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Research Papers

Aerodynamic Optimization Design of Airfoil Shape Using Entropy Generation as an Objective

[+] Author and Article Information
Wei Wang, Xiao-Pei Yang, Yan-Yan Ding

School of Energy and Power Engineering,
Huazhong University of Science and Technology,
Wuhan, Hubei Province 430074, China

Jun Wang

China-EU Institute for Clean
and Renewable Energy,
Huazhong University of Science and Technology,
Wuhan, Hubei Province 430074, China;
School of Energy and Power Engineering,
Huazhong University of Science and Technology,
Wuhan, Hubei Province 430074, China
e-mail: wangjhust@hust.edu.cn

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received August 4, 2018; final manuscript received October 15, 2018; published online December 6, 2018. Assoc. Editor: Gerard F. Jones.

J. Thermal Sci. Eng. Appl 11(2), 021015 (Dec 06, 2018) (9 pages) Paper No: TSEA-18-1387; doi: 10.1115/1.4041793 History: Received August 04, 2018; Revised October 15, 2018

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.

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References

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.
Jahangirian, A. , and Shahrokhi, A. , 2011, “ Aerodynamic Shape Optimization Using Efficient Evolutionary Algorithms and Unstructured CFD Solver,” Comput. Fluids, 46(1), pp. 270–276. [CrossRef]
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.
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
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. [CrossRef]
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. [CrossRef]
Jin, Y. , Du, J. , Li, Z. , and Zhang, H. , 2017, “ Second-Law Analysis of Irreversible Losses in Gas Turbines,” Entropy, 19(9), p. 470. [CrossRef]
Bejan, A. , 1996, Entropy Generation Minimization, CRC Press, New York.
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.
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.
Adeyinka, O. B. , and Naterer, G. F. , 2004, “ Modeling of Entropy Production in Turbulent Flows,” ASME J. Fluids Eng., 126(6), pp. 503–507. [CrossRef]
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. [CrossRef]
Sciubba, E. , 1997, “ Calculating Entropy With CFD,” Mech. Eng., 119(10), pp. 86–88.
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.
Vicini, A. , and Quagliarella, D. , 2012, “ Inverse and Direct Airfoil Design Using a Multi-Objective Genetic Algorithm,” AIAA J., 35(9), pp. 1499–1505. [CrossRef]
Quagliarella, D. , and Cioppa, A. D. , 2012, “ Genetic Algorithms Applied to the Aerodynamic Design of Transonic Airfoils,” J. Aircr., 32(4), pp. 889–991. [CrossRef]
Goldberg, D. E. , 1989, Genetic Algorithm in Search, Optimization, and Machine Learning, Addison-Wesley, Boston, MA, pp. 2104–2116.
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. [CrossRef]
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.
Sripawadkul, V. , Padulo, M. , and Guenov, M. , 2010, “ A Comparison of Airfoil Shape Parameterization Techniques for Early Design Optimization,” AIAA Paper No. 2010-9050.
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.
Ceze, M. , Hayashi, M. , and Volpe, E. , 2009, “ A Study of the CST Parameterization Characteristics,” AIAA Paper No. 2009-3767.
Buhmann, M. , 2003, Radial Basis Functions, 1st ed., Cambridge University Press, Cambridge, UK.
Wendland, H. , 2005, Scattered Data Approximation, 1st ed., Cambridge University Press, Cambridge, UK.
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.
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. [CrossRef]
Patankar, S. V. , 1981, “ A Calculation Procedure for Two-Dimensional Elliptic Situations,” Numer. Heat Transfer Fundam., 4(4), pp. 409–425.
Khosla, P. K. , and Rubin, S. G. , 1974, “ A Diagonally Dominant Second-Order Accurate Implicit Scheme,” Comput. Fluids, 2(2), pp. 207–209. [CrossRef]
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. [CrossRef]
Stone, H. L. , 1968, “ Iterative Solution of Implicit Approximations of Multidimensional Partial Differential Equations,” SIAM J. Numer. Anal., 5(3), pp. 530–558. [CrossRef]
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. [CrossRef]
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.
Holland, J. H. , 2015, “ Adaptation in Natural and Artificial Systems,” Control Artif. Intell., 6(2), pp. 126–137.
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.
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.
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

Figures

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Fig. 1

Class-shape function transform method's geometric parameters for airfoil parameterization

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Fig. 2

RAE2822 and NACA0012 parameterized by seven design variables

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Fig. 3

Computational domain around the airfoil: (a) complete grid and (b) fine grid around airfoil

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Fig. 4

Deformed meshes for RAE2822 and NACA0012 airfoils: (a) RAE2822 and (b) NACA0012 at 15 angle-of-attack

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Fig. 5

Comparisons of pressure distributions on NACA0012 at different angle-of-attack

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Fig. 6

Streamlines and contours of log(s•gen) at different angle-of-attack

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Fig. 7

Flowchart of the optimization iteration

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Fig. 8

Population distribution in optimization procedure based on entropy generation and lift-drag ratio

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Fig. 9

Pareto curve of the airfoil shapes optimization based on entropy generation and lift-drag ratio: (a) pressure contours and (b) log(s•gen)contours

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Fig. 10

Configuration and pressure distribution of three representative members of the Pareto front based on entropy generation and lift-drag ratio: (a) configuration and (b) pressure distribution

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Fig. 11

Local mesh of RAE2822

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Fig. 12

Comparison of pressure distributions on RAE2822

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Fig. 13

Pareto curve of the airfoil shapes optimization based on entropy generation and lift-drag ratio: (a) pressure contours and (b) log(s•gen)contours

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Fig. 14

Configuration and pressure distribution of four representative members of the Pareto front: (a) configuration and (b) pressure distribution

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