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On the pulsating instability of two-dimensional flames

Published online by Cambridge University Press:  16 July 2009

Carlos Alvarez Pereira  and
José M. Vega
Carlos Alvarez Pereira
Affiliation:
ETSI Aeronáuticos, Universidad Politécnica de Madrid, 28040 Madrid, Spain
José M. Vega
Affiliation:
ETSI Aeronáuticos, Universidad Politécnica de Madrid, 28040 Madrid, Spain
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Abstract

We consider a well-known thermo-diffusive model for the propagation of a premixed, adiabatic flame front in the large-activation-energy limit. That model depends only on one nondimensional parameter β, the reduced Lewis number. Near the pulsating instability limit, as β↓β0= 32/3, we obtain an asymptotic model for the evolution of a quasi-planar flame front, via a multi-scale analysis. The asymptotic model consists of two complex Ginzburg–Landau equations and a real Burgers equation, coupled by non-local terms. The model is used to analyse the nonlinear stability of the flame front.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 3 , Issue 1 , March 1992 , pp. 55 - 73
Copyright
Copyright © Cambridge University Press 1992

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References

Alvarez-Pereira, C. & Vega, J. M. In preparation.Google Scholar
Booty, M. R., Margolis, S. B. & Matkowsky, B. J. 1987 Interactions of pulsating and spinning waves in non-adiabatic flame propagation. SIAM J. Appl. Math. 47, 1241 86.Google Scholar
Booty, M. R., Matalon, M. & Matkowsky, B. J. 1988 A non-linear wave equation in non- adiabatic flame propagation. SIAM J. Appl. Math. 48, 519–35.Google Scholar
Cross, M. C. 1986 Travelling and standing waves in binary-fluid convection in finite geometries. Phys. Rev. Lett. 57, 2935–38.CrossRefGoogle ScholarPubMed
Fauve, S. 1987 Large scale instabilities of cellular flows. In Tirapegui, E. and Villarroel, D., editors, Instabilities and Nonequilibrium Structures. Reidel.Google Scholar
Ferguson, C. R. & Keck, J. C. 1979 Stand-off distances on a flat burner. Combustion and Flame 34, 85–98.Google Scholar
Hassard, B. D., Kazarinoff, N. D. & Wang, I. N. 1981 Theory and Applications of Hopf Bfurcation. Cambridge University Press.Google Scholar
Hohenberg, P. C. & Cross, M. C. 1989 An introduction to pattern formation in non-equilibrium systems. In Volume 268 of Lecture Notes in Physics. Springer-Verlag.Google Scholar
Knobloch, E. & De Luca, J. 1990 Amplitude equations of travelling wave convection. Preprint.CrossRefGoogle Scholar
Kuramoto, Y. 1984 Chemical Oscillations, Waves and Turbulence. Springer-Verlag.Google Scholar
Margolis, S. B. & Matkowsky, B. J. 1985 Flame propagation in channels: Secondary bifurcation to quasi-periodic pulsations. SIAM J. Appl. Math. 45, 93–129.Google Scholar
Margolis, S. B. & Matkowsky, B. J. 1988 New modes of quasi-periodic combustion near a degenerate Hopf bifurcation point. SIAM J. Appl. Math. 48, 828–53.Google Scholar
Markstein, G. H. 1964 Nonsteady Flame Propagation. Pergamon Press.Google Scholar
Matkowsky, B. J. & Olagunju, D. O. 1980 Propagation of a pulsating flame front in a gaseous combustible mixture. SIAM J. Appl. Math. 39, 290–300.Google Scholar
Matkowsky, B. J. & Olagunju, D. O. 1982 Travelling waves along the front of a pulsating flame. SIAM J. Appl. Math. 42, 486–501.Google Scholar
Matkowsky, B. J. & Sivashinsky, G. I. 1979 An asymptotic derivation of two models in flame theory associated with the constant density approximation. SIAM J. Appl. Math. 37, 686–99.Google Scholar
Michelson, D. M. & Sivashinsky, G. I. 1977 Nonlinear analysis of hydrodynamic instability in laminar flames. II. Numerical experiments. Acta Astronautica 4, 1207–21.Google Scholar
Newell, A. C. 1989 Dynamics of patterns: a survey. In NATO Workshop on Propagation in None quilibriutn Systems. Springer-Verlag.Google Scholar
Sabathier, F., Boyer, L. & Clavin, P. 1979 Experimental study of weak turbulent premixed flames. Combustion and Flame 35, 139–53.Google Scholar
Sivashinsky, G. I. 1977 Nonlinear analysis of hydrodynamic instability of laminar flames. I. Derivation of basic equations. Acta Astronautica 4, 1177–206.Google Scholar
Vega, J. M. 1991 On the oscillatory instability in pattern formation. (Submitted to SIAM J. on Math. Anal.)Google Scholar