Hostname: page-component-76fb5796d-22dnz Total loading time: 0 Render date: 2024-04-25T11:36:20.227Z Has data issue: false hasContentIssue false
  • English
  • Français

Theory of premixed-flame propagation in large-scale turbulence

Published online by Cambridge University Press:  19 April 2006

P. Clavin  and
F. A. Williams
P. Clavin
Affiliation:
Laboratoire de Dynamique et Thermophysique des Fluides, Université de Provence-Centre Saint Jerome, 13397 Marseille, France
F. A. Williams
Affiliation:
Laboratoire de Dynamique et Thermophysique des Fluides, Université de Provence-Centre Saint Jerome, 13397 Marseille, France Permanent address: Department of Applied Mechanics and Engineering Sciences, University of California, La Jolla, California 92903.
Get access Rights & Permissions [Opens in a new window]

Abstract

A statistical theory is developed for the structure and propagation velocity of premixed flames in turbulent flows with scales large compared with the laminar flame thickness. The analysis, free of usual closure assumptions, involves a regular perturbation for small values of the ratio of laminar flame thickness to turbulence scale, termed the scale ratio ε, and a singular perturbation for large values of the non-dimensional activation temperature β. Any effects of the flame on the flow are considered to be given. In this initial study, molecular coefficients for diffusion of heat and reactants are set equal. The results identify convective-diffusive and reactive-diffusive zones in the flame and predict thickening of the flame by turbulence through streamwise displacement of the reactive-diffusive zone. Profiles for intensities of temperature fluctuations and for streamwise turbulent transport are obtained. A fundamental quantity occurring in the analysis is the longitudinal displacement of the reactive-diffusive zone in an Eulerian frame by turbulent fluctuations, and to first order in the scale ratio this equals the longitudinal displacement of fluid elements in an Eulerian frame by turbulent fluctuations, herein termed simply the Eulerian displacement. To first order in the scale ratio it is found that, if the Eulerian displacement experiences the same type of statistical non-stationarity as the corresponding Lagrangian displacement, then the diffusion approximation is valid for streamwise turbulent transport but the turbulent flame thickens as time increases, while if the Eulerian displacement is statistically stationary then the diffusion approximation necessitates a negative coefficient of diffusion in part of the flame but the flame thickness remains constant. By carrying the analysis to second order in the scale ratio it is shown that the turbulent-flame speed exceeds the laminar-flame speed by an amount proportional to the mean square of the transverse gradient of the Eulerian displacement. This result can be understood from the mechanistic viewpoint of a wrinkled laminar flame in terms of the increase in flame area produced by turbulence. Thus the theory provides a precise statistical quantification of the model of the wrinkled laminar flame for describing structures of turbulent flames.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 90 , Issue 3 , 13 February 1979 , pp. 589 - 604
Copyright
© 1979 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

Ballal, D. R. & Lefebvre, A. H. 1974 Turbulence effects on enclosed flames. Acta Astronautica 1, 471–483.Google Scholar
Comte-Bellot, G. & Corrsin, S. 1971 Simple Eulerian time correlation and narrow-band velocity signals in grid-generated, ‘isotropic’ turbulence. J. Fluid Mech. 48, 273–337.Google Scholar
Joulin, G. & Clavin, P. 1978 Stability analysis of nonadiabatic flame. Submitted to Combust. Flame.Google Scholar
Kuznetsov, V. R. 1975 Certain peculiarities of movement of a flame front in a turbulent flow of homogeneous fuel mixtures. Fiz. Goreniya Vzryva 11, 574–581.Google Scholar
Landau, L. 1944 Theory of slow combustion. Acta Physicochima. USSR 19, 77–85.Google Scholar
Libby, P. A. & Williams, F. A. 1976 Turbulent flows involving chemical reactions. Ann. Rev. Fluid Mech. 8, 351–376.Google Scholar
Markstein, G. H. 1964 Nonsteady Flame Propagation. AGARDograph no. 75.
Sivashinsky, G. I. 1977a Diffusional-thermal theory of cellular flames. Combust. Sci. Tech. 15, 137–145.Google Scholar
Sivashinsky, G. I. 1977b Nonlinear analysis of hydrodynamic instability in laminar flames. Acta Astronautica 4, 1177–1206.Google Scholar
Williams, F. A. 1965 Combustion Theory. Addison-Wesley.
Williams, F. A. 1970 An approach to turbulent flame theory, J. Fluid Mech. 40, 401–421.Google Scholar
Williams, F. A. 1971 Theory of combustion in laminar flows. Ann. Rev. Fluid Mech. 3, 171–188.Google Scholar
Williams, F. A. 1975 A review of some theoretical considerations of turbulent flame structure. Analytical and Numerical Methods for Investigation of Flow Fields with Chemical Reactions, Especially Related to Combustion. AGARD Conf. Proc. no. 164, pp. III-1–III-25.