SPINNING WAVES IN GASEOUS COMBUSTION.

B. J. Matkowsky; D. O. Olagunju

doi:10.1137/0142078

SPINNING WAVES IN GASEOUS COMBUSTION.

B. J. Matkowsky^*, D. O. Olagunju

^*Corresponding author for this work

Engineering Sciences and Applied Mathematics

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

A diffusional-thermal model describing the combustion of a premixed gas in a cylindrical domain is considered. It is shown that a uniformly propagating plane flame is unstable when the Lewis number L exceeds a critical value L//c . A nonlinear analysis is employed to show that for L greater than L//c various types of solutions bifurcate from the uniformly propagating plane flame. The bifurcated solutions describe pulsating flames whose spatial distribution corresponds to combinations of axial, radial and tangential modes. The tangential modes are of two types, corresponding to standing waves on, and to traveling waves propagating in both clockwise and counterclockwise directions around, the cylinder. The latter describe spinning waves in which a hot spot (or spots) (local temperature maximum) propagates in a helical motion around the axis of the cylinder. Both single and multi-headed spins are obtained.

Original language	English (US)
Pages (from-to)	1138-1156
Number of pages	19
Journal	SIAM Journal on Applied Mathematics
Volume	42
Issue number	5
DOIs	https://doi.org/10.1137/0142078
State	Published - Jan 1 1982

ASJC Scopus subject areas

Applied Mathematics

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abstract = "A diffusional-thermal model describing the combustion of a premixed gas in a cylindrical domain is considered. It is shown that a uniformly propagating plane flame is unstable when the Lewis number L exceeds a critical value L//c . A nonlinear analysis is employed to show that for L greater than L//c various types of solutions bifurcate from the uniformly propagating plane flame. The bifurcated solutions describe pulsating flames whose spatial distribution corresponds to combinations of axial, radial and tangential modes. The tangential modes are of two types, corresponding to standing waves on, and to traveling waves propagating in both clockwise and counterclockwise directions around, the cylinder. The latter describe spinning waves in which a hot spot (or spots) (local temperature maximum) propagates in a helical motion around the axis of the cylinder. Both single and multi-headed spins are obtained.",

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N2 - A diffusional-thermal model describing the combustion of a premixed gas in a cylindrical domain is considered. It is shown that a uniformly propagating plane flame is unstable when the Lewis number L exceeds a critical value L//c . A nonlinear analysis is employed to show that for L greater than L//c various types of solutions bifurcate from the uniformly propagating plane flame. The bifurcated solutions describe pulsating flames whose spatial distribution corresponds to combinations of axial, radial and tangential modes. The tangential modes are of two types, corresponding to standing waves on, and to traveling waves propagating in both clockwise and counterclockwise directions around, the cylinder. The latter describe spinning waves in which a hot spot (or spots) (local temperature maximum) propagates in a helical motion around the axis of the cylinder. Both single and multi-headed spins are obtained.

AB - A diffusional-thermal model describing the combustion of a premixed gas in a cylindrical domain is considered. It is shown that a uniformly propagating plane flame is unstable when the Lewis number L exceeds a critical value L//c . A nonlinear analysis is employed to show that for L greater than L//c various types of solutions bifurcate from the uniformly propagating plane flame. The bifurcated solutions describe pulsating flames whose spatial distribution corresponds to combinations of axial, radial and tangential modes. The tangential modes are of two types, corresponding to standing waves on, and to traveling waves propagating in both clockwise and counterclockwise directions around, the cylinder. The latter describe spinning waves in which a hot spot (or spots) (local temperature maximum) propagates in a helical motion around the axis of the cylinder. Both single and multi-headed spins are obtained.

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SPINNING WAVES IN GASEOUS COMBUSTION.

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