Journal of computational fluids engineering (한국전산유체공학회지)

Korean Society of Computational Fluids Engineering (한국전산유체공학회)
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GAS-LIQUID TWO-PHASE HOMOGENEOUS MODEL FOR CAVITATING FLOW -Part II. HIGH SPEED FLOW PHENOMENA IN GAS-LIQUID TWO-PHASE MEDIA

캐비테이션 유동해석을 위한 기- 2상 국소균질 모델 -제2보: 기-액 2상 매체중의 고속유동현상

  • Shin, B.R. (Institute of Flow Informatics) ;
  • Park, S. (Dept. of Ocean Engineering, Korea Maritime and Ocean Univ.) ;
  • Rhee, S.H. (Dept. of Naval Architecture and Ocean Engineering, Seoul Nat'l Univ.)
  • Received : 2014.09.11
  • Accepted : 2014.09.23
  • Published : 2014.09.30
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Abstract

A high resolution numerical method aimed at solving cavitating flow was proposed and applied to gas-liquid two-phase shock tube problem with arbitrary void fraction. The present method with compressibility effects employs a finite-difference 4th-order Runge-Kutta method and Roe's flux difference splitting approximation with the MUSCL TVD scheme. The Jacobian matrix from the inviscid flux of constitute equation is diagonalized analytically and the speed of sound for the two-phase media is derived by eigenvalues. So that the present method is appropriate for the extension of high order upwind schemes based on the characteristic theory. By this method, a Riemann problem for Euler equations of one dimensional shock tube was computed. Numerical results of high speed flow phenomena such as detailed observations of shock and expansion wave propagations through the gas-liquid two-phase media and some data related to computational efficiency are made. Comparisons of predicted results and solutions at isothermal condition are provided and discussed.

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References

  1. 2000, Gopalan, S. and Katz, J., "Flow Structure and modeling Issues in the Closure Region of Attached Cavitation," Phys. of Fluids, Vol.12, No.4, pp.895-911. https://doi.org/10.1063/1.870344
  2. 1994, Chen, Y. and Heister, S.D., "A Numerical Treatment for Attached Cavitation," ASME J. Fluids Eng., Vol.116, No.3, pp.613-618. https://doi.org/10.1115/1.2910321
  3. 1998, Grogger, H.A. and Alajbegovic, A., "Calculation of Cavitating Flows in Venturi Geometries Using Two Fluid Model," ASME FEDSM 98-5295, Washington D.C.
  4. 1998, Shin, B.R. and Ikohagi, T., "A Numerical Study of Unsteady Cavitating Flows," Proc., 3rd Int., Sympo. on Cavitation, Vol.2, pp.301-306.
  5. 2000, Ventikos, Y. and Tzabiras, G., "A Numerical Method for the Simulation of Steady and Unsteady Cavitating Flows," Computers & Fluids, Vol.29, No.1, pp.63-88. https://doi.org/10.1016/S0045-7930(98)00061-9
  6. 1998, Merkle, C.L., Feng, J.Z. and Buelow, P.E.O., "Computational Modeling of the Dynamics of Sheet Cavitation," Proc., 3rd Int., Sympo. on Cavitation, Vol.2, pp.307-311.
  7. 2000, Kunz, R.F., Boger, D.A. and Stinebring, D.R., "Modeling Hydrodynamic Nonequilibrium in Cavitating Flows," Computers & Fluids, Vol.29, No.8, pp.849-875. https://doi.org/10.1016/S0045-7930(99)00039-0
  8. 1996, Chen, Y. and Heister, S.D., "A Preconditioned Navier-Stokes Method for Two-Phase Flows with Application to Cavitation Prediction," ASME J. Fluids Eng., Vol.118, No.1, pp.172-178. https://doi.org/10.1115/1.2817497
  9. 2001, Singhal, A.K., Athavale, M.M., Li, H. and Jiang, Yu., "Mathematical Basis and Validation of the Full Cavitation Model," ASME FEDSM-2001, New Orleans, Louisiana.
  10. 2003, Shin, B.R., Iwata, Y. and Ikohagi, T., "A Numerical Study of Unsteady Cavitating Flows Using a Homogenous Equilibrium Model," Computational Mechanics, Vol.30, No.5, pp.388-395. https://doi.org/10.1007/s00466-003-0414-7
  11. 2003, Iga, Y., Nohmi, M., Goto, A., Shin, B.R. and Ikohagi, T., "Numerical Study of Sheet Cavitation Break-off Phenomenon on a Cascade Hydrofoil," ASME J. Fluid Engng., Vol.125, No.4, pp.2002-2010.
  12. 2004, Shin, B.R., Yamamoto, S. and Yuan, X., "Application of Preconditioning Method to Gas-Liquid Two-Phase Flow Computations," ASME J. Fluid Engng., Vol.126, No.4, pp.605-612. https://doi.org/10.1115/1.1777230
  13. 2004, Yamamoto, S. and Shin, B.R., "A Numerical Method for Natural Convection and Heat Conduction around and in a Horizontal Circular Pipe," Int'l J. of Heat and Mass Transfer, Vol.47-12, pp.5781-5792. https://doi.org/10.1016/j.ijheatmasstransfer.2004.06.039
  14. 2008, Seo, J.H., Moon, Y.J. and Shin, B.R., "Prediction of Cavitating Flow Noise by Direct Numerical Simulation," J. Comput. Phys., Vol.227, No.13, pp.6511-6531. https://doi.org/10.1016/j.jcp.2008.03.016
  15. 2010, Dittakavi, N., Chunekar, A. and Frankel, S., "Large Eddy Simulation of Turbulent-Cavitation Interactions in a Venturi Nozzle," ASME J. Fluid Engng., Vol.132, No.12, pp.121301-1-11. https://doi.org/10.1115/1.4001971
  16. 2007, Shin, B.R., "Gas-Liquid Two-Phase Homogeneous Model for Cavitating Flow," J. of Comput. Fluids Eng., Vol.12, No.2, pp.53-62.
  17. 1971, Chen, H.T. and Collins, R., "Shock Wave Propagation Past on Ocean Surface," J. Comput. Phys., Vol.7, pp.89-101. https://doi.org/10.1016/0021-9991(71)90051-9
  18. 1979, van Leer, B., "Towards the Ultimate Conservative Difference Scheme V. A Second-Order Sequel to Godunov's Method," J. Comput. Phys., Vol.32, pp.101-136. https://doi.org/10.1016/0021-9991(79)90145-1
  19. 1981, Roe, P.L., "Approximate Riemann Solvers, Parameter Vectors and Difference Scheme," J. Comp. Phys., Vol.43, pp.357-372. https://doi.org/10.1016/0021-9991(81)90128-5
  20. 1981, Jameson, A., Schmidt, W. and Turkel, E., "Numerical Simulation of the Euler Equations by Finite Volume Method Using Runge-Kutta Stepping Schemes," AIAA paper 81-1259.
  21. 2003, Shin, B.R., "A Stable Numerical Method Applying a TVD Scheme for Incompressible Flow," AIAA J., Vol.41, No.1, pp.49-55. https://doi.org/10.2514/2.1912
  22. 1998, Laney, C.B., Computational Gasdynamics, Cambridge Univ. Press, Cambridge.
  23. 1984, John, J.E.A., Gas Dynamics, Allyn and Bacon, Inc., Boston.
  24. 1996, Quirk, J.J. and Karni, S., "On the Dynamics of a Shock-Bubble Interaction," J. Fluid Mech., Vol.318, pp.129-163. https://doi.org/10.1017/S0022112096007069
  25. 1994, Karni, S., "Multicomponent Flow Calculations by a Consistent Primitive Algorithm," J. Comput. Phys., Vol.112, pp.31-43. https://doi.org/10.1006/jcph.1994.1080