Physically Evocative Meso-Informed Burn Model: Topology of Evolving Hotspot Fields

Abstract

Reactive burn models for heterogeneous energetic material initiation must account for chemistry as well as microstructure to predict shock-to-detonation transition. Upon transient (strong) shock loading, the collapse of individual voids leads to ignition of hotspots, which then grow and interact to completely consume the surrounding material. This paper shows that a length scale measuring the perimeter of the evolving burn front in a field of hotspots, in combination with a topological function/form factor for the hotspot field, is a key input to a framework for constructing a meso-informed reaction rate model. The approach suggested in this paper provides a route to constructing reaction rate models with only two quantities of interest, viz., the burn front perimeter and burn front velocity, which are physically evocative of the underlying hotspot physics and can be quantified individually using meso-scale simulations. It overcomes the problem of calibrating many free parameters that appear in phenomenological burn models and therefore suggests a route to developing general frameworks for simulation-derived meso-informed burn models.