Thermoacoustic oscillations in a can-annular model combustor with asymmetries in the can-to-can coupling

Buschmann, Philip E.; Worth, Nicholas A.; Moeck, Jonas P.

doi:10.1016/j.proci.2022.07.060

Cited by 7 publications

(7 citation statements)

References 14 publications

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“…Furthermore, while in single-burner and annular multiburner systems, combustion instabilities most commonly manifest as single-mode oscillations, our calculations show that multimode oscillations routinely occur in a can-annular system, with a push-push or push-pull mode often being dominant. This is consistent with experimental observations by Moon et al (2020b), Guan et al (2022) and Buschmann et al (2023).…”

Section: Synchronisationsupporting

confidence: 94%

“…Eigenvalue clusters comprising all Bloch numbers and organised around the longitudinal can modes are a general feature of can-annular systems, as we have argued in § 3. Traces of these eigenvalue clusters can be seen in pressure spectra as multiple close acoustic resonances (Moon et al 2020b;Buschmann et al 2023). Furthermore, while in single-burner and annular multiburner systems, combustion instabilities most commonly manifest as single-mode oscillations, our calculations show that multimode oscillations routinely occur in a can-annular system, with a push-push or push-pull mode often being dominant.…”

Section: Synchronisationmentioning

confidence: 73%

“…For all the calculations in the following, we have set ( β − α)/2 ≈ 23 s −1 , ω 0 ≈ 2π × 180 rad s −1 and κ ≈ 50, and varied the strength of the (aero)acoustic coupling between the cans by varying Δ and Γ . The value of the driving ( β − α) term was chosen to be approximately 2 % that of ω 0 because (i) the method of averaging requires ( β − α) ω 0 to yield accurate results at first order and (ii) it was observed that the magnitude of this value is consistent with typical positive growth rates found in Orchini et al (2022), where the same experimental set-up of Buschmann et al (2023) was modelled. The nonlinear saturation coefficient κ was instead tuned in order to have oscillation amplitudes with a maximum value close to unity.…”

Section: Resultsmentioning

confidence: 99%

“…The specific value was chosen to balance the complexity of the dynamics to the manageability of the nonlinear terms in the equations. The configuration considered here models the atmospheric can-annular experimental set-up assembled at the Norwegian University of Science and Technology and described by Buschmann, Worth & Moeck (2023). We refer to the latter for details about the geometry.…”

Section: Resultsmentioning

confidence: 99%

“…Most of the experimental studies to date investigate two-can or four-can systems (Moon et al 2020a,b;Chen et al 2021;Guan et al 2022), which host a smaller number of Bloch modes. The laboratory-scale can-annular system investigated by Buschmann et al (2023) corresponds to the configuration considered in the present work, but a quantitative comparison would require detailed information about the linear and nonlinear flame responses, which is not available from the experiment. Lastly, most of the can-annular systems studied experimentally are turbulent, which adds significant noise to the thermoacoustic dynamics and partly obscures the attractor.…”

Section: Synchronisationmentioning

confidence: 99%

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Weakly nonlinear analysis of thermoacoustic oscillations in can-annular combustors

Orchini,

Moeck

2024

J. Fluid Mech.

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Can-annular combustors feature clusters of thermoacoustic eigenvalues, which originate from the weak acoustic coupling between $N$ identical cans at the downstream end. When instabilities occur, one needs to consider the nonlinear interaction between all $N$ modes in the unstable cluster in order to predict the steady-state behaviour. A nonlinear reduced-order model for the analysis of this phenomenon is developed, based on the balance equations for acoustic mass, momentum and energy. Its linearisation yields explicit expressions for the $N$ complex-valued eigenfrequencies that form a cluster. To treat the nonlinear equations semianalytically, a Galerkin projection is performed, resulting in a nonlinear system of $N$ coupled oscillators. Each oscillator represents the dynamics of a global mode that oscillates in the whole can-annular combustor. The analytical expressions of the equations reveal how the geometrical and thermofluid parameters affect the thermoacoustic response of the system. To gain further insights, the method of averaging is applied to obtain equations for the slow-time dynamics of the amplitude and phase of each mode. The averaged system, whose solutions compare very well with those of the full oscillator equations, is shown to be able to predict complex transient dynamics. A variety of dynamical states are identified in the steady-state oscillatory regime, including push–push (in-phase) and spinning oscillations. Notably, the averaged equations are able to predict the existence of synchronised states. These states occur when the frequencies of two (or more) unstable modes with nominally different frequencies lock onto a common frequency as a result of nonlinear interactions.

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Section: Synchronisationsupporting

confidence: 94%

Section: Synchronisationmentioning

confidence: 73%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Synchronisationmentioning

confidence: 99%

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Weakly nonlinear analysis of thermoacoustic oscillations in can-annular combustors

Orchini,

Moeck

2024

J. Fluid Mech.

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Low-order modeling of collective dynamics of four ring-coupled turbulent thermoacoustic oscillators

Liao,

Guan,

Liu

et al. 2024

Nonlinear Dyn

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We investigate the low-order modeling of collective dynamics in a can-annular combustor consisting of four ring-coupled turbulent lean-premixed combustors. Each combustor is treated as an individual thermoacoustic oscillator, and the entire combustion system is modeled using four Van der Pol oscillators ring-coupled with dissipative, time-delay, and reactive coupling terms. We show that this model, despite its simplicity, can reproduce many collective dynamics observed in experiments under various combinations of equivalence ratios and combustor lengths, such as 2-can anti-phase synchronization, alternating anti-phase synchronization, pairwise anti-phase synchronization, spinning azimuthal mode, and 4 steady thermoacoustic oscillators. The phase relationship in the majority of cases can be quantitatively modeled. Moreover, by incorporating a reactive coupling term, the model is able to reproduce the frequency shift observed experimentally. This study demonstrates the feasibility of using a simple low-order model to reproduce collective dynamics in complex turbulent combustion systems. This suggests that this model could be used (i) to facilitate the interpretation of experimental data within the synchronization framework, (ii) to identify potential parameter regimes leading to amplitude death, and (iii) to serve as a basis for modeling the collective dynamics observed in more complicated multi-combustors.

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Amplitude death in ring-coupled network with asymmetric thermoacoustic oscillators and nonlocal time-delay interactions

Zheng,

Liao,

Kim

et al. 2024

Nonlinear Dyn

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This numerical study examines the pressure amplitude distribution, focusing on amplitude death, in a ring-coupled network of nonlocally coupled asymmetric thermoacoustic oscillators. Each decoupled self-excited thermoacoustic oscillator is modeled using the classical Rijke tube model. We investigate three configurations with asymmetric thermoacoustic oscillators: localized asymmetry, side-by-side asymmetry, and alternating asymmetry. Asymmetries are introduced through frequency detuning and heater power mismatching. Our study reveals that the configuration with alternating asymmetry induces the largest region of amplitude death compared to the other two configurations, where all originally self-excited oscillators become quenched in the network. The remaining energy of oscillations often concentrates at the two ends of the axis of symmetry. The region of amplitude death generally increases with the number of thermoacoustic oscillators and remains unchanged when the number of oscillators is sufficiently large (n = 8). The variation of the global average pressure amplitude predicted by the proposed model qualitatively agrees with previous experimental observations. In summary, we conclude: (1) reduced-order models developed from a dynamical system approach can provide a qualitative prediction of the system’s pressure amplitude distribution, potentially offering useful information for avoiding operating parameters that lead to high-amplitude thermoacoustic oscillations in multi-combustor systems; and (2) introducing asymmetries into a ring-coupled network can potentially be leveraged to weaken self-excited oscillations in multi-combustor systems globally.

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Thermoacoustic oscillations in a can-annular model combustor with asymmetries in the can-to-can coupling

Cited by 7 publications

References 14 publications

Weakly nonlinear analysis of thermoacoustic oscillations in can-annular combustors

Weakly nonlinear analysis of thermoacoustic oscillations in can-annular combustors

Low-order modeling of collective dynamics of four ring-coupled turbulent thermoacoustic oscillators

Amplitude death in ring-coupled network with asymmetric thermoacoustic oscillators and nonlocal time-delay interactions

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