Self-similar shock waves in a relaxing, non-uniform gas

Abstract

Propagation of planar and spherical shock waves in a vibrational non-equilibrium medium, which may be initially inhomogeneous with prescribed property gradients, is investigated by a similarity transformation analysis. Similarity variables in exponential form are derived by a systematic one parameter group theory scheme. The basic equations governing the motion of the fluid are reduced to a set of four simultaneous nonlinear first-order ordinary differential equations, and are integrated numerically by a modified shooting technique to provide a complete description on the wave pattern. Results exhibit attenuation effects caused by the internal rate process and influences introduced by the initial non-uniform stream on the propagating shock strength, speed, and disturbed flow properties. Depending on the nature of the density gradient existing in the undisturbed medium, non-uniform effects may either compete with or enhance the relaxation of the shock waves.