Flame Zone Studies. II. Applicability of One-Dimensional Models to Three-Dimensional Laminar Bunsen Flame Fronts

Abstract

The applicability of one‐dimensional models in flame theories has been investigated experimentally in the case of a lean quarter‐atmosphere propane air flame. Studies of flow patterns through the flame fronts were made using particle track techniques. From this time‐position information, normal gas velocity, stream tube area, and gas density were calculated throughout the flame front. If the density is a single valued measure of the state of the gas, then one‐dimensional models can be tested for Bunsen flames. Unidimensionality was verified for this and several other propane‐air flames under a number of conditions. In the reaction region preceding the luminous zone it was also found that the velocity and density profiles were invariant with respect to changes in flame geometry, gas flow, and burner diameter. Therefore, it is a good approximation to speak of single reaction path for this flame, which is a function only of the initial state of the gas. The measurements indicate that one‐dimensional flame theories should be modified to include the effects of area expansion during the course of the reaction. Continuity, diffusion, and heat conduction equations should also be generalized to include the effect of expansion. It was noted that the hydrocarbon flame reaction consists of two regions: a fast propagating reaction associated with the luminous regions and the major portion of the heat release and a slow secondary reaction associated with the post luminous mantel of the flame. Flow in the primary region is a function only of the initial state of gas and independent of external influences such as gas velocity and flame geometry. Flow in the secondary region could be varied over wide limits with no measureable effect on the propagation of the flame. Burning velocity was found to be independent of gas velocity, flame geometry, and radius of curvature of flame front, and a function only of the initial state of the gas, providing it was defined as the minimum normal gas velocity ahead of the flame front. A discussion is given of the errors introduced by measuring burning velocity by flow measurements in the throat of the burner.