DEVELOPMENT OF AN UNSTRUCTURED HYBRID MESH FLOW SOLVER FOR 3-D STEADY/UNSTEADY INCOMPRESSIBLE FLOW SIMULATIONS

삼차원 정상/비정상 비압축성 유동해석을 위한 비정렬 혼합격자계 기반의 유동해석 코드 개발

  • 정문승 (한국과학기술원 항공우주공학과 대학원) ;
  • 권오준 (한국과학기술원 항공우주공학과)
  • Published : 2008.06.30

Abstract

An unstructured hybrid mesh flow solver has been developed for the simulation of three-dimensional steady and unsteady incompressible flow fields. The incompressible Navier-Stokes equations with an artificial compressibility method were discretized by using a node-based finite-volume method. For the unsteady time-accurate computation, a dual-time stepping method was adopted to satisfy a divergence-free flow field at each physical time step. An implicit time integration method with local time stepping was implemented to accelerate the convergence in the pseudo-time sub-iteration procedure. The one-equation Spalart-Allmaras turbulence model has been adopted to solve high-Reynolds number flow fields. The flow solver was parallelized to minimize the CPU time and to overcome the computational overhead. This method has been applied to calculate steady and unsteady flow fields around submarine configurations and a 3-D infinite cylinder. Validations were made by comparing the predicted results with those of experiments or other numerical results. It was demonstrated that the present method is efficient and robust for the prediction of steady and unsteady incompressible flow fields.

Keywords

References

  1. 1991, Volpe, G., "On the Use of Accuracy of Compressible Flow Codes at Low Mach Numbers," AIAA 91-1662
  2. 1965, Harlow, F. H. and Welch, J. E., "Numerical Calculation of Time-dependent Viscous Incompressible Flow of Fluid with Free Surface," Physics of Fluids, Vol.8, No.12, pp.2182-2189 https://doi.org/10.1063/1.1761178
  3. 1967, Chorin, A. J., "A Numerical Method for Solving Incompressible Viscous Flow Problems," Journal of Computational Physics, Vol.2, No.12, pp.12-26 https://doi.org/10.1016/0021-9991(67)90037-X
  4. 1991, Rogers, S. E., Kwak, D. and Kiris, C., "Steady and Unsteady Solutions of the Incompressible Navier-Stokes Equations," AIAA Journal, Vol.29, No.4, pp.603-610 https://doi.org/10.2514/3.10627
  5. 2000, Hyams, D. G., "An Investigation of Parallel Implicit Solution Algorithms for Incompressible Flows on Unstructured Topologies," Ph.D Dissertation, Mississippi State University
  6. 2004, Shin, S., Kim, C. K. and Bai, K. J., "Numerical Simulation on an Interaction of a Vortex Street with an Elliptic Leading Edge Using an Unstructured Grid," International Journal for Numerical Methods in Fluids, Vol.44, No.3, pp.331-346 https://doi.org/10.1002/fld.643
  7. 2005, Kallinderis, Y. and Ahn, H. T., "Incompressible Navier-Stokes Method with General Hybrid Meshes," Journal of Computational Physics, Vol.210, No.1, pp.75-108 https://doi.org/10.1016/j.jcp.2005.04.002
  8. 1985, Merkle, C. L. and Choi, D., "Application of Time-iterative Schemes to Incompressible Flow," AIAA Journal, Vol.23, No.10, pp.1518-1524 https://doi.org/10.2514/3.9119
  9. 1996, Anderson, W. K., Rausch, R. D. and Bonhaus, D. L., "Implicit/Multigrid Algorithms for Incompressible Turbulent Flows on Unstructured Grids," Journal of Computational Physics, Vol.128, No.2, pp.391-408 https://doi.org/10.1006/jcph.1996.0219
  10. 2007, 정문승, 권오준, "비정렬 혼합 격자계 기반의 삼차원 점성 유동 해석코드 개발," 한국항공우주학회지, 제 35권, 제8호, pp.677-684 https://doi.org/10.5139/JKSAS.2007.35.8.677
  11. 1996, Kallinderis, Y., "A 3-D Finite-Volume Method for the Navier-Stokes Equations with Adaptive Hybrid Grids," Applied Numerical Mathematics, Vol.20, No.4, pp.387-406 https://doi.org/10.1016/0168-9274(95)00102-6
  12. 1999, Nakahashi, K., Sharov, D., Kano, S. and Kodera, M., "Applications of Unstructured Hybrid Grid Method to High-Reynolds Number Viscous Flows," International Journal for Numerical Methods in Fluids, Vol.31, No.1, pp.97-111 https://doi.org/10.1002/(SICI)1097-0363(19990915)31:1<97::AID-FLD957>3.0.CO;2-D
  13. 1979, Thomas, P. D. and Lombard, C. K., "Geometric Conservation Law and Its Application to Flow Computations on Moving Grids," AIAA Journal, Vol.17, No.10, pp.1030-1037 https://doi.org/10.2514/3.61273
  14. 1992, Spalart, P. R. and Allmaras, S. R., "A One-Equation Turbulent Model for Aerodynamic Flows," AIAA 92-0439
  15. 1995, Bruner, W. S. C., "Geometric Properties of Arbitrary Polyhedra in Terms of Face Geometry," AIAA Journal, Vol.33, No.7, p.1350 https://doi.org/10.2514/3.12556
  16. 1991, Taylor, L. K. and Whitfield, D. L., "Unsteady Three-dimensional Incompressible Euler and Navier-Stokes Solver for Stationary and Dynamic Grids," AIAA 91-1650
  17. 2000, Haselbacher, A. and Blazek, J., "Accurate and Efficient Discretization of Navier-Stokes Equations on Mixed Grids," AIAA Journal, Vol.38, No.11, pp.2094-2102 https://doi.org/10.2514/2.871
  18. 1997, Mathur, S. R. and Murthy, J. Y., "A Pressure-based Method for Unstructured Meshes," Numerical Heat Transfer, Part B, Vol.31, No.2, pp.195-215 https://doi.org/10.1080/10407799708915105
  19. 1994, Anderson, W. K. and Bonhaus, D. L., "An Impicit Upwind Algorithm for Computing Turbulent Flows on Unstructured Grids," Computers & Fluid, Vol.23, No.1, pp.1-21 https://doi.org/10.1016/0045-7930(94)90023-X
  20. http://www.cs.umn.edu/~karypis
  21. http://www.unix.mcs.anl/gov/mpi/
  22. 1989, Groves, N. C., Huang, T. T. and Chang, M. S., "Geometric Characteristics of DAPRA SUBOFF Models(DTRC Model Nos. 5470 and 5471)," DTRC/SHD-1298-01, David Taylor Research Center
  23. 1997, Chesnakas, C. J. and Simpson, R. L., "Detailed investigation of the three-dimensional separation about a 6:1 prolate spheroid," AIAA Journal, Vol.35, No.6, pp.990-999 https://doi.org/10.2514/2.208
  24. 1992, Huang, T. T., Liu, H. L., Groves, N. C., Forlini, T. J., Blanton, J. N. and Gowing, S., "Measurement of Flows Over an Axisymmetric Body with Various Appendages," Nineteenth Symposium on Naval Hydrodynamics, Seoul, Korea
  25. 2001, Kiris, C. and Kwak, D., "Numerical Solution of Incompressible Navier-Stokes Equations Using a Fractional-step Approach," Computers & Fluids, Vol.30, No.7-8, pp.829-851 https://doi.org/10.1016/S0045-7930(01)00031-7
  26. 1982, Randon, R. H., "NACA0012 Oscillatory and Transient Pitching, Compendium of Unsteady Aerodynamic Measurement," AGARD Rept. 702
  27. www.centaursoft.com
  28. 2007, Hosder, S. and Simpson, R. L., "Experimental Investigation of Unsteady Flow Simulation on a Maneuvering Axisymmetric Body," Journal of Aircraft, Vol.44, No.4, pp.1286-1295 https://doi.org/10.2514/1.26804