Modeling the Response of Premixed Flames to Flow Disturbances Preetham 178 pages Directed by Dr. Tim Lieuwen Low emissions combustion systems for land based gas turbines rely on a premixed or partially premixed combustion process. These systems are exceptionally prone to combustion instabilities which are destructive to hardware and adversely affect performance and emissions. The success of dynamics prediction codes is critically dependent on the heat release model which couples the flame dynamics to the system acoustics. So the principal objective of the current research work is to predict the heat release response of premixed flames and to isolate the key non-dimensional parameters which characterize its linear and nonlinear dynamics. Explicit analytical solutions of the G- equation are derived in the linear and weakly nonlinear regime using the Small Perturbation Method (SPM). For the fully nonlinear case, the flame-flow interaction effects are captured by developing an unsteady, compressible, coupled Euler-G-equation solver with a Ghost Fluid Method (GFM) module for applying the jump conditions across the flame. The flame s nonlinear response is shown to exhibit two qualitatively different behaviors. Depending on the operating conditions and the disturbance field characteristics, it is shown that a combustor may exhibit supercritical bifurcations leading to a single stable limit cycle amplitude or exhibit sub-critical bifurcations wherein multiple stable solutions for the instability amplitude are possible. In addition, this study presents the first analytical model which captures the effects of unsteady flame stretch on the heat release response and thus extends the applicability of current models to high frequency instabilities, such as occurring during screech. It is shown that unsteady stretch effects, negligible at low frequencies (100 s of Hz) become significant at screeching frequencies (1000 s of Hz). Furthermore, the analysis also yields insight into the significant spatial dependence of the mean and perturbation velocity field induced by the coupling between the flame and the flow field. In order to meaningfully compare the heat release response across different flame configurations, this study has identified that the reference velocity (for defining the transfer function) should be based on the effective normal velocity perturbing the flame and the Strouhal number should be based on the effective residence time of the flame wrinkles.