Abstract

Effusion cooling represents the state-of-the-art for liner cooling technology in modern combustion chambers, combining a more uniform film protection of the wall and a significant heat sink effect by forced convection through a huge number of small holes. From a numerical point of view, a high-computational cost is required in a conjugate computational fluid dynamics (CFD) analysis of an entire combustor for a proper discretization of effusion holes in order to obtain accurate results in terms of liner temperature and effectiveness distributions. Consequently, simplified CFD approaches to model the various phenomena associated are required, especially during the design process. For this purpose, 2D boundary source models are attractive, replacing the effusion hole with an inlet (hot side) and an outlet (cold side) patches to consider the related coolant injection. However, proper velocity profiles at the inlet patch together with the correct mass flow rate are mandatory to accurately predict the interaction and the mixing between coolant air and hot gases as well as temperature and effectiveness distributions on the liners. In this sense, reduced-order (RO) model techniques from the machine learning framework can be used to derive a surrogate model (SM) for the prediction of these velocity profiles with a reduced computational cost, starting from a limited number of CFD simulations of a single effusion hole at different operating conditions. In this work, an application of these approaches will be presented to model the effusion system of a non-reactive single-sector linear combustor simulator equipped with a swirler and a multi-perforated plate, combining ansys fluent with a matlab code. The employed surrogate model has been constructed on a training set of CFD simulations of the single effusion hole with operating conditions sampled in the model parameter space and subsequently assessed on a different validation set.

References

1.
Mazzei
,
L.
,
Andreini
,
A.
,
Facchini
,
B.
, and
Turrini
,
F.
,
2016
, “
Impact of Swirl Flow on Combustor Liner Heat Transfer and Cooling: A Numerical Investigation With Hybrid Reynolds-averaged Navier–Stokes Large Eddy Simulation Models
,”
ASME J. Eng. Gas Turbines Power
,
138
(
5
), p.
051504
.
2.
Puggelli
,
S.
,
Bertini
,
D.
,
Mazzei
,
L.
, and
Andreini
,
A.
,
2016
, “
Assessment of Scale Resolved CFD Methods for the Investigation of Lean Burn Spray Flames
,”
ASME J. Eng. Gas Turbines Power
139
(
2
), p.
021501
.
3.
Bertini
,
D.
,
Mazzei
,
L.
,
Andreini
,
A.
, and
Facchini
,
B.
,
2019
, “
Multiphysics Numerical Investigation of an Aeronautical Lean Burn Combustor
,” Turbo Expo: Power for Land, Sea, and Air, Vol.
58653
,
American Society of Mechanical Engineers
, Paper No. V05BT17A004.
4.
Paccati
,
S.
,
Bertini
,
D.
,
Mazzei
,
L.
,
Puggelli
,
S.
, and
Andreini
,
A.
,
2021
, “
Large-Eddy Simulation of a Model Aero-Engine Sooting Flame With a Multiphysics Approach
,”
Flow Turbul. Combust.
,
106
(
4
), pp.
1329
1354
.
5.
Heidmann
,
J. D.
, and
Hunter
,
S. D.
,
2001
, “
Coarse Grid Modeling of Turbine Film Cooling Flows Using Volumetric Source Terms
,”
Volume 3: Heat Transfer; Electric Power; Industrial and Cogeneration
,
78521
.
6.
Burdet
,
A.
,
Abhari
,
R. S.
, and
Rose
,
M. G.
,
2007
, “
Modeling of Film Cooling—Part II: Model for Use in Three-Dimensional Computational Fluid Dynamics
,”
ASME J. Turbomach.
129
(
2
), pp.
221
231
.
7.
Kampe
,
T.
, and
Völker
,
S.
,
2010
, “
A Model for Cylindrical Hole Film Cooling: Part II—Model Formulation, Implementation and Results
,”
ASME J. Turbomach.
,
134
(
6
), p.
061011
.
8.
Voigt
,
S.
,
Noll
,
B.
, and
Aigner
,
M.
,
2012
, “
Development of a Macroscopic CFD Model for Effusion Cooling Applications
,”
ASME Turbo Expo 2012: Turbine Technical Conference and Exposition
,
Copenhagen, Denmark
,
June 11–15
, vol. 44700, pp.
1235
1243
.
9.
Andreini
,
A.
,
Da Soghe
,
R.
,
Facchini
,
B.
,
Mazzei
,
L.
,
Colantuoni
,
S.
, and
Turrini
,
F.
,
2014
, “
Local Source Based CFD Modeling of Effusion Cooling Holes: Validation and Application to an Actual Combustor Test Case
,”
ASME J. Eng. Gas Turbines Power
,
136
(
1
), p.
011506
.
10.
Andrei
,
L.
,
Innocenti
,
L.
,
Andreini
,
A.
,
Facchini
,
B.
, and
Winchler
,
L.
,
2017
, “
Film Cooling Modeling for Gas Turbine Nozzles and Blades: Validation and Application
,”
ASME J. Turbomach.
,
139
(
1
), p.
011004
.
11.
Mendez
,
S.
, and
Nicoud
,
F.
,
2008
, “
Adiabatic Homogeneous Model for Flow Around a Multiperforated Plate
,”
AIAA J.
,
46
(
10
), pp.
2623
2633
.
12.
Rida
,
S.
,
Reynolds
,
R.
,
Chakravorty
,
S.
, and
Gupta
,
K.
,
2012
, “
Imprinted Effusion Modeling and Dynamic CD Calculation in Gas Turbine Combustors
,”
ASME Turbo Expo 2012: Turbine Technical Conference and Exposition
,
Copenhagen, Denmark
,
June 11–15
, vol. 44687, pp.
589
599
.
13.
Lahbib
,
D.
,
2015
, “
Modélisation aérodynamique et thermique des multiperforations en LES
,”
Thèse de doctorat Mathématiques et modélisation, Montpellier
.
14.
Bizzari
,
R.
,
Dauptain
,
A.
,
Gicquel
,
L.
, and
Nicoud
,
F.
,
2017
, “
A Thickened-Hole Model for LES Over Multiperforated Liners
,”
Flow, Turbulence and Combustion
,
101
.
15.
Aversano
,
G.
,
Bellemans
,
A.
,
Li
,
Z.
,
Coussement
,
A.
,
Gicquel
,
O.
, and
Parente
,
A.
,
2019
, “
Application of Reduced-Order Models Based on PCA & Kriging for the Development of Digital Twins of Reacting Flow Applications
,”
Comput. Chem. Eng.
,
121
, pp.
422
441
.
16.
Haag
,
S.
, and
Anderl
,
R.
,
2018
, “
Digital Twin—Proof of Concept
,”
Manuf. Lett.
,
15
(Industry 4.0 and Smart Manufacturing), pp.
64
66
.
17.
Aversano
,
G.
,
Ferrarotti
,
M.
, and
Parente
,
A.
,
2020
, “
Digital Twin of a Combustion Furnace Operating in Flameless Conditions: Reduced-Order Model Development From CFD Simulations
,”
Proc. Combust. Inst.
38
(
4
), pp.
5373
5381
.
18.
Jolliffe
,
I. T.
, and
Cadima
,
J.
,
2016
, “
Principal Component Analysis: A Review and Recent Developments
,”
Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci.
,
374
(
2065
), p.
20150202
.
19.
Abdi
,
H.
, and
Williams
,
L. J.
,
2010
, “
Principal Component Analysis
,”
Wiley Interdiscip. Rev.: Comput. Statist.
,
2
(
4
), pp.
433
459
.
20.
Smola
,
A. J.
, and
Schölkopf
,
B.
,
2004
, “
A Tutorial on Support Vector Regression
,”
Statist. Comput.
,
14
(
3
), pp.
199
222
.
21.
Rasmussen
,
C. E.
, and
Nickisch
,
H.
,
2010
, “
Gaussian Processes for Machine Learning (GPML) Toolbox
,”
J. Mach. Learn. Res.
,
11
, pp.
3011
3015
.
22.
Freier
,
L.
,
Wiechert
,
W.
, and
von Lieres
,
E.
,
2017
, “
Kriging With Trend Functions Nonlinear in Their Parameters: Theory and Application in Enzyme Kinetics
,”
Eng. Life Sci.
,
17
(
8
), pp.
916
922
.
23.
Constantine
,
P. G.
,
Dow
,
E.
, and
Wang
,
Q.
,
2014
, “
Active Subspace Methods in Theory and Practice: Applications to Kriging Surfaces
,”
SIAM J. Sci. Comput.
,
36
(
4
), pp.
A1500
A1524
.
24.
Simpson
,
T.
,
Mistree
,
F.
,
Korte
,
J.
, and
Mauery
,
T.
,
1998
, “
Comparison of Response Surface and Kriging Models for Multidisciplinary Design Optimization
,”
7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization
,
St. Louis, MO
,
Sept. 2–4
, p.
4755
.
25.
Lenzi
,
T.
,
Palanti
,
L.
,
Picchi
,
A.
,
Bacci
,
T.
,
Mazzei
,
L.
,
Andreini
,
A.
, and
Facchini
,
B.
,
2020
, “
Time-Resolved Flow Field Analysis of Effusion Cooling System With Representative Swirling Main Flow
,”
ASME J. Turbomach.
,
142
(
6
), p.
061008
.
26.
Lenzi
,
T.
,
Picchi
,
A.
,
Bacci
,
T.
,
Andreini
,
A.
, and
Facchini
,
B.
,
2020
, “
Unsteady Flow Field Characterization of Effusion Cooling Systems With Swirling Main Flow: Comparison Between Cylindrical and Shaped Holes
,”
Energies
,
13
(
19
), p.
4993
.
27.
Menter
,
F. R.
,
1994
, “
Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications
,”
AIAA J.
,
32
(
8
), pp.
1598
1605
.
28.
Frank
,
T.
, and
Menter
,
F.
,
2015
, ““Validation of URANS SST and SBES in ANSYS CFD for the Turbulent Mixing of Two Parallel Planar Water Jets Impinging on a Stationary Pool,” Jets, pp.
1
9
.
29.
Germano
,
M.
,
Piomelli
,
U.
,
Moin
,
P.
, and
Cabot
,
W. H.
,
1991
, “
A Dynamic Subgrid-Scale Eddy Viscosity Model
,”
Phys. Fluids A
,
3
(
7
), pp.
1760
1765
.
30.
Sammut
,
C.
, and
Webb
,
G. I.
, eds.,
2010
,
Leave-One-Out Cross-Validation
,
Springer
,
Boston, MA
, pp.
600
601
.
31.
Géron
,
A.
,
2019
,
Hands-On Machine Learning With Scikit-Learn, Keras, and TensorFlow: Concepts, Tools, and Techniques to Build Intelligent Systems
,
O’Reilly Media
,
Sebastopol, CA
.
You do not currently have access to this content.