Extinction of spherical diffusion flames in the presence of radiant loss

In this paper we examine the structure and extinction characteristics of burner-generated spherical diffusion flames. Two important parameters in this problem are the dimensionless mass flow rate, a ratio of fuel injection velocity to diffusion velocity, and the Damköhler number, which is proportional to the surface area of the burner, the fuel concentration in the feeding stream, and the ambient pressure. Both parameters can be easily controlled in an experiment. Particular attention is given in this study to the effects of gas-phase radiation either from soot or from combustion products and intermediate species.We show that radiant loss may lead to flame extinction at sufficiently high flow rates. Combined with the extinction limit due to a short residence time, we identify a range of mass flow rates outside of which steady burning cannot be sustained. Consequently, we are able to predict conditions under which steady flames may or may not exist, in terms of the prescribed fuel and oxidant concentrations and the corresponding Lewis numbers.