FLAME PROPAGATION IN CHANNELS: SECONDARY BIFURCATION TO QUASI-PERIODIC PULSATIONS.

Stephen B. Margolis*, Bernard J. Matkowsky

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

Premixed flame propagation in long rectangular channels is considered. A steadily propagating planar flame is stable for Lewis numbers less than a critical value. For Lewis numbers exceeding this critical value a sequence of primary bifurcation states, corresponding to time-periodic pulsating cellular flames, emanates from the steadily propagating solution. The problem is analyzed in a neighborhood of a multiple primary bifurcation point. By varying the channel dimensions, the multiple bifurcation point is split, and it is shown that a stable quasi-periodic pulsating flame can arise as a secondary bifurcation from one of the primary bifurcation states. The phenomenon of mode-jumping, in which there is an exchange of stability between two primary states, is also exhibited.

Original languageEnglish (US)
Pages (from-to)93-129
Number of pages37
JournalSIAM Journal on Applied Mathematics
Volume45
Issue number1
DOIs
StatePublished - Jan 1 1985

ASJC Scopus subject areas

  • Applied Mathematics

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