The Asymptotic Structure of Strained Chain-Branching Premixed Flames Under Nonadiabatic Conditions

The present paper, which investigates the chain-branching premixed-flame dynamics under nonadiabatic conditions, is the third and final contribution to a series of studies on premixed flames with the modified Zel'dovich-Linan two-step mechanism under the three most prevailing physical influences, namely (i) flame stretch, (ii) differential diffusion, and (iii) heat loss to or gain from the flame downstream. Asymptotic analysis for the chain-branching premixed-flame structure is carried out within the framework of the intermediate recombination regime, in which the chain-recombination layer with a characteristic thickness of ${\rm{O}}({\beta <^>{ - 1/2}})$O(beta-1/2) is asymptotically thicker than the inner chain-branching layer but thinner than the outer convective-diffusive layer. The combustion characteristics are presented by the $\mathcal{M}$M-$\Delta $Delta plots, where the specific reaction intensity $\mathcal{M}$M is a measure of the reaction intensity and the reduced recombination Damkohler number $\Delta $Delta is a measure of the inverse of the flame stretch. The $\mathcal{M}$M-$\Delta $Delta plots are found to exhibit a striking resemblance to the AEA counterparts of Libby and Williams (1983), in that the S-shaped $\mathcal{M}$M-$\Delta $Delta curves emerge for sufficiently large downstream heat losses. The Damkohler number ratio ${D_I}/{D_{II}}$DI/DII is found to be another key parameter controlling the chain-branching flame dynamics. The greater ${D_I}/{D_{II}}$DI/DII, the slower the recombination reaction and the thicker the recombination layer tends to be, which results in a reduced overall nonlinearity for the Zel'dovich-Linan two-step mechanism. Consequently, abrupt extinction is less likely observable in the much slower recombination regime. Combining with the results of the previous two papers by the authors, the overall combustion characteristics of strained chain-branching premixed flames with the Zel'dovich-Linan two-step kinetics is found to be in qualitatively good agreement with that of one-step AEA, unless the recombination step is too slow or too fast to be reasonably described by the intermediate recombination regime.