Abstract

We assimilate experimental data from nonreacting flow in the SCARLET (SCaled Acoustic Rig for Low Emission Technologies) test rig using physics-based Bayesian inference. We model the complex geometry of the combustor with a qualitatively accurate one-dimensional low-order network model. At the first level of Bayesian inference, we assimilate experimental data to optimize the parameter values by minimizing the negative log posterior probability of the parameters of each model, given the prior assumptions and the data. At the second level of inference, we find the best model by comparing the marginal likelihoods of candidate models. We apply Laplace's method accelerated with first and second order adjoint methods to assimilate data efficiently. The first order adjoint is used for rapid data assimilation and optimization. The first and second order adjoints are used for inverse uncertainty quantification. We propose six candidate models for the burner and select the model with most evidence given the data. This produces an improved physical model of the rig, with known uncertainties.

References

1.
Culick
,
F. E. C.
,
2006
, “
Unsteady Motions in Combustion Chambers for Propulsion Systems
,” NATO, Brussels, Belgium, Report No.
NATO RTO-AG-AVT-039, AGARDograph
.https://www.sto.nato.int/publications/STO%20Technical%20Reports/RTO-AG-AVT-039/%24%24AG-AVT-039-ALL.pdf
2.
Poinsot
,
T.
,
2017
, “
Prediction and Control of Combustion Instabilities in Real Engines
,”
Proc. Combust. Inst.
,
36
(
1
), pp.
1
28
.10.1016/j.proci.2016.05.007
3.
Smagorinsky
,
J.
,
1963
, “
General Circulation Experiments With the Primitive Equations Part 1: The Basic Experiment
,”
Mon. Weather Rev.
,
91
(
3
), pp.
99
164
.10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2
4.
Mendez
,
S.
, and
Eldredge
,
J. D.
,
2009
, “
Acoustic Modeling of Perforated Plates With Bias Flow for Large-Eddy Simulations
,”
J. Comput. Phys.
,
228
(
13
), pp.
4757
4772
.10.1016/j.jcp.2009.03.026
5.
Zhang
,
H.
,
Garmory
,
A.
,
Cavaliere
,
D. E.
, and
Mastorakos
,
E.
,
2015
, “
Large Eddy Simulation/Conditional Moment Closure Modeling of Swirl-Stabilized Non-Premixed Flames With Local Extinction
,”
Proc. Combust. Inst.
,
35
(
2
), pp.
1167
1174
.10.1016/j.proci.2014.05.052
6.
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
.10.1016/j.combustflame.2004.03.008
7.
Pope
,
S. B.
,
2000
,
Turbulent Flows
,
Cambridge University Press
, Cambridge, UK.
8.
Li
,
J.
,
Yang
,
D.
,
Luzzato
,
C.
, and
Morgans
,
A. S.
,
2015
, “Open Source Combustion Instability Low Order Simulator (
OSCILOS-Long
) Technical Report,” Imperial College London, London, UK, Report.https://www.oscilos.com/download/OSCILOS_Long_Tech_report.pdf
9.
Dowling
,
A. P.
, and
Stow
,
S. R.
,
2003
, “
Acoustic Analysis of Gas Turbine Combustors
,”
J. Propul. Power
,
19
(
5
), pp.
751
764
.10.2514/2.6192
10.
Ghani
,
A.
,
Boxx
,
I.
, and
Noren
,
C.
,
2020
, “
Data-Driven Identification of Nonlinear Flame Models
,”
ASME J. Eng. Gas Turbines Power
,
142
(
12
), p.
121015
.10.1115/1.4049071
11.
Ghani
,
A.
, and
Albayrak
,
A.
,
2022
, “
From Pressure Time Series Data to Flame Transfer Functions: A Framework for Perfectly Premixed Swirling Flames
,”
ASME J. Eng. Gas Turbines Power
,
145
(
1
), p.
011005
.10.1115/GT2022-84357
12.
Gant
,
F.
,
Ghirardo
,
G.
,
Cuquel
,
A.
, and
Bothien
,
M. R.
,
2022
, “
Delay Identification in Thermoacoustics
,”
ASME J. Eng. Gas Turbines Power
,
144
(
2
), p.
021005
.10.1115/1.4052060
13.
MacKay
,
D. J. C.
,
2003
,
Information Theory, Inference, and Learning Algorithms
,
Cambridge University Press
, Cambridge, UK.
14.
Juniper
,
M. P.
, and
Yoko
,
M.
,
2022
, “
Generating a Physics-Based Quantitatively-Accurate Model of an Electrically-Heated Rijke Tube With Bayesian Inference
,”
J. Sound Vib.
,
535
, p.
117096
.10.1016/j.jsv.2022.117096
15.
Yoko
,
M.
, and
Juniper
,
M. P.
,
2024
, “
Optimal Experiment Bayesian Inference Design With Adjoint-Accelerated Bayesian Inference
,”
Data-Centric Eng.
,
5
, p. e17.10.1017/dce.2024.16
16.
Yoko
,
M.
, and
Juniper
,
M. P.
,
2024
, “
Adjoint-Accelerated Bayesian Inference Applied to the Thermoacoustic Behaviour of a Ducted Conical Flame
,”
J. Fluid Mech.
,
985
, p. A38.10.1017/jfm.2024.276
17.
Yoko
,
M.
, and
Juniper
,
M. P.
,
2024
, “
Inferring Flame Transfer Functions of Turbulent Conical Flames From Pressure Measurements
,”
ASME
Paper No. GT2024-122798.10.1115/GT2024-122798
18.
Alanyalıoğlu
,
Ç.
,
Reinhardt
,
H.
,
Fischer
,
A.
,
Lahiri
,
C.
, and
Hasse
,
C.
,
2022
, “
Acoustic Scattering Behaviour of an Aero Engine Injector: Numerical Investigation Using Compressible CFD and CAA
,”
ASME
Paper No. GT2022-82901.10.1115/GT2022-82901
19.
Fischer
,
A.
, and
Lahiri
,
C.
,
2021
, “
Ranking of Aircraft Fuel-Injectors Regarding Low Frequency Thermoacoustics Based on an Energy Balance Method
,”
ASME
Paper No. GT2021-59561.10.1115/GT2021-59561
20.
Magri
,
L.
,
2019
, “
Adjoint Methods as Design Tools in Thermoacoustics
,”
ASME Appl. Mech. Rev.
,
71
(
2
), p.
020801
.10.1115/1.4042821
21.
Aguilar
,
J. G.
,
Magri
,
L. M.
, and
Juniper
,
M. P.
,
2017
, “
Adjoint-Based Sensitivity Analysis of Low-Order Thermoacoustic Networks Using a Wave-Based Approach
,”
J. Comput. Phys.
,
341
, pp.
163
181
.10.1016/j.jcp.2017.04.013
22.
Hubbard
,
S.
, and
Dowling
,
A. P.
,
2001
, “
Acoustic Resonances of an Industrial Gas Turbine Combustion System
,”
ASME J. Eng. Gas Turbines Power
,
123
(
4
), pp.
766
773
.10.1115/1.1370975
23.
Schuermans
,
B. B. H.
,
Polifke
,
W.
, and
Paschereit
,
C. O.
,
1999
, “
Modeling Transfer Matrices of Premixed Flames and Comparison With Experimental Results
,”
ASME
Paper No. 99-GT-132.10.1115/99-GT-132
24.
Lahiri
,
C.
,
2014
, “
Acoustic Performance of Bias Flow Liners in Gas Turbine Combustors
,” Ph.D. thesis,
DLR Deutsches Zentrum für Luft- und Raumfahrt e.V. Forschungsberichte
, TU Berlin, Germany.
25.
Gustafsson
,
F.
, and
Hendeby
,
G.
,
2008
, “
On Nonlinear Transformations of Stochastic Variables and Its Application to Nonlinear Filtering
,”
IEEE International Conference on Acoustics, Speech and Signal Processing
, Las Vegas, NV, Mar. 31–Apr. 4, pp.
3617
3620
.10.1109/ICASSP.2008.4518435
26.
Gu
,
M.-H.
,
Cho
,
C.
,
Chu
,
H.-Y.
,
Kang
,
N.-W.
, and
Lee
,
J.-G.
,
2021
, “
Uncertainty Propagation on a Nonlinear Measurement Model Based on Taylor Expansion
,”
Meas. Control
,
54
(
3–4
), pp.
209
215
.10.1177/0020294021989740
27.
Schuermans
,
B.
,
2003
, “
Modeling and Control of Thermoacoustic Instabilities
,”
Ph.D. thesis
,
EPFL
,
Lausanne, Switzerland
.https://core.ac.uk/download/pdf/147900077.pdf
28.
Åbom
,
M.
,
1991
, “
Measurement of the Scattering-Matrix of Acoustical Two-Ports
,”
Mech. Syst. Signal Process.
,
5
(
2
), pp.
89
104
.10.1016/0888-3270(91)90017-Y
You do not currently have access to this content.