A DISCRETE METHOD TO TREAT HEAT CONDUCTION IN COMPRESSIBLE TWO-PHASE FLOWS

This paper deals with modeling of heat conduction in two-phase compressible flows. This kind of flow is predominant in propulsion, space, or defense applications. A total nonequilibrium model for two-phase compressible flows with heat conduction is first built. Without heat conduction, the Baer and Nunziato model is recovered. When heat conduction terms are present, extra nonconservative terms appear in the flow model and are responsible for interface condition satisfaction with heat conduction. When dealing with interface problems between compressible fluids, this model contains useless effects that may be omitted. That is why simpler models are derived. They are obtained by successive asymptotic reductions in the limit of stiff relaxation effects of velocities, pressures, and eventually temperature from the nonequilibrium model. The presented models respect conservation laws and guarantee entropy production. From a numerical point of view, a specific discrete explicit and implicit numerical method is developed to solve numerically heat conduction terms. Coupled with a suitable numerical method for two-phase compressible flows, an efficient method is obtained to simulate interface problems between compressible fluids with heat conduction. Analytical solutions of steady state problems of heat conduction in compressible single- and two-phase media are also specially derived to validate the numerical strategy.