Cylindrical Imploding Strong Shock Wave in Uniform Real Dusty Gas

Abstract

Chester-Chisnell-Whitham method has been used to study the behavior of dusty real gas on adiabatic propagation of cylindrical imploding strong shock waves. It is assumed that the dusty gas is the mixture of a real gas and a large number of small spherical solid particles of uniform size. Neglecting the effect of overtaking disturbances, the analytical expressions for shock strength and shock velocity immediately behind the shock have been derived for uniform initial density distribution. The expressions for the pressure and particle velocity have also been obtained. The variation of the flow variables have been calculated numerically and discussed through graphs. Finally the results accomplished here are compared with earlier results as well as those for ideal dusty gas. Keywords: CCW, dusty, imploding, real gas, shock. I.INTRODUCTION The study of the shock wave propagation in a dusty gas has received considerable attention due to its application to space science, bomb blast, lunar ash flow, coal mine explosions, nozzle flow, missiles and other engineering problems. Many scientists (Sedov . Vishwakarma [7] generalized Ray and Bhowmik[8] solution in gas to the mixture of gas and small solid particles with exponentially varying density, using a nonsimilarity method. He found that the presence of small dust particles in the gaseous medium has significant effects on the variation of flow variables. The problem of propagation of shock wave in dusty ideal gas have been tackled by Vishwakarma[9] using similarity method. Vishwakrma and Pandey[10] have studied one-dimensional unsteady self-similar adiabatic flow of a dusty ideal gas behind a spherical shock wave with time-dependent energy input. Motion of shock wave in a mixture of ideal gas and small dust particles with radiation heat flux and exponentially varying density has been studied by Vishwakarma et. al. [11]. Yadav et al. [12] studied the propagation of weak cylindrical shock in the mixture of ideal gas and dust particle in presence of constant axial magnetic field. Singh and Gogoi [13] have found similarity solution for the propagation of spherical shock wave in the mixture of non-ideal gas and small solid dust particles. They use the equation of state for non-ideal gases simplified by Anisimov and Spiner [14], which describes the behavior of non-idealness of gas on the problem of strong shock explosion. The aim of the present study is to investigate the motion of cylindrical imploding shock in a real dusty gas having uniform initial density distribution by using CCW ) method, without considering the effect of overtaking disturbances. It is assumed that the real (non-ideal) dusty gas is the mixture of real gas and a large number of small spherical solid particles of uniform size. The particles are inert and uniformly distributed in the gas. 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 nigligble. Initial density of the m...