Journal of Mechanical Science and Technology

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지

Finite Element Analysis of Fluid Flows with Moving Boundary

  • Cha, Kyung-Se (Graduate School, Department of mechanical Engineering, Chonnam National University) ;
  • Park, Jong-Wook (School of Mechanical and Automotive Engineering, Sunchon National University) ;
  • Park, Chan-Guk (Professor, Department of Mechanical Engineering, Chonnam National University)
  • Published : 2002.05.01
Download PDF
⟨ Previous Next ⟩

Abstract

The objective of the present study is to analyze the fluid flow with moving boundary using a finite element method. The algorithm uses a fractional step approach that can be used to solve low-speed flow with large density changes due to intense temperature gradients. The explicit Lax-Wendroff scheme is applied to nonlinear convective terms in the momentum equations to prevent checkerboard pressure oscillations. The ALE (Arbitrary Lagrangian Eulerian) method is adopted for moving grids. The numerical algorithm in the present study is validated for two-dimensional unsteady flow in a driven cavity and a natural convection problem. To extend the present numerical method to engine simulations, a piston-driven intake flow with moving boundary is also simulated. The density, temperature and axial velocity profiles are calculated for the three-dimensional unsteady piston-driven intake flow with density changes due to high inlet fluid temperatures using the present algorithm. The calculated results are in good agreement with other numerical and experimental ones.

Keywords

References

  1. Akin, J. E., 1994, Finite Elements for Analysis and Design, Academic Press Limited
  2. Choi, H. G., 1996, 'A Study on Segregated Finite Element Algorithms for the Navier-Stokes Equations,' Ph. D. Thesis, Seoul National University
  3. Codina, R., Vazquez. M. and Zienkiewicz. O. C., 1998, 'A General Algorithm for Compressible and Incompressible Flows. Part III: The Semi-Implicit Form,' Internat. J. Numer. Methods In Fluids, Vol. 27, pp. 13-32 https://doi.org/10.1002/(SICI)1097-0363(199801)
  4. Donea, J., Giuliani. S, Laval. H. and Quartapelle, L., 1982, 'Finite Element Solution of the Unsteady Navier-Stokes Equation by a Fractional Step Method,' Comput. Methods Apply. Mech. Engrg. Vol. 30, pp.349-388 https://doi.org/10.1016/0045-7825(82)90086-X
  5. Folch, A., Vazquez, M., Codina, R. and Marti. J., 1999, 'A Fractional-Step Finite-Element Method for the Navier-Stokes Equations Applied to Magma-Chamber withdrawal,' Computer & Geosciences, Vol. 25, pp.263-275 https://doi.org/10.1016/S0098-3004(98)00164-2
  6. Ghia, U., Ghia, K. N. and, Shin, C. T., 1982, 'High-Re Solutions for Incompressible Flow Using the Navier-Stokes Equations and a Multigrid Method,' J. Compo Phys., Vol. 48, pp.387-411 https://doi.org/10.1016/0021-9991(82)90058-4
  7. Hendriana, D. and Bathe, K. J., 2000, 'On a Parabolic Quadrilateral Finite Element for Compressible Flow,' Comput. Methods Appl. Mech. Engrg. Vol. 186, pp. 1-22 https://doi.org/10.1016/S0045-7825(99)00102-4
  8. Hirt, C. W., Cook, J. L. and Butler, T. D., 1970, 'A Lagrangian Method for Calculating the Dynamics of an Incompressible Fluid with Free Surface,' J. Comput. Phys., Vol. 5, pp. 103-124 https://doi.org/10.1016/0021-9991(70)90055-0
  9. Hirt, C. W., Amsden, A. A. and Cook, J. L., 1974, 'An Arbitrary Lagrangian-Eulerian Computing Method for All Flow Speeds,' J. Comput. Phys., Vol. 14, pp.227-253 https://doi.org/10.1016/0021-9991(74)90051-5
  10. 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
  11. Ikegawa, M., Kaiho, M. and Kato, C., 1994, 'FEM/FDM Composite Scheme for Viscous Incompressible Flow Analysis,' Computer Methods in Applied Mechanics and Engineering, Vol. 112, pp. 149-163 https://doi.org/10.1016/0045-7825(94)90023-X
  12. Kim., C. J., Ro, S. T. and Lee, J. S., 1993, 'An Effective Algorithm to Solve Moving Boundary Problems in Axisymmetric Coordinate Systems,' Transactions of KSME, Vol. 17, No.3, pp.670-679
  13. Pereira, J. C. F., 1986, 'Experimentelle und numerische Untersuchungen station rer and instation rer laminarer Str mungen mit Abl sung,' Dr.-Ing.-Dissertation, University of Erlangen-Nurnburg, Germany
  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. 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
  16. Ramaswany, B., 1988, 'Finite Element Solution for Advection and Natural Convection flow,' Comput. Fluids, Vol. 16, pp. 349-388 https://doi.org/10.1016/0045-7930(88)90023-0
  17. Soulaimani, A. and Saad, Y., 1998, 'An arbitrary Lagrangian-Eulerian Finite Element Method for Solving Three-Dimensional Free Flows,' Comput. Methods Appl. Mech. Engrg., Vol. 162, pp.79-106 https://doi.org/10.1016/S0045-7825(97)00330-7
  18. Stroll, H., Durst, F., Peric, M., Pereira, J. C. F. and Scheuerer, G., 1993, 'Study of Laminar, Unsteady Piston-Cylinder Flows,' ASME Journal of Fluids Engineering, Vol. 115, pp.687-693 https://doi.org/10.1115/1.2910200