Numerical studies of the behavior of heterogeneous explosives using the ignition-and-growth model

Heterogeneous explosive materials are extremely complex. The structure consists of microscopic crystal grains that are mixed with a plastic binder and pressed into a solid. Modelling the initiation and propagation of a detonation wave through such a material is a difficult task. There are several different approaches, of which a popular model is the ignition-and-growth model. The ignition-and-growth model has enjoyed considerable success in reproducing experimental results. It suffers from the drawback however that the model parameters must be carefully calibrated to corresond to particular experiments. While results have been reported for different classes of experiments, no systematic study of the model for a specific parameter set has been conducted. We address this issue in the first part of this thesis, by simulating a wide class of experiments for a specific parameter set using a high resolution numerical scheme employing adaptive mesh refinement.; Experiments have shown that the passage of a weak shock through a heterogeneous explosive desensitizes the explosive behind the shock. For instance, propagating detonations are extinguished in regions of an explosive that have been subjected to a weak preshock, just as the initiation of a detonation has been observed to fail within these regions. Simulations using the ignition-and-growth model show that the model does not account for desensitization, such that in some cases the numerical and experimental results are contradictory. In the second part of this thesis, we propose a modifcation to the ignition-and-growth model that renders it capable of capturing the effects of desensitization. This is accomplished by introducing a desensitization parameter that is coupled to the chemical reaction rate and whose evolution is governed by an additional pressure-dependent desensitiation rate law. The coupling modifies the chemical reaction rate in regions where the explosive is deemed to have been desensitized. We perform a host of numerical experiments using the augmented ignition-and-growth model to verify that it captures the effects of desensitization correctly and to study the solution set of the resulting model.