Thermoacoustic instabilities are a problem in modern pre-mixed combustors causing reduced performance and leading in the extreme to combustor failure from excessive pressure cycles. Much work has been done using linear controllers to eliminate these instabilities. Many experimenters in the field have used pulsed and subharmonic fuel controllers to eliminate these instabilities, but very little investigative work has been done on these controllers. The goal of this work is to explain the mechanism of control behind pulsed controllers. It is shown that the combustion system can be treated as a linear system, thus meaning that frequency components of the control signal at the desired instability frequency are the dominant means of control, with nonlinear effects only serving to slightly reduce the gain necessary for control. Fourier analysis is thus performed on pulsed signals and the components analyzed, showing that there will indeed be a component of a pulsed signal at the frequency of the instability, aside from a few select cases. It is then proven that this frequency component is largely responsible for control of the thermoacoustic system using proportional height pulse train signals, which will change pulse height based on the amplitude of the instability. This analysis is then used to predict the height of instabilities resulting from the use of fixed height pulse control signals. Finally, numerical simulations and experimental observations support the analytical constructs. Acoustic control is mainly used for these experiments, although some preliminary work with liquid fuel controllers is also presented. / Master of Science

Lean premixed fuel-air conditions in large gas turbines are used to improve efficiency and reduce emissions. These conditions give rise to large undamped pressure oscillations at the combustor's natural frequencies which reduce the turbine's longevity and reliability. Active control of the pressure oscillations, called thermoacoustic instabilities, has been sought as passive abatement of these instabilities does not provide adequate damping and is often impractical on a large scale. Phase shift control of the instabilities is perhaps the simplest and most popular technique employed but often does not provide good performance in that controller induced secondary instabilities are generated with increasing loop gain. This thesis investigates the general underlying cause of the secondary instabilities and shows that high average group delay through the frequency region of the instability is the root of the problem. This average group delay is then shown to be due not only the controller itself but can also be associated with other components and inherent characteristics of the control loop such as actuators and time delay, respectively. An "optimum" phase shift controller, consisting of an appropriate shift in phase and a low order, wide bandwidth bandpass filter, is developed for a Rijke tube combustor and shown to closely match the response of an LQG controller designed only for system stabilization. Both the optimal phase shifter and the LQG controller are developed based on a modified model of the thermoacoustic loop which takes into account the change in density of the combustion reactants at the flame location. Additionally, the system model is coupled with a model of the control loop and then validated by comparison of simulated results to experimental results using nearly identical controllers. / Master of Science