  In this work, we derive a model to investigate the generic thermoacoustic
behavior of an idealized can-annular combustor containing N cans. We start from
the acoustic wave equation, which simplifies to a Helmholtz equation in the
frequency domain. By projecting this equation onto the dominant natural
eigenmode of a single can, we derive a symmetric system of N coupled ordinary
differential equations (ODEs) in the frequency domain for the dynamics of the
dominant modal amplitudes. Assuming perfect symmetry, we use a Bloch wave
ansatz to reduce this system to an equivalent single ODE in the frequency
domain. The acoustic pressure fields in the cans are coupled at the annular
turbine inlet. To model the effect of mean flow in the cans on the acoustic
coupling, we use Howe's model for the Rayleigh conductivity of a rectangular
aperture under turbulent grazing flow. The resulting low-order model allows us
to study the influence of physical parameters such as natural eigenfrequency,
the mean flow speed, the aperture width, the base linear growth rate and the
can spacing on the frequency spectrum of an idealized can-annular combustor. We
show that, depending on the values of the system parameters, the acoustic
coupling can suppress or amplify thermoacoustic instabilities, raising the
potential for instabilities in nominally stable systems.
