Hot-spot initiated burn waves in heterogeneous-explosive detonation reaction zones: Mixed-mode reaction and the reactive-thermal wave model

Abstract

Heterogeneous detonation reaction spreads from sufficiently supercritical hot spots as burn waves, the growth and coalescence of which controls the bulk reaction rate. The statistical hot spot model formally homogenizes these effects, giving a rate term that depends on the number density of supercritical hot spots, η, and the burn wave speed, V. In order to completely specify statistical-hot-spot-based reaction rate laws for use in reactive flow models, one must obtain realistic expressions for η and V. The focus of this paper is upon the burn-wave structure and its speed, V. Specifically, a physically-based, temperature-dependent reactive-thermal wave prescription is developed which, when suitably nondimensionalized, depends on a single parameter, α. Numerical simulations show that α characterizes the reaction morphology. Specifically, α controls important elements of the degree-of-heterogeneity in mixed-mode reaction—transitional behavior that may lie anywhere between homogeneous and heterogeneous limiting cases. The model also yields an analytic, physical-properties-based formula for V. This expression enables the development of a new class of Arrhenius-based, formally-homogenized, mixed-mode-reaction-aware reaction rate law.