Coupling-induced instability in a ring of thermoacoustic oscillators

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.

Nonlinear acoustics of an aperture under grazing flow

“…7 and 8], yet it does not exhibit any negative resistance values. This is unfortunate, since the aforementioned effect could be an important phenomenon in the modelling of more practical systems such as an opening connecting neighbouring can-combustors in gas turbines for electrical power generation [43]. Nevertheless, the validation against experimental measurements confirms the requirement of normal velocity continuity across the aperture to be an effective design strategy, as discussed by Jing et al [4] and Peat et al [5,21].…”

Interplay of Clusters of Acoustic and Intrinsic Thermoacoustic Modes in Can-Annular Combustors

“…For each azimuthal order, the gap introduces a different phase shift, but there is no amplification nor damping. However, recent studies of Pedergnana and Noiray [38] and Orchini et al [39] showed that, when accounting for mean flow effects, the effective coupling impedance exhibit resistive effects. In particular, as shown in Fig.…”

“…Von Saldern et al [36] derived an effective impedance model for non-compact connections and analyzed the role of liners in damping azimuthal thermoacoustic modes. Orchini [37] and Pedergnana and Noiray [38] explored the effect of mean flow and derived effective impedance models that show explicit dependence on the grazing flow Mach number. Orchini et al [39] then showed that such effect gives rise to new sets of clusters of modes of aeroacoustic origin due to the coupling with the response of the shear layer in the apertures.…”