Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-19T01:11:11.183Z Has data issue: false hasContentIssue false
  • English
  • Français

Influence of hydrodynamics and diffusion upon the stability limits of laminar premixed flames

Published online by Cambridge University Press:  20 April 2006

Pierre Pelce  and
Paul Clavin
Pierre Pelce
Affiliation:
Laboratoire de Dynamique et Thermophysique des Fluides (LA 72). Université de Provence, Centre St Jérôme, rue H. Poincaré, 13397 Marseille cedex 13, France
Paul Clavin
Affiliation:
Laboratoire de Dynamique et Thermophysique des Fluides (LA 72). Université de Provence, Centre St Jérôme, rue H. Poincaré, 13397 Marseille cedex 13, France
Get access Rights & Permissions [Opens in a new window]

Abstract

An analytical theory is developed for the stability properties of planar fronts of premixed laminar flames freely propagating downwards in a uniform reacting mixture. The coupling between the hydrodynamics and the diffusion process is described for an arbitrary expansion of the gas across the flame. Viscous effects are included with an arbitrary Prandtl number. The flame structure is described for a large value of the reduced activation energy and for a Lewis number close to unity. The flame thickness is assumed to be small compared with the wavelength of the wrinkles of the front, this wavelength being also the characteristic lengthscale of the perturbations of the flow field outside the flame. A two-scale method is then used to solve the problem. The results show that the acceleration of gravity associated with the diffusion mechanisms inside the front can counterbalance the hydrodynamical instability when the laminar-flame velocity is low enough. The theory provides predictions concerning the instability threshold. In particular, the dimensions of the cells are predicted to be large compared with the flame thickness, and thus the basic assumption of the theory is verified. Furthermore, the quantitative predictions are in good agreement with the existing experimental data.

The bifurcation is shown to be of a different nature than predicted by the purely diffusive–thermal model.

The viscous diffusivities are supposed to be independent of the temperature, and then the viscosity is proved to have no effect at all on the dynamical properties of the flame front.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 124 , November 1982 , pp. 219 - 237
Copyright
© 1982 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Barenblatt, G. I., Zel'dovich, Ya. B. & Istratov, A. G.1962 On diffusional thermal stability of laminar flame. Prikl. Mekh. Tekh. Fiz. 2, 21–26.Google Scholar
Chu, B. T. & Parlange, J. Y. 1962 On the stability of laminar flame. J. Méc. 1, 293–312.Google Scholar
Clavin, P. 1982 Dynamical behavior of premixed flame fronts in laminar and turbulent flows. Prog. Energy Combust. Sci. (to appear).
Clavin, P. & Garcia, P. 1982 The influence of the temperature dependence of diffusivities on the dynamics of flame fronts. J. Méc. (to appear).Google Scholar
Clavin, P. & Joulin, G. 1982 Premixed flame propagation in high intensity turbulent flow. J. Physique (to appear).Google Scholar
Clavin, P. & Nicoli, C. 1983 Effects of the heat losses on the limits of stability of premixed flames propagating downwards. Combust. Flame (submitted).
Clavin, P. & Williams, F. A. 1982 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, 251–282.Google Scholar
Darrieus, G. 1938 Propagation d'un front de flamme. Essai de théorie des vitesses anormales de déflagration par développement spontané de la turbulence. Unpublished works presented at La Technique Moderne 1938 and at Le Congrès de Mécanique Appliquée 1945.
Eckhaus, W. 1961 Theory of flame-front stability. J. Fluid Mech. 10, 80–100.Google Scholar
Einbinder, H. 1953 The hydrodynamic stability of flame fronts. J. Chem. Phys. 21, 480–489.Google Scholar
Frankel, M. L. & Sivashinsky, G. I. 1982 The effect of viscosity on hydrodynamic stability of a plane flame front. Combust. Sci. Tech. (to appear).
Fristrom, R. M. & Westenberg, A. A. 1965 Flame Structure. McGraw-Hill.
Istratov, A. G. & Librovich, V. B. 1966 The effect of transport processes on the stability property of a plane flame front. Prikl. Mat. Mekh. 30, 451–466 (in Russian).Google Scholar
Joulin, G. & Clavin, P. 1979 Linear stability analysis of nonadiabatic flames: diffusional—thermal model. Combust. Flame 35, 139–153.Google Scholar
Joulin, G. & Mitani, T. 1981 Linear stability of two reactants flames. Combust. Flame 40, 235–246.Google Scholar
Kaskan 1957 The dependence of flame temperature on mass burning velocity. In Proc. 6th Symp. of Combustion Institute, pp. 134–143.
Landau, L. 1944 On the theory of slow combustion. Acta Physicochimica URSS 19, 77–85.Google Scholar
Lazarev, P. P. & Pleshanov, A. S. 1980 Linear stability of a laminar flame front. Fiz. Gor. Vzryva 16, 45–52 (English transl., Plenum).Google Scholar
Lewis, B. & von Elbe, G. 1961 Combustion, Flames and Explosions of Gases. Academic. (2nd edn 1967.)
Markstein, G. H. 1951 Experimental and theoretical studies of flame front stability. J. Aero. Sci. 18, 199.Google Scholar
Markstein, G. H. 1964 Nonsteady Flame Propagation. Pergamon.
Markstein, G. H. 1970 Flames as amplifiers of fluid mechanical disturbances. In Proc. 6th U.S. Nat. Congr. of Appl. Mech., Cambridge, Mass., pp. 11–33.
Markstein, G. H. & Somers, L. M. 1953 Cellular flame structure and vibratory flame movement in n-butane methane mixtures. In Proc. 4th Symp. on Combustion, pp. 527–535. Williams & Wilkins.
Matkowsky, B. J. & Sivashinsky, G. I. 1979 Acceleration effects on the stability of flame propagation. SIAM J. Appl. Math. 37, 669–685.Google Scholar
Sivashinsky, G. I. 1977a Diffusional—thermal theory of cellular flames. Combust. Sci. Tech. 15, 137–145.Google Scholar
Sivashinsky, G. I. 1977b Nonlinear analysis of hydrodynamic instability in laminar flames. I. Derivation of basic equations. Acta Astronautica 4, 1177–1206.Google Scholar
Zel'Dovich, Ya. B. & Frank-Kamenetzki, D. A.1938 A theory of thermal propagation of flame. Acta Physicochimica URSS, 9, 341–350.Google Scholar
Zel'Dovich, Ya. B., Barenblatt, G. I., Librovich, V. B. & Makhviladze, G. M. 1980 Mathematical Theory of Combustion and Explosion. Nauka. (In Russian.)
Zel'Dovich, Ya. B.1981 Structure and stability of steady laminar flame at moderately large Reynolds numbers. Combust. Flame 40, 225–234.Google Scholar