Spherical shock wave generated by a moving piston in mixture of a non-ideal gas and small solid particles under a gravitational field

Self-similar solutions are obtained for one-dimensional isothermal and adiabatic unsteady flows behind a strong spherical shock wave propagating in a dusty gas. The shock is assumed to be driven out by a moving piston and the dusty gas to be a mixture of a non-ideal (or perfect) gas and small solid particles, in which solid particles are continuously distributed. It is assumed that the equilibrium flow-conditions are maintained and variable energy input is continuously supplied by the piston. The medium is under the influence of the gravitational field due to a heavy nucleus at the origin (Roche model). The effects of an increase in the mass concentration of solid particles, the ratio of the density of the solid particles to the initial density of the gas, the gravitational parameter and the parameter of non-idealness of the gas in the mixture, are investigated. It is shown that due to presence of gravitational field the compressibility of the medium at any point in the flow-field behind the shock decreases and all other flow-variables and the shock strength increase. A comparison has also been made between the isothermal and adiabatic flows. It is investigated that the singularity in the density and compressibility distributions near the piston in the case of adiabatic flow are removed when the flow is isothermal.