Shock focusing and detonation initiation at a flame front

Abstract Multidimensional numerical simulations were performed to study the interaction of focused shock waves and a flame front leading to detonation initiation. The fully compressible Navier–Stokes equations, coupled with a chemical-diffusive model for energy release and conversion of fuel to product in a stoichiometric hydrogen–air mixture, were solved using a third-order method on a dynamically adapting mesh. Preliminary simulations of deflagration-to-detonation transition (DDT) in an obstructed channel, when compared to previous experiments, point to a DDT scenario where detonation initiation arises from multi-shock focusing at a flame front. A detailed examination of an idealized problem showed two mechanisms of detonation formation: (1) direct detonation initiation triggered at the collision spot by focusing shocks at the flame front, and (2) focusing of relatively weak shocks leading to a delayed transition to detonation through the reactivity-gradient mechanism. Comparisons between the detailed analysis of shock-focusing and experimentally observed DDT phenomena suggests that shock focusing plays an important role in the occurrence of DDT for this problem.