Shapes and speeds of steady forced premixed flamesReport as inadecuate

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1 PPRIME - Institut Pprime 2 IRPHE - Institut de Recherche sur les Phénomènes Hors Equilibre

Abstract : 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.

Keywords : premixed flame instability forcing turbulent flame speed

Author: G. Joulin - Bruno Denet -



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