Mach reflection of a ZND detonation wave

The Mach reflection of a ZND detonation wave on a wedge is investigated numerically. A two-step chain-branching reaction model is used giving a thermally neutral induction zone followed by a chemical reaction zone for the detonation wave. The presence of a finite reaction zone thickness renders the Mach reflection process non-self-similar. The variation of the height of the Mach stem with distance of propagation does not correspond to a straight curve from the wedge apex as governed by self-similar three-shock theory. However, the present results indicate that in the near field around the wedge apex, and in the far field where the reaction zone thickness is small compared to the distance of travel of the Mach stem, the behavior appears to be self-similar. This corresponds to the so-called frozen and equilibrium limit pointed out by Hornung and Sanderman for strong discontinuity shock waves and by Shepherd et al. for cellular detonations. The critical wedge angle for the transition from regular to Mach reflection is found to correspond to the value determined by self-similar three-shock theory, but not by reactive three-shock theory for a discontinuous detonation front.