Analysis of thermal ignition in supersonic flat-plate boundary layers

The ignition of the supersonic boundary layer flow of a combustible mixture over a flat plate is studied through both direct numerical integration and activation energy asymptotics. Since ignition can be induced through either internally generated viscous heating or heat transfer from a hot wall, analyses are conducted for both an adiabatic wall and an isothermal wall whose temperature can be either higher or lower than the maximum frozen temperature in the flow. The analyses provide a description of the flow structure under various ignition situations, especially the extent of flow non-similarity and the interaction between the inner reaction region and the outer frozen regions. Explicit expressions for the ignition distance are obtained for all ignition situations, and the corresponding effects of the physical parameters on the ignition delay are also assessed. Specifically, it is demonstrated that, for low free-stream Mach number M∞, the ignition distance increases linearly with M∞ because of the decreased residence time, and for high M∞it decreases exponentially with M∞ because of viscous heating. Results from the asymptotic analyses are found to compare well with those obtained from the direct numerical integration.