The effect of the stability on the Mach reflection of detonations on a wedge

The Mach reflection process of cellular detonations on a wedge is numerically studied with a two-step chemical reaction model in an attempt to elucidate the effect of the stability on the development and self-similarity on the Mach reflection. Considering the stiffness of the reactive source term, an additive Runge-Kutta method is also used to couple the stiff reactive source term and the non-stiff convection which is discretised with a fifth-order WENO scheme. The numerical results suggest that the Mach reflection of a regular cellular detonation is in accordance with that of a ZND detonation. The self-similarity is lost due to the presence of the characteristic length and the cellular structures only result in the local fluctuations of the triple-point trajectory. In the near field, the Mach reflection process is self-similar due to the high overdrive. In the far field, the Mach reflection can lead to self-similarity asymptotically. For unstable detonations, the stability of the detonation front is comparable with the Mach stem. Thus locating the boundary of the Mach reflection becomes difficult and it may not be meaningful to carry out a self-similar analysis.