AN ASYMPTOTIC ANALYSIS OF CHAIN-BRANCHING IGNITION IN THE LAMINAR WAKE OF A SPLITTER PLATE SEPARATING STREAMS OF HYDROGEN AND OXYGEN

The chain-branching process leading to ignition in the high-temperatur e laminar wake that forms at the trailing edge of a thin splitter plat e separating a stream of hydrogen from a stream of oxygen is investiga ted with a reduced chemistry description that employs H as the only ch ain-branching radical not in steady state. The analysis presented cove rs ignition events occurring in the Rott-Hakkinen and Goldstein region s, where self-similar solutions for the different flow variables are a vailable. It is found that the initiation reactions, which create the first radicals, are only important in a relatively small initial regio n, becoming negligible downstream as the radical mole fractions increa se ro values larger than the ratio of the characteristic branching tim e to the characteristic initiation time, a very small quantity at temp eratures of practical interest. As a result, most of the ignition hist ory is controlled by the autocatalytic branching reactions, giving ris e to a radical pool that increases exponentially with distance in a pr ocess that is described by using as a large parameter the ratio of the streamwise distance to the downstream extent of the initial region a here initiation reactions are significant. Comparisons of the asymptot ic results with numerical integrations of the conservation equations r eveal that a three-term expansion for the H-atom profile is necessary in this case to provide an accurate prediction for the ignition distan ce.