Edge-Flames and Their Stability

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Abstract
Flame sheets that arise in non-premixed combustion often have edges. The leading edge of a flame spreading over a fuel-bed, solid or liquid, is one example. The edge of a hemi-spherical candle flame in microgravity is another. We construct a one-dimensional model which contains some of the essential physics of these edge-flames, and use this model to describe stationary solutions and their stability. The model corresponds to a new class of combustion waves which resemble deflagrations in some respects yet exhibit important differences. Thus, in a uniform flow, wave-like solutions are possible with positive, negative or vanishing wave-speeds, depending on an assignable Damköhler number. At large activation energy, reaction is concentrated primarily in a thin region (the edge) but it persists, in diminished form, behind the edge. This residual reaction plays a key role in defining the flame - or edge-temperature which, in turn, controls the dynamics of the structure. The familiar Lewis-number stability boundaries of deflagrations are present in modified form and provide tentative explanations of pulsations and cellular structures that have been observed experimentally.

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