수자원 및 환경 모델 / Water & Environmental Models

물 및 환경 모델

3D 자유 표면 흐름을 모델링 할 때 FLOW-3D의 고유한 강점은 복잡한 수리 환경분야에 쉽게 적용할 수 있는 최적화된 플랫폼이 제공된다는 점 입니다.  FLOW-3D 소프트웨어는 수십년 동안 복잡한 흐름 역학,  흐름/구조 상호 작용 및 환경 예측을 위해 업계 전문가들이 사용해 왔습니다. FLOW-3D의 적용에는 수처리 시설물 , 하천 계획 및 복원 , 댐 안전, 수력 및 방수 작업 , 설계 및 최적화, 저수지 유지 관리 및 계획, 해안 및 하구 공학 분야가 포함됩니다.

독특한 모델링 도구

하이브리드 3D/천수(shallow water) 해석기능은 계산상 매우 효율적이고 정확합니다. 천수(shallow water) 모델 솔루션은 대규모 도메인 (수 킬로미터 이상)에서의 유동 모델링을 허용하고 hydraulic jumps 및 침전물 이송을 정확하게 포착합니다. 브리지 교각 및 방수로와 같이 수직 흐름 효과가 중요한 지역의 3D 솔루션과 매끄럽게 연결됩니다. 또한, 등각 메쉬 (conformal meshing)는 효율적인 메쉬 생성을 능률화하고 사용자가 기하학적인 세부 사항을 쉽게 해결할 수 있게 합니다.

강력한 물리 모델

FLOW-3D는 퇴적물 정련 및 수송, 밀도 층화 및 혼합, 기포 및 캐비테이션, 증발 및 상 변화, 화학적 예측 및 수송, 다공성 매체를 포함하는 강력한 물리 모델을 추가로 포함합니다. 정확한 3 차원 유동 모델링 및 물리학 패키지를 통해 FLOW-3D 는 매우 복잡한 환경에서도 정확하고 효과적인 시뮬레이션을 결과를 제공합니다. 제공된 사례는 미세한 뉴트리안 광산 꼬리끌림의 영향을받는 세밀한 3D 유압 영역을 매핑하고 파고를 예측하는 것입니다. FLOW-3D 의 다 기능성은 사용자가 하나의 응용 프로그램에서 다음 응용 프로그램으로 부드럽게 탐색 할 수있게하며, 가장 복잡한 문제에 대한 탁월한 정확성과 사용 편의성을 제공합니다.

금속 주조 모델 / Metal Casting Models

FLOW-3D 는 금속 주조를 위해 특별히 고안된 다양한 물리모델을 제공하고 있습니다. 제공되는 물리모델은 모든 종류의 금속 주조 응용 및 분석이 필요한 업무에 가장 정확한 솔루션을 제공합니다. 이를 통해 고객들은 지속적으로 주조 수율과 품질을보다 적은 시간과 비용으로 개선할 수 있습니다.

https://www.youtube.com/watch?v=KXRDBYSQXeY

자유 표면 흐름을 정확하게 예측하기 위한 특수 기능을 갖춘 FLOW-3D  는 금형 충진 및 공기 포집과 같은 관련 결함을 시뮬레이션하는데 가장 먼저 선택됩니다. 강력하고 유연한 열 전달 모델은 금속과 금형 사이의 열 교환을 빠르고 정확하게 예측할 수 있으며 응고, 냉각 채널 및 열 다이 사이클링 시뮬레이션을위한 견고한 기반을 마련합니다.

금형 충진과 결합 할 수있는 응고 및 수축 모델은 과도한 수축 또는 다공성 영역을 정확히 파악할 수 있으며, 고객이 라이저의 배치를 결정하여 이러한 결함이 완화되도록 할 수 있습니다. 세분화된 매체 모델 및 수분 건조 모델을 사용하여 모래 코어 분사 및 건조를 시뮬레이션 할 수 있습니다.

FLOW-3D  의 유한 요소 기반 열 응력 모델을 통해 고객은 응력이 발생하는 위치와 주조가 왜곡되는 현상을 정확하게 예측할 수 있으므로, 고객은 금속 주조에서 열 응력 결함을 제거 할 수 있습니다. 주철 모델은 공극 반응 동안 흑연, 감마철 및 탄화물 위상의 형성을 예측하여 FLOW-3D 의 적용 범위를 확장합니다 . 코어 가스 제품군의 독특한 특징으로 코어 가스 생성 및 모래 코어의 유동을 모델링하며, 이는 금속 주조에서 코어 가스 관련 결함을 예측할 수 있습니다.

FLOW-3D 는 금속 주조 모델링 및 시뮬레이션의 선두 주자입니다. 금속 주조 산업에 대한 오랜 연구개발과  고객과의 지속적인 협력을 통해 개발된 응용 프로그램으로 고객의 품질과 생산성을 향상시키고 지속적으로 혁신 할 수 있도록 지원할 것입니다.

점탄성 흐름 / Viscoelastic Flow

점탄성 흐름 / Viscoelastic Flow

FLOW-3D 는 국부 변형률 및 변형률 속도에 따라 액체와 고체처럼 거동하는 재료의 거동을 예측하는 점탄성 유동 모델을 포함합니다. 점탄성 물질은 고분자 용액, 용융물 및 고충진 입자의 현탁액을 포함합니다. Elasto-viscoplastic 소재는 항복 응력 한도까지 안정된 거동을 나타내며 그 이상의 재료는 액체와 같은 거동을 나타냅니다.

FLOW-3D에 포함 된 점탄성 모델에는 Oldroyd-B 모델과 Giesekus 모델이 있습니다. 추가 모델은 사용자 정의를 통해 구현 될 수 있습니다.
재료에 관계없이 탄성 응력은 하나의 시간 간격에서 점차적으로 계산되어 장시간 동안 큰 변형을 시뮬레이션 할 수 있습니다.

스퍼 기어의 사출 성형 / Injection molding of a spur gear

한 가지 예가 폴리에틸렌 용융물의 사출 성형입니다. 위의 애니메이션은 스퍼 기어의 사출 성형을 보여줍니다. 동일한 부품은 동일한 점성 속성을 갖는 다른 (허구의) 소재로 채워지지만 탄성 속성은 없습니다. 탄성 응력의 효과는 유체가 기어의 바깥 쪽 테두리에 도달 할 때 명확합니다. 여기서는 점탄성 물질의 압출 공정에서 볼 수 있듯이 쐐기에서 발생하는 탄성 응력이 대칭적인 “흘러 내림”에서 거의 수평 운동으로 흐름을 변경합니다.

난류 / Turbulence

난류 / Turbulence

FLOW-3D 는 완전 3 차원 유동, 2 차원 깊이 평균 (천수(shallow water)) 흐름 및 3 차원/2 차원 깊이 혼합 평균 흐름을 위한 포괄적인 난류 모델링 제품군을 제공합니다.

그림1. 부두 하류에서의 와류 검출을위한 Q- 기준의 3D지도

FLOW-3D 에는 8 가지 난기류 옵션이 있습니다.

  • Prandtl 혼합 길이 모델은 3 차원 난류 효과를 설명하기 위한 가장 초기의 시도 중 하나입니다. 가장 복잡한 모델이 아니며 더 이상 널리 사용되지 않습니다. FLOW-3D 는 주로 학술 연구에서의 유용성을 포함합니다.
  • 소위 1 방정식 모델은 난기류를 나타내는 초기 노력이기도 합니다. 시간 평균 난류 운동 에너지 k를 계산하고 모든 위치에서 알려진 난류 혼합 길이 LT 가 필요합니다. LT 는 일반적으로 미리 알려지지 않기 때문에, one-equation 모델은 복잡한 유량을 모델링하는 데 적합하지 않습니다.
  • 표준 k-ε 모델 (Harlow & Nakayama 1967)은 난류 운동 에너지 k와 소산 속도 ε를 계산하고 난류 혼합 길이 LT를 동적으로 찾는 2 방정식 모델입니다. 이것은 업계 표준이며 광범위한 흐름을 표현하는데 유용하다는 것이 발견되었습니다 (Rodi 1980).
  • 재 정규화 그룹 (RNG) k-ε 모델 (Yakhot & Orszag 1986, Yakhot & Smith 1992)은 2 방정식 k-ε 모델의 보다 견고한 버전이며, 대부분의 산업에서의 문제에 권장됩니다. 표준 k-ε 모델의 기능을 확장하여 과도기 난류, 곡선 흐름, 벽 열 전달 및 물질 전달의 더 나은 적용 범위를 제공합니다.
  • k-ω 2 방정식 모델 (Wilcox 1988, 1998, 2008)은 두 번째 변수를 난류 소산 ε이 아니라 ω ≡ ε / k로 정의한다 (Kolmogorov 1942). Wilcox는 1988 년부터 k-ω 2 방정식 모델을 개선했으며 1998 년에는 자유 전단 유동에 대한 모델의 정확성을 크게 개선 한 새로운 계수를 도입했습니다. FLOW-3D 의 k-ω 2 방정식 모델은 제트, 후류 및 플럼을 퍼 뜨리는 것과 같은 유선형 압력 구배를 갖는 자유 전단 흐름을 모델링하는 데 적합합니다.
    LES 모델은 평균 난류 운동 에너지를 나타내기 위해 스칼라를 사용하지 않고 대부분의 난류 변동을 직접 해결합니다. 그것은 2 방정식 모델보다 훨씬 더 미세한 메쉬 해상도를 필요로하며 난기류에 대한 보다 광범위한 통계를 제공합니다.
  • 2-D 심도 평균 얕은물 난류 모델은 대수적인 완전 난류 속도를 가정합니다. 첫 번째 옵션은 일정한 항력 계수 CD를 가정하며, 이는 공간적으로 변화 할 수 있습니다.
  • 두 번째 2-D 심도 평균 천수(shallow water) 난류 모델은 항력 계수 CD 를 유체 깊이와 공간적으로 가변되는 표면 거칠기의 동적 함수로 만듭니다.

완전한 3-D 테스트를 통해 LES 모델 출력을 시간 평균화하면 2 방정식 Reynolds REN (Reynolds Averaged Navier-Stokes) 모델 (표준 k-ε, RNG k-ε 및 k- ω).

아래의 물고기 통로 비디오에 나와 있습니다.

난류 시뮬레이션 – 모델 비교 / Turbulence Simulations – A Model Comparison

첫 번째 비디오에서는 FLOW-3D 의 LES (Large-Eddy Simulation) 난류 모델을 사용하여 어류 통과를 시뮬레이션하여 속도 변동의 크기를 분석합니다. 두 번째 비디오는 동일한 시뮬레이션의 시간 평균 결과를 보여줍니다. 여기에서 간단한 사용자 정의는 시간 평균 LES가 레이놀즈 평균 Navier-Stokes (RANS) 난류 모델 결과와 매우 유사하다는 것을 보여줍니다. 세 번째 비디오는 RNG (Renormalized Group) k-ε 난류 모델을 사용하여 시연하기 위해 동일한 시뮬레이션을 사용합니다. RNG k-ε 모델은 대부분의 레이놀즈 평균 Navier-Stokes (RANS) 난류 모델과 마찬가지로 속도 변동을 등방성 스칼라 값으로 처리하여 시간에 따른 속도 변동을 감쇠시킵니다. 결과는 두 번째 비디오에서 볼 수 있듯이 직접 LES 결과를 시간 평균하여 찾은 결과와 유사합니다.

참고 문헌

  • Driver, DM and Seegmiller, HL, 1985, AIAA Journal (23), 163-171의 다양한 채널 유동에서 재 부착하는 난류 전단 층의 특징 .
  • Harlow, FH and Nakayama, PI, 1967, 난류 수송 방정식 , 유체 역학 (10), 2323-2332.
  • Harlow, FH 및 Nakayama, PI, 1968, 난기류 에너지 감쇠율의 전송 , Los Alamos Scienti fi c 실험실 보고서 LA-3854.
  • Kolmogorov, AN, 1942, 비압축성 유체에서의 난류 운동 방정식 , Izvestia Academy of Sciences, 소련; Physics (6), 56-58.
  • Pope, S. B, 2000, Turbulent Flows , Cambridge University Press.
  • Rodi, W., 1980, 난류 모델과 유압 장치의 적용 : 최첨단 검토 , 국제 유압 연구 협회 (IAHR), 델프트, 네덜란드.
  • Saffman, PG, 1970, Inhomogeneous Turbulent Flow의 모델 , Royal Society London A (317), 417-433의 절차.
  • Speziale, CG, Abid, R., and Anderson, EC, 1992, AIAA 저널 (30), 324-331, 벽 근처 난류에 대한 2 방정식 모델의 중요성 평가.
  • Wilcox, DC, 1988, AIAA Journal (26), 1299-1310의 진보 된 난류 모델에 대한 스케일 결정 방정식의 재평가.
  • Wilcox, DC, 1998, CFD의 난류 모델링 , DCW Industries, Inc., 제 2 판.
  • Wilcox, DC, 2008, k-omega 난류 모델의 공식화 , AIAA Journal (46), 2823-2838.
  • Yakhot, V. and Orszag, SA, 1986, 난류의 재 정규화 그룹 분석 I. 기본 이론 , Journal of Scientific Computing (1), 3-51.
  • Yakhot, V. 및 Smith, LM, 1992, 재 정규화 그룹, 난류 모델의 전자 확장 및 유도 , Journal of Scientific Computing (7), 35-61.

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

다상 유동 / Multiphase Flows

다단계 흐름(다상 유동) / Multiphase Flows

극저온 액체 / 가스 조합 및 제 2 비응 축성 가스 성분을 함유하는 탱크

FLOW-3D 의 상 변화 모델은 액체 / 기체 계면에서의 기화 및 응축을 시뮬레이션합니다. 그것은 주위 액체에 증기 기포의 형성과 상호 작용을 예측합니다. 기포는 핵 생성을하고 액체 운동에 역동적으로 반응하며 주변 환경의 온도와 압력에 따라 성장하거나 줄어들 수 있습니다.
FLOW-3D 의 기존 상 변화 모델은 증기 기포와 주변 액체의 형성과 상호 작용을 예측하는 강력한 도구입니다. 기포는 액체 운동에 동적으로 반응 할 수 있으며 주위 환경의 온도와 압력에 따라 성장하거나 줄어들 수 있습니다 . 그러나, 증기와 함께 존재할 수 있는 응축되지 않는 가스의 효과를 기포 또는 다른 증기 공간 내부에 포함시키는 것은 아직 가능하지 않습니다.

예를 들어 수증기와 공기가 모두 포함 된 기포가 증기보다 더 낮은 온도 또는 더 낮은 조건에서 존재할 수있는 공기 / 물 / 증기 시스템의 역학에서 중요 할 수 있습니다. FLOW-3D 는 사용자가 비 응축 가스를 모델링 할 수있게 하여이 제한을 없앱니다.

하이라이트
  • 사용자는 가스 상수, 열용량 및 증발 데이터의 열을 제공하고 관련 초기 및 경계 조건 데이터 만 지정하면됩니다.
  • 기체 / 액체 계면이 존재하는 곳에서는 액체의 증발과 증기의 응축이 자동으로 계산됩니다.
  • 사용자는 응축되지 않는 가스 및 증기의 부피 분율을 그래픽으로 추적 할 수 있습니다.
모델 기본 사항

이 모델은 날카로운 인터페이스 추적과 함께 FLOW-3D 의 압축성 2-유체 흐름 옵션과 함께 사용해야합니다. 비 응축 가스의 국부적인 농도를 추적하는 새로운 양은 모델이 가스 / 증기상 내에서 가스의 효과를 예측할 수있게 합니다. 가스 상수 및 열용량에 대한 조정은 압력 – 밀도 관계를 변경시킵니다. 그러므로 기체 / 증기 혼합물에서 응축 가능한 상 (condensable phase)의 증기압의 계산은 증기의 체적 분율에 국소 절대 압력을 곱한 값입니다.

따라서 모델의 기초는 물질 전달률의 계산입니다 :

실험 및 시뮬레이션 데이터를 사용한 샘플 결과

극저온 탱크 내의 압력 도표 : 테스트 데이터 (빨간색)와 FLOW-3D 모델 (파란색)의 비교. 압력은 탱크 벽을 통한 점진적인 가열로 인해 상승하고 차가운 질소 스프레이의 도입으로 인해 급격히 감소합니다.
극저온 액체 / 가스 조합 및 제 2 비응축성 가스 성분을 함유하는 탱크의 이러한 예에서, 탱크의 벽은 특정 탱크 압력에 도달 할 때까지 서서히 가열되고,이 시점에서 차가운 액체 스프레이가 급속하게 도입되어 온도를 낮추는 탱크를 감압하십시오. 이 프로세스는 주기적입니다.

이 모델을 기반으로하는 연구는 미국 항공 우주 학회 (American Institute of Astronautics) 회의에서 발표 되었습니다. 이 연구에는 실제 테스트 데이터와 액화 가스를 포함하는 극저온 탱크의 계산 시뮬레이션을 비 응축 가스 (일반적으로 헬륨)와 비교하여 비교했습니다. 왼쪽의 플롯은 시간의 함수로서 질소 증기 및 헬륨 가스를 함유 한 가스 공간을 갖는 액체 질소를 함유하는 탱크의 증기 영역 내의 압력을 도시합니다. 예를 들어, 탱크의 벽에서 탱크 압력이 25 psi에 도달 할 때까지 서서히 가열합니다. 이 시점에서 차가운 액체 질소 스프레이가 도입되어 탱크를 급냉(따라서 감압) 합니다. 그런 다음 이 과정이 반복됩니다. 시뮬레이션 데이터는 실제 테스트 데이터와 잘 일치하였습니다. 오류는 일반적으로 ~ 10 % 정도입니다. FLOW-3D 모델과 테스트 데이터 간의 오차는 부분적으로 열 전달 계수를 측정하기 어렵기 때문에 모델에서의 열전달율이 일정하다고 가정하고 액체 스프레이를 탱크는 일정한 온도로 유지됩니다.

움직이는 물체 / Moving Objects

움직이는 물체 / Moving Objects


FLOW-3D 시뮬레이션에서 일반적인 움직이는 물체 (GMO)는 사용자가 규정하거나 유체 흐름과 동적으로 결합되는 모든 종류의 모션을 가진 강체입니다. 고정된 축 / 포인트와 같은 6 자유도 또는 모션 구속 조건을 가질 수 있습니다. 규정된 힘과 토크는 결합된 동작 하에서 GMO에 적용될 수 있습니다. GMO 모델은 충돌 및 연속 접촉을 포함하여 강체 상호 작용뿐만 아니라 독립적인 동작 유형에서 여러 개의 강체를 허용합니다. 이 모델은 견고하고 효율적이며 강력하고 상업용 전산 유체 역학 소프트웨어에서 FLOW-3D가 유일합니다.

FLOW-3D 자동차 차동 부분의 3D 시뮬레이션

 

모델링 기능

6 개의 DOF를 소유 할 수있는 최대 500 개의 움직이는 물체를 허용하거나 고정된 축 또는 고정된 점을 중심으로 회전 할 수 있습니다. 다른 모션 제약 패턴도 가능합니다.
물체는 유체 흐름과 완벽하게 결합되거나 사용자가 모션을 처리할 수 있습니다.
물체는 밀도로 특징 지어지는 여러 가지 재료로 만들 수 있습니다.
객체의 기하학 및 동작의 복잡성에 대한 제한이 없습니다.
지정된 시간에 따른 힘과 토크를 대상에 적용 할 수 있습니다.
모델 충돌 및 움직이는 물체와 움직이지 않는 물체 사이의 지속적인 접촉
스프링과 로프는 물체에 닿을 수 있습니다.
개체에서 다공성 허용
열전도 및 대류가 허용됩니다.
유압식, 중력 식, 비 관성식, 스프링 식, 사용자 정의 제어력 및 토크는 결합 된 모션이있는 물체에 대해 고려됩니다.
시각 및 수치 출력을 포함한 완벽한 후 처리 기능

움직이는 물체 시뮬레이션

FLOW-3D 고객은 처음 사용하는 방법보다 더욱 효율적으로 움직이는 물체 모델의 적용을 사용했습니다. waterwheels에서 shot sleeve, 에너지 디바이스 파동에 이르기까지 우리는 복잡한 메쉬 및 집중적인 컴퓨팅 리소스에 의존하지 않고도 엔지니어링 문제를 해결하는데 모델을 사용하는 방법에 깊은 인상을 받았습니다. 이 모델을 사용하는 진지하고 상상력이 좋은 예를 모두 검토하려면 YouTube 재생 목록 을 방문하십시오.





열전달 / Heat Transfer

열전달 / Heat Transfer

용융 금속으로 부품을 채우는 동안 금속 주조물의 온도 출력
FLOW-3D 의 열 전달 모델은 전도, 대류 및 기본 복사를 통해 유체, 고체 및 공간 간의 열 전달을 설명하는 전체 공액 열 전달 방정식을 해결합니다. 서로 다른 매체 간의 열 전달 계수는 사용자에 의해 정의되거나 흐름 유형에 따라 자동으로 계산될 수 있습니다. 1차 및 2차 열 에너지 전달 알고리즘을 모두 사용할 수 있습니다.

특정 열유속에서부터 전원, 규정된 온도에 이르기까지 유체와 고체 사이의 열 전달을 모델링 할 수 있는 몇 가지 옵션이 제공되어, 다양한 열처리 과정을 모델링 할 수 있는 유연성을 제공합니다.

기본 열 전달 모델과 결합된 추가 기능을 사용할 수 있습니다. 액체 / 고체 및 액체 / 증기 상 변화 모델을 사용하여 금속 응고, 물의 건조 및 비등 및 스프레이 냉각을 시뮬레이션 할 수 있습니다. 점성 가열 또한 고속 점성 유동에 포함될 수 있습니다.
위의 시뮬레이션은 고온에서 금형에 들어가고 open atmosphere와 금형을 포함하여 주변 환경에 의해 냉각된 유체의 상태를 보여줍니다.

Fluid Structure Interaction / 유체 구조 상호 작용

Fluid Structure Interaction / 유체 구조 상호 작용

유체 구조 상호 작용 모델은 주변 유체의 압력력, 온도 구배 및 지정된 구속 조건에 대한 응답으로 솔리드 구성 요소의 모델 응력 및 변형에 대한 유한 요소 접근법을 사용하여 유체와 솔리드 간의 완전 결합 상호 작용을 설명합니다. 현재 모델은 작은 변형으로 제한됩니다. FSI 모델의 가능한 응용 프로그램은 다음과 같습니다.
  • 수문, penstock 및 tainter 방수로 게이트
  • 잉크젯 프린터 노즐
FLOW-3D 의 유체 구조 상호 작용(FSI) 모델은 고체 역학뿐만 아니라 유체 역학에 결합 된 솔루션을 제공합니다. 유체 구조 상호 작용 및 열 응력 진화의 경우, 유체 압력, 온도 구배 및 체력이 고체의 변형에 영향을 줍니다. 그런 다음 변형이 유체 흐름으로 다시 공급됩니다. 유체 계산은 유한 차분 데카르트 메쉬에서 수행되고 변형률-스트레인 방정식은 FE(Finite Element) 바디 메쉬에서 해결됩니다.
사용자는 CAD 지오메트리(STL) 파일 또는 FLOW-3D의 지오메트리 입력을 통해 생성된 복잡한 형상에 대한 FE 메시를 생성 할 수 있습니다. FE 메시 생성기는 표준 FLOW-3D 데카르트 메쉬를 시작점으로 사용합니다. 그런 다음 솔리드 서페이스를 포함하는 요소의 모양이 솔리드의 인터페이스를 캡처합니다. FE 메시는 사용자로부터 입력이 거의 또는 전혀없이 생성됩니다. 그러나 사용자는 정교하고 복잡한 FE 메쉬를 생성 할 수 있습니다.
FLOW-3D 메쉬의 로컬 정련은 유한 요소 메쉬에 나타나는 디테일의 수준을 향상시킵니다.
플롯 (a)은 FLOW-3D의 STL (stereolithography) 파일 뷰어에서 생성된 부분을 보여줍니다.
Plot (b)은 거친 FE 메쉬의 샘플 결과를 보여주고 plot (c)는 포함하는 Cartesian 메쉬의 로컬 해상도를 증가시켜 FE 메쉬에서 미세 디테일을 해결할 수있는 방법을 보여줍니다.

Fluid Structure Interaction Videos

고체 역학 문제를 풀기 위해 필요한 탄성 특성은 온도에 따라 달라질 수 있습니다.

Flow Science는 MPDB (Material Property Database)와 파트너 관계를 맺어 수천 개의 고체 물질과 온도 의존 특성을 제공합니다. 시뮬레이션의 견고한 역학 측면에 대한 솔루션을 분석하는 출력 변수는 다음과 같습니다.

  • 전체 응력 텐서 (Full stress tensor)
  • 전체 변형 텐서 (Full strain tensor)
  • 3 차원에서의 변형 (Full strain tensor)
  • 정상 변위 (Normal displacement)
  • 볼륨 확장 (Volume expansion)
  • 평균 등방성 응력 (Mean isotropic stress)
  • 폰 미세스 스트레스 (Von Mises stress)

Dynamic Droplet Model for Two-Component Flows

Dynamic Droplet Model for Two-Component Flows / 두 구성 요소 흐름을 위한 동적인 방울 모델

실 세계에는 많은 2-유체 혼합물이 있습니다. 예를 들어, 공기와 물의 혼합물 또는 오일과 물은 환경 및 산업 공정에서 자주 발생합니다. 두 유체의 혼합물에 대한 FLOW-3D의 기존 모델링 기능은 부력과 점성력으로 인해 발생하는 두 구성 요소의 상대적 동작을 계산하는 DRIFT 루틴입니다. 이 모델은 단순성과 견고성으로 인해 많은 상황에서 잘 작동합니다.
두 유형의 두 가지 구성 요소 흐름이 있습니다. 하나는 밀도가 다른 두 유체의 혼합이지만 날카로운 두 유체 인터페이스는 없습니다. 다른 유형은 자유 표면을 가질 수 있지만 2개의 비압축성 성분의 혼합물로부터 발생하는 가변 밀도를 갖는 단일 유체입니다.
분산된 구성 요소는 구형 물방울 또는 거품으로 구성됩니다. 이 모델은 유용하지만 사용자가 분산 재료 요소의 평균 크기를 지정하여 상대 모션을 유도하는 힘을 계산할 수 있어야 합니다. 크기 지정은 종종 알려진 것이 아니기 때문에 한계가 있습니다. 또한, 크기는 공간 및 시간 모두에서 변할 수 있는데, 예를 들어, 임펠러를 포함하는 혼합 용기에서, 임펠러 부근에서 크기가 더 작고, 계속 혼합 될 때 더 감소 할 수 있습니다.
이 제한을 수정하기 위해 DRIFT 루틴 내에서 분산 된 유체 방울 크기를 동적으로 계산하기 위한 새로운 모델이 구현되었습니다. 이 모델은 중요한 Weber 및 Capillary 수에 의해 제어되는 분산된 물질의 분열 및 합체를 위한 간단한 메커니즘을 기반으로 합니다. 새 모델은 지역 흐름의 세부 사항에 맞게 공간과 시간이 모두 다른 크기를 생성합니다.

 

 

그림 1. 실험용 슈트의 레이아웃

새로운 모델의 좋은 적용은 방수로 또는 경 사진 슈트를 흐르는 물의 공기 포착입니다. K. Krammer의 논문 ( Aerated Chute Flow , ETH, Zürich, 2004)의 논문은 흐름 내에서의 기포 크기 분포에 대한 측정된 데이터를 포함하는 이러한 유형의 흐름에 대한 훌륭한 예를 제공합니다. Fig. 1, 가로 14m, 세로 0.5m, 기울기 5.71 °. 0.05 %의 유입 유동 깊이가 17.76%의 사전 혼합 공기 농도 및 10% 난류를 포함하여 사용되었습니다. 이 흐름은 0.1755m 3/s의 입구 유속을 가지며, 이는 프 루드 수 10.03에 해당합니다.
시뮬레이션은 수중 공기 혼합물의 부력과 부피를 포함하는 FLOW-3D의 첨단 공기 혼입 모델을 사용하여 수행되었습니다. 입구 흐름과 함께 도입된 비말 동반 된 공기에 추가하여, 그림2에 도시 된 바와 같이, 혼합물의 체적(부피)을 증가시키는 흐름의 표면에 공기가 동반된다. 그림2는 슈트의 제 1 미터를 따른 대칭 평면의 흐름을 도시합니다. 입구에서 첫 번째 미터 너머의 흐름은 거의 균일하고 공기와 기포 크기 분포가 균일합니다.

 

그림 2. 슈트의 첫 번째 미터에서 유체가 부피가 커지는 중심선 플롯
실험에서 흐름의 공칭 자유 표면은 공기 농도가 90 % (또는 10 % 물) 인 위치에 있다고 가정했습니다. 시뮬레이션에서 이 조건은 공기 배출 메커니즘을 사용하고 최소 수분 비율을 0.1로 제한함으로써 부과됩니다.
흐름이 거의 일정하고 균일한 슈트 끝에 있는 슈트 단면의 공기의 계산된 부피 분율이 그림 4에 나와 있습니다. 3. 측벽의 작은 외란은 슈트 측면의 마찰력에서 발생하는 관측된 롤 파와 관련되어 있습니다.

그림 3. 슈트 끝의 공기 농도 (Figure 3. Air concentration at end of chute)

계산된 깊이는 0.061m로 보고된 깊이 0.062m에 가깝습니다. 슈트 끝에서 보고된 평균 공기 함량은 약 16.7% 였고 시뮬레이션은 약 20%의 값을 보였습니다.

 

그림 4. 슈트의 중간 지점에서의 버블 직경과 깊이에 대한 실험 결과와 시뮬레이션 결과의 비교

실험 데이터와 비교하여 슈트끝에 있는 계산된 버블 직경 대 정규화된 깊이 계산 결과에 대한 오차 막대는, 단지 해가 준 안정적이기 때문에 시간에 따른 변화를 나타냅니다.

시뮬레이션된 크기가 흐름 상단 근처의 데이터보다 다소 작더라도 실험자들은 자유 표면 근처의 크기가 정확하게 측정하기가 어렵다고 보고했습니다. 어쨌든 일정한 기포 크기의 가정은 현실적이지 않으며 새로운 동적 방울 모델이 2-성분 흐름의 FLOW-3D 시뮬레이션에서 보다 사실감을 더했습니다.

FLOW-3D 수치모델링 기능

수치모델링 기능

범용 CFD 패키지인 FLOW-3D 는 비압축성 자유 표면의 내부, 극 초음속 외부 유동흐름, 열 전달, 난기류 등 유체 역학 문제 해결을 위해 36 년 이상 개발하고, 완성한 광범위한 물리 및 수치 기능을 갖추고 있습니다. 사용자는 FLOW-3D 를 사용하여 고체의 이동 및 변형, 표면 장력 및 상 변화 등의 모델을  통해 광범위한 공학 및 과학 문제를 해결하고, 설계를 최적화하며, 복잡한 프로세스에 대한 통찰력을 얻을 수 있습니다.

FLOW-3D의 단열 버블 및 표면장력 모델과 결합된 단일 유체 VOF 접근 방식을 사용하면 유체의 공극 영역을 매우 효과적으로 모델링할 수 있습니다. FLOW-3D는 빠르고 견고하며 매우 정확합니다.

2016년 FLOW-3D Korea Users Conference 발표자료

2016년 FLOW-3D Korea Users Conference 발표자료를 업로드 해 드립니다.
공개 불가 자료는 올려드리지 못하오니 양해 바랍니다.
다운로드에 문제가 있으신 분들은 아래 연락처 혹은 이메일로 연락주시면 보내드리도록 하겠습니다.

-연락처 : 02-2026-0455
-이메일 : flow3d@stikorea.co.kr

01_Developments and Improvements_FlowScience
02_Through Intuitive Interface Design_FlowScience
03_해상구조물 주변 세굴 수치모의 실험_해풍기술
04_FLOW-3D_활용사례_건기연
05_FLOW-3D 고급기능을 이용한 수리구조물 해석_STI

2015년 FLOW-3D Korea Users Conference 발표자료

2015년 FLOW-3D Korea Users Conference 발표자료를 업로드 해 드립니다.
공개 불가 자료는 올려드리지 못하오니 양해 바랍니다.
다운로드에 문제가 있으신 분들은 아래 연락처 혹은 이메일로 연락주시면 보내드리도록 하겠습니다.

-연락처 : 02-2026-0455
-이메일 : flow3d@stikorea.co.kr

다운로드 :
01_solver developments-MB
02_FLOW-3D를 이용한 등부표의 운동 모의
03_복합공진 파력발전장치의 수치실험
05_FLOW-3D 활용 사례 (관수로 및 터널 유동)_공개
06_User Interfacecs

Solution-Coating Technology for AMOLED Displays

Solution-Coating Technology for AMOLED Displays

FLOW-3D를 이용한 AMOLED 디스플레이용 – 코팅 기술 해석사례로 픽셀 층의 균일성 개선, 증발, 초과 용액 등에 대한 분석 수행.

01-11 Reid Chesterfield, Andrew Johnson, Charlie Lang, Matthew Stainer, and Jonathan Ziebarth, Solution-Coating Technology for AMOLED Displays, Information Display Magazine, 1/11 0362-0972/01/2011-024$1.00 + .00 © SID 2011.

[ 다운로드 ] DEC-frontline_technology_AMOLED.pdf

Predicting Defects Lform [Lost Form 결함 예측]

Introduction

There is increasing interest in the lost foam casting technique because of its ability to produce near-net-shaped components of high complexity. The idea is to first make a prototype of the part to be cast in foam. This is then used as a pattern that can be placed in a box and surrounded by sand. Finally, metal is poured such that it smoothly replaces the foam by melting and/or evaporating it.

The stiffness of the foam makes it possible to cast parts having thin walls or other fine-scale features, and since the foam does not have to be removed at the end of the casting process, parts can be made that require fewer gaskets to assemble. Furthermore, because the foam pattern holds the sand (mold) in place there is little need to use binders in the sand, which means that the sand doesn’t have to be disposed of and can be used again. All these features make the lost foam process highly attractive to manufacturers.

Unfortunately, one rarely gets a free lunch and lost foam casting is no exception. For the process to be successful there must be a high degree of process control. Foams must have the proper characteristics and be coated with just the right material, and pouring sprues and gates for delivering metal to the mold must be carefully arranged. Metal pour temperatures must be sufficiently high to prevent premature solidification. And finally, the filling pattern of a mold should be such that metal fronts do not merge in a way that traps liquefied foam material, which could cause internal defects in the cast part.

To help casters address some of these difficult problems the computational fluid dynamics (CFD) program FLOW-3DÒ has been outfitted with special modeling capabilities to simulate the lost foam process. Using these models, it is possible to simulate the filling of a lost foam mold and the subsequent solidification of the metal. An extra feature in FLOW-3DÒ is the capability to predict where folds or other defects associated with trapped foam products are likely to be located.

The purpose of this paper is to demonstrate the usefulness and accuracy of lost foam predictions made with FLOW-3DÒ by presenting a direct comparison between experimental and computational results. The example chosen for this comparison is described in the next section. Subsequent sections present the comparisons with an emphasis on how the computational results can be used to understand why things happened as they did. This last point is most important, because it offers the user direct evidence and insight into how a casting could be improved.

 

[다운로드]

Predicting Defects Lform

Microporosity [마이크로 기공]

FLOW-3D® now has a model for predicting the occurrence of small bubbles otherwise known as micro-porosity. The model is simple, requires only the basic material property data and adds virtually no CPU time to a solidification simulation.

As with macro-porosity, this porosity is caused by shrinkage, however, it develops at a later stage in the solidification process.

 

[다운로드]

Microporosity

Applications of FLOW-3Dr to MEMS (Multiphysics Capabilities)

One of the unique features of FLOW-3Dr is the FAVORTM advantage used to accurately represent complex geometry in a rectangular Cartesian mesh.
The tedious work of generating a mesh for complex geometry is avoided. Due to this advantage, FLOW-3Dr can be used to simulate °ow in complex mi-crochannels accurately and e±ciently. Figure 1 shows a novel design of a microchannel with obliquely ori-ented or staggered herringbone ridges on its bottom wall to generate chaotic mixing of °uids (Stroock et al., Science, 295, 647-651, 2002). Fluid °ow and mix-ing through this device can be easily simulated with complicated geometry resolved using FAVOR TM. Fig-ure 2 displays the secondary °ow in two typical cross sections along the channel axis of this device. The predicted °ow ¯elds matches the experimental obser-vations of Stroock et al. very well.

 

[다운로드]

Applications of FLOW-3Dr to MEMS (Multiphysics Capabilities)

FSR_01-13_Void-Regions-and-Bubble-Models-in-FLOW-3D

Introduction
The purpose of this technical note is to describe to the reader general details of the treatment of void regions and their interaction with fluid in FLOW-3D1 and to help better understand the program’s capabilities and results, as well as its limitations.

In one-fluid problems in FLOW-3D the volume-of-fluid (VOF) function F defines the location of fluid #1 in the mesh. For example, F(ijk)=1.0 in a cell full of fluid. An open cell with no fluid is a void cell; F(ijk)=0.0 in such a cell.

Void cells represent regions of gas in which spatial variation of pressure and temperature, inertia and friction at the interface with fluid can be neglected. These assumptions are generally valid if

– the gas density is much smaller than that of the fluid,
– the gas speed is comparable with that of the fluid,
– the speed of sound in the gas is much greater than the speed of the mean flow.

All these conditions are present in many situations such as mold filling with liquid metal, water flow in rivers and ducts (with the exception of high winds, which could be accounted for with a special type of a free surface boundary condition in FLOW-3D), micro-fluidic devices and so on.

The one-fluid/void approach to modeling free surface is a powerful method that provides efficient and accurate solutions to general free surface flows [1]. Including the details of gas flow in such cases is usually computationally expensive and unnecessary.

The terms ‘void’ and ‘bubble’ in this article largely refer to the same computational objects. A slight distinction is that a void region may be called a ‘bubble’ when it is surrounded by fluid and its pressure and temperature vary dynamically – as in an actual bubble moving through liquid. In the context of the solver all such objects are referred to as ‘void regions’.

Bubble models in FLOW-3D have many uses in complex flow situations involving non-equilibrium thermal and dynamic processes. Bubbles containing vapor can arise or disappear in a simulation because of phase change associated with cavitation or boiling. Gas bubbles can be affected or created by gas mass sources as well as through vents and valves connected to external
pressure reservoirs. Turbulent liquid surfaces may entrain gas from bubbles and be bulked up by the added gas volume. All these possibilities as well as several basic techniques dealing with the
identification and labeling of bubble regions are described in the remainder of this document.

 

[다운로드]

FSR_01-13_Void-Regions-and-Bubble-Models-in-FLOW-3D

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

The Sedimentation Scour Model [침전 세굴(쇄굴) 모델]

1. Introduction
The three-dimensional sediment scour model for non-cohesive soils was first introduced to FLOW-3D in Version 8.0 to simulate sediment erosion and deposition (Brethour, 2003). It was coupled with the three-dimensional fluid dynamics and considered entrainment, drifting and settling of sediment grains. In Version 9.4 the model was improved by introducing bedload transport and multiple sediment species (Brethour and Burnham, 2010). Although applications were successfully simulated, a major limitation of the model was the approximate treatment of the interface between the packed and suspended sediments. The packed bed was represented by scalars rather than FAVORTM (Fractional Area Volume Obstacle Representation, the standard treatment for solid components in FLOW-3D). As a result, limited information about the packed bed interface was available. That made accurate calculation of bed shear stress, a critical factor determining the model accuracy, challenging.

In this work, the 3D sediment scour model is mostly redeveloped and rewritten. The model is still fully coupled with fluid flow, allows multiple non-cohesive species and considers entrainment, deposition, bedload transport and suspended load transport. The fundamental difference from the old model is that the packed bed is described by the FAVORTM technique. At each time step, area and volume fractions describing the packed sediments are calculated throughout the domain. In the mesh cells at the bed interface, the location, orientation and area of the interface are calculated and used to determine the bed shear stress, the critical Shields parameter, the erosion rate and the bedload transport rate. Bed shear stress is evaluated using the standard wall function with consideration of bed surface roughness that is related to the median grain size d50. A sub-mesh method is developed and implemented to calculate bedload transport. Computation of erosion considers entrainment and deposition simultaneously in addition to bedload transport.

Furthermore, a shallow-water sediment scour model is developed in this work by adapting the new 3D model. It is coupled with the 2D shallow water flows to calculate depth-averaged properties for both suspended and packed sediments. Its main differences from the 3D model are 1) the settling velocity of grains is calculated using an existing equation instead of the drift-flux approach in the 3D model, and 2) turbulent bed shear stress is calculated using a well-accepted quadratic law rather than the log wall function. The drag coefficient for the bed shear stress is either user-given or locally evaluated using the water depth and the bed surface roughness that is proportional to d50 of the bed material. The following sections present the sediment theory used in the model and application and validation cases.

Comments on a comparison of CFD for microfluidic app

Introduction
A recent effort to compare the performance of four commercial computational fluid dynamics (CFD) software packages for microfluidic applications (T. Glatzel, 2008) was recently brought to the attention of the staff at Flow Science, Inc. The paper reported simulation results from the four CFD packages for a set of flow problems typically encountered in microfluidics. The intent of the paper was to compare the quality of the solvers by removing differentiating features (meshing, special numerical algorithms, etc.) from the analysis. While we acknowledge the worthiness and difficulty of the task, we believe there are some significant limitations to the usefulness of the comparisons made in the paper.
To begin, the modeling restrictions employed prevented the individual software programs from making use of particular options they might have for obtaining better simulations of particular flow problems. A second point, at least in connection with our software product, FLOW-3D®, we have noted numerous inaccuracies in the software’s description, an incorrect use of boundary conditions and several other failures to operate the software properly. This note is intended to correct these deficiencies and omissions as well as to present a repetition of the computational examples, as near as possible, from data given in the original paper. It will be shown that FLOW-3D® performs all the comparison problems as well or better than other software tools included in the original study.

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.

On the implementation of two-equation turbulence models in FLOW-3D

Abstract
Concerns have been raised as to the dependency of the solutions of turbulent flows in FLOW-3D® 1on the maximum ”turbulent mixing length,” 𝑇𝐿𝐸𝑁, which is set by the user when a two-equation turbulence model is used. This parameter acts as a limiter on the turbulent length scale which in turn limits the minimum turbulent dissipation. It has been observed that if the value is not chosen appropriately the results could become physically unrealistic. In order to resolve this issue, modifications have been made to the two-equation turbulence models to construct local bounds on turbulent length and time scales. This technical note shows that these changes effectively eliminate the sensitivity of the solution to the value of 𝑇𝐿𝐸𝑁.
Some valuable discoveries were made along the way which led to more modifications of the turbulence models in FLOW-3D that further improved the results. The test cases discussed here include both simple as well as complex flows. Starting with the simplest flow configurations and obtaining reasonably accurate results permits the consideration of more complex cases. The data and conclusions documented here should be used as a starting point for any other changes to the turbulence models in FLOW-3D.

Binder Gas Generation and Transport in Sand Cores and Molds

Overview
The making of resin-bonded sand castings has made great strides in quality over its long history. Even so, there remain some process-related defects that are not fully understood and can cause quality issues. For instance, chemical binders in the sand can produce gas when heated by the molten metal and if not vented adequately, the gas may flow into the metal resulting in a gas porosity defect. This is most likely with cores that form thin interior features of castings that heat up quickly and have long venting paths.

The core gas model in FLOW-3D1 is designed to predict the possibility of such gas defects and is intended to help design core venting that would evacuate safely all the binder product gas
from the cores.
Two major types of binders are used in core making practice: resin-based organic binders and inorganic binders such as sodium silicate [1]. The organic binders are either thermosetting, or cured at room temperature with an aid of a catalyst. These are favored in many applications due to their complete degradation even at aluminum casting temperatures and for the ease of subsequent sand shake out. The core gas model is developed with these binders in mind, but can be extended to inorganic binders if appropriate data on their decomposition is available.

Drift Model for Two-Component Flows [두 구성 요소 흐름에 대한 표류 모델]

Overview
In fluids composed of multiple components, e.g., fluid/particles, fluid/bubbles, fluid/fluid mixtures, where the components have different densities, it is observed that the components can assume different flow velocities. Velocity differences arise because the density differences result in non-uniform body forces. Often the differences in velocities can be very pronounced, for example, large raindrops falling through air or gravel sinking in water. Under many conditions, however, the relative velocities are small enough to be described as a “drift” of one component through the other. Examples are dust in air and silt in water.
The “drift” distinction has to do with whether or not the inertia of a dispersed component moving in a continuous component is significant. If the inertia of relative motion can be ignored, and the relative velocity reduced to a balance between a driving force (say gravity or a pressure gradient) and an opposing drag force between the components, then we can speak of a “drift-flux” approximation. Drift velocities are primarily responsible for the transport of mass and energy. Some momentum may be transported as well, but this is usually quite small and has been neglected in the FLOW-3D1 drift model. A more complete analysis of when the “drift” assumption is valid can be found in the Flow Science, Inc.

Improved Generalized Minimal Residual (GMRES) Solver in FLOW-3D—How it works and when to use it

Overview
In FLOW-3D1 there are three linear solvers (as of Version 9.2) with which to solve for pressure from the linear system of continuity equations throughout the domain: the successive over-relaxation (SOR) algorithm, the alternating direction implicit (ADI) algorithm and the generalized minimal residual (GMRES) solver. With GMRES, the system of equations is solved simultaneously throughout the domain by an iterative technique. This is quite unlike the approach used in the SOR algorithm, which adjusts the pressure on a cell-by-cell basis to enforce the continuity equation, or the ADI algorithm, which adjusts the pressures along each mesh column, whose direction alternates through the chosen directions. Although the SOR algorithm is very simple and memory efficient—no extra information from each cell needs to be stored—it can require a large number of iterations to converge, especially for problems where nearly uniform pressure adjustments must be made over a large region of the domain. However, it will always eventually converge so long as the relaxation parameter Ω is less than or equal to 1.
With GMRES, the number of iterations required for convergence is typically much smaller (less than 10) than for SOR; however, it does not always converge. Therefore, for many problems the GMRES algorithm is computationally much more efficient because it is able to converge with far fewer iterations than other solver schemes. This is especially true for problems where the pressures over a large region of the domain are intimately coupled; examples are incompressible flow through a piping network, compressing a gas within a storage tank and most confined flow problems. SOR still may be more computationally efficient for fairly shallow free-surface problems where the pressure is more or less controlled by the location of the free surface—the pressure between two points in the liquid are not strongly coupled.

Turbulent Flow Over a Backward-Facing Step Using the RNG Model

Abstract
Turbulent flow over a backward-facing step is one of the classical tests to validate turbulence models in CFD. In the present work, steady-state turbulent flow over a backward-facing step was simulated using FLOW-3D1 with the Renormalization-group (RNG) k-ε model to account for turbulent viscosity. The Reynolds number was computed using the step height h and the inlet free-stream velocity. The test case was run for two different Reynolds numbers: Reh=5100 and Reh=44,000.

The numerical predictions were compared with the experimental results with the same flow configuration. Streamwise velocity profiles at different locations in the flow direction were in good agreement both qualitatively and quantitatively with the experimental results.

One of the main objectives of this work is to study the sensitivity of the results to the turbulent mixing length parameter tlen in the RNG model. The steady-state velocity was used to compute the reattachment length behind the step for different values of tlen and compared with experimental data. A grid refinement study was performed to find the least mesh resolution needed to capture the essential flow physics of the problem.

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.

THE ELASTIC MEMBRANE AND WALL MODEL IN FLOW-3D [FLOW-3D의 탄성 멤브레인과 벽 모델]

1. Introduction
An elastic membrane and wall model has been developed to provide a limited Fluid-Structure Interaction (FSI) capability in FLOW-3D. In the model, deformation of an elastic membrane or an elastic wall impacts the adjacent fluid flow, while fluid pressure, in turn, affects the deformation. These interactions are described in the code in a fully coupled fashion.
The main assumption of the model is that the deformations are small, i.e., the deflections are much smaller than the size of the deforming object (for elastic membranes) or the characteristic lengths of fluid flow and wall thickness (for elastic walls), allowing for a few useful simplifications. The geometries of membranes and elastic walls are assumed to be time-invariant, while the effects of their deformation on fluid flow are described with volume sources and sinks distributed along the fixed fluid-structure interface. With the further assumption that the pressure force is uniformly distributed on the membrane surface, analytical solutions rather than structural analysis algorithms are used to determine the membrane deformation.
There are many potential applications for the model in microfluidic systems, e.g., chemical analysis systems, medical microdosage systems and inkjet devices. The model can be used to simulate flow in piezoelectric valveless pumps which convert membrane vibrations into a pumping action. The model can also be used to simulate droplet formation for piezoelectric inkjet printheads where a membrane or an elastic tube deforms under the force of a piezoelectric actuator to produce a droplet of ink.

AN IMPLICIT METHOD TO SOLVE PROBLEMS OF RIGID BODY MOTION COUPLED WITH FLUID FLOW

For general moving object (GMO) problems, when mass density of the moving object(s) under coupled motion is less than that of fluid, the existing explicit GMO method in FLOW-3D® often fails due to stability difficulties. In this work, an implicit GMO method was developed and incorporated into FLOW-3D®. The main difference between the implicit and the explicit GMO methods is that in each computational cycle, or time step, the former calculates the object motion and the fluid flow iteratively while the later calculates them separately. Unlike the explicit method, the implicit approach imposes no limitations on mass density of the moving objects. Tests show it possesses good stability for density of moving objects as low as 0.1% of that of fluid. Close matches between the computational and experimental results were obtained for simulations of a light boat under coupled motion in water stream.

THREE-DIMENSIONAL COLLISION MODELING FOR RIGID BODIES AND ITS COUPLING WITH FLUID FLOW COMPUTATION

A computational algorithm for 3-D rigid-body collision and its coupling with fluid flow was developed and implemented in FLOW-3D® as an addition to the existing General Moving Object (GMO) model. It is assumed that all the bodies have negligible deformation during collision and instantaneously change velocities when they collide. A set of existing equations of motion for collision under six degrees of freedom were adopted. Modifications were made for collisions of bodies with fixed axis, fixed point and prescribed motion. Numerical methods for collision detection and collision integration were developed. Stronge’s energetic coefficient of restitution was employed to determine completion of collision calculation. The model allows for simultaneous collisions of multiple bodies. Collisions can be perfectly elastic, partially plastic or completely plastic. Surfaces of bodies can be smooth or rough, allowing existence of impulse of friction during collision. Continuous contact between moving objects is modeled through a series of micro-collisions. Several applications of the model with and without presence of fluid flow were made. Good agreements of the computational results with analytical and experimental results were obtained and are presented at the end of the report.

Implicit_Advection

A powerful implicit advection technique has been incorporated into FLOW-3D®, Version 9.2. This paper illustrates uses of this technique to show its advantages, but also indicates certain limitations related to the accuracy of implicit methods.
Using the implicit advection scheme requires the selection of an input parameter impadv that activates the scheme according to:

impadv = 0, no implicit advection (i.e., explicit, the default);
1, implicit advection, with limited advection at free surfaces
controlling the time-step size for accuracy;
2, implicit advection, with no advection limit on time-step size.

When using FLOW-3D® to simulate transient problems, especially those involving sharp free surfaces and/or fluid-fluid interfaces the best implicit advection option is impadv=1. In this case, the program will limit time-step size by those fluid velocities at a free surface where the velocity is normal to the surface and the fluid fraction at that location has changed by more than 5% in the preceding cycle. Otherwise, the surface velocities will not impose a limit on time-step size.

A FIXED-MESH METHOD FOR GENERAL MOVING OBJECTS

A fixed-mesh method for general moving objects in fluid flow was developed and implemented into FLOW-3D®. A general moving object (GMO) is a rigid body with any type of six-degrees-of freedom, fixed-point and fixed-axis motion which can be either user-prescribed or dynamically coupled with fluid flow. The method allows for multiple independently general moving objects.

Equations of motion for rigid body are solved for coupled motion. Area and volume fractions are used to represent the objects in the fixed-grid at every time step to describe time-variation of object locations and orientations. Continuity and momentum equations for fluid and scalar transport equations are modified to account for the effects of object motion. Good agreement was achieved between computational and theoretical/experimental results in several application cases.

Modeling of Electroosmosis without Resolving Physics inside the Electric Double Layer

A model for electroosmosis has been developed and released in version 8.2 of FLOW-3Dr. It is a general model in which the zeta potential distribution is solved through the electric double layer (EDL). When the EDL thickness (¸D) is very small, such as ¸D < 0:1¹m or in nanoscale, it is very computationally expensive to resolve the physics inside the EDL. In this note, we describe a simple model that has been developed to simulate electroosmosis without resolving the EDL.

That is, the zeta potential distribution is not solved, instead, a zeta potential on the obstacle surface is used as a boundary condition to calculate a slip velocity. This velocity is imposed on the obstacle surface if a zeta potential exists around that obstacle. It is de¯ned by ³²Ex ¹ and called the Helmholtz-Smoluchowski velocity with ³, Ex, ¹ representing zeta potential, electric ¯eld intensity in x-direction, ² permittivity, and liquid viscosity respectively.

However, if the EDL thickness is large compared to the problem geometry such as channel width, the simpli¯ed model is not accurate, and the original model is recommended. The new model has been validated against the corresponding analytical solution in a channel °ow and its application to complex microchannel °ow is demonstrated. The new simpli¯ed model will be incorporated in a future version of FLOW-3D

Development of New Pressure-Velocity Solvers in FLOW-3D [FLOW-3D의 새로운 압력-속도 해법의 개발]

1 Introduction
The purpose of this note is to document the development of new pressure-velocity solvers in FLOW-3Dr. In the following section, new solvers are described ¯rst followed by a section of sample problems where typical simulations were performed to illustrate the application of these new solvers. Two appendices are added to describe in detail the general minimum residual (GMRES) and generalized conjugate gradient (GCG) algorithms used in the new solvers.

Lost Foam Variable Pattern Density

Overview
Making foam patterns for use in the lost foam casting process is a difficult business. To make a pattern foam beads are blown into a mold containing discrete vent locations for the displaced air and steam. This makes the density of the packed beads difficult to control. Patterns typically show final density variations of ±20%. Much larger variations are not uncommon.
One goal of the Lost Foam Consortium is to evaluate techniques for improving the uniformity of patterns. A related goal is to determine to what extent density variations in patterns are significant with respect to the quality of the parts produced.
Recent real-time X-Ray observations of the metal filling process reported by Dr. Wayne Sun (Advanced Lost Foam Casting Technology-Phase V Meeting, June 20-21, 2001) revealed several interesting facts about the behavior of foam patterns. In particular, when the foam has a low degree of fusion metal is observed to move very fast into the foam (e.g., 4 to 5 times faster than in normal fusion foam). The advancement of the metal is typically in the form of fingers, which subsequently spread sideways causing the meeting of metal fronts that result in many fold defects. Furthermore, the location of the fingering is significantly affected by density variations in the foam pattern.
In contrast, when the foam patterns consisted of normal fusion foam, the metal front moved smoothly (i.e., no fingering) and considerably fewer fold defects occur. Also, the presence of density variations in the foam has little effect on the propagation of the metal fronts.
Based on these findings it was concluded that no attempt should be made to model low fusion foam because this in not likely to be choice for production work. Instead, we report here the development and testing of a model for adding a variable foam density to the FLOW-3D® software package from Flow Science, Inc.

Modeling shrinkage induced microporosity [마이크로 미세기공 발생 예측]

Overview
Cast metal parts are sometimes unusable because they have internal gas pockets, or bubbles, which develop when the metal shrinks during solidification. A general term describing such bubbles or voids is “porosity.” When these bubbles are relatively large and localized the porosity is called macro-porosity. Prediction of macro-porosity in the interior of cast parts is a capability of most software packages currently used for the modeling of metal casting processes.
Another type of porosity, characterized by a more uniform distribution of small bubbles with a total average volume fraction on the order of one percent, is referred to as micro-porosity. This type of porosity is also caused by metal shrinkage during solidification, but its character is different from macro-porosity because it develops at a later stage in the solidification process. This distinction in types of porosity is important because each type requires a different modeling approach.
In this note we propose a new model that has been implemented in FLOW-3D® for predicting the occurrence of micro-porosity. The model is simple, requires only basic material property data, and adds virtually no noticeable CPU time to a solidification simulation. Best of all, the model is complimentary to macro-porosity models and may be used in conjunction with either a complete hydrodynamic shrinkage simulation that includes fluid flow or with simpler heat-transfer and shrinkage simulation having no fluid flow.
The new model has been checked using three sets of experimental test data. A final test, involving only qualitative results for the influence of pressure on micro-porosity formation has also been conducted.

Incremental Elastic Stress Model

Introduction
Elastic stress has been incorporated into FLOW-3D® to emulate viscoplastic materials, which are materials which behave as solids up to a yield stress, beyond which they behave like a viscous liquid.

The incremental elastic stress model recently incorporated into FLOW-3D® computes the elastic stress using linear Hookean theory (Equation 2 above). Although this constitutive equation predicts only a linear response to stress, implementation as an incremental model, in which the stress changes in each time step are accumulated, allows the prediction of highly nonlinear responses. This works because the response within each small time step can be well approximated as linear. Pictorially, with this model, FLOW-3D® predicts the total stress as a summation of the viscous stress and the elastic stress, as shown in Figure 1.

Lagrangian VOF Advection Method for FLOW-3D

1. Introduction
A new VOF advection method based on a 3-D reconstruction of the fluid interface has been developed and implemented in FLOW-3D® Version 8.2. The Volume-of-Fluid (VOF) function is moved in one step, without resorting to an operator splitting technique, which gives the present method increased accuracy when the flow is not aligned with a coordinate direction.
The existing VOF advection method in FLOW-3D® (hereinafter called the standard method) is based on the donor-acceptor approach first introduced by Hirt and Nichols [1]. Numerous enhancements have been made to the original algorithm to improve its accuracy and stability in complex one- and two- fluid flows with sharp interfaces1.
The standard method uses operator splitting and old time-level values of the VOF function to compute fluxes in three coordinate directions. The approach creates a possibility of overfilling or over-emptying computational cells when volume fluxes are significant in all three directions and the time step size is close to the local Courant stability limit.
The new advection method has been developed to alleviate these deficiencies of the standard algorithm. The fluid interface is reconstructed in 3D using a piecewise linear representation, where the interface is assumed to be planar in each control volume (or cell) containing the interface. The fluid volume bounded by the interface and cell faces is then moved according to the local velocity vector in a Lagrangian manner. Finally, the advected volume is overlaid back onto the Eulerian grid to obtain the new values of the fraction-of-fluid function. This combination of the Lagrangian and Eulerian methodology gives the new method its name (similar approaches have been used to approximate advection terms, for example, by Colella [2], Puckett et al [3], and Pilliod and Puckett [4]). The new option is activated in the code by setting IFVOF=5.

Sediment Scour [침전 / 세굴(쇄굴)]

Introduction
The sediment scour model predicts the behavior of packed and suspended sediment within the three-dimensional flow capabilities of FLOW-3D®. Potential applications include erosion around bridge piers, weirs, dams and underwater pipelines, and removal and drifting of sand or snow over terrain. The model consists of two basic components: drifting and lifting. Drifting acts on sediment that is suspended in the flow; gravity (along with other body forces) causes the settling of the sediment. This model is based on the drift-flux model already incorporated into FLOW-3D®. Lifting takes place only at the interface between the packed sediment and fluid and occurs where the local shear stress imposed by the liquid on the bed interface exceeds a critical value. The amount of lifting is proportional to the shear stress. In conjunction with the drifting and lifting models, a drag model is used to mimic the solid-like behavior of the sediment in regions where its concentration exceeds a cohesive solid fraction. The viscosity and density are functions of the sediment concentration; they are calculated as a function of the sediment concentration.

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.

Surface Tension Validation Tests

Modeling surface tension phenomena is computationally difficult because it requires the evaluation of second derivatives.
This is particulary true in the FLOW-3D program where the capability to represent highly complicated and multiple free surfaces difficulties are further compounded in three-dimensional calculations because one is often forced, for reasons of economy, to use marginal numerical resolution.

Multi-Block Gridding Technique for FLOW-3D [FLOW-3D에서 멀티블럭 설정 기법]

1. Introduction
A major new extension of the capabilities of FLOW-3D® — the multi-block grid model — has been incorporated into the code starting with Version 8.0. Multi-block gridding in FLOW-3D® will enable more efficient use of the software’s resources when modeling complex flow phenomena. Each block spans a certain region of the whole flow domain and contains the standard structured rectangular mesh. Two types of mesh blocks can be used: the nested blocks and the linked blocks.
Data transfer between any two mesh blocks is facilitated by special boundary (or ghost) cells. Solution quantities are interpolated from the real cells of a donor block into the boundary cells of the acceptor block. The interpolation technique varies depending on the variable at hand. Conserved quantities, like concentrations and thermal energy, are interpolated using the piecewise constant method. A special variant of this method is used for fluid fraction interpolation, where a reconstruction of the interface is performed to locate the interface within the donor cells before the interpolation.
Pressure and velocities are calculated using linear interpolation to preserve the gradients. A mixture of the Neumann- and Dirichlet-type boundary conditions is used for the solution of the Poisson equation for pressure. A weighing factor defines the contribution of each type of the boundary condition to the final solution, ensuring continuity of both pressure and velocities across the inter-block boundaries, convergence and local conservation of mass.

Modeling Thermal Expansion Effects in FLOW-3D

This note describes the modeling used in FLOW-3D® for thermal expansion processes in onefluid, incompressible flows. Volume changes are modeled in unconfined flows while the limited
compressibility model may be used to compute the change is pressure in flows that are confined and density cannot change.

Initiating Homogeneous Bubbles in Pure Liquid

Initiating Homogeneous Bubbles in Pure Liquid

  1. Barkhudarov and C.W. Hirt

Flow Science, Inc.

The combined Temperature-Dependent-Cavitation and Homogenous Bubble models work together as a way to simulate the formation and growth of vapor bubbles by locally heating a liquid. The Homogeneous Bubble model is only activated when a bubble has a size that encompasses at least one complete grid cell, i.e., can be resolved as a “bubble” or void region.

The Cavitation model contains a mechanism for the initiation of bubbles, which works in the follow way. At the end of each time cycle of a transient computation every grid cell containing liquid is tested to see if its pressure is less than the saturation pressure corresponding to the temperature in the cell. The saturation pressure is computed from the pressure-temperature saturation relation specified by the user (e.g., usually a Clapeyron relation). If the cell pressure is less than its saturation pressure it is assumed that boiling can begin. The essential assumption is that there exist sufficient impurities or nucleation sites for this to happen. A very simple model nucleation has been incorporated into FLOW-3D®.

Once a cell has been identified for possible boiling it is given a time delay before vaporization begins. For vaporization to occur it is necessary to have at least 1% void fraction in the cell. This small void can be thought of as the nucleation process. The time delay is input as variable CAVRT (denoted as Ccav in the following).

Addition of Dielectric Phenomena to FLOW-3D

Overview
There are situations where it would be helpful to account for the interaction of electric fields with liquid and solid materials. For example, electrostatic air cleaners rely on the ability to attract small particles in flowing air to a surface where they can be collected and removed from the air. In this case the primary attractive force arises from dielectric polarization of the particles.
Spraying liquid drops onto a surface, as in spray painting, is often improved by electrifying the drops so that they repel one another and produce a more uniform distribution. Also, electrified drops can be driven to overcome air resistance by suitable electric fields.
In many types of micro-electrical-mechanical-systems (MEMS) fluids are caused to move by the application of electric potentials. Usually this behavior is induced by electric forces acting on dielectric polarization charges generated at free fluid surfaces or at the interfaces between two fluids.

In some situations the effects of both dielectrically induced charges as well as free electric charges in a fluid must be considered. For these cases the fluid has some nonzero conductivity that must be accounted for by tracking charge densities and adding additional body forces to the fluid. The range of possibilities when conduction is present includes bound and free charges, recombination, ionization, currents without net charge densities, etc. As described next, we shall limit the present development to a useful subset of the many possibilities.

In this note we describe a set of program developments that give FLOW-3DÒ the capability to model fluid and particulate flows involving both free and induced charge densities. In the current released version of FLOW-3D® (Ver. 7.7) both particles and fluid can contain a fixed charge density, but there is no provision for dielectric materials.

Here we describe the addition of dielectric properties for particles, fluids, and solids. In addition, linear polarization forces acting on particles and fluids by electrostatic fields are added to the momentum equations for fluid and particles.

Movable Fluid Sources in FLOW-3D [FLOW-3D에서 움직이는 유체]

OVERVIEW


There are many examples of fluid flow simulation where it would be useful to have specified fluid sources located inside the computational grid. By “fluid sources” we mean a source of
fluid mass and momentum. Even more useful would be a capability where the location, flow rate, and flow direction of the fluid sources could be specified.
In this Technical Note, we describe a scheme that meets these goals in the FLOW-3D® program.
In the next section we describe the basic approach that was taken to add this capability and following that there are several examples illustrating the method.
MODELING APPROACH FOR GENERAL FLUID SOURCES
A recent addition to FLOW-3D® is the ability to have full momentum coupling between a continuum fluid and discrete mass particles. This addition is described in the Flow Science
Technical Note FSI-99-TN50, “Particle-Fluid Coupling.” It is this capability that forms the basis of our addition for general fluid sources.
For purposes of discussion, suppose that we want to model fluid exiting the end of a pipe placed somewhere inside a computational grid. Fluid exits the end of the pipe with a specified flow rate
and flow velocity, i.e., both magnitude and direction are specified. In the most general case, the velocity distribution over the cross section of the pipe exit could be non-uniform. The location
of the pipe end should be arbitrary, so that moving the pipe by relocating it every time step in a transient computation would be possible.
To meet these goals, we imagine covering the end of the pipe with a set of particles. Each particle is assigned a mass source rate and a velocity corresponding to the fluid flow direction at
its location. We may think of these particles as representing average values of the flow for small areas surrounding them. In this sense, summing up the particles is equivalent to a numerical
integration of the flow over the cross section of the pipe. The particles simply represent the discrete elements of the integration area.

Self-Consistent Electric Fields and Electric Forces On Charged Particles

SCOPE
A recent addition to the computational fluid dynamics program FLOW-3D® is a capability for modeling discrete mass particles moving through a continuum. This model implicitly couples
the particles and continuum so that they may exchange momentum in a conservative way.
This report addresses how that model has been extended to account for mass particles having an electric charge and moving in an electric field. The extension is self-consistent in the sense that
the particle charges contribute to the electric field. For this reason the field is time dependent and must be recomputed for each time step of a numerical simulation.
In addition to the charged particles, solid objects (obstacles) located within the computational region may be assigned arbitrary, but constant in time, potentials. Each obstacle may have a
fixed potential value consistent with the obstacle being a conductor. A zero potential value is the default value if not otherwise specified. It should be noted that an electric potential can be
computed even when there are no charged particles, although this field will have no effect on flow processes unless the user adds some kind of additional interaction to the model.
Mesh boundaries that are rigid walls may be assigned non-zero potential values. All other boundaries are treated as symmetry boundaries with respect to the potential. Furthermore, no
insulated obstacles are allowed in this model. It is also assumed that if there are free fluid surfaces or fluid-fluid interfaces then the dielectric constants (i.e., ratios of material permittivities
to that of vacuum) of the different materials must be the same, otherwise additional development will be needed to solve for the electric potential. In general, this is not correct because the
dielectric constant does vary with material type; for example, water has a dielectric constant about 81 times that for air.