Steady detonation propagation in thin channels with strong confinement

Mark Short,Carlos Chiquete,Stephen J Voelkel

doi:10.1017/jfm.2020.37

Abstract

We examine asymptotically the dynamics of two-dimensional, steady detonation wave propagation and failure for a strongly confined high explosive (HE), in which the width of the explosive is small relative to the reaction zone length. An energy balance equation is derived, which shows how the longitudinal acceleration of subsonic flow behind the detonation shock is influenced both by chemical reaction and by the effects of HE boundary streamline deflection, specifically via the induced rate of change of mass flux through the detonation wave. The latter serves to either counteract or reinforce the acceleration of longitudinal flow, depending on the sign of the gradient of the boundary streamline deflection at the detonation shock. The analysis is valid for general equations of state and chemical reaction rates in the HE. The asymptotically derived form of the energy equation represents an eigenvalue problem for the determination of the steady detonation propagation speed, solved via a shooting method. We explore specific results for ideal and stiffened equations of state, along with a pressure-dependent reaction rate for which changes in the pressure exponent and reaction order are also studied. We consider the influences of both straight and curved HE boundary streamline shapes. The asymptotic analysis reveals significant physical insights into how detonation propagation and failure are affected by strong confinement.

Highlights

A detonation in a condensed-phase high explosive (HE) consists of a shock sustained by the hydrodynamic flow induced by spatially distributed chemical reaction in the explosive
We have formulated an asymptotic theory for how the limit of strong confinement affects 2-D steady detonation propagation and failure in a 2-D planar or axisymmetric cylindrical geometry, where the detonation speed D0 departs from the Chapman– Jouguet speed DCJ by O(1) amounts, such that 1 − D0/DCJ = O(1)
The theory is based on the limit of a small channel width or radius relative to the detonation driving zone length

Summary

Introduction

A detonation in a condensed-phase high explosive (HE) consists of a shock sustained by the hydrodynamic flow induced by spatially distributed chemical reaction in the explosive. In many multi-dimensional flow configurations, lateral motion of the detonating explosive due to yielding of surrounding confinement induces streamline divergence, which causes the shock to become divergently curved, whereupon the dynamics of a steadily propagating detonation is controlled by the chemical energy release that occurs within a subsonic elliptic flow region known as the detonation driving zone, or DDZ. A review of this structure was recently presented by Short & Quirk (2018b). The DDZ is the region encompassing the detonation shock and sonic flow locus (relative to the frame of the detonation shock). Chiquete is influenced by the lateral size of the HE, the degree of reactivity and the strength of the confinement

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Results

Conclusion