Proceedings of ASME Turbo Expo 2012: Power for Land, Sea and Air ASME 2012 June 11-15, 2012, Copenhagen, Denmark GT2012-68243 THERMOACOUSTIC ANALYSIS OF COMBUSTION INSTABILITY THROUGH A DISTRIBUTED FLAME RESPONSE FUNCTION Giovanni Campa ∗ Sergio Mario Camporeale D.I.M.eG. Politecnico di Bari via Re David 200, 70125 Bari, Italy Email: g.campa@poliba.it Ezio Cosatto Giulio Mori Ansaldo Energia corso F. Perrone 118, 16161 Genoa, Italy ABSTRACT Modern gas turbines equipped with lean premixed dry low emission combustion systems suffer the problem of thermoacous- tic 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 in- stability 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 insta- bilities are expected and the growth rate of the pressure oscilla- tions at the onset of instability. The code is able to treat com- plex 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 κ -τ type as a function of the posi- tion within the chamber. The intensity coefficient, κ , is assumed to be proportional to the reaction rate of methane in a two-step mechanism. The time delay τ 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 κ and τ . The present ∗ Address all correspondence to this author. 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 en- trance to the combustion chamber. The distribution of the inten- sity 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 theo- retical relation of the characteristics of the flame (depending on the burner geometry and operating conditions) to the onset of the thermoacoustic instability. NOMENCLATURE A cross sectional area b length c speed of sound j imaginary unit k acoustical wave number l length LHV Lower Heating Value M Mach number p pressure q volumetric heat release rate Q rate of heat release per unit area RR Rate of Reaction s thickness 1 Copyright c  2012 by ASME