Interplay of Clusters of Acoustic and Intrinsic Thermoacoustic Modes in CanAnnular Combustors

Abstract

Thermoacoustic systems can exhibit selfexcited instabilities of two nature, namely cavity modes or intrinsic thermoacoustic (ITA) modes. In heavyduty landbased gas turbines with canannular combustors, the crosstalk between cans causes the cavity modes of various azimuthal order to create clusters, i.e., ensembles of modes with close frequencies. Similarly, in systems exhibiting rotational symmetry, ITA modes also have the peculiar behavior of forming clusters. In the present study, we investigate how such clusters interplay when they are located in the same frequency range. We first consider a simple Rijke tube configuration and derive a general analytical loworder network model using only dimensionless numbers. We investigate the trajectories of the eigenmodes when changing the downstream length and the flame position. In particular, we show that ITA and acoustic modes can switch nature and their trajectories are strongly influenced by the presence of exceptional points. We then study a generic canannular combustor. We show that such configuration can be approximated by an equivalent Rijke tube. We demonstrate that, in the absence of mean flow, the eigenvalues of the system necessarily lie on specific trajectories imposed by the upstream conditions.