Transport equations for reaction rate in laminar and turbulent premixed flames characterized by non-unity Lewis number
Artikel i vetenskaplig tidskrift, 2018

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 (T_Σ ) ̅ 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 T_Σ integrated along the normal to a laminar flame and a product of (i) the consumption velocity u_c 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 (T_Σ ) ̅∝(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 (T_Σ ) ̅ 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 (T_Σ ) ̅ and (ρWs ̇ ) ̅ helps to understand why the leading edge of a premixed turbulent flame brush can control its speed.

Lewis number



premixed turbulent combustion

mean reaction rate

turbulent flame speed


Andrei Lipatnikov

Chalmers, Mekanik och maritima vetenskaper, Förbränning och framdrivningssystem

N. Chakraborty

Newcastle University

Vladimir Sabelnikov

Central Aerohydrodynamic Institute (TsAGI)

ONERA Centre de Palaiseau

International Journal of Hydrogen Energy

0360-3199 (ISSN)

Vol. 43 45 21060-21069





Teknisk mekanik

Havs- och vattendragsteknik

Strömningsmekanik och akustik


Grundläggande vetenskaper



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