Approximate analytical solution for the propagation of shock wave in a mixture of small solid particles and non-ideal gas: isothermal flow

Abstract

Abstract This paper presents the development of mathematical model to obtain the approximate analytical solutions for isothermal flows behind the strong shock (blast) wave in a van der Waals gas and small solid particles mixture. The small solid particles are continuously distributed in the mixture and the equilibrium conditions for flow are maintained. To derive the analytical solutions, the physical variables such as density, pressure, and velocity are expanded using perturbation method in power series. The solutions are derived in analytical form for first approximation, and for second order approximation the set of differential equations are also obtained. The effects of an increase in the problem parameters value on the physical variables are investigated for first order approximation. A comparison is also, made between the solution of cylindrical shock and spherical shock. It is found that the fluid density and fluid pressure become zero near the point or axis of symmetry in spherical or cylindrical symmetry, respectively, and therefore a vacuum is created near the point or axis of symmetry which is in tremendous conformity with the physical condition in laboratory to generate the shock wave.