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.

45 pages, 10 figures

References in corpus (4)

• Quantifying acoustic damping using flame chemiluminescence
• Dynamics of coupled thermoacoustic oscillators under asymmetric forcing: Experiments and theoretical modeling
• Coupling-Induced Instability in a Ring of Thermoacoustic Oscillators
• Modeling the nonlinear aeroacoustic response of a harmonically forced side branch aperture under turbulent grazing flow

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