A reactive burn model for shock initiation in a PBX: scaling and separability based on the hot spot concept

In the formulation of a reactive burn model for shock initiation, we endeavor to incorporate a number of effects based on the underlying physical concept of hot spot ignition followed by the growth of reaction due to diverging deflagration fronts. The passage of a shock front sets the initial condition for reaction, leading to a fraction of the hot spots that completely burn while others will quench. The form of the rate model is chosen to incorporate approximations based on the physical picture. In particular, the approximations imply scaling relations that are then used to mathematically separate various contributions. That is, the model is modular and refinements can be applied separately without changing the other contributions. For example, the effect of initial temperature, porosity, etc. predominantly enter the characterization of the non-quenching hot spot distribution. A large collection of velocity gauge data is shown to be well represented by the model with a very small number of parameters.