Instabilities in Gaseous Combustion

  • Nickolai M. RubtsovEmail author
Part of the Heat and Mass Transfer book series (HMT)


By means of high-speed color cinematography, it was shown that the flames in lean Н2–air mixtures at an initial stage propagate symmetrically and the flame radius can be estimated from the frames of speed filming. It is shown that sufficiently strict calculation of cellular structure of the flame front of lean hydrogen mixtures requires consideration of a 3D problem, however, thermal diffusion instabilities at the initial stage of combustion have no effect on the velocity of flame which can be estimated assuming unperturbed flame front in the range of  8%<H2<15%. It was shown that the analysis of experimental data on flame propagation in lean mixtures does not allow taking apart the results of calculation by two-dimensional model with regard to convection and without convection. It was experimentally shown, that isobutene additives in quantities below a concentration limit (up to 1.5 %) tend to increase, and СО2 additives up to 15 %—to reduce the flame propagation velocity in lean Н2–air mixtures. The reasons for the acceleration of combustion in the presence of hydrocarbon additive are considered. The method of high-speed cinematography was used in investigation of transition of spherical flame front to flat front in n-pentane–air and methane–air mixtures initiated by a spark discharge. Cellular flame structures were observed in the transition. Modeling based on compressible reactive Navier–Stokes equations at low Mach number showed qualitative agreement with experiment. Features of combustion in flame cells caused by hydrodynamic instability are experimentally established. It was shown that each flame cell represents a separate “chemical reactor”; in the cell, the process of complete chemical transformation occurs. It was shown that inhomogeneities detected in light emission that arise after contact of a flame front with the walls of cylindrical reactor can be correlated with the occurrence of acoustic waves by the example of combustion of hydrogen–air mixtures containing 30 and 15 % of hydrogen. It was revealed that flame velocities in stoichiometric hydrogen–air mixtures at central spark initiation do not depend on the material of inner reactor surface but on its shape.   


Hydrogen Methne n-pentane Spherical flame front Flat Instabilities Thermal diffusion Hydrodynamic Acoustic Compressible reactive Navier-Stokes equations Low Mach number Flame cells 


  1. 1.
    Ronney, P.D.: Premixed-gas flames. In: Ross, H. (ed.) Microgravity Combustion: Fires in Free Fall, pp. 35–82. Academic Press, London (2001)Google Scholar
  2. 2.
    Rubtsov, N.M., Sepljarsky, B.S., Naboko, I.M., Troshin, K.Y., Chernysh, V.I., Tsvetkov, G.I.: Flame propagation regimes at combustion of lean hydrogen-air mixtures in the presence of additives at central spark initiation at atmospheric pressure. Glob. J. Sci. Frontier Res. B Chem. 14(2) (2014) Global Journals Inc. (USA)Google Scholar
  3. 3.
    Markstein, G.H.: Nonsteady Flame Propagation, p. 370. Pergamon Press, Oxford (1964)Google Scholar
  4. 4.
    YaB, Zeldovich: Theory of Combustion and Detonation of Gases, p. 320. Academy of Sciences (USSR), Moscow (1944)Google Scholar
  5. 5.
    Ronney, P.D., Whaling, K.N., Abbud-Madrid, A., Gatto, J.L., Pisowicz, V.L.: Stationary premixed flames in spherical and cylindrical geometries. AIAA J. 32, 569–577 (1994)CrossRefGoogle Scholar
  6. 6.
    Coward, H.F., Brinsley, F.: Influence of additives on flames. J. Chem. Soc. 105, 1859–1866 (1914)CrossRefGoogle Scholar
  7. 7.
    Ronney P.D.: Near-limit flame structures at low Lewis number. Combust. Flame 82, 1–14Google Scholar
  8. 8.
    YaB, Zeldovich, Drozdov, N.P.: Diffusion features in the vicinity of flame propagation limits. Russ. J. Phys. Chem. 17, 134–144 (1943) (in Russian)Google Scholar
  9. 9.
    Rubtsov, N.M., Seplyarsky, B.S., Tsvetkov, G.I., Chernysh, V.I.: Numerical investigation of the effects of surface recombination and initiation for laminar hydrogen flames at atmospheric pressure. Mendeleev Commun. 18, 220–222 (2008)CrossRefGoogle Scholar
  10. 10.
    Rubtsov, N.M., Seplyarsky, B.S., Troshin, K.Y., Tsvetkov, G.I., Chernysh, V.I.: Initiation and propagation of laminar spherical flames at atmospheric pressure. Mendeleev Commun. 85, 218–220 (2011)CrossRefGoogle Scholar
  11. 11.
    Rubtsov, N.M., Kotelkin, V.D., Seplyarskii, B.S., Tsvetkov, G.I., Chernysh, V.I.: Investigation into the combustion of lean hydrogen–air mixtures at atmospheric pressure by means of high-speed cinematography. Mendeleev Commun. 21, 215–217 (2011)CrossRefGoogle Scholar
  12. 12.
    Lewis, B., Von Elbe, G.: Combustion, Explosions and Flame in Gases, p. 566. Academic Press, New York (1987)Google Scholar
  13. 13.
    Dahoe, A.E.: Laminar burning velocities of hydrogen–air mixtures from closed vessel gas explosions. J. Loss Prev. Process Ind. 18, 152–169 (2005)CrossRefGoogle Scholar
  14. 14.
    Rubtsov, N.M., Kotelkin, V.D., Seplyarskii, B.S., Tsvetkov, G.I., Chernysh, V.I.: Investigation into the features of initiated combustion of lean hydrogen-air mixtures at atmospheric pressure by means of high-speed filming. Chem. Phys. Mesosc. 13, 331–339 (2011) (in Russian)Google Scholar
  15. 15.
    Backstrom, G.: Simple Fields of Physics by Finite Elements Analysis (Paperback), p. 324. GB Publishing, Norway (2005)Google Scholar
  16. 16.
    Macek, A.: Effect of additives on formation of spherical detonation waves in hydrogen-oxygen-mixtures. AIAA J. 8, 1915–1918 (1963)CrossRefGoogle Scholar
  17. 17.
    Rubtsov, N.M., Azatyan, V.V., Baklanov, D.I., Tsvetkov, G.I., Chernysh, V.I.: Effect of chemically active additives on the detonation wave velocity and the detonation limits in lean mixtures. Theor. Found. Chem. Eng. 41, 154–163 (2007)CrossRefGoogle Scholar
  18. 18.
    Rayleigh, J.W.: On convection currents in a horizontal layer of fluid, when the higher temperature is on the underside. Philos. Mag. 32, 529–546 (1916)CrossRefzbMATHGoogle Scholar
  19. 19.
    Polezhaev, V., Nikitin, S.: Thermo acoustics and heat transfer in an enclosure induced by a wall heating. In: 16th International Congress on Sound and Vibration, 2009, Kraków, Poland, 5–9 July, pp. 2–8Google Scholar
  20. 20.
    Zel’dovich, Y.B., Barenblatt, G.A., Librovich, V.B., Machviladze, D.V.: Mathematical Theory of Flame Propagation. Nauka, Moscow (1980) (in Russian)Google Scholar
  21. 21.
    Sokolik, A.S.: Self-ignition flame and detonation in gases. Academy of Sciences USSR, Moscow (1960) (in Russian)zbMATHGoogle Scholar
  22. 22.
    Zeldovich, Y.B., Barenblatt, G.I.: Theory of flame propagation. Combust. Flame 3, 61–74 (1959)CrossRefGoogle Scholar
  23. 23.
    Landau, L.: On the theory of slow combustion. Acta Phys. Chim. URSS 19, 77 (1944)Google Scholar
  24. 24.
    Sivashinsky, G.I.: Nonlinear analysis of hydrodynamic instability in laminar flames-I. Derivation of basic equations. Acta Astronaut. 4, 1177 (1977)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Clavin, P., Williams, F.A.: Effects of molecular diffusion and of thermal expansion on the structure and dynamics of premixed flames in turbulent flows of large scale and low intensity. J. Fluid Mech. 116, 251 (1982)CrossRefzbMATHGoogle Scholar
  26. 26.
    Pelcé, P., Clavin, P.: Influence of hydrodynamics and diffusion upon the stability limits of laminar premixed flames. J. Fluid Mech. 124, 219 (1982)CrossRefzbMATHGoogle Scholar
  27. 27.
    Clavin, P., Garcia, P.: The influence of the temperature dependence of diffusivities on the dynamics of flame fronts. J. Méc. Théor. Appl. 2, 245–263 (1983)MathSciNetzbMATHGoogle Scholar
  28. 28.
    Clanet, C., Searby, G.: First experimental study of the Darrieus-Landau instability. Phys. Rev. Lett. 27, 3867 (1998)CrossRefGoogle Scholar
  29. 29.
    van Kampen, J.F.: Acoustic pressure oscillations induced by confined turbulent premixed natural gas flames, Ph.D. thesis, University of Twente, Enschede, The Netherlands, March 2006, Printed by Febodruk BV, Enschede, The Netherlands. ISBN 90-365-2277-3Google Scholar
  30. 30.
    Lieuwen, T., Zinn, B.T.: The role of equivalence ratio oscillations in driving combustion instabilities in low NOx gas turbines. Proc. Combust. Inst. 27, 1809 (1998)CrossRefGoogle Scholar
  31. 31.
    Rubtsov, N.M., Seplyarskii, B.S., Troshin, K.Y., Chrenysh, V.I., Tsvetkov, G.I.: Initiation and propagation of laminar spherical flames at atmospheric pressure. Mendeleev Commun. 21, 218 (2011)CrossRefGoogle Scholar
  32. 32.
    Naboko, I.M., Rubtsov, N.M., Seplyarskii, B.S., Chrenysh, V.I., Tsvetkov, G.I.: Interaction of the laminar flames of methane–air mixtures with close-meshed spherical and planar obstacles in a closed cylindrical reactor under spark discharge initiation. Mendeleev Comm. 23, 163 (2013)Google Scholar
  33. 33.
    Naboko, I.M., Rubtsov, N.M., Seplyarskii, B.S., Chernysh, V.I.: Investigation of ignition of propane and pentane mixtures in a heated vessel initiated by a spark discharge by means of color peed cinematography. Physicochem. Kinet. Gas Dyn. 12 (2011).
  34. 34.
    Nicoud, F.: Conservative high-order finite-difference schemes for low-Mach number flows journal of computational physics. J. Comput. Phys. 158, 71 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Rubtsov, N.M., Seplyarskii, B.S., Naboko, I.M., Chernysh, V.I., Tsvetkov, G.I., Troshin, KYa.: Acoustic instabilities in hydrogen-air mixtures in the closed reactor at the central spark initiation PCAIJ 10(3), 073–079 (2015). ISSN: 0974-7524Google Scholar
  36. 36.
    Semenov, N.N.: On Some Problems of Chemical Kinetics and Reaction Ability, p. 685. Academy of Sciences of the USSR, Moscow (1958) (in Russian)Google Scholar
  37. 37.
    Akkerman, V., Bychkov, V., Petchenko, A., Eriksson, L.-E.: Flame oscillations in tubes with nonslip at the walls. Combust. Flame 145, 675 (2006)CrossRefGoogle Scholar
  38. 38.
    Kreiss, H.-O.: Problems with different time scales for partial differential equations. Comm. Pure Appl. Math. 33, 399 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  39. 39.
    Williams, F.A.: Combustion Theory, 2nd edn. The Benjamin/Cummings Pub. Co., Menlo Park (1985)Google Scholar
  40. 40.
    Voronkov, A.V., Zemskov, E.A., Sychugova, E.P., Churbanov, A.G.: Modeling of Thermal and Gas-Dynamical Processes in Containers for Storage Weapons-Grade Plutonium, PHYSOR 2002, Seoul, Korea, vol. 56, October 7–10 (2002)Google Scholar
  41. 41.
    Majda, A.: Equations for Low Mach Number Combustion. Center for Pure and Applied Mathematics, University of California, Berkeley (1982). PAM-112Google Scholar
  42. 42.
    Kikoin, I.K.: Tables of Physical Values. Atomizdat, Moscow, p. 1007 (1976) (in Russian)Google Scholar
  43. 43.
    Abugov, D.I., Bobuylev, V.M.: Theory and Calculations of Solid Fuel Rocket Jets. In: Mashinostroenie, M. (1987) (in Russian)Google Scholar
  44. 44.
    Clavin, P.: Premixed combustion and gasdynamics. Ann. Rev. Fluid Mech. 26, 321 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  45. 45.
    Lighthill, M.J.: On sound generated aerodynamically. II. Turbulence as a source of sound. Proc. Roy. Soc. Series A 222, 1148 (1954)MathSciNetCrossRefzbMATHGoogle Scholar
  46. 46.
    Backstrom, G.: Simple Fields of Physics by Finite Element Analysis (Paperback). GB Publishing, Norway (2005)Google Scholar
  47. 47.
    Zel’dovich, Y.B.: Selected works, chemical physics and hydrodynamics. In: Chariton, Y.A. (ed.) Nauka, Moscow (1984) (in Russian)Google Scholar
  48. 48.
    Naboko, I.M., Rubtsov, N.M., Seplyarskii, B.S., Troshin, K.Y., Tsvetkov, G.I., Chernysh, V.I.: Cellular combustion at the transition of a spherical flame front to a flat front at the initiated ignition of methane–air, methane–oxygen and n-pentane–air mixtures. Mendeleev Commun. 23, 358 (2013)CrossRefGoogle Scholar
  49. 49.
    Kalinin, A.P., Orlov, A.G., Rodionov, A.I., Troshin K.Y.: Demonstration of the probability of the investigation of combustion and explosion by hyperspectral methods. Physicochem. Kinet. Gas Dyn. (in Russian)
  50. 50.
    Herzberg, G.: Molecular spectra and molecular structure. In: Van Nostrand (ed.) Spectra of Diatomic Molecules, vol. 1, 2nd edn. New York (1950)Google Scholar
  51. 51.
    Coheur, P.-F., Bernath, P.F., Carleer, M., Colin, R., et al.: A 3000 K laboratory emission spectrum of water. J. Chem. Phys. 122, 074307 (2005)CrossRefGoogle Scholar
  52. 52.
    Lieuwen, T.C.: Experimental investigation of limit-cycle oscillations. J. Propul. Power 18, 61–83 (2002)CrossRefGoogle Scholar
  53. 53.
    Larionov, V.M., Zaripov, R.G.: Gas Self-Oscillations in Combustion Installations, p. 227. Publishing House State University of Kazan, Kazan (2003) (in Russian)Google Scholar
  54. 54.
    Kampen, J.F.: Acoustic Pressure Oscillations Induced by Confined Turbulent Premixed Natural Gas Flames, p. 260. University of Twente, Enschede (2006)Google Scholar
  55. 55.
    Rubtsov, N.M., Troshin, K.Y., Borisov, A.A., Seplyarsky, B.S., Chernysh, V.I., Tsvetkov, G.I.: Influence of inert and active additives on regularities of initiation and propagation of laminar spherical flames in stoichiometric mixes of methane, pentane and hydrogen with air. Chem. Phys. Mezosc. 13(2), 187–196 (2011) (in Russian)Google Scholar
  56. 56.
    Rayleigh, J.W.S.: The Theory of Sound, p. 688. Dover, New York (1945)Google Scholar
  57. 57.
    Putnam, A.A., Dennis, W.R.: Organ-pipe oscillations in a burner with deep ports. JASA 28, 260–271 (1956)CrossRefGoogle Scholar
  58. 58.
    Al-Shahrany, A.S., Bradley, D., Lawes, M., Liu, K., Woolley, R.: Darrieus-Landau and thermo-acoustic instabilities in closed vessel explosions. Combust. Sci. Technol. 178(10), 1771–1784 (2006)CrossRefGoogle Scholar
  59. 59.
    Maxwell, G.B., Wheeler, R.V.: Some flame characteristics of motor fuels. Ind. Eng. Chem. 20, 1041–1056 (1928)CrossRefGoogle Scholar
  60. 60.
    Megalchi, M., Keck, J.C.: Burning velocities of mixtures of air with methanol, isooctane and indolene at high pressure and temperature. Combust. Flame 48, 191–200 (1982)CrossRefGoogle Scholar
  61. 61.
    Clanet, C., Searby, G., Clavin, P.: Primary acoustic instability of flames propagating in tubes: cases of spray and premixed gas combustion. J. Fluid Mech. 385, 157–170 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  62. 62.
    Solovyanova, I.P., Shabunin, I.S.: Theory of Wave Processes. Acoustic Waves, p. 142. UGTU-UPI Publishing House, Yekaterinburg (2004) (in Russian)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Russian Academy of SciencesInstitute of Structural Macrokinetics and Materials ScienceMoscowRussia

Personalised recommendations