paper

Shapes and speeds of forced premixed flames

arXiv:1406.0629 · doi:10.1103/PhysRevE.89.063001

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.

arXiv commentRevised version submitted to Phys. Rev.E

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