Transport equations for reaction rate in laminar and turbulent premixed flames characterized by non-unity Lewis number |
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Authors: | Andrei N Lipatnikov Nilanjan Chakraborty Vladimir A Sabelnikov |
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Affiliation: | 1. Department of Mechanics and Maritime Sciences, Chalmers University of Technology, Gothenburg, 41296, Sweden;2. School of Mechanical and Systems Engineering, Newcastle University, Newcastle Upon Tyne, NE1 7RU, United Kingdom;3. ONERA – the French Aerospace Laboratory, F-91761 Palaiseau, France;4. Central Aerohydrodynamic Institute (TsAGI), 140180 Zhukovsky, Moscow Region, Russian Federation |
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Abstract: | Transport equations for (i) the rate of product creation and (ii) its Favre-averaged value are derived from the first principles by assuming that depends solely on the temperature and mass fraction of a deficient reactant in a premixed turbulent flame characterized by the Lewis number different from unity. The right hand side of the transport equation for 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 of the seven terms is sought. For this purpose, theoretical and numerical investigations of variously stretched laminar premixed flames characterized by are performed and the linear relation between integrated along the normal to a laminar flame and a product of (i) the consumption velocity and (ii) the stretch rate evaluated in the flame reaction zone is obtained. Based on this finding and simple physical reasoning, a joint closure relation of is hypothesized, where is the density and 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 , 0.6, or 0.8. In all three cases, the agreement between and extracted from the DNS is good with exception of large () values of the mean combustion progress variable in the case of . The developed linear relation between and helps to understand why the leading edge of a premixed turbulent flame brush can control its speed. |
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Keywords: | Premixed turbulent combustion Mean reaction rate Lewis number Turbulent flame speed Modeling DNS |
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