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

One-dimensional numerical simulations of non-ideal detonations were performed by using the inviscid reactive Euler equations. The 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 one-dimensional detonation wave was studied with the different exothermicity/endothermicity and the different degrees of overdrive. The results show that the increase of exothermicity, the reduction of endothermicity and the enhanced degrees of overdrive can stabilize the propagation of detonation waves. The influence of 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 c, proposed originally by Radulescu (PhD thesis, 2003), was improved based on the Zel'dovich-Neumann-Döring (ZND) structure of the non-ideal detonations. The values of the parameter were obtained to quantify the stability of the non-ideal detonations. The results show that the improved stability parameter can well match the stability boundary for all of cases in present study.