Numerical and theoretical analysis of the precursor shock wave formation at high-explosive channel detonation

Abstract

When a detonation propagates in an explosive layer that only partially fills a channel, the rapidly expanding detonation products can form a piston and drive a precursor shock wave (PSW) in the air gap between the explosive layer and the channel confinement, ahead of the detonation as illustrated in Fig. 1a (see [1] and references there). The experiments with nitromethane [2] demonstrated that the phenomena is sensitive to the initial air pressure in the channel: at high enough initial pressure a precursor will not form. Taking into account that the detonation products pressure is hundreds of thousands of atmospheres, it is surprising that the initial air pressure as low as 10 to 20 atmospheres may be high enough to prevent the formation of PSW. This was also confirmed by the numerical simulations [2] for a single value of air gap width. In the present paper we conduct a systematic numerical study to determine the influence of the initial air pressure on the formation of PSW for various sizes of air gap in the channel. We also include the case of an axisymmetrical channel (Fig. 1b). A simple analytical model was developed in [2] where the criterion for the formation of a precursor shock is Mach reflection of the oblique shock at the channel upper wall (see Fig. 2a). Although results from this simple model agreed quite well with experiments and CFD, it is noted in [2] that the model seems to be in contradiction with some experimental and numerical findings and it cannot predict the effect of width of the air gap. In the present paper we examine the unsteady numerical flowfields in detail to reveal the actual mechanism of the precursor shock formation, which is then subjected to an analytical treatment (both for the planar and axisymmetrical cases). The new analytical model is compared with the CFD results and experimental data for channels with various air gaps.