Near-limit characteristics of planar premixed flames in the Zel’dovich-Liñán models with first- and second-order recombination reactions

The characteristics of the planar premixed flame near the flammability limit were investigated by employing the Zel’dovich-Liñán two-step reaction model, focusing on the fast recombination regime. The structure of the reaction zone was numerically analyzed to examine the differences in flame characteristics between first-order and second-order recombination reactions, under the limit of a large chain branching Zel’dovich number, β. As the ratio of reaction rates between branching and recombination decreases, the concentration of chain carriers also decreases, leading to a reduction in flame speed, as expected. In the flammability limit condition where the flame speed is zero, there are notable differences in combustion characteristics between first and second recombination. As the flammable limit is approached, the ratio of reaction rates approaches the mathematical constant e in first-order recombination due to substantial fuel leakage from the reaction zone, whereas in second-order recombination, the ratio of reaction rates approaches zero as there is no fuel leakage. An asymptotic analysis was employed to derive the relevant expressions for the ratio of reaction rates at the flammable limit.