Perturbation solutions for blast waves in a low density gas

A solution for the propagation of blast waves in a low density gas, in which a virial power expansion in terms of the parameter lambda representing the product of the internal volume of the molecules which is assumed to be constant and the initial gas density is used in the equation of state, is presented. Analytical expressions are obtained by means of a perturbation technique showing the dependence of pressure, density, and gas velocity on the distance from the origin of the explosion and the distance of the shock front. The influence of the parameter lambda on the flow field and temperature distributions is studied at different stages of the explosion process. Shock velocity variations with the shock propagation distance and shock trajectories are also determined. A comparison is made with ideal gas solutions. It is found in a significant temperature drop near the origin.