A multiphase model for compressible flows with interfaces, shocks, detonation waves and cavitation

Abstract

A compressible multiphase unconditionally hyperbolic model is proposed. It is able to deal with a wide range of applications: interfaces between compressible materials, shock waves in condensed multiphase mixtures, homogeneous two-phase flows (bubbly and droplet flows) and cavitation in liquids. Here we focus on the generalization of the formulation to an arbitrary number of fluids, and to mass and energy transfers, and extend the associated Godunov method.

We first detail the specific problems involved in the computation of thermodynamic interface variables when dealing with compressible materials separated by well-defined interfaces. We then address one of the major problems in the modelling of detonation waves in condensed energetic materials and propose a way to suppress the mixture equation of state. We then consider another problem of practical importance related to high-pressure liquid injection and associated cavitating flow. This problem involves the dynamic creation of interfaces. We show that the multiphase model is able to solve these very different problems using a unique formulation.

We then develop the Godunov method for this model. We show how the non-conservative terms must be discretized in order to fulfil the interface conditions. Numerical resolution of interface conditions and partial equilibrium multiphase mixtures also requires the introduction of infinite relaxation terms. We propose a way to solve them in the context of an arbitrary number of fluids. This is of particular importance for the development of multimaterial reactive hydrocodes. We finally extend the discretization method in the multidimensional case, and show some results and validations of the model and method.