Simplified modeling of transition to detonation in porous energetic materials

A simplified model that can predict the transitions from compaction to detonation and shock to detonation is given with the aim of describing experiments in beds of porous HMX. In the case of compaction to detonation, the energy of early impact generates a slowly moving, convective-reactive deflagration that expands near the piston face and evolves in a manner that is characteristic of confined deflagration to detonation transition. A single-phase state variable theory is adopted in contrast to a two-phase axiomatic mixture theory. The ability of the porous material to compact is treated as an endothermic process. Reaction is treated as an exothermic process. The algebraic (Rankine-Hugoniot) steady wave analysis is given for inert compaction waves and steady detonation waves in a piston supported configuration, typical of the experiments carried out in porous HMX. A structure analysis of the steady compaction wave is given. Numerical simulations of deflagration to detonation are carried out for parameters that describe an HMX-like material and compared with the experiments. The simple model predicts the high density plug that is observed in the experiments and suggests that the leading front of the plug is a secondary compaction wave. A shock to detonation transition is also numerically simulated.