Thermoacoustic Analysis of Combustion Instability Through a Distributed Flame Response Function

Modern gas turbines equipped with lean premixed dry low emission combustion systems suffer the problem of thermoacoustic combustion instability. The acoustic characteristics of the combustion chamber and of the burners, as well as the response of the flame to the fluctuations of pressure and equivalence ratio, exert a fundamental influence on the conditions in which the instability may occur. A three dimensional finite element code has been developed in order to solve the Helmholtz equation with a source term that models the heat release fluctuations. The code is able to identify the frequencies at which thermoacoustic instabilities are expected and the growth rate of the pressure oscillations at the onset of instability. The code is able to treat complex geometries such as annular combustion chambers equipped with several burners. The adopted acoustic model is based upon the definition of the Flame Response Function (FRF) to acoustic pressure and velocity fluctuations in the burners. In this paper, data from CFD simulations are used to obtain a distribution of FRF of the k-t type as a function of the position within the chamber. The intensity coefficient, k, is assumed to be proportional to the reaction rate of methane in a two-step mechanism. The time delay t is estimated on the basis of the trajectories of the fuel particles from the injection point in the burner to the flame front. The paper shows the results obtained from the application of FRF with spatial distributions of both k and t. The present paper also shows the comparison between the application of the proposed model for the FRF and the traditional application of the FRF over a concentrated flame in a narrow area at the entrance to the combustion chamber. The distribution of the intensity coefficient and the time delay proves to have an influence, both on the eigenfrequency values and on the growth rates, in several of the examined modes. The proposed method is therefore able to establish a theoretical relation of the characteristics of the flame (depending on the burner geometry and operating conditions) to the onset of the thermoacoustic instability.