Abstract

Thermoacoustic systems can exhibit self-excited instabilities of two nature, namely cavity modes or intrinsic thermoacoustic (ITA) modes. In heavy-duty land-based gas turbines with can-annular combustors, the cross-talk between cans causes the cavity modes of various azimuthal order to create clusters, i.e., ensembles of modes with close frequencies. Similarly, in systems exhibiting rotational symmetry, ITA modes also have the peculiar behavior of forming clusters. In the present study, we investigate how such clusters interplay when they are located in the same frequency range. We first consider a simple Rijke tube configuration and derive a general analytical low-order network model using only dimensionless numbers. We investigate the trajectories of the eigenmodes when changing the downstream length and the flame position. In particular, we show that ITA and acoustic modes can switch nature and their trajectories are strongly influenced by the presence of exceptional points. We then study a generic can-annular combustor. We show that such configuration can be approximated by an equivalent Rijke tube. We demonstrate that, in the absence of mean flow, the eigenvalues of the system necessarily lie on specific trajectories imposed by the upstream conditions.

References

1.
Lieuwen
,
T.
, and
McManus
,
K.
,
2003
, “
Combustion Dynamics in Lean-Premixed Prevaporized (LPP) Gas Turbines
,”
J. Propul. Power
,
19
(
5
), pp.
721
721
.10.2514/2.6171
2.
Poinsot
,
T.
,
2017
, “
Prediction and Control of Combustion Instabilities in Real Engines
,”
Proc. Combust. Inst.
,
36
(
1
), pp.
1
28
.10.1016/j.proci.2016.05.007
3.
Lieuwen
,
T.
, and
Yang
,
V.
, eds.,
2005
, “
Combustion Instabilities in Gas Turbine Engines: Operational Experience, Fundamental Mechanisms and Modeling
,”
AIAA
Paper No. v. 210.10.2514/4.866807
4.
Culick
,
F.
,
1988
, “
Combustion Instabilities in Liquid-Fuelled Propulsion Systems - An Overview
,”
Combustion Instabilities in Liquid-Fuelled Propulsion Systems
, Vol.
450
,
Agard/NATO
, Neuilly-sur-Seine, France.
5.
Lieuwen
,
T. C.
,
2012
,
Unsteady Combustor Physics
,
Cambridge University Press
,
New York
.
6.
Hoeijmakers
,
M.
,
Lopez Arteaga
,
I.
,
Kornilov
,
V.
,
Nijmeijer
,
H.
, and
de Goey
,
P.
,
2013
, “
Experimental Investigation of Intrinsic Flame Stability
,”
European Combustion Meeting, ECM2013
,
Scandinavian-Nordic Section of the Combustion Institute
, Lund, Sweden, June 25–28.https://research.tue.nl/en/publications/experimental-investigation-of-intrinsic-flame-stability
7.
Hoeijmakers
,
M.
,
Kornilov
,
V.
,
Lopez Arteaga
,
I.
,
de Goey
,
P.
, and
Nijmeijer
,
H.
,
2014
, “
Intrinsic Instability of Flame-Acoustic Coupling
,”
Combust. Flame
,
161
(
11
), pp.
2860
2867
.10.1016/j.combustflame.2014.05.009
8.
Silva
,
C. F.
,
Emmert
,
T.
,
Jaensch
,
S.
, and
Polifke
,
W.
,
2015
, “
Numerical Study on Intrinsic Thermoacoustic Instability of a Laminar Premixed Flame
,”
Combust. Flame
,
162
(
9
), pp.
3370
3378
.10.1016/j.combustflame.2015.06.003
9.
Courtine
,
E.
,
Selle
,
L.
, and
Poinsot
,
T.
,
2015
, “
DNS of Intrinsic Thermoacoustic Modes in Laminar Premixed Flames
,”
Combust. Flame
,
162
(
11
), pp.
4331
4341
.10.1016/j.combustflame.2015.07.002
10.
Bomberg
,
S.
,
Emmert
,
T.
, and
Polifke
,
W.
,
2015
, “
Thermal Versus Acoustic Response of Velocity Sensitive Premixed Flames
,”
Proc. Combust. Inst.
,
35
(
3
), pp.
3185
3192
.10.1016/j.proci.2014.07.032
11.
Emmert
,
T.
,
Bomberg
,
S.
, and
Polifke
,
W.
,
2015
, “
Intrinsic Thermoacoustic Instability of Premixed Flames
,”
Combust. Flame
,
162
(
1
), pp.
75
85
.10.1016/j.combustflame.2014.06.008
12.
Emmert
,
T.
,
Bomberg
,
S.
,
Jaensch
,
S.
, and
Polifke
,
W.
,
2017
, “
Acoustic and Intrinsic Thermoacoustic Modes of a Premixed Combustor
,”
Proc. Combust. Inst.
,
36
(
3
), pp.
3835
3842
.10.1016/j.proci.2016.08.002
13.
Yong
,
K. J.
,
Silva
,
C. F.
, and
Polifke
,
W.
,
2021
, “
A Categorization of Marginally Stable Thermoacoustic Modes Based on Phasor Diagrams
,”
Combust. Flame
,
228
, pp.
236
249
.10.1016/j.combustflame.2021.01.003
14.
Dowling
,
A. P.
, and
Stow
,
S. R.
,
2003
, “
Acoustic Analysis of Gas Turbine Combustors
,”
J. Propul. Power
,
19
(
5
), pp.
751
764
.10.2514/2.6192
15.
Eckstein
,
J.
, and
Sattelmayer
,
T.
,
2006
, “
Low-Order Modeling of Low-Frequency Combustion Instabilities in Aeroengines
,”
J. Propul. Power
,
22
(
2
), pp.
425
432
.10.2514/1.15757
16.
Ghani
,
A.
,
Steinbacher
,
T.
,
Albayrak
,
A.
, and
Polifke
,
W.
,
2019
, “
Intrinsic Thermoacoustic Feedback Loop in Turbulent Spray Flames
,”
Combust. Flame
,
205
(
7
), pp.
22
32
.10.1016/j.combustflame.2019.03.039
17.
Albayrak
,
A.
,
Steinbacher
,
T.
,
Komarek
,
T.
, and
Polifke
,
W.
,
2018
, “
Convective Scaling of Intrinsic Thermo-Acoustic Eigenfrequencies of a Premixed Swirl Combustor
,”
ASME J. Eng. Gas Turbines Power
,
140
(
4
), p.
041510
.10.1115/1.4038083
18.
Hosseini
,
N.
,
Kornilov
,
V.
,
Lopez Arteaga
,
I.
,
Polifke
,
W.
,
Teerling
,
O.
, and
de Goey
,
L.
,
2018
, “
Intrinsic Thermoacoustic Modes and Their Interplay With Acoustic Modes in a Rijke Burner
,”
Int. J. Spray Combust. Dyn.
,
10
(
4
), pp.
315
325
.10.1177/1756827718782884
19.
Mensah
,
G. A.
,
Magri
,
L.
,
Silva
,
C. F.
,
Buschmann
,
P. E.
, and
Moeck
,
J. P.
,
2018
, “
Exceptional Points in the Thermoacoustic Spectrum
,”
J. Sound Vib.
,
433
, pp.
124
128
.10.1016/j.jsv.2018.06.069
20.
Silva
,
C.
,
Yong
,
K. J.
, and
Magri
,
L.
,
2019
, “
Thermoacoustic Modes of Quasi-One-Dimensional Combustors in the Region of Marginal Stability
,”
ASME J. Eng. Gas Turbines Power
,
141
(
2
), p.
021022
.10.1115/1.4041118
21.
Orchini
,
A.
,
Silva
,
C. F.
,
Mensah
,
G. A.
, and
Moeck
,
J. P.
,
2020
, “
Thermoacoustic Modes of Intrinsic and Acoustic Origin and Their Interplay With Exceptional Points
,”
Combust. Flame
,
211
, pp.
83
95
.10.1016/j.combustflame.2019.09.018
22.
Buschmann
,
P. E.
,
Mensah
,
G. A.
,
Nicoud
,
F.
, and
Moeck
,
J. P.
,
2020
, “
Solution of Thermoacoustic Eigenvalue Problems With a Noniterative Method
,”
ASME J. Eng. Gas Turbines Power
,
142
(
3
), p.
031022
.10.1115/1.4045076
23.
Buschmann
,
P. E.
,
Mensah
,
G. A.
, and
Moeck
,
J. P.
,
2020
, “
Intrinsic Thermoacoustic Modes in an Annular Combustion Chamber
,”
Combust. Flame
,
214
, pp.
251
262
.10.1016/j.combustflame.2019.11.006
24.
Fournier
,
G. J. J.
,
Haeringer
,
M.
,
Silva
,
C. F.
, and
Polifke
,
W.
,
2021
, “
Low-Order Modeling to Investigate Clusters of Intrinsic Thermoacoustic Modes in Annular Combustors
,”
ASME J. Eng. Gas Turbines Power
,
143
(
4
), p.
041025
.10.1115/1.4049356
25.
Bethke
,
S.
,
Krebs
,
W.
,
Flohr
,
P.
, and
Prade
,
B.
,
2002
, “
Thermoacoustic Properties of Can Annular Combustors
,”
AIAA
Paper No. 2002-2570.10.2514/6.2002-2570
26.
Kaufmann
,
P.
,
Krebs
,
W.
,
Valdes
,
R.
, and
Wever
,
U.
,
2008
, “
3D Thermoacoustic Properties of Single Can and Multi Can Combustor Configurations
,”
ASME
Paper No. GT2008-50755.10.1115/GT2008-50755
27.
Panek
,
L.
,
Farisco
,
F.
, and
Huth
,
M.
,
2017
, “
Thermo-Acoustic Characterization of Can-Can Interaction of a Can-Annular Combustion System Based on Unsteady CFD LES Simulation
,”
Proceedings of First Global Power and Propulsion Forum
, GPPS, Zurich, Switzerland, Jan. 16–18, Paper No. GPPF-2017-81.https://www.researchgate.net/publication/317400221_THERMOACOUSTIC_CHARACTERIZATION_OF_CAN-CAN_INTERACTION_OF_A_CANANNULAR_COMBUSTION_SYSTEM_BASED_ON_UNSTEADY_CFD_LES_SIMULATION
28.
Farisco
,
F.
,
Panek
,
L.
, and
Kok
,
J. B.
,
2017
, “
Thermo-Acoustic Cross-Talk Between Cans in a Can-Annular Combustor
,”
Int. J. Spray Combust. Dyn.
,
9
(
4
), pp.
452
469
.10.1177/1756827717716373
29.
Ghirardo
,
G.
,
Di Giovine
,
C.
,
Moeck
,
J. P.
, and
Bothien
,
M. R.
,
2019
, “
Thermoacoustics of Can-Annular Combustors
,”
ASME J. Eng. Gas Turbines Power
,
141
(
1
), p.
011007
.10.1115/1.4040743
30.
Jegal
,
H.
,
Moon
,
K.
,
Gu
,
J.
,
Li
,
L. K.
, and
Kim
,
K. T.
,
2019
, “
Mutual Synchronization of Two Lean-Premixed Gas Turbine Combustors: Phase Locking and Amplitude Death
,”
Combust. Flame
,
206
, pp.
424
437
.10.1016/j.combustflame.2019.05.017
31.
Moon
,
K.
,
Jegal
,
H.
,
Gu
,
J.
, and
Kim
,
K. T.
,
2019
, “
Combustion-Acoustic Interactions Through Cross-Talk Area Between Adjacent Model Gas Turbine Combustors
,”
Combust. Flame
,
202
, pp.
405
416
.10.1016/j.combustflame.2019.01.027
32.
Moon
,
K.
,
Jegal
,
H.
,
Yoon
,
C.
, and
Kim
,
K. T.
,
2020
, “
Cross-Talk-Interaction-Induced Combustion Instabilities in a Can-Annular Lean-Premixed Combustor Configuration
,”
Combust. Flame
,
220
, pp.
178
188
.10.1016/j.combustflame.2020.06.041
33.
Haeringer
,
M.
,
Fournier
,
G. J. J.
,
Meindl
,
M.
, and
Polifke
,
W.
,
2021
, “
A Strategy to Tune Acoustic Terminations of Single-Can Test-Rigs to Mimic Thermoacoustic Behavior of a Full Engine
,”
ASME J. Eng. Gas Turbines Power
,
143
(
7
), p. 0
71029
.10.1115/1.4048642
34.
von Saldern
,
J.
,
Orchini
,
A.
, and
Moeck
,
J.
,
2021
, “
Analysis of Thermoacoustic Modes in Can-Annular Combustors Using Effective Bloch-Type Boundary Conditions
,”
ASME J. Eng. Gas Turbines Power
,
143
(
7
), p.
071019
.10.1115/1.4049162
35.
Fournier
,
G. J. J.
,
Meindl
,
M.
,
Silva
,
C. F.
,
Ghirardo
,
G.
,
Bothien
,
M. R.
, and
Polifke
,
W.
,
2021
, “
Low-Order Modeling of Can-Annular Combustors
,”
ASME J. Eng. Gas Turbines Power
,
143
(
12
), p.
121004
.10.1115/1.4051954
36.
von Saldern
,
J. G. R.
,
Orchini
,
A.
, and
Moeck
,
J. P.
,
2021
, “
A Non-Compact Effective Impedance Model for Can-to-Can Acoustic Communication: Analysis and Optimization of Damping Mechanisms
,”
ASME J. Eng. Gas Turbines Power
,
143
(
12
), p.
121024
.10.1115/1.4052077
37.
Orchini
,
A.
,
2022
, “
An Effective Impedance for Modelling the Aeroacoustic Coupling of Ducts Connected Via Apertures
,”
J. Sound Vib.
,
520
, p.
116622
.10.1016/j.jsv.2021.116622
38.
Pedergnana
,
T.
, and
Noiray
,
N.
,
2022
, “
Coupling-Induced Instability in a Ring of Thermoacoustic Oscillators
,”
Proc. R. Soc. A Math., Phys. Eng. Sci.
,
478
(
2259
), p.
20210851
.10.1098/rspa.2021.0851
39.
Orchini
,
A.
,
Pedergnana
,
T.
,
Buschmann
,
P. E.
,
Moeck
,
J. P.
, and
Noiray
,
N.
,
2022
, “
Reduced-Order Modelling of Thermoacoustic Instabilities in Can-Annular Combustors
,”
J. Sound Vib.
,
526
, p.
116808
.10.1016/j.jsv.2022.116808
40.
Tay-Wo-Chong
,
L.
,
Bomberg
,
S.
,
Ulhaq
,
A.
,
Komarek
,
T.
, and
Polifke
,
W.
,
2012
, “
Comparative Validation Study on Identification of Premixed Flame Transfer Function
,”
ASME J. Eng. Gas Turbines Power
,
134
(
2
), p.
021502
.10.1115/1.4004183
41.
Chu
,
B.-T.
,
1953
, “
On the Generation of Pressure Waves at a Plane Flame Front
,”
Symp. (Int.) Combust.
,
4
(
1
), pp.
603
612
.10.1016/S0082-0784(53)80081-0
42.
Crocco
,
L.
,
1951
, “
Aspects of Combustion Stability in Liquid Propellant Rocket Motors Part1: Fundamentals. Low Frequency Instability With Monopropellants
,”
J. Am. Rocket Soc.
,
21
(
6
), pp.
163
178
.10.2514/8.4393
43.
Barenblatt
,
G. I.
,
2003
,
Scaling. Cambridge Texts in Applied Mathematics
,
Cambridge University Press
,
Cambridge, UK
.
44.
Silva
,
C. F.
, and
Polifke
,
W.
,
2019
, “
Non-Dimensional Groups for Similarity Analysis of Thermoacoustic Instabilities
,”
Proc. Combust. Inst.
,
37
(
4
), pp.
5289
5297
.10.1016/j.proci.2018.06.144
45.
Emmert
,
T.
,
Meindl
,
M.
,
Jaensch
,
S.
, and
Polifke
,
W.
,
2016
, “
Linear State Space Interconnect Modeling of Acoustic Systems
,”
Acta Acust. United Acust.
,
102
(
5
), pp.
824
833
.10.3813/AAA.918997
46.
Mensah
,
G. A.
,
2019
, “
Efficient Computation of Thermoacoustic Modes
,” Ph.D. thesis,
TU Berlin, Fak. V, Verkehrs- und Maschinensysteme
,
Berlin, Germany
.
47.
Sogaro
,
F. M.
,
Schmid
,
P. J.
, and
Morgans
,
A. S.
,
2019
, “
Thermoacoustic Interplay Between Intrinsic Thermoacoustic and Acoustic Modes: Non-Normality and High Sensitivities
,”
J. Fluid Mech.
,
878
, pp.
190
220
.10.1017/jfm.2019.632
48.
Polifke
,
W.
,
2020
, “
Modeling and Analysis of premixed flame Dynamics by Means of Distributed Time Delays
,”
Prog. Energy Combust. Sci.
,
79
, p.
100845
.10.1016/j.pecs.2020.100845
49.
Æsøy
,
E.
,
Nygård
,
H. T.
,
Worth
,
N. A.
, and
Dawson
,
J. R.
,
2022
, “
Tailoring the Gain and Phase of the Flame Transfer Function Through Targeted Convective-Acoustic Interference
,”
Combust. Flame
,
236
, p.
111813
.10.1016/j.combustflame.2021.111813
50.
Yong
,
K. J.
,
Silva
,
C. F.
,
Fournier
,
G. J. J.
, and
Polifke
,
W.
,
2021
, “
Categorization of Thermoacoustic Modes in an Ideal Resonator With Phasor Diagrams
,”
Combust. Flame, epub.
51.
Mukherjee
,
N. K.
, and
Shrira
,
V.
,
2017
, “
Intrinsic Flame Instabilities in Combustors: Analytic Description of a 1-D Resonator Model
,”
Combust. Flame
,
185
, pp.
188
209
.10.1016/j.combustflame.2017.07.012
52.
Schaefer
,
F.
,
Guo
,
S.
, and
Polifke
,
W.
,
2021
, “
The Impact of Exceptional Points on the Reliability of Thermoacoustic Stability Analysis
,”
ASME J. Eng. Gas Turbines Power
, 143(2), p.
021010
.10.1115/1.4049351
53.
Sogaro
,
F.
,
Schmid
,
P.
, and
Morgans
,
A. S.
,
2017
, “
Sensitivity Analysis of Thermoacoustic Instabilities
,”
24th International Congress on Sound and Vibration (ICSV 24), IIAV
, London, UK, July 23–27.
54.
Marble
,
F. E.
, and
Candel
,
S. M.
,
1977
, “
Acoustic Disturbance From Gas Non-Uniformities Convected Through a Nozzle
,”
J. Sound Vib.
,
55
(
2
), pp.
225
243
.10.1016/0022-460X(77)90596-X
55.
Bauerheim
,
M.
,
Duran
,
I.
,
Livebardon
,
T.
,
Wang
,
G.
,
Moreau
,
S.
, and
Poinsot
,
T.
,
2016
, “
Transmission and Reflection of Acoustic and Entropy Waves Through a Stator–Rotor Stage
,”
J. Sound Vib.
,
374
, pp.
260
278
.10.1016/j.jsv.2016.03.041
56.
Morgans
,
A. S.
, and
Duran
,
I.
,
2016
, “
Entropy Noise: A Review of Theory, Progress and Challenges
,”
Int. J. Spray Combust. Dyn.
,
8
(
4
), pp.
285
298
.10.1177/1756827716651791
57.
Bloch
,
F.
,
1929
, “
Über Die Quantenmechanik Der Elektronen in Kristallgittern
,”
Z. Phys.
,
52
(
7–8
), pp.
555
600
.10.1007/BF01339455
58.
Mensah
,
G. A.
,
Campa
,
G.
, and
Moeck
,
J. P.
,
2016
, “
Efficient Computation of Thermoacoustic Modes in Industrial Annular Combustion Chambers Based on Bloch-Wave Theory
,”
ASME J. Eng. Gas Turbines Power
,
138
(
8
), p.
081502
.10.1115/1.4032335
59.
Ghirardo
,
G.
,
Moeck
,
J. P.
, and
Bothien
,
M. R.
,
2020
, “
Effect of Noise and Nonlinearities on Thermoacoustics of Can-Annular Combustors
,”
ASME J. Eng. Gas Turbines Power
,
142
(
4
), p.
041005
.10.1115/1.4044487
60.
Bauerheim
,
M.
,
Parmentier
,
J.-F.
,
Salas
,
P.
,
Nicoud
,
F.
, and
Poinsot
,
T.
,
2014
, “
An Analytical Model for Azimuthal Thermoacoustic Modes in an Annular Chamber Fed by an Annular Plenum
,”
Combust. Flame
,
161
(
5
), pp.
1374
1389
.10.1016/j.combustflame.2013.11.014
61.
Bauerheim
,
M.
,
Salas
,
P.
,
Nicoud
,
F.
, and
Poinsot
,
T.
,
2014
, “
Symmetry Breaking of Azimuthal Thermo-Acoustic Modes in Annular Cavities: A Theoretical Study
,”
J. Fluid Mech.
,
760
, pp.
431
465
.10.1017/jfm.2014.578
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