Analytical Solution for Unsteady Adiabatic Flow Behind the Blast Wave in a Non-ideal Gas and Small Inert Solid Particles Mixture

Abstract

In this paper, the self-similar solutions for a strong cylindrical or spherical blast (shock) wave in real gas and inert solid particles mixture are analyzed on the basis of the perturbation method. The similarity solution in analytical forms is derived for first-order approximation, and a set of ODE for second-order approximations is also derived using the perturbation method proposed by Sakurai in perfect gas. The physical variable’s distribution in the entire flow field after the blast wave is shown in the figures. The effects of the ratio of the density of the solid inert particles to the initial gas density, mass concentration of particles, and the parameter of real gas effect on the physical variables, the peak pressure on blast wave and the damage radius of blast wave are investigated. It is found that the peak pressure on the blast wave and the damage radius of the blast wave both decrease with an increase in the value mass concentration of solid particles or non-idealness of the gas in the mixture. A comparison has also been made between the cylindrical and spherical geometries. It is found that the blast (shock) wave is more influential in the case of spherical geometry in contrast to that in the cylindrical geometry case. Also, the blast wave decay is due to an increase in the solid particle’s mass concentration or gas non-idealness parameter, and its strength increases with an increase in the ratio of the solid particles to the initial gas density.