Premixed flame kinematics in a harmonically oscillating velocity field
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Air pollution regulations have driven modern power generation systems to move from diffusion to premixed combustion. However, these premixed combustion systems are prone to combustion instability, causing high fluctuations in pressure and temperature. This results in shortening of component life, system failure, or even catastrophic disasters. A large number of studies have been performed to understand and quantify the onset of combustion instability and the limit cycle amplitude. However, much work remains due to the complexity of the process associated with flow dynamics and chemistry. This thesis focuses on identifying, quantifying and predicting mechanisms of flame response subject to disturbances. A promising tool for predicting combustion instability is a flame transfer function. The flame transfer function is obtained by integrating unsteady heat release over the combustor domain. Thus, the better understanding of spatio-temporal characteristics of flame is required to better predict the flame transfer function. The spatio-temporal flame response is analyzed by the flame kinematic equation, so called G-equation. The flame is assumed to be a thin interface separating products and reactant, and the interface is governed by the local flow and the flame propagation. Much of the efforts were done to the flame response subject to the harmonic velocity disturbance. A key assumption allowing for analytic solutions is that the velocity is prescribed. For the mathematical tools, small perturbation theory, Hopf-Lax formula and numerical simulation were used. Solutions indicated that the flame response can be divided into three regions, referred to here as the near-field, mid-field, and farfield. In each regime, analytical expressions were derived, and those results were compared with numerical and experimental data. In the near field, it was shown that the flame response grows linearly with the normal component of the velocity disturbance. In the mid field, the flame response shows peaks in gain, and the axial location of these peaks can be predicted by the interference pattern by two characteristic waves. Lastly, in the far field where the flame response decreases, three mechanisms are studied; they are kinematic restoration, flame stretch, and turbulent flow effects. For each mechanism, key parameters are identified and their relative significances are compared.