On the shock-induced explosion resulting from an impact by a planar detonation

We analyse the processes which occur when a planar detonation propagating from the fixed end of a donor explosive charge impacts on an acceptor homogeneous explosive. We propose a model for estimating the minimal length of the donor charge for which an explosion can be generated in the acceptor. We show that the self-similarity of the donor flow imposes a minimal length on the donor charge so its piston effect be capable of keeping the volumetric-expansion rate of the shocked acceptor to small-enough values and, thereby, of triggering explosion in a finite time. The donor detonation is represented as a Chapman-Jouguet discontinuity; the chemical decomposition in the acceptor is described by the Arrhenius global rate law. The model reproduces the experimental trend according to which the smaller minimal lengths are obtained with donor explosives that have larger heats of reaction and initial pressures. The minimal lengths predicted by the model agree well with those obtained by means of one-dimensional numerical simulations. Additional simulations show that the minimal length for generating an explosion is smaller than, but perhaps of the same order as, the minimal length for generating a transition to detonation. Further work is necessary to (i) analyse the case of donor explosives with finite reaction rates, and to (ii) account for the detonation cellular structure in the simulations of shock-to-detonation transitions.