Modelling the Combustion of Explosives

When an explosive burns, gaseous products are formed as a result. The interaction of the burning solid and gas is not well understood. More specifically, the process of the gaseous product heating the explosive is yet to be explored in detail. The present work is aimed towards filling that gap using mathematical modelling: this aims to track the temperature profile in the explosive and the gas’s response. This work begins by modelling single step reactions using the simple Arrhenius model. An alternative asymptotic approach is also employed. There is close agreement between the results for the full reaction-diffusion problem and the asymptotic problem. The model is then extended to include three step reaction kinetics, where we again apply asymptotic analysis in addition to direct computation. Further work outlined briefly at the end includes the motion of gas being incorporated in the existing model with temperature and pressure distributions considered.