Heavy-duty gas turbines are commonly designed with can-annular combustors, in which all flames are physically separated. Acoustically, however, the cans communicate via the upstream located compressor plenum, or at the downstream gaps found at the transition to the turbine inlet. In the present study, a coupling condition that is based on a Rayleigh conductivity and acoustic flux conservation is derived. It enables acoustic communication between adjacent cans, in which one-dimensional acoustic waves propagate. In addition, because can-annular systems commonly feature a discrete rotational symmetry, the acoustic field can be expressed as a Bloch-periodic wave in the azimuthal direction. We demonstrate how the coupling conditions resulting in a combustion system with $N$ cans can be expressed as an effective impedance for a single can. By means of this Bloch-type boundary condition, the thermoacoustics of a can-annular system can be analyzed considering only one can, thus reducing the size of the problem by a factor of N. Using this method, we investigate in frequency domain the effect of the coupling strength of a generic can-annular combustor consisting of 12 identical cans, which are connected at the downstream end. We describe generic features of can-annular systems and derive results on the frequency response of the cans at various Bloch numbers in the low-frequency and high-frequency limits. Furthermore, the formation of eigenvalue clusters with eigenvalues of close frequency and growth rate, but very different mode shapes is discussed.

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