The Asymptotic Structure of Strained Chain-Branching Premixed Flames

The asymptotic structure of stretched chain-branching premixed flames with unity Lewis numbers is analyzed with the Zel’dovich-Liñán two-step mechanism, including (I) temperature-sensitive autocatalytic chain-branching step and (II) first-order chain-recombination step with combustion heat release. Depending on the order-of-magnitude of the Damköhler number ratio between the branching and recombination reactions, three distinct asymptotic limits, namely the fast, intermediate and slow recombination regimes, emerge with their own distinct multi-layer asymptotic structures. Our attention is focused on the asymptotic chain-branching flame-structure analysis within the framework of the intermediate recombination regime, in which the recombination layer is asymptotically thicker than the branching layer, but thinner than the outer convective-diffusive layer. The multi-layer asymptotics, involving the Damköhler number asymptotics for the recombination layer and the activation-energy asymptotics for the branching layer, yields the chain-branching flame-structure solution. The calculation results reveal the unique characteristics of strained chain-branching flames. First, the chain-carrier concentration and temperature at the branching reaction sheet are found to be constant irrespective of the strain rate. The chain-carrier concentration increases as the recombination reaction becomes slower. Moreover, the chain-carrier concentration at the branching reaction sheet is found to be proportional to the laminar flame speed. However, no quasisteady extinction was observed in any calculation results because the branching-reaction rate manages to maintain its strength thanks to the invariant branching-layer temperature. It is worthwhile to note that the present two-step model for chain-branching flames is perhaps the simplest asymptotic model, involving the minimum number of kinetic parameters to properly describe the asymptotic structure without losing any physical essence.