Modeling of flame transfer function of a diverging premixed flame with developing flame speed under velocity disturbances

A theoretical study was conducted to examine the flame transfer function (FTF) of a diverging premixed flame subject to uniform and/or convective velocity disturbances considering developing turbulent flame speed. The FTF under uniform velocity disturbances with developing flame speed is less oscillatory compared with constant flame speed, and the magnitude of the aforementioned FTF is decreased more rapidly with an increase in turbulent time scale or flame length. The peak overshoot of the FTF under convective velocity disturbances is observed in a certain frequency range, which is known to be a typical nature of the FTF of a diverging flame under convective velocity disturbances. Such peak overshoot is quite sensitive to how the turbulent flame speed varies along the flame front in case of developing flame speed while the amplitude of the peak overshoot rarely changes with the mean flame length in case of constant flame speed.