Modeling of shock development and transition to detonation initiated by burning in porous propellant beds

This paper deals with the analyses of deflagration-to-detonation transition (DDT) occurring in a packed bed of granular, high-energy solid propellant. A reactive two-phase flow model of this phenomena is solved by utilizing a Lax-Wendroff finite differencing technique. Utilizing an appropriate gas phase nonideal equation of state and high-pressure gas permeability relations with an improved numerical integration technique, one can predict the transition to a steady detonation from initiation by deflagration. Analyses are presented that clearly indicate the effect of the propellant physical and chemical parameters on the predicted run-up length to detonation. Predictions of this run-up length to detonation are presented as a function of propellant chemical energy, burning rate, bed porosity, and granulation (size). Limited comparison with actual DDT data in the literature indicates qualitative agreement with these predictions.