A study of pulsating behavior and stability parameter for one-dimensional non-ideal detonations

Abstract

One-dimensional numerical simulations of non-ideal detonations were performed by using inviscid reactive Euler equations. Chemical reactions in the equations were described by two-step consecutive irreversible reactions A → B → C, which include an exothermic step (A → B) followed by an endothermic step (B → C). Non-ideal detonations are achieved when endothermicity exists in the system. The periodic oscillation behavior of peak pressure during the propagation of a one-dimensional detonation wave was studied with the different exothermicity/endothermicity and different degrees of overdrive. The results show that the increase in exothermicity, the reduction in endothermicity, and the enhanced degrees of overdrive can stabilize the propagation of detonation waves. The influence of the exothermic reaction plays a dominant role for the stability of the one-dimensional non-ideal detonations, which is further confirmed by a theoretical analysis. In addition, the stability parameter χ, proposed originally by Radulescu “The propagation and failure mechanism of gaseous detonations: experiments in porous-walled tubes,” Ph.D. thesis (McGill University, Montreal, Canada, (2003), was extended to predict the stability of non-ideal detonations, based on the Zel'dovich–Neumann–Döring structure of the non-ideal detonations. The results show that the extended stability parameter can well match the stability boundary for all of cases in the present study.