Journal of Engineering Mathematics

, Volume 31, Issue 2–3, pp 119–130 | Cite as

A WKB analysis of radical growth in the hydrogen-air mixing layer

  • Antonio L. SÁnchez
  • Amable LiñÁn
  • Forman A. Williams


The chain-branching process leading to ignition in the hydrogen-air mixing layer is studied by application of a novel WKB-like method with a four-step reduced scheme adopted for the chemistry description. Attention is restricted to initial free-stream temperatures above the crossover temperature corresponding to the second explosion limit of H2-O2 mixtures, thereby causing three-body recombination reactions to be negligible in the ignition process. 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, because of the effect of radical diffusion, the radical growth rate is uniform across the mixing layer in the first approximation, with an exponent given by that of a premixed branching explosion evaluated at the location where the effective Damköhler number based on the flow velocity is maximum. This exponent, as well as the leading-order representation of the radical profiles, are easily obtained by the imposition of a bounded, nonoscillatory behavior on the solution.

chain branching mixing layer ignition WKB 


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Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Antonio L. SÁnchez
    • 1
  • Amable LiñÁn
    • 2
  • Forman A. Williams
    • 3
  1. 1.Area de Mecánica de FluidosEscuela Politécnica Superior Universidad Carlos III de MadridLeganésSpain
  2. 2.Departamento de Motopropulsión y Termofluidodinámica, E. T. S. I. AeronauticosUniversidad Politécnica de MadridMadridSpain
  3. 3.Center for Energy and Combustion Research University of California San DiegoLa JollaUSA

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