On the Universal Role of Turbulence in the Propagation of Deflagrations and Detonations

  • John H. S. Lee
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 12)


A given explosive mixture has two limiting burning rates; the lower limit of a molecular diffusion controlled laminar flame and the upper limit of Chapman-Jouguet detonation. Experiments indicate that nature always tends to maximize the burning rate under the constraints imposed by the initial and boundary conditions. Between the two limiting cases, the burning rate or the effective flame speed is a continuous spectrum. Turbulence plays the universal role in determining the burning rate that spans the three orders of magnitude from laminar flame (δ ≃ 0.5 m/s) to Chapman-Jouguet detonations (VCJ ≃ 1800 m/s). Weak turbulent flames are essentially laminar flames in which turbulence increases the burning surface area and hence the burning rate or effective burning velocity. The flame surface being a density interface is subjected to dynamics and diffusive instabilities and interface instability mechanisms become important as the turbulent intensity increases. The instability mechanisms play important roles in the break-up of the flame surface and control the fine structure and hence the details of the mixing and reaction processes. Shock waves become important for even higher levels of turbulence. Apart from inducing interface instability (Rayleigh-Taylor, etc.), creation of vortex structures, adiabatic heating of the mixtures, shock wave Mach interactions also produce shear layers and subsequent turbulence via Kelvin-Helmholtz instability. Boundary conditions control the effectiveness of the various mechanisms and it appears that there is no sharp distinction between high speed turbulence deflagrations and detonations. The lecture emphasizes the need to develop models to describe the mechanisms correctly and investigate the cooperative effects among themselves.


Burning Rate Detonation Wave Burning Velocity Flame Propagation Vortex Tube 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Notes on Numerical Fluid Mechanics, Vol. 6, “Numerical Methods in Laminar Flame Propagation”, Eds. Norbert Peters and Jürgen Warnatz. Friedr. Vieweg &Sohn. Braunschweig/Wiesbaden (1981).Google Scholar
  2. 2.
    Chapman, W.R. and Wheeler, R.V. (1926) and (1927), J. chem. Soc. (London), Vol. 37 and Vol. 38.Google Scholar
  3. 3.
    Laffitte, P., Compt. Rend. 186, 95, 1 (1928).Google Scholar
  4. 4.
    Shchelkin, K.I., JETP, Vol. 10, p. 823 (1940).Google Scholar
  5. 5.
    Guenoche, H. and Manson, N., Rev. de l’Insitut Francais du Petrole, No. 2, pp. 53–69 (1979).Google Scholar
  6. 6.
    Brochet, C., “Contribution a l’etude des detonations instables dans les melanges gazeux. Doctoral thesis, Univ. Poitiers, France (1966).Google Scholar
  7. 7.
    Lee, J.H.S., “The Propagation of Turbulent Flames and Detonations in Tubes”, in ‘Advances in Chemical Reaction Dynamics’, Eds. Rentzepis, P. and Capellos, C., D. Reidel Publ. Co. (1985).Google Scholar
  8. 8..
    Lee, J.H.S., “Recent Advances in Gaseous Detonations”, AIAA paper 79–0287, 17th Aerospace Sciences Meeting, New Orleans (1979).Google Scholar
  9. 9.
    Manton, J., Von Elbe, G., Lewis, B., Jour. Chem. Phys., Vol. 20, No. 1 (1952).Google Scholar
  10. 10.
    Taylor, G.I., Proc. Roy. Soc. (London), A201, 192 (1950).ADSGoogle Scholar
  11. 11.
    Markstein, G., Jour. Aero. Sci., Vol. 24, No. 3 (1957).Google Scholar
  12. 12.
    Markstein, G. and Squire, W., Jour. Acoustical Sec., Vol. 27, No. 3, p. 416 (1955).CrossRefGoogle Scholar
  13. 13.
    Rayleicfli, Lord., “The Theory of Sound”, Vol. II. Dover Publ. (1945).Google Scholar
  14. 14.
    Markstein, G., “Non-Steady Flame Propagation”, Pergamon Press (1964).Google Scholar
  15. 15.
    Lee, J.H.S. and Moen, I., Progr. Energy Comb. Sci., Vol. 6, p. 389 (1980).CrossRefGoogle Scholar
  16. 16.
    Sivashinsky, G.I., Ann. Rev. Fluid Mech., Vol. 15, pp. 179–199 (1983).ADSCrossRefGoogle Scholar
  17. 17.
    Clavin, P., Progr. Energy Comb. Sci., Vol. 11, pp. 1–59 (1985).CrossRefGoogle Scholar
  18. 18.
    Rundinger, G. and Somers, L., J. Fluid Mech. 7, 161–176 (1960).ADSCrossRefGoogle Scholar
  19. 19.
    Haas, J.F., “Interaction of Weak Shock Waves and Discrete Gas Inhomogeneities”, GALCTT thesis (1983), Calif. Inst, of Technology.Google Scholar
  20. 20.
    Emergy, M.H., Gardner, J., Boris, J., Cooper, A.C., Phys. of Fluids, 27(5), 1984.Google Scholar
  21. 21.
    Dryden, H.L., Q. Appl. Math, 1, 7 (1943).MathSciNetzbMATHGoogle Scholar
  22. 22.
    Taylor, G.I., Proc. Roy. Soc. (London), Ser. A, 151, 421 (1935).ADSzbMATHCrossRefGoogle Scholar
  23. 23.
    Tennekes, H., Phys. of Fluids, 669 (1968).Google Scholar
  24. 24.
    Fickett, W. and Davies, W., “Detonation”, Los Alamos series in basic and Applied Sciences. University of California Press (1979).Google Scholar
  25. 25.
    Shchelkin, K.I. and Troshin, Ya.K., “Gasdynamics of Osmbustion”, Mono Book Corp. (1965).Google Scholar
  26. 26.
    Soloukhin, R.I., “Shock Waves and Detonations in Gases”, Mono Book Corp. (1966).Google Scholar
  27. 27.
    Strehlow, R., “Fundamentals of Combustion”, Int. Textbook Co. (1968).Google Scholar
  28. 28.
    Bach, G., Khystautas, R. and Lee, J.H.S., 12th Comb. Symp. (Int’l), pp. 883–67 (1968), Combustion Institute, Pittsburgh.Google Scholar
  29. 29.
    Thomas, G.O. and Edwards, D.H., J. Phys. D., Appl. Phys 16, pp. 1881–1892 (1983).ADSCrossRefGoogle Scholar
  30. 30.
    Oran, E.S., Young, T.R., Boris, J.P., Picone, J.M. and Edwards, D.H.,19th Comb. Symp. (Int’l), p. 573 (1982), Combustion Institute, Pittsburgh.Google Scholar
  31. 31.
    Dupre, G., Peraldi, O., Lee, J.H.S. and Knystautas, R., “Propagation of Detonation Waves in an Acoustic Attenuating Wall Tube”, paper submitted to the 11th ICDERS, Warsaw, Poland, Aug. 3–7 (1987).Google Scholar
  32. 32.
    Knystautas, R., Lee, J.H.S., Moen, I. and Wagner, H.Gg., 17th Comb. Symp. (Int’l), pp. 1235–1245 (1979). Combustion Institute, Pittsburgh.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1988

Authors and Affiliations

  • John H. S. Lee
    • 1
  1. 1.Mechanical Engineering DepartmentMcGill UniversityMontrealCanada

Personalised recommendations