Shapes, Velocities and Propagation Limits of a Non-Adiabatic Cellular Flame

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Abstract
We study a non-linear evolution equation which describes a non-adiabatic flame near the propagation limit due to heat losses, and takes into account the cellular instability of thermal and diffusional origin: Using numerical integration and shooting methods, we show that: i) Heat loss induced regime multiplicity also exists for cellular fronts, even when the cell size is prescribed. ii) Extinction by heat losses still occurs when cells are present, but is shifted; the new limit changes with the cell size. iii) Cellularity widens the propagation range, the shift being larger for lighter fuels. iv) For a fixed lateral flame dimension, many steady cellular patterns coexist for the same heat loss intensity, each one having its own velocity and propagation limit.