Schmitt,
P.
,
Poinsot,
T.
,
Schuermans,
B.
, and
Geigle,
K. P.
, 2007, “
Large-Eddy Simulation and Experimental Study of Heat Transfer, Nitric Oxide Emissions and Combustion Instability in a Swirled Turbulent High-Pressure Burner,” J. Fluid Mech.,
570(2), pp. 17–46.

[CrossRef]
Sengissen,
A. X.
,
Van Kampen,
J. F.
,
Huls,
R. A.
,
Stoffels,
G. G. M.
,
Kok,
J. B. W.
, and
Poinsot,
T. J.
, 2007, “
LES and Experimental Studies of Cold and Reacting Flow in a Swirled Partially Premixed Burner With and Without Fuel Modulation,” Combust. Flame,
150(1–2), pp. 40–53.

[CrossRef]
Krediet,
H. J.
,
Portillo,
J.
,
Krebs,
W.
, and
Kok,
J.
, 2010, “
Prediction of Thermoacoustic Limit Cycles During Premixed Combustion Using the Modified Galerkin Approach,” AIAA Paper No. 2010-7150.

Krebs,
W.
,
Krediet,
H.
,
Portillo,
E.
,
Hermeth,
S.
,
Poinsot,
T.
,
Schimek,
S.
, and
Paschereit,
O.
, 2013, “
Comparison of Nonlinear to Linear Thermoacoustic Stability Analysis of a Gas Turbine Combustion System,” ASME J. Eng. Gas Turbines Power,
135(8), p. 081503.

[CrossRef]
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.

[CrossRef]
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.

[CrossRef]
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.

[CrossRef]
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.

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.

[CrossRef]
Dowling,
A. P.
, and
Stow,
S. R.
, 2003, “
Acoustic Analysis of Gas Turbine Combustors,” J. Propul. Power,
19(5), pp. 751–764.

[CrossRef]
Laera,
D.
,
Prieur,
K.
,
Durox,
D.
,
Schuller,
T.
,
Camporeale,
S. M.
, and
Candel,
S.
, 2017, “
Impact of Heat Release Distribution on the Spinning Modes of an Annular Combustor With Multiple Matrix Burners,” ASME J. Eng. Gas Turbines Power,
139(5), p. 051505.

[CrossRef]
Kim,
K. T.
,
Lee,
J. G.
,
Quay,
B. D.
, and
Santavicca,
D. A.
, 2010, “
Spatially Distributed Flame Transfer Functions for Predicting Combustion Dynamics in Lean Premixed Gas Turbine Combustors,” Combust. Flame,
157(9), pp. 1718–1730.

[CrossRef]
Campa,
G.
,
Camporeale,
S. M.
,
Cosatto,
E.
, and
Mori,
G.
, 2012, “
Thermoacoustic Analysis of Combustion Instability Through a Distributed Flame Response Function,” ASME Paper No. GT2012-68243.

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.

[CrossRef]
Hummel,
T.
,
Temmler,
C.
,
Schuermans,
B.
, and
Sattelmayer,
T.
, 2015, “
Reduced-Order Modeling of Aeroacoustic Systems for Stability Analyses of Thermoacoustically Noncompact Gas Turbine Combustors,” ASME J. Eng. Gas Turbines Power,
138(5), p. 051502.

[CrossRef]
Paschereit,
C. O.
,
Schuermans,
B.
,
Polifke,
W.
, and
Mattson,
O.
, 2002, “
Measurement of Transfer Matrices and Source Terms of Premixed Flames,” ASME J. Eng. Gas Turbines Power,
124(2), pp. 239–247.

[CrossRef]
Jang,
S.-H.
, 1998, “
On the Multiple Microphone Method for Measuring In-Duct Acoustic Properties in the Presence of Mean Flow,” J. Acoust. Soc. Am.,
103(3), pp. 1520–1526.

[CrossRef]
Åbom,
M.
, and
Bodén,
H.
, 1988, “
Error Analysis of Two-Microphone Measurements in Ducts With Flow,” J. Acoust. Soc. Am.,
83(6), pp. 2429–2438.

[CrossRef]
Law,
C. K.
, 2006, Combustion Physics,
Cambridge University Press,
Cambridge, UK.

Rofi,
L.
,
Campa,
G.
,
Anisimov,
V.
,
Daccá,
F.
,
Bertolotto,
E.
,
Gottardo,
E.
, and
Bonzani,
F.
, 2015, “
Numerical Procedure for the Investigation of Combustion Dynamics in Industrial Gas Turbines: LES, RANS and Thermoacoustics,” ASME Paper No. GT2015-42168.

Laera,
D.
,
Gentile,
A.
,
Camporeale,
S. M.
,
Bertolotto,
E.
,
Rofi,
L.
, and
Bonzani,
F.
, 2015, “
Numerical and Experimental Investigation of Thermo-Acoustic Combustion Instability in a Longitudinal Combustion Chamber: Influence of the Geometry of the Plenum,” ASME Paper No. GT2015-42322.

Polifke,
W.
,
Paschereit,
C. O.
, and
Döbbeling,
K.
, 2001, “
Constructive and Destructive Interference of Acoustic and Entropy Waves in a Premixed Combustor With a Choked Exit,” J. Acoust. Vib.,
6(3), pp. 135–146.

Campa,
G.
, and
Camporeale,
S. M.
, 2010, “
Influence of Flame and Burner Transfer Matrix on Thermoacoustic Combustion Instability Modes and Frequencies,” ASME Paper No. GT2010-23104.

Campa,
G.
, and
Camporeale,
S.
, 2012, “
Eigenmode Analysis of the Thermoacoustic Combustion Instabilities Using a Hybrid Technique Based on the Finite Element Method and the Transfer Matrix Method,” Adv. Appl. Acoust.,
1(1), pp. 1–14.

Alemela,
P. R.
,
Fanaca,
D.
,
Ettner,
F.
,
Hirsch,
C.
,
Sattelmayer,
T.
, and
Schuermans,
B.
, 2008, “
Flame Transfer Matrices of a Premixed Flame and a Global Check With Modelling and Experiments,” ASME Paper No. GT2008-50111.

Laera,
D.
,
Campa,
G.
,
Camporeale,
S. M.
,
Bertolotto,
E.
,
Rizzo,
S.
,
Bonzani,
F.
,
Ferrante,
A.
, and
Saponaro,
A.
, 2014, “
Modelling of Thermoacoustic Combustion Instabilities Phenomena: Application to an Experimental Test Rig,” Energy Procedia,
45, pp. 1392–1401.

[CrossRef]
Laera,
D.
,
Campa,
G.
,
Camporeale,
S. M.
,
Bertolotto,
E.
,
Rizzo,
S.
,
Bonzani,
F.
, and
Ferrante,
A.
, 2014, “
Modelling of Thermoacoustic Combustion Instabilities Phenomena: Application to an Experimental Rig for Testing Full Scale Burners,” ASME Paper No. GT2014-25273.

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.

[CrossRef]
Hermeth,
S.
,
Staffelbach,
G.
,
Gicquel,
L. Y.
,
Anisimov,
V.
,
Cirigliano,
C.
, and
Poinsot,
T.
, 2014, “
Bistable Swirled Flames and Influence on Flame Transfer Functions,” Combust. Flame,
161(1), pp. 184–196.

[CrossRef]
Poinsot,
T.
, and
Veynante,
D.
, 2005, Theoretical and Numerical Combustion,
T. Poinsot
and
D. Veynante
, eds., R. T. Edwards, Philadelphia, PA.

Dowling,
A.
, 1995, “
The Calculation of Thermoacoustic Oscillations,” J. Sound Vib.,
180(4), pp. 557–581.

[CrossRef]
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.

Nicoud,
F.
, and
Wieczorek,
K.
, 2009, “
About the Zero Mach Number Assumption in the Calculation of Thermoacoustic Instabilities,” Int. J. Spray Combust. Dyn.,
1(1), pp. 67–111.

[CrossRef]
Gikadi,
J.
,
Sattelmayer,
T.
, and
Peschiulli,
A.
, 2012, “
Effects of the Mean Flow Field on the Thermo-Acoustic Stability of Aero-Engine Combustion Chambers,” ASME Paper No. GT2012-69612.

Dowling,
A. P.
, 1997, “
Nonlinear Self-Excited Oscillations of a Ducted Flame,” J. Fluid Mech.,
346, pp. 271–290.

[CrossRef]
Li,
J.
, and
Morgans,
A. S.
, 2015, “
Time Domain Simulations of Nonlinear Thermoacoustic Behaviour in a Simple Combustor Using a Wave-Based Approach,” J. Sound Vib.,
346(1), pp. 345–360.

[CrossRef]
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.

[CrossRef]
Laera,
D.
, 2015, “
Nonlinear Combustion Instabilities Analysis of Azimuthal Mode in Annular Chamber,” Energy Procedia,
82, pp. 921–928.

[CrossRef]
Munjal,
M. L.
, 1987, Acoustics of Ducts and Mufflers With Application to Exhaust and Ventilation System Design,
Wiley, New York.

Goh,
C. S.
, and
Morgans,
A. S.
, 2013, “
The Influence of Entropy Waves on the Thermoacoustic Stability of a Model Combustor,” Combust. Sci. Technol.,
185(2), pp. 249–268.

[CrossRef]
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.

[CrossRef]
Balusamy,
S.
,
Li,
L. K.
,
Han,
Z.
, and
Hochgreb,
S.
, 2016, “
Extracting Flame Describing Functions in the Presence of Self-Excited Thermoacoustic Oscillations,” Proc. Combust. Inst.,
36(3), pp. 3851–3861.

[CrossRef]
Bourgouin,
J.-F. 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.

[CrossRef]
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.

[CrossRef]
Han,
X.
,
Li,
J.
, and
Morgans,
A. S.
, 2015, “
Prediction of Combustion Instability Limit Cycle Oscillations by Combining Flame Describing Function Simulations With a Thermoacoustic Network Model,” Combust. Flame,
162(10), pp. 3632–3647.

[CrossRef]
Laera,
D.
,
Campa,
G.
, and
Camporeale,
S. M.
, 2017, “
A Finite Element Method for a Weakly Nonlinear Dynamic Analysis and Bifurcation Tracking of Thermo-Acoustic Instability in Longitudinal and Annular Combustors,” Appl. Energy,
187, pp. 216–227.

[CrossRef]