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

The Korean Society of Mechanical Engineers (대한기계학회)
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Numerical Analysis of Three-dimensional Sloshing Flow Using Least-square and Level-set Method

최소자승법과 Level-set 방법을 적용한 3차원 슬로싱 유동의 수치해석

  • Jeon, Byoung Jin (Integrative Cardiovascular Imaging Research Center, Yonsei Univ.) ;
  • Choi, Hyoung Gwon (Dept. of Mechanical and Automotive Engineering, Seoul Nat'l Univ. of Science and Technology)
  • 전병진 (연세대학교 심장융합영상연구센터) ;
  • 최형권 (서울과학기술대학교 기계자동차공학과)
  • Received : 2017.06.18
  • Accepted : 2017.08.28
  • Published : 2017.11.01
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Abstract

In this study, a three-dimensional least-square, level-set-based two-phase flow code was developed for the simulation of three-dimensional sloshing problems using finite element discretization. The code was validated by solving some benchmark problems. The proposed method was found to provide improved results against other existing methods, by using a coarser mesh. The results of the numerical experiments conducted during the course of this study showed that the proposed method was both robust and accurate for the simulation of three-dimensional sloshing problems. Using a substantially coarse grid, historical results of the dynamic pressure at a selected position corresponded with existing experimental data. The pressure history with a finer grid was similar to that of a coarse grid; however, a fine grid provided higher peak pressures. The present method could be extended to the analysis of a sloshing problem in a complex geometrical configuration using unstructured meshes owing to the features of FEM.

본 연구에서는 유한요소 최소자승법에 기반한 level-set 방정식의 이류방정식과 재초기화 방정식의 이산화기법을 3차원 슬로싱 문제에 적용한 코드를 개발하고, 그 성능을 평가한다. 사용된 수치기법은 정렬 격자계를 이용하여 다양한 표준 예제들에 대하여 검증이 수행되었다. 제안된 방법은 상대적으로 성긴 격자계에서 다른 기법들에 비하여 개선된 해를 줌을 확인하였다. 두 가지의 격자계에 대하여 수행한 3차원 슬로싱 해석은 상당히 성긴 격자계에서도 압력의 시간 이력이 실험결과와 잘 일치함을 보여주며, 조밀한 격자계에서는 최대압력의 크기가 크게 예측이 됨을 확인하였다. 한편, 본 연구에서 개발한 기법은 유한요소법의 특성에 의해서 비정렬 격자계를 이용하여 복잡한 형상을 가지는 용기 내의 슬로싱 문제의 해석으로 바로 확장할 수 있다.

Keywords

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. 39, pp. 201-225. https://doi.org/10.1016/0021-9991(81)90145-5
  2. Unverdi, S. O. and Tryggavason, G., 1992, "A Front Tracking Method for Viscous, Incompressible, Multifluid Flows," J. Comput. Phys., 100, pp. 25-37. https://doi.org/10.1016/0021-9991(92)90307-K
  3. Ryskin, G. and Leal, L. G., 1984, "Numerical Solution of Free-boundary Problems in Fluid Mechanics. Part 1. The Finite-difference Technique," J. Fluid. Mech., Vol. 148, pp. 1-17. https://doi.org/10.1017/S0022112084002214
  4. Sussman, M., Smereka, P. and Osher, S., 1994, "A Level Set Approach for Computing Solutions to Incompressible Two-phase Flow," J. Comput. Phys., Vol. 114, pp. 146-159. https://doi.org/10.1006/jcph.1994.1155
  5. Ushijima, S., 1998, "Three-dimensional Arbitrary Lagrangian-Eulerian Numerical Prediction Method for Non-linear Free Surface Oscillation," Int J. Numer. Meth. Fluids, Vol. 26, pp. 605-623. https://doi.org/10.1002/(SICI)1097-0363(19980315)26:5<605::AID-FLD668>3.0.CO;2-W
  6. Lee, S. H., 2004, "A Validation Study for Tank Sloshing using a Navier-Stokes Solver," Proc. 23rd International conference on offshore mechanics and arctic engineering, Vancouver, British Columbia, Canada, June 2004.
  7. Lohner, R., Yang, C. and Onate E., 2006, "On the Simulation of Flows with Violent Free Surface Motion," Comput. Methods. Appl. Engrg., Vol. 195, pp. 5597-5620. https://doi.org/10.1016/j.cma.2005.11.010
  8. Kim, Y., Shin, Y. and Lee, K. H., 2004, "Numerical Study on Slosh-induced Impact Pressures on Threedimensional Prismatic Tanks," Applied Ocean Research, Vol. 26, pp. 213-226. https://doi.org/10.1016/j.apor.2005.03.004
  9. Chen, B. and Nokes, R., 2005, "Time-independent Finite Difference Analysis of Fully Non-linear and Viscous Fluid Sloshing in a Rectangular Tank," J. Comput. Phys., Vol. 209, pp. 47-81. https://doi.org/10.1016/j.jcp.2005.03.006
  10. Choi, H. G., 2008, "Finite Element Analysis of Free Surface Flows using Least Square/level-set Formulation," Proc. 5th International conference on computational fluid dynamics, Seoul, Korea, July 2008.
  11. Choi, H. G., Choi, H. and Yoo, J. Y., 1997, "A Fractional 4 Step Finite Element Formulation of the Unsteady Incompressible Navier-Stokes Equations using SUPG and Linear Equal-order Element Methods," Comput. Methods. Appl. Engrg., Vol. 143, pp. 333-348. https://doi.org/10.1016/S0045-7825(96)01156-5
  12. Cho, M. H., Choi, H. G. and Yoo, J. Y., 2008, "Study on the Solution of Reinitialization Equation for Level Set Method in the Simulation of Incompressible Twophase Flows," Trans. Korean Soc. Mech. Eng. B, Vol. 32, No. 10, pp. 754-760. https://doi.org/10.3795/KSME-B.2008.32.10.754
  13. Choi, H. G., 2012, "A Least-square Weighted Residual Method for Level Set Formulation," Int J. Numer. Meth. Fluids, Vol. 68, No. 7, pp. 887-904. https://doi.org/10.1002/fld.2585
  14. Lin, C., Lee, H., Lee, T. and Weber, L. J., 2005, "A Level Set Characteristic Galerkin Finite Element Method for Free Surface Flows," Int J. Numer. Meth. Fluids, Vol. 49, pp. 521-547. https://doi.org/10.1002/fld.1006
  15. LeVeque, R. J., 1996, "High-resolution Conservative Algorithms for Advection in Incompressible Flow," SIAM Journal on Numerical Analysis, Vol. 33, pp. 627-665. https://doi.org/10.1137/0733033
  16. Yue, W., Lin, C. L. and Patel, V. C., 2003, "Numerical Simulation of Unsteady Multidimensional Free Surface Motions by Level Set Method," Int. J. Numer. Methods Fluid, Vol. 42, pp. 853-884. https://doi.org/10.1002/fld.555
  17. Martin, J. C. and Moyce, W. J., 1952, "An Experimental Study of the Collapse of Liquid Columns on a Rigid Horizontal Plane," Philos. Trans. Roy. Soc. London Ser. A, Math. Phys. Sci., Vol. 244, pp. 312-324. https://doi.org/10.1098/rsta.1952.0006
  18. Tanaka, Y., Ando, T. and Miyamoto, T., 2000, "Experimental Study on Sloshing Load Measured by Panel-type Pressure Gauge," Proc. 74th General Meeting of Ship Research Institute, Ship Research Institute, Tokyo, Japan, June 2000, pp.137-142.