Abstract

Resolvent analysis is applied to a nonreacting and a reacting swirled jet flow. Time-averaged flows as input for the resolvent analysis and validation for the results of the resolvent analysis are obtained by experiments. We show that in the nonreacting (cold) flow case, the resolvent analysis is capable of predicting the hydrodynamic response to upstream harmonic acoustic forcing if the flow shows low-rank behavior. This is the case for low and moderate acoustic forcing amplitudes. Even for very strong acoustic velocity amplitudes that are of the same order of magnitude as the flow velocity, the resolvent analysis still provides reasonable results. The method also yields very good results for the reacting flow in terms of velocity fluctuation and heat release response to the acoustic forcing. This confirms the idea that the resolvent method could be applied to estimate the flame transfer function (FTF) based on the mean flow and flame.

References

1.
Poinsot
,
T. J.
,
Trouve
,
A. C.
,
Veynante
,
D. P.
,
Candel
,
S. M.
, and
Esposito
,
E. J.
,
1987
, “
Vortex-Driven Acoustically Coupled Combustion Instabilities
,”
J. Fluid Mech.
,
177
, pp.
265
292
.10.1017/S0022112087000958
2.
Stöhr
,
M.
,
Boxx
,
I.
,
Carter
,
C. D.
, and
Meier
,
W.
,
2012
, “
Experimental Study of Vortex-Flame Interaction in a Gas Turbine Model Combustor
,”
Combust. Flame
,
159
(
8
), pp.
2636
2649
.10.1016/j.combustflame.2012.03.020
3.
Docquier
,
N.
, and
Candel
,
S.
,
2002
, “
Combustion Control and Sensors: A Review
,”
Prog. Energy Combust. Sci.
,
28
(
2
), pp.
107
150
.10.1016/S0360-1285(01)00009-0
4.
Barkley
,
D.
,
2006
, “
Linear Analysis of the Cylinder Wake Mean Flow
,”
Europhys. Lett.
,
75
(
5
), p.
750
.10.1209/epl/i2006-10168-7
5.
Terhaar
,
S.
,
Oberleithner
,
K.
, and
Paschereit
,
C. O.
,
2015
, “
ScienceDirect Key Parameters Governing the Precessing Vortex Core in Reacting Flows: An Experimental and Analytical Study
,”
Proc. Combust. Inst.
,
35
(
3
), pp.
3347
3354
.10.1016/j.proci.2014.07.035
6.
Tammisola
,
O.
, and
Juniper
,
M. P.
,
2015
, “
Adjoint Sensitivity Analysis of Hydrodynamic Stability in a Gas Turbine Fuel Injector
,”
ASME
Paper No. GT2015-42736.
10.1115/GT2015-42736
7.
Kaiser
,
T. L.
,
Poinsot
,
T.
, and
Oberleithner
,
K.
,
2018
, “
Stability and Sensitivity Analysis of Hydrodynamic Instabilities in Industrial Swirled Injection Systems
,”
ASME J. Eng. Gas Turbines Power
,
140
(
5
), pp.
51506
51510
.10.1115/1.4038283
8.
Tissot
,
G.
,
Lajús
,
F. C.
, Jr
,
Cavalieri
,
A. V.
, and
Jordan
,
P.
,
2017
, “
Wave Packets and Orr Mechanism in Turbulent Jets
,”
Phys. Rev. Fluids
,
2
(
9
), p.
093901
.10.1103/PhysRevFluids.2.093901
9.
Palies
,
P.
,
Durox
,
D.
,
Schuller
,
T.
, and
Candel
,
S.
,
2011
, “
AcousticPConvective Mode Conversion in an Aerofoil Cascade
,”
J. Fluid Mech.
,
672
, pp.
545
569
.10.1017/S0022112010006142
10.
Schuller
,
T.
,
Cuquel
,
A.
,
Palies
,
P.
,
Moeck
,
J.
,
Durox
,
D.
, and
Candel
,
S.
,
2012
, “
Modeling the Response of Premixed Flame Transfer Functions—Key Elements and Experimental Proofs
,”
AIAA
Paper No. 2012-985.
10.2514/6.2012-985
11.
Trefethen
,
L. N.
,
Trefethen
,
A. E.
,
Reddy
,
S. C.
, and
Driscoll
,
T. A.
,
1993
, “
Hydrodynamic Stability Without Eigenvalues
,”
Science
,
261
(
5121
), pp.
578
584
.10.1126/science.261.5121.578
12.
Beneddine
,
S.
,
Sipp
,
D.
,
Arnault
,
A.
,
Dandois
,
J.
, and
Lesshafft
,
L.
,
2016
, “
Conditions for Validity of Mean Flow Stability Analysis
,”
J. Fluid Mech.
,
798
, pp.
485
504
.10.1017/jfm.2016.331
13.
McKeon
,
B.
, and
Sharma
,
A.
,
2010
, “
A Critical-Layer Framework for Turbulent Pipe Flow
,”
J. Fluid Mech.
,
658
, pp.
336
382
.10.1017/S002211201000176X
14.
Yi
,
T.
, and
Santavicca
,
D. A.
,
2009
, “
Forced Flame Response of Turbulent Liquid-Fueled Lean-Direct-Injection Combustion to Fuel Modulations
,”
J. Propul. Power
,
25
(
6
), pp.
1259
1271
.10.2514/1.42379
15.
Gentemann
,
A.
,
Hirsch
,
C.
,
Kunze
,
K.
,
Kiesewetter
,
F.
,
Sattelmayer
,
T.
, and
Polifke
,
W.
,
2004
, “
Validation of Flame Transfer Function Reconstruction for Perfectly Premixed Swirl Flames
,”
ASME
Paper No. GT2004-53776
. 10.1115/GT2004-53776
16.
Kaiser
,
T.
,
ztarlik
,
G.
,
Selle
,
L.
, and
Poinsot
,
T.
,
2018
, “
Impact of Symmetry Breaking on the Flame Transfer Function of a Laminar Premixed Flame
,”
Proc. Combust. Inst.
,
37
(
2
), pp.
1953
1960
.10.1016/j.proci.2018.06.047
17.
Fleifil
,
M.
,
Annaswamy
,
A. M.
,
Ghoneim
,
Z.
, and
Ghoniem
,
A. F.
,
1996
, “
Response of a Laminar Premixed Flame to Flow Oscillations: A Kinematic Model and Thermoacoustic Instability Results
,”
Combust. Flame
,
106
(
4
), pp.
487
510
.10.1016/0010-2180(96)00049-1
18.
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
.10.1016/S0010-2180(03)00042-7
19.
Schmidt
,
O.
,
Towne
,
A.
,
Rigas
,
G.
,
Colonius
,
T.
, and
Brès
,
G.
,
2018
, “
Spectral Analysis of Jet Turbulence
,”
J. Fluid Mech.
,
855
, pp.
953
982
.10.1017/jfm.2018.675
20.
Lesshafft
,
L.
,
Semeraro
,
O.
,
Jaunet
,
V.
,
Cavalieri
,
A. V. G.
, and
Jordan
,
P.
,
2018
, “
Resolvent-Based Modelling of Coherent Wavepackets in a Turbulent Jet
,” preprint arXiv: 1810.09340.
21.
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
.10.1016/j.combustflame.2013.03.020
22.
Schuermans
,
B.
,
Bellucci
,
V.
, and
Paschereit
,
C. O.
,
2003
, “
Thermoacoustic Modeling and Control of Multi Burner Combustion Systems
,”
ASME
Paper No. GT2003-38688.
10.1115/GT2003-38688
23.
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
24.
Oberleithner
,
K.
, and
Paschereit
,
C. O.
,
2016
, “
Modeling Flame Describing Functions Based on Hydrodynamic Linear Stability Analysis
,”
ASME
Paper No. GT2016-57316
. 10.1115/GT2016-57316
25.
Reichel
,
T. G.
,
Goeckeler
,
K.
, and
Paschereit
,
O.
,
2015
, “
Investigation of Lean Premixed Swirl-Stabilized Hydrogen Burner With Axial Air Injection Using OH-PLIF Imaging
,”
ASME J. Eng. Gas Turbines Power
,
137
(
11
), p.
111510
.10.1115/1.4031181
26.
Willert
,
C. E.
, and
Gharib
,
M.
,
1991
, “
Digital Particle Image Velocimetry
,”
Exp. Fluids
,
10
(
4
), pp.
181
193
.10.1007/BF00190388
27.
Soria
,
J.
,
1996
, “
An Investigation of the Near Wake of a Circular Cylinder Using a Video-Based Digital Cross-Correlation Particle Image Velocimetry Technique
,”
Exp. Therm. Fluid Sci.
,
12
(
2
), pp.
221
233
.10.1016/0894-1777(95)00086-0
28.
Huang
,
H.
,
Fiedler
,
H.
, and
Wang
,
J.
,
1993
, “
Limitation and Improvement of PIV
,”
Exp. Fluids
,
15
(
4–5
), pp.
263
273
.10.1007/BF00189883
29.
Terhaar
,
S.
, and
Paschereit
,
C. O.
,
2012
, “
High-Speed PIV Investigation of Coherent Structures in a Swirl-Stabilized Combustor Operating at Dry and Steam-Diluted Conditions
,”
16th International Symposium on Applications of Laser Techniques to Fluid Mechanics
,
Lisbon, Portugal
,
July 9–12
, pp.
9
12
.
30.
Hussain
,
A. K. M. F.
, and
Reynolds
,
W. C.
,
1970
, “
The Mechanics of an Organized Wave in Turbulent Shear Flow
,”
J. Fluid Mech.
,
41
(
2
), pp.
241
258
.10.1017/S0022112070000605
31.
Manoharan
,
K.
, and
Hemchandra
,
S.
,
2015
, “
Absolute/Convective Instability Transition in a Backward Facing Step Combustor: Fundamental Mechanism and Influence of Density Gradient
,”
ASME J. Eng. Gas Turbines Power
,
137
(
2
), p.
021501
.10.1115/1.4028206
32.
Hussain
,
A.
, and
Reynolds
,
W.
,
1972
, “
The Mechanics of an Organized Wave in Turbulent Shear Flow—Part 2: Experimental Results
,”
J. Fluid Mech.
,
54
(
2
), pp.
241
261
.10.1017/S0022112072000667
33.
Ivanova
,
E. M.
,
Noll
,
B. E.
, and
Aigner
,
M.
,
2013
, “
A Numerical Study on the Turbulent Schmidt Numbers in a Jet in Crossflow
,”
ASME J. Eng. Gas Turbines Power
,
135
(
1
), p.
11505
.10.1115/1.4007374
34.
Pope
,
S. B.
,
2000
,
Turbulent Flows
,
Cambridge University Press
,
Cambridge, UK
.
35.
Poinsot
,
T.
, and
Veynante
,
D.
,
2005
,
Theoretical and Numerical Combustion
, Vol.
3
, R.T. Edwards, Inc.
36.
Sipp
,
D.
,
Marquet
,
O.
,
Meliga
,
P.
, and
Barbagallo
,
A.
,
2010
, “
Dynamics and Control of Global Instabilities in Open-Flows: A Linearized Approach
,”
ASME Appl. Mech. Rev.
,
63
(
3
), p.
030801
.10.1115/1.4001478
37.
Hecht
,
F.
,
2012
, “
New Development in FreeFem
‘++’,”
J. Numer. Math.
,
20
(
3–4
), pp.
251
265
.10.1515/jnum-2012-0013
38.
Garnaud
,
X.
,
Lesshafft
,
L.
,
Schmid
,
P. J.
, and
Huerre
,
P.
,
2013
, “
The Preferred Mode of Incompressible Jets: Linear Frequency Response Analysis
,”
J. Fluid Mech.
,
716
, pp.
189
202
.10.1017/jfm.2012.540
39.
Oberleithner
,
K.
,
Paschereit
,
C. O.
, and
Wygnanski
,
I.
,
2014
, “
On the Impact of Swirl on the Growth of Coherent Structures
,”
J. Fluid Mech.
,
741
, pp.
156
199
.10.1017/jfm.2013.669
40.
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
.10.1016/j.combustflame.2010.02.011
41.
Schimek
,
S.
,
Ćosić
,
B.
,
Moeck
,
J. P.
,
Terhaar
,
S.
, and
Paschereit
,
C. O.
,
2012
, “
Amplitude-Dependent Flow Field and Flame Response to Axial and Tangential Velocity Fluctuations
,”
ASME
Paper No. GT2012-69785
. 10.1115/GT2012-69785
42.
Avdonin
,
A.
,
Meindl
,
M.
,
Polifke
,
W.
, and
in
,
P.
,
2018
, “
Thermoacoustic Analysis of a Laminar Premixed Flame Using a Linearized Reactive Flow Solver
,”
Proc. Combust. Inst.
,
37
(
4
), pp.
5307
5314
.10.1016/j.proci.2018.06.142
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