The propagation of premixed flames in closed tubes

Moshe Matalon, Philippe Metzener

Research output: Contribution to journalArticle

Abstract

A nonlinear evolution equation that describes the propagation of a premixed flame in a closed tube has been derived from the general conservation equations. What distinguishes it from other similar equations is a memory term whose origin is in the vorticity production at the flame front. The two important parameters in this equation are the tube's aspect ratio and the Markstein parameter. A linear stability analysis indicates that when the Markstein parameter α is above a critical value αc the planar flame is the stable equilibrium solution. For α below αc the planar flame is no longer stable and there is a band of growing modes. Numerical solutions of the full nonlinear equation confirm this conclusion. Starting with random initial conditions the results indicate that, after a short transient, a flat flame develops when α > αc and it remains flat until it reaches the end of the tube. When α < αc, on the other hand, stable curved flames may develop down the tube. Depending on the initial conditions the flame assumes either a cellular structure, characterized by a finite number of cells convex towards the unburned gas, or a tulip shape characterized by a sharp indentation at the centre of the tube pointing toward the burned gases. In particular, if the initial conditions are chosen so as to simulate the elongated finger-like flame that evolves from an ignition source, a tulip flame evolves downstream. In accord with experimental observations the tulip shape forms only after the flame has travelled a certain distance down the tube, it does not form in short tubes and its formation depends on the mixture composition. While the initial deformation of the flame front is a direct result of the hydrodynamic instability, the actual formation of the tulip flame results from the vortical motion created in the burned gas which is a consequence of the vorticity produced at the flame front.

Original languageEnglish (US)
Pages (from-to)331-350
Number of pages20
JournalJournal of Fluid Mechanics
Volume336
DOIs
StatePublished - Apr 10 1997

Fingerprint

premixed flames
flames
tubes
Vorticity
propagation
Gases
Linear stability analysis
flame propagation
Indentation
Nonlinear equations
Ignition
Aspect ratio
Conservation
Hydrodynamics
Data storage equipment
vorticity
Chemical analysis
gases
nonlinear evolution equations
conservation equations

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

The propagation of premixed flames in closed tubes. / Matalon, Moshe; Metzener, Philippe.

In: Journal of Fluid Mechanics, Vol. 336, 10.04.1997, p. 331-350.

Research output: Contribution to journalArticle

Matalon, Moshe ; Metzener, Philippe. / The propagation of premixed flames in closed tubes. In: Journal of Fluid Mechanics. 1997 ; Vol. 336. pp. 331-350.
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