We report the occurrence of amplitude death (AD) of limit cycle oscillations in a bluff body stabilized turbulent combustor through delayed acoustic self-feedback. Such feedback control is achieved by coupling the acoustic field of the combustor to itself through a single coupling tube attached near the anti-node position of the acoustic standing wave. We observe that the amplitude and dominant frequency of the limit cycle oscillations gradually decrease as the length of the coupling tube is increased. Complete suppression (AD) of these oscillations is observed when the length of the coupling tube is nearly 3 / 8 times the wavelength of the fundamental acoustic mode of the combustor. Meanwhile, as we approach this state of amplitude death, the dynamical behavior of acoustic pressure changes from the state of limit cycle oscillations to low-amplitude chaotic oscillations via intermittency. We also study the change in the nature of the coupling between the unsteady flame dynamics and the acoustic field as the length of the coupling tube is increased. We find that the temporal synchrony between these oscillations changes from the state of synchronized periodicity to desynchronized aperiodicity through intermittent synchronization. Furthermore, we reveal that the application of delayed acoustic self-feedback with optimum feedback parameters completely disrupts the positive feedback loop between hydrodynamic, acoustic, and heat release rate fluctuations present in the combustor during thermoacoustic instability, thus mitigating instability. We anticipate this method to be a viable and cost-effective option to mitigate thermoacoustic oscillations in turbulent combustion systems used in practical propulsion and power systems.
REFERENCES
1.
T. C.
Lieuwen
and V.
Yang
, Combustion Instabilities in Gas Turbine Engines: Operational Experience, Fundamental Mechanisms, and Modeling
(American Institute of Aeronautics and Astronautics
, 2005
).2.
R. I.
Sujith
and S. A.
Pawar
, Thermoacoustic Instability—A Complex Systems Perspective
(Springer Nature
, 2021
).3.
F. E. C.
Culick
, “Unsteady motions in combustion chambers for propulsion systems,” Technical Report (AGARDograph, NATO/RTO-AG-AVT-039, 2006).4.
A. P.
Dowling
and A. S.
Morgans
, “Feedback control of combustion oscillations
,” Annu. Rev. Fluid Mech.
37
, 151
–182
(2005
). 5.
D.
Zhao
and X.
Li
, “A review of acoustic dampers applied to combustion chambers in aerospace industry
,” Prog. Aerosp. Sci.
74
, 114
–130
(2015
). 6.
R.
Rajaram
and D. M.
Ritland
, “Attenuation of combustion dynamics using a Herschel–Quincke filter,” U.S. patent 8,336,312 (2012).7.
R. C.
Steele
, L. H.
Cowell
, S. M.
Cannon
, and C. E.
Smith
, “Passive control of combustion instability in lean premixed combustors
,” J. Eng. Gas Turbines Power
122
, 412
–419
(2000
). 8.
K. O.
Smith
and J.
Blust
, “Combustion instabilities in industrial gas turbines: Solar turbines' experience
,” in Combustion Instabilities In Gas Turbine Engines: Operational Experience, Fundamental Mechanisms, and Modeling
(American Institute of Aeronautics and Astronautics
, 2005
), pp. 29
–41
. 9.
K.
Schadow
and E.
Gutmark
, “Combustion instability related to vortex shedding in dump combustors and their passive control
,” Prog. Energy Combust. Sci.
18
, 117
–132
(1992
). 10.
Y.
Huang
and V.
Yang
, “Dynamics and stability of lean-premixed swirl-stabilized combustion
,” Prog. Energy Combust. Sci.
35
, 293
–364
(2009
). 11.
V.
Bellucci
, P.
Flohr
, C. O.
Paschereit
, and F.
Magni
, “On the use of Helmholtz resonators for damping acoustic pulsations in industrial gas turbines
,” J. Eng. Gas Turbines Power
126
, 271
–275
(2004
). 12.
M.
Lakshmanan
and K.
Murali
, Chaos in Nonlinear Oscillators: Controlling and Synchronization
(World Scientific
, 1996
), Vol. 13.13.
A.
Pikovsky
, M.
Rosenblum
, and J.
Kurths
, Synchronization: A Universal Concept in Nonlinear Sciences
(Cambridge University Press
, 2003
), Vol. 12.14.
W.
Zou
, D. V.
Senthilkumar
, M.
Zhan
, and J.
Kurths
, “Quenching, aging, and reviving in coupled dynamical networks
,” Phys. Rep.
931
, 1
–72
(2021
). 15.
N.
Thomas
, S.
Mondal
, S. A.
Pawar
, and R. I.
Sujith
, “Effect of time-delay and dissipative coupling on amplitude death in coupled thermoacoustic oscillators
,” Chaos
28
, 033119
(2018
). 16.
H.
Hyodo
, M.
Iwasaki
, and T.
Biwa
, “Suppression of Rijke tube oscillations by delay coupling
,” J. Appl. Phys.
128
, 094902
(2020
). 17.
A.
Ghosh
, S.
Mondal
, and R. I.
Sujith
, “Occasional coupling enhances amplitude death in delay-coupled oscillators
,” Chaos
32
, 101106
(2022
). 18.
S.
Dange
, K.
Manoj
, S.
Banerjee
, S. A.
Pawar
, S.
Mondal
, and R. I.
Sujith
, “Oscillation quenching and phase-flip bifurcation in coupled thermoacoustic systems
,” Chaos
29
, 093135
(2019
). 19.
S.
Srikanth
, S. A.
Pawar
, K.
Manoj
, and R. I.
Sujith
, “Dynamical states and bifurcations in coupled thermoacoustic oscillators
,” Chaos
32
, 073129
(2022
). 20.
M. H.
Doranehgard
, V.
Gupta
, and L. K. B.
Li
, “Quenching and amplification of thermoacoustic oscillations in two nonidentical Rijke tubes interacting via time-delay and dissipative coupling
,” Phys. Rev. E
105
, 064206
(2022
). 21.
F. M.
Atay
, “Total and partial amplitude death in networks of diffusively coupled oscillators
,” Physica D
183
, 1
–18
(2003
). 22.
N.
Thomas
, S.
Mondal
, S. A.
Pawar
, and R. I.
Sujith
, “Effect of noise amplification during the transition to amplitude death in coupled thermoacoustic oscillators
,” Chaos
28
, 093116
(2018
). 23.
H.
Jegal
, K.
Moon
, J.
Gu
, L. K. B.
Li
, and K. T.
Kim
, “Mutual synchronization of two lean-premixed gas turbine combustors: Phase locking and amplitude death
,” Combust. Flame
206
, 424
–437
(2019
). 24.
K.
Moon
, Y.
Guan
, L. K. B.
Li
, and K. T.
Kim
, “Mutual synchronization of two flame-driven thermoacoustic oscillators: Dissipative and time-delayed coupling effects
,” Chaos
30
, 023110
(2020
). 25.
Y.
Guan
, K.
Moon
, K. T.
Kim
, and L. K. B.
Li
, “Low-order modeling of the mutual synchronization between two turbulent thermoacoustic oscillators
,” Phys. Rev. E
104
, 024216
(2021
). 26.
T.
Pedergnana
and N.
Noiray
, “Coupling-induced instability in a ring of thermoacoustic oscillators
,” Proc. Math. Phys. Eng. Sci.
478
, 20210851
(2022
).27.
G. J.
Fournier
, M.
Meindl
, C. F.
Silva
, G.
Ghirardo
, M. R.
Bothien
, and W.
Polifke
, “Low-order modeling of can-annular combustors
,” J. Eng. Gas Turbines Power
143
, 121004
(2021
). 28.
K.
Moon
, H.
Jegal
, C.
Yoon
, and K. T.
Kim
, “Cross-talk-interaction-induced combustion instabilities in a can-annular lean-premixed combustor configuration
,” Combust. Flame
220
, 178
–188
(2020
). 29.
T.
Pedergnana
and N.
Noiray
, “Steady-state statistics, emergent patterns and intermittent energy transfer in a ring of oscillators
,” Nonlinear Dyn.
108
, 1133
–1163
(2022
). 30.
A.
Sahay
, A.
Roy
, S. A.
Pawar
, and R. I.
Sujith
, “Dynamics of coupled thermoacoustic oscillators under asymmetric forcing
,” Phys. Rev. Appl.
15
, 044011
(2021
). 31.
K.
Manoj
, S. A.
Pawar
, J.
Kurths
, and R. I.
Sujith
, “Rijke tube: A nonlinear oscillator
,” Chaos
32
, 072101
(2022
). 32.
V.
Nair
, G.
Thampi
, and R. I.
Sujith
, “Intermittency route to thermoacoustic instability in turbulent combustors
,” J. Fluid Mech.
756
, 470
–487
(2014
). 33.
T.
Biwa
, Y.
Sawada
, H.
Hyodo
, and S.
Kato
, “Suppression of spontaneous gas oscillations by acoustic self-feedback
,” Phys. Rev. Appl.
6
, 044020
(2016
). 34.
S.
Srikanth
, A.
Sahay
, S. A.
Pawar
, K.
Manoj
, and R. I.
Sujith
, “Self-coupling: An effective method to mitigate thermoacoustic instability
,” Nonlinear Dyn.
110
, 2247
–2261
(2022
). 35.
A. M.
Annaswamy
and A. F.
Ghoniem
, “Active control of combustion instability: Theory and practice
,” IEEE Control Syst.
22
, 37
–54
(2002
). 36.
T.
Biwa
, S.
Tozuka
, and T.
Yazaki
, “Amplitude death in coupled thermoacoustic oscillators
,” Phys. Rev. Appl.
3
, 034006
(2015
). 37.
M.
Basso
, R.
Genesio
, L.
Giovanardi
, A.
Tesi
, and G.
Torrini
, “On optimal stabilization of periodic orbits via time delayed feedback control
,” Int. J. Bifurc. Chaos Appl. Sci. Eng.
8
, 1699
–1706
(1998
). 38.
T.
Pierre
, G.
Bonhomme
, and A.
Atipo
, “Controlling the chaotic regime of nonlinear ionization waves using the time-delay autosynchronization method
,” Phys. Rev. Lett.
76
, 2290
(1996
). 39.
O.
Lüthje
, S.
Wolff
, and G.
Pfister
, “Control of chaotic Taylor–Couette flow with time-delayed feedback
,” Phys. Rev. Lett.
86
, 1745
(2001
). 40.
P.
Parmananda
, R.
Madrigal
, M.
Rivera
, L.
Nyikos
, I.
Kiss
, and V.
Gáspár
, “Stabilization of unstable steady states and periodic orbits in an electrochemical system using delayed-feedback control
,” Phys. Rev. E
59
, 5266
(1999
). 41.
H.
Benner
and W.
Just
, “Control of chaos by time-delayed feedback in high-power ferromagnetic resonance experiments
,” J. Korean Phys. Soc.
40
, 1046
–1050
(2002
).42.
T.
Lato
, A.
Mohany
, and M.
Hassan
, “A passive damping device for suppressing acoustic pressure pulsations: The infinity tube
,” J. Acoust. Soc.
146
, 4534
–4544
(2019
). 43.
L.
Magri
and M. P.
Juniper
, “Sensitivity analysis of a time-delayed thermo-acoustic system via an adjoint-based approach
,” J. Fluid Mech.
719
, 183
–202
(2013
). 44.
C. S.
Skene
and K.
Taira
, “Phase-reduction analysis of periodic thermoacoustic oscillations in a Rijke tube
,” J. Fluid Mech.
933
, A35
(2022
). 45.
C.
Wilke
, “A viscosity equation for gas mixtures
,” J. Chem. Phys.
18
, 517
–519
(1950
). 46.
D. R.
Reddy
, A.
Sen
, and G. L.
Johnston
, “Dynamics of a limit cycle oscillator under time delayed linear and nonlinear feedbacks
,” Phys. D: Nonlinear Phenom.
144
, 335
–357
(2000
). 47.
A.
Seshadri
and R. I.
Sujith
, “A bifurcation giving birth to order in an impulsively driven complex system
,” Chaos
26
, 083103
(2016
). 48.
V.
Flunkert
and E.
Schöll
, “Suppressing noise-induced intensity pulsations in semiconductor lasers by means of time-delayed feedback
,” Phys. Rev. E
76
, 066202
(2007
). 49.
E.
Schöll
, P.
Hövel
, V.
Flunkert
, and M. A.
Dahlem
, “Time-delayed feedback control: From simple models to lasers and neural systems,” in Complex Time-Delay Systems (Springer, 2009), pp. 85–150.50.
H.
Dai
, A.
Abdelkefi
, L.
Wang
, and W.
Liu
, “Time-delay feedback controller for amplitude reduction in vortex-induced vibrations
,” Nonlinear Dyn.
80
, 59
–70
(2015
). 51.
S. A.
Pawar
, A.
Seshadri
, V. R.
Unni
, and R. I.
Sujith
, “Thermoacoustic instability as mutual synchronization between the acoustic field of the confinement and turbulent reactive flow
,” J. Fluid Mech.
827
, 664
–693
(2017
). 52.
V.
Godavarthi
, S. A.
Pawar
, V. R.
Unni
, R. I.
Sujith
, N.
Marwan
, and J.
Kurths
, “Coupled interaction between unsteady flame dynamics and acoustic field in a turbulent combustor
,” Chaos
28
, 113111
(2018
). 53.
P.
Kasthuri
, S. A.
Pawar
, R.
Gejji
, W.
Anderson
, and R. I.
Sujith
, “Coupled interaction between acoustics and unsteady flame dynamics during the transition to thermoacoustic instability in a multi-element rocket combustor
,” Combust. Flame
240
, 112047
(2022
). 54.
S.
Murayama
and H.
Gotoda
, “Attenuation behavior of thermoacoustic combustion instability analyzed by a complex-network-and synchronization-based approach
,” Phys. Rev. E
99
, 052222
(2019
). 55.
Y.
Guan
, L. K.
Li
, B.
Ahn
, and K. T.
Kim
, “Chaos, synchronization, and desynchronization in a liquid-fueled diffusion-flame combustor with an intrinsic hydrodynamic mode
,” Chaos
29
, 053124
(2019
). 56.
A. K.
Dutta
, G.
Ramachandran
, and S.
Chaudhuri
, “Investigating thermoacoustic instability mitigation dynamics with a Kuramoto model for flamelet oscillators
,” Phys. Rev. E
99
, 032215
(2019
). 57.
Y.
Guan
, K.
Moon
, K. T.
Kim
, and L. K.
Li
, “Synchronization and chimeras in a network of four ring-coupled thermoacoustic oscillators
,” J. Fluid Mech.
938
, A5
(2022
). 58.
A.
Grinsted
, J. C.
Moore
, and S.
Jevrejeva
, “Application of the cross wavelet transform and wavelet coherence to geophysical time series
,” Nonlinear Process. Geophys.
11
, 561
–566
(2004
). 59.
S. A.
Pawar
, S.
Mondal
, N. B.
George
, and R. I.
Sujith
, “Temporal and spatiotemporal analyses of synchronization transition in a swirl-stabilized combustor
,” AIAA J.
57
, 836
–847
(2019
). 60.
J. M.
Gonzalez-Miranda
, “Amplitude envelope synchronization in coupled chaotic oscillators
,” Phys. Rev. E
65
, 036232
(2002
). 61.
A.
Krishnan
, R. I.
Sujith
, N.
Marwan
, and J.
Kurths
, “On the emergence of large clusters of acoustic power sources at the onset of thermoacoustic instability in a turbulent combustor
,” J. Fluid Mech.
874
, 455
–482
(2019
). © 2023 Author(s). Published under an exclusive license by AIP Publishing.
2023
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