Effect of spatial heterogeneity on near-limit propagation of a pressure-dependent detonation

Effect of spatial discretization of energy on detonation wave propagation

“…Examina-tion of detonation propagation in the limit of spatially randomized, point-like sources in three dimensional clouds may have some relevance to the anomalous scaling between experiments in axisymmetric geometries (tubes) and two-dimensional slab geometries (rectangular geometries) [18,43,44,21,23]. A preliminary step in this direction was made in the recent computational study of Li et al [35], in which a two-dimensional sinusoidal ripple in properties was introduced in a medium prior to detonation propagation through it. Extension of this study using perturbations with greater discreteness than sinusoidal would be of great interest.…”

“…In spray detonations with millimeter-sized droplets of fuel, a similar propagation mechanism, i.e., blast waves generated by each individual droplet releasing its energy, merging with and reinforcing the leading shock wave, was experimentally identified by Dabora et al [8] and theoretically described Pierce & Nicholls [45]. Propagation of detonation in media with a sinusoidal variation in properties was explored computationally by Morano & Shepherd [39] in one dimension and extended to two dimensions by Li et al [35]. In these studies, no significant deviation greater than 2% away from CJ was observed when the detonation propagated without losses present.…”

“…In these studies, no significant deviation greater than 2% away from CJ was observed when the detonation propagated without losses present. Li et al [35] did observe enhanced wave speeds when the detonation propagated in a layer with inhomogenities and yielding confinement (in comparison to a detonation propagating in a homogeneous layer with the same yielding confinement). The enhanced wave speeds were attributed to accelerated reaction rates resulting from the shock interactions caused by the inhomogeneities.…”

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

“…This type of behavior has been recently demonstrated in detonation simulations using the reactive Euler equations with a medium in which a spatial inhomogeneity has been introduced. [29] This approach to detonation dynamics may provide a theoretical framework to account for the anomalous results in highly heterogeneous explosives. [30] Since the resulting wave structure in the system studied in this paper is seen to be an interacting ensemble of decaying sawtooth-profile blast waves described by the classical inviscid Burgers equation, it would be of interest to further explore these results within the framework of Burgers turbulence.…”

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

“…In the case of weak confinement, the scaling is observed to be slightly less than 2 : 1, meaning that the two-dimensional results lie slightly to the left of the axisymmet- ing results obtained with large-scale heterogeneity, namely, the mechanism of propagation becomes influenced by the local structure of the heterogeneous media. The fact that a pressure-dependent reaction rate, resulting in a stable detonation wave structure, was used in the Li et al study 39 allowed the effect of introducing heterogeneity to be clearly identified.…”