Effects of finite-rate droplet evaporation on the extinction of spherical burner-stabilized diffusion flames

Multi-scale asymptotic analysis is conducted for spherical burner-stabilized spray diffusion flames with finite-rate droplet evaporation and nonunity Lewis number. The radiative loss is considered and the effects of radiation on flame extinction are examined. The structure function of the spray diffusion flame is derived, based on which the effects of finite-rate droplet vaporization on flame radius, flame temperature, and kinetic and radiative extinction limits are assessed. The flame is found to be affected by droplet vaporization in two ways: (1) the latent heat absorbed for droplet vaporization reduces the flame temperature; and (2) the decrease in the flame radius results in the decrease in radiative loss and residence time. For a given the mass flow rate, only the conventional kinetic extinction limit at low reaction Damköhler numbers exists. The extinction Damköhler number increases with the radiation intensity and it is significantly affected by droplet evaporation. When the reaction intensity is fixed and the mass flow rate varies, there exists two extinction limits: a kinetic extinction limit at a low-flow rate and a radiative extinction limit at a high-flow rate. Steady burning only exists between these two extinction limits. The flammable range is shown to be greatly affected by droplet evaporation and Lewis number.