡처 된 pinch-off 하기 전에 형성된 원추형 necking은 실험을 통해 얻은 necking 모양과 유사합니다.

    Modeling Approach and Parameter Space

    표면 장력 및 중력 모델을 적용한 FLOW-3D 에서 균일한 메쉬 크기를 사용하여 노즐에서 드롭 형성 및 분리에 대한 시뮬레이션을 수행하였습니다. 유한 체적의 유체를 떨어뜨리거나 분리하는 일은 물방울의 성장과 드롭, 노즐에 연결되는 모세관 현상, 관성, 점도 및 중력에 대한 상호 작용을 수반합니다. 시뮬레이션에서 스테인레스 강 노즐 ( {{D} _ {0}} = 2 {{R} _ {0}} = 1.7 \, \ text {mm}) 에서 유한 체적의 뉴턴 유체가 발생합니다. 표면 장력이 중력을 겪으면 새로 형성된 액적 분리가 발생합니다 (mg> 2 \ pi \ sigma {{R} _ {0}}). 시뮬레이션은 유체점도의 영향을 설명하기 위해 두 그룹으로 나누어져 있습니다: 저점도 유체 (글리세롤 함량이 40 % 미만인 물과 글리세롤/물 혼합물) 및 점도가 높은 유체 (예 : 글리세롤과 글리세롤/물 혼합물 점도 > 100x 물 점도). 두 그룹의 유체 특성은 각각 표 1과 2에 나와 있습니다.

    계산 분석 드롭 형성 저점도

    그림 2 : FLOW-3D를 사용하여 시뮬레이션 한 저점도 유체의 드롭형성 및 분리에 대한 전산 해석 : 반경 플롯에서 4개의 고점도 뉴톤유체에 대해 necking 반경을 시간변화에 따라 표시합니다. 낙하 분리 중 모세관 현상이 스냅 샷으로 표시됩니다. 컬러 맵은 Fluid 8의 속도 크기 (단위 : cm/s)의 변화를 포착합니다 (표2 참조). 화살표는 성장하는 물방울과 얇아지는 물방울내에서 흐름방향을 나타냅니다. FLOW-3D 시뮬레이션으로 얻은 necking 모양은 고점도의 뉴턴유체에 대한 특징인 원통형 유체요소로 이어집니다.

     

    <표 1 : FLOW-3D를 사용하여 시뮬레이션 된 저점도 유체의 특성>
    Fluid PropertyFluid 1Fluid 2Fluid 3Fluid 4Fluid 5
    Viscosity [Pa · s]0.050.020.010.00750.005
    Surface Tension  [mN / m]6868686868
    Density [g / cm 3 ]11111
    Ohnesorge Number0.210.080.040.030.021
     저점도 유체 (표 1의 유체 2) 가 노즐에서 떨어지는 것을 시뮬레이션 합니다. 색상변수는 속도크기 (단위 : cm / s)이며 속도벡터가 표시됩니다.

     

    <표 2 : FLOW-3D를 사용하여 시뮬레이션 된 고점도 유체의 특성>
    Fluid PropertyFluid 6Fluid 7Fluid 8Fluid 9
    Viscosity [Pa · s]1.50.80.50.25
    Surface Tension  [mN / m ]68686868
    Density [g / cm 3 ]1111
    Ohnesorge Number6.243.332.081.04

    고점도 유체 (표 2의 유체 8) 가 노즐에서 떨어지는 것을 시뮬레이션 합니다. 색상변수는 속도크기 (단위 : cm / s) 이며 속도 벡터가 표시됩니다.

    Discussion of the Simulation Results

    드롭 형성 및 분리는 표1과 표2에 열거 된 유체에 대해 FLOW-3D 를 사용하여 시뮬레이션 하였고, 시간 경과에 따른 necking 모양, 반경을 분석하였습니다. 물방울의 necking 모양과 저점도에서의 necking에 대한 역학(그림 1 참조)은 실험, 흐름 이론, 1D 시뮬레이션, 자기유사 관성에 대한 모세현상의 특성을 나타냅니다 (1, 2, 6, 7, 13) :

    (1)  \ displaystyle \ frac {{R (t)}} {{{{R} _ {0}}}} \ approx 0.8 R {{{{왼쪽} {R} {0} 3}}} 오른쪽}) ^ {{{{frac {1} {3}}} {{왼쪽 {{{{왼쪽}}} {2} {3}}}}

    여기서 R (t)가  necking의 순간 반경이고, R0는 노즐의 외부반경이며,  \ displaystyle \ sigma 는 표면 장력,  \ displaystyle \ rho 는 유체의 밀도 tC 는 pinch-off 시간이다. 마찬가지로, 이러한 더 높은 점도의 뉴턴유체에 대한 반경 변화데이터는 시간에 따른 반경의 감소를 나타내는 것이며,  Papageorgiou’s visco-capillary scaling (8, 9)은 아래의 식으로 표현된다.

    (2)  \ {0 \} {} {} {} {} {} {} {} {} {} {} {} {} { } ({{t} _ {p}} - t)

    모세관 속도(표면 장력과 점도의 비)의 측정 값은 McKinley와 Tripathi (8)에 의해 Capillary Break-Up Extensional Rheometer (CaBER)라고 불리는 상업적으로 이용 가능한 장비를 사용하여 얻은 값과 모세관 속도는 공칭 표면 장력과 점도를 사용하여 계산됩니다.

    FLOW-3D 는 물방울의 necking부분을 속도 벡터로 시각화하여 유체의 흐름을 나타낼 수 있습니다. 또한, 이는 그림 1과 같이 전단, 확장을 겪은 후 얇아지는 물방울이 흐르는 과정의 순간을 결정할 수 있는 가능성을 줍니다. 추가로, 낮은 점도의 뉴턴유체는 높은 점도의 뉴턴 유체에 비해 질적으로 다른 거동을 보여준다(그림 2참조). 낮은 점도의 뉴턴 유체에 대한 necking 프로파일은 이론(6,13)에 따라 자기 유사성이 됩니다.

    Conclusions, Outlook and Ongoing work

    우리의 예비결과는 FLOW-3D 기반의 전산해석이 액적 형성과 탈착의 기초가 되는 프로토타입의 자유 표면흐름을 시뮬레이션하는데 사용될 수 있음을 보여줍니다 . 시뮬레이션된 반경변화 프로파일이 실험적으로 관찰된 높은 유체 및 이론적으로 예측된 유체인 스케일링 법칙 및 pinch-off dynamics과 일치하는 것을 발견하였습니다.

    자주 사용되는 1D 또는 2D 모델과 달리 FLOW-3D 는 기본 응력 및 확장 유동장 (균일도 및 크기)의 강도와 얇은 액체 필라멘트 내 흐름에 대한 시각화를 나타낼 수 있습니다(그림1과 2 참조). 확장 유동장과 연관된 흐름 방향 속도 구배는 모세관현상이 나타나는 물방울의 얇은 부분 내에서 발생합니다. 유동학적으로 복잡한 유체에서 non Newtonian shear 및 신장, 점도뿐만 아니라 그외의 탄성 응력이 nonlinear pinch-off dynamics을 급격하게 변화시킵니다(2, 10-12). 우리는 현재 점탄성과 non-Newtonian 유동학을 사용하여 FLow-3D에 복합 유체의 처리 성능평가를 위한 강력한 연산 프로토콜을 개발하고 있습니다.

    References

    1. J. Eggers, Nonlinear dynamics and breakup of free-surface flows. Rev. Mod. Phys. 69, 865-929 (1997).
    2. G. H. McKinley, Visco-elasto-capillary thinning and break-up of complex fluids. Rheology Reviews, 1-48 (2005).
    3. B. Derby, Inkjet Printing of Functional and Structural Materials: Fluid Property Requirements, Feature Stability, and Resolution. Annual Review of Materials Research 40, 395-414 (2010).
    4. O. A. Basaran, H. Gao, P. P. Bhat, Nonstandard Inkjets. Annual Review of Fluid Mechanics 45, 85-113 (2013).
    5. S. Kumar, Liquid Transfer in Printing Processes: Liquid Bridges with Moving Contact Lines. Annual Review of Fluid Mechanics 47, 67-94 (2014).
    6. R. F. Day, E. J. Hinch, J. R. Lister, Self-similar capillary pinchoff of an inviscid fluid. Phys. Rev. Lett. 80, 704-707 (1998).
    7. J. Eggers, M. A. Fontelos, Singularities: Formation, Structure, and Propagation. (Cambridge University Press, Cambridge, UK, 2015), vol. 53.
    8. G. H. McKinley, A. Tripathi, How to extract the Newtonian viscosity from capillary breakup measurements in a filament rheometer. J. Rheol. 44, 653-670 (2000).
    9. D. T. Papageorgiou, On the breakup of viscous liquid threads. Phys. Fluids 7, 1529-1544 (1995).
    10. J. Dinic, L. N. Jimenez, V. Sharma, Pinch-off dynamics and dripping-onto-substrate (DoS) rheometry of complex fluids. Lab on a Chip 17, 460-473 (2017).
    11. J. Dinic, Y. Zhang, L. N. Jimenez, V. Sharma, Extensional Relaxation Times of Dilute, Aqueous Polymer Solutions. ACS Macro Letters 4, 804-808 (2015).
    12. V. Sharma et al., The rheology of aqueous solutions of Ethyl Hydroxy-Ethyl Cellulose (EHEC) and its hydrophobically modified Analogue (hmEHEC): Extensional flow response in capillary break-up, jetting (ROJER) and in a cross-slot extensional rheometer. Soft Matter 11, 3251-3270 (2015).
    13. J. R. Castrejón-Pita et al., Plethora of transitions during breakup of liquid filaments. Proc. Natl. Acad. Sci. U.S.A. 112, 4582-4587 (2015).

    표면 장력 / Surface Tension

    표면 장력 / Surface Tension

    FLOW-3D에 추가 된 최초의 물리 모델 중 하나는 표면 장력이었습니다.

    이 모델은 잉크젯, 무중력 환경에서의 액체 연료 거동 및 다양한 MEMS (마이크로 전자 기계 시스템) 장치와 같이 다양한 종류의 응용 분야에서 수년 동안 널리 사용되어 왔습니다. 이 후에 모델의 개선 및 확장에 대한 많은 사용자 요청이 처리되었습니다.
    표면 장력에 대해 보다 나은 성능개선을 위해 FLOW-3D 버전 11에 대한 새로운 모델이 개발되었습니다. 이 모델은 계산된 모든 표면 장력의 정확성과 임의 형상의 솔리드 표면을 잡아 당기는 접착력의 정확성을 향상시킵니다. 또한 이 새로운 모델은 다공성 물질의 모세관 압력과 비 균일한 표면 장력으로 인한 접선 표면 장력을 가지고 있습니다.

    새로운 모델의 예는 무중력에 포함된 원형 벽을 적시는 단순한 문제입니다.

    그림 1은 실린더와 접촉각이 0 도인 물로 채워진 0.25m 직경의 실린더 75 %의 경우를 보여줍니다. 버블은 10 초 전에 벽에서 깨끗하게 분리되어 탱크를 가로 질러 움직입니다. 비 구형은 기포 표면에서 모세관 파가 전파되기 때문입니다.

    그림 1. 0.0, 2.5, 5.0 및 10.0 초에 무중력에서 접촉 각이 0 인 실린더 표면의 유체 (적색) 습윤 표면.

    다른 예가 그림5에 도시되어 있습니다. 2에서 서로 다른 밀도의 2 개의 초기 구형 방울이 (플롯의 색으로 표시됨) 단단한 벽을 향해 아래로 이동합니다. 플롯의 시간은 0.0, 0.01, 0.02 및 0.03 초입니다. 방울은 직경이 0.0017m, 밀도가 다르지만 표면 장력 계수는 1.872 뉴턴 / m입니다.

    그림 2. 접시쪽으로 움직이는 구형의 물방울. 새로운 표면 장력 모델로 시뮬레이션. 색상은 밀도를 나타냅니다.

    표면 장력 모델에 대해 자세히 알아보십시오.

    Download the Flow Science Report on Surface Tension

    Download Surface Tension Validation – Simple Test Problems

    FSR_01-12_Air-Entrainment-Report [공기 혼입 모델 분석]

    Overview
    In free-surface flows the turbulence in the liquid may be sufficient to disturb the surface to the point of entraining air into the flow. This process is important, for example, in water treatment where air is needed to sustain microorganisms for water purification and in rivers and streams for sustaining a healthy fish population. Air entrainment is typically engineered into spillways downstream of hydropower plants to reduce the possibility of cavitation damage at the base of the spillway. Situations where air entrainment is undesirable are in the sprue and runner systems used by metal casters, and in the filling of liquid containers used for consumer products.
    The importance of being able to predict the amount and distribution of entrained air at a free liquid surface has led to the development of a unique model in FLOW-3D®. The model has two options. One option, to be used when the volume fraction of entrained air is relatively low, uses a passive scalar variable to record and transport the air volume fraction. This model is passive in that it does not alter the dynamics of the flow.
    The second air-entrainment model option is based on a variable density formulation. This model includes the “bulking” of fluid volume by the addition of air and the buoyancy effects associated with entrained air. This dynamically coupled model cannot, however, be used in conjunction with heat transport and natural (thermal) convection.
    In addition, when using the variable density formulation, the model can include a relative drifting of air in water, the possible escape of air if it rises to the surface of the water and the removal or addition of air to trapped bubble regions represented as adiabatic bubbles.
    The same basic entrainment process is used in both options. It is based on a competition between the stabilizing forces of gravity and surface tension and the destabilizing effects of surface turbulence.
    Because turbulence is the main cause of entrainment, a turbulence-transport model must be used in connection with the air-entrainment model. It is recommended that the RNG version of the more traditional k-epsilon turbulence model be employed. All the validation tests reported in this Technical Note were performed using the RNG model.

     

    [다운로드]

    FSR_01-12_Air-Entrainment-Report

    Salt dissolution model [소금 용해 모델]

    Introduction
    Dissolution of salt in liquid is of interest in several applications – from solution mining to food processing to medical applications. This article describes a new model in FLOW-3D1 version 10.0 for dissolving salt in fluids and tracking the solute in the brine.
    The dissolution of salt increases the density of the fluid and thus may affect the flow. In addition, as salt is dissolved, the flow domain increases. It is of interest, therefore, to predict these changes in the flow as well as the transport of the dissolved salt in the fluid.
    The model accounts for the basic physical phenomena, such as mass transfer at the interface between salt and fluid, the change of volume and shape of the solid salt, diffusion and convection of dissolved salt in fluid and, finally, the change in fluid density, viscosity and surface tension coefficient.

    Simulating the Residue left by Evaporating Drops

    Background
    The “coffee ring” effect is the name given to a well known observation where the evaporative drying of a drop of coffee leaves behind a ring of dark material at the edge of the original drop. On first thought one would expect that the coffee particles, which are uniformly distributed in the drop, would simply be deposited uniformly over the area wetted by the drop. It has only been in recent years that researchers have uncovered the mechanisms that produce the ring effect (Deegan, R.D., et al).
    As currently understood, the edges of drops can become pinned because of roughness or chemical elements on the surface on which they lie. Heat transfer to the drops from the substrate or the air induces evaporation, which is usually greater near the drop edge. Surface tension forces then adjust the curvature of the remaining liquid consistent with the pinned edge, which results in a net flow of liquid toward the edge. This flow replenishes the evaporative loss but also moves solute to the edge where it is concentrated by evaporation. Eventually, this mechanism builds up a ring deposit of solute at the original edge of the drop.
    The residue from dried drops has implications for many useful applications, including general coating processes, formation of pixel arrays of organic materials for video displays and for a variety of micro-electro-mechanical (MEMS) devices.
    Because many factors control the distribution of dried residue it is desirable to have some means to model the fluid dynamics of the process to aid engineers in making the best choices for each specific application. Such a capability has been incorporated into FLOW-3D1 making it possible to computationally investigate the influence of such parameters as the initial solute concentration, fluid viscosity, volatility of the solvent, evaporation rate, surface tension and initial shape of the drop.
    This technical note presents a brief description of the residue formation model and illustrates it with several computations of an evaporating drop subject to different physical conditions.

    Modeling Turbulent Entrainment of Air at a Free Surface

    Overview
    In free-surface flows the turbulence in the liquid may be sufficient to disturb the surface to the point of entraining air into the flow. This process is important, for example, in water treatment where air is needed to sustain microorganisms for water purification and in rivers and streams for sustaining a healthy fish population. Air entrainment is typically engineered into spillways downstream of hydropower plants to reduce the possibility of cavitation damage at the base of the spillway. Other situations where air entrainment is undesirable are in the sprue and runner systems used by metal casters, and in the filling of liquid containers used for consumer products.
    The importance of being able to predict the amount and distribution of entrained air at a free liquid surface has led to the development of a unique model that can be easily inserted into FLOW-3D® as a user customization. The model has two options. One option, to be used when the volume fraction of entrained air is relatively low, uses a scalar variable to record the air volume fraction. This model is passive in that it does not alter the dynamics of the flow.
    A second air-entrainment model, option two, is based on a variable density formulation. This model includes the “bulking” of fluid volume by the addition of air and the buoyancy effects associated with entrained air. However, this dynamically coupled model cannot be used in connection with heat transport and natural (thermal) convection.
    In both model options the same basic entrainment process is used that is based on a competition between the stabilizing forces of gravity and surface tension and the destabilizing effects of surface turbulence. The model is described in the next section. Because turbulence is the main cause of entrainment, a turbulence-transport model must be used in connection with the air-entrainment model (i.e., ifvis=3 or 4). It is recommended that the RNG version of the more traditional k-epsilon turbulence model be employed. All the validation tests reported in this Technical Note were performed using the RNG turbulence model.