This article presents numerical prediction of a thermoacoustic limit cycle in an industrial gas turbine combustor. The case corresponds to an experimental high pressure test rig equipped with the full-scale Siemens SGT-100 combustor operated at two mean pressure levels of 3 bar and 6 bar. The Flame Transfer Function (FTF) characterising the global unsteady response of the flame to velocity perturbations is obtained for both operating pressures by means of incompressible Large Eddy Simulations (LES). A linear stability analysis is then performed by coupling the FTFs with a wave-based low order thermoacoustic network solver. All the thermoacoustic modes predicted at 3 bar pressure are stable; whereas one of the modes at 6 bar is found to be unstable at a frequency of 231 Hz, which agrees with the experiments. A weakly nonlinear stability analysis is carried out by combining the Flame Describing Function (FDF) predicted by LES with the low order thermoacoustic network solver. The frequency, mode shape and velocity amplitude corresponding to the predicted limit cycle at 209 Hz are used to compute the absolute pressure fluctuation amplitude in the combustor. The numerically reconstructed amplitude is found to be reasonably close to the measured dynamics.

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