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The effect of introducing a spatial heterogeneity into an explosive medium isstudied computationally by examining the detonation velocity near the limit topropagation in a thin explosive layer. The explosive system studied is an idealgas with a single exothermic reaction governed by a pressure-dependent reactionrate ($p^n$) with a pressure exponent of $n = 3$. A pressure-dependent reactionrate, rather than the exponential dependence of reaction on temperature ofArrhenius kinetics, is used so that the detonation wave is stable in thehomogeneous case and can be modelled with simple, analytical techniques, andthus the effect of introducing heterogeneity can be clearly identified. Thetwo-dimensional slab of explosive is bounded by a layer of inert gas with thesame thermodynamic properties as the explosive. The heterogeneity is introducedinto the explosive via a large-amplitude, two-dimensional sinusoidal ripple indensity in the initialization of the simulation, while maintaining a constantpressure. The computational simulations are initialized with a ZND solution forthe ideal CJ detonation, and the detonation is allowed to propagate into theexplosive layer. The simulations show that the detonation in the heterogeneousmedia exhibits a cellular-like structure of complex shock interactions. Thedetonation is able to propagate into a significantly thinner layer of explosiveand can exhibit a greater velocity than the corresponding homogeneous case. Aparametric study of varying the wavelength of the sinusoid shows the existenceof an optimal size of heterogeneity at which the favorable effect is thegreatest corresponding to a wavelength that is approximately 10 to 50 times thehalf reaction zone length of the ideal CJ detonation. As the wavelength isdecreased to the size of the reaction zone length, the behavior reverts back tothe homogeneous case.

Effect of Spatial Heterogeneity on Near-Limit Propagation of a Stable Detonation