The Asymptotic Structure of Strained Chain-Branching Premixed Flames with Nonunity Lewis Numbers and Their Extinction

ABSTRACT

Extinction of strained chain-branching premixed flames with nonunity fuel and chain-carrier Lewis numbers is asymptotically analyzed by employing an NEF (Nearly Equidiffusional Flame) limit modified specifically for the Zel’dovich-Liñán two-step mechanism. The asymptotic chain-branching flame-structure analysis is carried out within the framework of the intermediate recombination regime, in which the recombination layer is asymptotically thicker than the inner chain-branching layer, but thinner than the outer convective-diffusive layer. In order to construct a consistent activation-energy asymptotics for the thinnest chain branching layer, thickness of the intermediate recombination-layer as well as deviation of the chain-carrier Lewis number from unity is scaled by the inverse square root of the chain-branching Zel’dovich number. Because the fuel is consumed only by the chain-branching reaction, characterized by a large chain-branching Zel’dovich number, the influences of nonunity fuel Lewis number on extinction with two-step chemistry is found to be qualitatively almost identical to that with overall one-step chemistry. Therefore, strained chain-branching flames can be extinguished by increasing the flow strain rate if the fuel Lewis number is sufficiently large. However, the chain-carrier Lewis number is found to be not capable of qualitatively influencing the extinction characteristics because the peak chain-carrier concentration tends to remain almost invariant with varying flow strain rate. Abrupt extinction is more readily observed for the faster recombination regime, for which the overall effective nonlinearity of the two-step mechanism becomes larger. Finally, the critical Lewis number boundary for extinction is predominantly dependent on the fuel Lewis number. Consequently, the overall extinction characteristics of strained chain-branching flames is found to be qualitatively similar to that found within the framework of the overall single-step activation-energy asymptotics.

KEYWORDS:

• Activation-Energy asymptotics
• chain-branching premixed flame
• Zel’Dovich-Liñán two-step mechanism
• intermediate recombination regime
• nonunity lewis number

Acknowledgements

SRL was supported by the Research Program funded by Seoul National University of Science and Technology.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Notes

¹ According to the footnote on the page 358 of Williams (1985), the idea of diffusional-thermal instability was first presented in the Zel’dovich’s 1944 book of Theory of Combustion and Gas Detonation Moscow, Akad. Nauk USSR, which was republished in 1992 as a part of the Zel’dovich’s selected works in Zeldovich (1992).