Lean combustion technologies in gas turbines reduce the generation of NOx but increase the susceptibility to thermoacoustic oscillations. These oscillations can produce structural damage and need to be eliminated. The stability of a given configuration can be examined with a thermoacoustic model. In this thesis a wave-based network model is used. Using adjoint methods the gradients of the eigenvalue with respect to system parameters can be obtained at a low computational cost. This information is used as an input to an optimization routine to find stable thermoacoustic configurations.

In this thesis thermocaoustic oscillations are analysed using a linear low order network model. This modelling approach is used to predict the unstable modes of five different configurations: a Rijke tube, a choked combustor, a longitudinal combustor, a generic lean premix prevaporized annular combustor and the laboratory scale annular combustor built in Cambridge University Engineering Department. The continuous and discrete adjoint equations for the low order network model are derived. Using the adjoint equations the sensitivities of the eigenvalues to changes in base state parameters such as time delays, areas, lengths and mean radii are computed. Similarly, the sensitivity of the eigenvalues to the introduction of a feedback device such as a drag mesh or a secondary heat source is investigated. By fitting experimental data to a low Mach number model of the Rijke tube, the predictions of the growth rate and frequency shifts due to the presence of these mechanisms are improved. Finally, using the sensitivity information, two different optimization algorithms are developed to stabilize the thermoacoustic systems. Different stabilization scenarios are presented, showing the changes required in each section of the configurations to eliminate thermoacoustic oscillations.

The techniques presented as part of this thesis are readily scalable to more complex models and geometries and the inclusion of further constraints. This demonstrates that adjoint-based sensitivity analysis and optimization could become an indispensable tool for the design of thermoacoustically-stable combustors.