Synchronization-based model for turbulent thermoacoustic systems

Weng, Yue; Unni, Vishnu R.; Sujith, R. I.; Saha, Abhishek

doi:10.1007/s11071-023-08368-z

Cited by 6 publications

(6 citation statements)

References 62 publications

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“…The exact form considered in Eq. ( 3) is inspired from the theory of interacting phase oscillators encountered in complex systems theory 38,39,45 and is a natural choice, as we intend to study the underlying synchronization behavior of the thermoacoustic system. We express the overall heat release rate fluctuations (q ) as a summation of the contribution from all the instantaneous phase oscillators,…”

Section: B Flame Modelingmentioning

confidence: 99%

“…Further, to aid comparison between the model and experiments, we normalize the non-dimensionalized equations using the expression: A LCO = β cos(kx f )N/α, where A LCO is the amplitude of acoustic pressure during limit cycle oscillations (see Appendix A and also refer Ref. 39). Thus, we obtain the following set of normalized and non-dimensionalized equations,…”

Section: Mean-field Model Of Synchronizationmentioning

confidence: 99%

“…Therefore, in this study, we couple the acoustic elements with the heat release rate model to capture the dynamics observed during suppression experiments. We extend the model introduced by Dutta et al 37 and build upon our recent work on the mean-field model of thermoacoustic transitions 39 to explain the method of suppression observed in the swirl-controlled experiments. The effect of the actuated swirler is included by accounting for the time scale of the swirler rotation.…”

Section: Introductionmentioning

confidence: 95%

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Mean-field model of synchronization for open-loop, swirl controlled thermoacoustic system

Singh

Dutta

Dhadphale

et al. 2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Open-loop control is known to be an effective strategy for controlling self-excited periodic oscillations, known as thermoacoustic instability, in turbulent combustors. Here, we present experimental observations and a synchronization model for the suppression of thermoacoustic instability achieved by rotating the otherwise static swirler in a lab-scale turbulent combustor. Starting with the state of thermoacoustic instability in the combustor, we find that a progressive increase in the swirler rotation rate leads to a transition from the state of limit cycle oscillations to the low-amplitude aperiodic oscillations through a state of intermittency. To model such a transition while also quantifying the underlying synchronization characteristics, we extend the model of Dutta et al. [Phys. Rev. E 99, 032215 (2019)] by introducing a feedback between the ensemble of phase oscillators and the acoustic. The coupling strength in the model is determined by considering the effect of the acoustic and swirl frequencies. The link between the model and experimental results is quantitatively established by implementing an optimization algorithm for model parameter estimation. We show that the model is capable of replicating the bifurcation characteristics, nonlinear features of time series, probability density function, and amplitude spectrum of acoustic pressure and heat release rate fluctuations at various dynamical states observed during the transition to the state of suppression. Most importantly, we discuss the flame dynamics and demonstrate that the model without any spatial inputs qualitatively captures the characteristics of the spatiotemporal synchronization between the local heat release rate fluctuations and the acoustic pressure that underpins a transition to the state of suppression. As a result, the model emerges as a powerful tool for explaining and controlling instabilities in thermoacoustic and other extended fluid dynamical systems, where spatiotemporal interactions lead to rich dynamical phenomena.

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Section: B Flame Modelingmentioning

confidence: 99%

Section: Mean-field Model Of Synchronizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

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Mean-field model of synchronization for open-loop, swirl controlled thermoacoustic system

Singh

Dutta

Dhadphale

et al. 2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…Weng et al [21] developed a phenomenological coupled-oscillator model to qualitatively capture the bifurcation behavior in Kabiraj et al [20]. Recently, Weng et al [22] proposed a coupled oscillator model for the behavior of the acoustic and heat-release-rate fluctuations in the Pawar et al [1] experiments. This model consisted of two oscillator equations for just the heat-release-rate fluctuations and a separate oscillator equation for the acoustic pressure fluctuations.…”

Section: Introductionmentioning

confidence: 99%

A Nonlinear Acoustic--Flame Synchronization Model for Thermoacoustic Instability in a Bluffbody-Stabilized Combustor

kumar,

Rani

2024

Preprint

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A nonlinear coupled-oscillator model is developed that can predict the various stages of synchronization between the acoustic and heat-release oscillations in the lead-up to thermoacoustic instability in a dump combustor with a bluffbody-anchored flame. The flame is perturbed by vortices shed from the shear layer formed at the combustor dump plane. The resulting heat-release-rate fluctuations generate acoustic waves that travel upstream and interact with the shear layer, thereby modulating the vortex shedding process and closing the feedback loop. Coupled nonlinear equations governing the temporal evolution of pressure and heat-release-rate fluctuations are derived and evolved along with an equation for the build-up of circulation at the dump plane, as well as an equation for vortex advection. The effects of vortex impingement on the flame are modeled as a localized, instantaneous source term in the flame oscillator equation. With the mean flow velocity $\Bar{u}$ as the control parameter, the nonlinear model is applied to investigate the acoustic--flame--vortex interactions. For smaller $\Bar{u}$, chaotic combustion noise is observed with essentially no synchronization between the pressure and heat-release-rate fluctuations, $p'$ and $\dot{q}'$, respectively. As $\Bar{u}$ is increased, intermittent bursts of periodic fluctuations are seen in $p'$ and $\dot{q}'$, which is followed by a weakly periodic state with only frequency synchronization. Eventually, when $\Bar{u}$ exceeds a critical value, limit-cycle oscillations are seen with both frequency and amplitude synchronization between $p'$ and $\dot{q}'$ (also known as generalized synchronization). Thus, the model qualitatively captures the successive stages of acoustic--flame coupling seen in the experiments of \citet{pawar2017}. Furthermore, the derived nonlinear equations accurately predict the natural frequencies of the pressure and heat-release oscillators, as well as the lock-on frequency of the two oscillators with vortex shedding.

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“…Specifically, multifractal detrended fluctuation analysis (MFDFA) [1] is a powerful method for detecting long-range correlations and multifractal scaling properties in time series. It has been widely analyzed [2,3] and employed with success in different fields, such as financial markets [4], meteorology [5], traffic speed [6], biology [7], acoustics [8], neuroimaging [9,10], and seismicity [11,12], among others. However, the application of MFDFA for studying uncertain systems is not straightforward.…”

Section: Introductionmentioning

confidence: 99%

Multi-Signal Multifractal Detrended Fluctuation Analysis for Uncertain Systems —Application to the Energy Consumption of Software Programs in Microcontrollers

de la Torre,

Pavón-Domínguez,

Dorronsoro

et al. 2023

Fractal Fract

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Uncertain systems are those wherein some variability is observed, meaning that different observations of the system will produce different measurements. Studying such systems demands the use of statistical methods over multiple measurements, which allows overcoming the uncertainty, based on the premise that a single measurement is not representative of the system’s behavior. In such cases, the current multifractal detrended fluctuation analysis (MFDFA) method cannot offer confident conclusions. This work presents multi-signal MFDFA (MS-MFDFA), a novel methodology for accurately characterizing uncertain systems using the MFDFA algorithm, which enables overcoming the uncertainty of the system by simultaneously considering a large set of signals. As a case study, we consider the problem of characterizing software (Sw) consumption. The difficulty of the problem mainly comes from the complexity of the interactions between Sw and hardware (Hw), as well as from the high uncertainty level of the consumption measurements, which are affected by concurrent Sw services, the Hw, and external factors such as ambient temperature. We apply MS-MFDFA to generate a signature of the Sw consumption profile, regardless of the execution time, the consumption levels, and uncertainty. Multiple consumption signals (or time series) are built from different Sw runs, obtaining a high frequency sampling of the instant input current for each of them while running the Sw. A benchmark of eight Sw programs for analysis is also proposed. Moreover, a fully functional application to automatically perform MS-MFDFA analysis has been made freely available. The results showed that the proposed methodology is a suitable approximation for the multifractal analysis of a large number of time series obtained from uncertain systems. Moreover, analysis of the multifractal properties showed that this approach was able to differentiate between the eight Sw programs studied, showing differences in the temporal scaling range where multifractal behavior is found.

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Synchronization-based model for turbulent thermoacoustic systems

Cited by 6 publications

References 62 publications

Mean-field model of synchronization for open-loop, swirl controlled thermoacoustic system

Mean-field model of synchronization for open-loop, swirl controlled thermoacoustic system

A Nonlinear Acoustic--Flame Synchronization Model for Thermoacoustic Instability in a Bluffbody-Stabilized Combustor

Multi-Signal Multifractal Detrended Fluctuation Analysis for Uncertain Systems —Application to the Energy Consumption of Software Programs in Microcontrollers

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