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Transport equations for reaction rate in laminar and turbulent premixed flames characterized by non-unity Lewis number

Lookup NU author(s): Professor Nilanjan ChakrabortyORCiD



This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND).


© 2018 Hydrogen Energy Publications LLC Transport equations for (i) the rate W of product creation and (ii) its Favre-averaged value W˜ are derived from the first principles by assuming that W depends solely on the temperature and mass fraction of a deficient reactant in a premixed turbulent flame characterized by the Lewis number Le different from unity. The right hand side of the transport equation for W˜ involves seven unclosed terms, with some of them having opposite signs and approximately equal large magnitudes when compared to the left-hand-side terms. Accordingly, separately closing each term does not seem to be a promising approach, but a joint closure relation for the sum TΣ¯ of the seven terms is sought. For this purpose, theoretical and numerical investigations of variously stretched laminar premixed flames characterized by Le<1 are performed and the linear relation between TΣ integrated along the normal to a laminar flame and a product of (i) the consumption velocity uc and (ii) the stretch rate s˙w evaluated in the flame reaction zone is obtained. Based on this finding and simple physical reasoning, a joint closure relation of TΣ¯∝ρWs˙¯ is hypothesized, where ρ is the density and s˙ is the stretch rate. The joint closure relation is tested against 3D DNS data obtained from three statistically 1D, planar, adiabatic, premixed turbulent flames in the case of a single-step chemistry and Le=0.34, 0.6, or 0.8. In all three cases, the agreement between TΣ¯ and ρWs˙¯ extracted from the DNS is good with exception of large (c¯>0.4) values of the mean combustion progress variable c¯ in the case of Le=0.34. The developed linear relation between TΣ¯ and ρWs˙¯ helps to understand why the leading edge of a premixed turbulent flame brush can control its speed.

Publication metadata

Author(s): Lipatnikov AN, Chakraborty N, Sabelnikov VA

Publication type: Article

Publication status: Published

Journal: International Journal of Hydrogen Energy

Year: 2018

Volume: 43

Issue: 45

Pages: 21060-21069

Print publication date: 08/11/2018

Online publication date: 06/10/2018

Acceptance date: 11/09/2018

Date deposited: 11/09/2018

ISSN (print): 0360-3199

ISSN (electronic): 1879-3487

Publisher: Elsevier Ltd


DOI: 10.1016/j.ijhydene.2018.09.082


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