Abstract

Turbulence modeling plays a crucial role in swirl-stabilized gas turbine combustors, typically relying on scale-resolved simulations (SRS) such as large eddy simulations (LES). However, LES is computationally expensive due to the need for fine mesh resolution and small time-steps required to capture the combustor's large-scale turbulence motion accurately. On the other hand, Reynolds-averaged Navier–Stokes (RANS) models while computationally efficient, lack fidelity in predicting complex flow characteristics such as swirl accurately. In this study, the GEKO model is used for simulating RANS predictions of turbulence in a swirling flow scenario, whereas high-fidelity LES predictions serve as target data enabling field inversion via gradient-based optimization using the Adjoint solver in ansysfluent. Machine learning via neural network (NN) Training is employed to establish correlations between turbulent flow features and optimal GEKO parameters, enabling the trained model's generalization. This approach allows computationally faster simulations of swirling flow using an optimized GEKO model matching the predictions of LES. This methodology is tested on the DLR PRECCINSTA burner considering a nonreacting, isothermal flow scenario. The velocity field variance between LES and GEKO-RANS solutions is defined as the objective function, with the turbulent kinetic energy (TKE) source coefficient serving as the tuning parameter. Results using the optimized GEKO model demonstrate qualitative and quantitative agreement with LES and experiments. The trained neural network (NN) model's generalization is tested on various flow conditions, including six additional Reynolds numbers and a reacting flow scenario, showcasing significant improvements over the baseline model solution. This optimized workflow holds promise for future studies involving different geometries with similar flow fields.

References

1.
Hall
,
M. B. C. R.
, and
Smooke
,
M. D.
,
1997
, “
Physical and Chemical Aspects of Combustion: A Tribute to Irvin Glassman
,”
Combustion Science Technology Book Series
, Vol.
4
, Gordon and Breach Science Publishers, The Netherlands.
2.
Lee
,
K. B.
,
Thring
,
M. W.
, and
Beér
,
J. M.
,
1962
, “
On the Rate of Combustion of Soot in a Laminar Soot Flame
,”
Combust. Flame
,
6
(
C
), pp.
137
145
.10.1016/0010-2180(62)90082-2
3.
Janicka
,
J.
, and
Sadiki
,
A.
,
2005
, “
Large Eddy Simulation of Turbulent Combustion Systems
,”
Proc. Combust. Inst.
,
30
(
1
), pp.
537
547
.10.1016/j.proci.2004.08.279
4.
Pitsch
,
H.
,
2006
, “
Large-Eddy Simulation of Turbulent Combustion
,”
Annu. Rev. Fluid Mech.
,
38
(
1
), pp.
453
482
.10.1146/annurev.fluid.38.050304.092133
5.
Smagorinsky
,
J.
,
1963
, “
General Circulation Experiments With the Primitive Equations
,”
Mon. Weather Rev.
,
91
(
3
), pp.
99
164
.10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2
6.
Lilly
,
D. K.
,
1992
, “
A Proposed Modification of the Germano Subgrid-Scale Closure Method
,”
Phys. Fluids A
,
4
(
3
), pp.
633
635
.10.1063/1.858280
7.
Duraisamy
,
K.
,
Iaccarino
,
G.
, and
Xiao
,
H.
,
2019
, “
Turbulence Modeling in the Age of Data
,”
Annu. Rev. Fluid Mech.
,
51
(
1
), pp.
357
377
.10.1146/annurev-fluid-010518-040547
8.
Marusic
,
I.
,
Candler
,
G. V.
,
Interrante
,
V.
,
Subbareddy
,
P. K.
, and
Moss
,
A.
,
2001
, “
Real Time Feature Extraction for the Analysis of Turbulent Flows
,”
Data Mining for Scientific and Engineering Applications, Massive Computing
,
Springer
,
Boston, MA
.
9.
Cheung
,
S. H.
,
Oliver
,
T. A.
,
Prudencio
,
E. E.
,
Prudhomme
,
S.
, and
Moser
,
R. D.
,
2011
, “
Bayesian Uncertainty Analysis With Applications to Turbulence Modeling
,”
Reliab. Eng. Syst. Safety
,
96
(
9
), pp.
1137
1149
.10.1016/j.ress.2010.09.013
10.
Edeling
,
W. N.
,
Cinnella
,
P.
,
Dwight
,
R. P.
, and
Bijl
,
H.
,
2014
, “
Bayesian Estimates of Parameter Variability in the k-ε Turbulence Model
,”
J. Comput. Phys.
,
258
, pp.
73
94
.10.1016/j.jcp.2013.10.027
11.
Dow
,
E.
, and
Wangy
,
Q.
,
2011
, “
Uncertainty Quantification of Structural Uncertainties in RANS Simulations of Complex Flows
,”
AIAA
Paper No. 2011-3865.10.2514/6.2011-3865
12.
Brunton
,
S. L.
,
Noack
,
B. R.
, and
Koumoutsakos
,
P.
,
2020
, “
Machine Learning for Fluid Mechanics
,”
Annu. Rev. Fluid Mech.
,
52
(
1
), pp.
477
508
.10.1146/annurev-fluid-010719-060214
13.
Ling
,
J.
,
Kurzawski
,
A.
, and
Templeton
,
J.
,
2016
, “
Reynolds Averaged Turbulence Modelling Using Deep Neural Networks With Embedded Invariance
,”
J, Fluid Mech
.,
807
, pp.
155
166
.10.1017/jfm.2016.615
14.
Parish
,
E. J.
, and
Duraisamy
,
K.
,
2016
, “
A Paradigm for Data-Driven Predictive Modeling Using Field Inversion and Machine Learning
,”
J. Comput. Phys.
,
305
, pp.
758
774
.10.1016/j.jcp.2015.11.012
15.
Holland
,
J. R.
,
Baeder
,
J. D.
, and
Duraisamy
,
K.
,
2019
, “
Field Inversion and Machine Learning With Embedded Neural Networks: Physics-Consistent Neural Network Training
,”
AIAA
Paper No. 2019-3200.10.2514/6.2019-3200
16.
Ho
,
J.
, and
West
,
A.
,
2021
, “
Field Inversion and Machine Learning for Turbulence Modelling Applied to Three-Dimensional Separated Flows
,”
AIAA
Paper No. 2021-2903.10.2514/6.2021-2903
17.
Wu
,
H.
,
Zhou
,
H.
,
Xu
,
S.
,
Ren
,
C.
,
Chen
,
Q.
, and
Jadhav
,
T.
,
2022
, “
Adjoint-Based Model Tuning and Machine Learning Strategy for Turbulence Model Improvement
,”
SAE
Paper No. 2022-01-0899.10.4271/2022-01-0899
18.
Menter
,
F. R.
,
Matyushenko
,
A.
, and
Lechner
,
R.
,
2020
, “
‘Development of a Generalized K-ω Two-Equation Turbulence Model’
,”
Notes on Numerical Fluid Mechanics and Multidisciplinary Design
, Vol.
142
, Springer International Publishing, Cham, Switzerland.
19.
Meier
,
W.
,
Weigand
,
P.
,
Duan
,
X. R.
, and
Giezendanner-Thoben
,
R.
,
2007
, “
Detailed Characterization of the Dynamics of Thermoacoustic Pulsations in a Lean Premixed Swirl Flame
,”
Combust. Flame
,
150
(
1–2
), pp.
2
26
.10.1016/j.combustflame.2007.04.002
20.
Ansys
,
2022
, “
Ansys Fluent User's Guide
,”
Ansys
,
Canonsburg, PA
.
21.
Heaton
,
J.
,
2018
, “
Ian Goodfellow, Yoshua Bengio, and Aaron Courville: Deep Learning
,”
Genet. Program. Evolvable Mach.
,
19
(
1–2
), pp.
305
307
.10.1007/s10710-017-9314-z
22.
Verma
,
I.
,
Yadav
,
R.
,
Sharkey
,
P.
,
Li
,
S.
, and
Meeks
,
E.
,
2019
, “
Modeling of Turbulent Swirl Stabilized Flame With Flamelet Generated Manifold and Hybrid LES-RANS Turbulence Model
,”
ASME
Paper No. GT2019-91147. 10.1115/GT2019-91147
23.
Apicella
,
A.
,
Donnarumma
,
F.
,
Isgrò
,
F.
, and
Prevete
,
R.
,
2021
, “
A Survey on Modern Trainable Activation Functions
,”
Neural Networks
,
138
, pp.
14
32
.10.1016/j.neunet.2021.01.026
24.
Ling
,
J.
,
Jones
,
R.
, and
Templeton
,
J.
,
2016
, “
Machine Learning Strategies for Systems With Invariance Properties
,”
J. Comput. Phys.
,
318
, pp.
22
35
.10.1016/j.jcp.2016.05.003
25.
Kelsall
,
G.
, and
Troger
,
C.
,
2004
, “
Prediction and Control of Combustion Instabilities in Industrial Gas Turbines
,”
Appl. Therm. Eng.
,
24
(
11–12
), pp.
1571
1582
.10.1016/j.applthermaleng.2003.10.025
26.
Lartigue
,
G.
,
Meier
,
U.
, and
Bérat
,
C.
,
2004
, “
Experimental and Numerical Investigation of Self-Excited Combustion Oscillations in a Scaled Gas Turbine Combustor', in
,”
Appl. Therm. Eng.
,
24
(
11–12
), pp.
1583
1592
.10.1016/j.applthermaleng.2003.10.026
27.
Roux
,
S.
,
Lartigue
,
G.
,
Poinsot
,
T.
,
Meier
,
U.
, and
Bérat
,
C.
,
2005
, “
Studies of Mean and Unsteady Flow in a Swirled Combustor Using Experiments, Acoustic Analysis, and Large Eddy Simulations
,”
Combust. Flame
,
141
(
1–2
), pp.
40
54
.10.1016/j.combustflame.2004.12.007
You do not currently have access to this content.