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

A 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 the experimentally measured Flame Frequency Response, FFR(iω). The conventional approach requires a system identification procedure to obtain the FTF(s) from the measured FFR(iω). Next, root-finding techniques are applied to define the complex eigenfrequencies. The common practice is to fit the FTF(s) by a rational function that may lead to artifacts like spurious poles and zeros. The purpose of the present work is to establish instability criteria which are directly applicable in the frequency domain. The particular case is considered where the acoustic boundary conditions at both sides of the flame are anechoic. Therefore, the pure ITA mode is treated. First, the causality of the measured FFR(iω) is checked. Then, the criteria of the ITA mode instability applicable to the FFR(iω) phase and magnitude, are derived. Causality properties are used to find the unstable frequency, growth rate, and even the maximum possible value of the linear growth rate. In addition, a procedure is explained to reconstruct the flame transfer function in the complex plane s from the measured flame frequency response which could be an alternative method to study the FTF behavior in the complex domain instead of its estimation with a rational function.