On problems involving gas flows associated with gasdynamic discontinuities

Abstract

A review is given concerning the formulation of problems of nonviscous gas flows with discontinuities associated with a deposition of energy in the flowing medium. It is shown that with a known amount of energy at the exothermic front it is not possible to determine the solution of the problem uniquely. To find a unique solution, supplementary information is required; in particular, the mode of the propagation of the exothermic front must be known. In a number of cases this supplementary information can be obtained by considering the initial phases of the motion on the basis of a more detailed model of the gaseous medium and by the examination of the stationary structure of the discontinuity. Examples are given for the establishment of such criteria corresponding to different modes of the propagation of the exothermic front in problems where concentrated energy is deposited in media capable of self-generation of an exothermic process as a consequence of a chemical or a thermonuclear reaction. It is also demonstrated that when an exothermic front propagates under variable conditions, additional criteria are required in order to determine possible changes in the mode of its propagation. Example is given of an establishment of such a criterion in a simple problem involving a detonation wave.