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Theory of flame-front stability

Published online by Cambridge University Press:  28 March 2006

Wiktor Eckhaus
Wiktor Eckhaus
Affiliation:
Massachusetts Institute of Technology
[dagger]Now at the Institut Henri Poincaré, Paris.
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Abstract

A study of the stability of a plane laminar flame front is made. The effects of disturbances on the flame structure are investigated by a small perturbations technique, taking into account the mechanism of diffusion, heat conduction and unsteady combustion. By use of a simplified model of the flame structure, and the assumption that the flame thickness is small compared with the wavelength of disturbances, a formula for the perturbation of the flame propagation velocity is derived. The flame velocity is shown to depend on the curvature of the flame, and on the rates of change of fluid velocities at the flame boundary. From stability analysis it then follows that properties of the mixture, as expressed in terms of the coefficient of heat conductivity and various coefficients of diffusion, play an important role in determining the stability picture. For some estimated values of these parameters the theoretical results are shown to agree with the general trend of the experimentally observed behaviour.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 10 , Issue 1 , February 1961 , pp. 80 - 100
Copyright
© 1961 Cambridge University Press

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References

Erdelyi, A. 1953 (Director, Bateman Project). Higher Transcendental Functions. New York: McGraw-Hill.
Eckhaus, W. 1959 On the stability of laminar flame-fronts. M.I.T. Fluid Dynamics Research Group Report no. 59-9.Google Scholar
Emmons, H. W. (Editor) 1958 Fundamentals of Gas Dynamics. Princeton University Press.
Hirschfelder, J. O., Curtiss, C. F. & Bird, R. B. 1954 Molecular Theory of Gases and Liquids. New York: John Wiley and Sons.
Landau, L. D. & Lifschitz, E. M. 1953 Mechanics of Continuous Media. Moscow.
Markstein, G. H. 1951 Experimental and theoretical studies of flame-stability. J. Aero. Sci. 18.Google Scholar
Spalding, D. B. 1955 Some Fundamentals of Combustion. Gas Turbine Series, Vol. 2.