Existence of self-similar solutions in reacting gases

Abstract

In this paper, the Lie group theoretical method is used to establish the entire class of self-similar solutions to the problem of shock wave propagation through reacting polytropic gases with the same $$\gamma $$ -law. The system consists of two species, burnt gas and unburnt gas. Necessary conditions for the existence of similarity solutions for shocks of arbitrary strength as well as for strong shocks are obtained. The arbitrary constants, occurring in the expressions of the infinitesimals of Lie group of transformations give rise to different cases of possible solutions with a power law, exponential and logarithmic shock paths. For the existence of self-similar solutions, the forms of reaction rate are found out in different cases. A particular solution is considered to study the effect of reaction rate on the similarity exponent.