Abstract
The intrinsic thermoacoustic (ITA) feedbackloop constitutes a coupling between flow, flame and acoustics that does not involve the natural acoustic modes of the system. One recent study showed that ITA modes in annular combustors come in significant number and with the peculiar behavior of clusters, i.e. several modes with close frequencies. In the present work, an analytical model of a typical annular combustor is derived via Riemann invariants and Bloch theory. The resulting formulation describes the full annular system as a longitudinal combustor with an outlet reflection coefficient that depends on frequency and the azimuthal mode order. The model explains the underlying mechanism of the clustering phenomena and the structure of the clusters associated with ITA modes of different azimuthal orders. In addition, a phasor analysis is proposed, which encloses the conditions for which the 1D model remains valid when describing the thermoacoustic behavior of an annular combustor.
Issue Section:
Research Papers
References
1.
Lieuwen
,
T.
, and
McManus
,
K.
, 2003
, “
Introduction: Combustion Dynamics in Lean-Premixed Prevaporized (LPP) Gas Turbines
,” J. Propul. Power
,
19
(5
), pp. 721
–721
.10.2514/2.61712.
Poinsot
,
T.
, 2017
, “
Prediction and Control of Combustion Instabilities in Real Engines
,” Proc. Combust. Inst.
,
36
(1
), pp. 1
–28
.10.1016/j.proci.2016.05.0073.
Lieuwen
,
T.
, and
Yang
,
V.
, eds., 2005
, Combustion Instabilities in Gas Turbine Engines: Operational Experience, Fundamental Mechanisms and Modeling
, Progress in Astronautics and Aeronautics. American Institute of Aeronautics and Astronautics, Reston, VA, No. v. 210.10.2514/5.9781600866807.0000.00004.
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.2014.07.0325.
Gentemann
,
A.
, and
Polifke
,
W.
, 2007
, “
Scattering and Generation of Acoustic Energy by a Premix Swirl Burner
,” ASME
Paper No. GT2007-27238.10.1115/GT2007-272386.
Polifke
,
W.
, 2011
, “
Thermo-Acoustic Instability Potentiality of a Premix Burner
,” European Combustion Meeting, ECM2011
,
British Section of the Combustion Institute
, Cardiff, UK, June 27–July 1.https://www.researchgate.net/publication/255738407_Thermo-acoustic_instability_potentiality_of_a_premix_burners7.
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.2014.06.0088.
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-stability9.
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.2014.05.00910.
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.2015.06.00311.
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.2015.07.00212.
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.2016.08.00213.
Lieuwen
,
T. C.
, 2012
, Unsteady Combustor Physics
,
Cambridge University Press
,
New York
.14.
Dowling
,
A. P.
, and
Stow
,
S. R.
, 2003
, “
Acoustic Analysis of Gas Turbine Combustors
,” J. Propul. Power
,
19
(5
), pp. 751
–764
.10.2514/2.619215.
Mukherjee
,
N.
, 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.2017.07.01216.
Eckstein
,
J.
, and
Sattelmayer
,
T.
, 2006
, “
Low-Order Modeling of Low-Frequency Combustion Instabilities in Aeroengines
,” J. Propul. Power
,
22
(2
), pp. 425
–432
.10.2514/1.1575717.
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.2019.03.03918.
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
.10.1115/1.403808319.
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
.10.1177/175682771878288420.
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.2019.63221.
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
.10.1115/1.404111822.
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.2019.09.01823.
Buschmann
,
P. E.
,
Mensah
,
G. A.
,
Nicoud
,
F.
, and
Moeck
,
J. P.
, 2019
, “
Solution of Thermoacoustic Eigenvalue Problems With a Non-Iterative Method
,” ASME
Paper No. GT2019-90834.10.1115/GT2019-9083424.
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.2019.11.00625.
Staffelbach
,
G.
,
Gicquel
,
L. Y. M.
,
Boudier
,
G.
, and
Poinsot
,
T.
, 2009
, “
Large Eddy Simulation of Self Excited Azimuthal Modes in Annular Combustors
,” Proc. Combust. Inst.
,
32
(2
), pp. 2909
–2916
.10.1016/j.proci.2008.05.03326.
Wolf
,
P.
,
Staffelbach
,
G.
,
Gicquel
,
L. Y. M.
,
Müller
,
J.-D.
, and
Poinsot
,
T.
, 2012
, “
Acoustic and Large Eddy Simulation Studies of Azimuthal Modes in Annular Combustion Chambers
,” Combust. Flame
,
159
(11
), pp. 3398
–3413
.10.1016/j.combustflame.2012.06.01627.
Avdonin
,
A.
,
Meindl
,
M.
, and
Polifke
,
W.
, 2019
, “
Thermoacoustic Analysis of a Laminar Premixed Flame Using a Linearized Reacting Flow Solver
,” Proc. Combust. Inst.
,
37
(4
), pp. 5307
–5314
.10.1016/j.proci.2018.06.14228.
Gikadi
,
J.
, 2013
, “
Prediction of Acoustic Modes in Combustors Using Linearized Navier-Stokes Equations in Frequency Space
,” Ph.D. thesis
,
Technische Universität München
,
Garching, Germany
.https://mediatum.ub.tum.de/doc/1166369/1166369.pdf29.
Schulze
,
M.
,
Hummel
,
T.
,
Klarmann
,
N.
,
Berger
,
F. M.
,
Schuermans
,
B.
, and
Sattelmayer
,
T.
, 2017
, “
Linearized Euler Equations for the Prediction of Linear High-Frequency Stability in Gas Turbine Combustors
,” ASME J. Eng. Gas Turbines Power
,
139
(3
), p. 031510
.10.1115/1.403445330.
Nicoud
,
F.
,
Benoit
,
L.
,
Sensiau
,
C.
, and
Poinsot
,
T.
, 2007
, “
Acoustic Modes in Combustors With Complex Impedances and Multidimensional Active Flames
,” AIAA J.
,
45
(2
), pp. 426
–441
.10.2514/1.2493331.
Krüger
,
U.
,
Hüren
,
J.
,
Hoffmann
,
S.
,
Krebs
,
W.
, and
Bohn
,
D.
, 1999
, “
Prediction of Thermoacoustic Instabilities With Focus on the Dynamic Flame Behavior for the 3A-Series Gas Turbine of Siemens KWU
,” ASME
Paper No. 99-GT-111.10.1115/99-GT-11132.
Evesque
,
S.
, and
Polifke
,
W.
, 2002
, “
Low-Order Acoustic Modelling for Annular Combustors: Validation and Inclusion of Modal Coupling
,” ASME
Paper No. GT-2002-30064.10.1115/GT-2002-3006433.
Parmentier
,
J.-F.
,
Salas
,
P.
,
Wolf
,
P.
,
Staffelbach
,
G.
,
Nicoud
,
F.
, and
Poinsot
,
T.
, 2012
, “
A Simple Analytical Model to Study and Control Azimuthal Instabilities in Annular Combustion Chambers
,” Combust. Flame
,
159
(7
), pp. 2374
–2387
.10.1016/j.combustflame.2012.02.00734.
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.2013.11.01435.
Yang
,
D.
,
Laera
,
D.
, and
Morgans
,
A. S.
, 2019
, “
A Systematic Study of Nonlinear Coupling of Thermoacoustic Modes in Annular Combustors
,” J. Sound Vib.
,
456
, pp. 137
–161
.10.1016/j.jsv.2019.04.02536.
Bloch
,
F.
, 1929
, “
Über Die Quantenmechanik Der Elektronen in Kristallgittern
,” Z. Für Phys.
,
52
(7–8
), pp. 555
–600
.10.1007/BF0133945537.
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
.10.1115/1.403233538.
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
.10.1115/1.404074339.
Haeringer
,
M.
, and
Polifke
,
W.
, 2019
, “
Time Domain Bloch Boundary Conditions for Efficient Simulation of Thermoacoustic Limit-Cycles in (Can-)Annular Combustors
,” ASME J. Eng. Gas Turbines Power
,
141
(12
), p. 121005
.10.1115/1.404486940.
Poinsot
,
T.
, and
Veynante
,
D.
, 2012
, Theoretical and Numerical Combustion
, 3rd ed.,
CNRS
,
Paris
.41.
Schuller
,
T.
,
Durox
,
D.
,
Palies
,
P.
, and
Candel
,
S.
, 2012
, “
Acoustic Decoupling of Longitudinal Modes in Generic Combustion Systems
,” Combust. Flame
,
159
(5
), pp. 1921
–1931
.10.1016/j.combustflame.2012.01.01042.
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-X43.
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.2016.03.04144.
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
.10.1177/175682771665179145.
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)80081-046.
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
.10.2514/8.439347.
Bauerheim
,
M.
,
Cazalens
,
M.
, and
Poinsot
,
T.
, 2015
, “
A Theoretical Study of Mean Azimuthal Flow and Asymmetry Effects on Thermo-Acoustic Modes in Annular Combustors
,” Proc. Combust. Inst.
,
35
(3
), pp. 3219
–3227
.10.1016/j.proci.2014.05.05348.
Haeringer
,
M.
,
Fournier
,
G. J. J.
,
Meindl
,
M.
, and
Polifke
,
W.
, 2020
, “
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
, ePub.10.1115/1.404864249.
Emmert
,
T.
, 2016
, “
State Space Modeling of Thermoacoustic Systems With Application to Intrinsic Feedback
,” Ph.D. thesis
,
TU München
,
München, Germany
.https://mediatum.ub.tum.de/doc/1306410/1306410.pdf50.
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.91899751.
Mensah
,
G. A.
, 2019
, “
Efficient Computation of Thermoacoustic Modes
,” Ph.D. thesis
,
Technische Universität Berlin
.https://depositonce.tu-berlin.de/bitstream/11303/9942/4/mensah_georg.pdfCopyright © 2021 by ASME
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