Modeling of the flame transfer function of a premixed M-flame and its implications for the N-tau model

An analytical investigation was conducted to examine a linearized heat release response of a premixed annular enveloped M-flame to velocity disturbances. The flame transfer function (FTF) of the M-flame, consisting of a converging and a diverging part with equal tip angles, acts as a low pass filter with frequency in an overall manner. The FTF magnitude of the M-flame exhibits the smallest magnitude, compared with that of a one-sided (converging or diverging) flame subject to acoustic velocity disturbance, and it vanishes at some periodic frequencies in the same manner as the flame tip fluctuation does. The phase of the FTF of the M-flame undergoes some uncertain variations, which are bounded roughly by the phase of each of the inner and the outer part of the flame. The time lag of the FTF of the M-flame is estimated as an average of two characteristic time scales in a low frequency regime, beyond which the time lag is bounded between these two characteristic time scales.