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.
• Analytical correlations for flame radius, flame temperature and extinction limits are derived.
• The flammable zone is significantly affected by droplet evaporation and is also very sensitive to Lewis number.
• The extinction Damköhler number increases with the radiation intensity and it is significantly affected by droplet evaporation.
• The flame is found to be affected by droplet vaporization in two ways.

Multiscale asymptotic analysis is conducted for spherical burner-stabilized spray diffusion flames with finite-rate droplet evaporation and nonunity Lewis number. The radiative heat 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 evaporation on flame radius, flame temperature, and kinetic and radiative extinction limits are assessed. The flame is found to be affected by droplet evaporation in two ways: (1) the latent heat absorbed for droplet evaporation 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 number exists. The extinction Damköhler number increases with the radiation intensity and it is significantly affected by droplet evaporation. It is found that at higher radiation intensity, the spray flame with the lower vaporization Damköhler number is relatively more difficult to be extinguished than the purely gaseous flame. 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 zone is shown to be greatly affected by droplet evaporation and is very sensitive to Lewis number.