The asymptotic solution of near-limit chain-branching premixed flames with the Zel’dovich–Liñán two-step mechanism in the linear and fast recombination regime

Abstract

Near-limit characteristics of chain-branching premixed flames is investigated numerically and asymptotically by employing the Zel’dovich–Liñán two-step mechanism with linear and (sufficiently) fast recombination, for which both chain-branching and -recombination steps take place in a thin reactive layer of O(β−1), with β being the chain-branching Zel’dovich number. The numerical and asymptotic results reveal that the rate-ratio eigenvalue r between the chain branching and recombination steps approaches a minimum critical value of rmin→e as the chain-recombination step becomes infinitely fast. The existence of the finite asymptotic value of r=e indicates that no steadily propagating flame solution can be found for fuel concentrations lower than its critical value, corresponding to the criticality of r=e, thereby explaining the (lean) flammability limit. This intrinsic flammability characteristics with linear recombination is the most outstanding contrast to the quadratic recombination counterpart, for which flammability is achieved only with external heat loss added to the model.Novelty and significance statementNear-limit combustion characteristics of chain-branching flames is investigated numerically and asymptotically by employing the Zel’dovich–Linan two-step chemical kinetics with linear and fast recombination. This work demonstrates that the rate-ratio eigenvalue between the chain-branching and -recombination steps asymptotically approaches a critical minimum value, corresponding to the flammability limit. The existence of flammability limit with the linear recombination is found to be the most significant contrast to the quadratic recombination model, which is incapable of predicting flammability limit. By this study, a formal asymptotic procedure, by which the crossover temperature and lean flammability limit condition can be determined without assuming a steady-state approximation of intermediate species, is established and can be applied to analyze flame structures with multi-step reduced mechanisms.