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The Complex Dynamics of Wrinkled Flames

  • G. Joulin
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 48)

Abstract

We summarize recent analytical attempts to understand the dynamics of hydrodynamically unstable, hence wrinkled, premixed flames. Exact solutions to qualitatively correct, non-linear evolution equations are displayed, and used as a basis to study the role of large scale geometry in the local flame dynamics. The flame response to external hydrodynamic noise also is evoked.

Keywords

Flame Front Flame Propagation Premix Flame Flame Speed Laminar Flame 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    F.A. Williams (1985), “Combustion theory”, 2nd Edition, Benjamin-Cummings, Menlo Park.Google Scholar
  2. 2.
    P. Clavin (1985), “Dynamic behavior of premixed flames in laminar and turbulent flow”, Prog. En. Comb. Sci., 11, 1–59.CrossRefGoogle Scholar
  3. 3.
    Ya.B. Zel’Dovitch, G.I. Barenblatt, V.B. Librovitch, G.M. Markhviladze (1985), “The mathematical theory of combustion and explosions”, Consultant Bureau, New York.CrossRefGoogle Scholar
  4. 4.
    L.D. Landau (1944), “On the theory of slow combustion”, Acta Physicochim. USSR, 19, 77.Google Scholar
  5. 5.
    G. Darrieus (1938), “Propagation d’un front de flamme; essai de théorie de vitesses anormales de déflagration par développement spontané de la turbulence”, unpublished work presented at “La Technique Moderne”, Paris.Google Scholar
  6. 6.
    G.S.S. Ludford, J. Buckmaster (1982), “Theory of laminar flames”, Cambridge University Press, Cambridge.zbMATHGoogle Scholar
  7. 7.
    P. Clavin, G. Joulin (1983), “Premixed flames in high-intensity, large-scale turbulent flows”, J. de Physique-Lettres (France), 1, 1–12.CrossRefGoogle Scholar
  8. 8.
    P. Cambray, B. Deshaies, G. Joulin (1987), “Gaseous premixed flames in nonuniform flows”, AGARD PEP Conference no 422, 36.1–36.6.Google Scholar
  9. 9.
    G.H. Markstein (1965), “Non-steady flame propagation”, Pergamon Press, New York.Google Scholar
  10. 10.
    G.I. Sivashinsky (1977), “Nonlinear analysis of hydrodynamic instability in laminar flames; Part I”. Acta Astron., 4, 1177–1206.CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    D.M. Michelson, G.I. Sivashinsky (1977), “Nonlinear analysis of hydrodynamic instability in laminar flames; Part II”. Acta Astron., 4, 1207–1221.CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    G.I. Sivashinsky (1983), “Instabilities, pattern formation and turbulence in flames”, Ann. Rev. Fluid. Mech., 15, 179–199.ADSCrossRefGoogle Scholar
  13. 13.
    G.I. Sivashinsky, P. Clavin (1987), “On the nonlinear theory of hydrodynamic instability in flames”, J. Physique (France), 48, 193–198.CrossRefGoogle Scholar
  14. 14.
    O. Thual, M. Henon, U. Frisch (1985), “Application of pole decomposition to an equation governing the dynamics of wrinkled flames”, J. Physique (France), 46, 1485–1494.CrossRefGoogle Scholar
  15. 15.
    M. Renardy (1987), “A model equation in combustion theory exhibiting an infinite number of secondary bifurcations”, Physica D, 28, 155–167.ADSCrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    G. Joulin (1987), “On the hydrodynamic stability of flat-burner flames”, Comb. Sci. and Techn., 53, 315–338.CrossRefGoogle Scholar
  17. 17.
    G. Joulin (1989), “On the hydrodynamic stability of curved flames”, J. Physique (France), 50, 1069–1082.CrossRefMathSciNetGoogle Scholar
  18. 18.
    Ya. B. Zel’Dovitch, D. Istratov, A.G. Kidin, V.B. Librovitch (1980), “Flame propagation in tubes: hydrodynamics and stability”, Comb. Sci. and Techn., 24, 1–13.CrossRefGoogle Scholar
  19. 19.
    P. Pelce (1989), “Dynamics of curved fronts”, Academic Press, New York.Google Scholar
  20. 20.
    D.M. Michelson, G.I. Sivashinsky (1983), “Thermal — expansion — induced cellular flames”, Comb. and Flame, 48, 41–47.Google Scholar
  21. 21.
    G. Joulin (1989), “On the nonlinear theory of hydrodynamic instabilities of expanding flames”, submitted.Google Scholar
  22. 22.
    A. Palm-Leis, R.A. Strehlow (1969), “On the propagation of turbulent flames”, Comb. and Flame, 13, 111–129.CrossRefGoogle Scholar
  23. 23.
    G. Joulin (1988), “On a model for the response of unstable flames to turbulence”, Comb. Sci. and Techn., 53, 1–6.CrossRefGoogle Scholar
  24. 24.
    B. Denet (1988) “Simulation numérique d’instabilités de front de flamme”, Thèse, Université de Marseille.Google Scholar
  25. 25.
    I.S. Gradshteyn, I.M. Ryzhik “Tables of integrals, series and products”, Academic Press, N.Y.Google Scholar
  26. 26.
    H. Chate (1989) “A minimal model for turbulent flame fronts”, in “Mathematical Modelling in Combustion and related topics”, NATO AS I Series, E140, 441-448, Brauner & Schmidt-Laine Eds., M. Nijhoff Pub., Dordrecht.Google Scholar
  27. 27.
    Y.C. Lee, H.H. Chen (1982) “Non-linear dynamical models of plasma turbulence”, Phys. Scri., T.2, 41–47.ADSCrossRefMathSciNetGoogle Scholar
  28. 28.
    Sherlock Holmes; quoted in: C.M. Bender, S.A. Orszag (1984) “Advanced mathematical methods for scientists and engineers”, 61, McGraw Hill Intern. Book Company, Auckland.Google Scholar

Copyright information

© Springer-Verlag Berlin, Heidelberg 1990

Authors and Affiliations

  • G. Joulin
    • 1
  1. 1.U.A. 193 CNRS, ENSMAPoitiersFrance

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