Predicting runaway reaction in a solid explosive containing a single crack

Mechanically damaged high explosive (HE) undergoing defiagration has recently been shown capable of generating combustion pressures and flame speeds dramatically in excess of those observed in undamaged HE. Flame penetration of HE cracks large enough to support the reaction zone serves to increase the burning surface area and the rate of gas production. Cracks confine the product gas, elevating the local pressure and reducing the reaction zone thickness such that the flame can enter smaller-width cracks. As the reaction zone decreases sufficiently to enter the smallest cracks, the flame surface area will grow appreciably, rapidly pressurizing the cracks. This runaway of pressure and burning area, termed combustion bootstrapping, can dramatically accelerate the combustion mode and in the most extreme cases may result in deflagration-to-detonation transition [3, 4]. The current study is intended to help predict the conditions required for the onset of reaction runaway in a narrow slot in HE. We review experiments [5] where flames were observed to propagate though a narrow slot (intended to simulate a well-formed crack) in high explosive at velocities up to 10 km/s, reaching pressures in excess of 1 kbar. Pressurization of the slot due to gas-dynamic choking is then used to predict the onset of runaway reaction. This model agrees with experimental pressure measurements of observed reaction runaway in slots