Similarity solutions for unsteady flow behind an exponential shock in a dusty gas

Abstract

One-dimensional self-similar unsteady flow behind a strong exponential shock driven out by a piston moving with time according to an exponential law is investigated. The medium is assumed to be a mixture of small solid particles and a perfect gas. In order to get some essential features of the shock propagation, small solid particles are considered as pseudo-fluid and it is assumed that the equilibrium flow condition is maintained in the flow-field, and that the viscous-stress and heat conduction of the mixture are negligible. Solutions are obtained, in both cases, when the flow between the shock and the piston is isothermal or adiabatic. It is found that the assumption of zero temperature gradient brings a profound change in the density distribution as compared to that of the adiabatic case. Effects of a change in the mass concentration of the solid particles in the mixture Kp and the ratio of the density of solid particles to that of initial density of the gas G1 are also obtained.