Coupling-Induced Instability in a Ring of Thermoacoustic Oscillators

TL;DR

This paper develops a simplified coupled oscillator model to analyze thermoacoustic instabilities in gas turbine combustors, revealing how acoustic coupling can either suppress or amplify these instabilities, impacting system stability.

Contribution

The work introduces a low-order, coupled oscillator model using Bloch-wave analysis to study thermoacoustic instability mechanisms in can-annular combustors.

Findings

Acoustic coupling can suppress or amplify instabilities.

The model predicts potential for instability in nominally stable systems.

Linear stability analysis reveals the influence of can-to-can interactions.

Abstract

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 multi-scale, multiphysical nature of the full problem makes a detailed analysis challenging. In this work, we derive a low-order, coupled oscillator 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 neighboring 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.