ANALYTIC DESCRIPTION OF THE EVOLUTION OF 2-DIMENSIONAL FLAME SURFACES

The passive propagation of wrinkled, non-folding, premixed flames in q uiescent and spatially periodic how fields is investigated by employin g the scalar held, G-equation formulation. Rather than solving the G-e quation directly, we transform it into a g-equation, which is a differ ential equation governing the evolution of the slope of the flame shap e in two-dimensional flows. For the Landau limit of flame propagation with constant flame speed, the resulting g-equation degenerates to a q uasi-linear wave equation in a quiescent flow. For the stretch-affecte d propagation mode in which the flame propagation speed is curvature-d ependent, the resulting g-equation is in the general form of the Burge rs' equation. Analytical solutions were obtained for several flame and flow types, revealing some interesting characteristics of the geometr y and propagation of the flame, including the formation of cusps and t heir inner structure, and the augmentation of the average burning velo city through flame wrinkling.