Modeling deflagration-to-detonation transition in granular explosive pentaerythritol tetranitrate

Based on an approach suggested by Stewart et al. [Phys. Fluids 6, 2515 (1994)] we develop a model to simulate deflagration-to-detonation transition (DDT) in pentaerythritol tetranitrate (PETN) powders. The model uses a continuum mechanics formulation of conservation laws for a mixture of solid reactants and gas products, written in terms of mixture quantities plus two independent variables used to account for exothermic conversion of solid reactants into gas products, and compaction associated with pore collapse and grain rearrangement. We propose a simple empirical dependence of the reaction rate on the initial bed compaction that allows us to calibrate the model for a wide range of initial conditions. For the solid reactants we use a wide-ranging equation of state (EOS) developed by Davis and co-workers in a series of papers [Proceedings of the Tenth International Symposium on Detonation, 1993, pp. 369-376; Explosive Effects and Applications (Springer, New York, 1998), Chap. 1, Combust. Flame 120, 399 (2000); Proceedings of the 12th International Symposium Detonation, San Diego, CA, 2002, pp. 624-631;. ONR 333-05-2; Proceedings of the Eighth Detonation Symposium, 1985, pp. 785-795; Proceedings of the 11th International Symposium on Detonation, 1998, pp. 303-308]. The EOS for powder uses the P-a model of Herrmann [J. Appl. Phys. 40, 2490 (1969)] and Carrol and Holt [J. Appl. Phys. 43, 759 (1972)]. To close the system, we suggest phenomenological closure relations, consistent with the limit of a compressible inert material and of a solid fully reactive material, such that the EOS can be posed only in terms of mixture quantities and the reaction and compaction variables. We demonstrate the model's ability to capture DDT in PETN powders by matching transients typically observed in experiments through simulation. We show that for flows calculated using nonideal EOSs and complex reaction kinetics such as those formulated in our model, it is possible to define a separatrix, i.e., the C+ characteristic that separates the C+ characleristics that evolve into the detonation front from those that evolve away from it. We comment on the effects that the variability in the grain microstructure in PETN explosive powder beds can have on the overall mechanics of DDT and discuss possible ways to model this. (c) 2008 American Institute of Physics.