An entropy analysis and design optimization methodology is combined with airfoil shape optimization to demonstrate the impact of entropy generation on aerodynamics designs. In the work herein, the entropy generation rate is presented as an extra design objective along with lift-drag ratio, while the lift coefficient is the constraint. Model equation, which calculates the local entropy generation rate in turbulent flows, is derived by extending the Reynolds-averaging of entropy balance equation. The class-shape function transform (CST) parametric method is used to model the airfoil configuration and combine the radial basis functions (RBFs) based mesh deformation technique with flow solver to compute the quantities such as lift-drag ratio and entropy generation at the design condition. From the multi-objective solutions which represent the best trade-offs between the design objectives, one can select a set of airfoil shapes with a low relative energy cost and with improved aerodynamic performance. It can be concluded that the methodology of entropy generation analysis is an effective tool in the aerodynamic optimization design of airfoil shape with the capability of determining the amount of energy cost.

References

References
1.
Wang
,
J.
,
Xie
,
F.
,
Zheng
,
Y.
,
Zhang
,
J.
,
Yang
,
B.
, and
Ji
,
T.
, 2017, “
Virtual Stackelberg Game Coupled With the Adjoint Method for Aerodynamic Shape Optimization
,”
Eng. Optim.
,
50
(10), pp. 1–22.
2.
Jahangirian
,
A.
, and
Shahrokhi
,
A.
,
2011
, “
Aerodynamic Shape Optimization Using Efficient Evolutionary Algorithms and Unstructured CFD Solver
,”
Comput. Fluids
,
46
(
1
), pp.
270
276
.
3.
Roberts
,
R. A.
, and
Doty
,
J. H.
,
2012
, “
Implementation of a Non-Equilibrium Exergy Analysis for an Aircraft Thermal Management System
,”
AIAA
Paper No. 2012-1126.
4.
Li
,
H.
,
Stewart
,
J.
, and
Figliola
,
R. S.
,
2006
, “
Exergy-Based Design Methodology for Airfoil Shape Optimization and Wing Analysis
,”
25th International Congress of the Aeronautical Sciences
, Hamburg, Germany, Sept. 3–8.http://www.icas.org/ICAS_ARCHIVE/ICAS2006/PAPERS/515.PDF
5.
Mortazavi
,
S. M.
,
Soltani
,
M. R.
, and
Motieyan
,
H.
,
2015
, “
A Pareto Optimal Multi-Objective Optimization for a Horizontal Axis Wind Turbine Blade Airfoil Sections Utilizing Exergy Analysis and Neural Networks
,”
J. Wind Eng. Ind. Aerodyn.
,
136
(
136
), pp.
62
72
.
6.
Li
,
Z.
,
Du
,
J.
,
Ottavy
,
X.
, and
Zhang
,
H.
,
2018
, “
Quantification and Analysis of the Irreversible Flow Loss in a Linear Compressor Cascade
,”
Entropy
,
20
(
7
), p.
486
.
7.
Jin
,
Y.
,
Du
,
J.
,
Li
,
Z.
, and
Zhang, H.
,
2017
, “
Second-Law Analysis of Irreversible Losses in Gas Turbines
,”
Entropy
,
19
(
9
), p.
470
.
8.
Bejan
,
A.
,
1996
,
Entropy Generation Minimization
,
CRC Press
,
New York
.
9.
Moore
,
J.
, and
Moore
,
J. G.
,
1983
, “
Entropy Production Rates From Viscous Flow Calculations—I: A Turbulent Boundary Layer Flow
,”
ASME
Paper No. 83-GT-70.
10.
Adeyinka
,
O. B.
, and
Naterer
,
G. F.
,
2013
, “
Predicted Entropy Production and Measurements With Particle Image Velocimetry for Recirculating Flows
,”
AIAA
Paper No. 2002-3090.
11.
Adeyinka
,
O. B.
, and
Naterer
,
G. F.
,
2004
, “
Modeling of Entropy Production in Turbulent Flows
,”
ASME J. Fluids Eng.
,
126
(
6
), pp.
503
507
.
12.
Kock
,
F.
, and
Herwig
,
H.
,
2004
, “
Local Entropy Production in Turbulent Shear Flows: A High-Reynolds Number Model With Wall Functions
,”
Int. J. Heat Mass Transfer
,
47
(
10–11
), pp.
2205
2215
.
13.
Sciubba
,
E.
,
1997
, “
Calculating Entropy With CFD
,”
Mech. Eng.
,
119
(
10
), pp.
86
88
.
14.
Alabi
,
K.
,
Ladeinde
,
F.
,
Vonspakovsky
,
M.
,
Moorhouse, D.
, and
Camberos, J.
,
2006
, “
Assessing CFD Modeling of Entropy Generation for the Air Frame Subsystem in an Integrated Aircraft Design/Synthesis Procedure
,”
AIAA
Paper No. 2006-587.
15.
Vicini
,
A.
, and
Quagliarella
,
D.
,
2012
, “
Inverse and Direct Airfoil Design Using a Multi-Objective Genetic Algorithm
,”
AIAA J.
,
35
(
9
), pp.
1499
1505
.
16.
Quagliarella
,
D.
, and
Cioppa
,
A. D.
,
2012
, “
Genetic Algorithms Applied to the Aerodynamic Design of Transonic Airfoils
,”
J. Aircr.
,
32
(
4
), pp.
889
991
.
17.
Goldberg
,
D. E.
,
1989
,
Genetic Algorithm in Search, Optimization, and Machine Learning,
Addison-Wesley, Boston, MA, pp.
2104
2116
.
18.
Rendall
,
T. C. S.
, and
Allen
,
C. B.
,
2008
, “
Unified Fluid–Structure Interpolation and Mesh Motion Using Radial Basis Functions
,”
Int. J. Numer. Methods Eng.
,
74
(
10
), pp.
1519
1559
.
19.
Poole
,
D. J.
,
Allen
,
C. B.
, and
Rendall
,
T.
,
2014
, “
Application of Control Point-Based Aerodynamic Shape Optimization to Two-Dimensional Drag Minimization
,”
AIAA
Paper No. 2014-0413.
20.
Sripawadkul
,
V.
,
Padulo
,
M.
, and
Guenov
,
M.
,
2010
, “
A Comparison of Airfoil Shape Parameterization Techniques for Early Design Optimization
,”
AIAA
Paper No. 2010-9050.
21.
Masters
,
D. A.
,
Taylor
,
N. J.
,
Rendall
,
T.
,
Allen
,
C. B.
, and
Poole
,
D. J.
, 2016, “
A Geometric Comparison of Aerofoil Shape Parameterisation Methods
,”
AIAA
Paper No. 2016-0558.
22.
Ceze
,
M.
,
Hayashi
,
M.
, and
Volpe
,
E.
,
2009
, “
A Study of the CST Parameterization Characteristics
,”
AIAA
Paper No. 2009-3767.
23.
Buhmann
,
M.
, 2003,
Radial Basis Functions
,
1st ed.
,
Cambridge University Press
,
Cambridge, UK
.
24.
Wendland
,
H.
, 2005,
Scattered Data Approximation
,
1st ed.
,
Cambridge University Press
,
Cambridge, UK
.
25.
Bejan
,
A.
,
2002
, “
Fundamentals of Exergy Analysis, Entropy Generation Minimization, and the Generation of Flow Architecture
,”
Int. J. Energy Res.
,
26
(
7
), pp.
545
565
.
26.
Herwig
,
H.
, and
Kock
,
F.
,
2007
, “
Direct and Indirect Methods of Calculating Entropy Generation Rates in Turbulent Convective Heat Transfer Problems
,”
Heat Mass Transfer
,
43
(
3
), pp.
207
215
.
27.
Patankar
,
S. V.
,
1981
, “
A Calculation Procedure for Two-Dimensional Elliptic Situations
,”
Numer. Heat Transfer Fundam.
,
4
(
4
), pp.
409
425
.
28.
Khosla
,
P. K.
, and
Rubin
,
S. G.
,
1974
, “
A Diagonally Dominant Second-Order Accurate Implicit Scheme
,”
Comput. Fluids
,
2
(
2
), pp.
207
209
.
29.
Murthy
,
S. R.
, and
Murthy
,
J. Y.
,
1997
, “
A Pressure-Based Method for Unstructured Meshes
,”
Numer. Heat Transfer, Part B
,
31
(
2
), pp.
195
215
.
30.
Stone
,
H. L.
,
1968
, “
Iterative Solution of Implicit Approximations of Multidimensional Partial Differential Equations
,”
SIAM J. Numer. Anal.
,
5
(
3
), pp.
530
558
.
31.
Rhie
,
C. M.
, and
Chow
,
W. L.
,
1983
, “
Numerical Study of the Turbulent Flow Past an Airfoil With Trailing Edge Separation
,”
AIAA J.
,
21
(
11
), pp.
1525
1532
.
32.
Gregory
,
N.
, and
O'Reilly
,
1970
, “
Low-Speed Aerodynamic Characteristics of NACA0012 Aerofoil Section, Including the Effects of Upper-Surface Roughness Simulating Hoar Frost
,”
Cheminform
,
23
(
48
), pp.
6697
6700
.
33.
Holland
,
J. H.
,
2015
, “
Adaptation in Natural and Artificial Systems
,”
Control Artif. Intell.
,
6
(
2
), pp.
126
137
.
34.
Deb
,
K.
,
Agrawal
,
S.
,
Pratap
,
A.
, and
Meyarivan, T.
,
2000
, “
A Fast Elitist Non-Dominated Sorting Genetic Algorithm for Multi-Objective Optimization: NSGA2
,”
Parallel Problem Solving From Nature VI Conference
,
Paris, France
,
Sept. 18–20
, pp.
849
858
.
35.
Luo
,
B.
,
Zheng
,
J.
,
Xie
,
J.
, and
Wu, J.
,
2008
, “
Dynamic Crowding Distance—A New Diversity Maintenance Strategy for MOEAs
,”
Fourth International Conference on Natural Computation
(
ICNC 2008
),
Jinan, China
,
Oct. 18–20
, pp.
580
585
.
36.
Cook
,
P. H.
,
McDonald
,
M. A.
, and
Firmin
,
M. C. P.
,
1979
, “
Aerofoil RAE2822 Pressure Distributions, and Boundary Layer and Wake Measurements
,” Experimental Data Base for Computer Program Assessment,
AGARD
Report No. AR 138.https://www.sto.nato.int/publications/AGARD/AGARD-AR-138/AGARD-AR-138.pdf
You do not currently have access to this content.