Bifurcation of pulsating and spinning reaction fronts in condensed two-phase combustion

Stephen B. Margolis; Hans G. Kaper; Gary K. Leaf; Bernard J. Matkovvsky

doi:10.1080/00102208508947001

Bifurcation of pulsating and spinning reaction fronts in condensed two-phase combustion

Stephen B. Margolis^*, Hans G. Kaper, Gary K. Leaf, Bernard J. Matkovvsky

^*Corresponding author for this work

Engineering Sciences and Applied Mathematics

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

84 Scopus citations

Abstract

We employ a nonlinear stability analysis to describe the bifurcation of pulsating and spinning modes of combustion in condensed media. We adopt the two-phase model of Margolis (1983) in which the modified nondimensional activation energy S of the reaction is large, but finite, and in which the limiting component of the mixture melts during the reaction process, as characterized by a nondimensional melting parameter M. We identify several types of nonsteady solution branches which bifurcate from the steady planar solution and show that they are supercritical and stable only for certain realistic ranges of M. For example, the spinning modes, though supercritical and stable for a range of M >0, are subcritical and unstable for M=0.

Original language	English (US)
Pages (from-to)	127-165
Number of pages	39
Journal	Combustion science and technology
Volume	43
Issue number	3-4
DOIs	https://doi.org/10.1080/00102208508947001
State	Published - Jul 1 1985

Funding

This work was supported by the Applied Mathematics Program of the Office of Energy Research, U.S. Department of Energy.

ASJC Scopus subject areas

General Chemistry
General Chemical Engineering
Fuel Technology
Energy Engineering and Power Technology
General Physics and Astronomy

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title = "Bifurcation of pulsating and spinning reaction fronts in condensed two-phase combustion",

abstract = "We employ a nonlinear stability analysis to describe the bifurcation of pulsating and spinning modes of combustion in condensed media. We adopt the two-phase model of Margolis (1983) in which the modified nondimensional activation energy S of the reaction is large, but finite, and in which the limiting component of the mixture melts during the reaction process, as characterized by a nondimensional melting parameter M. We identify several types of nonsteady solution branches which bifurcate from the steady planar solution and show that they are supercritical and stable only for certain realistic ranges of M. For example, the spinning modes, though supercritical and stable for a range of M >0, are subcritical and unstable for M=0.",

author = "Margolis, {Stephen B.} and Kaper, {Hans G.} and Leaf, {Gary K.} and Matkovvsky, {Bernard J.}",

note = "Funding Information: This work was supported by the Applied Mathematics Program of the Office of Energy Research, U.S. Department of Energy.",

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doi = "10.1080/00102208508947001",

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T1 - Bifurcation of pulsating and spinning reaction fronts in condensed two-phase combustion

AU - Margolis, Stephen B.

AU - Kaper, Hans G.

AU - Leaf, Gary K.

AU - Matkovvsky, Bernard J.

N1 - Funding Information: This work was supported by the Applied Mathematics Program of the Office of Energy Research, U.S. Department of Energy.

PY - 1985/7/1

Y1 - 1985/7/1

N2 - We employ a nonlinear stability analysis to describe the bifurcation of pulsating and spinning modes of combustion in condensed media. We adopt the two-phase model of Margolis (1983) in which the modified nondimensional activation energy S of the reaction is large, but finite, and in which the limiting component of the mixture melts during the reaction process, as characterized by a nondimensional melting parameter M. We identify several types of nonsteady solution branches which bifurcate from the steady planar solution and show that they are supercritical and stable only for certain realistic ranges of M. For example, the spinning modes, though supercritical and stable for a range of M >0, are subcritical and unstable for M=0.

AB - We employ a nonlinear stability analysis to describe the bifurcation of pulsating and spinning modes of combustion in condensed media. We adopt the two-phase model of Margolis (1983) in which the modified nondimensional activation energy S of the reaction is large, but finite, and in which the limiting component of the mixture melts during the reaction process, as characterized by a nondimensional melting parameter M. We identify several types of nonsteady solution branches which bifurcate from the steady planar solution and show that they are supercritical and stable only for certain realistic ranges of M. For example, the spinning modes, though supercritical and stable for a range of M >0, are subcritical and unstable for M=0.

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Bifurcation of pulsating and spinning reaction fronts in condensed two-phase combustion

Abstract

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