Aerodynamics of Premixed Flames in Flat Plate Boundary Layerst

Abstract

An analysis is conducted of the structure of a premixed flame stabilized in the boundary layer flow over a hot, impermeable, flat plate. The cases of a noncatalytic and catalytic plate are considered. The governing equations are solved by series expansion of a small parameter that controls the longitudinal diffusive processes. The zeroth order solution corresponds to the boundary layer approximation and the first order solution gives the correction to that solution for the distributions of pressure, velocity,temperature and fuel concentration. The magnitude of the correction is largest in the vicinity of the flame leading edge and depends on the plate temperature or equivalently on the activation energy of the chemical reaction. These last parameters also affect the character of the correction and, consequently, the aerodynamic structure of the flame. For low plate temperatures a region of elevated pressure is generated in front of the flame leading edge. This region becomes weaker and is displaced above the flame and downstream from its leading edge as the plate temperature is increased. The perturbed velocity field is in agreement with the pressure distribution with regions of low longitudinal velocity appearing wherever elevated pressures are present. The presence of low gas velocities favors the longitudinal diffusion of heat and mass. These diffusive processes, and in particular the upstream diffusion of combustion products, affect the rate of the chemical reaction. The interaction between diffusive and chemical kinetic effects is of primary importance in the determination of the final structure of the flame.