The critical conditions for the formation of the Mach shock from shock reflections*

The goal of this study is to determine the critical conditions for the generation of a detonation wave from shock reflections. This objective is achieved by implementing a novel technique of converging-diverging nozzle, inspired by White (1963). In this method by propagating the detonation wave in the converging section, it will be overdriven, and the cellular instability will be reduced to a smaller scale. In the diverging section, the detonation wave restores a quasi-laminar structure, consisting of a leading shock wave followed by a reaction wave. The interaction of the two decaying incident shocks generates a Mach reflection. To identify the local conditions of the formation and determine the role of the dynamics of reflecting shocks the controlling parameters are systematically changed. The critical conditions were found to closely correspond to the condition where the time scale of gas expansion behind the resulting Mach shock is comparable with the ignition delay time.