Detonation initiation on the microsecond time scale: DDTs

Spatially resolved, thermal power deposition of limited duration into a finite volume of reactive gas is the initiator for a deflagration-to-detonation transition (DDT) on the microsecond time scale. The reactive Euler equations with one-step Arrhenius kinetics are used to derive a novel formula for the gas velocity supporting the lead shock in a detonation. Numerical solutions of the reactive Euler equations are used to describe the detailed sequence of reactive gasdynamic transients leading to a planar detonation, characterised by unusually large power output, far from the power deposition location. Results are presented for deposition into a region isolated from the planar boundary of the reactive gas as well as for that adjacent to the boundary. The quantitative dependences of DDT evolution on the location and magnitude of thermal power deposition and activation energy are identified.