Shock wave propagation in a rotational axisymmetric dusty gas for adiabatic flow using group invariance method

Abstract

The main purpose of this investigation is to discuss the entire class of similarity solutions for adiabatic flow behind the cylindrical shock wave in a dusty gas (a mixture of non-ideal gas and small solid particles) using the Lie group invariance method. The group invariance method is used to derive the similarity transformations and the similarity variable, which transforms the set of partial differential equations into a set of ordinary differential equations. The obtained set of ordinary differential equations is solved numerically using the Runge–Kutta method of fourth order in Mathematica software. It is found that the shock wave decays with the variation of the gas non-idealness parameter. Also, the shock strength enhanced with an increase in the ratio of the specific heat of the solid particles to the specific heat of the gas at constant volume or the initial azimuthal velocity variation exponent or the ratio of the density of solid particles to the initial density of the gas. The behavior of the flow variables behind the shock wave is analyzed graphically. This study may be helpful in understanding the astrophysical phenomena such as supernovae explosion, in a dusty gas environment.