J. Fluid Mech. zyxwvutsrqp (1996), zyxwvutsr 001. zyxwvutsrqponm 322, pp. 275-296 Copyright zyxwvutsrq @ 1996 Cambridge University Press 275 Ignition in the supersonic hydrogedair mixing layer with reduced reaction mechanisms By H. G. IM, B. T. HELENBROOK, S. R. LEE AND c. K. LAW Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544. USA (Received 1 February 1994 and in revised form 22 March 1996) Asymptotic analysis of ignition within the supersonic hydrogen/air mixing layer is performed using reduced mechanisms. Two distinct reduced mechanisms for the high-temperature and the low-temperature regimes are used depending on the characteristic temperature of the reaction zone relative to the crossover temperature at which the reaction rates of the H + 02 branching and termination steps are equal. Each regime further requires two distinct analyses for the hot-stream and the viscous-heating cases, depending on the relative dominance of external and internal ignition energy sources. These four cases are analysed separately, and it is shown that the present analysis successfully describes the ignition process by exhibiting turning point or thermal runaway behaviour in the low-temperature regime, and radical branching followed by thermal runaway in the high-temperature regime. Results for the predicted ignition distances are then mapped out over the entire range of the parameters, showing consistent behaviour with the previous one-step model analysis. Furthermore, it is demonstrated that ignition in the low-temperature regime is controlled by a larger activation energy process, so that the ignition distance is more sensitive to its characteristic temperature than that in the high-temperature regime. The ignition distance is also found to vary non-monotonically with the system pressure in the manner of the well-known hydrogen/oxygen explosion limits, thereby further substantiating the importance of chemical chain mechanisms in this class of chemically reacting boundary layer flows. 1. Introduction A major perceived difficulty in the development of scramjet technology is the ex- tremely short residence time within the combustion chamber because of the associated high flow speed. Since flame holding in jet engines is mostly through ignition and combustion in the mixing layer (Marble & Adamson zyxw 1954), one of the fundamental phenomena of interest here is ignition in the laminar mixing layer. Understanding gained from such a simple configuration should provide insight into the more realistic, and complex situations involving turbulent mixing layers. An interesting, and potentially important, recent theoretical result in the study of high-speed chemically reacting mixing layers is the recognition that ignition can actually be facilitated by increasing flow speed through the viscous conversion of the flow kinetic energy to thermal energy, which in turn increases the reaction rate. Specifically, the effect of viscous heating on ignition of supersonic mixing layers has been studied through an asymptotic approach (Jackson & Hussaini 1988; Grosch &