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The propagation of detonation waves in reactive media bounded by an inert,compressible layer is examined via computational simulations in two differentgeometries, axisymmetric cylinders and two dimensional, planar slabs. Forsimplicity, an ideal gas equation of state is used with a pressure-dependentreaction rate that results in a stable detonation wave structure. Thedetonation is initiated as an ideal Chapman-Jouguet (CJ) detonation with aone-dimensional structure, and then allowed to propagate into a finite diameteror thickness layer of explosive surrounded by an inert layer. The yieldingconfinement of the inert layer results in the detonation wave decaying to asub-CJ steady state velocity or failing entirely. Simulations are performedwith different values of the reaction rate pressure exponent (n = 2 and 3) anddifferent impedance confinement (greater than, less than, and equal to theconfinement of the explosive). The velocity decrement and critical dimension(critical diameter or thickness) are determined, and a 2:1 scaling between thecylinder diameter and slab thickness results is confirmed, in good agreementwith curvature-based models of detonation propagation. The measured shock frontcurvature and detonation velocity relation agrees with the classic model ofWood and Kirkwood. The computational simulations are compared to a simple,analytic model that treats the interaction of the confinement with thedetonation products via Newtonian theory and a model that assumes a continuousvariation in shock front curvature with the shock angle at the interface withthe confinement matching the angle determined by shock polar analysis. TheNewtonian model works very well for the case of high impedance confinement,while the shock front curvature model agrees with the simulations for the caseof low impedance confinement.

Geometric Scaling for a Detonation Wave Governed by a Pressure-Dependent Reaction Rate and Yielding Confinement