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Activation-Energy Asymptotics of the Plane Premixed Flame

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Book cover Numerical Methods in Laminar Flame Propagation

Part of the book series: Notes on Numerical Fluid Mechanics ((NONUFM,volume 6))

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Abstract

The plane premixed flame is considered in the limit of large activation energy for various chemical reactions. A full account of the one-reactant model is given, including its equivalence to a two-reactant model away from stoichiometry. The behaviour of the two-reactant model close to stoichiometry is then sketched. A brief discussion is given of more complex kinetic schemes, namely: the two-reactant model with dissociation of the product; sequential decomposition reactions; and the autocatalytic chain reaction introduced by Zeldovich. Emphasis throughout is on explaining the method of activation-energy asymptotics and what it offers in the computation of plane flames.

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References

  1. F.A. Williams: Asymptotic methods in deflagrations. In First International Specialists Meeting of the Combustion Institute, pp. LXX-LXXIV. Section Francaise du Combustion Institute, 1981.

    Google Scholar 

  2. F.A. Williams: Combustion Theory. Reading, Massachu: setts: Addison-Wesley, 1965.

    Google Scholar 

  3. N. Peters: Theoretical implications of nonequal diffusivities of heat and matter on the stability of a plane premixed flame. This volume.

    Google Scholar 

  4. J.D. Buckmaster & G.S.S. Ludford: Theory of Laminar Flames. Cambridge: University Press, 1981.

    Google Scholar 

  5. Y.B. Zeldovich & D.A. Frank-Kamenetskii: A theory of thermal propagation of flame. Acta Physicochimica U.R.S.S., 9, 341–50 (1938).

    Google Scholar 

  6. W.B. Bush & F.E. Fendell: Asymptotic analysis of laminar flame propagation for general Lewis numbers. Combustion Science and Technology, 1, 421–8 (1970).

    Article  Google Scholar 

  7. J.F. Clarke: The pre-mixed flame with large activation energy and variable mixture strenth: elementary asymptotic analysis. Combustion Science and Technology, 10, 189–94 (1975).

    Article  Google Scholar 

  8. G.F. Carrier, F.E. Fendell & W.B. Bush: Stoichiometry and flame-holder effects on a one-dimensional flame. Combustion Science and Technology, 18, 33–46 (1978).

    Article  Google Scholar 

  9. T. Mitani: Propagation velocities of two-reactant flames. Combustion Science and Technology, 21, 175–7 (1980).

    Article  Google Scholar 

  10. A.K. Sen & G.S.S. Ludford: The near-stoichiometric behavior of combustible mixtures. Part I: Diffusion of the reactants. Combustion Science and Technology, 21, 15–23 (1979).

    Article  Google Scholar 

  11. G.S.S. Ludford & A.K. Sen: Burning rate maximum of a plane premixed flame. Progress in Astronautics and Aeronautics, 76, 427–36 (1981). (Combustion in Reactive Systems, ed. J. Ray Bowen, N. Manson, Antoni K. Oppenheim, and R.I. Soloukhin.)

    Google Scholar 

  12. A.K. Sen & G.S.S. Ludford: Effects of mass diffusion on the burning rate of non-dilute mixtures. In Eighteenth International Symposium on Combustion, pp. 417–24. Pittsburgh: The Combustion Institute, 1981.

    Google Scholar 

  13. A.K. Sen & G.S.S. Ludford: The near-stoichiometric behavior of combustible mixtures. Part II: Dissociation of the products. Combustion Science and Technology, 26, 183–91 (1981).

    Article  Google Scholar 

  14. A.K. Sen & G.S.S. Ludford: Maximum flame temperature and burning rate of combustible mixtures. Submitted for publication.

    Google Scholar 

  15. G.S.S. Ludford & A.K. Sen: The effect of dissociation on the near-stoichiometric burning of non-dilute mixtures. Submitted for publication.

    Google Scholar 

  16. A.K. Kapila & G.S.S. Ludford: Two-step sequential reactions for large activation energy. Combustion and Flame, 29, 167–76 (1977).

    Article  Google Scholar 

  17. S.B. Margolis & B.J. Matkowsky: Flame propagation with a sequential reaction mechanism. SIAM Journal on Applied Mathematics (to appear).

    Google Scholar 

  18. Y.B. Zeldovich: Theory of flame propagation. NACA Technical Memorandum 1282, 1951. Translation of: K Teorii Rasprostranenia Plameni. Zhurnal Fizicheskoi Khimii, 22, 27–49 (1948).

    Google Scholar 

  19. A. Linân: A theoretical analysis of premixed flame propagation with an isothermal chain reaction. Instituto Nacional de Tecnica Aerospacial “Esteban Terradas”, USAF Contract No. E00AR 68–0031, Technical Report No. 1, 1971.

    Google Scholar 

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© 1982 Springer Fachmedien Wiesbaden

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Ludford, G.S.S. (1982). Activation-Energy Asymptotics of the Plane Premixed Flame. In: Peters, N., Warnatz, J. (eds) Numerical Methods in Laminar Flame Propagation. Notes on Numerical Fluid Mechanics, vol 6. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-14006-1_2

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  • DOI: https://doi.org/10.1007/978-3-663-14006-1_2

  • Publisher Name: Vieweg+Teubner Verlag, Wiesbaden

  • Print ISBN: 978-3-528-08080-8

  • Online ISBN: 978-3-663-14006-1

  • eBook Packages: Springer Book Archive

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