Simulation of Multiphase Flows Using a Modified Upwind-Splitting Scheme

Authors: David J. Robbins, R. Stewart Cant, Lynn F. Gladden

Abstract:

A robust AUSM+ upwind discretisation scheme has been developed to simulate multiphase flow using consistent spatial discretisation schemes and a modified low-Mach number diffusion term. The impact of the selection of an interfacial pressure model has also been investigated. Three representative test cases have been simulated to evaluate the accuracy of the commonly-used stiffenedgas equation of state with respect to the IAPWS-IF97 equation of state for water. The algorithm demonstrates a combination of robustness and accuracy over a range of flow conditions, with the stiffened-gas equation tending to overestimate liquid temperature and density profiles.

Keywords: Multiphase flow, AUSM+ scheme, liquid EOS, low Mach number models

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1073319

References:

[1] FLUENT Documentation for ANSYS 13, ANSYS, Inc.
[2] S. Soo, "On one-dimensional motion of a single component in twophases," International Journal of Multiphase Flow, vol. 3, pp. 79-82,1976.
[3] C. Hirt and B. Nichols, "Volume of Fluid (VOF) methood for the dynamics of free boundaries," Journal of Computational Physics, vol. 39, pp. 201-225, 1975.
[4] M. Ishii, Thermofluid dynamic theory of two-phase flow. Paris, France: Eyrolles, 1975.
[5] K. Shyue, "A fluid-mixture type algorithm for barotropic two-fluid flow problems," Journal of Computational Physics, vol. 200, pp. 718-748,2004.
[6] CFX solver theory guide for ANSYS 13, ANSYS, Inc.
[7] C. Chang and M. Liou, "A new approach to the simulation of compressible multifluid flows with the ausm+ scheme," in 16th AIAA Computational Fluid Dynamics conference, Orlando, Florida, USA, June 2003.
[8] H. Paill`ere, C. Corre, and J. Garc'─▒a Cascales, "On the extension of the AUSM+ scheme to compressible two-fluid models," Computers & Fluids, vol. 32, pp. 891-916, 2003.
[9] C. Chang and M. Liou, "A robust and accurate approach to computing compressible multiphase flow: stratified flow model and AUSM+-up scheme," Journal of Computational Physics, vol. 225, pp. 840-873,2007.
[10] M. Liou, C. Chang, L. Nguyen, and T. Theofanous, "A robust and accurate approach to computing compressible multiphase flow: stratified flow model and AUSM+-up scheme," AIAA Journal, vol. 46, pp. 2345-2356, 2008.
[11] Y. Niu, Y. Lin, and C. Chang, "A further work on multi-phase two-fluid approach for compressible multi-phase flows," Numerical Methods in Fluids, vol. 58, pp. 879-896, 2008.
[12] J. Stuhmiller, "The influence of interfacial pressure forces on the character of two=phase flow model equations,” International Journal of Multiphase Flow, vol. 3, pp. 551–560, 1977.
[13] A. Zanotti, C. M´endez, N. Nigro, and M. Storti, “A preconditioning mass matrix to avoid the ill-poised two-fluid model,” Transactions of the ASME, vol. 74, pp. 732–739, 2007.
[14] M. Liou, “A sequel to AUSM, part II: AUSM+-up for all speeds,” Journal of Computational Physics, vol. 214, pp. 137–170, 2005.
[15] W. Wagner, J. Cooper, A. Dittmann, K. Kijima, H. Kretzschmar, A. Kruse, R. Mare˘s, K. Oguchi, H. Sato, I. St¨ocker, O. ˘ Sifner, Y. Takaishi, I. Tanishita, J. Tr¨ubenbach, and T. Willkommen, “The IAPWS industrial formulation 1997 for the thermodynamic properties of water and steam,” Transactions of the ASME, vol. 122, pp. 150–182, 2000.
[16] V. Ransom, “Numerical benchmark tests,” in Multiphase science and technology, G. Hewitt, J. Delhaye, and N. Zuber, Eds. Hemisphere publishing coporation, 1987, vol. 3.
[17] I. Toumi, “An upwind numerical method for two-fluid two-phase models,” Nuclear Science & Engineering, vol. 123, pp. 147–168, 1996.
[18] R. Saurel and R. Abgrall, “A multiphase Godunov method for compressible multifuid and multiphase flows,” Journal of Computational Physics, vol. 150, pp. 425–467, 1999. character of two=phase flow model equations," International Journal of Multiphase Flow, vol. 3, pp. 551-560, 1977.
[13] A. Zanotti, C. M'endez, N. Nigro, and M. Storti, "A preconditioning mass matrix to avoid the ill-poised two-fluid model," Transactions of the ASME, vol. 74, pp. 732-739, 2007.