Prediction of limit cycle pressure oscillations in gas turbine combustion systems using the flame describing function

Thermo-acoustic analysis is crucial for a successful development of new gas turbine combustion systems. In this context, it becomes more and more necessary to predict the limit cycle pressure amplitude of thermo-acoustic combustion instabilities to figure out if they are within the critical design limit or will cause damage to the engine. For the prediction of limit cycle pressure amplitudes, the nonlinear flame response of the combustion system is needed, which is represented in this work by the Flame Describing Function (FDF). It is investigated if the limit cycle can be predicted using a combination of the FDF, which is calculated from Computational Fluid Dynamics (CFD) simulations, and a low order thermoacoustic stability code. Two test cases are investigated. The first test case is a generic atmospheric swirl flame. The nonlinear saturation of the heat release response of the flame which was observed during measurements, was correctly captured by the CFD, meaning that the calculated and measured FDF showed good comparison. Next the FDF from CFD was used together with the low order thermo-acoustic stability code GIM to predict the limit cycle pressure amplitude. The frequency of the instability was predicted within 5%, the pressure amplitude within 3.3 dB. A sensitivity study, however, showed that small deviations between the measured and simulated FDF’s can lead to significant differences in the predicted limit cycle pressure amplitude. This shows that high fidelity CFD simulations are a must for these kinds of limit cycle predictions. Most limit cycle predictions presented in this work correspond well to the experimental data, indicating a good quality of the simulated FDF. The second test case corresponds to an industrial combustion system. The pressure amplitude is predicted within 4.8 dB and the frequency within 6%, compared to the measurements. An important design change was identified: it was found that the stability of the burner could be improved by shifting the location of the fuel injection downstream, towards the flame. This analysis therefore demonstrates the strength of the proposed method for limit cycle prediction.