A hyperbolic phase-transition model with non-instantaneous EoS-independent relaxation procedures

This article deals with the thermodynamic equilibrium recovery mechanisms in two-phase flows and their numerical modeling. The two phases, initially at different pressures, temperatures and chemical potentials, are supposed to be driven towards equilibrium conditions by three relaxation processes. First, a mechanical process applies to relax phasic pressures, then a thermal process, to allow the sensible heat transfer between the phases at different temperatures, and, lastly, a chemical process that is responsible for the mass transfer. The two-phase flow model is composed of six partial differential equations with source terms that allow the description of mixtures at full thermodynamic disequilibrium. Its homogeneous portion is hyperbolic and it is solved by a second-order accurate finite volume scheme that uses a HLLC-type approximate Riemann solver. The source terms modeling the relaxation processes are separately integrated as three systems of ordinary differential equations. The main contributions of this paper are: the capability of describing the possibly non-instantaneous time delay of equilibrium recover in a novel way, the equation of state independence of the numerical scheme, and the possibility to take into account the morphology of the flow pattern by using the interfacial area between phases.