Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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ANALYSIS OF TWOPHASE FLOW MODEL EQUATIONS

  • Received : 2013.11.13
  • Accepted : 2013.12.10
  • Published : 2014.03.25
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Abstract

In this paper, we propose closures for multi-phase flow models, which satisfy boundary conditions and conservation constraints. The models governing the evolution of the fluid mixing are derived by applying an ensemble averaging procedure to the microphysical equations characterized by distinct phases. We consider compressible multi species multi-phase flow with surface tension and transport.

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References

  1. R. Abgrall and R. Saurel, Discrete equations for physical and numerical compresible multiphase mixtures, J. Comp. Phys., 186 (2003), 361-396. https://doi.org/10.1016/S0021-9991(03)00011-1
  2. R. Bird, W. Stewart, and E. Lightfoot, Transport Phenomena Second Edition, John Wiley & Sons, New York, 2002.
  3. Y. Chen, Two Phase Flow Analysis of Turbulent Mixing in the Rayleigh-Taylor Instability, PhD thesis, University at Stony Brook, 1995.
  4. Y. Chen, J. Glimm, D. H. Sharp, and Q. Zhang, A two-phase flow model of the Rayleigh-Taylor mixing zone, Phys. Fluids, 8(3) (1996), 816-825. https://doi.org/10.1063/1.868863
  5. B. Cheng, J. Glimm, D. Saltz, and D. H. Sharp, Boundary conditions for a two pressure two phase flow model, Physica D, 133 (1999), 84-105. https://doi.org/10.1016/S0167-2789(99)00100-1
  6. B. Cheng, J. Glimm, and D. H. Sharp, Multi-temperature multiphase flow model, ZAMP, 53 (2002), 211-238. https://doi.org/10.1007/s00033-002-8153-8
  7. B. Cheng, J. Glimm, D. H. Sharp, and Y. Yu, A multiphase flow model for the unstable mixing of layered incompressible materials, Phys. of Fluids, 17:087102-1-07102-8, 2005. Paper No. 087102. LANL Preprint Number LA-UR-05-0078. Stony Brook University Preprint Number SUNYSB-AMS-05-01. https://doi.org/10.1063/1.2001007
  8. A. Chinnayya, E. Daniel, and R. Saurel, Modelling detonation waves in heterogeneous energetic materials, J. Comp. Phys., 196 (2004), 490-538. https://doi.org/10.1016/j.jcp.2003.11.015
  9. D. A. Drew, Mathematical modeling of two-phase flow, Ann. Rev. Fluid Mech., 15 (1983), 261-291. https://doi.org/10.1146/annurev.fl.15.010183.001401
  10. R. Gaskell, Introduction to the Thermodynamics of Materials, Taylor and Francis, Philadelphia, PA, 1995.
  11. J. Glimm, H. Jin, M. Laforest, F. Tangerman, and Y. Zhang, A two pressure numerical model of two fluid mixing, Multiscale Model. Simul., 1 (2003), 458-484. https://doi.org/10.1137/S1540345903408464
  12. J. Glimm, D. Saltz, and D. H. Sharp, Two-pressure two-phase flow, In G.-Q. Chen, Y. Li, and X. Zhu, editors, Nonlinear Partial Differential Equations, pages 124-148. World Scientific, Singapore, 1998.
  13. J. Glimm, D. Saltz, and D. H. Sharp, Statistical evolution of chaotic fluid mixing, Phys. Rev. Lett., 80(4) (1998), 712-715. https://doi.org/10.1103/PhysRevLett.80.712
  14. J. Glimm, D. Saltz, and D. H. Sharp, Two-phase modeling of a fluid mixing layer, J. Fluid Mech., 378 (1999), 119-143. https://doi.org/10.1017/S0022112098003127
  15. H. Jin, The averaged equations of compressible multiphase flow, Research Institute of Basic Science, Jeju University, to appear, 2013.
  16. H. Jin, X. F. Liu, T. Lu, B. Cheng, J. Glimm, and D. H. Sharp, Rayleigh-Taylor mixing rates for compressible flow, Phys. Fluids, 17:024104-1-024104-10, 2005. https://doi.org/10.1063/1.1843155
  17. H. Jin, J. Glimm, and D. H. Sharp, Compressible two-pressure two-phase flow models, Phys. Lett. A, 353 (2006), 469-474. https://doi.org/10.1016/j.physleta.2005.11.087
  18. L. Malvern, Introduction to the Mechanics of Continuous Medium, Prentice Hall, 1969.
  19. R. Menikoff and B. Plohr, The Riemann problem for fluid flow of real materials, Rev. Mod. Phys., 61 (1989), 75-130. https://doi.org/10.1103/RevModPhys.61.75
  20. V. H. Ransom and D. L. Hicks, Hyperbolic two-pressure models for two-phase flow, J. Comp. Phys., 53 (1984), 124-151. https://doi.org/10.1016/0021-9991(84)90056-1
  21. D. Saltz, W. Lee, and T.-R. Hsiang, Two-phase flow analysis of unstable fluid mixing in one-dimensional geometry, Phy. Fluids, 12(10) (2000), 2461-2477. https://doi.org/10.1063/1.1287925
  22. R. Saurel and R. Abgrall, A multiphase Godunov method for compressible multifluid and multiphase flows, J. Comput. Phys., 150 (1999), 425-467. https://doi.org/10.1006/jcph.1999.6187
  23. H. B. Stewart and B. Wendroff, Two-phase flow: Models and methods, J. Comp. Phys., 56 (1984), 363-409. https://doi.org/10.1016/0021-9991(84)90103-7
  24. G. Wallis, One-Dimensional Two-Phase Flow, McGraw-Hill, New York, 1969.
  25. Forman Williams, Combustion Theory, Addison-Wesley Co., Reading, 1965.

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