Mach reflection of detonation waves with velocity deficits

Abstract

Velocity deficits, which exist universally in the process of detonation propagation, were not considered in the problem of detonation Mach reflection in previous studies. Thus, an experimental study of the Mach reflections of gaseous detonations with velocity deficits is reported in this paper. Remarkable velocity deficits were achieved by a porous wall channel. The soot foil technique was utilized to monitor the cellular pattern variation and the evolution of triple-point trajectory. Two detonable mixtures, i.e., 2H₂+O₂+3Ar and 2H₂+O₂, were used to obtain stable detonation and unstable detonation. The results show that along with velocity deficits, the detonation tends to be unstable and the cell size increases. The induction length must be taken into consideration since the specific heat ratio could be different from that of a Chapman-Jouguet (CJ) detonation. Therefore, three modes of self-similarity were determined, i.e., non-self-similarity with significant velocity deficits (mode 1), global self-similarity with moderate velocity deficits (mode 2) and localized self-similarity with slight velocity deficits (mode 3). The Mach stem height of mode 1 is higher than the non-reactive three-shock theory. The triple-point trajectory of mode 2 corresponds to that of an inert shock. In the case of mode 3, the well-known frozen and equilibrium limits in detonation Mach reflections can be found. Considering the measured cell size ($\lambda$) as the length scale, the required transition distance for the occurrence of the equilibrium limit was found to be approximately (8–10)$\lambda$. A threshold value ${\alpha }_i$=0.95 was found above which the Mach reflection characteristics of a detonation agree well with those of a CJ detonation (${\alpha }_i$ is the overdrive degree of the incident wave). Below the threshold value, the triple-point trajectory angle decreases linearly with the increase of ${\alpha }_i$, and the Mach stem overdrive degree is a constant.