A numerical model for multiphase liquid–vapor–gas flows with interfaces and cavitation

Abstract

We are interested in multiphase flows involving the liquid and vapor phases of one species and a third inert gaseous phase. We describe these flows by a hyperbolic single-velocity multiphase flow model composed of the phasic mass and total energy equations, the volume fraction equations, and the mixture momentum equation. The model includes stiff mechanical and thermal relaxation source terms for all the phases, and chemical relaxation terms to describe mass transfer between the liquid and vapor phases of the species that may undergo transition. First, we present an analysis of the characteristic wave speeds associated to the hierarchy of relaxed multiphase models corresponding to different levels of activation of infinitely fast relaxation processes, showing that sub-characteristic conditions hold. We then propose a mixture-energy-consistent finite volume method for the numerical solution of the multiphase model system. The homogeneous portion of the equations is solved numerically via a second-order wave propagation scheme based on robust HLLC-type Riemann solvers. Stiff relaxation source terms are treated by efficient numerical procedures that exploit algebraic equilibrium conditions for the relaxed states. We present numerical results for several three-phase flow problems, including two-dimensional simulations of liquid–vapor–gas flows with interfaces and cavitation phenomena.