The prediction of laminar jet diffusion flame sizes: Part I. Theoretical model

Abstract This paper modifies the Burke-Schumann theory of diffusion flame size, so as to satisfy continuity when the mass velocity of the fuel gas is not constant. The resulting theory makes no assumptions about the reaction rate of fuel and oxidant, and so applies to flames with equilibrium-broadened reaction zones. The paper considers the flame height for circular, square, and long slot burners, but extension to other burner geometries is possible. The diffusion flame height of a circular port burner is found to be a special case. It is substantially independent of buoyancy forces and secondary air velocity. Thus any theory of jet diffusion flames must be tested on nonaxisymmetric burner geometries. For the slot burner, the diffusion flame height may be controlled by the momentum of the fuel jet or by buoyancy effects. The two conditions differ greatly, for instance in their sensitivity to burner slot width. The transition between buoyancy and momentum control is determined by a modified form of the Froude number. The paper also shows how the gas composition profiles may be calculated in the tail of the diffusion flame. The paper goes on to survey previous theories of diffusion flame size, and to compare them with the present work. Experimental verification of the theory given here will be presented in a second paper, which follows.