Interaction of rarefaction waves with a finite-thickness layer near a rigid boundary. Equilibrium approximation

Interaction of a rarefaction wave with a layer of solid particles near the end face of a shock tube is considered. A one-dimensional unsteady approximation of mechanics of heterogeneous media with identical pressures of the phases and with allowance for a finite volume concentration of particles in the layer is used as a mathematical model. The wave pattern of the flow and the mechanism of wave interaction with the layer, including the dynamics of the layer boundary depending on the layer thickness and rarefaction-wave width, are determined. The mathematical model proposed is verified against the dependence of the layer-boundary coordinate on time and also the dependence of the velocity of upward motion of the layer on the difference in pressures between the high-pressure and low-pressure chambers.