Effects of thermodiffusive instability on the spherical premixed flames anchored to a porous-plug burner

Steady state burning and thermodiffusive instability of spherical premixed flames stabilized on a spherical porous-plug burner are analyzed using large-activation-energy asymptotic approach. The steady-state solution and linear stability solution are validated by comparing them to the published theoretical studies since there is limited experiment result. Within the frame of the flame-sheet model, the analytic solutions depend on the temperature and mass fraction within the flame front. The coupling between the temperature and the stand-off distance for the steady state are analyzed in detail. The spherical flames show two types of dual flame behavior and are stabilized by either heat losses to the burner or flow divergence. Subsequently, the growth rates of disturbances superimposed on the spherical burner-stabilized flames depend on the wavenumbers and are resolved. Results show that the flames are stabilized, lost stability and being re-stabilized with increasing flow velocity. It is further shown that, with increasing Lewis number (Le), the instability of the spherical flame is suppressed and only the pulsating instability appears once the Le exceeds unity. Increasing the heat release parameter and the radius of the porous-plug can enhance flame instability. The porosity μ and thickness h of the porous-plug burner have the contradictive effect on flame stability. Moreover, with increasing the ratio of μ/h, the flame becomes more stable.