The present article reports a numerical analysis of instability coupled by a spinning mode in an annular combustor. This corresponds to experiments carried out on the MICCA test facility equipped with 16 matrix burners. Each burner response is represented by means of a global experimental flame describing function (FDF). A harmonic balance nonlinear stability analysis is carried out by combining the FDF with a Helmholtz solver to determine the system dynamics trajectories in a frequency-growth rate plane. The influence of the distribution of the volumetric heat release corresponding to each burner is investigated in a first stage. Even though each of the 16 burners is compact with respect to the transverse mode wavelength, and the 16 flames occupy the same volume, this distribution of heat release is not compact in the azimuthal direction and simulations reveal an influence of this volumetric distribution on frequencies and growth rates. This study emphasizes the importance of providing a suitable description of the flame zone geometrical extension and correspondingly an adequate representation of the level of heat release rate fluctuation per unit volume. It is found that these two items can be deduced from a knowledge of the heat release distribution under steady-state operating conditions. Once the distribution of the heat release fluctuations is unequivocally defined, limit cycle simulations are performed. For the conditions explored, simulations retrieve the spinning nature of the self-sustained mode that was identified in the experiments both in the plenum and in the combustion chamber.

References

References
1.
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
.
2.
Candel
,
S. M.
,
1992
, “
Combustion Instabilities Coupled by Pressure Waves and Their Active Control
,”
Symp. Combust.
,
24
(
1
), pp.
1277
1296
.
3.
Bourgouin
,
J. F.
,
Durox
,
D.
,
Moeck
,
J. P.
,
Schuller
,
T.
, and
Candel
,
S.
,
2015
, “
A New Pattern of Instability Observed in an Annular Combustor: The Slanted Mode
,”
Proc. Combust. Inst.
,
35
(
3
), pp.
3237
3244
.
4.
Prieur
,
K.
,
Durox
,
D.
,
Schuller
,
T.
, and
Candel
,
S.
, “
A Hysteresis Phenomenon Leading to Spinning or Standing Azimuthal Instabilities in an Annular Combustor
,”
Combust. Flame
in press.http://dx.doi.org/10.1016/j.combustflame.2016.05.021
5.
Durox
,
D.
,
Bourgouin
,
J.
,
Moeck
,
J.
,
Philip
,
M.
,
Schuller
,
T.
, and
Candel
,
S.
,
2013
, “
Nonlinear Interactions in Combustion Instabilities Coupled by Azimuthal Acoustic Modes
,”
International Workshop on Non-Normal and Nonlinear Effects in Aero-and Thermo-Acoustics
, Munich, Germany, June 18–21, pp.
18
21
.https://mediatum.ub.tum.de/doc/1253524/1253524.pdf
6.
Bourgouin
,
J.-F.
,
Durox
,
D.
,
Moeck
,
J. P.
,
Schuller
,
T.
, and
Candel
,
S.
,
2014
, “
Characterization and Modeling of a Spinning Thermoacoustic Instability in an Annular Combustor Equipped With Multiple Matrix Injectors
,”
ASME J. Eng. Gas Turbines Power
,
137
(
2
), p.
21503
.
7.
Worth
,
N. A.
, and
Dawson
,
J. R.
,
2013
, “
Self-Excited Circumferential Instabilities in a Model Annular Gas Turbine Combustor: Global Flame Dynamics
,”
Proc. Combust. Inst.
,
34
(
2
), pp.
3127
3134
.
8.
Worth
,
N. A.
, and
Dawson
,
J. R.
,
2013
, “
Modal Dynamics of Self-Excited Azimuthal Instabilities in an Annular Combustion Chamber
,”
Combust. Flame
,
160
(
11
), pp.
2476
2489
.
9.
Krebs
,
W.
,
Flohr
,
P.
,
Prade
,
B.
, and
Hoffmann
,
S.
,
2002
, “
Thermoacoustic Stability Chart for High-Intensity Gas Turbine Combustion Systems
,”
Combust. Sci. Technol.
,
174
(
7
), pp.
99
128
.
10.
Bothien
,
M. R.
,
Noiray
,
N.
, and
Schuermans
,
B.
,
2015
, “
Analysis of Azimuthal Thermo-Acoustic Modes in Annular Gas Turbine Combustion Chambers
,”
ASME J. Eng. Gas Turbines Power
,
137
(
6
), p.
61505
.
11.
Mastrovito
,
M.
,
Camporeale
,
S.
,
Forte
,
A.
, and
Fortunato
,
B.
,
2005
, “
Analysis of Pressure Oscillations Data in Gas Turbine Annular Combustion Chamber Equipped With Passive Damper
,”
ASME
Paper No. GT2005-69056.
12.
Schuermans
,
B.
,
Paschereit
,
C.
, and
Monkewitz
,
P.
,
2006
, “
Non-Linear Combustion Instabilities in Annular Gas-Turbine Combustors
,”
AIAA
Paper No. 2006-549.
13.
Noiray
,
N.
,
Bothien
,
M.
, and
Schuermans
,
B.
,
2011
, “
Investigation of Azimuthal Staging Concepts in Annular Gas Turbines
,”
Combust. Theory Model.
,
15
(
5
), pp.
585
606
.
14.
Ghirardo
,
G.
, and
Juniper
,
M. P.
,
2013
, “
Azimuthal Instabilities in Annular Combustors: Standing and Spinning Modes
,”
Proc. R. Soc. A
,
469
(
2157
), p.
20130232
.
15.
Noiray
,
N.
, and
Schuermans
,
B.
,
2013
, “
On the Dynamic Nature of Azimuthal Thermoacoustic Modes in Annular Gas Turbine Combustion Chambers
,”
Proc. R. Soc. A
,
469
(
2151
), p.
20120535
.
16.
Ghirardo
,
G.
,
Ćosić
,
B.
,
Juniper
,
M. P.
, and
Moeck
,
J. P.
,
2015
, “
State-Space Realization of a Describing Function
,”
Nonlinear Dyn.
,
82
(
1
), pp.
9
28
.
17.
Ghirardo
,
G.
,
Juniper
,
M. P.
, and
Moeck
,
J. P.
,
2015
, “
Stability Criteria for Standing and Spinning Waves in Annular Combustors
,”
ASME
Paper No. GT2015-43127.
18.
Selle
,
L.
,
Lartigue
,
G.
,
Poinsot
,
T.
,
Koch
,
R.
,
Schildmacher
,
K. U.
,
Krebs
,
W.
,
Prade
,
B.
,
Kaufmann
,
P.
, and
Veynante
,
D.
,
2004
, “
Compressible Large Eddy Simulation of Turbulent Combustion in Complex Geometry on Unstructured Meshes
,”
Combust. Flame
,
137
(
4
), pp.
489
505
.
19.
Wolf
,
P.
,
Balakrishnan
,
R.
,
Staffelbach
,
G.
,
Gicquel
,
L. Y. M.
, and
Poinsot
,
T.
,
2012
, “
Using LES to Study Reacting Flows and Instabilities in Annular Combustion Chambers
,”
Flow, Turbul. Combust.
,
88
(
1
), pp.
191
206
.
20.
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
.
21.
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
.
22.
Pankiewitz
,
C.
, and
Sattelmayer
,
T.
,
2003
, “
Time Domain Simulation of Combustion Instabilities in Annular Combustors
,”
ASME J. Eng. Gas Turbines Power
,
125
(
3
), pp.
677
685
.
23.
Stow
,
S. R.
, and
Dowling
,
A. P.
,
2009
, “
A Time-Domain Network Model for Nonlinear Thermoacoustic Oscillations
,”
ASME J. Eng. Gas Turbines Power
,
131
(
3
), p.
031502
.
24.
Morgans
,
A. S.
, and
Stow
,
S. R.
,
2007
, “
Model-Based Control of Combustion Instabilities in Annular Combustors
,”
Combust. Flame
,
150
(
4
), pp.
380
399
.
25.
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
.
26.
Campa
,
G.
, and
Camporeale
,
S. M.
,
2014
, “
Prediction of the Thermoacoustic Combustion Instabilities in Practical Annular Combustors
,”
ASME J. Eng. Gas Turbines Power
,
136
(
9
), p.
91504
.
27.
Silva
,
C. F.
,
Nicoud
,
F.
,
Schuller
,
T.
,
Durox
,
D.
, and
Candel
,
S.
,
2013
, “
Combining a Helmholtz Solver With the Flame Describing Function to Assess Combustion Instability in a Premixed Swirled Combustor
,”
Combust. Flame
,
160
(
9
), pp.
1743
1754
.
28.
Camporeale
,
S. M.
,
Fortunato
,
B.
, and
Campa
,
G.
,
2010
, “
A Finite Element Method for Three-Dimensional Analysis of Thermo-Acoustic Combustion Instability
,”
ASME J. Eng. Gas Turbines Power
,
133
(
1
), p.
11506
.
29.
Bourgouin
,
J.-F.
,
Durox
,
D.
,
Moeck
,
J. P.
,
Schuller
,
T.
, and
Candel
,
S.
,
2013
, “
Self-Sustained Instabilities in an Annular Combustor Coupled by Azimuthal and Longitudinal Acoustic Modes
,”
ASME
Paper No. GT2013-95010.
30.
Durox
,
D.
,
Prieur
,
K.
,
Schuller
,
T.
, and
Candel
,
S.
,
2015
, “
Different Flame Patterns Linked With Swirling Injector Interactions in an Annular Combustor
,”
ASME
Paper No. GT2015-42034.
31.
Pierce
,
A. D.
,
1991
,
Acoustics: An Introduction to Its Physical Principles and Applications
,
Acoustical Society of America
,
Melville, NY
.
32.
Munjal
,
M. L.
,
1987
,
Acoustics of Ducts and Mufflers With Application to Exhaust and Ventilation System Design
,
Wiley
,
New York
.
33.
Noiray
,
N.
,
Durox
,
D.
,
Schuller
,
T.
, and
Candel
,
S.
,
2008
, “
A Unified Framework for Nonlinear Combustion Instability Analysis Based on the Flame Describing Function
,”
J. Fluid Mech.
,
615
, pp.
139
167
.
34.
Boudy
,
F.
,
Durox
,
D.
,
Schuller
,
T.
,
Jomaas
,
G.
, and
Candel
,
S.
,
2011
, “
Describing Function Analysis of Limit Cycles in a Multiple Flame Combustor
,”
ASME J. Eng. Gas Turbines Power
,
133
(
6
), p.
061502
.
35.
Palies
,
P.
,
Durox
,
D.
,
Schuller
,
T.
, and
Candel
,
S.
,
2010
, “
The Combined Dynamics of Swirler and Turbulent Premixed Swirling Flames
,”
Combust. Flame
,
157
(
9
), pp.
1698
1717
.
36.
Palies
,
P.
,
Durox
,
D.
,
Schuller
,
T.
, and
Candel
,
S.
,
2011
, “
Experimental Study on the Effect of Swirler Geometry and Swirl Number on Flame Describing Functions
,”
Combust. Sci. Technol.
,
183
(
7
), pp.
704
717
.
37.
Schuller
,
T.
,
Durox
,
D.
, and
Candel
,
S.
,
2003
, “
A Unified Model for the Prediction of Laminar Flame Transfer Functions
,”
Combust. Flame
,
134
(
1–2
), pp.
21
34
.
38.
Sensiau
,
C.
,
Nicoud
,
F.
, and
Poinsot
,
T.
,
2008
, “
Thermoacoustic Analysis of an Helicopter Combustion Chamber
,”
AIAA
Paper No. AIAA-2008-2947.http://arc.aiaa.org/doi/pdf/10.2514/6.2008-2947
39.
Cuquel
,
A.
,
Silva
,
C.
,
Nicoud
,
F.
,
Durox
,
D.
, and
Schuller
,
T.
,
2013
, “
Prediction of the Nonlinear Dynamics of a Multiple Flame Combustor by Coupling the Describing Function Methodology With a Helmholtz Solver
,”
ASME
Paper No. GT2013-95659.
40.
Comsol
,
A.
,
2005
, COMSOL Multiphysics User's Guide, The Comsol Group, Stockholm, Sweden.
41.
Lehoucq
,
R. B.
,
Sorensen
,
D. C.
, and
Yang
,
C.
,
1998
,
ARPACK Users’ Guide: Solution of Large-Scale Eigenvalue Problems With Implicitly Restarted Arnoldi Methods
, Vol.
6
.,
SIAM
,
Philadelphia, PA
.
42.
Kinsler
,
L. E.
,
Frey
,
A. R.
,
Coppens
,
A. B.
, and
Sanders
,
J. V.
,
1999
, “
Fundamentals of Acoustics
,”
Fundamentals of Acoustics
,
4th ed.
,
Lawrence E.
Kinsler
,
A. R.
Frey
,
A. B.
Coppens
, and
J. V.
Sanders
, eds.,
Wiley-VCH
,
Weinheim, Germany
, p.
560
.
43.
Palies
,
P.
,
Durox
,
D.
,
Schuller
,
T.
, and
Candel
,
S.
,
2011
, “
Nonlinear Combustion Instability Analysis Based on the Flame Describing Function Applied to Turbulent Premixed Swirling Flames
,”
Combust. Flame
,
158
(
10
), pp.
1980
1991
.
44.
Vagelopoulos
,
C. M.
,
Egolfopoulos
,
F. N.
, and
Law
,
C. K.
,
1994
, “
Further Considerations on the Determination of Laminar Flame Speeds With the Counterflow Twin-Flame Technique
,”
Symp. Combust.
,
25
(
1
), pp.
1341
1347
.
45.
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
.
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