Premixed flames in closed cylindrical tubes

Philippe Metzener, Moshe Matalon

Research output: Contribution to journalArticlepeer-review


We consider the propagation of a premixed flame, as a two-dimensional sheet separating unburned gas from burned products, in a closed cylindrical tube. A nonlinear evolution equation, that describes the motion of the flame front as a function of its mean position, is derived. The equation contains a destabilizing term that results from the gas motion induced by thermal expansion and has a memory term associated with vorticity generation. Numerical solutions of this equation indicate that, when diffusion is stabilizing, the flame evolves into a non-planar form whose shape, and its associated symmetry properties, are determined by the Markstein parameter, and by the initial data. In particular, we observe the development of convex axisymmetric or non-axisymmetric flames, tulip flames and cellular flames.

Original languageEnglish (US)
Pages (from-to)463-483
Number of pages21
JournalCombustion Theory and Modelling
Issue number3
StatePublished - 2001
Externally publishedYes

ASJC Scopus subject areas

  • General Chemistry
  • General Chemical Engineering
  • Modeling and Simulation
  • Fuel Technology
  • Energy Engineering and Power Technology
  • General Physics and Astronomy


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