Asymptotic calculation of the dynamics of self-sustained detonations in condensed phase explosives

We use the weak-curvature, slow-time asymptotics of detonation shock dynamics (DSD) to calculate an intrinsic relation between the normal acceleration, the normal velocity and the curvature of a lead detonation shock for self-sustained detonation waves in condensed phase explosives. The formulation uses the compressible Euler equations for an explosive that is described by a general equation of state with multiple reaction progress variables. The results extend an earlier asymptotic theory for a polytropic equation of state and a single-step reaction rate model discussed by Kasimov (Theory of instability and nonlinear evolution of self-sustained detonation waves. PhD thesis, University of Illinois Urbana-Champaign, Urbana, Illinois) and by Kasimov & Stewart (Phys. Fluids, vol. 16, 2004, pp. 3566–3578). The asymptotic relation is used to study the dynamics of ignition events in solid explosive PBX-9501 and in porous PETN powders. In the case of porous or powdered explosives, two composition variables are used to represent the extent of exothermic chemical reaction and endothermic compaction. Predictions of the asymptotic formulation are compared against those of alternative DSD calculations and against shock-fitted direct numerical simulations of the reactive Euler equations.