Asymptotic analysis of nonadiabatic chain-branching premixed flames near the flammability limit

The present study analyzes the behavior of chain-branching premixed flames near or below the flammability limit. By applying the Zel’dovich–Liñán two-step reaction model and large activation energy asymptotic analysis within the fast recombination regime, a quantitative study was conducted to examine how flame stretch, heat transfer downstream, and the fuel Lewis number influence near-limit or sublimit flames. The results indicate that the ratio between the reaction rates of the chain-branching and recombination (r) tends toward a critical minimum value as the recombination Damköhler number (Δ) increases, which serves as an important criterion defining the flammability condition. The flammability limit extends under super-adiabatic conditions or fuel Lewis numbers of less than unity; under sub-adiabatic conditions or fuel Lewis numbers of greater than unity, it narrows. The four-term asymptotic approximation for r(Δ) closely matches the numerical results. Near the flammability limit, super-adiabatic conditions intensify flames with increasing flame stretch, whereas sub-adiabatic conditions lead to a turning-point behavior of the flame with increasing strain rates. Below the flammability limit, flames sustained by heat gain from downstream remain confined near the stagnation plane, which serves as a key factor in extending the flammability limit. Finally, it was confirmed that the fuel Lewis number and downstream heat transfer have similar effects on the total enthalpy at flame, and both similarly influence flame behavior near or below the flammability limit. However, under low strain rate conditions, the effect of the Lewis number is more dominant.