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Implications of laminar flame finite thickness on the structure of turbulent premixed flames

  • Kim Q. N. Kha (a1), Vincent Robin (a1), Arnaud Mura (a1) and Michel Champion (a1)


A layered description of the structure of turbulent flame brushes is provided for situations featuring large but finite values of the Damköhler number, which correspond to the wrinkled flame regime of turbulent premixed combustion. One special focus of this study is placed on the description of the leading edge of the turbulent flame brush, the role of which is known to be essential with respect to propagation, transport and stabilization issues. On the basis of rather simple and well-identified working hypotheses, the influence of slight increases in the Karlovitz number values is revealed. The phenomenology and associated statistics are also investigated analytically, which leads to a mathematical description of the leading edge internal structure. With respect to the progress variable statistics, i.e. probability density function, this leading edge can indeed be thought of as the inner part of a boundary layer where the influence of the finite thickness of laminar flamelets can no longer be neglected. From the proposed description, standard fast-chemistry closures, which are currently used to perform the numerical simulation of turbulent combustion, may easily be generalized to account for the finite-rate chemistry effects occurring in this sublayer, thus emphasizing the interest of the present analysis for turbulent combustion theory and modelling.


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Amato, A. & Lieuwen, T. C. 2014 Analysis of flamelet leading point dynamics in an inhomogeneous flow. Combust. Flame 161, 13371347.
Anand, M. S. & Pope, S. B. 1984 Calculations of premixed turbulent flames by PDF methods. Combust. Flame 67, 127142.
Aspden, A. J., Day, M. S. & Bell, J. B. 2011 Turbulence-flame interactions in lean premixed hydrogen: transition to the distributed burning regime. J. Fluid Mech. 680, 287320.
Barrère, M. 1974 Modèles de combustion turbulente. Rev. Gén. Therm. 148, 295308.
Borghi, R. 1984 Mise au point sur la structure des flammes turbulentes. J. Chim. Phys. 81, 361370.
Borghi, R. 1985 On the structure and morphology of turbulent premixed flames. In Recent Advances in the Aerospace Science (ed. Casci, C.), pp. 117138. Plenum.
Borghi, R. 1988 Turbulent combustion modelling. Prog. Energy Combust. Sci. 14, 245292.
Borghi, R., Argueyrolles, B., Gauffie, S. & Souhaite, P. 1986 Application of a presumed pdf model of turbulent combustion to reciprocating engines. Proc. Combust. Inst. 21, 15911599.
Bowman, C. T., Hanson, R. K., Gardiner, W. C., Frenklach, V., Lissianski, M., Goldenberg, M., Smith, G. P., Crosley, D. R. & Golden, D. M.1997 An optimized detailed chemical reaction mechanism for methane combustion and no formation and reburning Tech. Rep. GRI-97/0020. Gas Research Institute, Chicago IL.
Bray, K. N. C. 1980 Turbulent flows with premixed reactants. In Turbulent Reacting Flows (ed. Libby, P. A. & Williams, F. A.), pp. 115184. Springer.
Bray, K. N. C., Champion, M., Libby, P. A. & Swaminathan, N. 2006 Finite rate chemistry and presumed pdf models for premixed turbulent combustion. Combust. Flame 146, 665673.
Bray, K. N. C. & Libby, P. A. 1994 Recent developments in the BML model of premixed turbulent combustion. In Turbulent Reactive Flows (ed. Libby, P. A. & Williams, F. A.), pp. 115147. Academic Press.
Bray, K. N. C., Libby, P. A., Masuya, G. J. & Moss, J. B. 1981 Turbulence production in premixed turbulent flames. Combust. Sci. Technol. 25, 127140.
Bray, K. N. C. & Moss, J. B. 1977 A unified statistical model of the premixed turbulent flame. Acta Astronaut. 4, 291319.
Buckmaster, J. D. & Ludford, G. S. S. 1982 Theory of Laminar Flames, 1st edn. Cambridge University Press.
Clavin, P. 1985 Dynamic behavior of premixed flame fronts in laminar and turbulent flows. Prog. Energy Combust. Sci. 11, 159.
Clavin, P. & Williams, F. A. 1979 Theory of premixed-flame propagation in large-scale turbulence. J. Fluid Mech. 90 (3), 589604.
Corless, R. M., Gonnet, G. H., Hare, D. E. G., Jeffrey, D. J. & Knuth, D. E. 1996 On the Lambert W function. Adv. Comput. Math. 5, 329359.
Damköhler, G.1947 The effects of turbulence on the flame velocity in gas mixtures. NACA Tech. Mem. 1112.
Dong, Q., Robin, V., Mura, A. & Champion, M. 2013 Analysis of algebraic closures of the mean scalar dissipation rate of the progress variable applied to stagnating turbulent flames. Flow Turbul. Combust. 90, 301323.
Ern, A. & Giovangigli, V. 1995 Fast and accurate multicomponent transport property evaluation. J. Comput. Phys. 120, 105116.
Kalt, P. A. M., Chen, Y. C. & Bilger, R. W. 2002 Experimental investigation of turbulent scalar flux in premixed stagnation type flames. Combust. Flame 129, 401415.
Klimov, A. M. 1963 Laminar flame in a turbulent flow. Zh. Prikl. Mekh. Tekh. Fiz. 3, 4958.
Kolmogorov, A. N. 1941 Dissipation of energy in the locally isotropic turbulence. Proc. USSR Acad. Sci. 32, 1618.
Kolmogorov, A. N., Petrovskii, I. & Piskunov, N. 1937 A study of the diffusion equation with increase in the amount of substance and its application to a biology problem. Bull. Univ. Moscow Ser. Int. A 1, 116; see also, Selected Works of A. N. Kolmogorov (ed. V. M. Tikhomirov), vol. I, pp. 242, Kluwer Academic (1991).
Libby, P. A. & Bray, K. N. C. 1981 Counter gradient diffusion in premixed turbulent flames. AIAA J. 19, 205213.
Libby, P. A. & Williams, F. A. 2000 Presumed pdf analysis of partially premixed turbulent combustion. Combust. Sci. Technol. 161, 351390.
Liñán, A. & Williams, F. A. 1993 Fundamental Aspects of Combustion, 1st edn. Oxford University Press.
Lipatnikov, A. N. 2013 Fundamentals of Premixed Turbulent Combustion, 1st edn. CRC Press, Taylor and Francis.
Mantel, T. & Borghi, R. 1994 A new model of premixed wrinkled flame propagation based on a scalar dissipation equation. Combust. Flame 96, 443457.
Mura, A. & Champion, M. 2009 Relevance of the Bray number in the small-scale modeling of turbulent premixed flames. Combust. Flame 156, 729733.
Mura, A., Galzin, F. & Borghi, R. 2003 A unified pdf-flamelet model for turbulent premixed combustion. Combust. Sci. Technol. 175, 15731609.
Mura, A., Tsuboi, K. & Hasegawa, T. 2008 Modelling of the correlation between velocity and reactive scalar gradients in turbulent premixed flames based on DNS data. Combust. Theor. Model. 12, 671698.
Peters, N. 1986 Laminar flamelet concepts in turbulent combustion. Proc. Combust. Inst. 21, 12311250.
Peters, N. 1999 The turbulent burning velocity for large scale and small scale turbulence. J. Fluid Mech. 384, 107132.
Poludnenko, A. Y. & Oran, E. S. 2010 The interaction of high-speed turbulence with flames: global properties and internal flame structure. Combust. Flame 157, 9951011.
Pope, S. B. 1987 Turbulent premixed flames. Annu. Rev. Fluid Mech. 19, 237270.
Pope, S. B. & Anand, M. S. 1984 Flamelet and distributed combustion in premixed turbulent flames. Proc. Combust. Inst. 20, 403410.
Robin, V., Mura, A. & Champion, M. 2011 Direct and indirect thermal expansion effects in turbulent premixed flames. J. Fluid Mech. 689, 149182.
Robin, V., Mura, A., Champion, M. & Hasegawa, T. 2010 Modelling the effects of thermal expansion on scalar fluxes in turbulent flames. Combust. Sci. Technol. 182, 449464.
Rutland, C. J. & Cant, R. S. 1994 Turbulent transport in premixed flames. In Proc. Summer Program, Center for Turbulence Research, NASA Ames/Stanford University.
Sabel’nikov, V. A. & Lipatnikov, A. N. 2013 Transition from pulled to pushed premixed turbulent flames due to countergradient transport. Combust. Theor. Model. 17, 11541175.
Savre, J., Carlsson, H. & Bai, X. S. 2013 Turbulent methane/air premixed flame structure at high Karlovitz numbers. Flow Turbul. Combust. 90, 325341.
Spalding, D. B. 1971 Mixing and chemical reaction in confined turbulent flames. Proc. Combust. Inst. 13, 649657.
Spalding, D. B. 1976 Development of the eddy break up model of turbulent combustion. Proc. Combust. Inst. 16, 16571663.
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.
Veynante, D., Trouvé, A., Bray, K. N. C. & Mantel, T. 1997 Gradient and counter-gradient scalar transport in turbulent premixed flames. J. Fluid Mech. 332, 263293.
Williams, F. A. 1976 Criteria for existence of wrinkled laminar flame structure of turbulent premixed flames. Combust. Flame 26, 269270.
Williams, F. A. 1985 Combustion Theory, 2nd edn. Benjamin Cummings.
Zel’dovich, Ya. B., Barenblatt, G. I., Librovich, V. B. & Makhviladze, G. M. 1985 The Mathematical Theory of Combustion and Explosion. Consultant Bureau.
Zel’dovich, Ya. B. & Frank-Kamenetskii, D. A. 1947 Turbulent and Heterogeneous Combustion. Moscow MMI, (in Russian).
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Implications of laminar flame finite thickness on the structure of turbulent premixed flames

  • Kim Q. N. Kha (a1), Vincent Robin (a1), Arnaud Mura (a1) and Michel Champion (a1)


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