The Burke-Schumann spray diffusion flame in a nonuniform flow field

Abstract

The uniform, constant velocity profile assumption of the classical Burke-Schumann diffusion flame model is relaxed to permit more realistic duct entrance velocity profiles to be accounted for. An approximate model is formulated to include the supply of a spray of liquid fuel in the inner duct of the coflow configuration. For appropriate operating conditions (the characteristic flow time less than the characteristic vaporization time) it is shown that a fully developed parabolic velocity profile located at a short distance downstream of the inlet region provides the background flow field for the establishment of a homogeneous spray diffusion flame. The characteristic constriction of the streamlines immediately downstream of the inlet is also taken into consideration. Analytic solutions are found for the cases of negligible and notable axial diffusion. Due to difficulties that arise in the numerical calculation of the solutions, the large eigenvalues of the problem are derived asymptotically, thus enabling the full range of parametric values to be employed in predicting the spray flame characteristics. Computed results for flame shapes and heights are compared with those of a model from the literature that is based on the assumption of a uniform velocity profile. The sensitivity of the flame profiles to the initial droplet loading, the Peclet number, the vaporization Damköhler number, and the use of a parabolic velocity profile are clearly demonstrated. The net effect of the nonuniform flow field is found to be expressible in terms of a rescaling of the vaporization Damköhler number.