Model for Converging Detonations in Solid Explosives

Abstract

The fluid-dynamic equations which describe converging detonation fronts in high explosives are solved over a coordinate system that changes from circular to a pleated pattern as the detonation converges. There are three reasons for introducing such a coordinate system rather than making the usual assumption that when a spherical or cylindrical explosive charge is initiated simultaneously on its curved surface the detonation front maintains its symmetry as the detonation converges to the center: (1) Calculations made elsewhere show that a converging circular shock wave is unstable. (2) Calculations in this paper show that if spherical or cylindrical symmetry is maintained, density and velocity become infinite, but if the detonation front folds these quantities remain finite except at a few points which can be removed by cuts. The average fluid velocity remains almost constant over 99% of the detonation front. (3) Experiments indicate that a cylindrical detonation front becomes rather symmetrically deformed.