Conservative Hyperbolic Model for Compressible Two-phase Flow with Different Phase Pressures and Temperatures

A model for two-phase compressible flow is presented, the derivation of which is based on extended irreversible thermodynamics principles. An isentropic two-phase flow model proposed earlier and the hyperbolic model for heat transfer underlie the developed theory of this paper. The governing equations of the model form a hyperbolic system of differential equations in conservation-law form. A set of interfacial exchange processes such as pressure relaxation, interfacial friction, temperature relaxation and phase transition are taken into account by source terms in the balance equations. It is shown that the heat flux relaxation limit of governing equations can be written in the Baer-Nunziato form, in which the Furier thermal conductivity diffusion terms for each phase are included.