Abstract

The deflagration-to-detonation transition via the interaction of a weak shock with a series of discrete laminar flames is analyzed computationally based on the unsteady reactive Navier-Stokes equations with one-step Arrhenius chemistry. For comparison, simulations with the Euler equations are also performed. The numerical setup aims to mimic an array of laminar flames ignited at different spark times, artificially inducing chemical activity to stimulate the coupling between the gas dynamics and the chemical energy release for the deflagration-to-detonation transition. The interaction of the weak shock with the first cylindrical flame demonstrates a very good agreement with the results in the literature and that a single weak shock-flame interaction is insufficient to cause a prompt DDT. However, a high degree of Richtmyer-Meshkov instabilities induced by repetitive shock-flame and shock-boundary interactions generate turbulence that accelerates the flame surface, referred to as the flame brush, until eventually a hot spot ignition in the unreacted material develops into a multi-headed detonation wave. In the absence of physical diffusion in the Euler simulation, the enhanced burning rate of the turbulent flame brush is suppressed. Nevertheless, the intense flow fluctuations generated by the interactions of shocks, boundary and flames create the conditions under which a deflagration-to-detonation transition can potentially occur at later times. A parametric study is also reported in this paper to assess the influence of various physical parameters on the transition event and to explore scaling relationships among these parameters.