Abstract
This paper studies governing equations describing the turbulent fluid mixing behavior effectively. The goal is to propose a closure for compressible multiphase flow models with transport and surface tension, which satisfy the boundary conditions at the mixing zone edges, the conservation requirements, and an entropy inequality constraint. Implicitness of positivity for the entropy of averaging requires entropy inequality as opposed to conservation of entropy for microphysically adiabatic processes.
Similar content being viewed by others
References
Chen, Y. Two Phase Flow Analysis of Turbulent Mixing in the Rayleigh-Taylor Instability, Ph. D. dissertation, State University of New York (1995)
Chen, Y., Glimm, J., Sharp, D. H., and Zhang, Q. A two-phase flow model of the Rayleigh-Taylor mixing zone. Physics of Fluids, 8(3), 816–825 (1996)
Glimm, J., Saltz, D., and Sharp, D. H. Two-pressure two-phase flow. Nonlinear Partial Differential Equations, World Scientific, Singapore, 124–148 (1998)
Cheng, B., Glimm, J., and Sharp, D. H. Multi-temperature multiphase flow model. Zeitschrift fur Angewandte Mathematik und Physik (ZAMP), 53, 211–238 (2002)
Saurel, R. and Abgrall, R. A multiphase Godunov method for compressible multifluid and multiphase flows. Journal of Computational Physics, 150, 425–467 (1999)
Ransom, V. H. and Hicks, D. L. Hyperbolic two-pressure models for two-phase flow. Journal of Compatational Physics, 53, 124–151 (1984)
Jin, H. Analysis of twophase flow model equations. Honam Mathematical Journal, 36(1), 11–27 (2014)
Jin, H., Glimm, J., and Sharp, D. H. Compressible two-pressure two-phase flow models. Physics Letters A, 353, 469–474 (2006)
Jin, H. The Incompressible Limit of Compressible Multiphase Flow Equations, Ph. D. dissertation, State University of New York (2001)
Glimm, J. and Jin, H. An asymptotic analysis of two-phase fluid mixing. Bulletin/Brazilian Mathematical Society, 32, 213–236 (2001)
Glimm, J., Jin, H., Laforest, M., Tangerman, F., and Zhang, Y. A two pressure numerical model of two-fluid mixing. Multiscale Modeling and Simulation, 1, 458–484 (2003)
Sharp, D. H. An overview of Rayleigh-Taylor instability. Physica D, 12, 3–18 (1984)
Drew, D. A. Mathematical modeling of two-phase flow. Annual Review of Fluid Mechanics, 15, 261–291 (1983)
Bird, R., Stewrt, W., and Lightfoot, E. Transport Phenomena, 2nd ed., John Wiley & Sons, New York (2002)
Cheng, B., Glimm, J., Saltz, D., and Sharp, D. H. Boundary conditions for a two pressure two phase flow model. Physica D, 133, 84–105 (1999)
Freed, N., Ofer, D., Shvarts, D., and Orszag, S. Two-phase flow analysis of self-similar turbulent mixing by Rayleigh-Taylor instability. Physics of Fluids A, 3(5), 912–918 (1991)
Author information
Authors and Affiliations
Corresponding author
Additional information
Project supported by the Basic Science Research Program through the National Research Foundation (NRF) of Korea funded by the Ministry of Education, Science and Technology (No.NRF-2010-0010164)
Rights and permissions
About this article
Cite this article
Jin, H. Compressible closure models for turbulent multifluid mixing. Appl. Math. Mech.-Engl. Ed. 37, 97–106 (2016). https://doi.org/10.1007/s10483-016-2018-9
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10483-016-2018-9