Derivation of averaged compressible two-phase flow models

From the combustion chamber of space launchers to circuits of pressurized water reactors of nuclear plants, the understanding of compressible multiphase flows has become a real challenge and a crucial do- main of research during the last decades. Because of their complexity and the limited capacity of numerical computations, compressible multiphase flows are often described by macroscopical models obtained by averaging the Navier-Stokes equations. Furthermore, the source terms governing the relaxation to ther- modynamical equilibrium between the phases (pressure, velocity, temperature) are closed by empirical relations. It is a key issue to provide a mathematical theory of derivation of inviscid compressible multiphase models with no empirical closures. Starting from multiphase Navier-Stokes models, mathematical methodologies may enable to derive original average multiphase models, or to validate existing models. In this talk, I will present a formal derivation of a compressible two-phase flow model in the case of a stratified flow by dimension reduction. The model is obtained by averaging the compressible Navier-Stokes equations in the stratification direction. While standard procedures seem to be profoundly related to one-velocity models, our approach — formal for the time being — suppresses this constraint. However, it is important to note that this modelling process necessarily leads to one-pressure models. We are also able to recover one-velocity, one-pressure models when we study the standard framework — with continuity of the velocity field at the interface.

Seventh Workshop on Compressible Multiphase Flows