The Shock-Wave Structure in a Gas−Particle Mixture with Chaotic Pressure

Abstract

We consider the propagation of a shock wave in a mixture of a gas and fine solid particles with allowance for the difference in their velocities and the availability of the proper pressure of the phase of particles; here, equations of the Anderson type and others are used. We propose an approximate mathematical model of the flow; in this model, the dependence of the pressure of the first (gaseous) phase from the particles’ volume-concentration can be ignored, but the terms that present the phase volume-concentration multiplied by the pressure gradient of the gas are taken into account. It turns out that with this representation of the equation of state, the mathematical model has the hyperbolic type. For this system of equations of mechanics of heterogeneous media, we carry out the classification of the types of shock waves implemented in the considered mixture. The presented statements about the types are illustrated by numerical computations in stationary and nonstationary formulations; for this purpose, the numerical method of the TVD type is developed.