Burner-stabilized cellular flames
Authors:
David O. Olagunju and Bernard J. Matkowsky
Journal:
Quart. Appl. Math. 48 (1990), 645-664
MSC:
Primary 80A25
DOI:
https://doi.org/10.1090/qam/1079911
MathSciNet review:
MR1079911
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Abstract: We consider a model that governs the behavior of a premixed flame anchored on a flat burner. We show that a steady planar flame is stable for Lewis numbers $L$ in the interval ${L_l} < L < {L_u}$ where ${L_l} < 1$ and ${L_u} > 1$ and unstable otherwise.
- D. J. Benney and A. C. Newell, The propagation of nonlinear wave envelopes, J. Math. and Phys. 46 (1967), 133–139. MR 241052
J. I. Blackshear, J. W. Mapp, and M. Gorman, An experimental study of pulsating low pressure flames, Comb. Sc. Tech. 35, 311–315 (1984)
- J. Buckmaster, Polyhedral flames—an exercise in bimodal bifurcation analysis, SIAM J. Appl. Math. 44 (1984), no. 1, 40–55. MR 730000, DOI https://doi.org/10.1137/0144005
- J. D. Buckmaster and G. S. S. Ludford, Lectures on mathematical combustion, CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 43, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1983. MR 765073
G. F. Carrier, F. E. Fendell, and W. B. Bush, Stoichiometry and flameholder effects on a one-dimensional flame, Comb. Sc. Tech. 18, 33–46 (1978)
- Donald S. Cohen, Frank C. Hoppensteadt, and Robert M. Miura, Slowly modulated oscillations in nonlinear diffusion processes, SIAM J. Appl. Math. 33 (1977), no. 2, 217–229. MR 447810, DOI https://doi.org/10.1137/0133013
- Wiktor Eckhaus, Studies in non-linear stability theory, Springer Tracts in Natural Philosophy, Vol. 6, Springer-Verlag New York, New York, Inc., 1965. MR 0196298
A. A. Gaydon and H. G. Wolfhard, Flames, Chapman and Hall, London, 1978
B. Lewis and G. von Elbe, Combustion, Flames and Explosion of Gases, Academic Press, New York, 1987
J. W. Mapp, J. I. Blackshear, and M. Gorman, Nonsteady, nonplanar modes of propagation in premixed burner-stabilized flames, Comb. Sc. Tech. 43, 217–225 (1985)
S. B. Margolis, H. G. Kaper, G. K. Leaf, and B. J. Matkowsky, Bifurcation of pulsating and spinning reaction fronts in condensed two-phase combustion, Comb. Sc. Tech. 43, 127–165 (1985)
S. B. Margolis and B. J. Matkowsky, Nonlinear stability and bifurcation in transition from laminar to turbulent flame propagation, Comb. Sc. Tech. 34, 45–77 (1983)
- Stephen B. Margolis and Bernard J. Matkowsky, Flame propagation in channels: secondary bifurcation to quasiperiodic pulsations, SIAM J. Appl. Math. 45 (1985), no. 1, 93–129. MR 775484, DOI https://doi.org/10.1137/0145004
- Stephen B. Margolis and Gregory I. Sivashinsky, Flame propagation in vertical channels: bifurcation to bimodal cellular flames, SIAM J. Appl. Math. 44 (1984), no. 2, 344–368. MR 739308, DOI https://doi.org/10.1137/0144024
G. H. Markstein, Nonsteady Flame Propagation, Pergamon Press, Oxford, 1964
- Bernard J. Matkowsky and David O. Olagunju, Propagation of a pulsating flame front in a gaseous combustible mixture, SIAM J. Appl. Math. 39 (1980), no. 2, 290–300. MR 588501, DOI https://doi.org/10.1137/0139025
- Bernard J. Matkowsky and David O. Olagunju, Pulsations in a burner-stabilized premixed plane flame, SIAM J. Appl. Math. 40 (1981), no. 3, 551–562. MR 614749, DOI https://doi.org/10.1137/0140046
- B. J. Matkowsky and D. O. Olagunju, Traveling waves along the front of a pulsating flame, SIAM J. Appl. Math. 42 (1982), no. 3, 486–501. MR 659408, DOI https://doi.org/10.1137/0142035
- B. J. Matkowsky and D. O. Olagunju, Spinning waves in gaseous combustion, SIAM J. Appl. Math. 42 (1982), no. 5, 1138–1156. MR 673530, DOI https://doi.org/10.1137/0142078
- B. J. Matkowsky, L. J. Putnick, and G. I. Sivashinsky, A nonlinear theory of cellular flames, SIAM J. Appl. Math. 38 (1980), no. 3, 489–504. MR 579433, DOI https://doi.org/10.1137/0138039
- B. J. Matkowsky and G. I. Sivashinsky, Propagation of a pulsating reaction front in solid fuel combustion, SIAM J. Appl. Math. 35 (1978), no. 3, 465–478. MR 507948, DOI https://doi.org/10.1137/0135038
- Alan C. Newell and J. A. Whitehead, Finite bandwidth, finite amplitude convection, J. Fluid Mech. 38 (1969), no. 2, 279–303. MR 3363403, DOI https://doi.org/10.1017/S0022112069000176
L. A. Segel, Distant side-walls cause slow amplitude modulation of cellular convection, J. Fluid. Mech. 38, 203–224 (1969)
G. I. Sivashinsky, Diffusional thermal theory of cellular flames, Comb. Sc. Tech. 15, 137 (1977)
G. I. Sivashinsky, Instabilities, pattern formation, and turbulence in flames, Annual Review of Fluid Mechanics 15, 179–199 (1983)
D. J. Benney and A. C. Newell, The propagation of nonlinear wave envelopes, J. Math. Phys. 46, 133–139 (1967)
J. I. Blackshear, J. W. Mapp, and M. Gorman, An experimental study of pulsating low pressure flames, Comb. Sc. Tech. 35, 311–315 (1984)
J. D. Buckmaster, Polyhedral flames—an exercise in bimodal bifurcation analysis, SIAM J. Appl. Math. 44, 40–55 (1984)
J. D. Buckmaster and S. S. Ludford, Lectures on Mathematical Combustion, CBMS Regional Conference Series in Applied Mathematics 43 (1983), SIAM, Philadelphia
G. F. Carrier, F. E. Fendell, and W. B. Bush, Stoichiometry and flameholder effects on a one-dimensional flame, Comb. Sc. Tech. 18, 33–46 (1978)
D. S. Cohen, F. C. Hoppennsteadt, and R. M. Miura, Slowly modulated oscillations in nonlinear diffusion processes, SIAM J. Appl. Math. 33, 217–229 (1977)
W. Eckhaus, Studies in Nonlinear Stability Theory, Springer-Verlag, New York, 1965
A. A. Gaydon and H. G. Wolfhard, Flames, Chapman and Hall, London, 1978
B. Lewis and G. von Elbe, Combustion, Flames and Explosion of Gases, Academic Press, New York, 1987
J. W. Mapp, J. I. Blackshear, and M. Gorman, Nonsteady, nonplanar modes of propagation in premixed burner-stabilized flames, Comb. Sc. Tech. 43, 217–225 (1985)
S. B. Margolis, H. G. Kaper, G. K. Leaf, and B. J. Matkowsky, Bifurcation of pulsating and spinning reaction fronts in condensed two-phase combustion, Comb. Sc. Tech. 43, 127–165 (1985)
S. B. Margolis and B. J. Matkowsky, Nonlinear stability and bifurcation in transition from laminar to turbulent flame propagation, Comb. Sc. Tech. 34, 45–77 (1983)
S. B. Margolis and B. J. Matkowsky, Flame propagation in channels: secondary bifurcation to quasi-periodic pulsations, SIAM J. Appl. Math. 45, 93–129 (1985)
S. B. Margolis and G. I. Sivashinsky, Flame propagation in vertical channels: bifurcation to bimodal cellular flames, SIAM J. Appl. Math. 44, 344–368 (1984)
G. H. Markstein, Nonsteady Flame Propagation, Pergamon Press, Oxford, 1964
B. J. Matkowsky and D. O. Olagunju, Propagation of a pulsating reaction front in a gaseous combustible mixture, SIAM J. Appl. Math. 39, 290–300 (1980)
B. J. Matkowsky and D. O. Olagunju, Pulsations in a burner-stabilized premixed plane flame, SIAM J. Appl. Math. 40, 551–562 (1981)
B. J. Matkowsky and D. O. Olagunju, Travelling waves along the front of a pulsating flame, SIAM J. Appl. Math. 42, 486–501 (1982)
B. J. Matkowsky and D. O. Olagunju, Spinning waves in gaseous combustion, SIAM J. Appl. Math. 42, 1138–1156 (1982)
B. J. Matkowsky, L. J. Putnick, and G. I. Sivashinsky, A nonlinear theory of cellular flames, SIAM J. Appl. Math. 38, 489–504 (1980)
B. J. Matkowsky and G. I. Sivashinsky, Propagation of a pulsating reaction front in solid fuel combustion, SIAM J. Appl. Math. 35, 465–478 (1978)
A. C. Newell and J. A. Whitehead, Finite bandwidth, finite amplitude convection, J. Fluid Mech. 38, 279–303 (1969)
L. A. Segel, Distant side-walls cause slow amplitude modulation of cellular convection, J. Fluid. Mech. 38, 203–224 (1969)
G. I. Sivashinsky, Diffusional thermal theory of cellular flames, Comb. Sc. Tech. 15, 137 (1977)
G. I. Sivashinsky, Instabilities, pattern formation, and turbulence in flames, Annual Review of Fluid Mechanics 15, 179–199 (1983)
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© Copyright 1990
American Mathematical Society