Nonpremixed spontaneous ignition in the laminar wake of a splitter plate

Abstract

Ignition in the laminar wake that forms at the trailing edge of a thin splitter plate separating two parallel streams of fuel and oxidizer is studied in the limit of large activation energy. The analysis presented covers ignition events ocurring in the Rott–Hakkinen and Goldstein regions, where self-similar solutions for the different frozen flow variables are available. Because of the strong exponential sensitivity of the reaction rate on the temperature, ignition becomes a self-accelerating phenomenon on the temperature increment that leads to a thermal runaway a finite distance downstream from the splitter plate. The dependence of the ignition distance on the values of the velocity and temperature gradients that exist at the trailing edge of the splitter plate is investigated. In particular, it is seen that, for sufficiently large values of the activation energy, the small temperature variations that exist across the wake must be taken into account in calculating the ignition distance. As the transverse gradient of temperature at the trailing edge increases, the reaction zone becomes thinner and migrates towards the hotter side of the mixing layer, where convection becomes the dominant transport mechanism, causing the thermal runaway distance to be determined in the first approximation by a convective-reactive balance across the thin reaction layer. Ignition in the wake when one of the streams is initially stagnant is also addressed. The character of the resulting solution is seen to depend strongly on the Lewis number of the reactant supplied by the colder stream, yielding three distinct ignition regimes that are analyzed separately.