Buoyancy Effects on the Shape of a Small Axisymmetric Diffusion Flame

Abstract

This paper discusses the effects of buoyancy on the shape of an axisymmetric diffusion flame above a submillimeter burner, with a focus on the deviation of flame height from the well-known Péclet number scaling. Experiments of butane-air flame were conducted for two different burner diameters, 0.5 and 0.9 mm, to vary the relative strength of buoyancy. On the other hand, numerical simulations were conducted at a fixed burner diameter, 0.5 mm, but at varied gravity levels. Both experimental and numerical results showed that enhanced buoyancy tends to increase the flame height while decreasing the flame width. In particular, the flame height increased by as much as a factor of two. A simple analytical model was then developed. The model is an extension to the one developed by Roper, in which the axial velocity was assumed to be uniform in the radial direction, r. The present model adopts a more realistic axial-velocity distribution that decreases with an increase in r. The use of the point-source approximation enables a simple analytical solution for the flame shape. The change in flame shape owing to enhanced buoyancy predicted by the present model qualitatively agrees with experimental and numerical observations.