Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-16T14:45:21.923Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  08 December 2015

Kim Q. N. Kha ,
Vincent Robin ,
Arnaud Mura  and
Michel Champion
Kim Q. N. Kha
Affiliation:
Institut Pprime UPR 3346 CNRS - ENSMA - 86961 Futuroscope, France
Vincent Robin
Affiliation:
Institut Pprime UPR 3346 CNRS - ENSMA - 86961 Futuroscope, France
Arnaud Mura*
Affiliation:
Institut Pprime UPR 3346 CNRS - ENSMA - 86961 Futuroscope, France
Michel Champion
Affiliation:
Institut Pprime UPR 3346 CNRS - ENSMA - 86961 Futuroscope, France
*
†Email address for correspondence: arnaud.mura@ensma.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

JFM classification

Reacting Flows: Combustion Reacting Flows: Flames Reacting Flows: Reacting Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 787 , 25 January 2016 , pp. 116 - 147
Check for updates
Copyright
© 2015 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Amato, A. & Lieuwen, T. C. 2014 Analysis of flamelet leading point dynamics in an inhomogeneous flow. Combust. Flame 161, 1337–1347.CrossRefGoogle Scholar
Anand, M. S. & Pope, S. B. 1984 Calculations of premixed turbulent flames by PDF methods. Combust. Flame 67, 127–142.CrossRefGoogle Scholar
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, 287–320.CrossRefGoogle Scholar
Barrère, M. 1974 Modèles de combustion turbulente. Rev. Gén. Therm. 148, 295–308.Google Scholar
Borghi, R. 1984 Mise au point sur la structure des flammes turbulentes. J. Chim. Phys. 81, 361–370.CrossRefGoogle Scholar
Borghi, R. 1985 On the structure and morphology of turbulent premixed flames. In Recent Advances in the Aerospace Science (ed. Casci, C.), pp. 117–138. Plenum.CrossRefGoogle Scholar
Borghi, R. 1988 Turbulent combustion modelling. Prog. Energy Combust. Sci. 14, 245–292.CrossRefGoogle Scholar
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, 1591–1599.CrossRefGoogle Scholar
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.Google Scholar
Bray, K. N. C. 1980 Turbulent flows with premixed reactants. In Turbulent Reacting Flows (ed. Libby, P. A. & Williams, F. A.), pp. 115–184. Springer.CrossRefGoogle Scholar
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, 665–673.CrossRefGoogle Scholar
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. 115–147. Academic Press.Google Scholar
Bray, K. N. C., Libby, P. A., Masuya, G. J. & Moss, J. B. 1981 Turbulence production in premixed turbulent flames. Combust. Sci. Technol. 25, 127–140.CrossRefGoogle Scholar
Bray, K. N. C. & Moss, J. B. 1977 A unified statistical model of the premixed turbulent flame. Acta Astronaut. 4, 291–319.CrossRefGoogle Scholar
Buckmaster, J. D. & Ludford, G. S. S. 1982 Theory of Laminar Flames, 1st edn. Cambridge University Press.CrossRefGoogle Scholar
Clavin, P. 1985 Dynamic behavior of premixed flame fronts in laminar and turbulent flows. Prog. Energy Combust. Sci. 11, 1–59.CrossRefGoogle Scholar
Clavin, P. & Williams, F. A. 1979 Theory of premixed-flame propagation in large-scale turbulence. J. Fluid Mech. 90 (3), 589–604.CrossRefGoogle Scholar
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, 329–359.CrossRefGoogle Scholar
Damköhler, G.1947 The effects of turbulence on the flame velocity in gas mixtures. NACA Tech. Mem. 1112.Google Scholar
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, 301–323.CrossRefGoogle Scholar
Ern, A. & Giovangigli, V. 1995 Fast and accurate multicomponent transport property evaluation. J. Comput. Phys. 120, 105–116.CrossRefGoogle Scholar
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, 401–415.CrossRefGoogle Scholar
Klimov, A. M. 1963 Laminar flame in a turbulent flow. Zh. Prikl. Mekh. Tekh. Fiz. 3, 49–58.Google Scholar
Kolmogorov, A. N. 1941 Dissipation of energy in the locally isotropic turbulence. Proc. USSR Acad. Sci. 32, 16–18.Google Scholar
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, 1–16; see also, Selected Works of A. N. Kolmogorov (ed. V. M. Tikhomirov), vol. I, pp. 242, Kluwer Academic (1991).Google Scholar
Libby, P. A. & Bray, K. N. C. 1981 Counter gradient diffusion in premixed turbulent flames. AIAA J. 19, 205–213.CrossRefGoogle Scholar
Libby, P. A. & Williams, F. A. 2000 Presumed pdf analysis of partially premixed turbulent combustion. Combust. Sci. Technol. 161, 351–390.CrossRefGoogle Scholar
Liñán, A. & Williams, F. A. 1993 Fundamental Aspects of Combustion, 1st edn. Oxford University Press.CrossRefGoogle Scholar
Lipatnikov, A. N. 2013 Fundamentals of Premixed Turbulent Combustion, 1st edn. CRC Press, Taylor and Francis.Google Scholar
Mantel, T. & Borghi, R. 1994 A new model of premixed wrinkled flame propagation based on a scalar dissipation equation. Combust. Flame 96, 443–457.CrossRefGoogle Scholar
Mura, A. & Champion, M. 2009 Relevance of the Bray number in the small-scale modeling of turbulent premixed flames. Combust. Flame 156, 729–733.CrossRefGoogle Scholar
Mura, A., Galzin, F. & Borghi, R. 2003 A unified pdf-flamelet model for turbulent premixed combustion. Combust. Sci. Technol. 175, 1573–1609.CrossRefGoogle Scholar
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, 671–698.CrossRefGoogle Scholar
Peters, N. 1986 Laminar flamelet concepts in turbulent combustion. Proc. Combust. Inst. 21, 1231–1250.CrossRefGoogle Scholar
Peters, N. 1999 The turbulent burning velocity for large scale and small scale turbulence. J. Fluid Mech. 384, 107–132.CrossRefGoogle Scholar
Poludnenko, A. Y. & Oran, E. S. 2010 The interaction of high-speed turbulence with flames: global properties and internal flame structure. Combust. Flame 157, 995–1011.CrossRefGoogle Scholar
Pope, S. B. 1987 Turbulent premixed flames. Annu. Rev. Fluid Mech. 19, 237–270.CrossRefGoogle Scholar
Pope, S. B. & Anand, M. S. 1984 Flamelet and distributed combustion in premixed turbulent flames. Proc. Combust. Inst. 20, 403–410.CrossRefGoogle Scholar
Robin, V., Mura, A. & Champion, M. 2011 Direct and indirect thermal expansion effects in turbulent premixed flames. J. Fluid Mech. 689, 149–182.CrossRefGoogle Scholar
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, 449–464.CrossRefGoogle Scholar
Rutland, C. J. & Cant, R. S. 1994 Turbulent transport in premixed flames. In Proc. Summer Program, Center for Turbulence Research, NASA Ames/Stanford University.Google Scholar
Sabel’nikov, V. A. & Lipatnikov, A. N. 2013 Transition from pulled to pushed premixed turbulent flames due to countergradient transport. Combust. Theor. Model. 17, 1154–1175.CrossRefGoogle Scholar
Savre, J., Carlsson, H. & Bai, X. S. 2013 Turbulent methane/air premixed flame structure at high Karlovitz numbers. Flow Turbul. Combust. 90, 325–341.CrossRefGoogle Scholar
Spalding, D. B. 1971 Mixing and chemical reaction in confined turbulent flames. Proc. Combust. Inst. 13, 649–657.CrossRefGoogle Scholar
Spalding, D. B. 1976 Development of the eddy break up model of turbulent combustion. Proc. Combust. Inst. 16, 1657–1663.CrossRefGoogle Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.CrossRefGoogle Scholar
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, 263–293.CrossRefGoogle Scholar
Williams, F. A. 1976 Criteria for existence of wrinkled laminar flame structure of turbulent premixed flames. Combust. Flame 26, 269–270.CrossRefGoogle Scholar
Williams, F. A. 1985 Combustion Theory, 2nd edn. Benjamin Cummings.Google Scholar
Zel’dovich, Ya. B., Barenblatt, G. I., Librovich, V. B. & Makhviladze, G. M. 1985 The Mathematical Theory of Combustion and Explosion. Consultant Bureau.CrossRefGoogle Scholar
Zel’dovich, Ya. B. & Frank-Kamenetskii, D. A. 1947 Turbulent and Heterogeneous Combustion. Moscow MMI, (in Russian).Google Scholar