Modeling of flame transfer function of a conical turbulent premixed flame with variable flame speed

An analytical study was conducted on the heat release response of a turbulent conical flame to velocity fluctuation considering turbulent flame development. The flame with developing variable flame speed is longer and more oscillatory along the flame front than the flame with constant flame speed. As the flame speed develops more slowly with increasing turbulent time scale, the magnitude of the flame transfer function (FTF) decreases more rapidly with frequency in a more oscillatory manner, and its phase increases more rapidly at low frequencies, approaching to a higher value with increasing frequencies. A linear dependence of the FTF phase upon frequency was observed at low frequencies for variable flame speed, and the gain and the time lag of n-tau model were estimated at low frequencies for various turbulent time scale.