Asymptotic Theory for Hot Spot Formation and Transition to Detonation in ReactiveGranular Materials

摘要

The transition to detonation in energetic granular materials is a complexmultiphase process. The idea is proposed and developed that, under appropriate conditions, the resonant interaction of a fast-moving compaction burning front with a gas acoustic mode is an essential process in triggering the transition to detonation. The approach involves the study of solutions of a simple quantitative asymptoic model consisting of two nonlinear coupled partial differential equations that has been derived recently in the asymptotic limit from the full reactive multiphase equations. These equations retain some of the resonant mechanisms involving the gas acoustics and the compaction burn front. An analysis of the properties of solutions of the simplified system is developed. This analysis, involving simple resonant mechanisms, is able to qualitatively capture a number of phenomena observed in experiments and numerical simulations.... Combustion, Multiphase flow, Nonlinear equations, Asymptotics, resonance, Hot spot, Detonation.