A linear model for control of thermoacoustic instabilities on annular domain

We present a distributed linear model of thermoacoustic instability in form of a set of coupled PDEs including an acoustic model based on potential Euler formulation, a fully distributed fuel transport model based on advection equation, and a fuel-sensitive heat release model based on assumption of fixed flame location. The damping in the distributed model is provided on the acoustic boundaries using local acoustic impedance models. The model is suitable for analysis and control of multiple acoustic modes in annular combustors with bluff body stabilized flames and for optimization of fuel control architecture. We also derive a low order model for control using Galerkin projection of the potential Euler equations on finite number of acoustic basis functions and analytically solving the linearized fuel advection equation. The resulting frequency domain model has a form of coupled system involving undamped oscillators representing acoustic modes, distributed delays representing effect of acoustic perturbation on the fuel transport and combustion, and positive real transfer functions representing acoustic impedances of the boundaries. A simple control algorithm to suppress pressure oscillations is derived using the reduced order model.