Abstract
Thermoacoustic instabilities in can-annular combus-tors of stationary gas turbines lead to unstable Bloch modes which appear as rotating acoustic pressure waves along the turbine annulus. The multiscale, multiphysical nature of the full problem makes a detailed analysis challenging. In this work, we derive a low-order, coupled oscillators model of an idealized can-annular combustor. The unimodal projection of the Helmholtz equation for the can acoustics is combined with the Rayleigh conductivity, which describes the aeroacoustic coupling between neighbouring cans. Using a Bloch-wave ansatz, the resulting system is reduced to a single equation for the frequency spectrum. A linear stability analysis is then performed to study the perturbation of the spectrum by the can-to-can interaction. It is observed that the acoustic coupling can suppress or amplify thermoacoustic instabilities, raising the potential for instabilities in nominally stable systems.
Highlights
Thermoacoustic instabilities in can-annular combustors of stationary gas turbines lead to unstable Bloch modes which appear as rotating acoustic pressure waves along the turbine annulus
The unimodal projection of the Helmholtz equation for the can acoustics is combined with the Rayleigh conductivity, which describes the aeroacoustic coupling between neighbouring cans
In our application of Bloch wave theory, we follow the approach presented in [33], where a Bloch wave ansatz is combined with the Rayleigh conductivity to derive effective Bloch-type boundary condition (BC) for a modelled can-annular combustor in the frequency domain
Summary
Thermoacoustic instabilities are caused by the constructive interaction of unsteady combustion and the acoustics of the chamber. The can-annular system is simplified to a network model, where the azimuthal pressure dynamics are represented by the coupling of longitudinal acoustic modes through compact apertures [36,37]. In our application of Bloch wave theory, we follow the approach presented in [33], where a Bloch wave ansatz is combined with the Rayleigh conductivity to derive effective Bloch-type BCs for a modelled can-annular combustor in the frequency domain. This enables the analysis of a canannular system consisting of N cans by considering a single can, reducing the number of equations by a factor N.
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