Low-Order Modeling of Can-Annular Combustors

Abstract

Heavy-duty land-based gas turbines are often designed with can-annular combustors, which consist of a set of identical cans, acoustically connected on the upstream side via the compressor plenum, and, downstream, with a small annular gap located at the transition with the first turbine stage. The modeling of this cross-talk area is crucial to predict the thermo-acoustic modes of the system. Thanks to the discrete rotational symmetry, Bloch wave theory can be exploited to reduce the system to a longitudinal combustor with a complex-valued equivalent outlet reflection coefficient, which models the annular gap. The present study reviews existing low-order models based purely on geometrical parameters and compares them to 2D Helmholtz simulations. We demonstrate that the modeling of the gap as a thin annulus is not suited for can-annular combustors and that the Rayleigh conductivity model only gives qualitative agreement. We then propose an extension for the equivalent reflection coefficient that accounts not only for geometrical but also flow parameters, by means of a characteristic length. The proposed model is in excellent agreement with 2D simulations and is able to correctly capture the eigenfrequencies of the system. We then perform a Design of Experiments study that allows us to explore various configurations and build correlations for the characteristic length. Finally, we discuss the validity limits of the proposed low-order modeling approach.

Acoustic Boundary Conditions for Can-Annular Combustors

“…Their predictions are qualitatively similar to the can transfer functions from the simulations of Ghirardo et al [3]. Fournier et al [5] showed that augmenting the Rayleigh conductivity with a characteristic length, a function of azimuthal mode empirically fitted from two-dimensional Helmholtz simulations, matches acoustic impedance phase results to within 2%.…”

Coupling-induced instability in a ring of thermoacoustic oscillators

“…As previously mentioned, by taking into account the acoustic-hydrodynamic interaction in the apertures between the cans, we observe resistive effects due to the coupling which have either been neglected or not investigated in detail in previous studies [29,30,[32][33][34]36,37]. Our model describes simultaneously the can acoustics and the turbulent wake dynamics in the apertures.…”

“…The dynamics of two coupled thermoacoustic oscillators under asymmetric forcing is investigated in [ 35 ]. In two recent studies, 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 the latter study, the same Rayleigh conductivity is used as in [ 33 ], and the model equations are simplified using Bloch BCs to study the coupling in more detail.…”

“…In the present work, a coupled oscillator model is combined with Howe’s Rayleigh conductivity of a turbulent wake in a rectangular aperture of thickness [ 38 ] to perform a linear stability analysis of an idealized can-annular combustor and present findings about the hitherto unexplored aeroacoustic component of the coupling. Similar to [ 37 ], we assume longitudinal thermoacoustic modes in the cans which communicate through such compact apertures. We provide below elementary first-principles calculations to quantify the validity range of this assumption.…”

Weakly nonlinear analysis of thermoacoustic oscillations in can-annular combustors

“…From a can perspective, this can be taken into account as an acoustic mass source/sink along the extension of the aperture (Fournier et al. 2021; von Saldern et al. 2021 c ).…”