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Density-based kinetics for mesoscale simulations of detonation initiation in energetic materials

In this work we present one- and two-dimensional mesoscale simulations of detonation initiation in energetic materials. We solve the reactive Euler equations, with the energy equation augmented by a power deposition term. The reaction rate at the mesoscale is modelled using a density-based kinetics scheme, adapted from standard ‘Ignition and Growth’ models. The deposition term is based on previous results of simulations of void collapse at the microscale, modelled at the mesoscale as hot spots. For an isolated hot spot in a homogeneous medium, it is found that a critical size of the hot spots exists. If the hot spots exceed the critical size, initiation of detonation can be achieved. For sub-critical hot-spot sizes, we show that it takes a collection of hot spots to achieve detonation. We also carry out two-dimensional mesoscale simulations of random packs of HMX crystals in a binder, and show that the transition between no detonation and detonation depends on the number density of the hot spots, the initial radius of the hot spot, the post-shock pressure of an imposed shock, and the amplitude of the power deposition term.