Thermo-acoustic cross-talk between cans in a can-annular combustor

Farisco, Federica; Panek, Łukasz; Kok, Jacobus B.W.

doi:10.1177/1756827717716373

Cited by 49 publications

(24 citation statements)

References 41 publications

(43 reference statements)

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“…The normalized potential U P is independent of the signs in k, see Eq. (21). However, the signs do impact the projection of the slow-flow equations ( 5) and (6) onto the quasi-limit cycle solutions…”

Section: Potential Landscape Of the Deterministic Systemmentioning

confidence: 99%

“…The cans are thermodynamically decoupled from each other, but the annular turbine inlet is shared by all can outlets and allows for acoustic cross-talk between neighboring cans. Theoretical, numerical and experimental studies performed at Siemens [18][19][20][21], General Electric [22][23][24] and Ansaldo Energia Switzerland [25,26] are testament to the increased interest of industry in the thermoacoustics of can-annular combustors. In Ref.…”

Section: Thermoacoustic Instabilities In Can-annular Combustorsmentioning

confidence: 99%

“…For 0 > Λ > Λ c , which we call the "transition region" in the following, the minima of the projected potential U P , given by Eq. (21), lie between B = 0 and B = ±π/2. This parameter range is further investigated below.…”

Section: Potential Landscape Of the Deterministic Systemmentioning

confidence: 99%

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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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Section: Potential Landscape Of the Deterministic Systemmentioning

confidence: 99%

Section: Thermoacoustic Instabilities In Can-annular Combustorsmentioning

confidence: 99%

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

Pedergnana

Noiray

2022

Nonlinear Dyn

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“…2008; Luque et al. 2015; Farisco, Panek & Kok 2017; Bonciolini & Noiray 2019; Ghirardo et al. 2019; von Saldern, Moeck & Orchini 2021 a ).…”

Section: Introductionmentioning

confidence: 99%

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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“…Acoustic mode shapes that involve multiple cans, and thus cannot be found by examining a single isolated can only, were observed. The effect of the cross-talk gap between adjacent cans at the turbine inlet on the acoustic cross-talk between the cans was numerically examined in [3]. In [4], it was theoretically discussed how azimuthal modes can arise in can-annular combustors even for a weak acoustic can-to-can coupling.…”

Section: Introductionmentioning

confidence: 99%

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

Saldern

Orchini

Moeck

2021

Journal of Engineering for Gas Turbines and Power

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Heavy-duty gas turbines are commonly designed with can-annular combustors, in which all flames are physically separated. Acoustically, however, the cans communicate via the upstream located compressor plenum, or at the downstream gaps found at the transition to the turbine inlet. In the present study, a coupling condition that is based on a Rayleigh conductivity and acoustic flux conservation is derived. It enables acoustic communication between adjacent cans, in which one-dimensional acoustic waves propagate. In addition, because can-annular systems commonly feature a discrete rotational symmetry, the acoustic field can be expressed as a Bloch-periodic wave in the azimuthal direction. We demonstrate how the coupling conditions resulting in a combustion system with $N$ cans can be expressed as an effective impedance for a single can. By means of this Bloch-type boundary condition, the thermoacoustics of a can-annular system can be analyzed considering only one can, thus reducing the size of the problem by a factor of N. Using this method, we investigate in frequency domain the effect of the coupling strength of a generic can-annular combustor consisting of 12 identical cans, which are connected at the downstream end. We describe generic features of can-annular systems and derive results on the frequency response of the cans at various Bloch numbers in the low-frequency and high-frequency limits. Furthermore, the formation of eigenvalue clusters with eigenvalues of close frequency and growth rate, but very different mode shapes is discussed.

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Thermo-acoustic cross-talk between cans in a can-annular combustor

Cited by 49 publications

References 41 publications

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

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

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

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

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