SIMILARITY SOLUTIONS FOR REACTIVE SHOCK WAVES

Abstract

Possibilities for similarity solutions of the flow following the impact of a piston on a reactive γ-law gas are delineated for the cases where the transmitted shock is strong or of constant strength. Reaction-rate functions that can be used with power-law, exponential and logarithmic shock paths are obtained. A particular case is worked out, namely, plane reactive flow with the reaction rate proportional to the internal energy and the shock velocity varying exponentially with time. For certain values of the parameters, the solution is shown to contain an envelope of characteristics which corresponds to a singular point of the ordinary differential equation which determines the flow. Results are obtained regarding the behaviour of the flow variables, a special case where Whitham's rule holds exactly, and the possibility of accelerating a strong shock indefinitely, without introducing secondary shocks into the flow.