Using measured hot spot temperatures in the statistical hot spot model of shock initiation

The Statistical Hot Spot (SHS) model of shock initiation and detonation of solid explosives was developed to quantitatively model reactive flows for mesoscale and continuum geometries in the ALE3D code using Arrhenius temperature based chemical kinetic rate laws. The model describes the formation of hot spots by shock compression, the ignition (or failure to react) of these hot spots, the growth (or decay) of reacting hot spots, and the coalescence of the reacting volumes as the chemical reaction is completed. Although the SHS model has successfully demonstrated several unique capabilities, it has been limited by the lack of experimental data on the temperatures of hot spots before and after exothermic reaction. Recently Dlott et al. have developed several new capabilities to measure these temperatures with nanosecond resolution. Approximate temperatures during shock compression, pore collapse to form hot spots, reaction of these hot spots, and spreading of reaction are estimated using the CHEETAH chemical equilibrium code. These calculated temperatures are compared to recently measured hot spot temperatures in HMX-, PETN- and TATB-based explosives. The results indicate that the estimated temperatures are close to the experimental values and that these temperatures are high enough to cause nanosecond reaction rates based on the extension of chemical kinetic models based on thermal explosion experiments.