Definition of Burning Velocity and a Geometric Interpretation of the Effects of Flame Curvature

The burning velocity, v0, has been a subject of controversy for curved flames. This curvature is the macroscopic result of stream tube area variation. The flow can not be one-dimensional, but for small curvatures it is quasi-one-dimensional. As usually defined, v0, varies with curvature due to ducting. However, if the primary reaction zone is narrow, the velocity there, vr, is approximately independent of curvature. vr is a function of the reaction rate and is related to v0 by the density ratio ρr/ρ0 and the stream tube area ratio A0, a geometric factor. Thus, the burning velocity in the absence of curvature, v0*, can be defined by v0* = vrρr/ρ0 = v0A0. It can be derived from measurements on flame tips or expanding flame kernels, and appears to be reproducible and independent of external variables such as geometry, inlet flow and flame curvature. The concept was substantiated by measurements on the microstructure of matched flames of differing curvature and by quantitatively correlating the variation of v0 with flame curvature in flame tips, expanding flame kernels and turbulent flamelets.