Potential-flow models for channelled two-dimensional premixed flames around near-circular obstacles.

The dynamics of two-dimensional thin premixed flames is addressed in the framework of mathematical models where the flow field on either side of the front is piecewise incompressible and vorticity free. Flames confined in channels with asymptotically straight impenetrable walls are considered. Besides a few free propagations along straight channels, attention is focused on flames propagating against high-speed flows and positioned near a round central obstacle or near two symmetric bumps protruding inward. Combining conformal maps and Green's functions, a regularized generalization of Frankel's integro-differential equation for the instantaneous front shape in each configuration is derived and solved numerically. This produces a variety of real looking phenomena: steady fronts (symmetric or not), noise-induced subwrinkles, flashback events, and breathing fronts in pulsating flows. Perspectives and open mathematical and physical problems are finally evoked.