Ignition between a shock and a contact surface: Influence of the downstream temperature

Slow chemistry in a finite zone of reactive mixture behind an inert shock results in the formation of a hot spot and eventually triggers ignition dose to the surface where the shock originated, which, depending upon the specific scenario, could consist of a piston, a contact surface, or a flame. The current study assumed high activation energy and a ratio of the specific heats close to unity. The various scenarios can then be translated into different values of the acoustic reflection coefficient or of the ratio of die speeds of sound across the contact surface, with the piston being equivalent to a zero speed of sound downstream. Thus this study proceeds as a generalization of the work of Blythe and Crighton, who studied piston-induced ignition, for arbitrary downstream acoustic reflection coefficients. It is found that in ail cases except for the piston, ignition occurs at a small distance from the contact surface. initially, a shockless supersonic wave appears, moving toward the contact surface at a speed initially infinite but decreasing. For a ratio of the speeds of sounds below a critical value equal to the inverse of the Chapman-Jouguet (CJ) speed, this wave eventually reaches the contact surface at a speed still above the CJ value. But above this threshold, the speed reaches the CI value, a shock appears, and the wave proceeds as a strong CJ wave. Finally for higher temperatures behind the contact surface, a spatially uniform thermal explosion eventually occurs in the largely unburned mixture ahead of the CJ wave before it reaches die contact surface. Thus, a variety of possible scenarios leading to detonation were uncovered. The last and strongest one is particularly applicable to flames, and it provides for a transition mechanism in the region immediately in front of the flame.