Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-19T06:57:52.587Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  26 April 2006

Arnaud Trouvé  and
Thierry Poinsot
Arnaud Trouvé
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA 94305, USA Present address: Institut Français du Pétrole, 1 et 4, avenue de Bois-Préau, BP 311, 92506 Rueil-Malmaison, France
Thierry Poinsot
Affiliation:
CNRS, Institut de Mécanique des Fluides de Toulouse, 31400, France
Get access Rights & Permissions [Opens in a new window]

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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 278 , 10 November 1994 , pp. 1 - 31
Copyright
© 1994 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

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. 505–512. 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, 487–511.Google Scholar
Ashurst, W. T., Peters, N. & Smooke, M. D. 1987 Numerical simulation of turbulent flame structure with non-unity Lewis number. Combust. Sci. Tech. 53, 339–375.Google Scholar
Borghi, R. 1990 Turbulent premixed combustion: further discussion on the scales of the fluctuations. Combust. Flame 80, 304–312.Google Scholar
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. 115–183. Springer.
Bray, K. N. C. 1990 Studies of the turbulent burning velocity. Proc. R. Soc. Lond. A 431, 315–335.Google Scholar
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. 541–563. 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, 143–172.Google Scholar
Candel, S. M. & Poinsot, T. 1990 Flame stretch and the balance equation for the flame surface area. Combust. Sci. Tech. 70, 1–15.Google Scholar
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. 809–815. 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. 771–780. 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, 65–82.Google Scholar
Clavin, P. 1985 Dynamic behavior of premixed flame fronts in laminar and turbulent flows. Prog. Energy Combust. Sci. 11, 1–59.Google Scholar
Clavin, P. & Garcia, P. 1983 The influence of temperature dependence of diffusivities on the dynamics of flame fronts. J. Méc. 2, 245–263.Google Scholar
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, 251–282.CrossRefGoogle Scholar
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. 591–637. 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, 131–152.Google Scholar
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, 101–117.Google Scholar
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, 405–436.Google Scholar
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, 2728–2731.Google Scholar
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. 1381–1402. 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, 121–132.Google Scholar
Lele, S. K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103, 16–42.Google Scholar
Libby, P. & Williams, F. A. 1983 Strained premixed laminar flames under nonadiabatic conditions. Combust. Sci. Tech. 31, 1–42.Google Scholar
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, 443–457.Google Scholar
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, 169–181.Google Scholar
Matalon, M. & Matkowsky, B. J. 1982 Flames are gasdynamic discontinuities. J. Fluid Mech. 124, 239–259.Google Scholar
Meneveau, C. & Poinsot, T. 1991 Stretching and quenching of flamelets in premixed turbulent combustion. Combust. Flame 86, 311–332.Google Scholar
Pelcé, P. & Clavin, P. 1982 Influence of hydrodynamics and diffusion upon the stability limits of laminar premixed flames. J. Fluid Mech. 124, 219–237.Google Scholar
Peters, N. 1986 Laminar flamelet concepts in turbulent combustion. In Twenty-First Symp. (Intl) on Combustion, pp. 1231–1250. The Combustion Institute.
Poinsot, T. & Lele, S. K. 1992 Boundary conditions for direct simulations of compressible viscous flows. J. Comput. Phys. 101, 104–129.Google Scholar
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, 45–73.Google Scholar
Poinsot, T., Veynante, D. & Candel, S. M. 1991 Quenching processes and premixed turbulent combustion diagrams. J. Fluid Mech. 228, 561–605.Google Scholar
Pope, S. B. 1988 Evolution of surfaces in turbulence. Intl J. Engng Sci. 26, 445–469.Google Scholar
Pope, S. B. 1990 Computations of turbulent combustion: progress and challenges. In Twenty-Third Symp. (Intl) on Combustion, pp. 591–612. 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. 781–789. 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, 58–69.Google Scholar
Rutland, C. J. & Trouvé, A. 1993 Direct simulations of premixed turbulent flames with non-unit Lewis numbers. Combust. Flame 94, 41–57.Google Scholar
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, 327–350.Google Scholar