Ignition and flame sptead in laminar mixing layers

Abstract

In order to identify some of the mathematical problems encoun-tered in analyzing the ignition and ñame spread in mixing layéis, \ve shall describe the structure of the laminar mixing layer between two parallel streams of a fu el and air, initially separated by a splitter píate, undergoing an Arrhenius reaction. If the activation energy of the reaction is lower than a critical valué, there is only one steady solution of the problein, showing a transition from nearly frozen mixing to diffusion controlled combustión downstream of the píate. For higher, typical, valúes of the activation energy we may find a multiplicity of solutions, depending on the valué of the Damkohler number D, characterized by the temperature of the hotter of the two streams. For valúes of the Damkohler number lower than a critical valué Dc, there is a solution where a thermal runaway is found to oceur, after an induction length, at a point that serves as the origin of premixed flames that do not propágate upstream. For valúes of D larger than a critical lift-ofif valué D¡(< Dc) we find a solution with diffusion controlled combustión in a diffusion fíame. This fíame is anchored, with a triple-fíame structure, in the near wake of the splitter píate, where upstream heat conduction to the píate plays a dominant role. In the interval D¡ < D < Dc there is a third, unstable, solution. This solution determines where an external ignition source shonld be placed so that, by means of upstream triple-flame propagation to the splitter píate, transition to diffusion controlled combustión can take place