Abstract

With advances in additive manufacturing of metal components, commercial production of complex turbine components is becoming feasible. Thus, designers are not constrained to the limitations of conventional manufacturing methods. A new conjugate optimization technique is proposed, which is not computationally demanding and can be used when several heat transfer modes are working simultaneously. For this study, film cooling holes in the leading edge of a gas turbine airfoil are optimized without trial and error simulations. Since the machine learning technique is not dependent on thermal analysis, the optimization technique can be applied to any nonlinear problem. Film hole sizes are optimized to minimize coolant flow rate while reducing the temperature variations in the stationary vane. The technique used a transfer function based iterative optimization process with unsupervised machine learning that has been termed nonlinear optimization with replacement strategy (NORS). It uses a grading metric to replace the worst performing hole combinations with one that has been optimized with a given objective and several constraints. Optimized results show significant reductions in vertical temperature variations along the leading edge while minimizing coolant flow rate. Reduced temperature variation results in reduced thermal stresses. The finite element (FE) model and the associated correlations are not part of the unsupervised machine learning technique; therefore, the proposed optimization model can be generalized for any engineering design with multiple inputs for learning and multiple outputs for grading.

References

1.
Han
,
J. C.
,
Dutta
,
S.
, and
Ekkad
,
S.
,
2012
,
Gas Turbine Heat Transfer and Cooling Technology
,
Taylor and Francis
,
Boca Raton, FL
.
2.
Mensch
,
A.
, and
Thole
,
K. A.
,
2014
, “
Overall Effectiveness of a Blade Endwall With Jet Impingement and Film Cooling
,”
ASME J. Eng. Gas Turbines Power
,
136
(
3
), p.
031901
.10.1115/1.4025835
3.
Kistenmacher
,
D.
,
2013
, “
Experimental Investigation of Film Cooling and Thermal Barrier Coatings on a Gas Turbine Vane With Conjugate Heat Transfer Effects
,” Master's thesis,
University of Texas at Austin
.
Austin, TX
.
4.
Williams
,
R. P.
,
Dyson
,
T. E.
,
Bogard
,
D. G.
, and
Bradshaw
,
S. D.
,
2014
, “
Sensitivity of the Overall Effectiveness to Film Cooling and Internal Cooling on a Turbine Vane Suction Side
,”
ASME J. Turbomach.
,
136
(
3
), p.
031006
.10.1115/1.4024681
5.
Hwang
,
S.
,
Son
,
C.
,
Seo
,
D.
,
Rhee
,
D.-H.
, and
Cha
,
B.
,
2016
, “
Comparative Study on Steady and Unsteady Conjugate Heat Transfer Analysis of a High Pressure Turbine Blade
,”
Appl. Therm. Eng.
,
99
, pp.
765
775
.10.1016/j.applthermaleng.2015.12.139
6.
Jennings
,
T.
,
2011
, “
Film-Cooled Gas Turbine Vane Temperature Calculations With an Iterative Conjugate Heat Transfer Approach Using Empirical Film Correlations
,” Master's thesis,
The Pennsylvania State University. State College
,
PA
.
7.
Zhang
,
X.
, and
Jaluria
,
Y.
,
2018
, “
Optimization of Microchannel-Based Cooling Systems
,”
Numer. Heat Transfer, Part A
,
74
(
3
), pp.
1053
1067
.10.1080/10407782.2018.1513285
8.
Xu
,
S. Z.
,
Fang
,
X. J.
, and
Yin
,
Z.
,
2013
, “
Application of Conjugate Heat Transfer in Multidisciplinary Design Optimization of Internal-Cooled Turbine Blade
,”
Appl. Mech. Mater.
,
423–426
, pp.
1693
1699
.10.4028/www.scientific.net/AMM.423-426.1693
9.
Song
,
Y.
,
Guo
,
Z.
,
Song
,
L.
,
Li
,
J.
, and
Feng
,
Z.
,
2017
, “
Knowledge-Based Aero-Thermal Multi-Disciplinary Design Optimization of a High Temperature Blade
,”
ASME
Paper No. GT2017-63880.10.1115/GT2017-63880
10.
Betts
,
J. T.
, and
Huffman
,
W. P.
,
1993
, “
Path-Constrained Trajectory Optimization Using Sparse Sequential Quadratic Programming
,”
AIAA J. Guid., Control, Dyn.
,
16
(
1
), pp.
59
68
.10.2514/3.11428
11.
Ghobadi
,
K.
,
2006
, “
A Heat-Transfer Optimization Problem
,” Master's thesis,
McMaster University
,
Hamilton, ON, Canada
.
12.
Dutta
,
S.
, and
Smith
,
R.
,
2020
, “
Transfer Function Based Optimization of Film Hole Sizes With Conjugate Heat Transfer Analysis
,”
ASME
Paper No. GT2020-14137.10.1115/GT2020-14137
13.
Kraft
,
D.
,
1988
, “
A Software Package for Sequential Quadratic Programming
,” Institut fuer Dynamik der Flugsysteme, Oberpfaffenhofen, Germany, Report No. DFVLR-FB
88
28
.
14.
SciPy,
2020
, “
Minimize(Method='SLSQP')—SciPy Reference Guide Version 1.4.1
,” SciPy.org, accessed July 22, 2020, https://docs.scipy.org/doc/scipy/reference/optimize.minimize-slsqp.html
15.
Alpaydin
,
E.
,
2020
,
Introduction to Machine Learning
,
MIT Press
,
Cambridge, MA
.
16.
Kote
,
V.
,
2019
, “
Unsupervised-Learning Assisted Artificial Neural Network for Optimization
,” Master's thesis,
Old Dominion University
,
Norfolk, VA
.
17.
Chang
,
C.-W.
, and
Dinh
,
N. T.
,
2019
, “
Classification of Machine Learning Frameworks for Data-Driven Thermal Fluid Models
,”
Int. J. Therm. Sci.
,
135
, pp.
559
579
.10.1016/j.ijthermalsci.2018.09.002
18.
Baby
,
R.
, and
Balaji
,
C.
,
2013
, “
Thermal Optimization of PCM Based Pin Fin Heat Sinks: An Experimental Study
,”
Appl. Therm. Eng.
,
54
(
1
), pp.
65
77
.10.1016/j.applthermaleng.2012.10.056
19.
Park
,
S. J.
,
Yu
,
H.
, and
Swaminathan
,
M.
,
2016
, “
Preliminary Application of Machine-Learning Techniques for Thermal-Electrical Parameter Optimization in 3-D IC
,” IEEE International Symposium Electromagnetic Compatibility (
EMC
), Ottawa, ON, Canada, July 25–29, pp.
402
405
.10.1109/ISEMC.2016.7571681
20.
Wang
,
G.
,
Zhao
,
G.
,
Li
,
H.
, and
Guan
,
Y.
,
2011
, “
Research on Optimization Design of the Heating/Cooling Channels for Rapid Heat Cycle Molding Based on Response Surface Methodology and Constrained Particle Swarm Optimization
,”
Expert Syst. Appl.
,
38
(
6
), pp.
6705
6719
.10.1016/j.eswa.2010.11.063
21.
Nowak
,
G.
, and
Wróblewski
,
W.
,
2011
, “
Optimization of Blade Cooling System With Use of Conjugate Heat Transfer Approach
,”
Int. J. Therm. Sci.
,
50
(
9
), pp.
1770
1781
.10.1016/j.ijthermalsci.2011.04.001
22.
Dennis
,
B. H.
,
Egorov
,
I. N.
,
Dulikravich
,
G. S.
, and
Yoshimura
,
S.
,
2003
, “
Optimization of a Large Number of Coolant Passages Located Close to the Surface of a Turbine Blade
,”
ASME
Paper No. GT2003-3805110.1115/GT2003-38051.
23.
Han
,
H.-Z.
,
Li
,
B.-X.
,
Wu
,
H.
, and
Shao
,
W.
,
2015
, “
Multi-Objective Shape Optimization of Double Pipe Heat Exchanger With Inner Corrugated Tube Using RSM Method
,”
Int. J. Therm. Sci.
,
90
, pp.
173
186
.10.1016/j.ijthermalsci.2014.12.010
24.
Najafi
,
H.
, and
Najafi
,
B.
,
2010
, “
Multi-Objective Optimization of a Plate and Frame Heat Exchanger Via Genetic Algorithm
,”
Heat Mass Transfer
,
46
(
6
), pp.
639
647
.10.1007/s00231-010-0612-8
25.
Jia
,
H.
,
Liu
,
Z. C.
,
Liu
,
W.
, and
Nakayama
,
A.
,
2014
, “
Convective Heat Transfer Optimization Based on Minimum Entransy Dissipation in the Circular Tube
,”
Int. J. Heat Mass Transfer
,
73
, pp.
124
129
.10.1016/j.ijheatmasstransfer.2014.02.005
26.
Sanaye
,
S.
, and
Hajabdollahi
,
H.
,
2010
, “
Thermal-Economic Multi-Objective Optimization of Plate Fin Heat Exchanger Using Genetic Algorithm
,”
Appl. Energy
,
87
(
6
), pp.
1893
1902
.10.1016/j.apenergy.2009.11.016
27.
Zhang
,
K.
,
Guliani
,
A.
,
Ogrenci-Memik
,
S.
,
Memik
,
G.
,
Yoshii
,
K.
,
Sankaran
,
R.
, and
Beckman
,
P.
,
2018
, “
Machine Learning-Based Temperature Prediction for Runtime Thermal Management Across System Components
,”
IEEE Trans. Parallel Distrib. Syst.
,
29
(
2
), pp.
405
419
.10.1109/TPDS.2017.2732951
28.
Team CCJ
,
2020
, “
Turbine Blade, Vane Cooling—A Primer
,” CCJ, PSI Media, Las Vegas, NV, accessed July 22, 2020, https://www.ccj-online.com/turbine-blade-vane-cooling-a-primer/
29.
Funazaki
,
K.
,
Yokota
,
M.
, and
Yamawaki
,
S.
,
1997
, “
Effect of Periodic Wake Passing on Film Effectiveness of Discrete Cooling Holes Around the Leading Edge of a Blunt Body
,”
ASME J. Turbomach.
,
119
(
2
), pp.
292
301
.10.1115/1.2841112
30.
Munson
,
B. R.
,
Young
,
D. F.
,
Okiishi
,
T. H.
, and
Huebsch
,
W. W.
,
2009
,
Fundamentals of Fluid Mechanics
,
Wiley
,
Hoboken, NJ
.
31.
Huang
,
Y.
,
Ekkad
,
S. V.
, and
Han
,
J. C.
,
1998
, “
Detailed Heat Transfer Distributions Under an Array of Orthogonal Impinging Jets
,”
AIAA J. Thermophys. Heat Transfer
,
12
(
1
), pp.
73
79
.10.2514/2.6304
32.
Molki
,
M.
, and
Sparrow
,
E. M.
,
1986
, “
An Empirical Correlation for the Average Heat Transfer Coefficient in Circular Tubes
,”
ASME J. Heat Transfer
,
108
(
2
), pp.
482
484
.10.1115/1.3246957
33.
Franklin
,
G. F.
,
Powell
,
J. D.
, and
Emani-Naeini
,
A.
,
2006
,
Feedback Control of Dynamic Systems
,
Pearson
,
Upper Saddle River, NJ
.
34.
Palm
,
W.
,
2010
,
System Dynamics
,
McGraw-Hill
,
New York
.
35.
Duffy
,
D.
,
2011
,
Advanced Engineering Mathematics With MATLAB
,
Taylor and Francis
,
Boca Raton, FL
.
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