Conservative hyperbolic formulation for compressible two-phase flow with different phase pressures and temperatures

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