NONLINEAR THEORY OF CELLULAR FLAMES.

B. J. Matkowsky*, L. J. Putnick, G. I. Sivashinsky

*Corresponding author for this work

Research output: Contribution to journalArticle

27 Scopus citations

Abstract

Experiments with laminar flames in gaseous combustible mixtures show that for certain mixtures a flame front will often break up into numerous cells. Cellular flames are periodic structures with pointed crests, pointing in the direction of the burned gas. The smoother sections (troughs) of the front are convex toward the fresh mixture. The flame appears darker at its crests than at its troughs, which indicates that the temperature at the crests is lower than in other parts of the cell. Sometimes the flame in the vicinity of the crests disappears entirely. This study considers the stability of a uniformly curved propagating flame front. It is shown that the uniform front becomes unstable if the Lewis number L of the limiting reaction component is less than some critical number L//c, and if the radius of the front is greater than a critical value R//c. When the critical values are exceeded, perturbations of the uniform front evolve to a cellular front which bifurcates supercritically from the uniform front.

Original languageEnglish (US)
Pages (from-to)489-504
Number of pages16
JournalSIAM Journal on Applied Mathematics
Volume38
Issue number3
DOIs
StatePublished - Jan 1 1980

ASJC Scopus subject areas

  • Applied Mathematics

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    Matkowsky, B. J., Putnick, L. J., & Sivashinsky, G. I. (1980). NONLINEAR THEORY OF CELLULAR FLAMES. SIAM Journal on Applied Mathematics, 38(3), 489-504. https://doi.org/10.1137/0138039