Numerical simulation of detonation initiation in a flame brush: the role of hot spots

Abstract

This is the final paper in a series describing numerical simulations of deflagration-to-detonation transition (DDT) for conditions similar to reflected shock-tube experiments in an acetylene–air mixture (100 Torr, 298 K). In the experiments and calculations, the interaction of a shock wave and an expanding flame front leads to the rapid creation of a turbulent flame brush and, for sufficiently high Mach numbers of the incident shock, to the subsequent transition to a detonation. The two-dimensional reactive Navier-Stokes equations, including the effects of viscosity, thermal conduction, molecular diffusion, and chemical reaction, are solved on a high-resolution adapting mesh. Shock-flame interactions, through the Richtmyer-Meshkov instability, create and maintain a highly turbulent flame brush and are responsible for injecting unburned material into the region of burned material. Hot spots are created by pressure fluctuations and shocks generated in the flame brush. At relatively low Mach numbers, hot spots that transition to detonation are created outside of the flame brush. For higher Mach numbers, such hot spots are created in pockets of unreacted material inside the flame brush. In both cases, the hot spots give rise to detonations by the gradient mechanism, in which a gradient in induction time leads to a supersonic spontaneous wave that later becomes a detonation.