Abstract

The design of film cooling systems relies heavily on Reynolds-averaged Navier–Stokes (RANS) simulations, which solve for mean quantities and model all turbulent scales. Most turbulent heat flux models, which are based on isotropic diffusion with a fixed turbulent Prandtl number (Prt), fail to accurately predict heat transfer in film cooling flows. In the present work, machine learning models are trained to predict a non-uniform Prt field using various datasets as training sets. The ability of these models to generalize beyond the flows on which they were trained is explored. Furthermore, visualization techniques are employed to compare distinct datasets and to help explain the cross-validation results.

References

1.
Bogard
,
D. G.
, and
Thole
,
K. A.
,
2006
, “
Gas Turbine Film Cooling
,”
J. Propul. Power
,
22
(
2
), pp.
249
270
. 10.2514/1.18034
2.
Nikparto
,
A.
,
Rice
,
T.
, and
Schobeiri
,
M. T.
,
2017
, “
Experimental and Numerical Investigation of Heat Transfer and Film Cooling Effectiveness of a Highly Loaded Turbine Blade Under Steady and Unsteady Wake Flow Condition
,”
ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition
,
Charlotte, NC
,
June 26–30
,
American Society of Mechanical Engineers
, p.
V05CT19A029
V05CT19A029
.
3.
Kays
,
W. M.
,
1994
, “
Turbulent Prandtl Number — Where Are We?
,”
ASME J. Heat Transfer
,
116
(
2
), pp.
284
295
. 10.1115/1.2911398
4.
Kohli
,
A.
, and
Bogard
,
D. G.
,
2005
, “
Turbulent Transport in Film Cooling Flows
,”
ASME J. Heat Transfer
,
127
(
5
), pp.
513
520
. 10.1115/1.1865221
5.
Muppidi
,
S.
, and
Mahesh
,
K.
,
2008
, “
Direct Numerical Simulation of Passive Scalar Transport in Transverse Jets
,”
J. Fluid Mech.
,
598
, pp.
335
360
. 10.1017/S0022112007000055
6.
Schreivogel
,
P.
,
Abram
,
C.
,
Fond
,
B.
,
Straußwald
,
M.
,
Beyrau
,
F.
, and
Pfitzner
,
M.
,
2016
, “
Simultaneous kHz-rate Temperature and Velocity Field Measurements in the Flow Emanating From Angled and Trenched Film Cooling Holes
,”
Int. J. Heat. Mass. Transfer
,
103
, pp.
390
400
. 10.1016/j.ijheatmasstransfer.2016.06.092
7.
Oliver
,
T. A.
,
Anderson
,
J. B.
,
Bogard
,
D. G.
,
Moser
,
R. D.
, and
Laskowski
,
G.
,
2017
, “
Implicit LES for Shaped-Hole Film Cooling Flow
,”
ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition
,
Charlotte, NC
,
June 26–30
,
American Society of Mechanical Engineers
,
New York
, p.
V05AT12A005
.
8.
Daly
,
B. J.
, and
Harlow
,
F. H.
,
1970
, “
Transport Equations in Turbulence
,”
Phys. Fluids
,
13
(
11
), pp.
2634
2649
. 10.1063/1.1692845
9.
Abe
,
K.
, and
Suga
,
K.
,
2001
, “
Towards the Development of a Reynolds-Averaged Algebraic Turbulent Scalar-Flux Model
,”
Int. J. Heat Fluid Flow
,
22
(
1
), pp.
19
29
. 10.1016/S0142-727X(00)00062-X
10.
Ling
,
J.
,
Ryan
,
K. J.
,
Bodart
,
J.
, and
Eaton
,
J. K.
,
2016
, “
Analysis of Turbulent Scalar Flux Models for a Discrete Hole Film Cooling Flow
,”
ASME J. Turbomach.
,
138
(
1
), p.
011006
. 10.1115/1.4031698
11.
Ryan
,
K. J.
,
Bodart
,
J.
,
Folkersma
,
M.
,
Elkins
,
C. J.
, and
Eaton
,
J. K.
,
2017
, “
Turbulent Scalar Mixing in a Skewed Jet in Crossflow: Experiments and Modeling
,”
Flow, Turbulence Combust.
,
98
(
3
), pp.
781
801
. 10.1007/s10494-016-9785-7
12.
Bishop
,
C.
,
2006
,
Pattern Recognition and Machine Learning
,
Springer
,
New York, NY
.
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.
Sandberg
,
R.
,
Tan
,
R.
,
Weatheritt
,
J.
,
Ooi
,
A.
,
Haghiri
,
A.
,
Michelassi
,
V.
, and
Laskowski
,
G.
,
2018
, “
Applying Machine Learnt Explicit Algebraic Stress and Scalar Flux Models to a Fundamental Trailing Edge Slot
,”
ASME J. Turbomach.
,
140
(
10
), p.
101008
. 10.1115/1.4041268
15.
Singh
,
A. P.
,
Medida
,
S.
, and
Duraisamy
,
K.
,
2017
, “
Machine-Learning-Augmented Predictive Modeling of Turbulent Separated Flows Over Airfoils
,”
AIAA J.
,
55
(
7
), pp.
2215
2227
. 10.2514/1.J055595
16.
Milani
,
P. M.
,
Ling
,
J.
,
Saez-Mischlich
,
G.
,
Bodart
,
J.
, and
Eaton
,
J. K.
,
2018
, “
A Machine Learning Approach for Determining the Turbulent Diffusivity in Film Cooling Flows
,”
ASME J. Turbomach.
,
140
(
2
), p.
021006
. 10.1115/1.4038275
17.
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
18.
Shih
,
T.-H.
,
Zhu
,
J.
, and
Lumley
,
J. L.
,
1995
, “
A New Reynolds Stress Algebraic Equation Model
,”
Comput. Methods Appl. Mech. Eng.
,
125
(
1
), pp.
287
302
. 10.1016/0045-7825(95)00796-4
19.
Ling
,
J.
, and
Templeton
,
J.
,
2015
, “
Evaluation of Machine Learning Algorithms for Prediction of Regions of High Reynolds Averaged Navier Stokes Uncertainty
,”
Phys. Fluids
,
27
(
8
), p.
085103
. 10.1063/1.4927765
20.
Pedregosa
,
F.
,
Varoquaux
,
G.
,
Gramfort
,
A.
,
Michel
,
V.
,
Thirion
,
B.
,
Grisel
,
O.
,
Blondel
,
M.
,
Prettenhofer
,
P.
,
Weiss
,
R.
,
Dubourg
,
V.
,
Vanderplas
,
J.
,
Passos
,
A.
,
Cournapeau
,
D.
,
Brucher
,
M.
,
Perrot
,
M.
, and
Duchesnay
,
E.
,
2011
, “
Scikit-Learn: Machine Learning in Python
,”
J. Machine Learning
,
12
(
Oct.
), pp.
2825
2830
.
21.
Louppe
,
G.
,
2014
,
arXiv preprint arXiv:1407.7502. Jul 28
, https://arxiv.org/abs/1407.7502.
22.
Bodart
,
J.
,
Coletti
,
F.
,
Bermejo-Moreno
,
I.
, and
Eaton
,
J.
,
2013
, “
High-Fidelity Simulation of a Turbulent Inclined Jet in a Crossflow
,”
Center Turbulence Res. Annu. Res. Briefs
, pp.
263
275
.
23.
Vreman
,
A.
,
2004
, “
An Eddy-Viscosity Subgrid-Scale Model for Turbulent Shear Flow: Algebraic Theory and Applications
,”
Phys. Fluids
,
16
(
10
), pp.
3670
3681
. 10.1063/1.1785131
24.
Milani
,
P. M.
,
Gunady
,
I. E.
,
Ching
,
D. S.
,
Banko
,
A. J.
,
Elkins
,
C. J.
, and
Eaton
,
J. K.
,
2019
, “
Enriching MRI Mean Flow Data of Inclined Jets in Crossflow with Large Eddy Simulations
,”
Int. J. Heat Fluid Flow
,
80
, p.
108472
. 10.1016/j.ijheatfluidflow.2019.108472
25.
Folkersma
,
M.
, and
Bodart
,
J.
,
2018
, “
Large Eddy Simulation of an Asymmetric Jet in Crossflow
,”
Direct Large-Eddy Simul. X
, pp.
85
91
.
26.
Rossi
,
R.
,
Philips
,
D.
, and
Iaccarino
,
G.
,
2010
, “
A Numerical Study of Scalar Dispersion Downstream of a Wall-Mounted Cube Using Direct Simulations and Algebraic Flux Models
,”
Int. J. Heat Fluid Flow
,
31
(
5
), pp.
805
819
. 10.1016/j.ijheatfluidflow.2010.05.006
27.
Ling
,
J.
,
Rossi
,
R.
, and
Eaton
,
J. K.
,
2015
, “
Near Wall Modeling for Trailing Edge Slot Film Cooling
,”
J. Fluids Eng.
,
137
(
2
), p.
021103
. 10.1115/1.4028498
28.
Milani
,
P. M.
, and
Eaton
,
J. K.
,
2018
, “
Magnetic Resonance Imaging, Optimization, and Machine Learning to Understand and Model Turbulent Mixing
,”
21st Australasian Fluid Mechanics Conference, Australasian Fluid Mechanics Society
,
Adelaide, Australia
,
Dec. 10–13
.
29.
Milani
,
P. M.
,
Ling
,
J.
, and
Eaton
,
J. K.
,
2019
, “
Physical Interpretation of Machine Learning Models Applied to Film Cooling Flows
,”
ASME J. Turbomach.
,
141
(
1
), p.
011004
. 10.1115/1.4041291
30.
Bro
,
R.
, and
Smilde
,
A. K.
,
2014
, “
Principal Component Analysis
,”
Anal. Methods
,
6
(
9
), pp.
2812
2831
. 10.1039/C3AY41907J
31.
Maaten
,
L. v. d.
, and
Hinton
,
G.
,
2008
, “
Visualizing Data Using T-SNE
,”
J. Machine Learning Res.
,
9
(
Nov
.), pp.
2579
2605
.
32.
Wu
,
J.
,
Wang
,
J.
,
Xiao
,
H.
, and
Ling
,
J.
,
2017
, “
Visualization of High Dimensional Turbulence Simulation Data Using t-SNE
,”
19th AIAA Non-Deterministic Approaches Conference, American Institute of Aeronautics and Astronautics
,
Grapevine, TX
,
Jan. 9–13
, p.
1770
.
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