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The evolution equation for the flame surface density in turbulent premixed combustion

  • Arnaud Trouvé (a1) (a2) and Thierry Poinsot (a3)

Abstract

One basic effect of turbulence in turbulent premixed combustion is for the fluctuating velocity field to wrinkle the flame and greatly increase its surface area. In the flamelet theory, this effect is described by the flame surface density. An exact evolution equation for the flame surface density, called the Σ-equation, may be written, where basic physical mechanisms like production by hydrodynamic straining and destruction by propagation effects are described explicitly. Direct numerical simulation (DNS) is used in this paper to estimate the different terms appearing in the Σ-equation. The numerical configuration corresponds to three-dimensional premixed flames in isotropic turbulent flow. The simulations are performed for various mixture Lewis numbers in order to modify the strength and nature of the flame-flow coupling. The DNS-based analysis provides much information relevant to flamelet models. In particular, the flame surface density, and the source and sink terms for the flame surface density, are resolved spatially across the turbulent flame brush. The geometry as well as the dynamics of the flame differ quite significantly from one end of the reaction zone to the other. For instance, contrary to the intuitive idea that flame propagation effects merely counteract the wrinkling due to the turbulence, the role of flame propagation is not constant across the turbulent brush and switches from flame surface production at the front to flame surface dissipation at the back. Direct comparisons with flamelet models are also performed. The Bray-Moss-Libby assumption that the flame surface density is proportional to the flamelet crossing frequency, a quantity that can be measured in experiments, is found to be valid. Major uncertainties remain, however, over an appropriate description of the flamelet crossing frequency. In comparison, the coherent flame model of Marble & Broadwell achieves closure at the level of the Σ-equation and provides a more promising physically based description of the flame surface dynamics. Some areas where the model needs improvement are identified.

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Abdel-Gayed, R. G., Bradley, D., Hamid, M. N. & Lawes, M. 1984 Lewis number effects on turbulent burning velocity. In Twentieth Symp. (Intl) on Combustion, pp. 505512. The Combustion Institute.
Aldredge, R. C. & Williams, F. A. 1991 Influence of wrinkled premixed-flame dynamics on largescale, low-intensity turbulent flow. J. Fluid Mech. 228, 487511.
Ashurst, W. T., Peters, N. & Smooke, M. D. 1987 Numerical simulation of turbulent flame structure with non-unity Lewis number. Combust. Sci. Tech. 53, 339375.
Borghi, R. 1990 Turbulent premixed combustion: further discussion on the scales of the fluctuations. Combust. Flame 80, 304312.
Bray, K. N. C. 1980 Turbulent flows with premixed reactants. In Turbulent Reacting Flows (ed. P. A. Libby & F. A. Williams). Topics in Applied Physics, vol. 44, pp. 115183. Springer.
Bray, K. N. C. 1990 Studies of the turbulent burning velocity. Proc. R. Soc. Lond. A 431, 315335.
Bray, K. N. C., Champion, M. & Libby, P. A. 1989 The interaction between turbulence and chemistry in premixed turbulent flames. In Turbulent Reactive Flows (ed. R. Borghi & S. N. B. Murthy). Lecture Notes in Engineering, vol. 40, pp. 541563. Springer.
Bray, K. N. C., Libby, P. A. & Moss, J. B. 1984 Flamelet crossing frequencies and mean reaction rates in premixed turbulent combustion. Combust. Sci. Tech. 41, 143172.
Candel, S. M. & Poinsot, T. 1990 Flame stretch and the balance equation for the flame surface area. Combust. Sci. Tech. 70, 115.
Candel, S. M., Veynante, D., Lacas, F., Maistret, E., Darabiha, N. & Poinsot, T. 1990 Coherent flame model: applications and recent extensions. In Recent Advances in Combustion Modelling (ed. B. Larrouturou). World Scientific.
Cant, R. S., Pope, S. B. & Bray, K. N. C. 1990 Modelling of flamelet surface-to-volume ratio in turbulent premixed combustion. In Twenty-Third Symp. (Intl) on Combustion, pp. 809815. The Combustion Institute.
Cheng, R. K., Shepherd, I. G. & Talbot, L. 1988 Reaction rates in premixed turbulent flames and their relevance to the turbulent burning speed. In Twenty-Second Symp. (Intl) on Combustion, pp. 771780. The Combustion Institute.
Chew, T. C., Bray, K. N. C. & Britter, R. E. 1990 Spatially resolved flamelet statistics for reaction rate modeling. Combust. Flame 80, 6582.
Clavin, P. 1985 Dynamic behavior of premixed flame fronts in laminar and turbulent flows. Prog. Energy Combust. Sci. 11, 159.
Clavin, P. & Garcia, P. 1983 The influence of temperature dependence of diffusivities on the dynamics of flame fronts. J. Méc. 2, 245263.
Clavin, P. & Williams, F. A. 1982 Effects of molecular diffusion and of thermal expansion on the structure and dynamics of premixed flames in turbulent flows of large scale and low intensity. J. Fluid Mech. 216, 251282.
Darabiha, N., Giovangigli, V., Trouvé, A., Candel, S. M. & Esposito, E. 1987 Coherent flame description of turbulent premixed ducted flames. In Turbulent Reactive Flows (ed. R. Borghi & S. N. B. Murthy). Lecture Notes in Engineering, vol. 40, pp. 591637. Springer.
Driscoll, J. F. & Gulati, A. 1988 Measurement of various terms in turbulent kinetic energy balance within a flame and comparison with theory. Combust. Flame 72, 131152.
Driscoll, J. F., Sutkus, D. J., Roberts, W. L., Post, M. E. & Goss, L. P. 1993 The strain exerted by a vortex on a flame - Determined from velocity field images. 31st Aerospace Sciences Meeting, Reno NV, Paper 0362. AIAA.
Duclos, J. M., Veynante, D. & Poinsot, T. 1993 A comparison of flamelet models for premixed turbulent combustion. Combust. Flame 95, 101117.
Goix, P. J. & Shepherd, I. G. 1992 Lewis number effects on turbulent premixed flame structure. Fall Meeting of the Western States Section. The Combustion Institute.
Haworth, D. C. & Poinsot, T. 1992 Numerical simulations of Lewis number effects in turbulent premixed flames. J. Fluid Mech. 244, 405436.
Kerstein, A. R., Ashurst, W. T. & Williams, F. A. 1988 Field equation and interface propagation in an unsteady homogeneous flow field. Phys. Rev. A 37, 27282731.
Kuznetsov, V. R. & Sabel'Nikov, V. A. 1990 Turbulence and Combustion. Hemisphere.
Law, C. K. 1988 Dynamics of stretched flames. In Twenty-Second Symp. (Intl) on Combustion, pp. 13811402. The Combustion Institute.
Lee, T. W., North, G. L. & Santavicca, D. A. 1992 Curvature and orientation statistics of turbulent premixed flame fronts. Combust. Sci. Tech. 84, 121132.
Lele, S. K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103, 1642.
Libby, P. & Williams, F. A. 1983 Strained premixed laminar flames under nonadiabatic conditions. Combust. Sci. Tech. 31, 142.
Maistret, E., Darabiha, N., Poinsot, T., Veynante, D., Lacas, F., Candel, S. M. & Esposito, E. 1989 Recent developments in the coherent flamelet description of turbulent combustion. In Proc. 3rd Intl SIAM Conf. on Numerical Combustion .
Mantel, T. & Borghi, R. 1994 A new model of premixed wrinkled flame propagation based on a scalar dissipation equation. Combust. Flame 96, 443457.
Marble, F. E. & Broadwell, J. E. 1977 The coherent flame model for turbulent chemical reactions. Project Squid Tech. Rep. TRW-9-PU.
Matalon, M. 1983 On flame stretch. Combust. Sci. Tech. 31, 169181.
Matalon, M. & Matkowsky, B. J. 1982 Flames are gasdynamic discontinuities. J. Fluid Mech. 124, 239259.
Meneveau, C. & Poinsot, T. 1991 Stretching and quenching of flamelets in premixed turbulent combustion. Combust. Flame 86, 311332.
Pelcé, P. & Clavin, P. 1982 Influence of hydrodynamics and diffusion upon the stability limits of laminar premixed flames. J. Fluid Mech. 124, 219237.
Peters, N. 1986 Laminar flamelet concepts in turbulent combustion. In Twenty-First Symp. (Intl) on Combustion, pp. 12311250. The Combustion Institute.
Poinsot, T. & Lele, S. K. 1992 Boundary conditions for direct simulations of compressible viscous flows. J. Comput. Phys. 101, 104129.
Poinsot, T., Echekki, T. & Mungal, M. G. 1992 A study of the laminar flame tip and implications for premixed turbulent combustion. Combust. Sci. Tech. 81, 4573.
Poinsot, T., Veynante, D. & Candel, S. M. 1991 Quenching processes and premixed turbulent combustion diagrams. J. Fluid Mech. 228, 561605.
Pope, S. B. 1988 Evolution of surfaces in turbulence. Intl J. Engng Sci. 26, 445469.
Pope, S. B. 1990 Computations of turbulent combustion: progress and challenges. In Twenty-Third Symp. (Intl) on Combustion, pp. 591612. The Combustion Institute.
Pope, S. B. & Cheng, W. K. 1988 The stochastic flamelet model of turbulent premixed combustion. In Twenty-Second Symp. (Intl) on Combustion, pp. 781789. The Combustion Institute.
Roberts, W. L., Driscoll, J. F., Drake, M. C. & Goss, L. P. 1993 Images of the quenching of a flame by a vortex: to quantify regimes of turbulent combustion. Combust. Flame 94, 5869.
Rutland, C. J. & Trouvé, A. 1993 Direct simulations of premixed turbulent flames with non-unit Lewis numbers. Combust. Flame 94, 4157.
Williams, F. A. 1985 Combustion Theory, 2nd edn. Benjamin Cummings.
Wray, A. A. 1990 Minimal storage time-advancement schemes for spectral methods. Tech. Rep. NASA Ames Research Center, M. S. 202 A-1.
Wu, M. S., Kwon, S., Driscoll, J. F. & Faeth, G. M. 1990 Turbulent premixed hydrogen/air flames at high reynolds numbers. Combust. Sci. Tech. 73, 327350.
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The evolution equation for the flame surface density in turbulent premixed combustion

  • Arnaud Trouvé (a1) (a2) and Thierry Poinsot (a3)

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