A Compressible Single Temperature Conservative Two-Phase Model with Phase Transitions

A model for compressible two-phase flow with pressure and velocity relaxations and phase transition is presented. The model assumes for each phase its own pressure and velocity, while a common temperature is considered. The governing equations form an hyperbolic system in conservative form and are derived through the theory of thermodynamically compatible system. The phase pressure equalizing process and the interfacial friction are introduced in the balance laws for the volume fractions of one phase and for the relative velocity by adding two relaxation source terms, while the phase transition is modeled in the balance equation for the mass of one phase through the relaxation of the Gibbs free energies of the two phases. A modification of the central finite-volume Kurganov-Noelle-Petrova method is adopted in this work to solve the homogeneous hyperbolic part, while the relaxation source terms are treated implicitly. A 2D numerical simulation of shock wave bubble interaction using laser-induced cavitation bubbles, as described in the laboratory experiments of [1], is presented.