Journal of Korean Society of Coastal and Ocean Engineers (한국해안해양공학회지)

Korean Society of Coastal and Ocean Engineers (한국해안·해양공학회)
권호 표지

Level Set Method Applied on Pseudo-compressibility Method for the Analysis of Two-phase Flow

Pseudo-compressibility 방법에서 이상유동 해석을 위한 Level Set방법의 적용

  • Ihm Seung-Won (School of Mechanical and Aerospace Engineering, Seoul National University) ;
  • Kim Chongam (School of Mechanical and Aerospace Engineering, Seoul National University) ;
  • Shim Jae-Seol (Coastal and Harbour Engineering Research Division, KORDI) ;
  • Lee Dong-Young (Coastal and Harbour Engineering Research Division, KORDI)
  • 임승원 (서울대학교 기계항공공학부) ;
  • 김종암 (서울대학교 기계항공공학부) ;
  • 심재설 (한국해양연구원 연안,항만공학연구본부) ;
  • 이동영 (한국해양연구원 연안,항만공학연구본부)
  • Published : 2005.09.01
Download PDF
⟨ Previous Next ⟩

Abstract

In order to analyze incompressible two-phase flow, Level Set method was applied on pseudo-compressibility formulation. Level Set function is defined as a signed distance function from the phase interface, and gives the information of the each phase location and the geometric data to the flow. In this study, Level Set function transport equation was coupled with flow conservation equations, and owing to pseudo-compressibility technique we could solve the resultant vector equation iteratively. Two-phase flow analysis code was developed on general curvilinear coordinate, and numerical tests of bubble dynamics and surging wave problems demonstrate its capability successfully.

Level Set방법을 사용하여 액체와 기체의 서로 다른 상을 함께 해석하는 연구를 수행하였다. Level Set함수는 상의 경계면에서부터 부호를 갖는 거리함수로 정의되며,계산 격자에서 함수 값의 부호에 따라 각 상을 구분하고 물성치를 부여한다. 본 논문에서는 비압축성 유체의 보존식에 Level Set함수의 이동식을 연계하여 이상유동을 모사하는 지배방정식을 구성하였으며, 이를 pseudo-compressibility 방법으로 함께 풀었다. 이 때 다양한 문제에 적용이 가능하도록 일반 곡선 좌표계에서 식을 유도하였고, 수치해석을 위한 행렬식들을 함께 유도하였다. 개발된 해석 코드를 표면장력이 있는 기포 동역학 문제와 수중익에 의한 파도 발생 문제에 적용하여 타당한 결과를 얻을 수 있었다.

Keywords

References

  1. 김도삼, 이광호, 김정수 (2002). 수중토과성구조물에 의한 쇄파를 수반한 파랑변형 및 유속장 해석. 한국해안.해양공학회지, 14(2). 171-181
  2. 노오현 (1992). 점성유체역학기초, 박영사
  3. 임승원, 최영심, 김종암 (2003). 다상 유동 해석을 위한 Level Set 기법과 volume of fluid 기법의 비교 연구. 한국항공우주학회 추계학술대회 논문집, KSAS03-2214
  4. 허동수, 김도삼 (2003). 경사수역에 설치된 잠제 주변의 유속장과 와의 발생에 대한 수치모의. 한국해안.해양공학회지, 15(3), 151-158
  5. Barone, M.F. (2003). Receptivity of compressible mixing layers. Ph.D. Dissertation, Stanford Univ., U.S.A
  6. Brackbill, J.U., Kothe, D.B. and Zemach, C. (1992). A continuum method for modeling surface tension. J. Comput. Phys., 100, 335-354 https://doi.org/10.1016/0021-9991(92)90240-Y
  7. Chang, Y.C., Hou, T.Y., Merrian, B. and Osher, S. (1996). A level set formulation of Eularian interface capturing methods for incompressible fluid flow. J. Comput. Phys., 124, 449-464 https://doi.org/10.1006/jcph.1996.0072
  8. Chorin, A.J. (1967). A numerical method for solving incompressible viscous tlow problems. J. Comput. Phys., 2, 12-26 https://doi.org/10.1016/0021-9991(67)90037-X
  9. Hirsch, C. (1989). Numerical Computation of Internal and External Flows. John Wiley & Sons, U.K
  10. Hirt, C. W. and Nichols, B.D. (1981). Volume of tluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys., 39, 201-225 https://doi.org/10.1016/0021-9991(81)90145-5
  11. Hoffmann, K.A. and Chiang, S.T. (2000). Computational Fluid Dynamics, 4th Ed. Engineering Education System, Kansas, U.S.A
  12. Liou, B.H. (2001). Calculation of nonlinear free surface waves with a fully-implicit adaptive-grid method. Ph.D. Dissertation, Princeton Univ., U.S.A
  13. Ok, H. (1993). Development of an incompressible NavierStokes solver and its application to the calculation of separated tlow. Ph.D. Dissertation, Univ. of Washington, U.S.A
  14. Osher, S. and Fedkiw, R.P. (2001). Level set methods: an overview and some recent results. J. Comput. Phys., 169,463-502 https://doi.org/10.1006/jcph.2000.6636
  15. Osher, S. and Sethian, J .A. (1988). Front propagation with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys., 79, 12-49 https://doi.org/10.1016/0021-9991(88)90002-2
  16. Rogers, S.E. and Kwak, D. (1990). Upwind differencing scheme for the time-accurate incompressible Navier-Stokes equations. AIAA J., 28(2), 253-262 https://doi.org/10.2514/3.10382
  17. Sussman, M., Smereka, P. and Osher, S. (1994). A level set approach for computing solutions to incompressible twophase tlow. J. Comput. Phys., 114, 146-159 https://doi.org/10.1006/jcph.1994.1155
  18. Unverdi, S.O. and Tryggvason, G. (1992). A front-tracking method for viscous, incompressible, multi-fluid tlows. J. Comput. Phys., 100, 25-37 https://doi.org/10.1016/0021-9991(92)90307-K
  19. Yoon, S. and Jameson, A. (1988). Lower-upper symmetric-Gauss-Seidel method for the Euler and Navier-Stokes equations. AIAA J., 26(9), 1025-1026 https://doi.org/10.2514/3.10007
  20. Zhu, J. and Sethian, J. (1992). Projection methods coupled to level set interface techniques. J. Comput. Phys., 102, 128-138 https://doi.org/10.1016/S0021-9991(05)80011-7