Branched-chain ignition in strained mixing layers

Abstract

The time-dependent evolution of the radical pool in an initially inert hydrogen-air counterflow mixing layer subject to variable strain is investigated analytically. Although the initial chemistry description contains three different chain carriers, namely, H, O and OH, it is shown that the ignition problem can be accurately described in terms of a single radical-pool variable that incorporates steady-state assumptions for the radicals O and OH. Use of this non-standard procedure reduces the problem to the integration of a single conservation equation, whose solution depends on the existing Damkohler number Delta, defined as the ratio of the diffusion time across the mixing layer to the characteristic branching time. Ignition takes place when Delta remains predominantly above a critical value of the order of unity. The exponentially growing radical pool, which extends across the mixing layer, can be described analytically by separation of variables in configurations with a slowly varying strain rate, providing a solution that is used to investigate the parametric dependences of the ignition time. Weakly strained solutions are studied separately by addressing the asymptotic limit of large Damkohler numbers. It is seen that the reaction zone then becomes a thin layer of relative thickness Delta(-1/4) centred at the location where the branching rate is maximum. The analysis employs asymptotic expansions in decreasing powers of Delta for the shape and for the exponential growth rate of the radical pool. The accurate description of the solution necessitates computation of three terms in the asymptotic expansion for the growth rate, yielding predictions for the ignition time that remain accurate even for values of Delta of the order of unity.