Length scale effect on Mach reflection of cellular detonations

Abstract

An experimental study of the Mach reflection of cellular detonations over the wedge is reported in this paper. Throughout the experiments, high-quality smoked foil is obtained to record cell pattern variation. The initial pressures are varied to yield cellular detonations with varied transverse wave spacing (or cell size). This paper focuses on length scales controlling the deviation and recovery of self-similarity in an unsteady Mach reflection process. The results show that the frozen limit and equilibrium limit both exist for all the mixture compositions. The Mach reflection undergoes a frozen condition in the near field, and then goes through a transition process before asymptotically approaching an equilibrium state in the far field. The cell size variation in the Mach stem region also confirms the transient process. Although the final triple-point trajectory angle in the equilibrium state disagrees with classical three-shock theories, it is in agreement with the reactive three-shock theory when the wedge angle is less than 30°. The triple-point trajectory angle asymptotically approaches zero as the wedge angle increases to approximately 50°, indicating the critical wedge angle from Mach to regular reflection. The transition length associated with the equilibrium limit is found to be dependent on the mixture composition and has the same order of a hydrodynamic thickness, which is approximately a few cell lengths. This means that the hydrodynamic thickness is the characteristic length scale that most significantly dominates the Mach reflection process of cellular detonations.