Branched-chain ignition in strained mixing layers

The time-dependent evolution of the radical pool in an initially inert hydr ogen-air counterflow mixing layer subject to variable strain is investigate d analytically. Although the initial chemistry description contains three d ifferent 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 vari able that incorporates steady-state assumptions for the radicals O and OH. Use of this non-standard procedure reduces the problem to the integration o f a single conservation equation, whose solution depends on the existing Da mkohler number Delta, defined as the ratio of the diffusion time across the mixing layer to the characteristic branching time. Ignition takes place wh en Delta remains predominantly above a critical value of the order of unity . The exponentially growing radical pool, which extends across the mixing l ayer, can be described analytically by separation of variables in configura tions with a slowly varying strain rate, providing a solution that is used to investigate the parametric dependences of the ignition time. Weakly stra ined 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 i n decreasing powers of Delta for the shape and for the exponential growth r ate of the radical pool. The accurate description of the solution necessita tes computation of three terms in the asymptotic expansion for the growth r ate, yielding predictions for the ignition time that remain accurate even f or values of Delta of the order of unity.