Abstract

Mathematical and Numerical Modeling of Two-Phase Compressible Flows with Micro-Inertia

S.Gavrilyuk (Laboratory of Modeling in Mechanics and Thermodynamics, University Aix-Marseille III, Marseille, France); R.Saurel (l'IUSTI, University Aix-Marseille I, Marseille, France)

e-mail: sergey.gavrilyuk@univ.u-3mrs.fr

A new model with full coupling between micro-and macro-scale motion is being developed for compressible multiphase mixtures. Equations of motion and a coupling micro-structural equation (an analogue of the Rayleigh-Lamb equation) are obtained by using the Hamilton principle of stationary action. In the particular case of bubbly fluids the deduced model contains eight partial differential equations (one-dimensional case) and it is unconditionally hyperbolic. The equations are solved numerically by an adapted method based on the Godunov scheme. The model and methods are validated for two diverse test problems. The first one is the wave propagation in a liquid containing a small quantity of gas bubbles. Computed oscillating shock waves are in excellent agreement with experimental data. Next, the one-dimensional multiphase model is used as a reduction tool for a multi-dimensional interaction of shock wave with a large bubble. For the second, a good agreement is also observed. References 1. S. Gavrilyuk and R. Saurel, 2002, Mathematical and Numerical Modeling of Two-Phase Compressible Flows with Micro-Inertia, J. Comp. Physics, v.175,326-360.

Section : 4