Comparison of experiments and a nonlinear model equation for spatially developing flame instability
Résumé
We extend the Michelson – Sivashinsky equation, for arbitrary gas density ratio, to model the dynamics of an inclined anchored flame front. A flow velocity component tangential to the flame front transforms temporally developing structures into spatially developing ones. Closer investigation shows that a transition from absolute to convective instability should occur for a finite flow velocity. Using pole decomposition, we give a particular solution to this equation in the limit of high flow velocity compared to laminar flame speed. The analytical results are compared to measurements on a two-dimensional laminar flame. The growth rate, shape, and amplitude of the saturated structures, as well as the width of the crossover region are all well described. However, we experimentally observe the presence of a large scale transverse gas circulation not predicted by the analysis. We attribute this effect to the streamwise variation of the pressure jump across the flame brush.