Study of non-self similar flows behind shock waves in a dusty gas

Non-self-similar solutions for plane, cylindrical and spherical unsteady flows of dusty gas (mixture of gas and small solid particles) behind shock waves of arbitrary strength initiated by the instantaneous release of finite energy and propagating into a uniform medium at rest are investigated. Two methods based upon the assumptions, namely, (1) power law density and (2) linear velocity, are employed to study the effects of the parameters characterizing the initial volume fraction, mass concentration of the solid particles in the dusty gas and the ratio of the density of the solid particles to that of the initial density of the gas on shock trajectory and the flow field behind the shock. A comparative study of the results obtained by the two assumptions is also made. A simple formula is derived to study the effect of the solid particles on the shock strength in the strong regime.