Nonlinear thermoacoustic stability analysis of gas turbine combustion chambers

Currently, the stationary gas turbine is the core technology for the highest energy conversion rates available. Additionally, gas turbines are very flexible and can complement the power production of wind turbines and solar power stations very well and they are widely used as propulsion engines in the aviation industry. Liquid and gaseous fuels are burnt at very high temperatures of approximately 1600◦C and electricity is produced at a conversion efficiency of more than 60%. The strict emission regulations are satisfied with the help of the lean premixed combustion technology. Here, large amounts of air are mixed with the fuel prior to burning it. This drastically limits the peak temperature in the flame and thereby reduces the NOx emissions. The major drawback of this technology is the susceptibility to thermoacoustic instabilities. These are coupled high amplitude heat release and pressure oscillations, which can significantly limit the operation range of engines. Thermoacoustic instabilities are difficult to predict and can, in the worst case, destroy essential parts of the gas turbine. These combustion instabilities restrain the operational range of gas turbines and are a reason for increased emissions and decreased efficiency. Therefore, models and prediction tools are of high importance in the design process of combustion chambers. Moreover, the understanding of the physical effects causing nonlinear damping and the nonlinear flame response is of utmost importance. The scope of this thesis is the prediction of limit cycle amplitudes of an industrially relevant combustion system with realistic acoustic boundary conditions and, furthermore, the improved understanding of the relevant nonlinear effects. Firstly, the nonlinear response of a perfectly and partially premixed flame is investigated by means of microphone, chemiluminescence, and flow field measurements. The degree of spatial unmixedness is varied and the impact of temporal mixture inhomogeneities is assessed. Subsequently, the amplitude-dependent acoustic response of Helmholtz dampers and of the other boundary conditions are analyzed with the help of acoustic and flow field measurements. These dampers are used by all gas turbine manufactures in gas turbines to control and attenuate thermoacoustic instabilities. The experiments were conducted under realistic conditions by exposing the damper to hot exhaust gas. Finally, the stability map of a premixed combustor is predicted and compared to extensive stability experiments. The present work significantly extends the state of the art in flame describing function based nonlinear network modeling in several ways. The nonlinear response of a turbulent swirl flame is studied up to extremely high excitation amplitudes. Nonlinear mechanisms of the practically relevant flame are investigated in detail allowing for a better understanding and future modeling of the complex mechanisms. The identified saturation mechanisms are associated to mixture inhomogeneities and to hydrodynamic effects. The correct assessment of the nonlinearity of the acoustic dampers is of crucial importance for the prediction of instabilities in a real engine. For the first time, the temperature differences between the grazing flow and the cross-flow emanating from a Helmholtz resonator are investigated in terms of the influence on the acoustic response of the resonator. It is shown that density gradients between the cooling flow of the damper and the combustor flow significantly affect the damper efficiency and resonance frequency. These effects are successfully modeled and explained in detail. The nonlinear flame and damper response can be used in a nonlinear stability analysis to predict the frequency and amplitude of thermoacoustic instabilities. This is done for the first time for an industrially relevant combustor for a range of combustor lengths, thus, allowing for a realistic assessment of the accuracy of the method. Additionally, a theoretical analysis of the interaction between damper and flame paves the way for encouraging investigations in the future.