Exceptional points in the thermoacoustic spectrum of longitudinal configurations

Exceptional points (EPs) are found in the spectrum of a longitudinal thermoacoustic system as the parameters of the flame transfer function are varied. EPs occur when two eigenvalue trajectories with different physical nature collide: One trajectory originates from an acoustic mode, whereas the other trajectory originates from an intrinsic thermoacoustic mode. The system's sensitivity to changes in the parameters is infinite because the EP is a square-root branch point of the determinant. Traditional iterative methods to find eigenvalues are not robust in the vicinity of EPs. A contour-integration-based approach is deployed to enable the robust computation of the thermoacoustic spectrum. The appropriate expansion at the EP, which can be used to calculate sensitivities to the system’s parameters for passive control, is in fractional powers (Puiseux series) of the parameters. The large sensitivity at an EP may help design new control schemes to mitigate thermoacoustic instabilities with small changes in the design variables. The existence of EPs in thermoacoustic systems has implications for physical understanding, computing, modelling and control.