Hayesian Inference: Exploring the Relationship between Supercritical Hot Spot Number Density & the Speed of Deflagration Waves they Trigger

On Jan 2, 2023, the SCCM community lost one of its most senior and vital members: Dennis B. Hayes, formerly of Sandia and (in his retirement) Los Alamos National Laboratories. Although Dennis was primarily known as a shock-wave theorist, he made forays into x-rays, detonation, and many other topics. He independently derived the Statistical Hot Spot (SHS) model in 1981, and was the first to apply it to HE reaction zones. (The first derivation was by Soviet mathematician Andrey Kolmogorov, of turbulence fame, in 1937, his interest being heterogeneous phase transition in metals.) Dennis realized that the SHS result provides a relationship between the number density of supercritical hot spots, eta, and the speed of deflagration waves, V, that they trigger. He applied this relationship to experiments on HNS explosive. Based on the powder granularity he estimated eta, and hence (via SHS) V-values between about 5 and 50 m/s. These estimates are fairly consistent with more recent measurements and estimates of V. Here we refine his method—which we call Hayesian Inference—to explore the same relationship for two PBXs. The results show that eta is exceedingly large, 10⁹/mm³ being a conservative number in many cases. This tells us that, although detonation reaction zones are very thin, the continuum approximation does conveniently hold. It also tells us that most efforts we make to seed homogenous explosives with artificial heterogeneities have eta-values orders of magnitude smaller than do PBXs.