Shapes and speeds of steady forced premixed flames

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

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

Steady premixed flames subjected to space-periodic steady forcing are studied via inhomogeneous Michelson-Sivashinsky (MS) and then Burgers equations. For both, the flame slope is posited to comprise contributions from complex poles to locate, and from a base-slope profile chosen in three classes (pairs of cotangents, single-sine functions or sums thereof). Base-slope-dependent equations for the pole locations, along with formal expressions for the wrinkling-induced flame-speed increment and the forcing function, are obtained on excluding movable singularities from the latter. Besides exact few-pole cases, integral equations that rule the pole-density for large wrinkles are solved analytically. Closed-form flame-slope and forcing-function profiles ensue, along with flame-speed increment vs forcing-intensity curves; numerical checks are provided. The Darrieus-Landau instability mechanism allows MS flame speeds to initially grow with forcing intensity much faster than those of identically forced Burgers fronts; only the fractional difference in speed increments slowly decays at intense forcing, which numerical (spectral) timewise integrations also confirm. Generalizations and open problems are evoked.

Mots clés: premixed flame; instability; forcing; turbulent flame speed

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

G. Joulin, Bruno Denet. Shapes and speeds of steady forced premixed flames. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2014, 89 (6), pp.063001. ⟨10.1103/PhysRevE.89.063001⟩. ⟨hal-01000896⟩