Numerical simulation of detonation initiation with a shock wave entering a cloud of aluminum particles

Based on the mathematical model of a reacting two-phase medium in the two-velocity, two-temperature approximation, the process of planar shock wave entering a cloud of aluminum particles is numerically studied. The incident shock wave may have either a rectangular or a triangular profile, i.e., it may be accompanied by a rarefaction wave. An analysis of numerical data allowed us to determine conditions of possible establishment of a steady detonation regime in the cloud. Scenarios of initiation and types of detonation flows in the cloud are determined as functions of the amplitude of the incident shock wave and initiation energy. Criteria of detonation initiation for various fractions of particles are obtained, which express the dependence of the energy stored in the shock wave on its Mach number.