Theoretical model of azimuthal combustion instability subject to non-trivial boundary conditions

The problem of evaluating the sensitivity of non-trivial boundary conditions to the onset of azimuthal combustion instability is a longstanding challenge in the development process of modern gas turbines. The difficulty lies in how to describe three-dimensional in- and outlet boundary conditions in an artificial computational domain. To date, the existing analytical models have still failed to quantitatively explain why the features of the azimuthal combustion instability of a combustor in laboratory environment are quite different from that in a real gas turbine, making the stability control devices developed in laboratory generally lose the effectiveness in practical applications. To overcome this limitation, we provide a novel theoretical framework to directly include the effect of non-trivial boundary conditions on the azimuthal combustion instability. A key step is to take the non-trivial boundary conditions as equivalent distributed sources so as to uniformly describe the physical characteristics of the inner surface in an annular enclosure along with different in- and outlet configurations. Meanwhile, a dispersion relation equation is established by the application of three-dimensional Green’s function approach and generalized impedance concept. Results show that the effects of the generalized modal reflection coefficients on azimuthal unstable modes are extremely prominent, and even prompt the transition from stable to unstable mode, thus reasonably explaining why the thermoacoustic instability phenomena in a real gas turbine are difficult to observe in an isolated combustion chamber. Overall, this work provides an effective tool for analysis of the azimuthal combustion instability including various complicated boundary conditions.