Modeling and observation of detonation front formation with microwave interferometry during the deflagration-to-detonation transition

The detonation front in condensed explosives has been shown to be electrically conductive, and microwaves have long been used to track the detonation front. In this work we make microwave interferometry measurements of a deflagration-to-detonation transition in a confined, granular explosive, with simultaneous characterization of the expansion of the confinement tube by Photonic Doppler Velocimetry. We use Cheetah to calculate the properties of explosive products including electrical conductivity and the dielectric constant (relative permittivity) as functions of temperature and mass density. We track the evolving properties during the transition from deflagration to detonation with the HERMES model in ALE 3D calculations. We use these results to help interpret the reflections of microwave signals from the burning and detonating fronts. At present, the electrical properties calculated by Cheetah include only the contribution of ionization. For under-oxidized explosives, the presence of carbon is known to increase the conductivity. As a result, our model locates the transition from burning to detonation but underestimates the conductivity. For elements that are partially reacted we use mixture rules for the dielectric constant and the conductivity.