Kinetic and radiative extinctions of spherical burner-stabilized diffusion flames

Extinction of steady, spherical diffusion flames stabilized by a spherical porous burner was investigated by activation energy asymptotics. An optically-thin radiation model was employed to study the effect of radiation on flame extinction. Four model flames with the same adiabatic flame temperature and fuel consumption rate but different stoichiometric mixture fraction and flow direction, namely the flames with fuel issuing into air, diluted fuel issuing into oxygen, air issuing into fuel, and oxygen issuing into diluted fuel, were adopted to understand the relative importance of residence time and radiation intensity. Results show that for a specified flow rate emerging from the burner, only the kinetic extinction limit at low Damköhler numbers (low residence times) exists. In the presence of radiative heat loss, extinction is promoted so that it occurs at a larger Damköhler number. By keeping the radiation intensity constant while varying the flow rate, both the kinetic and radiative extinction limits, representing the smallest and largest flow rates, between which steady burning is possible, are exhibited. For flames with low radiation intensity, extinction is primarily dominated by residence time such that the high-flow rate flames are easier to be extinguished. The opposite is found for flames suffering strong radiative heat loss. The kinetic extinction limit might occur at mass flow rates lower than what is needed to keep the flame outside of the burner and not observable. An extinction state on the radiative extinction branch can be either kinetic or radiative depending on the process.