Abstract
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 novel formulas for velocity and temperature variation that describe the physical phenomena characteristic of DDTs. A transformation of the variables is shown to yield a canonical equation system, independent of the activation energy. Numerical solutions of the reactive Euler equations are used to describe the detailed sequence of reactive gasdynamic processes leading to an overdriven planar detonation 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 role of compressions and shocks reflected from the boundary into the partially reacted hot gas is described. The quantitative dependences of DDT evolution on the magnitude of thermal power deposition and activation energy are identified.