Propagation of Strong Spherical Shock Waves in a Dusty Gas

In this paper, we have examined one-dimensional unsteady self-similar adiabatic flow of a dusty gas behind a spherical shock wave with time dependent energy input. The dusty gas is assumed to be a mixture of small solid particles and perfect gas. The solid particles are continuously distributed in the perfect gas. In order to get some essential features of shock propagation, the solid particles are considered as a pseudo-fluid and it is assumed that the equilibrium flow condition is maintained in the flow-field, and viscous stress and heat conduction of the mixture are negligible. The presence of small solid particles affects the medium in two ways. On the one hand, the volume fraction of solid particles lowers the compressibility of the mixture; and on the other hand, the particle load increases the inertia of the mixture. It is found that if the density of the solid particles and that of the perfect gas are equal, by an increase in the mass fraction of solid particles in the mixture, the strength of the shock is decreases and its distance from the inner expanding surface is increased. Also, by an increase in the ratio of density of solid particles and that of the perfect gas in the mixture, the strength of the shock is increased and its distance from the inner surface is decreased. Further, an increase in the rate of energy input increases the shock velocity and decreases the distance between the shock front and the inner surface.