Chain-Branching Explosions in Mixing Layers

The chain-branching process leading to ignition in the high-temperature hydrogen-oxygen mixing layer is studied by application of a novel WKB-like method when, as is typically the case, two branching radicals cannot be assumed to maintain steady state. It is shown that the initiation reactions, responsible for the early radical buildup, cease being important when the radical mass fractions reach values of the order of the ratio of the characteristic branching time to the characteristic initiation time, a very small quantity at temperatures of practical interest. The autocatalytic character of the chain-branching reactions causes the radical concentrations to grow exponentially with downstream distance in the process that follows. It is shown that the transverse radical profiles that emerge can be described by exponential series of the WKB type in inverse powers of the streamwise coordinate. The analysis reveals that, because of the effect of radical diffusion, the rate of radical growth is uniform across ...

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