Simplified Asymptotic Equations for the Transition to Detonation in ReactiveGranular Materials

摘要

In this paper a simplified asymptotic system of equations to describe combustionin reactive granular materials is derived. In contrast with one-phase flow, the continuum equations for two-phase flow develop resonant behavior at choked flow states, where one of the gas-acoustic speeds equals the solid particle speed. The asymptotic model is valid near these choked flow states and near ignition temperature conditions, and incorporates nonlinear resonant effects of gas acoustic waves, compaction of the granular material and grain burning. The asymptotic system is derived with a combination of nonlinear geometrical optics and large activation energy asymptotics near the resonant point. A general abstract derivation of the asymptotic system is provided, and the results are then specialized to the continuum equations for reactive granular materials.... Combustion, Multiphase flow, Nonlinear optics, Asymptotics, Choked flow, Resonance.