Nonlinear dynamic analysis and feedback control of thermoacoustic instability

This dissertation mainly studies the nonlinear dynamic behaviors of thermoacoustic instability and feedback control of thermoacoustic oscillations numerically and experimentally. Rijke-type thermoacoustic systems are modeled for numerical investigation, and experimental investigations are conducted on a Rijke tube. Coupling the heat input with Galerkin series expansion of flow disturbances provides a platform to gain insights on the time evolution of system's response. The effects of the heat source on the process of transition to thermoacoustic instability are studied. Two different premixed flame models are proposed to characterize the relation between the unsteady heat release and acoustic pressure: a 3rd-order polynomial and a 5th-order polynomial. Experiment is conducted to examine the transition process on a Rijke tube, within which both subcritical and supercritical bifurcations are observed. By comparison between the systems with different order heat source model, it is found that the nonlinearity of heat source determines the transition process of thermoacoustic system, i.e., via subcritical or supercritical bifurcation. The effects of the noisy fluctuation on the stability behaviors of thermoacoustic systems are studied. The noisy fluctuation is characterized by a Gaussian white noise, and the stochastic stability is measured by stationary probability function. With the increase of noise intensity, it is found that the thermoacoustic system near the hysteresis area shows a stochastic P-bifurcation. In addition, the theoretical results show that increasing the noise intensity would decrease the hysteresis region and expand the unstable area. Then the noise-induced motions near the bifurcation point are experimentally and numerically studied. Resonance-like behaviors of signal to noise ratio (SNR) are observed, denoting the occurrence of coherence resonance. When the system approaches the critical bifurcation point, SNR is found to become larger, and the optimal noise intensity is decreased to a smaller value. Qualitative agreements are obtained in the theoretical and experimental results in terms of SNR, the peak height of power spectrum, and the width of the frequency. Coherence resonance is also observed in supercritical thermoacoustic systems. By comparison, it is found that the characteristics of coherence resonance in thermoacoustic systems depend on whether the system loses stability via subcritical bifurcation or supercritical one. To suppress large-amplitude thermoacoustic oscillations in Rijke tube, two different state-feedback controllers are proposed. One is a Lyapunov-function-based controller (LFC), and the other is a sliding mode controller (SMC). The non-uniformity of the temperature field within the combustor is considered, and it is approximated according to the experimental measurement. First, it is found that implementing the developed LFC can make the system achieve strict dissipativity and reduce approximately 25 dB sound pressure level (SPL). Then, the performances of SMC are evaluated in two thermoacoustic systems with either 1 eigenmode or 4 eigenmodes. Both thermoacoustic systems are stabilized by reducing around 40 dB SPL, and the proposed controller shows a good performance in the system with multiple unstable modes.Doctor of Philosophy (MAE