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

Abstract

An analog to the equations of compressible flow that is based on the inviscid Burgers equation is utilized to investigate the effect of spatial discreteness of energy release on the propagation of a detonation wave. While the traditional Chapman-Jouguet (CJ) treatment of a detonation wave assumes that the energy release of the medium is homogeneous through space, the system examined here consists of sources represented by δ-functions embedded in an otherwise inert medium. The sources are triggered by the passage of the leading shock wave following a delay that is either of fixed period or randomly generated. The solution for wave propagation through a large array (10 3 -10 4 ) of sources in one dimension can be constructed without the use of a finite difference approximation by tracking the interaction of sawtooth-profiled waves for which an analytic solution is available. A detonation-like wave results from the interaction of the shock and rarefaction waves generated by the sources. The measurement of the average velocity of the leading shock front for systems of both regular, fixed-period and randomized sources is found to be in close agreement with the velocity of the equivalent CJ detonation in a uniform medium wherein the sources have been spatially homogenized. This result may have implications for the applicability of the CJ criterion to detonations in highly heterogeneous media (e.g., polycrystalline, solid explosives) and unstable detonations with a transient and multidimensional structure (e.g., gaseous detonation waves).

Investigation of detonation velocity in heterogeneous explosive system using the reactive Burgers’ analog

“…In the present work, we consider again the analog model [3], which essentially consists of a one-dimensional inviscid Burgers' equation with an added reactive term given as:…”

“…The motivation for the present study is, once again, to verify if the CJ criterion can predict the average propagation velocity of the detonation wave in system with discrete, finite-rate energy release. Following the same approach as outlined in [3], the detonation analog is used as well in the present study.…”

“…To address the aforementioned question, an interesting study has been conducted recently by Mi and Higgins [3] who model the heterogeneity of explosive mixtures using a discrete energy release source approach. Notably, their study was carried using a simple reactive Burgers' equation-type analog system to investigate the behavior of detonation waves.…”

“…This study is essentially the extension of [3] and a continuous effort on the modeling of detonation dynamics in heterogeneous explosives. Unsteady, finite-volume calculations are carried out here to look at discrete-source detonations where finite-rate energy release governed by an Arrhenius rate law is considered.…”

“…In [3], the solution of wave propagation through a series of instantaneous, discrete energy releases triggered by the passage of the shock front in one-dimension is constructed. The nature of the model equation makes it possible to treat the problem analytically without the use of numerical approximations by tracking the interaction of resulting sawtooth-like travelling waves.…”