Suppressing azimuthal thermoacoustic instabilities through symmetry-breaking flame response staging and exceptional points

The impacts of non-uniform flame response distributions on the stability of azimuthal thermoacoustic modes in annular combustors are investigated theoretically and illustrated in an experimental annular combustor test-rig with electroacoustic feedback. First, we exploit analytical results from an existing reduced-order model to establish and apply a general passive control strategy based on flame response staging to mitigate thermoacoustic instabilities stemming from both degenerate and non-degenerate eigenvalues. By means of a suitable pattern, an acoustics-flame response interaction that has a destabilising effect in the baseline symmetric configuration can be suppressed or turned into a stabilising interaction. For a mode pair whose degeneracy is lifted by the flame response staging pattern, our mitigation strategy exploits the presence of symmetry-breaking-induced exceptional points, which were recently identified in a previous study. The mitigation rules obtained when considering a degenerate or a non-degenerate mode in an isolated fashion are finally combined to establish a multi-mode strategy to prevent all azimuthal modes from being linearly unstable. The mitigation strategy is devised using a low-order model, and validated using an existing experimentally-determined state-space model and experiments in an electroacoustic feedback annular combustor test-rig. In addition, we show that if accurate estimates of the acoustic and thermoacoustic eigenvalues in the reference (symmetric) configuration are available, they can be exploited to calibrate the low-order model and then analytically predict the eigenvalues in the asymmetric configurations with good accuracy.