Exceptional points in a thermoacoustic model of a can-annular combustor

Gas turbines for power generation often feature can-annular combustors. This combustor architecture consists of a set of nominally identical cans, which host individual, spatially separated flames; the cans are, however, acoustically coupled at the turbine inlet. The thermoacoustic dynamics in this type of configuration can be modeled as a system of weakly coupled identical oscillators with a time delayed feedback. Such a system generally exhibits eigenvalue clustering and, as a result, high eigenfunction sensitivity and possibly mode localization under asymmetric perturbations. We investigate the existence and parameter dependence of exceptional points (EPs) in this type of system. EPs are generally found for every azimuthal mode order, and because of the weak coupling, frequency and growth rate are typically close. As in single-flame systems, the eigenvalue collision at the EP is linked to modes of intrinsic and acoustic origin. We show that the location of all EPs as a function of the number of cans, the Bloch wavenumber, and the can-to-can coupling strength can be obtained from solutions of a one-parameter problem. This allows for an effective prediction of all EPs, given initial solutions from a corresponding single-can system and assuming weak coupling.