Analysis of Thermoacoustic Modes in Can-Annular Combustors Using Effective Bloch-Type Boundary Conditions

Saldern, Jakob G. R. von; Orchini, Alessandro; Moeck, Jonas P.

doi:10.1115/1.4049162

Cited by 20 publications

(33 citation statements)

References 25 publications

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“…In the literature on can-annular combustors, this is known as a push–pull mode, which Ghirardo, Moeck & Bothien (2020) and von Saldern et al. (2021 b ), among others, have recently studied via low-order modelling. Owing to the ring-coupled architecture of our system, the fact that anti-phase synchronization occurs between any two directly coupled oscillators (C1–C2, C2–C3, C3–C4, C4–C1) implies that in-phase synchronization occurs between any two indirectly coupled oscillators (C1–C3, C2–C4).…”

Section: Resultsmentioning

confidence: 99%

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Synchronization and chimeras in a network of four ring-coupled thermoacoustic oscillators

et al. 2022

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We take a complex systems approach to investigating experimentally the collective dynamics of a network of four self-excited thermoacoustic oscillators coupled in a ring. Using synchronization metrics, we find a wide variety of emergent multi-scale behaviour, such as (i) a transition from intermittent frequency locking on a $\mathbb {T}^{3}$ quasiperiodic attractor to a breathing chimera, (ii) a two-cluster state of anti-phase synchronization on a periodic limit cycle, and (iii) a weak anti-phase chimera. We then compute the cross-transitivity from recurrence networks to identify the dominant direction of the coupling between the heat-release-rate ( $q^{\prime }_{\mathbb {X}}$ ) and pressure ( $p^{\prime }_{\mathbb {X}}$ ) fluctuations in each individual oscillator, as well as that between the pressure ( $p^{\prime }_{\mathbb {X}}$ and $p^{\prime }_{\mathbb {Y}}$ ) fluctuations in each pair of coupled oscillators. We find that networks of non-identical oscillators exhibit circumferentially biased $p^{\prime }_{\mathbb {X}}$ – $p^{\prime }_{\mathbb {Y}}$ coupling, leading to mode localization, whereas networks of identical oscillators exhibit globally symmetric $p^{\prime }_{\mathbb {X}}$ – $p^{\prime }_{\mathbb {Y}}$ coupling. In both types of networks, we find that the $p^{\prime }_{\mathbb {X}}$ – $q^{\prime }_{\mathbb {X}}$ coupling can be symmetric or asymmetric, but that the asymmetry is always such that $q^{\prime }_{\mathbb {X}}$ exerts a greater influence on $p^{\prime }_{\mathbb {X}}$ than vice versa. Finally, we show through a cluster analysis that the $p^{\prime }_{\mathbb {X}}$ – $p^{\prime }_{\mathbb {Y}}$ interactions play a more critical role than the $p^{\prime }_{\mathbb {X}}$ – $q^{\prime }_{\mathbb {X}}$ interactions in defining the collective dynamics of the system. As well as providing new insight into the interplay between the $p^\prime_{\mathbb{X}}\text{--}p^\prime_{\mathbb{Y}}$ and $p^\prime_{\mathbb{X}}\text{--}q^\prime_{\mathbb{X}}$ coupling, this study shows that even a small network of four ring-coupled thermoacoustic oscillators can exhibit a wide variety of collective dynamics. In particular, we present the first evidence of chimera states in a minimal network of coupled thermoacoustic oscillators, paving the way for the application of oscillation quenching strategies based on chimera control.

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Section: Resultsmentioning

confidence: 99%

“…In can-annular combustors, the existence of clusters of thermoacoustic modes with similar frequencies was first revealed by Ghirardo et al. (2019) and was subsequently explained by von Saldern, Orchini & Moeck (2021 b ) using Bloch-wave theory. On the experimental front, Moon et al.…”

Section: Introductionmentioning

confidence: 95%

Synchronization and chimeras in a network of four ring-coupled thermoacoustic oscillators

et al. 2022

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“…The theoretical studies in Refs. [27,28] use periodic (Bloch-type) boundary conditions to simplify the analysis of reduced-order models of canannular combustors. The effect of resistive (damperlike) and reactive (mass-or spring-like) coupling on the linear stability of a ring of thermoacoustic oscillators is investigated in Ref.…”

Section: Thermoacoustic Instabilities In Can-annular Combustorsmentioning

confidence: 99%

Steady-state statistics, emergent patterns and intermittent energy transfer in a ring of oscillators

Pedergnana

Noiray

2022

Nonlinear Dyn

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Networks of coupled nonlinear oscillators model a broad class of physical, chemical and biological systems. Understanding emergent patterns in such networks is an ongoing effort with profound implications for different fields. In this work, we analytically and numerically study a symmetric ring of N coupled self-oscillators of van der Pol type under external stochastic forcing. The system is proposed as a model of the thermo- and aeroacoustic interactions of sound fields in rigid enclosures with compact source regions in a can-annular combustor. The oscillators are connected via linear resistive coupling with nonlinear saturation. After transforming the system to amplitude-phase coordinates, deterministic and stochastic averaging is performed to eliminate the fast oscillating terms. By projecting the potential of the slow-flow dynamics onto the phase-locked quasi-limit cycle solutions, we obtain a compact, low-order description of the (de-)synchronization transition for an arbitrary number of oscillators. The stationary probability density function of the state variables is derived from the Fokker–Planck equation, studied for varying parameter values and compared to time series simulations. We leverage our analysis to offer explanations for the intermittent energy transfer between Bloch waves observed in acoustic pressure spectrograms observed of real-world gas turbines.

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“…An empirical expression is used in this reference to model the acoustic coupling, and the mode shapes obtained from this low-order model are successfully compared to FEM simulations of the Helmholtz equation. In [ 33 ], an FTF is computed from a solver based on the G-equation to model the heat release fluctuations of the flame and the Rayleigh conductivity of a compact circular aperture with bias flow is used for the (purely reactive) acoustic can-to-can coupling. The authors study the linear stability of the modelled can-annular combustor.…”

Section: Introductionmentioning

confidence: 99%

“…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. Focusing on reactive coupling effects, the modelled phase response of the connecting gap is successfully compared to experiments.…”

Section: Introductionmentioning

confidence: 99%

Coupling-induced instability in a ring of thermoacoustic oscillators

Pedergnana

Noiray

2022

Proc. R. Soc. A.

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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.

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Analysis of Thermoacoustic Modes in Can-Annular Combustors Using Effective Bloch-Type Boundary Conditions

Cited by 20 publications

References 25 publications

Synchronization and chimeras in a network of four ring-coupled thermoacoustic oscillators

Synchronization and chimeras in a network of four ring-coupled thermoacoustic oscillators

Steady-state statistics, emergent patterns and intermittent energy transfer in a ring of oscillators

Coupling-induced instability in a ring of thermoacoustic oscillators

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