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 stable detonation wave structure. The detonation is initiated as an ideal Chapman-Jouguet (CJ) detonation with a one-dimensional structure, and then al-

Influence of discrete sources on detonation propagation in a Burgers equation analog system

“…While this technique is well defined for a smooth, laminar-like wave structure in a homogeneous medium (see Ref. [28]), the procedure for heterogeneous or multiphase detonations has yet to be formulated, and must be treated via direct numerical simulation. Results in recent years examining detonations in condensedphase explosives with large-scale heterogeneities have generated results that cannot be explained using conventional front curvature theory, which assumes a laminar-like wave structure.…”

Transients following the loss of detonation confinement

“…In the supersonic flow of the PM fan, the streamline angle increases from Θ = 9.5 • at the sonic point to Θ = 11.9 • and a pressure of P = 9.9 GPa, where the Lexan shock polar crosses the HE's PM fan. What we see as the differences between figure 1(a,b), is the classical result for how differences in confinement affect the edge flow for a steady-state, multidimensional detonation (Sichel 1966;Bdzil and Stewart 2007;Li, Mi & Higgins 2015;. The question we ask in this paper is as follows: Given an initially 1-D, steady-state ZND detonation with ω = 90 • , what are the transients that move this 1-D detonation to the steady states shown in figure 1, when the rigid confinement necessary to support a 1-D detonation is suddenly reduced?…”

Effect of spatial inhomogeneities on detonation propagation with yielding confinement

“…In each case where a detonation wave successfully propagated, the length (in x-direction) of the entire simulation domain was approximately 3000 times the half-reaction-zone length l 1/2 for an ideal, homogeneous case. The technique of an advancing computational window, which was developed in several recent studies for simulating detonation waves propagating over a long distance [43][44][45]10], was used in this study in order to reduce the computational cost. Instead of the entire domain, the simulations were only performed in a window that enclosed the leading wave complex.…”

“…The smoothly curved leading wave front can then be geometrically constructed knowing the D n -κ relation using the method first developed by Eyring et al [57] This theoretical model, combining Wood and Kirkwood's solution and Eyring et al's geo-metric construction (see more details in Appendices of Refs. [45,22]), was used by Li et al [45,44] to predict the V avg vs. 1/h relation. As demonstrated by Li et al [45], given the appropriate D n -κ relation and shock angle at the confinement-explosive interface, the steady-state wave front constructed using Eyring et al's method is identical to those obtained using the Detonation Shock Dynamic model [58][59][60].…”