Transactions of the Korean Society of Mechanical Engineers B (대한기계학회논문집B)

The Korean Society of Mechanical Engineers (대한기계학회)
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A New VOF-based Numerical Scheme for the Simulation of Fluid Flow with Free Surface(II)-New Free Surface Tracking Algorithm and Its Verification-

자유 표면이 존재하는 유체 유동 해석을 위한 VOF 방법 기반의 새로운 수치 기법(II)-캐비터 충전 문제와 슬로싱 문제에의 응용-

  • Published : 2000.12.01
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Abstract

Finite element analysis of fluid flow with moving free surface has been carried out in two and tree dimensions. The new VOF-based numerical algorithm that has been proposed by the present authors was applied to several 2-D and 3-D free surface flow problems. The proposed free surface tracking scheme is based on two numerical tools that have been newly introduced by the present authots; the orientation vector to represent the free surface orientation in each cell and the baby-cell to determine the fluid volume flux at each cell boundary. The proposed numerical algorithm has been applied to 2-D and 3-D cavity filling and sloshing problems, which demonstrated versatility and effectiveness of the new free surface tracking scheme as well as the overall solution procedure. The proposed numerical algorithm resolved successfully the interacting free surface with each other. The simulated results demonstrated the applicability of proposed numerical algorithm to the practical problems of large free surface motion. Also, it has been demonstrated that the proposed free surface tracking scheme can be easily implemented in any irregular non-uniform grid systems and can be extended to the 3-D free surface flow problem without additional efforts.

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References

  1. Hirt, C. W. and Nichols, B. D., 1981, 'Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries,' J. Comput. Phys., Vol. 9, pp.201-225 https://doi.org/10.1016/0021-9991(81)90145-5
  2. 김민수, 신수호, 이우일, '자유 표면이 존재하는 유체 유동 해석을 위한 VOF 방법 기반의 새로운 수치 기법 (I) - 새로운 자유 표면 추적 알고리듬 및 검증,' 대한기계학회논문집 (제출)
  3. 김민수, 1998, '자유 표면이 존재하는 유체 유동의 유한 요소 해석,' 공학박사 학위논문, 서울대학교
  4. Dhatt, G., Gao, D. M. and Cheikh, A. B., 1990, 'A Finite Element Simulation of Metal flow in Moulds,' Int. J. Numer. Methods Engrg., Vol. 30, pp. 821-831 https://doi.org/10.1002/nme.1620300416
  5. Chan, K. S., Pericleous, K. and Cross, M., 1991, 'Numerical Simulation of Flows Encountered during Mold-Filling,' Appl. Math. Modelling, Vol. 15, pp. 624-631
  6. Minaie, B., Stelson, K. A. and Voller, V. R., 1991, 'Analysis of Flow Patterns and Solidification Phenomena in the Die Casting Process,' J. Engrg. Materials Technology, Vol. 113, pp. 296-302
  7. Usmani, A. S., Cross, J. T. and Lewis R. W., 1992, 'A Finite Element Model for the Simulations of Mould Filling in Metal Casting and the Associated Heat Transfer,' Int. J. Numer. Methods Engrg., Vol. 35, pp. 787-806 https://doi.org/10.1002/nme.1620350410
  8. Rice, A. B., 1993, 'Numerical Simulation of Mold Filling Process,' Ph.D. Thesis, Purdue University
  9. Swaminathan, C. R. and Voller, V. R., 1994, 'A Time-Implicit Filling Algorithm,' Appl. Math. Modelling, Vol. 18, pp. 101-108 https://doi.org/10.1016/0307-904X(94)90165-1
  10. Lewis, R. W., Usmani, A. S. and Cross, J. T., 1995, 'Efficient Mould Filling simulation in Casings by an Explicit finite Element Method,' Int. J. Numer. Methods Fluids, Vol. 20, pp. 493-506 https://doi.org/10.1002/fld.1650200606
  11. Shin, S. and Lee. W. I., 2000, 'Finite Element Analysis of Incompressible Viscous Flow with Moving Free Surface by Selective Volume of Fluid Method,' Int. J. Heat. Fluid Flow, Vol. 21, pp. 197-206 https://doi.org/10.1016/S0142-727X(99)00083-1
  12. 김우승, 권용복, 임익태, 1998, '암시적 VOF 방법을 이용한 주조공정의 충전과정 해석,' 대한기계학회논문집 B권, 22, 10, pp. 1401-1409
  13. 임익태, 김우승, 1998, '암시적 방법을 이용한 충전 알고리즘의 개발,' 대한기계학회논문집 B권,22, 1, pp. 104-112
  14. Ramaswamy, B., Kawahara, M. and Nakayama, T., 1986, 'Lagrangian Finite Element Method for the Analysis of Two-Dimensional sloshing Problems,' Int. J. Numer. Methods Fluids, Vol. 6, pp. 659-670 https://doi.org/10.1002/fld.1650060907
  15. Okamoto, T. and Kawahara, M., 1990, 'Two-Dimensional Sloshing Analysis by Lagrangian Finite Element Method,' Int. J. Numer. Methods Fluids, Vol. 11, pp. 453-477 https://doi.org/10.1002/fld.1650110502
  16. Ramaswamy, B. and Kawahara, M., 1987, 'Arbitrary Lagrangian-Eulerian Finite Element Method for Unsteady, Convective, Incompressible Viscous Free Surface Fluid Flow,' Int. J. Numer. Methods Fluids, Vol. 7, pp. 1053-1075 https://doi.org/10.1002/fld.1650071005
  17. Huerta, A. and Liu, W. K., 1988, 'Viscous flow with Large Free Surface Motion Comput. Methods,' Appl. Mech. Engrg., Vol. 69,pp. 277-324 https://doi.org/10.1016/0045-7825(88)90044-8
  18. Partom, I. S., 1987, 'Application of the VOF Method to the Sloshing of a Fluid in a Patially filled Cylindrical Container,' Int. J. Numer. Methods Fluids, Vol. 7,pp. 535-550 https://doi.org/10.1002/fld.1650070602
  19. Jun, L., and Spalding, D. B., 1988, 'Numerical Simulation of Flows with Moving Interfaces,' PhysicoChemical Hydrodynamics, Vol. 10, No. 5/6, pp. 625-637
  20. Kothe, D. B., Mjolsness, R. C. and Torret, M. D., 1994, 'RIPPLE: A Computer Program for Incompressible Flow with Free Surfaces,' Los Alamos National Laboratory Report, LA-12007-MS
  21. White, F. M., 1988, Fluid Mechanics, Second Edition, McGraw-Hill Book Company, New York