Numerical simulation of Mach reflection of cellular detonations

The Mach reflection of cellular detonation waves on a wedge is investigated numerically in an attempt to elucidate the effect of cellular instabilities on Mach reflection, the dependence of self-similarity on the thickness of a detonation wave, and the initial development of the Mach stem near the wedge apex. A two-step chain-branching reaction model is used to give a thermally neutral induction zone followed by a chemical reaction zone for the detonation wave. A sufficiently large distance of travel of the Mach stem is computed to observe the asymptotic behavior in the far field. Depending on the scale at which the Mach reflection process occurs, it is found that the Mach reflection of a cellular detonation behaves essentially in the same way as a planar ZND detonation wave. The cellular instabilities, however, cause the triple-point trajectory to fluctuate. The fluctuations are due to interactions of the triple point of the Mach stem with the transverse waves of cellular instabilities. In the vicinity of the wedge apex, the Mach reflection is found to be self-similar and corresponds to that of a shock wave of the same strength, since the Mach stem is highly overdriven initially. In the far field, the triple-point trajectory approaches a straight line, indicating that the Mach reflection becomes self-similar asymptotically. The distance of the approach to self-similarity is found to decrease rapidly with decreasing thickness of the detonation front.