Radiation Effects on the Thermodiffusive Instability of Premixed Flames on a Cylindrical Porous Flame Holder

A linear analysis method was used to investigate the mechanics of radiation heat loss and mass transfer in the porous wall of premixed annular flames and their effect on thermodiffusive instability. The dispersion relation between the disturbance wave growth rate and wavenumber was calculated numerically. Results showed that radiation heat loss elevated the annular flame slightly away from the porous wall. In the annular flame with small Lewis numbers, radiation heat loss changed the thermodiffusive instability from a pulsating to a cellular state, while for the large Lewis numbers, only the pulsating instability was represented. Increasing radiation heat loss and the radius of the porous wall enhanced the instability of the annular flames. Heat losses decreased with the continued increase in thickness of the porous wall and the decrease in porosity. Annular flames with long-wave mode along the angular direction were more unstable than the shortwave mode.