Abstract

The propagation of detonations in layers of reactive gas bounded by inert gas is simulated computationally in both homogeneous and inhomogeneous systems described by the two-dimensional Euler equations with the energy release governed by an Arrhenius rate equation. The thickness of the reactive layer is varied and the detonation velocity is recorded as the layer thickness approaches the critical value necessary for successful propagation. In homogeneous systems, as activation energy is increased, the detonation wave exhibits increasingly irregular cellular structure characteristic of the inherent multidimensional instability. The critical layer thickness necessary to observe successful propagation increases rapidly, by a factor of five, as the activation energy is increased from Ea/RT0=20–30; propagation could not be observed at higher activation energies due to computational limitations. For simulations of inhomogeneous systems, the source energy is concentrated into randomly positioned squares of reactive medium embedded in inert gas; this discretization is done in such a way that the average energy content and the theoretical Chapman–Jouguet (CJ) speed remain the same. In the limit of highly discrete systems with layer thicknesses much greater than critical, velocities greater than the CJ speed are obtained, consistent with our prior results in effectively infinite width systems. In the limit of highly discretized systems wherein energy is concentrated into pockets representing 10% or less of the area of the reactive layer, the detonation is able to propagate in layers much thinner (by an order of magnitude) than the equivalent homogeneous system. The critical layer thickness increases only gradually as the activation energy is increased from Ea/RT0=20−55, a behavior that is in sharp contrast to the homogeneous simulations. The dependence of the detonation velocity on layer thickness and the critical layer thickness is remarkably well described by a front curvature model derived from the classic, ZND-based model of Wood and Kirkwood. The results of discrete sources are discussed as a conceptual link to the behavior that is experimentally observed in cellular detonations with highly irregular cellular structure in which intense turbulent burning rapidly consumes detached pockets behind the main shock front. The fact that highly discrete systems are well described by classical, curvature-based mechanisms is offered as a possible explanation as to why curvature-based models are successful in describing heterogeneous, condensed-phase explosives.