Intrinsic thermo-acoustic instability criteria based on frequency response of flame transfer function

The study of Intrinsic Thermo-Acoustic (ITA) instability behavior of flames anchored to a burner deck is performed by introducing a mapping between the Flame Transfer Function, FTF(s), defined in the complex (Laplace) domain and experimentally measured frequency response, FTF(iω). The conventional approach requires a system identification procedure to obtain the FTF(s) from the FTF(iω); next, root-finding techniques are applied to define the complex eigenfrequencies. The purpose of the present work is to establish instability criteria which are directly applicable in the frequency domain. The particular case is considered when the acoustic boundary conditions at both sides of the flame are anechoic. At first place, the causality of the measured FTF(iω) is checked. Then, the criteria of the ITA mode instability applicable to the FTF(iω) phase and magnitude, are derived. Cauchy's theorem and the path-independence Lemma are used to find the scaling factor of the mapping which allows to determine bounds of the unstable frequency and the maximum value of the linear growth rate. The proposed method is applied to study the behavior of burners with premixed burner-stabilized Bunsen-type flames. The comparison of the measured oscillation frequencies and the growth rates of observed unstable oscillations with that obtained from the derived bounds reveal good correspondence.