Analytical Study of Cylindrical Imploding Strong Shock in a Uniform Real Dusty Gas

Abstract

In the present study, we have investigated the motion of cylindrical imploding shock in a real dusty gas having uniform initial density distribution by using (CCW) Chester2 -Chisnell3 -Whitham (1958) method. It is considered that the real dusty gas is the mixture of real gas and a large number of small spherical solid particles of uniform size. Initial volume fraction of the solid particles is also assumed constant in this particular study. The particles do not interact with each other therefore their thermal motion is negligible. Initial density of the medium is taken to be constant and medium ahead of the shock front is at rest with small counter pressure. Here the particles behave like a pseudo-fluid. Maintaining the equilibrium flow condition in the flow field, the analytical expressions for the shock velocity, shock strength, pressure, and flow velocity have been derived. The variation of flow variables with propagation distance (r), mass concentration of solid particles in the mixture (kp) and the ratio of the density of solid particles to the initial density of gas (G) are obtained and discussed through figures. The results accomplished are compared with those for dusty ideal gas Yadavet, al. 28