Theoretical studies of detonation waves

Theoretical studies of reactive shock waves were performed to obtain a fundamental understanding of the initiation and propagation of detonation in condensed explosives. The differential equation governing a shock discontinuity was used to determine different conditions associated with a single shock trajectory for build-up to detonation. One of these conditions was used to construct the type of flow observed in PBX 9404 during the early stages of initiation produced by a flying plate. Various aspects of initiation induced by a constant velocity piston were considered. Equations relating the initial flow to the initial energy release rate were derived. Conditions were also determined for the shock to accelerate with either a positive or a negative pressure gradient. These conditions demonstrate how the mechanism of initiation depends on the energy release rate, the sound speed, and on the relationship between these quantities. A critical energy was defined for waves that build up to detonation with a positive particle velocity gradient. Work on the reactive shock problem was continued and integral relationships for unsteady flow were derived as generalized Rankine-Hugoniot equations without making approximations.