Steady deflagration of HMX with simple kinetics: A gas phase chain reaction model

A new approach is presented for modeling steady combustion of energetic solids, in particular HMX. A simplified, global, gas phase chain reaction kinetic mechanism is employed. Specifically, a zero-order, high activation energy thermal decomposition initiation reaction in the condensed phase followed by a second-order, low activation energy chain reaction in the gas phase is assumed. A closed-form solution is obtained, which is based on the activation energy asymptotics analysis of Lengelle in the condensed phase and the assumption of zero activation energy in the gas phase. Comparisons between the model and a variety of experimental observations over a wide range of pressures and initial temperatures are presented and demonstrate the validity of the approach. The model provides excellent agreement with burning rate data (including sensitivity to pressure and initial temperature) and temperature profile data (in particular the gas phase). This suggests that in the realm of simplified, approximate kinetics modeling of energetic solids, the low gas phase activation energy limit is a more appropriate model than the classical high activation energy limit or heuristic flame sheet models. The model also indicates that the condensed phase reaction zone plays an important role in determining the deflagration rate of HMX, underscoring the need for better understanding of the chemistry in this zone.