Geometric scaling for a detonation wave governed by a pressure-dependent reaction rate and yielding confinement

Abstract

The propagation of detonation waves in reactive media bounded by an inert, compressible layer is examined via computational simulations in two different geometries, axisymmetric cylinders, and two dimensional, planar slabs. For simplicity, an ideal gas equation of state is used with a pressure-dependent reaction rate that results in a detonation wave structure that does not exhibit cellular instability. The detonation is initiated as an ideal Chapman-Jouguet (CJ) detonation with a one-dimensional structure, and then allowed to propagate into a finite diameter or thickness layer of explosive surrounded by an inert layer. The yielding confinement of the inert layer results in the detonation wave decaying to a sub-CJ steady state velocity or failing entirely. Simulations are performed with different values of the reaction rate pressure exponent (n = 2 and 3) and different impedance confinement (greater than, less than, and equal to that of the explosive). The velocity decrement and critical dimension (critical diameter or thickness) are determined, and a 2:1 scaling between the cylinder diameter and slab thickness results is confirmed, in good agreement with curvature-based models of detonation propagation. The measured shock front curvature and detonation velocity relation (DN-κ) agrees with the classic model of Wood and Kirkwood. The computational simulations are compared to a simple, analytic model that treats the interaction of the confinement with the detonation products via Newtonian theory and a model that assumes a continuous variation in shock front curvature with the shock angle at the interface with the confinement matching the angle determined by shock polar analysis. The Newtonian model works very well for the case of high impedance confinement, while the shock front curvature model agrees with the simulations for the case of low impedance confinement.