Combustion Behind Shock Waves

Laminar hydrocarbon flames, which have adiabatic flame speeds on the order of a meter per second, are conventionally described by a leading convective-diffusive zone followed by an energyreleasing reactive-diffusive region. On the other hand, combustion induced by a strong shock wave is typically modeled as a convective-reactive balance with negligible diffusion, which may be called a convective explosion or fast flame. The transition between these two modes of combustion is an important issue in flame acceleration and transition from deflagration to detonation. In this study, we examine the range of pre-mixed combustion modes possible behind shock waves through numerical solutions of the one-dimensional, steady reactive Navier-Stokes equations with a detailed chemical reaction mechanism for stoichiometric methane-air mixtures. Shock Mach numbers ranging between one and the Chapman-Jouguet (CJ) value, a maximum of about five for typical fuel-air mixtures, are considered. The mixture examined in this study is stoichiometric methane-air. Two issues are considered in depth; one is the transition from diffusion-controlled to diffusionless combustion when the combustion wave speed is specified; the other is the question of the existence of a well-defined adiabatic flame speed behind a strong shock wave.