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Detailed Analysis of the Acoustic Mode Shapes of an Annular Combustion ChamberTo get a better understanding of the formation of thermoacoustic oscillations in an annular gas turbine combustor, an analysis of the acoustic eigenmodes has been conducted using the finite element method. The influence of different boundary conditions and a space-dependent velocity of sound has been investigated. The boundary conditions actually define the eigenfrequency spectrum. Hence, it is crucial to know, e.g., the burner impedance. In case of the combustion system without significant mixing air addition considered in this paper, the space-dependence of the velocity of sound is of minor importance for the eigenfrequency spectrum leading to a maximum deviation of only five percent in the eigenvalues. It is demonstrated that the efficiency of the numerical eigenvalue analysis can be improved by making use of symmetry, by splitting the problem into several steps with alternate boundary conditions, and by choosing the shift frequency s in the range of frequencies one is interested in. Downloaded From: http://gasturbinespower.asmedigitalcollection.asme.org/ on 02/19/2015 Terms of Use: http://asme.org/terms Journal of Engineering for Gas Turbines and Power JANUARY 2002, Vol. 124 Õ 7 Downloaded From: http://gasturbinespower.asmedigitalcollection.asme.org/ on 02/19/2015 Terms of Use: http://asme.org/termsFig. 7 Selected eigenmodes of the annular combustor with boundary conditions of Problem III. The normalized pressure distribution is shown.

For the development of modern Low-NOx gas turbine combustors featuring high power densities due to their compact design a detailed knowledge about thermoacoustically induced combustion oscillations is required. In order to design passive and active means to suppress thermoacoustic oscillations and to extend the stable operation range of the gas turbine an investigation of the acoustic eigenmodes of the combustor already in the design phase is necessary. In a combined experimental and computational project, tools to determine the mode shapes of a gas turbine combustor have been developed. The mode shapes of an annular combustor of the 3A series have been identified under operating conditions in the test bed of Berlin by cross correlating pressure signals mounted on twelve different azimuthal locations. These data have been used in order to validate the new numerical steady state response method. It has been found that taking into account appropriate acoustic boundary conditions at the burner outlet the numerical predictions are in good agreement with the measurements.

To get a better understanding of the formation of thermoacoustic oscillations in an annular gasturbine combustor, an analysis of the acoustic eigenmodes has been conducted using the Finite Element (FE) method. The influence of different boundary conditions and a space dependent velocity of sound has been investigated. The boundary conditions actually define the eigenfrequency spectrum. Hence, it is crucial to know e.g. the burner impedance. In case of the combustion system without significant mixing air addition considered in this paper, the space dependence of the velocity of sound is of minor importance for the eigenfrequency spectrum leading to a maximum deviation of only 5% in the eigenvalues. It is demonstrated that the efficiency of the numerical eigenvalue analysis can be improved by making use of symmetry, by splitting the problem into several steps with alternate boundaries conditions, and by choosing the shift frequency ωs in the range of frequencies one is interested in.

Freestanding turbine blades have typically low structural damping and thus require additional friction damping devices, such as underplatform dampers. The friction coupling between neighboring blades reduces response amplitude and increases resonance frequency. Along with forced response excitation large blades, especially of last stage, could be excited by fluid structural interaction (flutter). To prevent such excitation alternate mistuned blade patterns are beneficial disturbing traveling waves in the stage. In this paper the influence of alternate mistuning is investigated with a simplified oscillator chain as well as a bladed disk assembly coupled by frictional contacts. It is pointed out that the performance of friction coupling can be improved by alternate mistuning as long as the engine order of the excitation is below quarter of the number of blades. Alternate mistuning causes a mode coupling between two nodal diameter vibration mode shapes allowing for energy transfer. The in-house developed software code DATAR is enhanced and alternate mistuning can be applied to the blades as well as to the damping elements. For validation the DATAR code was applied to an alternate mistuned last stage blade of a Siemens gas turbine and compared with available field engine measurement.