Necessary Conditions for the Development of Inviscid Instabilities in a Vibrationally Excited Dissociating Gas

Abstract

For a plane flow of a vibrationally excited dissociating diatomic gas the necessary conditions of the existence of growing (neutral) inviscid perturbations, similar to the Rayleigh criterion of a “generalized” inflection point, are obtained. The corresponding formulas are presented for cases with a certain physical interpretation. In particular, the model of a vibrationally excited one-component gas is considered as the initial stage of thermal dissociation, as well as a widespread model with one dissociation-recombination reaction. The case of a binary molecular-atomic mixture with a vibrationally excited molecular component and a frozen gas-phase dissociation-recombination reaction is considered as an intermediate one. Comparative numerical calculations are carried out, which show, in particular, that under conditions of developed dissociation, the use of the criterion of the generalized inflection point does not take into account the specifics of the process. The wavenumbers and phase velocities of the I and II inviscid modes calculated on its basis may differ significantly from the results obtained with using the new necessary condition.