Reactive burn models and ignition & growth concept

Plastic-bonded explosives are heterogeneous materials. Experimentally, shock initiation is sensitive to small amounts of porosity, due to the formation of hot spots (small localized regions of high temperature). This leads to the Ignition & Growth concept, introduced by LeeTarver in 1980, as the basis for reactive burn models. A homo- genized burn rate needs to account for three meso-scale physical effects: (i) the density of active hot spots or burn centers; (ii) the growth of the burn fronts triggered by the burn centers; (iii) a geometric factor that accounts for the overlap of deflagration wavelets from adjacent burn centers. These effects can be combined and the burn model defined by specifying the reaction progress variable λ = g(s) as a function of a dimensionless reaction length s(t) = rbc/ℓbc, rather than by specifying an explicit burn rate. The length scale ℓbc(Ps) = [Nbc(Ps)]−1/3 is the average distance between burn centers, where Nbc is the number density of burn centers activated by the lead shock. The reaction length rbc(t) = ∫t0 D(P(t′))dt′ is the distance the burn front propagates from a single burn center, where D(P) is the deflagration speed as a function of the local pressure and t is the time since the shock arrival. A key implementation issue is how to determine the lead shock strength in conjunction with a shock capturing scheme. We have developed a robust algorithm for this purpose based on the Hugoniot jump condition for the energy. The algorithm utilizes the time dependence of density, pressure and energy within each cell. The method is independent of the numerical dissipation used for shock capturing. It is local and can be used in one or more space dimensions. The burn model has a small number of parameters which can be calibrated to fit velocity gauge data from shock initiation experiments