Diffusion flame-holes

Recent models of straight diffusion flame edges are extended to consider th e effect of a curved edge forming the perimeter of an axisymmetric 'hole', where a burning flame surrounds a quenched inner region. For 'free' flame-h oles (without a heat sink near the axis), at small Damkohler number (Da), t he holes grow if the initial radius is large but shrink if it is small. For large Da, the holes shrink for any initial radius. Thus, free flame-holes are not stable for any Da, which is consistent with experimental observatio ns. When the flame-hole is 'anchored' by a heat sink near to the axis, stat ionary holes of finite radius can exist for sufficiently high Da, but the s olutions revert to 'free' hole behaviour for radii sufficiently larger than the heat sink radius. Based on these results, it is suggested that quasi-s tationary flame-holes are not likely to be a common feature of turbulent di ffusion flames, except possibly when large lateral gradients of Da are pres ent due to intense vortices passing through the flame front.