Coupling-Induced Instability in a Ring of Thermoacoustic Oscillators

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.

arXiv comment45 pages, 10 figures

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Cited by in corpus (4)

• Coupling-Induced Instability in a Ring of Thermoacoustic Oscillators
• Dynamical States and Bifurcations in Coupled Thermoacoustic Oscillators
• Mitigation of limit cycle oscillations in a turbulent thermoacoustic system via delayed acoustic self-feedback
• Steady State Statistics of Emergent Patterns in a Ring of Oscillators