A method for predicting the onset of acoustically driven combustion instabilities in gas turbine combustor is examined. The basic idea is that the governing equations of the acoustic waves can be coupled with a flame heat release model and solved in the frequency domain. The paper shows that a complex eigenvalue problem is obtained that can be solved numerically by implementing the governing equations in a finite element code. This procedure allows one to identify the frequencies at which thermo-acoustic instabilities are expected and the growth rate of the pressure oscillations, at the onset of instability, when the hypothesis of linear behavior of the acoustic waves can be applied. The method can be applied virtually to any three-dimensional geometry, provided the necessary computational resources that are, anyway, much less than those required by computational fluid dynamics methods proposed for analyzing the combustion chamber under instability condition. Furthermore, in comparison with the “lumped” approach that characterizes popular acoustics networks, the proposed method allows one for much more flexibility in defining the geometry of the combustion chamber. The paper shows that different types of heat release laws, for instance, heat release concentrated in a flame sheet, as well as distributed in a larger domain, can be adopted. Moreover, experimentally or numerically determined flame transfer functions, giving the response of heat release to acoustic velocity fluctuations, can be incorporated in the model. To establish proof of concept, the method is validated at the beginning against simple test cases taken from literature. Over the frequency range considered, frequencies and growth rates both of stable and unstable eigenmodes are accurately evaluated. Then the method is applied to a much more complex annular combustor geometry in order to evaluate frequencies and growth rates of the unstable modes and to show how the variation in the parameters of the heat release law can influence the transition to instability.

Most annular combustors feature a discrete rotational symmetry so that the full configuration can be obtained by copying one burner-flame segment a certain number of times around the circumference. A thermoacoustic model based on the Helmholtz equation then admits special solutions of the so-called Bloch type that can be obtained by considering one segment only. We show that a significant reduction in computational effort for the determination of thermoacoustic modes can be achieved by exploiting this concept. The framework is applicable even in complex cases including an inhomogeneous temperature field and a frequency-dependent, spatially distributed flame response. A parametric study on a three-dimensional combustion chamber model is conducted using both the full-scale chamber simulation and a one-segment model with the appropriate Bloch-type boundary conditions. The results for both computations are compared in terms of mode frequencies and growth rates as well as the corresponding mode shapes. The same is done for a more complex industrial configuration. These comparisons demonstrate the benefits of the Bloch-wave based analysis.

A three-dimensional finite element code is used for the eigenvalue analysis of the ther moacoustic combustion instabilities modeled through the Helmholtz equation. A full an nular combustion chamber, equipped with several burners, is examined. Spatial distributions for the heat release intensity and for the time delay are used for the linear flame model. Burners, connecting the plenum and the chamber, are modeled by means of the transfer matrix method. The influence of the parameters characterizing the burners and the flame on the stability levels of each mode of the system is investigated. The obtained results show the influence of the 3D distribution of the flame on the modes. Addi tionally, the results show what types of modes are most likely to yield humming in an an nular combustion chamber. The proposed methodology is intended to be a practical tool for the interpretation of the thermoacoustic phenomenon (in terms of modes, frequencies, and stability maps) both in the design stage and in the check stage of gas turbine combus tion chambers. I n t r o d u c t io nModem gas turbines for power generation are generally equipped with lean premixed (LP) combustion burners able to produce very low NOx emissions in order to satisfy the strict regu lations for pollutant emissions. Unfortunately, LP combustion sys tems are often affected by combustion instabilities that emerge as a problem to be avoided since they may generate structural vibra tions that may lead to failure of the system in the worst case. The thermoacoustic interaction between acoustic pressure oscillations and flame heat release fluctuations is regarded as the main origin of combustion instabilities in gas turbines, according to the Ray leigh criterion [1], Over the years, several authors have proposed different approaches to model this phenomenon [2][3][4], Low order models can be applied when simplified geometries, such as simple one dimensional or annular ducts, are examined. Initial studies were carried out by Merk [5], Afterwards, other studies were carried out on afterburners by Bloxsidge et al. [6] and on the Rijke tube by Heckl [7]. Bohn and Deuker [8] were the first to suggest the use of the low-order models as an acoustic network. In this case, the combustor system is modeled as a series of subsystems, using mathematical transfer function matrices to connect these lumped acoustic elements, one to each other. This methodology had a very large spread in the analysis of the influence of flow parame ters on the thermoacoustic oscillations, giving rise to several in-house codes [9][10][11][12].More recently, large eddy simulation (LES) [13][14][15][16][17] has been also proposed in order to investigate the phenomenon of combus tion instability aiming at coupling pressure oscillations with turbu lent combustion phenomena. Selle et al. [13], Benoit [14], and Huang et al. [16] demonstrated the potentiality of LES simulations to solve the thermoacoustic problem. Giauque et al. [15] showed the potentiality of LES simulations in obtaining detailed r...

Lean premixed combustion chambers fuelled by natural gas and used in modern gas turbines for power generation are often affected by combustion instabilities generated by mutual interactions between pressure fluctuations and heat oscillations produced by the flame. Due to propagation and reflection of the acoustic waves in the combustion chamber, very strong pressure oscillations are generated and the chamber may be damaged. This phenomenon is generally referred as thermoacoustic instability, or humming, owing to the cited coupling mechanism of pressure waves and heat release fluctuations.Over the years, several different approaches have been developed in order to model this phenomenon and to define a method able to predict the onset of thermoacoustic instabilities. In order to validate analytical and numerical thermoacoustic models, experimental data are required. In this context, an experimental test rig is designed and operated in order to characterize the propensity of the burner to determine thermoacoustic instabilities.In this paper, a method able to predict the onset of thermoacoustic instabilities is examined and applied to a test rig in order to validate the proposed methodology. The experimental test is designed to evaluate the propensity to thermoacoustic instabilities of full scale Ansaldo Energia burners used in gas turbine systems for production of energy.The experimental work is conducted in collaboration with Ansaldo Energia and CCA (Centro Combustione e Ambiente) at the Ansaldo Caldaie facility in Gioia del Colle (Italy).Under the hypotheses of low Mach number approximation and linear behaviour of the acoustic waves, the heat release fluctuations are introduced in the acoustic equations as source term. In the frequency domain, a complex eigenvalue problem is solved. It allow us to identify the frequencies of thermoacoustic instabilities and the growth rate of the pressure oscillations.The Burner Transfer Matrix (BTM) approach is used to characterize the influence of the burner characteristics. Furthermore, the influence of different operative conditions is examined considering temperature gradients along the combustion chamber.

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