CFD + Physical Modeling Results

CFD + Physical Modeling Results

This material was provided by Kevin Sydor, M.Sc., P.Eng., Section Head, Hydrotechnical and Oceanographic Studies, Water Resources Engineering; Manitoba Hydro; Joe Groeneveld, Western Canada Discipline Practice Lead – Hydrotechnical, Hatch Ltd.; Graham Holder, Consultant, LaSalle; D.G. Murray, P.Eng., M.Sc., Discipline Practice Lead – Hydrotechnical, Hatch Ltd.

 

10년이 넘는 기간 동안 Manitoba Hydro는 Flow-3D의 힘으로 수력 발전소 설계의 복잡성을 해결해 왔습니다. 최근 Manitoba Hydro는 급류, 다중 채널, 그리고 natural contours을 포함한 복잡한 장소에서 제안된 Keeyask생성에 대한 사전연구에 집중해 왔습니다. FLOW-3D사용 이전에는 초기 설계를 토대로 시뮬레이션과 물리적 모델링의 결합 결과가 서로의 성능을 검증하고 향상시키는 통합 연구를 수행했습니다.

Water velocities (m/s) as determined in CFD simulation at left, compared with photo of physical model in operation at right, for Stage 1 Cofferdam operation at a construction length of 450m.

 

실제 발전소와 제철소를 건설하기 위해서는 두 단계의 강 유역이 필요했습니다. Manitoba Hydro는 임시 코퍼 댐 건설 중 물리적 조건이 변화함에 따라 다양한 지역에서의 수위와 속도가 어떻게 변할 것인지를 추정하는 시뮬레이션을 수행했습니다. 그런 다음, 그들은 연안 공사, 우회 구조, 하천 폐쇄 및 배수로의 1/120 축척모델에서 측정된 결과와, 배수로 구역의 1/50 축척모델에서 측정된 결과를 비교했습니다. 1/120 축척모델의 연산에서 관찰된 수치는 수정되었고, CFD시뮬레이션 내 경계 조건을 나타내는 STL모델의 변경 사항으로 세부 사항이 피드백 되었습니다. 여러 가지의 상세한 공정은 물리적 축척 모형의 거동을 약 5%이내에서 예측했을 뿐만 아니라 공사비를 절감할 수 있는 설계 변경 사항도 찾아냈습니다.

 

Setting up and Calibrating the CFD Model

Simulation of final Keeyask spillway structure, verifying water velocities (m/s) to compare with physical scale model operation.

 

CFD모델은 약 3km x 2km의 영역을 커버하였으며, 탐지 속도 경계로 설정된 경계 조건을 통해 상류 쪽으로의 흐름을 제어하고 하류 쪽 끝의 지속적인 유출 경계를 설정하였습니다. 설계자들은 교각, 교대, 여수로 구조 및 코퍼댐과 같은 기하학적 객체의 STL AutoCAD파일을 가져와 물리적 경계를 나타낸 다음 매개 변수를 정의 했습니다.

강 급류의 특성과 레일 통로의 평행 부분을 통해 생성되는 예상 유량 범위를 모두 수용하기 위해 CFD모델이 다시 정규화되도록 설정되었습니다. 일반화된 최소 잔류 방법에 기초한 회전 난류 모드 및 implicit의 압력-속도 솔버를 설정했습니다. 메쉬는 데카르트 좌표로 설정되었고 보다 정밀한 메쉬 처리가 필요한 영역에서 grid를 다듬기 위해 중첩된 메쉬 블록을 사용했습니다. 배수로 구조 주위 영역의 격자 간격은 1m x 1m x 1m로 설정되었습니다. 즉, 배수로 및 배수로 용마루의 형상을 포함하는 데 필요했던 것입니다.

시뮬레이션의 목적은 건설 일정상 다양한 지점에서의 방전 용량, 수위, 속도 및 흐름 패턴, 다양한 위치, 경로 게이트(부분에서 완전히 열림)등을 추정하는 것이었습니다.  이 계산된 값들은 코페르담 건축에서 암석 덩어리에 필요한 돌의 크기를 결정하는데 중요합니다. 건축의 모든 단계에서 그들을 제자리와 하류로 이동시키는 항력에 저항할 만큼 암석들은 충분히 커야 합니다.

Excellent agreement in flow-rate prediction of spillway behavior between numeric and measured physical model values.

 

Physical Modeling

수력 발전소 설계로 인해 처음에는 제대로 하지 못하는 일이 너무 많습니다. 중요한 지형에서의 용량, 압력, 속도 및 배수로 게이트 동작(완전 개방)을 검증하기 위해서는 중요한 흐름 영역의 규모 물리적 모델을 구축해야 합니다. Manitoba Hydro는 LaSalle Consulting Group에 1/120 스케일의 하나의 포괄적 인 레이아웃과 1/50 스케일의 2 개의 전체구역과 2 개의 절반 구역을 가진 방수 모델을 구축할 것을 요청했습니다.

 

Integrated Modeling Results

실제 모델의 크기에 대한 힘의 이동 관계를 살펴보면, 바위 크기 예측에 대한 시뮬레이션은 약간 보존적입니다. 그러나 초기 수위 데이터 곡선은 시뮬레이션과 물리적 모델 행동 사이에 일치를 보여주었고 추가 시험을 위한 단계를 설정했습니다. 모델에서 코퍼댐이 서서히 생성됨에 따라 후속 수위 CFD시뮬레이션 결과를 정확하게 예측했음을 보여주었습니다.

완성된 코퍼댐의 테스트에 따르면 제어 구조가 아닌 채널 입구에서 흐름이 제어되고 있는 것으로 나타났습니다. 이것은 원하는 것보다 높은 상류수위가 나타났습니다. 접근 채널의 입구를 낮추도록 물리적 모델을 재구성하여 CFD에 사용된 고도를 반영했습니다. 출입구가 더 낮게 발굴되어, 수로의 왼쪽 둑을 따라 굴착하는 것은 입구 근처의 작은 지역에서만 필요했습니다.

 

Conclusion

Manitoba Hydro는 CFD모델링이 미래의 수력 발전소뿐만 아니라 Keeyask 발전소의 건설과 운영을 계획하는 데에도 여러 가지 이점을 제공한다는 사실을 발견했습니다 두 가지 접근법의 결과간에 매우 잘 일치했을 뿐만 아니라 FLOW-3D 시뮬레이션과 스케일 모델 테스트를 결합하면 두 가지 설계 옵션의 유효성을 개선하는 반복적 인 방법이 제공되었습니다. 또한 시뮬레이션을 통해 사용자는 실제 사용할 수 있는 값의 수가 제한되어 있지 않고 CFD모델 도메인 내의 어디서나 속도, 수위 및 유량을 쉽고 빠르게 추출할 수 있습니다.

Coastal & Maritime Bibliography

다음은 연안 및 해양 분야의 기술 문서 모음입니다.
이 모든 논문은 FLOW-3D  결과를 포함하고 있습니다. FLOW-3D를 사용하여 연안 및 해양 시설물을 성공적으로 시뮬레이션 하는 방법에 대해 자세히 알아보십시오.

Coastal & Maritime Bibliography

Below is a collection of technical papers in our Coastal & Maritime Bibliography. All of these papers feature FLOW-3D results. Learn more about how FLOW-3D can be used to successfully simulate Coastal & Maritime applications.

51-20       Yupeng Ren, Xingbei Xu, Guohui Xu, Zhiqin Liu, Measurement and calculation of particle trajectory of liquefied soil under wave action, Applied Ocean Research, 101; 102202, 2020. doi.org/10.1016/j.apor.2020.102202

50-20       C.C. Battiston, F.A. Bombardelli, E.B.C. Schettini, M.G. Marques, Mean flow and turbulence statistics through a sluice gate in a navigation lock system: A numerical study, European Journal of Mechanics – B/Fluids, 84; pp.155-163, 2020. doi.org/10.1016/j.euromechflu.2020.06.003

49-20     Ahmad Fitriadhy, Nur Amira Adam, Nurul Aqilah Mansor, Mohammad Fadhli Ahmad, Ahmad Jusoh, Noraieni Hj. Mokhtar, Mohd Sofiyan Sulaiman, CFD investigation into the effect of heave plate on vertical motion responses of a floating jetty, CFD Letters, 12.5; pp. 24-35, 2020. doi.org/10.37934/cfdl.12.5.2435

40-20       P. April Le Quéré, I. Nistor, A. Mohammadian, Numerical modeling of tsunami-induced scouring around a square column: Performance assessment of FLOW-3D and Delft3D, Journal of Coastal Research (preprint), 2020. doi.org/10.2112/JCOASTRES-D-19-00181

38-20       Sahameddin Mahmoudi Kurdistani, Giuseppe Roberto Tomasicchio, Daniele Conte, Stefano Mascetti, Sensitivity analysis of existing exponential empirical formulas for pore pressure distribution inside breakwater core using numerical modeling, Italian Journal of Engineering Geology and Environment, 1; pp. 65-71, 2020. doi.org/10.4408/IJEGE.2020-01.S-08

36-20       Mohammadamin Torabi, Bruce Savage, Efficiency improvement of a novel submerged oscillating water column (SOWC) energy harvester, Proceedings, World Environmental and Water Resources Congress (Cancelled), Henderson, Nevada, May 17–21, 2020. doi.org/10.1061/9780784482940.003

32-20       Adriano Henrique Tognato, Modelagem CFD da interação entre hidrodinâmica costeira e quebra-mar submerso: estudo de caso da Ponta da Praia em Santos, SP (CFD modeling of interaction between sea waves and submerged breakwater at Ponta de Praia – Santos, SP: a case study, Thesis, Universidad Estadual de Campinas, Campinas, Brazil, 2020.

29-20   Ana Gomes, José L. S. Pinho, Tiago Valente, José S. Antunes do Carmo and Arkal V. Hegde, Performance assessment of a semi-circular breakwater through CFD modelling, Journal of Marine Science and Engineering, 8.3, art. no. 226, 2020. doi.org/10.3390/jmse8030226

23-20  Qi Yang, Peng Yu, Yifan Liu, Hongjun Liu, Peng Zhang and Quandi Wang, Scour characteristics of an offshore umbrella suction anchor foundation under the combined actions of waves and currents, Ocean Engineering, 202, art. no. 106701, 2020. doi.org/10.1016/j.oceaneng.2019.106701

04-20  Bingchen Liang, Shengtao Du, Xinying Pan and Libang Zhang, Local scour for vertical piles in steady currents: review of mechanisms, influencing factors and empirical equations, Journal of Marine Science and Engineering, 8.1, art. no. 4, 2020. doi.org/10.3390/jmse8010004

104-19   A. Fitriadhy, S.F. Abdullah, M. Hairil, M.F. Ahmad and A. Jusoh, Optimized modelling on lateral separation of twin pontoon-net floating breakwater, Journal of Mechanical Engineering and Sciences, 13.4, pp. 5764-5779, 2019. doi.org/10.15282/jmes.13.4.2019.04.0460

103-19  Ahmad Fitriadhy, Nurul Aqilah Mansor, Nur Adlina Aldin and Adi Maimun, CFD analysis on course stability of an asymmetrical bridle towline model of a towed ship, CFD Letters, 11.12, pp. 43-52, 2019.

90-19   Eric P. Lemont and Karthik Ramaswamy, Computational fluid dynamics in coastal engineering: Verification of a breakwater design in the Torres Strait, Proceedings, pp. 762-768, Australian Coasts and Ports 2019 Conference, Hobart, Australia, September 10-13, 2019.

86-19   Mohammed Arab Fatiha, Benoît Augier, François Deniset, Pascal Casari, and Jacques André Astolfi, Morphing hydrofoil model driven by compliant composite structure and internal pressure, Journal of Marine Science and Engineering, 7:423, 2019. doi.org/10.3390/jmse7120423

83-19   Cong-Uy Nguyen, So-Young Lee, Thanh-Canh Huynh, Heon-Tae Kim, and Jeong-Tae Kim, Vibration characteristics of offshore wind turbine tower with gravity-based foundation under wave excitation, Smart Structures and Systems, 23:5, pp. 405-420, 2019. doi.org/10.12989/sss.2019.23.5.405

68-19   B.W. Lee and C. Lee, Development of an equation for ship wave crests in a current in whole water depths, Proceedings, 10th International Conference on Asian and Pacific Coasts (APAC 2019), Hanoi, Vietnam, September 25-28, 2019; pp. 207-212, 2019. doi.org/10.1007/978-981-15-0291-0_29

62-19   Byeong Wook Lee and Changhoon Lee, Equation for ship wave crests in the entire range of water depths, Coastal Engineering, 153:103542, 2019. doi.org/10.1016/j.coastaleng.2019.103542

23-19     Mariano Buccino, Mohammad Daliri, Fabio Dentale, Angela Di Leo, and Mario Calabrese, CFD experiments on a low crested sloping top caisson breakwater, Part 1: Nature of loadings and global stability, Ocean Engineering, Vol. 182, pp. 259-282, 2019. doi.org/10.1016/j.oceaneng.2019.04.017

21-19     Mahsa Ghazian Arabi, Deniz Velioglu Sogut, Ali Khosronejad, Ahmet C. Yalciner, and Ali Farhadzadeh, A numerical and experimental study of local hydrodynamics due to interactions between a solitary wave and an impervious structure, Coastal Engineering, Vol. 147, pp. 43-62, 2019. doi.org/10.1016/j.coastaleng.2019.02.004

15-19     Chencong Liao, Jinjian Chen, and Yizhou Zhang, Accumulation of pore water pressure in a homogeneous sandy seabed around a rocking mono-pile subjected to wave loads, Vol. 173, pp. 810-822, 2019. doi.org/10.1016/j.oceaneng.2018.12.072

09-19     Yaoyong Chen, Guoxu Niu, and Yuliang Ma, Study on hydrodynamics of a new comb-type floating breakwater fixed on the water surface, 2018 International Symposium on Architecture Research Frontiers and Ecological Environment (ARFEE 2018), Wuhan, China, December 14-16, 2018, E3S Web of Conferences Vol. 79, Art. No. 02003, 2019. doi.org/10.1051/e3sconf/20197902003

08-19     Hongda Shi, Zhi Han, and Chenyu Zhao, Numerical study on the optimization design of the conical bottom heaving buoy convertor, Ocean Engineering, Vol. 173, pp. 235-243, 2019. doi.org/10.1016/j.oceaneng.2018.12.061

06-19   S. Hemavathi, R. Manjula and N. Ponmani, Numerical modelling and experimental investigation on the effect of wave attenuation due to coastal vegetation, Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Vol. 2, pp. 99-110, 2019. doi.org/10.1007/978-981-13-3134-3_9

87-18   Muhammad Syazwan Bazli, Omar Yaakob and Kang Hooi Siang, Validation study of u-oscillating water column device using computational fluid dynamic (CFD) simulation, 11thInternational Conference on Marine Technology, Kuala Lumpur, Malaysia, August 13-14, 2018.

86-18   Nur Adlina Aldin, Ahmad Fitriadhy, Nurul Aqilah Mansor, and Adi Maimun, CFD analysis on unsteady yaw motion characteristic of a towed ship, 11th International Conference on Marine Technology, Kuala Lumpur, Malaysia, August 13-14, 2018.

78-18 A.A. Abo Zaid, W.E. Mahmod, A.S. Koraim, E.M. Heikal and H.E. Fath, Wave interaction of partially immersed semicircular breakwater suspended on piles using FLOW-3D, CSME Conference Proceedings, Toronto, Canada, May 27-30, 2018.

73-18   Jian Zhou and Subhas K. Venayagamoorthy, Near-field mean flow dynamics of a cylindrical canopy patch suspended in deep water, Journal of Fluid Mechanics, Vol. 858, pp. 634-655, 2018. doi.org/10.1017/jfm.2018.775

69-18   Keisuke Yoshida, Shiro Maeno, Tomihiro Iiboshi and Daisuke Araki, Estimation of hydrodynamic forces acting on concrete blocks of toe protection works for coastal dikes by tsunami overflows, Applied Ocean Research, Vol. 80, pp. 181-196, 2018. doi.org/10.1016/j.apor.2018.09.001

68-18   Zegao Yin, Yanxu Wang and Xiaoyu Yang, Regular wave run-up attenuation on a slope by emergent rigid vegetation, Journal of Coastal Research (in-press), 2018. doi.org/10.2112/JCOASTRES-D-17-00200.1

65-18   Dagui Tong, Chencong Liao, Jinjian Chen and Qi Zhang, Numerical simulation of a sandy seabed response to water surface waves propagating on current, Journal of Marine Science and Engineering, Vol. 6, No. 3, 2018. doi.org/10.3390/jmse6030088

61-18   Manuel Gerardo Verduzco-Zapata, Aramis Olivos-Ortiz, Marco Liñán-Cabello, Christian Ortega-Ortiz, Marco Galicia-Pérez, Chris Matthews, and Omar Cervantes-Rosas, Development of a Desalination System Driven by Low Energy Ocean Surface Waves, Journal of Coastal Research: Special Issue 85 – Proceedings of the 15th International Coastal Symposium, pp. 1321 – 1325, 2018. doi.org/10.2112/SI85-265.1

37-18   Songsen Xu, Chunshuo Jiao, Meng Ning and Sheng Dong, Analysis of Buoyancy Module Auxiliary Installation Technology Based on Numerical Simulation, Journal of Ocean University of China, vol. 17, no. 2, pp. 267-280, 2018. doi.org/10.1007/s11802-018-3305-4

36-18   Deniz Velioglu Sogut and Ahmet Cevdet Yalciner, Performance comparison of NAMI DANCE and FLOW-3D® models in tsunami propagation, inundation and currents using NTHMP benchmark problems, Pure and Applied Geophysics, pp. 1-39, 2018. doi.org/10.1007/s00024-018-1907-9

26-18   Mohammad Sarfaraz and Ali Pak, Numerical investigation of the stability of armour units in low-crested breakwaters using combined SPH–Polyhedral DEM method, Journal of Fluids and Structures, vol. 81, pp. 14-35, 2018. doi.org/10.1016/j.jfluidstructs.2018.04.016

25-18   Yen-Lung Chen and Shih-Chun Hsiao, Numerical modeling of a buoyant round jet under regular waves, Ocean Engineering, vol. 161, pp. 154-167, 2018. doi.org/10.1016/j.oceaneng.2018.04.093

13-18   Yizhou Zhang, Chencong Liao, Jinjian Chen, Dagui Tong, and Jianhua Wang, Numerical analysis of interaction between seabed and mono-pile subjected to dynamic wave loadings considering the pile rocking effect, Ocean Engineering, Volume 155, 1 May 2018, Pages 173-188, doi.org/10.1016/j.oceaneng.2018.02.041

11-18  Ching-Piao Tsai, Chun-Han Ko and Ying-Chi Chen, Investigation on Performance of a Modified Breakwater-Integrated OWC Wave Energy Converter, Open Access Sustainability 2018, 10(3), 643; doi:10.3390/su10030643, © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018.

58-17   Jian Zhou, Claudia Cenedese, Tim Williams and Megan Ball, On the propagation of gravity currents over and through a submerged array of circular cylinders, Journal of Fluid Mechanics, Vol. 831, pp. 394-417, 2017. doi.org/10.1017/jfm.2017.604

56-17   Yu-Shu Kuo, Chih-Yin Chung, Shih-Chun Hsiao and Yu-Kai Wang, Hydrodynamic characteristics of Oscillating Water Column caisson breakwaters, Renewable Energy, vol. 103, pp. 439-447, 2017. doi.org/10.1016/j.renene.2016.11.028

47-17   Jae-Nam Cho, Chang-Geun Song, Kyu-Nam Hwang and Seung-Oh Lee, Experimental assessment of suspended sediment concentration changed by solitary wave, Journal of Marine Science and Technology, Vol. 25, No. 6, pp. 649-655 (2017) 649 DOI: 10.6119/JMST-017-1226-04

45-17   Muhammad Aldhiansyah Rifqi Fauzi, Haryo Dwito Armono, Mahmud Mustain and Aniendhita Rizki Amalia, Comparison Study of Various Type Artificial Reef Performance in Reducing Wave Height, Regional Conference in Civil Engineering (RCCE) 430 The Third International Conference on Civil Engineering Research (ICCER) August 1st-2nd 2017, Surabaya – Indonesia.

44-17   Fabio Dentale, Ferdinando Reale, Angela Di Leo, and Eugenio Pugliese Carratelli, A CFD approach to rubble mound breakwater design, International Journal of Naval Architecture and Ocean Engineering, Available online 30 December 2017.

39-17   Milad Rashidinasab and Mehdi Behdarvandi Askar, Modeling the Pressure Distribution and the Changes of Water Level around the Offshore Platforms Exposed to Waves, Using the Numerical Model of FLOW-3D, Computational Water, Energy, and Environmental Engineering, 2017, 6, 97-106, http://www.scirp.org/journal/cweee, ISSN Online: 2168-1570, ISSN Print: 2168-1562

30-17   Omid Nourani and Mehdi Behdarvandi Askar, Comparison of the Effect of Tetrapod Block and Armor X block on Reducing Wave Overtopping in Breakwaters, Open Journal of Marine Science, 2017, 7, 472-484 http://www.scirp.org/journal/ojms ISSN Online: 2161-7392.

29-17   J.A. Vasquez, Modelling the generation and propagation of landslide generated waves, Leadership in Sustainable Infrastructure, Annual Conference – Vancouver, May 31 – June 3, 2017

28-17   Manuel G. Verduzco-Zapata, Francisco J. Ocampo-Torres, Chris Matthews, Aramis Olivos-Ortiz, Diego E. and Galván-Pozos, Development of a Wave Powered Desalination Device Numerical Modelling, Proceedings of the 12th European Wave and Tidal Energy Conference 27th Aug -1st Sept 2017, Cork, Ireland

20-17   Chu-Kuan Lin, Jaw-Guei Lin, Ya-Lan Chen, Chin-Shen Chang, Seabed Change and Soil Resistance Assessment of Jack up Foundation, Proceedings of the Twenty-seventh (2017) International Ocean and Polar Engineering Conference, San Francisco, CA, USA, June 25-30, 2017, Copyright © 2017 by the International Society of Offshore and Polar Engineers (ISOPE), ISBN 978-1-880653-97-5; ISSN 1098-6189.

19-17   Velioğlu Deniz, Advanced Two- and Three-Dimensional Tsunami – Models Benchmarking and Validation, Ph.D Thesis:, Middle East Technical University, June 2017

18-17   Farrokh Mahnamfar and Abdüsselam Altunkaynak, Comparison of numerical and experimental analyses for optimizing the geometry of OWC systems, Ocean Engineering 130 (2017) 10–24.

07-17   Jonas Čerka, Rima Mickevičienė, Žydrūnas Ašmontas, Lukas Norkevičius, Tomas Žapnickas, Vasilij Djačkov and Peilin Zhou, Optimization of the research vessel hull form by using numerical simulation, Ocean Engineering 139 (2017) 33–38

05-17   Liang, B.; Ma, S.; Pan, X., and Lee, D.Y., Numerical modelling of wave run-up with interaction between wave and dolosse breakwater, In: Lee, J.L.; Griffiths, T.; Lotan, A.; Suh, K.-S., and Lee, J. (eds.), 2017, The 2nd International Water Safety Symposium. Journal of Coastal Research, Special Issue No. 79, pp. 294-298. Coconut Creek (Florida), ISSN 0749-0208.

02-17   A. Yazid Maliki, M. Azlan Musa, Ahmad M.F., Zamri I., Omar Y., Comparison of numerical and experimental results for overtopping discharge of the OBREC wave energy converter, Journal of Engineering Science and Technology, In Press, © School of Engineering, Taylor’s University

01-17   Tanvir Sayeed, Bruce Colbourne, David Molyneux, Ayhan Akinturk, Experimental and numerical investigation of wave forces on partially submerged bodies in close proximity to a fixed structure, Ocean Engineering, Volume 132, Pages 70–91, March 2017

101-16 Xin Li, Liang-yu Xu, Jian-Min Yang, Study of fluid resonance between two side-by-side floating barges, Journal of Hydrodynamics, vol. B-28, no. 5, pp. 767-777, 2016. doi.org/10.1016/S1001-6058(16)60679-0

81-16   Loretta Gnavi, Deep water challenges: development of depositional models to support geohazard assessment for submarine facilities, Ph.D. Thesis: Politecnico di Torino, May 2016

80-16   Mohammed Ibrahim, Hany Ahmed, Mostafa Abd Alall and A.S. Koraim, Proposing and investigating the efficiency of vertical perforated breakwater, International Journal of Scientific & Engineering Research, Volume 7, Issue 3, March 2016, ISSN 2229-5518

72-16   Yen-Lung Chen and Shih-Chun Hsiao, Generation of 3D water waves using mass source wavemaker applied to Navier–Stokes model, Coastal Engineering 109 (2016) 76–95.

64-16   Jae Nam Cho, Dong Hyun Kim and Seung Oh Lee, Experimental Study of Shape and Pressure Characteristics of Solitary Wave generated by Sluice Gate for Various Conditions, Journal of the Korean Society of Safety, Vol. 31, No. 2, pp. 70-75, April 2016, Copyright @ 2016 by The Korean Society of Safety (pISSN 1738-3803, eISSN 2383-9953) All right reserved. http://dx.doi.org/10.14346/JKOSOS.2016.31.2.70

56-16   Ali A. Babajani, Mohammad Jafari and Parinaz Hafezi Sefat, Numerical investigation of distance effect between two Searasers for hydrodynamic performance, Alexandria Engineering Journal, June 2016.

53-16   Hwang-Ki Lee, Byeong-Kuk Kim, Jongkyu Kim and Hyeon-Ju Kim, OTEC thermal dispersion in coastal waters of Tarawa, Kiribati, OCEANS 2016 – Shanghai, April 2016, 10.1109/OCEANSAP.2016.7485548, © IEEE.

50-16   Mohsin A. R. Irkal, S. Nallayarasu and S. K. Bhattacharyya, CFD simulation of roll damping characteristics of a ship midsection with bilge keel, Proceedings of the ASME 2016 35th International Conference on Ocean, Offshore and Arctic Engineering, OMAE2016, June 19-24, 2016, Busan, South Korea

49-16   Bill Baird, Seth Logan, Wim Van Der Molen, Trevor Elliot and Don Zimmer, Thoughts on the future of physical models in coastal engineering, Proceedings of the 6th International Conference on the Application of Physical Modelling in Coastal and Port Engineering and Science (Coastlab16) Ottawa, Canada, May 10-13, 2016 Copyright ©: Creative Commons CC BY-NC-ND 4.0

47-16   KH Kim et. al, Numerical analysis on the effects of shoal on the ship wave, Applied Engineering, Materials and Mechanics: Proceedings of the 2016 International Conference on Applied Engineering, Materials and Mechanics (ICAEMM 2016)

17-16  Nan-Jing Wu, Shih-Chun Hsiao, Hsin-Hung Chen, and Ray-Yeng Yang, The study on solitary waves generated by a piston-type wave maker, Ocean Engineering, 117(2016)114–129

13-16   Maryam Deilami-Tarifi, Mehdi Behdarvandi-Askar, Vahid Chegini, and Sadegh Haghighi-Pou, Modeling of the Changes in Flow Velocity on Seawalls under Different Conditions Using FLOW-3DSoftware, Open Journal of Marine Science, 2016, 6, 317-322, Published Online April 2016 in SciRes.

01-16   Mohsin A.R. Irkal, S. Nallayarasu, and S.K. Bhattacharyya, CFD approach to roll damping of ship with bilge keel with experimental validation, Applied Ocean Research, Volume 55, February 2016, Pages 1–17

121-15   Josh Carter, Scott Fenical, Craig Hunter and Joshua Todd, CFD modeling for the analysis of living shoreline structure performance, Coastal Structures and Solutions to Coastal Disasters Joint Conference, Boston, MA, Sept. 9-11, 2015. © 2017 by the American Society of Civil Engineers. doi.org/10.1061/9780784480304.047

114-15   Jisheng Zhang, Peng Gao, Jinhai Zheng, Xiuguang Wu, Yuxuan Peng and Tiantian Zhang, Current-induced seabed scour around a pile-supported horizontal-axis tidal stream turbine, Journal of Marine Science and Technology, Vol. 23, No. 6, pp. 929-936 (2015) 929, DOI: 10.6119/JMST-015-0610-11

108-15  Tiecheng Wang, Tao Meng, and Hailong Zha, Analysis of Tsunami Effect and Structural Response, ISSN 1330-3651 (Print), ISSN 1848-6339 (Online), DOI: 10.17559/TV-20150122115308

107-15   Jie Chen, Changbo Jiang, Wu Yang, Guizhen Xiao, Laboratory study on protection of tsunami-induced scour by offshore breakwaters, Natural Hazards, 2015, 1-19

85-15   Majid A. Bhinder, M.T. Rahmati, C.G. Mingham and G.A. Aggidis, Numerical hydrodynamic modelling of a pitching wave energy converter, European Journal of Computational Mechanics, Volume 24, Issue 4, 2015, DOI: 10.1080/17797179.2015.1096228

65-15   Giancarlo Alfonsi, Numerical Simulations of Wave-Induced Flow Fields around Large-Diameter Surface-Piercing Vertical Circular CylinderComputation 20153(3), 386-426; doi:10.3390/computation3030386

61-15   Bingchen Liang, Duo Li, Xinying Pan and Guangxin Jiang, Numerical Study of Local Scour of Pipeline under Combined Wave and Current Conditions, Proceedings of the Twenty-fifth (2015) International Ocean and Polar Engineering Conference Kona, Big Island, Hawaii, USA, June 21-26, 2015 Copyright © 2015 by the International Society of Offshore and Polar Engineers (ISOPE) ISBN 978-1-880653-89-0; ISSN 1098-6189.

60-15   Chun-Han Ko, Ching-Piao Tsai, Ying-Chi Chen, and Tri-Octaviani Sihombing, Numerical Simulations of Wave and Flow Variations between Submerged Breakwaters and Slope Seawall, Proceedings of the Twenty-fifth (2015) International Ocean and Polar Engineering Conference Kona, Big Island, Hawaii, USA, June 21-26, 2015 Copyright © 2015 by the International Society of Offshore and Polar Engineers (ISOPE) ISBN 978-1-880653-89-0; ISSN 1098-6189.

57-15   Giacomo Viccione and Settimio Ferlisi, A numerical investigation of the interaction between debris flows and defense barriers, Advances in Environmental and Geological Science and Engineering, ISBN: 978-1-61804-314-6, 2015

56-15   Vittorio Bovolin, Eugenio Pugliese Carratelli and Giacomo Viccione, A numerical study of liquid impact on inclined surfaces, Advances in Environmental and Geological Science and Engineering, ISBN: 978-1-61804-314-6, 2015

49-15   Fabio Dentale, Giovanna Donnarumma, Eugenio Pugliese Carratelli, and Ferdinando Reale, A numerical method to analyze the interaction between sea waves and rubble mound emerged breakwaters, WSEAS TRANSACTIONS on FLUID MECHANICS, E-ISSN: 2224-347X, Volume 10, 2015

45-15   Diego Vicinanza, Daniela Salerno, Fabio Dentale and Mariano Buccino, Structural Response of Seawave Slot-cone Generator (SSG) from Random Wave CFD Simulations, Proceedings of the Twenty-fifth (2015) International Ocean and Polar Engineering Conference, Kona, Big Island, Hawaii, USA, June 21-26, 2015, Copyright © 2015 by the International Society of Offshore and Polar Engineers (ISOPE), ISBN 978-1-880653-89-0; ISSN 1098-6189

38-15   Yen-Lung Chen, Shih-Chun Hsiao, Yu-Cheng Hou, Han-Lun Wu and Yuan Chieh Wu, Numerical Simulation of a Neutrally Buoyant Round Jet in a Wave Environment, E-proceedings of the 36th IAHR World Congress, 28 June – 3 July, 2015, The Hague, the Netherlands

34-15   Dieter Vanneste and Peter Troch, 2D numerical simulation of large-scale physical model tests of wave interaction with a rubble-mound breakwater, Coastal Engineering, Volume 103, September 2015, Pages 22–41.

29-15   Masanobu Toyoda, Hiroki Kusumoto, and Kazuo Watanabe, Intrinsically Safe Cryogenic Cargo Containment System of IHI-SPB LNG Tank, IHI Engineering Review, Vol. 47, No. 2, 2015.

24-15   Xixi Pan, Shiming Wang, and Yongcheng Liang, Three-dimensional simulation of floating wave power device, International Power, Electronics and Materials Engineering Conference (IPEMEC 2015)

05-15   M. A. Bhinder, A. Babarit, L. Gentaz, and P. Ferrant, Potential Time Domain Model with Viscous Correction and CFD Analysis of a Generic Surging Floating Wave Energy Converter, (2015), doi: http://dx.doi.org/10.1016/j.ijome.2015.01.005

137-14   A. Najafi-Jilani, M. Zakiri Niri and Nader Naderi, Simulating three dimensional wave run-up over breakwaters covered by antifer units, Int. J. Nav. Archit. Ocean Eng. (2014) 6:297~306

128-14   Dong Chule Kim, Byung Ho Choi, Kyeong Ok Kim and Efim Pelinovsky, Extreme tsunami runup simulation at Babi Island due to 1992 Flores tsunami and Okushiri due to 1993 Hokkido tsunami, Geophysical Research Abstracts, Vol. 16, EGU2014-1341, 2014, EGU General Assembly 2014, © Author(s) 2013. CC Attribution 3.0 License.

123-14   Irkal Mohsin A.R., S. Nallayarasu and S.K. Bhattacharyya, Experimental and CFD Simulation of Roll Motion of Ship with Bilge Keel, International Conference on Computational and Experimental Marine Hydrodynamics MARHY 2014 3-4 December 2014, Chennai, India.

101-14  Dieter Vanneste, Corrado Altomare, Tomohiro Suzuki, Peter Troch and Toon Verwaest, Comparison of Numerical Models for Wave Overtopping and Impact on a Sea Wall, Coastal Engineering 2014

91-14   Fabio Dentale, Giovanna Donnarumma, and Eugenio Pugliese Carratelli, Numerical wave interaction with tetrapods breakwater, Int. J. Nav. Archit. Ocean Eng. (2014) 6:0~0, http://dx.doi.org/10.2478/IJNAOE-2013-0214, ⓒSNAK, 2014, pISSN: 2092-6782, eISSN: 2092-6790

87-14   Philipp Behruzi, Simulation of breaking wave impacts on a flat wall, The 15th International Workshop on Trends In Numerical and Physical Modeling for Industrial Multiphase Flows, Cargèse, Corsica, October 13th–17th, 2014

86-14   Chuan Sim and Sung-uk Choi, Three-Dimensional Scour at Submarine Pipelines under Indefinite Boundary Conditions, 2014

83-14   Hongda Shi, Dong Wang, Jinghui Song, and Zhe Ma, Systematic Design of a Heaving Buoy Wave Energy Device, 5th International Conference on Ocean Energy, 4th November, Halifax, 2014

71-14   Hadi Sabziyan, Hassan Ghassemi, Farhood Azarsina, and Saeid Kazemi, Effect of Mooring Lines Pattern in a Semi-submersible Platform at Surge and Sway Movements, Journal of Ocean Research, 2014, Vol. 2, No. 1, 17-22 Available online at http://pubs.sciepub.com/jor/2/1/4 © Science and Education Publishing DOI:10.12691/jor-2-1-4

56-14   Fernandez-Montblanc, T., Izquierdo, A., and Bethencourt, M., Modelling the oceanographic conditions during storm following the Battle of Trafalgar, Encuentro de la Oceanografıa Fısica Espanola 2014

52-14   Fabio Dentale, Giovanna Donnarumma, and Eugenio Pugliese Carratelli, A new numerical approach to the study of the interaction between wave motion and roubble mound breakwaters, Latest Trends in Engineering Mechanics, Structures, Engineering Geology, ISBN: 978-960-474-376-6

49-14   H. Ahmed and A. Schlenkhoff, Numerical Investigation of Wave Interaction with Double Vertical Slotted Walls, World Academy of Science, Engineering and Technology, International Journal of Environmental, Ecological, Geological and Mining Engineering Vol:8 No:8, 2014

32-14  Richard Keough, Victoria Mullaley, Hilary Sinclair, and Greg Walsh, Design, Fabrication and Testing of a Water Current Energy Device, Memorial University of Newfoundland, Faculty of Engineering and Applied Science, Mechanical Design Project II – ENGI 8926, April 2014

25-14    Paulius Rapalis, Vytautas Smailys, Vygintas Daukšys, Nadežda Zamiatina, and Vasilij Djačkov, Vandens  – Duju Silumos Mainai Gaz-Lifto Tipo Skruberyje,Technologijos mokslo darbai Vakarų Lietuvoje, Vol 9 > Rapalis. Available for download at http://journals.ku.lt/index.php/TMD/article/view/259.

92-13   Matteo Tirindelli, Scott Fenical and Vladimir Shepsis, State-of-the-Art Methods for Extreme Wave Loading on Bridges and Coastal Highways, Seventh National Seismic Conference on Bridges and Highways (7NSC), May 20-22, 2013, Oakland, CA

89-13 Worakanok Thanyamanta, Don Bass and David Molyneux, Prediction of sloshing effects using a coupled non-linear seakeeping and CFD code, Proceedings of the ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering, OMAE2013, June 9-14, 2013, Nantes, France. Available for purchase online at ASME.

83-13   B.W. Lee and C. Lee, Development of Wave Power Generation Device with Resonance Channels, Proceedings of the 7th International Conference on Asian and Pacific Coasts (APAC 2013) Bali, Indonesia, September 24-26, 2013

68-13   Fabio Dentale, Giovanna Donnarumma, and Eugenio Pugliese Carratelli, Rubble Mound Breakwater Run-Up, Reflection and Overtopping by Numerical 3D Simulation, ICE Conference, September 2013, Edinburgh (UK).

66-13  Peter Arnold, Validation of FLOW-3D against Experimental Data for an Axi-Symmetric Point Absorber WEC, © wavebob™, 2013

62-13 Yanan Li, Junwei Zhou, Dazheng Wang and Yonggang Cui, Resistance and Strength Analysis of Three Hulls with ifferent Knuckles, Advanced Materials Research Vols. 779-780 (2013) pp 615-618, © (2013) Trans Tech Publications, Switzerland, doi:10.4028/www.scientific.net/AMR.779-780.615.

61-13  M.R. Soliman, Satoru Ushijima, Nobu Miyagi and Tetsuay Sumi, Density Current Simulation Using Two-Dimensional High Resolution Model, Annuals of Disas. Prev. Res. Inst., Kyoto Univ., No 56 B, 2013.

59-13  Guang Wei Liu, Qing He Zhang, and Jin Feng Zhang, Wave Forces on the Composite Bucket Foundation of Offshore Wind Turbines, Applied Mechanics and Materials, 405-408, 1420, September 2013. Available for purchase online at Scientific.net.

50-13  Joel Darnell and Vladimir Shepsis, Pontoon Launch Analysis, Design and Performance, Ports 2013, © ASCE 2013. Available for purchase online at ASCE.

45-13 Min-chi Li, Numerical Simulation of Wave Overtopping Rate at Sloping Seawalls with Different Configurations of Wave Dissipators, Master’s Thesis: Department of Marine Environment and Engineering, National Sun Yat-Sen University. Abstract only available here: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0701113-144919.

22-13  Nahidul Khan, Jonathan Smith, and Michael Hinchey, Models with all the right curves, © Journal of Ocean Technology, The Journal of Ocean Technology, Vol. 8, No. 1, 2013.

20-13  Efim Pelinovsky, Dong-Chul Kim, Kyeong-Ok Kim and Byung-Ho Choi, Three-dimensional simulation of extreme runup heights during the 2004 Indonesian and 2011 Japanese tsunamis, EGU General Assembly 2013, held 7-12 April, 2013 in Vienna, Austria, id. EGU2013-1760. Online at: http://adsabs.harvard.edu/abs/2013EGUGA..15.1760P.

18-13 Dazheng Wang, Fei Ma, and Lei Mei, Optimization of a 17m Catamaran based on the Resistance Performance, Advanced Materials Research Vols. 690-693, pp 3414-3418, © Trans Tech Publications, Switzerland, doi:10.4028/www.scientific.net/AMR.690-693.3414, May 2013.

16-13  Dong Chule Kim, Kyeong Ok Kim, Efim Pelinovsky, Ira Didenkulova, and Byung Ho Choi, Three-dimensional tsunami runup simulation for the port of Koborinai on the Sanriku coast of Japan, Journal of Coastal Research, Special Issue No. 65, 2013.

15-13  Dong Chule Kim, Kyeong Ok Kim, Byung Ho Choi, Kyung Hwan Kim, and Efin Pelinovsky, Three –dimensional runup simulation of the 2004 Ocean tsunami at the Lhok Nga twin peaks, Journal of Coastal Research, Special Issue No. 65, 2013.

14-13  Jae-Seol Shim, Jinah Kim, Dong-Shul Kim, Kiyoung Heo, Kideok Do, and Sun-Jung Park, Storm surge inundation simulations comparing three-dimensional with two-dimensional models based on Typhoon Maemi over Masan Bay of South Korea, Journal of Coastal Research, Special Issue No. 65, 2013.

115-12  Worakanok Thanyamanta and David Molyneux, Prediction of Stabilizing Moments and Effects of U-Tube Anti-Roll Tank Geometry Using CFD, ASME 2012 31st International Conference on Ocean, Offshore and Arctic Engineering, Volume 5: Ocean Engineering; CFD and VIV, Rio de Janeiro, Brazil, July 1–6, 2012, ISBN: 978-0-7918-4492-2, Copyright © 2012 by ASME

114-12   Dane Kristopher Behrens, The Russian River Estuary: Inlet Morphology, Management, and Estuarine Scalar Field Response, Ph.D. Thesis: Civil and Environmental Engineering, UC Davis, © 2012 by Dane Kristopher Behrens. All Rights Reserved.

111-12  James E. Beget, Zygmunt Kowalik, Juan Horrillo, Fahad Mohammed, Brian C. McFall, and Gyeong-Bo Kim, NEeSR-CR Tsunami Generation by Landslides Integrating Laboratory Scale Experiments, Numerical Models and Natural Scale Applications, George E. Brown, Jr. Network for Earthquake Engineering Simulation Research, July 2012, Boston, MA.

110-12   Gyeong-Bo Kim, Numerical Simulation of Three-Dimensional Tsunami Generation by Subaerial Landslides, M.S. Thesis: Texas A&M University, Copyright 2012 Gyeong-Bo Kim, December 2012

109-12 D. Vanneste, Experimental and Numerical study of Wave-Induced Porous Flow in Rubble-Mound Breakwaters, Ph.D. thesis (Chapters 5 and 6), Faculty of Engineering and Architecture, Ghent University, Ghent (Belgium), 2012.

104-12 Junwoo Choi, Kab Keun Kwon, and Sung Bum Yoon, Tsunami Inundation Simulation of a Built-up Area using Equivalent Resistance Coefficient, Coastal Engineering Journal, Vol. 54, No. 2 (2012) 1250015 (25 pages), © World Scientific Publishing Company and Japan Society of Civil Engineers, DOI: 10.1142/S0578563412500155

94-12 Parviz Ghadimi, Abbas Dashtimanesh, Mohammad Farsi, and Saeed Najafi, Investigation of free surface flow generated by a planing flat plate using smoothed particle hydrodynamics method and FLOW-3D simulations, Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment, December 7, 2012 1475090212465235. Available for purchase online at sage journals.

92-12    Panayotis Prinos, Maria Tsakiri, and Dimitris Souliotis, A Numerical Simulation of the WOS and the Wave Propagation along a Coastal Dike, Coastal Engineering 2012.

88-12  Nahidul Khan and Michael Hinchey, Adaptive Backstepping Control of Marine Current Energy Conversion System, PKP Open Conference Systems, IEEE Newfoundland and Labrador Section, 2012.

72-12   F. Dentale, G. Donnarumma, and E. Pugliese Carratelli, Wave Run Up and Reflection on Tridimensional Virtual, Journal of Hydrogeology & Hydrologic Engineering, 2012, 1:1, http://dx.doi.org/10.4172/jhhe.1000102.

64-12  Anders Wedel Nielsen, Xiaofeng Liu, B. Mutlu Sumer, Jørgen Fredsøe, Flow and bed shear stresses in scour protections around a pile in a current, Coastal Engineering, Volume 72, February 2013, Pages 20–38.

56-12  Giancarlo Alfonsi, Agostino Lauria, Leonardo Primavera, Flow structures around large-diameter circular cylinder, Journal of Flow Visualization and Image Processing, 2012. DOI:10.1615/JFlowVisImageProc.2012005088.

51-12  Chun-Ho Chen, Study on the Application of FLOW-3D for Wave Energy Dissipation by a Porous Structure, Master’s Thesis: Department of Marine Environment and Engineering, National Sun Yat-sen University, July 2012. In Chinese.

37-12  Yu-Ren Chen, Numerical Modeling on Internal Solitary Wave propagation over an obstacle using FLOW-3D, Master’s Thesis: Department of Marine Environment and Engineering, National Sun Yat-sen University June 2012. In Chinese.

26-12  D.C. Lo Numerical simulation of hydrodynamic interaction produced during the overtaking and the head-on encounter process of two ships, Engineering Computations: International Journal for Computer-Aided Engineering and Software, Vol. 29 No. 1, 2012. pp. 83-10, Emerald Group Publishing Limited, www.emeraldinsight.com/0264-4401.htm.

14-12  Bahaa Elsharnouby, Akram Soliman, Mohamed Elnaggar, and Mohamed Elshahat, Study of environment friendly porous suspended breakwater for the Egyptian Northwestern Coast, Ocean Engineering 48 (2012) 47-58. Available for purchase online at Science Direct.

11-12  Sang-Ho Oh, Young Min Oh, Ji-Young Kim, Keum-Seok Kang, A case study on the design of condenser effluent outlet of thermal power plant to reduce foam emitted to surrounding seacoast, Ocean Engineering, Volume 47, June 2012, Pages 58–64. Available for purchase online at SciVerse.

101-11 Tsunami – A Growing Disaster, edited by Mohammad Mokhtari, ISBN 978-953-307-431-3, 232 pages, Publisher: InTech, Chapters published December 16, 2011 under CC BY 3.0 license, DOI: 10.5772/922. Available for download at Intech.

100-11 Kwang-Oh Ko, Jun-Woo Choi, Sung-Bum Yoon, and Chang-Beom Park, Internal Wave Generation in FLOW-3D Model, Proceedings of the Twenty-first (2011) International Offshore and Polar Engineering Conference, Maui, Hawaii, USA, June 19-24, 2011, Copyright © 2011 by the International Society of Offshore and Polar Engineers (ISOPE), ISBN 978-1-880653-96-8 (Set); ISSN 1098-6189 (Set); www.isope.org

95-11  S. Brizzolara, L. Savio, M. Viviani, Y. Chen, P. Temarel, N. Couty, S. Hoflack, L. Diebold, N. Moirod and A. Souto Iglesias, Comparison of experimental and numerical sloshing loads in partially filled tanks, Ships and Offshore StructuresVol. 6, Nos. 1–2, 2011, 15–43. Available for purchase online at Francis & Taylor.

85-11 Andrew Eoghan Maguire, Hydrodynamics, control and numerical modelling of absorbing wavemakers, thesis: The University of Edinburgh, 2011.

74-11  Jonathan Smith, Nahidul Khan and Michael Hinchey, CFD Simulation of AUV Depth Control, Paper presented at NECEC 2011, St. John’s, Newfoundland and Labrador, Canada. Abstract available online.

70-11  G. Kim, S.-H. Oh, K.S. Lee, I.S. Han, J.W. Chae, and S.-J Ahn, Numerical Investigation on Water Discharge Capability of Sluice Caisson of Tidal Power Plant, Proceedings of the Sixth International Conference on Asian and Pacific Coasts (APAC 2011), December 14-16, 2011, Hong Kong, China.

69-11  G. Alfonsi, A. Lauria, and L. Primavera, Wave-Field Flow Structures Developing Around Large-Diameter Vertical Circular Cylinder, Proceedings of the Sixth International Conference on Asian and Pacific Coasts (APAC 2011), December 14-16, 2011, Hong Kong, China.

68-11    C. Lee, B.W. Lee, Y.J. Kim, and K.O. Ko, Ship Wave Crests in Intermediate-Depth Water, Proceedings of the Sixth International Conference on Asian and Pacific Coasts (APAC 2011), December 14-16, 2011, Hong Kong, China.

63-11   Worakanok Thanyamanta, Paul Herrington, and David Molyneux, Wave patterns, wave induced forces and moments for a gravity based structure predicted using CFD, Proceedings of the ASME 2011, 30th International Conference on Ocean, Offshore and Arctic Engineering, OMAE2011, Rotterdam, The Netherlands, June 19-24, 2011.

61-11  Jun Jin and Bo Meng, Computation of wave loads on the superstructures of coastal highway bridges, Ocean Engineering, available online October 19, 2011, ISSN 0029-8018, 10.1016/j.oceaneng.2011.09.029. Available for purchase at Science Direct.

36-11    Nadir Yilmaz, Geoffrey E. Trapp, Scott M. Gagan, Timothy R. Emmerich, CFD Supported Examination of Buoy Design for Wave Energy Conversion, IGEC-VI-2011-173, pp: 537-541

28-11  Rodolfo Bolaños, Laurent O. Amoudry and Ken Doyle, Effects of Instrumented Bottom Tripods on Process Measurements, Journal of Atmospheric and Oceanic Technology, June 2011, Vol. 28, No. 6: pp. 827-837. Available online at: AMS Journals Online.

81-10    Ashwin Lohithakshan Parambath, Impact of Tsunamis on Near Shore Wind Power Units, M.S. Thesis: Texas A&M University, Copyright 2010 Ashwin Lohithakshan Parambath December 2010.

80-10    Juan J. Horrillo, Amanda L. Wood, Charles Williams, Ashwin Parambath, and Gyeong-Bo Kim, Construction of Tsunami Inundation Maps in the Gulf of Mexico, Report to the National Tsunami Hazard Mitigation Program, December 2010.

69-10    George A Aggidis and Clive Mingham, A Joint Numerical and Experimental Study of a Surging Point Absorbing Wave Energy Converter (WRASPA), Joule Centre Research Grant Joint Final Report (Lancaster University and Macnhester Metropolitan University), Joule Grant No: JIRP306/02, 2010

67-10  Kazuhiko Terashima, Ryuji Ito, Yoshiyuki Noda, Yoji Masui and Takahiro Iwasa, Innovative Integrated Simulator for Agile Control Design on Shipboard Crane Considering Ship and Load Sway, 2010 IEEE International Conference on Control Applications, Part of 2010 IEEE Multi-Conference on Systems and Control, Yokohama, Japan, September 8-10, 2010

66-10  Shan-Hwei Ou, Tai-Wen Hsu, Jian-Feng Lin, Jian-Wu Lai, Shih-Hsiang Lin, Chen-Chen Chang, Yuan-Jyh Lan, Experimental and Numerical Studies on Wave Transformation over Artificial Reefs, Proceedings of the International Conference on Coastal Engineering, No 32 (2010), Shanghai, China, 2010.

65-10 Tai-Wen Hsu, Jian-Wu Lai, Yuan-Jyh Lan, Experimental and Numerical Studies on Wave Propagation over Coarse Grained Sloping Beach, Proceedings of the International Conference on Coastal Engineering, No 32 (2010), Shanghai, China, 2010.

26-10 R. Marcer, C. Berhault, C. de Jouëtte, N. Moirod and L. Shen, Validation of CFD Codes for Slamming, V European Conference on Computational Fluid Dynamics, ECCOMAS CFD 2010, J.C.F. Pereira and A. Sequeira (Eds), Lisbon, Portugal, 14-17 June 2010

25-10 J.M. Zhan, Z. Dong, W. Jiang, and Y.S. Li, Numerical Simulation of wave transformation and runup incorporating porous media wave absorber and turbulence models, Ocean Engineering (2010), doi: 10.1016/j.oceaneng.2010.06.005. Available for purchase at Science Direct.

17-10 F. Dentale, S.D. Russo, E. Pugliese Carratelli, S. Mascetti, A New Numerical Approach to Study the Wave Motion with Breakwaters and the Armor Stability, Marine Technology Reporter, May 2010

01-10 F. Dentale, S.D. Russo, E. Pugliese Carratelli, Innovative Numerical Simulation to Study the Fluid withing Rubble Mound Breakwaters and the Armour Stability, 17th Armourstone Wallingford Armourstone Meeting, Wallingford, UK, February 2010.

52-09  Mark Reed, Øistein Johansen, Frode Leirvik, and Bård Brørs, Numerical Algorithm to Compute the Effects of Breaking Waves on Surface Oil Spilled at Sea, Final Report, Second revision, SINTEF, October 2009.

49-09  Anna Pellicioli, Indagine Numerica Sulla Resistenza Idrodinamica Di Uno Scafo In Presenza Di Superficie Libera, thesis: Univerista Degli Studi Di Bergamo, 2008/2009. In Italian. Available upon request.

46-09 Carlos Guedes Soares, P.K. Das, Analysis and Design of Marine Structures, CRC Press; 1 Har/Cdr edition (March 2, 2009), 0415549345

32-09 M.A. Binder, C.G. Mingham, D.M. Causon, M.T. Rahmati, G.A. Aggidis, R.V. Chaplin, Numerical Modelling of a Surging Point Absorber Wave Energy Converter, 8th European Wave and Tidal Energy Conference EWTEC 2009, Uppsala, Sweden, 7-10 September 2009

28-09 D. C. Lo, Dong-Taur Su and Jan-Ming Chen (2009), Application of Computational Fluid Dynamics Simulations to the Analysis of Bank Effects in Restricted Waters, Journal of Navigation, 62, pp 477-491, doi:10.1017/S037346330900527X; Purchase the article online (clicking on this link will take you to the Cambridge Journals website).

26-09 Fabio Dentale, E. Pugliese Carratelli, S.D. Russo, and Stefano Mascetti, Advanced Numerical Simulations on the Interaction between Waves and Rubble Mound Breakwaters, Journal of the Engineering Association for Offshore and Marine in Italy, (translation from the Italian)

25-09 F. Dentale, B. Messina, E. Pugliese Carratelli, S. Mascetti, Studio numerico avanzato sul moto di filtrazione in ambito marittimo, A & C, Analisi e Calcolo, Giugno 2009 (in Italian)

22-09 M.A. Bhinder, C.G. Mingham, D.M. Causon, M.T. Rahmati, G.A. Aggidis and R.V. Chaplin, A Joint Numerical And Experimental Study Of a Surging Point Absorbing Wave Energy Converter (WRASPA)2, Proceedings of the ASME 28th International Conference on Ocean, Offshore and Arctic Engineering, OMAE2009-79392, Honolulu, Hawaii, May 31-June 5, 2009

8-09 Basu, D., S. Green, K. Das, R. Janetzke, and J. Stamatakos, Numerical Simulation of Surface Waves Generated by a Subaerial Landslide at Lituya Bay, 28th International Conference on Ocean, Offshore and Arctic Engineering, May 31–June 5, 2009, Honolulu, Hawaii

17-09 Das, K., R. Janetzke, D. Basu, S. Green, and J. Stamatakos, Numerical Simulations of Tsunami Wave Generation by Submarine and Aerial Landslides Using RANS and SPH Models, 28th International Conference on Ocean, Offshore and Arctic Engineering, May 31–June 5, 2009, Honolulu, Hawaii

16-09 Basu, D., S. Green, K. Das, R. Janetzke, and J. Stamatakos, Navier-Stokes Simulations of Surface Waves Generated by Submarine Landslides Effect of Slide Geometry and Turbulence, 2009 Society of Petroleum Engineering Americas E&P Environmental & Safety Conference, March 23–25, 2009, San Antonio, Texas.

48-08    Osamu Kiyomiya1 and Kazuya Kuroki, Flap Gate to Prevent Urban Area from Tsunami, The 14th World Conference on Earthquake Engineering, October 12-17, 2008, Beijing, China

43-08  Eldina Fatimah, Ahmad Khairi Abd. Wahab, and Hadibah Ismail, Numerical modeling approach of an artificial mangrove root system (ArMs) submerged breakwater as wetland habitat protector, COPEDEC VII, Dubai UAE, 2008.

40-08 Giacomo Viccione, Fabio Dentale, and Vittorio Bovolin, Simulation of Wave Impact Pressure on Vertical Structures with the SPH Method, 3rd ERCOFTAC SPHERIC workshop on SPH applications, Laussanne, Switzerland, June 4-6, 2008.

39-08 Kang, Young-Seung, Kim, Pyeong-Joong, Hyun, Sang-Kwon and Sung, Ha-Keun, Numerical Simulation of Ship-induced Wave Using FLOW-3D, Journal of Korean Society of Coastal and Ocean Engineers / v.20, no.3, 2008, pp.255-267, ISSN: 1976-8192, http://ksci.kisti.re.kr/search/article/articleView.ksci?articleBean.artSeq=HOHODK_2008_v20n3_255

35-08 B.W. Nam, S.H. Shin, K.Y. Hong, S.W. Hong, Numerical Simulation of Wave Flow over the Spiral-Reef Overtopping Device, Proceedings of the Eighth (2008) ISOPE Pacific/Asia Offshore Mechanics Symposium, Bangkok, Thailand, November 10-14, 2008, © 2008 by The International Society of Offshore and Polar Engineers, ISBN 978-1-880653-52-4

34-08 B. H. Choi, E. Pelinovsky, D.C. Kim, I. Didenkulova and S.-B. Woo, Two and three-dimensional computation of solitary wave runup on non-plane beach, Nonlin. Processes Geophys., 15, 489-502, 2008, www.nonlin-processes-geophys.net/15/489/2008 (c) Author(s) 2008.

23-08 Barb Schmitz, Tecplot, Nastran & FLOW-3D Win the Race, Desktop Engineering’s Elements of Analysis, September 2008

38-07 Choi, B.-H., Kim, D. C., Pelinovsky, E., and Woo, S. B., Three-dimensional simulation of tsunami run-up around conical island, Coast. Eng., Vol. 54, Issue 8, 618-629, 2007.

33-07 Mirela Zalar, Sime Malenica, Zoran Mravak, Nicolas Moirod, Some Aspects of Direct Calculation Methods for the Assessment of LNG Tank Structure Under Sloshing Impacts, La Asociación Española del Gas (sedigas) Spain 2007

20-07 Oceanic Consulting Corporation, Berthing Studies for LNG Carriers in the Calcasieu River Waterway, Making Waves: Newsletter of Oceanic Consulting Corporation, Winter 2007

10-07 Gildas Colleter, Breaking wave uplift and overtopping on a horizontal deck using physical and numerical modeling, Coasts and Ports 2007 Conference in Melbourne, Australia

18-06 Brizzolara, Stefano and Rizzuto, Enrico, Wind Heeling Moments on Very Large Ships. Some Insights through CFD Results, Proceedings on the 9th International Conference on Stability of Ships and Ocean Vehicles, Rio de Janeiro, September 25, 2006

16-06 Ransau, Samuel R, and Hansen, Ernst W.M., Numerical Simulations of Sloshing in Rectangular Tanks, Proceedings of OMAE2006, 25th International Conference on Offshore Mechanics and Arctic Engineering, Hamburg, Germany, June 4-9, 2006

15-06 Ema Muk-Pavic, Shin Chin and Don Spencer, Validation of the CFD code FLOW-3D for the free surface flow around the ships’; hulls, 14th Annual Conference of the CFD Society of Canada, Kingston, Canada, July 16-18, 2006

3-06 Hansen, E.W.M. and Geir J. Rørtveit, Numerical Simulation of Fluid Mechanisms and Separation Behaviour in Offshore Gravity Separators, Chapter 16 in Emulsions and Emulsion Stability, 2nd Edition, edited by Johan Sjøblom, Taylor & Francis, 2006

24-05 Hansen E.W., Separation Offshore Survey – Design-Redesign of Gravity Separators, Exploration & Production: The Oil & Gas Review 2005 – Issue 2

8-05 T. Kristiansen, R. Baarholm, C.T. Stansberg, G. Rortveit and E.W.M. Hansen, Kinematics in a Diffracted Wave Field Particle Image Velocimetry (PIV) and Numerical Models, Presented at the 24th International Conference on Offshore Mechanics and Arctic Engineering, OMAE 67176, Halkidiki, Greece, June 12-17, 2005

7-05 C.T. Stansberg, R. Baarholm, T. Kristiansen, E.W.M. Hansen and G. Rortveit, Extreme Wave Amplification and Impact Loads on Offshore Structures, presented at the 2005 Offshore Technology Conference, Houston, TX, May 2-5, 2005

16-04 Carl Trygve Stansberg, Kjetil Berget, Oyvind Hellan, Ole A. Hermundstad, Jan R. Hoff and Trygve Kristiansen and Ernst Hansen, Prediction of Green Sea Loads on FPSO in Random Seas, presented at the 14th International Offshore and Polar Engineering Conference (ISOPE 2004), Toulon, France, May 2004

15-04 Š. Malenica, M. Zalar, J.M. Orozco, B. LeGallo & X.B. Chen, Linear and Non-Linear Effects of Sloshing on Ship Motions, 23rd International Conference on Offshore Mechanics and Artic Engineering, OMAE 2004, Vancouver, June 2004

11-04 Don Bass, David Molyneux, Kevin McTaggart, Simulating Wave Action in the Well Deck of Landing Platform Dock Ships Using Computational Fluid Dynamics

37-03  Sreenivasa C Chopakatla, A CFD Model for Wave Transformations and Breaking in the Surf Zone, thesis: Master of Science, The Ohio State Univeristy, 2003.

29-02   O. Bayle, V. L’Hullier, M. Ganet, P. Delpy, J.L. Francart and D. Paris, Influence of the ATV Propellant Sloshing on the GNC Performance, AIAA Guidance, Navigation, and Control Conference and Exhibit, Monterey, California, 5-8 August 2002, © 2002 by EADS Launch Vehicles

25-02 Y. Kim, Numerical Analysis of Sloshing Problem, American Bureau of Shipping, Research Dept, Houston, TX

10-02 Peter Chang III & Xiongjun Wu, Entrainment Correlations Based on a Fuel-Water Stratified Shear Flow, Proceedings of FEDSM2002, 2002 ASME Fluids Engineering Decision Summer Meeting, July 14-18, 2002, Montreal, Quebec, Canada

37-01 Ismail B. Celik, Allen E. Badeau Jr., Andrew Burt and Sherif Kandil, A Single Fluid Transport Model For Computation of Stratified Immiscible Liquid-Liquid Flows, Mechanical and Aerospace Engineering Department, West Virginia University, Proceedings of the XXIX IAHR Congress, September 2001. Beijing, China

14-01 Charles Ortloff, CTC/United Defense, Computer Simulation Analyzed Typhoon Damage to FPSOs, Marine News, April 30, 2001, pp. 22-23

8-01 Charles Ortloff, Computer Simulations Analyze Wave Damage to Offloading Vessels, Marine News, April 30, 2001, pp. 22-23

25-00 Faltinsen, O.A. and Rognebakke, O.F., Sloshing in Rectangular Tanks and Interaction with Ship Motions-Sloshing, Int. Conf. on Ship and Shipping Research NAV, Venice, Italy, 2000.

20-97   C.R. Ortloff, Numerical Test Tank Simulation of Ocean Engineering Problems by Computational Fluid Dynamics, Offshore Technology Conference Paper 8269B, Houston, TX, 1997

19-97   C.R. Ortloff and M. Krafft, Numerical Test Tanks-Computer Simulation-Test Verification of Major Ocean Engineering Problems for the Off-Shore Oil Industry, OTC 8269A, Offshore Technology Conference, Copyright 1997, Houston, Texas, May 1997

9-94 P. A. Chang, C-W Lin, CD-NSWC, Hydrodynamic Analysis of Oil Outflow from Double Hull Tankers, The Advanced Double-Hull Technical Symposium, Gaithersburg, MD, October 25-26, 1994.

8-90 C. W. Hirt, Computational Modeling of Cavitation, Flow Science report, July 1990, presented at the 2nd International Symposium on Performance Enhancement for Marine Applications, Newport, RI, October 14-16, 1990

10-87 H. W. Meldner, USA’s Revolutionary Appendages and CFD, CORDTRAN Corp. Report presented at AIAA and SNAME 17th Annual International Symposium on Sailing, Stanford University, Palo Alto, CA, Oct. 31-Nov. 1, 1987

3-85 C. W. Hirt and J. M. Sicilian, A Porosity Technique for the Definition of Obstacles in Rectangular Cell Meshes, Fourth International Conference on Ship Hydrodynamics, Washington, DC, September 1985

Free Surface Fluid Flow

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 Fluid Flow

Fluid flow problems often involve free surfaces in complex geometry and in many cases are highly transient. Examples in hydraulics are flows over spillways, in rivers, around bridge pilings, flood overflows, flows in sluices, locks, and a host of other structures. A capability to computationally model these types of flows is attractive if such computations can be done accurately and with reasonable computational resources. To be useful, simulations should be much faster and less expensive than using physical models.

자유 표면 유체 흐름

유체 흐름 문제는 복잡한 기하학적 구조의 자유 표면과 관련되는 경우가 많으며 대부분 매우 일시적입니다. 수력학의 예로는 배수로, 강, 교각 주변, 홍수 범람, 수문, 잠금 장치 및 다수의 기타 구조물의 흐름이 있습니다. 이러한 유형의 흐름을 계산적으로 모델링 하는 능력은 이러한 계산이 정확하고 합리적인 계산 자원으로 수행될 수 있다면 매력적입니다. 유용하게 사용하려면 시뮬레이션은 물리적 모델을 사용하는 것보다 훨씬 빠르고 저렴해야 합니다.

Many computer programs can solve the partial differential equations describing the dynamics of fluids. Not many programs are capable of including free surfaces in their simulations. The difficulty is a classical mathematical one often referred to as the free-boundary problem. A free boundary poses the difficulty that on the one hand the solution region changes when its surface moves, and on the other hand, the motion of the surface is in turn determined by the solution. Changes in the solution region include not only changes in size and shape, but in some cases, may also include the coalescence and break up of regions (i.e., the loss and gain of free surfaces).

많은 컴퓨터 프로그램은 유체의 역학을 설명하는 편미분 방정식을 풀 수 있습니다. 시뮬레이션에 자유 표면을 포함 할 수있는 프로그램은 많지 않습니다.  그 이유는 Free Surface 경계 문제로 잘 알려진 수학적인 문제입니다.  자유 경계 문제는 다루기 어려운 표면이 이동함에 따라 계산 영역이 변화하는 한편, 그 표면 이동 자체가 계산에 의해 결정된다는 점에 있습니다.  계산 영역의 변화는 그 크기와 모양의 변화뿐만 아니라, 경우에 따라서는 영역의 결합과 분리(즉, 자유 표면의 발생과 소멸)을 포함합니다.

In this note a computational modeling technique for fluid flows with arbitrary free surfaces is discussed. The technique is based on the Volume-of-Fluid (VOF) technique. This technique has many unique properties that make it especially applicable to flows having free surfaces. The goal of this discussion is to show why the VOF approach offers a natural way to capture free surfaces and their evolution with great efficiency.

이 책에서는 모든 자유 표면을 고려한 유체흐름 현상을 수치 해석용으로 모델링하는 방법에 대해 설명합니다.  이 기술은 VOF (Volume-of-Fluid) 법에 근거한 것으로, 특히 자유 표면 흐름에 적합한 다양한 기능을 제공합니다.  이 책에서는 VOF 법이 자유 표면과 그 발생과 소멸을 해석하는데 가장 자연스럽고 매우 효율적인 방법을 제시합니다.

A good recommendation for the VOF method is to demonstrate its capabilities on a simple hydraulic flow problem, one that is far from trivial. The example selected is of flow over a step. This flow has conceptual simplicity and good experimental data available for validation (see N. Rajaratnam and M.R. Chamani, “Energy Loss at Drops,” J. Hydraulic Res. Vol. 33, p.373, 1995).

VOF 법의 특징을 잘 보여주기 위해 간단하지만 매우 중요한 유동 현상에 관한 문제를 다룹니다.  여기에서는 계단 낙차형상의 낙하류를 예로 들어 있습니다.  개념적으로 간단한 흐름인 동시에 결과의 타당성을 확인하기위한 좋은 실험 데이터도 제공되어 있습니다 (N. Rajaratnam and MR Chamani “Energy Loss at Drops”J. Hydraulic Res. Vol. 33 p.373,1995 참조).

Prototype Hydraulic Flow with Free Surfaces

Figure 1a shows the flow problem after it has reached a steady-state condition. The overflow (sheet of liquid or nappe) leaving the top of the step has both an upper and lower free surface. At the bottom of the overflow a pool has formed between the overflow and the face of the step, while downstream, liquid is flowing to the right with a flat, steady surface. Strictly speaking, the flow conditions in the pool region are not steady because turbulent mixing is generated in the pool by the impinging fluid. There is, however, an average configuration and that is what is reported in the experiments.

자유 표면을포함한 유동 현상의 프로토타입

그림 1a는 정상 상태에 도달 한 후 흐름의 문제를 보여줍니다.  계단 낙차형상 상부로부터의 월류(액체 또는 스냅 시트)에는 상하 모두의 자유 표면이 있습니다.  월류의 아래쪽에는 월류와 계단 가공면 사이에 웅덩이가 형성되어 있으며, 하류에서는 액체는 평평한 정상 표면에서 오른쪽으로 흐르고 있습니다.  엄밀히 말하면, 웅덩이 영역의 흐름 상태는 정상입니다.  이것은 충돌하는 액체에 의해 풀에 난류 혼합이 발생하고 있기 때문입니다.  그러나 평균적인 구성이 존재하고 그것은 실험에서도 보고됩니다.

For all practical purposes the flow is two-dimensional, that is, it does not have any significant variation in the direction normal to the illustration in Fig. 1a. In actuality, to have an air space above the pool there must be some opening to the atmosphere otherwise it would close up.

실용 목적은 흐름은 항상 2 차원입니다.  즉, 그림 1a에서 수직 방향에서는 큰 변화는 없습니다.  현실에서는 웅덩이 위쪽으로 공간을 만들기 위해서는 대기에 여유공간이 필요하고, 그게 없으면 닫힐 것입니다.

The flow speed at the top of the step is critical, that is, it has a speed equal to or greater than the speed of surface waves, so that no disturbances from downstream can penetrate through this region to affect flow upstream (to the left of the step), which is why the flow is exceptionally smooth and steady in that region.

계단 낙차형상 상단의 유속은 중요합니다.  즉, 이것은 표면파와 같거나 그 이상의 속도이기 때문에 하류에서의 교란이 영역을 관통하고 상류 흐름 (계단 낙차형상의 왼쪽)에 영향을 줄 수 없습니다.  따라서 이 영역에서의 흐름은 예외적으로 원활하고 정상입니다.

There are many geometric features in this problem that can be compared with a numerical simulation; such as flow heights before and after the step, the angle of the overflow stream when it strikes the bottom and the depth of the pool formed under the overflow. Additionally, an important comparison for practical applications is the amount of energy (i.e., kinetic plus potential) lost by the flow in passing over the step.

이 문제는 수치 시뮬레이션과 비교할 수 있는 기하 형상 기능이 많이 있습니다.  예를 들어, 계단 낙차형상의 전후 흐름의 높이, 월류가 바닥에 충돌 할 때의 각도, 월류 아래에 형성되는 웅덩이의 깊이 등입니다.  또한 실용화를 위한 중요한 비교 항목으로는, 계단 낙차형상을 통해 떨어지는 낙하 류에 의해 손실되는 에너지의 양 (운동 에너지와 위치 에너지의 합)가 있습니다.

Simulation of Prototype Problem

Figure 1a is from a simulation. For this example all of the geometric and material properties used in the experiments were used in the simulation. The height of the step used in the laboratory test is 62cm and the fluid is ordinary water (density=1.0 gm/cc and dynamic viscosity=0.01dynes/cm). The depth of water entering the computational region was 15.5cm and was given a near critical velocity of 123.0cm/s. Of course, gravity was in the vertical direction with magnitude g=-980cm/s^2.

프로토 타입 문제의 시뮬레이션

그림 1a는 시뮬레이션의 결과입니다.  이 예에서는 실험에 사용된 모든 기하 형상 및 물질의 특성이 시뮬레이션에 사용되었습니다.  실험실 테스트에서 사용한 계단 낙차형상의 높이가 62cm에서 액체는 보통의 물 (밀도 = 1.0gm / cc 어떻게 점성 = 0.01dynes / cm)입니다.  계산 영역에 들어가는 물의 깊이는 15.5cm에서 속도가 임계에 가까운 123.0cm/s 였습니다.  물론, 중력은 수직 방향으로 크기는 g = -980cm / s^2입니다.

 

Figure 1a. Simulation of flow over a step.
Figure 1b. Grid used in simulation.

Because some turbulence was expected to develop in the pool to the left of the overflow, a turbulence model (the Renormalization Group or RNG model) was used in the simulation. Subsequent simulations without a turbulence model produced very similar results, which is not too surprising since most of the important elements of the flow are smooth (i.e., non-turbulent) inflow, overflow and outflow streams.

월류 왼쪽에 있는 웅덩이에 난류가 발생 할 것으로 예상 되었기 때문에, 시뮬레이션에서는 난류 모델 (the Renormalization Group, 즉 RNG 모델)을 사용했습니다.  그 후, 난류 모델을 사용하지 않고 한 시뮬레이션에서도 비슷한 결과를 얻을 수 있었지만, 이것은 그다지 놀라운 일이 아닙니다.  흐름의 중요한 요소의 대부분은 매끄러운 (즉 난류가 아닌) 유입, 유출, 월류 때문입니다.

The simulation region shown in Fig. 1b is 170cm wide and 100cm high and has been subdivided into a grid of equal sized rectangular cells consisting of 80 cells in the horizontal direction and 60 cells in the vertical direction, for a total of 4800 cells. This grid is used as the basis for finite-difference approximations of the governing differential equations of fluid dynamics (the Navier-Stokes equations). The number and size of the grid cells was chosen with the goal of capturing the smallest expected features of the flow. The number can be easily increased or decreased if the results seem to warrant some adjustment. In fact, it is often a good idea to repeat a simulation with a change of resolution to make sure that the solution is not too sensitive to such changes.

그림 1b 시뮬레이션 영역은 폭 170cm, 높이 100cm에 가로 80 개, 세로 60 개, 총 4800 개의 셀로 구성되는 같은 크기의 사각형 셀의 격자로 세분화되어 있습니다.  이 격자는 유체 역학의 지배 미분 방정식 (나비에 – 스토크스 방정식)의 유한 차분 근사의 기초로 사용됩니다.  격자 셀의 수와 크기는 흐름 속에서 예측되는 최소의 특성을 파악하는 목적으로 선택되었습니다.  결과를보고 어떤 조정이 필요하다고 생각되는 경우는 숫자를 쉽게 늘리거나 줄일 수 있습니다.  사실, 해상도를 바꾸어 시뮬레이션을 반복하여 계산이 그러한 변화에 영향을 많이 들어 있지 않은지 확인하는 것이 좋습니다.

The left boundary was a specified velocity boundary (also with a specified fluid height). The right boundary was an outflow boundary where all flow quantities have a zero gradient normal to the boundary to encourage a uniform outflow. The top and bottom boundaries are rigid walls, while in the third direction the boundaries were treated as planes of symmetry (i.e., walls with zero viscous drag). The surface of the step was also treated as a free-slip boundary.

왼쪽의 경계는 지정된 속도 경계입니다 (유체의 높이도 지정).  오른쪽의 경계는 유출 경계에서 모든 유량이 경계에 수직 제로 기울기이며, 균일 한 유출이 촉진됩니다.  상하 경계는 단단한 벽으로 세 번째 방향의 경계는 대칭면 (점성 저항 제로의 벽)으로 처리되었습니다.  계단 낙차형상의 표면도 자유-미끄럼(free slip) 경계로 처리되었습니다.

Initial conditions could have been set to roughly approximate the expected flow arrangement, but since the flow configuration is one of the things that one would like to compute, especially for situations where one doesn’t know what the distribution of fluid is likely to be, a simpler approach is needed. Because a transient flow simulator was used for this example a simple initial condition could be defined that consisted of just a block of fluid on top of the step, Fig. 1a with the same horizontal velocity and height assigned to the left boundary. The simulation then followed the development of the steady flow, which occurs after about 8.0s. The simulation was run out to a time of 10.0s to assure that steady conditions had been reached. Figure 2 shows two intermediate times; 2.b at 0.2s and 2.c at 0.5s plus the final time in 2.d at 10.0s.

초기 조건은 예측되는 흐름의 배열을 대략적으로 근사하도록 설정할 수 있었지만, 흐름의 구성은 계산하고 싶은 것 중 하나이기 때문에 유체가 어떻게 분포되는지를 모르는 경우에는 간단한 방법이 필요합니다.  이 예제에서는 비정상 흐름 시뮬레이터를 사용했기 때문에 그림 1a의 계단 낙차형상에 유체의 블록만 있고 왼쪽 경계의 같은 수평 속도와 높이가 할당된 간단한 초기 조건을 정의할 수 있습니다.  시뮬레이션은 이후 정상 흐름으로 발전하고 있지만, 이것은 약 8.0 초 후에 발생합니다.  시뮬레이션은 정상 상태에 도달 한 것을 보장하기 위해, 10.0 초의 시간까지 실행되었습니다.  그림 2는 중간 시간을 두 보여줍니다.  도 2b는 0.2 초, 그림 2c는 0.5 초 시점에서 그림 2d는 마지막 10.0 초 시점을 보여줍니다.

 

Figures 2a-2d. Simulation times of 0.0, 0.2, 0.5 and 10.0s.

It should be noted that what starts as a single, connected free surface changes to two independent free surfaces (upper and lower nappe surfaces) after the fluid strikes the bottom. No difficulties are experienced with this separation of the flow into portions flowing to the left and right of the impact point on the bottom boundary. This will be discussed at further length in the next section.

처음에는 단일 결합하고 있는 자유 표면이었던 것이 액체가 바닥에 충돌한 후 2 개의 독립적인 자유 표면 (상하 스냅 표면)으로 변화하는 것에 주목하십시오.  아래 경계의 충격점의 좌우로 흐름이 분리되도 문제는 없습니다.  이에 대해서는 다음 섹션에서 자세히 설명합니다.

Comparisons between experiment and simulation are given in the following table and are in excellent agreement.

실험과 시뮬레이션의 비교는 다음 표와 같으며 매우 잘 일치하고 있습니다.

Comparison Table Experimental Results Simulation Results
Outflow Height/Step Height 0.094 0.094
Pool Height/Step Height 0.41 0.41
Angle of Nappe at Bottom 57° 59°
Energy Loss/Initial Energy 0.29 0.296

In view of these results it might be expected that a considerable amount of computational time would be required to achieve such accuracy. In fact, the total cpu time on a desktop Pentium 4, 3.20GHz computer was only 88s. Such a short computational time requires explanation and that is the purpose of the following sections.

이러한 결과를 고려하면이 같은 정밀도를 달성하려면 상당한 계산시간이 필요할 것으로 생각될지도 모릅니다.  그러나 실제로는 Pentium 4, 3.20GHz의 데스크톱 컴퓨터의 총 CPU 시간은 단 88 초였습니다. 계산시간이 너무 짧은 것은 설명이 필요하며, 이것은 다음 섹션의 목적입니다.

 

Figures 2a-2d. Simulation times of 0.0, 0.2, 0.5 and 10.0s.

Why the VOF Technique Works Well / VOF 법이 적합한 이유

There are a few general concepts about computational methods and the VOF technique in particular that can be used to gain an understanding of how and why VOF works so efficiently.

VOF 법의 구조와 그것이 매우 효율적인 방법인 이유를 이해하기 위해 다양한 계산법 중에서도 특히 VOF 법에 대한 몇 가지 기본 개념을 나타냅니다.

Basic Theory

All numerical methods must use some simplification to reduce a fluid flow problem to a finite set of numerical values that can then be manipulated using elementary arithmetical operations. A typical procedure for approximating a continuous fluid by a discrete set of numerical values is to subdivide the space occupied by the fluid into a grid consisting of a set of small, often rectangular “bricks.” Within each element an averaging process is applied to obtain representative element values for the fluid’s pressure, density, velocity and temperature.

모든 수치해석 방법에서 흐름의 문제를 단순하게 산술 계산하도록 유한의 수치 세트로 단순화해야합니다.  연속 유체를 이산화된 수치 세트에 근사하기 위해서 일반적으로 사용되는 것이 유체가 차지하는 공간을 격자로 분할하는 방법입니다.  이 격자는 일반적으로 다수의 작은 직사각형의 블록(요소)로 구성됩니다.  이러한 각 요소에 대해 평균화 처리를 실시함으로써 그 요소의 유체의 압력, 밀도, 속도 및 온도의 대표 값을 얻을 수 있습니다.

Simple equations can be devised to approximate how each element’s values interact with neighboring elements over time. For instance, the density of an element can only change when there is a net flow of mass exchanged between an element and its neighbors (i.e., conservation of mass). The material velocity that carries mass between elements is computed from the conservation of momentum principal, usually expressed in the form of the Navier-Stokes equations, which uses the pressures and viscous stresses acting between neighboring elements to approximate the changing fluid velocities in the elements.

간단한 수식을 사용해, 어느 시간에 걸친 각 요소 값과 인접한 요소의 상호 작용을 근사할 수 있습니다.  예를 들어, 요소의 밀도는 그 요소와 인접 요소 사이에서 (질량 보존에 의한) 질량 유량이 교환된 경우에만 변경됩니다.  요소 사이에서 질량이 교환되는 물질의 속도는 운동량 보존 법칙에 의해 계산되며 일반적으로 나비에-스토크스 방정식으로 표현됩니다.  나비에-스토크스 방정식은 인접한 요소 사이에 작용하는 압력과 점성 응력을 이용하여 요소에서 변화하는 유체 속도를 근사합니다.

This idea of an element interacting with its neighbors is essentially what is meant by a partial differential equation; that is, evaluating the effects of small changes caused by the variation in quantities nearby. Partial differential equations are typically derived in engineering text books as the limit of approximations made with small control volumes whose sizes are then reduced to infinitesimal values. In a numerical simulation the same thing is done except that the control volume sizes cannot be taken to the limit because that would require too many elements to keep track of. In practice, the goal is to use enough elements to resolve the phenomena of interest, and no more, so that computing times are kept to a minimum.

이러한 요소와 인접 요소 사이의 상호 작용에 따른 아이디어는 편미분 방정식 근방의 양의 변화에 의해 생기는 작은 변화의 효과를 평가하는 것과 본질적으로 동일합니다.  공학계의 교과서에서 파생된 작은 컨트롤 볼륨을 사용하여 그 크기를 무한대까지 작게 한 근사치의 극한으로 편미분 방정식이 유도됩니다.  수치 시뮬레이션에서도 같은 방식을 취하고 있지만, 요소 수가 너무 많으면 추적이 어렵게  되어 컨트롤 볼륨의 크기를 최대한 작게 만들 수 없습니다.  실제 시뮬레이션 현상을 해결하는데 충분하고 계산 시간을 최소한으로 억제 할 수 있는 요소수를 설정하는 것이 목표입니다.

Arithmetical operations associated with an element generally involve only simple addition, subtraction, multiplication and division. For instance, the change of mass in an element involves the addition and subtraction of mass entering and leaving through the faces of the element over a fixed interval of time. A simulation requires that these operations be done for thousands or even millions of elements as well as repeated for many small time intervals. Computers are ideal for performing these types of repetitive operations very rapidly.

요소에 사용되는 연산은 기본적으로 더하기, 빼기, 곱하기 및 나누기만 포함된 간단한 것입니다.  예를 들어, 요소의 질량의 변화는 일정한 시간 간격에 걸쳐 요소의 측면에서 유입 및 유출된 질량의 가산 및 감산에서 구할 수 있습니다. 그러나 시뮬레이션에서는 이러한 연산을 수천, 때로는 수백만 요소에 대해 매우 짧은 시간 간격에 대해 반복 계산해야합니다.  따라서 이러한 반복 계산의 고속 처리는 컴퓨터가 적합합니다.

Simulating fluid motion with free surfaces introduces the complexity of having to deal with solution regions whose shapes are changing. A convenient way to deal with this is to use the Volume of Fluid (VOF) technique described next.

자유 표면을 수반하는 유체 운동의 시뮬레이션에서는 형상이 변화하는 계산 영역을 다루어야합니다.  이 복잡성에 대응할 수있는 분석 방법이 아래에서 설명하는 VOF 법입니다.

The VOF Concept

The VOF technique is based on the idea of recording in each grid cell the fractional portion of the cell volume that is occupied by liquid. Typically the fractional volume is represented by the quantity F. Because it is a fractional volume, F must have a value between 0.0 and 1.0.

VOF 법은 각 격자 셀의 체적 중 액체가 차지하는 비율, 즉 체적 점유율을 기록한다는 생각에 근거합니다.  일반적으로 부피 점유율은  F로 표시됩니다.  F는 부피 점유율이기 때문에 값이 취할 수있는 범위는 0.0 ~ 1.0입니다.

In interior regions of liquid the value of F would be 1.0, while outside of the liquid, in regions of gas (air for example), the value of F is zero. The location of a free surface is where F changes from 0.0 to 1.0. Thus, any element having an F value lying between 0.0 and 1.0 must contain a surface.

액체 내부의 영역에서는 F 값은 1.0이 액체의 외부, 즉 (공기 등) 기체 영역에서 F 값은 0입니다.  F 값이 0.0과 1.0 사이에서 변화하는 장소가 자유 표면이 존재하는 위치입니다.  즉 0.0보다 크고 1.0보다 작은 F 값을 가지는 요소는 반드시 표면을 가지고 있습니다.

It is important to emphasize that the VOF technique does not directly define a free surface, but rather defines the location of bulk fluid. It is for this reason that fluid regions can coalesce or break up without causing computational difficulties. Free surfaces are simply a consequence of where the fluid volume fraction passes from 1.0 to 0.0. This is a very desirable feature that makes the VOF technique applicable to just about any kind of free surface problem.

여기서 유의해야 할 것은 VOF 법에서 자유 표면을 직접적으로 정의하는 것이 아니라 벌크 유체의 위치를 정의한다는 점입니다.  이렇게하면 계산상의 어려움을 초래하지 않고 유체 영역을 결합 또는 분할 할 수 있습니다.  자유 표면은 단순히 유체의 체적 점유율이 1.0과 0.0 사이에서 변화하는 장소로 정의됩니다.  이것은 자유 표면을 수반하는 거의 모든 문제에 적용 할 수 VOF 법의 뛰어난 특징이기도합니다.

Another important feature of the VOF technique is that it records the location of fluid by assigning a single numerical value (F) to each grid element. This is completely consistent with the recording of all other fluid properties in an element such as pressure and velocity components by their average values.

또한 격자의 각 요소에 단일 수치 (F)를 할당하여 유체의 위치를 기록 할 수 있는 점도 VOF 법의 중요한 특징입니다.  이것은 평균값을 기준으로 압력과 속도 등 다른 모든 유체 물성의 기록과 완전히 일치합니다.

Some Details of the VOF Technique

 

Figure 3. Surface in 1D column of elements.

For accuracy purposes it is desirable to have a way to locate a free surface within an element. Considering the F values in neighboring elements can easily do this. For example, imagine a one-dimensional column of elements in which a portion of the column is filled with liquid, Fig. 3. The liquid surface is in an element in the central region of the column, which will be referred to as the surface element. Because we assume the values of F must be either 0.0 or 1.0, except in the surface element, we can use this to locate the exact position of the surface. First a test is made to see if the surface is a top or bottom surface. If the element above the surface element is empty of liquid, the surface must be a top surface. It the element above is full of liquid then, of course, the surface is a bottom surface. For a top surface we compute its exact location as lying above the bottom edge of the surface element by a distance equal to F times the vertical size of the element. A bottom surface is similarly located a distance equal to F times the vertical size of the element below the top edge of the surface element. Locating the surface within an element in this way follows from the definition of F as a fractional volume of liquid in the element.

정확도를 위해 요소 내에 자유 표면을 배치하는 방법을 갖는 것이 바람직합니다. 인접 요소의 F 값을 고려하면 이를 쉽게 할 수 있습니다.  예를 들어, 열의 일부에 액체가 충전되어있는 1 차원 요소를 상상하십시오 (그림 3).  액체의 표면은 열 중앙 영역의 요소에 있습니다.  이것을 표면 요소라고합니다.  여기에서는 표면 요소를 제외하고 F 값은 0.0 또는 1.0이어야한다고 가정하고 있기 때문에 이를 사용하여 표면의 정확한 위치를 파악할 수 있습니다.  우선, 표면이 표면 또는 바닥을 확인하는 테스트를 실시합니다.  표면요소에 대해 액체가 없을 경우에는 표면으로 간주합니다.  위의 요소에 액체가 들어있는 경우는 물론, 그 표면은 바닥입니다.  윗면에 관해서는 정확한 위치는 표면 요소의 아래쪽에서 위쪽으로 요소의 세로 크기를 F 배 한 거리에있는로 계산합니다.  바닥도 마찬가지로 표면 요소의 상단에서 아래로, 요소의 세로 크기를 F 배 한 거리에 있습니다.  이 방법에 의한 요소의 표면 위치의 특정은 요소 내의 액체의 부피 점유율로 F를 정의한 후에 합니다.

Calculating surface locations in one-dimensional columns is simple, accurate and requires very little arithmetic. In two and three dimensional situations, however, computing a location is a little more complicated because there is a continuous range of surface orientations possible within a surface cell. Nevertheless, dealing with this is not difficult. A two-dimensional example, Fig. 4, will illustrate a simple way to not only compute the location of the surface, but also to get a good idea of its slope and curvature.

1 차원 열의 표면 위치 계산은 간단하고 정확하며 계산이 거의 필요없습니다. 그러나 2 차원 및 3 차원의 경우 하나의 표면 셀에 연속적인 표면 방향이 존재할 가능성이 있기 때문에 위치 계산은 조금 복잡해집니다.  그럼에도 불구하고 이를 취급하는 것은 어렵지 않습니다.  그림 4의 이차원의 예는 표면의 위치를 계산할 뿐만 아니라 경사와 곡률도 이해할 수 있는 쉬운 방법을 보여줍니다.

 

Figure 4. Surface in 2D grid of elements.

As in the one-dimensional case, it is first necessary to find the approximate orientation of the surface by testing the neighboring elements. In Fig. 4 the outward normal would be closest to the upward direction because the difference in neighboring values in that direction is larger than in any other direction. Next, local heights of the surface are computed in element columns that lie in the approximate normal direction. For the two-dimensional case in Fig. 4 these heights are indicated by arrows. Finally, the height in the column containing the surface element gives the location of the surface in that element, while the other two heights can be used to compute the local surface slope and surface curvature.

1 차원의 경우처럼 먼저 인근 요소를 테스트하여 표면의 대략적인 방향을 찾아야합니다.  그림 4는 바깥 쪽의 법선이 상승 방향에 가장 가깝게 됩니다.  이것은 그 방향 밖의 값의 차이가 다른 방향보다 크기 때문입니다.  그럼 거의 수직으로 있는 요소 열에서 표면의 국소적인 높이가 계산됩니다.  그림 4의 2 차원의 경우에는 이러한 높이가 화살표로 표시되어 있습니다.  마지막으로, 표면 요소를 포함하는 컬럼의 높이에 따라 그 요소의 표면의 위치를 확인합니다.  다른 2 개의 높이를 사용하면 국소적인 표면 경사와 표면 곡률을 계산할 수 있습니다.

In three-dimensions the same procedure is used although column heights must be evaluated for nine columns around the surface element. Although a little more computation is needed, it consists primarily of simple summations in the columns and then sums and differences of column heights for evaluating the slope and curvature. Based on this discussion, the reader should now see how the fractional fluid volume can be used to quickly and easily evaluate all the information needed to define free surfaces.

3 차원에서도 동일한 절차를 사용하지만, 표면 요소의 주위에 있는 9개의 열에 대해 열 높이를 요구해야합니다.  필요한 계산은 조금 더 걸리지만, 주된 내용은 열의 간단한 덧셈과 경사와 곡률을 추구하는 열의 높이의 합과 차이가 있습니다.  이 토론을 토대로, 이제 자유 표면을 정의하는 데 필요한 모든 정보를 빠르고 쉽게 평가하기 위해 부분 유체 체적을 사용하는 방법을 알아야합니다.

There are two remaining issues to deal with. One issue is that a simulation like that in Figs. 1 and 2 is only solving for the fluid dynamics in regions where there is fluid. This is another reason for the computational efficiency of the VOF method. The region occupied by fluid in the flow over a step problem is much less than half of the open region in the computational grid. If it were necessary to also solve for the flow of gas surrounding the liquid, then considerably more computational time would be required. In order to perform solutions only in the liquid, however, it is necessary to specify boundary conditions at free surfaces. These conditions are the vanishing of the tangential stress and application of a normal pressure at the surface that equals the pressure of the gas.

다루어야 할 문제가 앞으로 2 개 남아 있습니다.  하나는 그림 1 및 2와 같은 시뮬레이션은 유체가 존재하는 영역에는 유체 역학만으로 해결합니다.  이것은 VOF 법의 계산 효율이 높은 또 하나의 이유입니다.  계단 형상의 낙하류의 문제로 유체가 차지하는 영역은 계산 격자의 오픈 공간의 절반 이하입니다.  액체를 둘러싼 기체의 흐름을 계산할 필요가 있다면 필요한 계산 시간이 크게 늘어납니다.  그러나 액체만으로 계산을 할 경우 자유 표면 경계 조건을 지정해야합니다.  이 조건은 접선 응력의 소실과 기체의 압력에 동일한 표준 압력을 표면에 추가하는 것입니다.

A second issue is that movement and deformation of a free surface must be computed by solving for the fraction of fluid variable, F, as it moves with the fluid. Because the variable F is discontinuous (i.e., primarily 0.0 or 1.0) some care must be taken to maintain this discontinuity as it moves through a computational grid. In the VOF method, special advection algorithms are used for this purpose.

두 번째 문제는 자유 표면이 유체와 함께 움직일 때의 움직임과 변형을 유체 점유율 변수 F를 구함으로써 계산해야 한다는 것입니다.  변수 F는 불연속 (주로 0.0 또는 1.0)이기 때문에 계산 격자를 이동할 때 이 불연속성이 유지되도록주의해야합니다.  VOF 법은이 목적으로 특수 이류(advection) 알고리즘이 사용되고 있습니다.

Illustration of Free-Surface Tracking by VOF Technique

Figure 6a is an illustration of how well this works; the fluid volume fraction is colored uniformly in each grid element to represent its value in that element. The free surface is sharply defined nearly everywhere. Only in the lowest and narrowest part of the nappe is there any noticeable loss of a sharp fluid fraction distribution, Fig. 5b. This was expected because in this region the nappe is less than three elements in thickness and this allows some of the smaller F values associated with partially filled surface elements to mix in with the central element, which should have a value of 1.0. For computational purposes this doesn’t really matter because the simulation method treats elements interior to the liquid as though they are pure liquid elements.

그림 6a는 이것의 적합 여부를 보여줍니다.  유체의 체적 점유율은 격자 요소마다 균일하게 분류되고 그 요소의 값을 나타냅니다.  자유 표면은 거의 모든 곳에서 선명하게 정의되어 있습니다.  스냅의 가장 낮은 가장 좁은 부분에만 선명한 유체 분포의 손실을 확인할 수 있습니다 (그림 5b).  이것은 예상대로입니다.  이 영역에서는 스냅의 두께는 3 가지 요소보다 작고, 따라서 부분 충전된 표면 요소에 연결된 작은 F 값이 어떤 중심 요소 (값 1.0)에 혼입하기 때문입니다.  계산 목적으로 이 것은 별로 문제가 되지 않습니다.  이 시뮬레이션 방법은 액체 내부의 요소는 순수한 액체 성분과 같은 방식으로 처리되기 때문입니다.

It should also be pointed out that in the region shown in Fig. 5b turbulence and air entrainment are observed in actual experiments. Thus, the appearance of fluid fraction values a little less than unity is somewhat realistic. This is not entirely accidental because the intersection of jet of liquid with a pool, which is responsible for turbulence and air entrainment, is also responsible for the “entrainment” of fluid fraction values into the interior of the liquid.

그림 5b에 나타내는 영역에서는 실제 실험에서 난류 및 공기 혼입이 관찰된 것도 지적해 두지 않으면 안됩니다.  따라서 유체 점유율의 값을 1보다 조금 작게 보이는 것이 다소 현실적입니다.  이것은 전혀 의외라는 것은 없습니다.  난류와 공기 유입을 담당하는 풀의 액체 제트의 교점은 난류와 공기 유입의 원인이 되지만, 유체 점유율 값(fluid fraction values )은 액체 내부에 “유입” 원인이 되기 때문에 실수가 아닙니다.

 

Figure 5a (left): Fluid fraction values in elements, showing sharpness of surface definition. Figure 5b (right): Close up of fluid fraction values where the overflow hits bottom.

Summary

At first it may seem somewhat magical that a computer can simply perform repeated arithmetic operations on arrays of numbers and produce a realistic simulation of a complex, time-dependent, fluid dynamics problem. It was the purpose of this discussion to explain an approach that does this with relatively elementary procedures.

Using a simple, but non-trivial, hydraulic flow example it has been demonstrated that computational simulations can produce detailed results in excellent agreement with physical measurements. It has been further demonstrated that the simulation, which was based on the Volume of Fluid (VOF) technique, uses simple approximation methods that are both accurate and efficient.

Clearly, real world examples involving complex hydraulic structures such as those used in hydroelectric power stations, must consume more than the few seconds of computational time used in our example to obtain useful results. Nevertheless, those results can be generated in reasonable times (both man and computer) and contain a richness of detail rarely possible in physical experiments. For examples visit our water and environmental application pages. In addition, the ability to easily test the influence of just about any kind of change in geometry, flow condition or fluid property is another powerful reason to employ simulations. Current software and hardware for hydraulic flow simulations offer a significant cost advantage over traditional physical modeling.

처음에는 컴퓨터가 단순히 반복적인 산술 연산을 수행하고, 복잡하고 시간에 의존적인 유체 역학 문제에 대해, 현실적인 시뮬레이션을 할 수 있다는 것이 다소 마술처럼 보일 수 있습니다. 이 논의의 목적은 비교적 기본적인 절차로 이를 수행하는 접근법을 설명하는 것입니다.

간단하지만 사소한 유압 흐름 예제를 사용하여 계산된 시뮬레이션이 물리적인 측정 결과와 매우 일치하는 세부 결과를 생성 할 수 있음이 입증되었습니다. VOF (Volume of Fluid) 기술을 기반으로 한 시뮬레이션은 정확하고, 매우 효율적인 것이 추가로 입증되었습니다.

분명하게, 수력 발전소에서 사용되는 것과 같은 복잡한 유압 구조와 관련된 실제 예는 유용한 결과를 얻기 위해서는 이 예에서 사용되는 몇 초 이상의 많은 계산 시간을 소비해야합니다. 그럼에도 불구하고 이러한 결과는 합리적인 시간 (사람과 컴퓨터 모두)에서 수행 될 수 있으며, 실제 실험에서는 거의 불가능한 세부 사항들을 포함합니다. 또한, 지오메트리, 유동 조건 또는 유체 특성의 거의 모든 종류의 변화의 영향을 쉽게 테스트 할 수있는 능력은 시뮬레이션을 사용하는 또 다른 강력한 이유입니다. 기술의 발전에 따라 hydraulic flow 시뮬레이션을 위한 현재 소프트웨어 및 하드웨어는 기존의 물리적 모델링에 비해 상당한 비용 이점을 제공합니다.

Postscript

The first detailed description of the VOF method was in 1981 by C.W. Hirt and B.D. Nichols, J. Comp. Phys., 39, p.201. All simulations appearing in this article were performed with the commercial software package FLOW-3D developed by Flow Science, Inc. This program uses an enhanced variant of the VOF concept called TruVOF.

FLOW-3D/MP Features List

FLOW-3D/MP Features

FLOW-3D/MP v6.1 은 FLOW-3D v11.1 솔버에 기초하여 물리 모델, 특징 및 그래픽 사용자 인터페이스가 동일합니다. FLOW-3D v11.1의 새로운 기능은 아래 파란색으로 표시되어 있으며 FLOW-3D/MP v6.1 에서 사용할 수 있습니다. 새로운 개발 기능에 대한 자세한 설명은 FLOW-3D v11.1에서 새로운 기능을 참조하십시오.

Meshing & Geometry

  • Structured finite difference/control volume meshes for fluid and thermal solutions
  • Finite element meshes in Cartesian and cylindrical coordinates for structural analysis
  • Multi-Block gridding with nested, linked, partially overlapping and conforming mesh blocks
  • Fractional areas/volumes (FAVOR™) for efficient & accurate geometry definition
  • Mesh quality checking
  • Basic Solids Modeler
  • Import CAD data
  • Import/export finite element meshes via Exodus-II file format
  • Grid & geometry independence
  • Cartesian or cylindrical coordinates
Flow Type Options
  • Internal, external & free-surface flows
  • 3D, 2D & 1D problems
  • Transient flows
  • Inviscid, viscous laminar & turbulent flows
  • Hybrid shallow water/3D flows
  • Non-inertial reference frame motion
  • Multiple scalar species
  • Two-phase flows
  • Heat transfer with phase change
  • Saturated & unsaturated porous media
Physical Modeling Options
  • Fluid structure interaction
  • Thermally-induced stresses
  • Plastic deformation of solids
  • Granular flow
  • Moisture drying
  • Solid solute dissolution
  • Sediment transport and scour
  • Cavitation (potential, passive tracking, active tracking)
  • Phase change (liquid-vapor, liquid-solid)
  • Surface tension
  • Thermocapillary effects
  • Wall adhesion
  • Wall roughness
  • Vapor & gas bubbles
  • Solidification & melting
  • Mass/momentum/energy sources
  • Shear, density & temperature-dependent viscosity
  • Thixotropic viscosity
  • Visco-elastic-plastic fluids
  • Elastic membranes & walls
  • Evaporation residue
  • Electro-mechanical effects
  • Dielectric phenomena
  • Electro-osmosis
  • Electrostatic particles
  • Joule heating
  • Air entrainment
  • Molecular & turbulent diffusion
  • Temperature-dependent material properties
  • Spray cooling
Flow Definition Options
  • General boundary conditions
    • Symmetry
    • Rigid and flexible walls
    • Continuative
    • Periodic
    • Specified pressure
    • Specified velocity
    • Outflow
    • Grid overlay
    • Hydrostatic pressure
    • Volume flow rate
    • Non-linear periodic and solitary surface waves
    • Rating curve and natural hydraulics
    • Wave absorbing layer
  • Restart from previous simulation
  • Continuation of a simulation
  • Overlay boundary conditions
  • Change mesh and modeling options
  • Change model parameters
Thermal Modeling Options
  • Natural convection
  • Forced convection
  • Conduction in fluid & solid
  • Fluid-solid heat transfer
  • Distributed energy sources/sinks in fluids and solids
  • Radiation
  • Viscous heating
  • Orthotropic thermal conductivity
  • Thermally-induced stresses
Turbulence Models
  • RNG model
  • Two-equation k-epsilon model
  • Two-equation k-omega model
  • Large eddy simulation
Metal Casting Models
  • Thermal stress & deformations
  • Iron solidification
  • Sand core blowing
  • Sand core drying
  • Permeable molds
  • Solidification & melting
  • Solidification shrinkage with interdendritic feeding
  • Micro & macro porosity
  • Binary alloy segregation
  • Thermal die cycling
  • Surface oxide defects
  • Cavitation potential
  • Lost-foam casting
  • Semi-solid material
  • Core gas generation
  • Back pressure & vents
  • Shot sleeves
  • PQ2 diagram
  • Squeeze pins
  • Filters
  • Air entrainment
  • Temperature-dependent material properties
  • Cooling channels
  • Fluid/wall contact time
Numerical Modeling Options
  • TruVOF Volume-of-Fluid (VOF) method for fluid interfaces
  • First and second order advection
  • Sharp and diffuse interface tracking
  • Implicit & explicit numerical methods
  • GMRES, point and line relaxation pressure solvers
  • User-defined variables, subroutines & output
  • Utilities for runtime interaction during execution
Fluid Modeling Options
  • One incompressible fluid – confined or with free surfaces
  • Two incompressible fluids – miscible or with sharp interfaces
  • Compressible fluid – subsonic, transonic, supersonic
  • Stratified fluid
  • Acoustic phenomena
  • Mass particles with variable density or diameter
Shallow Flow Models
  • General topography
  • Raster data interface
  • Subcomponent-specific surface roughness
  • Wind shear
  • Ground roughness effects
  • Laminar & turbulent flow
  • Sediment transport and scour
  • Surface tension
  • Heat transfer
  • Wetting & drying
Advanced Physical Models
  • General Moving Object model with 6 DOF–prescribed and fully-coupled motion
  • Rotating/spinning objects
  • Collision model
  • Tethered moving objects (springs, ropes, mooring lines)
  • Flexing membranes and walls
  • Porosity
  • Finite element based elastic-plastic deformation
  • Finite element based thermal stress evolution due to thermal changes in a solidifying fluid
  • Combusting solid components
Chemistry Models
  • Stiff equation solver for chemical rate equations
  • Stationary or advected species
Porous Media Models
  • Saturated and unsaturated flow
  • Variable porosity
  • Directional porosity
  • General flow losses (linear & quadratic)
  • Capillary pressure
  • Heat transfer in porous media
  • Van Genunchten model for unsaturated flow
Discrete Particle Models
  • Massless marker particles
  • Mass particles of variable size/mass
  • Linear & quadratic fluid-dynamic drag
  • Monte-Carlo diffusion
  • Particle-Fluid momentum coupling
  • Coefficient of restitution or sticky particles
  • Point or volumetric particle sources
  • Charged particles
  • Probe particles
Two-Phase & Two-Component Models
  • Liquid/liquid & gas/liquid interfaces
  • Variable density mixtures
  • Compressible fluid with a dispersed incompressible component
  • Drift flux
  • Two-component, vapor/non-condensable gases
  • Phase transformations for gas-liquid & liquid-solid
  • Adiabatic bubbles
  • Bubbles with phase change
  • Continuum fluid with discrete particles
  • Scalar transport
  • Homogeneous bubbles
  • Super-cooling
Coupling with Other Programs
  • Geometry input from Stereolithography (STL) files – binary or ASCII
  • Direct interfaces with EnSight®, FieldView® & Tecplot® visualization software
  • Finite element solution import/export via Exodus-II file format
  • PLOT3D output
  • Neutral file output
  • Extensive customization possibilities
  • Solid Properties Materials Database
Data Processing Options
  • State-of-the-art post-processing tool, FlowSight™
  • Batch post-processing
  • Report generation
  • Automatic or custom results analysis
  • High-quality OpenGL-based graphics
  • Color or B/W vector, contour, 3D surface & particle plots
  • Moving and stationary probes
  • Measurement baffles
  • Arbitrary sampling volumes
  • Force & moment output
  • Animation output
  • PostScript, JPEG & Bitmap output
  • Streamlines
  • Flow tracers
User Conveniences
  • Active simulation control (based on measurement of probes)
  • Mesh generators
  • Mesh quality checking
  • Tabular time-dependent input using external files
  • Automatic time-step control for accuracy & stability
  • Automatic convergence control
  • Mentor help to optimize efficiency
  • Change simulation parameters while solver runs
  • Launch and manage multiple simulations
  • Automatic simulation termination based on user-defined criteria
  • Run simulation on remote servers using remote solving
Multi-Processor Computing

FLOW-3D Features

The features in blue are newly-released in FLOW-3D v12.0.

Meshing & Geometry

  • Structured finite difference/control volume meshes for fluid and thermal solutions
  • Finite element meshes in Cartesian and cylindrical coordinates for structural analysis
  • Multi-Block gridding with nested, linked, partially overlapping and conforming mesh blocks
  • Conforming meshes extended to arbitrary shapes
  • Fractional areas/volumes (FAVOR™) for efficient & accurate geometry definition
  • Closing gaps in geometry
  • Mesh quality checking
  • Basic Solids Modeler
  • Import CAD data
  • Import/export finite element meshes via Exodus-II file format
  • Grid & geometry independence
  • Cartesian or cylindrical coordinates

Flow Type Options

  • Internal, external & free-surface flows
  • 3D, 2D & 1D problems
  • Transient flows
  • Inviscid, viscous laminar & turbulent flows
  • Hybrid shallow water/3D flows
  • Non-inertial reference frame motion
  • Multiple scalar species
  • Two-phase flows
  • Heat transfer with phase change
  • Saturated & unsaturated porous media

Physical Modeling Options

  • Fluid structure interaction
  • Thermally-induced stresses
  • Plastic deformation of solids
  • Granular flow
  • Moisture drying
  • Solid solute dissolution
  • Sediment transport and scour
  • Sludge settling
  • Cavitation (potential, passive tracking, active tracking)
  • Phase change (liquid-vapor, liquid-solid)
  • Surface tension
  • Thermocapillary effects
  • Wall adhesion
  • Wall roughness
  • Vapor & gas bubbles
  • Solidification & melting
  • Mass/momentum/energy sources
  • Shear, density & temperature-dependent viscosity
  • Thixotropic viscosity
  • Visco-elastic-plastic fluids
  • Elastic membranes & walls
  • Evaporation residue
  • Electro-mechanical effects
  • Dielectric phenomena
  • Electro-osmosis
  • Electrostatic particles
  • Joule heating
  • Air entrainment
  • Molecular & turbulent diffusion
  • Temperature-dependent material properties
  • Spray cooling

Flow Definition Options

  • General boundary conditions
    • Symmetry
    • Rigid and flexible walls
    • Continuative
    • Periodic
    • Specified pressure
    • Specified velocity
    • Outflow
    • Outflow pressure
    • Outflow boundaries with wave absorbing layers
    • Grid overlay
    • Hydrostatic pressure
    • Volume flow rate
    • Non-linear periodic and solitary surface waves
    • Rating curve and natural hydraulics
    • Wave absorbing layer
  • Restart from previous simulation
  • Continuation of a simulation
  • Overlay boundary conditions
  • Change mesh and modeling options
  • Change model parameters

Thermal Modeling Options

  • Natural convection
  • Forced convection
  • Conduction in fluid & solid
  • Fluid-solid heat transfer
  • Distributed energy sources/sinks in fluids and solids
  • Radiation
  • Viscous heating
  • Orthotropic thermal conductivity
  • Thermally-induced stresses

Numerical Modeling Options

  • TruVOF Volume-of-Fluid (VOF) method for fluid interfaces
  • Steady state accelerator for free-surface flows
  • First and second order advection
  • Sharp and diffuse interface tracking
  • Implicit & explicit numerical methods
  • Immersed boundary method
  • GMRES, point and line relaxation pressure solvers
  • User-defined variables, subroutines & output
  • Utilities for runtime interaction during execution

Fluid Modeling Options

  • One incompressible fluid – confined or with free surfaces
  • Two incompressible fluids – miscible or with sharp interfaces
  • Compressible fluid – subsonic, transonic, supersonic
  • Stratified fluid
  • Acoustic phenomena
  • Mass particles with variable density or diameter

Shallow Flow Models

  • General topography
  • Raster data interface
  • Subcomponent-specific surface roughness
  • Wind shear
  • Ground roughness effects
  • Manning’s roughness
  • Laminar & turbulent flow
  • Sediment transport and scour
  • Surface tension
  • Heat transfer
  • Wetting & drying

Turbulence Models

  • RNG model
  • Two-equation k-epsilon model
  • Two-equation k-omega model
  • Large eddy simulation

Advanced Physical Models

  • General Moving Object model with 6 DOF–prescribed and fully-coupled motion
  • Rotating/spinning objects
  • Collision model
  • Tethered moving objects (springs, ropes, breaking mooring lines)
  • Flexing membranes and walls
  • Porosity
  • Finite element based elastic-plastic deformation
  • Finite element based thermal stress evolution due to thermal changes in a solidifying fluid
  • Combusting solid components

Chemistry Models

  • Stiff equation solver for chemical rate equations
  • Stationary or advected species

Porous Media Models

  • Saturated and unsaturated flow
  • Variable porosity
  • Directional porosity
  • General flow losses (linear & quadratic)
  • Capillary pressure
  • Heat transfer in porous media
  • Van Genunchten model for unsaturated flow

Discrete Particle Models

  • Massless marker particles
  • Multi-species material particles of variable size and mass
  • Solid, fluid, gas particles
  • Void particles tracking collapsed void regions
  • Non-linear fluid-dynamic drag
  • Added mass effects
  • Monte-Carlo diffusion
  • Particle-fluid momentum coupling
  • Coefficient of restitution or sticky particles
  • Point or volumetric particle sources
  • Initial particle blocks
  • Heat transfer with fluid
  • Evaporation and condensation
  • Solidification and melting
  • Coulomb and dielectric forces
  • Probe particles

Two-Phase & Two-Component Models

  • Liquid/liquid & gas/liquid interfaces
  • Variable density mixtures
  • Compressible fluid with a dispersed incompressible component
  • Drift flux with dynamic droplet size
  • Two-component, vapor/non-condensable gases
  • Phase transformations for gas-liquid & liquid-solid
  • Adiabatic bubbles
  • Bubbles with phase change
  • Continuum fluid with discrete particles
  • Scalar transport
  • Homogeneous bubbles
  • Super-cooling
  • Two-field temperature

Coupling with Other Programs

  • Geometry input from Stereolithography (STL) files – binary or ASCII
  • Direct interfaces with EnSight®, FieldView® & Tecplot® visualization software
  • Finite element solution import/export via Exodus-II file format
  • PLOT3D output
  • Neutral file output
  • Extensive customization possibilities
  • Solid Properties Materials Database

Data Processing Options

  • State-of-the-art post-processing tool, FlowSight™
  • Batch post-processing
  • Report generation
  • Automatic or custom results analysis
  • High-quality OpenGL-based graphics
  • Color or B/W vector, contour, 3D surface & particle plots
  • Moving and stationary probes
  • Visualization of non-inertial reference frame motion
  • Measurement baffles
  • Arbitrary sampling volumes
  • Force & moment output
  • Animation output
  • PostScript, JPEG & Bitmap output
  • Streamlines
  • Flow tracers

User Conveniences

  • Active simulation control (based on measurement of probes)
  • Mesh generators
  • Mesh quality checking
  • Tabular time-dependent input using external files
  • Automatic time-step control for accuracy & stability
  • Automatic convergence control
  • Mentor help to optimize efficiency
  • Units on all variables
  • Custom units
  • Component transformations
  • Moving particle sources
  • Change simulation parameters while solver runs
  • Launch and manage multiple simulations
  • Automatic simulation termination based on user-defined criteria
  • Run simulation on remote servers using remote solving
  • Copy boundary conditions to other mesh blocks

Multi-Processor Computing

  • Shared memory computers
  • Distributed memory clusters

FlowSight

  • Particle visualization
  • Velocity vector fields
  • Streamlines & pathlines
  • Iso-surfaces
  • 2D, 3D and arbitrary clips
  • Volume render
  • Probe data
  • History data
  • Vortex cores
  • Link multiple results
  • Multiple data views
  • Non-inertial reference frame
  • Spline clip