An asymptotic analysis of chain-branching ignition in the laminar wake of a splitter plate separating streams of hydrogen and oxygen

Abstract

The chain-branching process leading to ignition in the high-temperature laminar wake that forms at the trailing edge of a thin splitter plate separating a stream of hydrogen from a stream of oxygen is investigated with a reduced chemistry description that employs H as the only chain-branching radical not in steady state. The analysis presented covers ignition events occurring in the Rott–Hakkinen and Goldstein regions, where self-similar solutions for the different flow variables are available. It is found that the initiation reactions, which create the first radicals, are only important in a relatively small initial region, becoming negligible downstream as the radical mole fractions increase to values larger than the ratio of the characteristic branching time to the characteristic initiation time, a very small quantity at temperatures of practical interest. As a result, most of the ignition history is controlled by the autocatalytic branching reactions, giving rise to a radical pool that increases exponentially with distance in a process that is described by using as a large parameter the ratio of the streamwise distance to the downstream extent of the initial region where initiation reactions are significant. Comparisons of the asymptotic results with numerical integrations of the conservation equations reveal that a three-term expansion for the H-atom profile is necessary in this case to provide an accurate prediction for the ignition distance.