Nonstationary one-dimensional flows of a two-temperature dissociating gas: Group analysis and invariant solutions

Abstract

Modern problems such as detonation engines and hypersonic reentry are reviving interest in the point explosion theory, which gives simple gasdynamics models of similar processes. This work is devoted to the study, using group analysis methods of mathematical properties of gasdynamics equations with thermochemical nonequilibrium, which is a typical problem in the theory of a point explosion. For this purpose, the system of equations under study was slightly corrected without distorting the physical meaning. This made it possible to obtain self-similar solutions. Solutions of two different models describing: a second-order endothermic dissociation reaction with vibrational exiting and a first-order exothermic reaction with spontaneous decay, are given in the paper. The problem of strong explosion of linear charge was considered. As in the classical case, the solution of the problem is reduced to integrating a system of ordinary differential equations in self-similar variables. The calculations show that the solutions to the modified system of equations is physically consistent and adequately describes the known effects of thermochemical nonequilibrium behind the wave front.