Abstract

Thermoacoustic stability analysis is an essential part of the engine development process. Typically, thermoacoustic stability is determined by hybrid approaches. These approaches require information on the flame dynamic response. The combined approach of advanced system identification (SI) and large eddy simulation (LES) is an efficient strategy to compute the flame dynamic response to flow perturbation in terms of the finite impulse response (FIR). The identified FIR is uncertain due in part to the aleatoric uncertainties caused by applying SI on systems with combustion noise and partly due to epistemic uncertainties caused by lack of knowledge of operating or boundary conditions. Carrying out traditional uncertainty quantification techniques, such as Monte Carlo, in the framework of LES/SI would be computationally prohibitive. As a result, the present paper proposes a methodology to build a surrogate model in the presence of both aleatoric and epistemic uncertainties. Specifically, we propose a univariate Gaussian Process (GP) surrogate model, where the final trained GP takes into account the uncertainty of SI and the uncertainty in the combustor back plate temperature, which is known to have a considerable impact on the flame dynamics. The GP model is trained on the FIRs obtained from the LES/SI of turbulent premixed swirled combustor at different combustor back plate temperatures. Due to the change in the combustor back plate temperature the flame topology changes, which in turn influences the FIR. The trained GP model is successful in interpolating the FIR with confidence intervals covering the “true” FIR from LES/SI.

References

1.
Lieuwen
,
T. C.
,
2012
,
Unsteady Combustor Physics
,
Cambridge University Press
,
New York, NY
.
2.
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
.10.2514/1.24933
3.
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
4.
Ducruix
,
S.
,
Durox
,
D.
, and
Candel
,
S.
,
2000
, “
Theoretical and Experimental Determinations of the Transfer Function of a Laminar Premixed Flame
,”
Proc. Combust. Inst.
,
28
(
1
), pp.
765
773
.10.1016/S0082-0784(00)80279-9
5.
Giauque
,
A.
,
Poinsot
,
T.
, and
Nicoud
,
F.
,
2008
, “
Validation of a Flame Transfer Function Reconstruction Method for Complex Turbulent Configurations
,”
AIAA
Paper No. 2008-2943.10.2514/6.2008-2943
6.
Polifke
,
W.
,
2014
, “
Black-Box System Identification for Reduced Order Model Construction
,”
Ann. Nucl. Energy
,
67
, pp.
109
128
.10.1016/j.anucene.2013.10.037
7.
Duchaine
,
F.
,
Boudy
,
F.
,
Durox
,
D.
, and
Poinsot
,
T.
,
2011
, “
Sensitivity Analysis of Transfer Functions of Laminar Flames
,”
Combust. Flame
,
158
(
12
), pp.
2384
2394
.10.1016/j.combustflame.2011.05.013
8.
Mejia
,
D.
,
Miguel-Brebion
,
M.
,
Ghani
,
A.
,
Kaiser
,
T.
,
Duchaine
,
F.
,
Selle
,
L.
, and
Poinsot
,
T.
,
2018
, “
Influence of Flame-Holder Temperature on the Acoustic Flame Transfer Functions of a Laminar Flame
,”
Combust. Flame
,
188
(
2
), pp.
5
12
.10.1016/j.combustflame.2017.09.016
9.
Kedia
,
K.
,
Altay
,
H.
, and
Ghoniem
,
A.
,
2011
, “
Impact of Flame-Wall Interaction on Premixed Flame Dynamics and Transfer Function Characteristics
,”
Proc. Combust. Inst.
,
33
(
1
), pp.
1113
1120
.10.1016/j.proci.2010.06.132
10.
Miguel-Brebion
,
M.
,
Mejia
,
D.
,
Xavier
,
P.
,
Duchaine
,
F.
,
Bedat
,
B.
,
Selle
,
L.
, and
Poinsot
,
T.
,
2016
, “
Joint Experimental and Numerical Study of the Influence of Flame Holder Temperature on the Stabilization of a Laminar Methane Flame on a Cylinder
,”
Combust. Flame
,
172
, pp.
153
161
.10.1016/j.combustflame.2016.06.025
11.
Tay-Wo-Chong
,
L.
, and
Polifke
,
W.
,
2013
, “
Large Eddy Simulation-Based Study of the Influence of Thermal Boundary Condition and Combustor Confinement on Premix Flame Transfer Functions
,”
ASME J. Eng. Gas Turbines Power
,
135
(
2
), p.
021502
.10.1115/1.4007734
12.
Juniper
,
M. P.
, and
Sujith
,
R. I.
,
2018
, “
Sensitivity and Nonlinearity of Thermoacoustic Oscillations
,”
Annu. Rev. Fluid Mech.
,
50
(
1
), pp.
661
689
.10.1146/annurev-fluid-122316-045125
13.
McManus
,
K. R.
,
Poinsot
,
T.
, and
Candel
,
S. M.
,
1993
, “
A Review of Active Control of Combustion Instabilities
,”
Prog. Energy Combust. Sci.
,
19
(
1
), pp.
1
29
.10.1016/0360-1285(93)90020-F
14.
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
15.
Ndiaye
,
A.
,
Bauerheim
,
M.
, and
Nicoud
,
F.
,
2015
, “
Uncertainty Quantification of Thermoacoustic Instabilities on a Swirled Stabilized Combustor
,”
ASME
Paper No. GT2015-44133.10.1115/GT2015-44133
16.
Magri
,
L.
,
Bauerheim
,
M.
,
Nicoud
,
F.
, and
Juniper
,
M. P.
,
2016
, “
Stability Analysis of Thermo-Acoustic Nonlinear Eigenproblems in Annular Combustors. Part II. Uncertainty Quantification
,”
Comput. Phys.
,
325
, pp.
411
421
.10.1016/j.jcp.2016.08.043
17.
Silva
,
C. F.
,
Magri
,
L.
,
Runte
,
T.
, and
Polifke
,
W.
,
2017
, “
Uncertainty Quantification of Growth Rates of Thermoacoustic Instability by an Adjoint Helmholtz Solver
,”
ASME J. Eng. Gas Turbines Power
,
139
(
1
), p.
011901
.10.1115/1.4034203
18.
Avdonin
,
A.
,
Jaensch
,
S.
,
Silva
,
C. F.
,
Češnovar
,
M.
, and
Polifke
,
W.
,
2018
, “
Uncertainty Quantification and Sensitivity Analysis of Thermoacoustic Stability With Non-Intrusive Polynomial Chaos Expansion
,”
Combust. Flame
,
189
, pp.
300
310
.10.1016/j.combustflame.2017.11.001
19.
Guo
,
S.
,
Silva
,
C. F.
,
Ghani
,
A.
, and
Polifke
,
W.
,
2019
, “
Quantification and Propagation of Uncertainties in Identification of Flame Impulse Response for Thermoacoustic Stability Analysis
,”
ASME J. Eng. Gas Turbines Power
,
141
(
2
), p. 021032–10.10.1115/1.4041652
20.
Avdonin
,
A.
, and
Polifke
,
W.
,
2019
, “
Quantification of the Impact of Uncertainties in Operating Conditions on the Flame Transfer Function With Non-Intrusive Polynomial Chaos Expansion
,”
ASME J. Eng. Gas Turbines Power
,
141
(
1
), p.
011020
.10.1115/1.4040745
21.
Guo
,
S.
,
Silva
,
C. F.
, and
Polifke
,
W.
,
2020
, “
Efficient Robust Design for Thermoacoustic Instability Analysis: A Gaussian Process Approach
,”
ASME J. Eng. Gas Turbines Power
,
142
(
3
), p. 031026. 10.1115/1.4044197
22.
Forrester
,
A.
,
Sóbester
,
A.
, and
Keane
,
A.
,
2008
,
Engineering Design Via Surrogate Modelling: A Practical Guide
,
John Wiley & Sons, Ltd.,
UK.
23.
Merk
,
M.
,
Gaudron
,
R.
,
Gatti
,
M.
,
Mirat
,
C.
,
Schuller
,
T.
, and
Polifke
,
W.
,
2018
, “
Measurement and Simulation of Combustion Noise and Dynamics of a Confined Swirl Flame
,”
AIAA J.
,
56
(
5
), pp.
1930
1942
.10.2514/1.J056502
24.
CERFACS, and IMFT
,
2008
, The AVBP HandBook, accessed July 21, 2021, http://www.cerfacs.fr/avbp7x/
25.
Colin
,
O.
,
Ducros
,
F.
,
Veynante
,
D.
, and
Poinsot
,
T.
,
2000
, “
A Thickenend Flame Model for Large Eddy Simulation of Turbulent Premixed Combustion
,”
Phys. Fluids
,
12
(
7
), pp.
1843
1863
.10.1063/1.870436
26.
Poinsot
,
T.
, and
Lele
,
S. K.
,
1992
, “
Boundary Conditions for Direct Simulation of Compressible Viscous Flows
,”
J. Comput. Phys.
,
101
(
1
), pp.
104
129
.10.1016/0021-9991(92)90046-2
27.
Selle
,
L.
,
Nicoud
,
F.
, and
Poinsot
,
T.
,
2004
, “
Actual Impedance of Nonreflecting Boundary Conditions: Implications for Computation of Resonators
,”
AIAA J.
,
42
(
5
), pp.
958
964
.10.2514/1.1883
28.
Polifke
,
W.
,
Wall
,
C.
, and
Moin
,
P.
,
2006
, “
Partially Reflecting and Non-Reflecting Boundary Conditions for Simulation of Compressible Viscous Flow
,”
J. Comput. Phys.
,
213
(
1
), pp.
437
449
.10.1016/j.jcp.2005.08.016
29.
Merk
,
M.
,
Silva
,
C.
,
Polifke
,
W.
,
Gaudron
,
R.
,
Gatti
,
M.
,
Mirat
,
C.
, and
Schuller
,
T.
,
2019
, “
Direct Assessment of the Acoustic Scattering Matrix of a Turbulent Swirl Combustor by Combining System Identification, Large Eddy Simulation and Analytical Approaches
,”
ASME J. Eng. Gas Turbines Power
,
141
(
2
), pp.
021035
021035-9
.10.1115/1.4040731
30.
Merk
,
M.
,
Gaudron
,
R.
,
Silva
,
C.
,
Gatti
,
M.
,
Mirat
,
C.
,
Schuller
,
T.
, and
Polifke
,
W.
,
2019
, “
Prediction of Combustion Noise of an Enclosed Flame by Simultaneous Identification of Noise Source and Flame Dynamics
,”
Proc. Combust. Inst.
,
37
(
4
), pp.
5263
5270
.10.1016/j.proci.2018.05.124
31.
Tangirala
,
A. K.
,
2014
,
Principles of System Identification: Theory and Practice
,
CRC Press
,
Boca Raton, FL
.
32.
Zhu
,
M.
,
Dowling
,
A. P.
, and
Bray
,
K. N. C.
,
2005
, “
Transfer Function Calculations for Aeroengine Combustion Oscillations
,”
ASME J. Eng. Gas Turbines Power
,
127
(
1
), pp.
18
26
.10.1115/1.1806451
33.
Schuermans
,
B.
,
Luebcke
,
H.
,
Bajusz
,
D.
, and
Flohr
,
P.
,
2005
, “
Thermoacoustic Analysis of Gas Turbine Combustion Systems Using Unsteady CFD
,”
ASME
Paper No. GT2005-68393.10.1115/GT2005-68393
34.
Föller
,
S.
, and
Polifke
,
W.
,
2011
, “
Advances in Identification Techniques for Aero-Acoustic Scattering Coefficients From Large Eddy Simulation
,”
18th International Congress on Sound and Vibration
(
ICSV18
), Rio de Janeiro, Brazil , July 10–14, Vol.
4
, pp.
3122
3129
.https://www.researchgate.net/publication/255738384_Advances_in_Identification_Techniques_for_Aero-Acoustic_Scattering_Coefficients_from_Large_Eddy_Simulation
35.
Blumenthal
,
R. S.
,
Subramanian
,
P.
,
Sujith
,
R.
, and
Polifke
,
W.
,
2013
, “
Novel Perspectives on the Dynamics of Premixed Flames
,”
Combust. Flame
,
160
(
7
), pp.
1215
1224
.10.1016/j.combustflame.2013.02.005
36.
Jaensch
,
S.
,
Merk
,
M.
,
Emmert
,
T.
, and
Polifke
,
W.
,
2018
, “
Identification of Flame Transfer Functions in the Presence of Intrinsic Thermoacoustic Feedback and Noise
,”
Combust. Theory Model.
,
22
(
3
), pp.
613
634
.10.1080/13647830.2018.1443517
37.
Sovardi
,
C.
,
Jaensch
,
S.
, and
Polifke
,
W.
,
2016
, “
Concurrent Identification of Aero-Acoustic Scattering and Noise Sources at a Flow Duct Singularity in Low Mach Number Flow
,”
J. Sound Vib.
,
377
, pp.
90
105
.10.1016/j.jsv.2016.05.025
38.
Tay-Wo-Chong
,
L.
,
Zellhuber
,
M.
,
Komarek
,
T.
,
Im
,
H. G.
, and
Polifke
,
W.
,
2016
, “
Combined Influence of Strain and Heat Loss on Turbulent Premixed Flame Stabilization
,”
Flow Turbul. Combust.
,
97
(
1
), pp.
263
294
.10.1007/s10494-015-9679-0
39.
Chterev
,
I.
,
Foley
,
C. W.
,
Foti
,
D.
,
Kostka
,
S.
,
Caswell
,
A. W.
,
Jiang
,
N.
,
Lynch
,
A.
,
Noble
,
D. R.
,
Menon
,
S.
,
Seitzman
,
J. M.
, and
Lieuwen
,
T. C.
, and
others
,
2014
, “
Flame and Flow Topologies in an Annular Swirling Flow
,”
Combust. Sci. Technol.
,
186
(
8
), pp.
1041
1074
.10.1080/00102202.2014.882916
40.
Taamallah
,
S.
,
Shanbhogue
,
S. J.
,
Sanusi
,
Y. S.
,
Mokhiemer
,
E. M. A.
, and
Ghoniem
,
A. F.
,
2015
, “
Transition From a Single to a Double Flame Structure in Swirling Reacting Flows: Mechanism, Dynamics, and Effect of Thermal Boundary Conditions
,”
ASME
Paper No. GT2015-43998.10.1115/GT2015-43998
41.
Polifke
,
W.
, and
Lawn
,
C. J.
,
2007
, “
On the Low-Frequency Limit of Flame Transfer Functions
,”
Combust. Flame
,
151
(
3
), pp.
437
451
.10.1016/j.combustflame.2007.07.005
42.
Guo
,
S.
,
Silva
,
C. F.
, and
Polifke
,
W.
,
2020
, “
Reliable Calculation of Thermoacoustic Instability Risk Using an Imperfect Surrogate Model
,”
ASME
Paper No.
GT2020-14434.10.1115/GT2020-14434
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