A mixture-energy-consistent six-equation two-phase numerical model for fluids with interfaces, cavitation and evaporation waves

Abstract : We model liquid-gas flows with cavitation by a variant of the six-equation single-velocity two-phase model with stiff mechanical relaxation of Saurel–Petitpas–Berry [J. Comput. Phys. 228 (2009), 1678–1712]. In our approach we employ phasic total energy equations instead of the phasic internal energy equations of the classical six-equation system. This alternative formulation allows us to easily design a simple numerical method that ensures consistency with mixture total energy conservation at the discrete level and agreement of the relaxed pressure at equilibrium with the correct mixture equation of state. Temperature and Gibbs free energy exchange terms are included in the equations as relaxation terms to model heat and mass transfer and hence liquid-vapor transition. The algorithm uses a high-resolution wave propagation method for the numerical approximation of the homogeneous hyperbolic portion of the model. In two dimensions a fully-discretized scheme based on a hybrid HLLC/Roe Riemann solver is employed. Thermo-chemical terms are handled numerically via a stiff relaxation solver that forces thermodynamic equilibrium at liquid-vapor interfaces under metastable conditions. We present numerical results of sample tests in one and two space dimensions that show the ability of the proposed model to describe cavitation mechanisms and evaporation wave dynamics.