Shock wave driven out by a piston in a mixture of a non-ideal gas and small solid particles under the influence of the gravitation field with monochromatic radiation

Abstract

Similarity solutions for a spherical shock wave in a mixture of small solid particles of micro size and a non-ideal gas are discussed under the influence of the gravitational field with monochromatic radiation. The solid particles are uniformly distributed in the mixture, and the shock wave is assumed to be driven by a piston. It is assumed that the equilibrium flow-conditions are maintained and the moving piston continuously supplies the variable energy input. Due to the central mass (m¯) at the origin (Roche model), the medium is considered to be under the influence of the gravitational field. In comparison to the attraction of the central mass at the origin, the gravitational effect of the mixture itself is neglected. The density of the undisturbed medium is assumed to be constant in order to obtain the self-similar solutions. The effect of the parameter of non-idealness of the gas b¯, the mass concentration of solid particles in the mixture μp, the ratio of the density of solid particles to the initial density of the gas Ga and the gravitational parameter G0 are obtained. It is shown that due to an increase in the gravitational parameter the compressibility of the medium at any point in the flow field behind the shock front decrease and the flow variables velocity, pressure, radiation flux and shock strength are increased. Also, an increase in the ratio of the density of solid particles to the initial density of the gas Ga and the gravitational parameter G0 has the same effect on the shock strength and the reverse effect on the compressibility. The non-idealness of the gas causes a decrease in the shock strength and widens the disturbed region between the piston and the shock.