Wrinkled flames and geometrical stretch

Bruno Denet (1) , G. Joulin (2)

1 IRPHE - Institut de Recherche sur les Phénomènes Hors Equilibre
2 PPrime [Poitiers] - Institut Pprime [UPR 3346]

Localized wrinkles of thin premixed flames subject to hydrodynamic instability and geometrical stretch of uniform intensity ( S ) are studied. A stretch-affected nonlinear and nonlocal equation, derived from an inhomogeneous Michelson-Sivashinsky equation, is used as starting point and pole-decompositions as tool. Analytical and numerical descriptions of isolated (centred or multi-crested) wrinkles with steady shapes (in a frame) and various amplitudes are provided; their number increases rapidly with 1/ S > 0. A large constant S > 0 weakens or suppresses all localized wrinkles (the larger ones, the easier) whereas S < 0 strengthens them; oscillations of S further restrict their existence domain. Self-similar evolutions of unstable many-crest patterns are obtained. A link between stretch, nonlinearity and instability with the cut-off size of wrinkles in turbulent flames is suggested. Open problems are evoked.

Mots clés: premixed flames; hydrodynamic instability; Sivashinsky equation; pole decomposition; curved flames

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Milieux fluides et réactifs; Formation de Structures et Solitons [nlin.PS]

Bruno Denet, G. Joulin. Wrinkled flames and geometrical stretch. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2011, 84, pp.016315. ⟨10.1103/PhysRevE.84.016315⟩. ⟨hal-00622285⟩