A numerical optimization chain combining computational fluid dynamics and surrogate analysis for the aerodynamic design of airfoils

Abstract

The aim of this study is to present a fully automated computational fluid dynamics-based optimization chain, implementing a radial basis function meta-model combined with an improved Latin hypercube design of experiments strategy. The objective function (aerodynamic performance) is evaluated through computational fluid dynamics calculations by using the commercial code ANSYS-CFX. The optimization strategy is hybridization between a stochastic bi-objective non-dominated sorting genetic algorithm and a gradient-based method known as modified method of feasible direction to get benefit from their combined capabilities. The testing of this optimization chain consisted in finding the optimal operating conditions of an airfoil NACA0012. This methodology may help to a great extent in the better exploration of the design space and to guide numerical and experimental studies to the potentially optimal design parameters.

Keywords

Optimization radial basis function design of experiments Latin hypercube sampling computational fluid dynamics aerodynamic airfoil

Get full access to this article

View all access options for this article.

References

Ahuja V and Hosangadi A. Design optimization of complex flow fields using evolutionary algorithms and hybrid unstructured CFD. In: 17th AIAA computational fluid dynamics conference, Toronto, ON, Canada, 6–9 June 2005, paper no. AIAA-2005-4984.

Pierret S. Multi-objective optimization of three-dimensional turbomachinery blades. In: International conference on computational methods for coupled problems in science and engineering, Santorini Island, Greece, 25–28 May 2005.

Pagano A, Federico L, Barbarino M, et al. Multi-objective aeroacoustic optimization of an aircraft propeller. In: 12th AIAA/ISSMO multidisciplinary analysis and optimization conference, Victoria, BC, Canada, 10–12 September 2008.

Queipo

Haftka

Shyy

. Surrogate-based analysis and optimisation. Prog Aerospace Sci 2005; 41: 1–28.

Trigg

Tubby

Sheard

. Automatic genetic optimization approach to two-dimensional blade profile design for steam turbines. J Turbomach 1999; 121: 11–17.

Ahn

Kim

. Aerodynamic design optimization of a compressor rotor with Navier-Stokes analysis. Proc IMechE, Part A: J Power and Energy 2003; 217(2): 179–183.

Pierret S. Multi-objective and multi-disciplinary optimization of three-dimensional turbomachinery blades. In: 6th world congresses of structural and multidisciplinary optimization, Rio de Janeiro, Brazil, 30 May–3 June 2005.

Pierret

Filomeno Coelho

Kato

. Multi-disciplinary and multiple operating points shape optimization of three-dimensional compressor blades. Struct Multidisc Optim 2007; 33(1): 61–70.

Jin-Hyuk Kim, Jae-Ho Choi and Kwang-Yong Kim. Design optimization of a centrifugal compressor impeller using radial basis neural network method. In: Proceedings of ASME Turbo Expo 2009: power for land, sea and air, Orlando, FL, 8–12 June 2009, paper no. GT2009-59666, pp. 443–451.

10.

Samad A, Kwang-Yong Kim KY, Goel T, et al. Shape optimization of turbomachinery blade using multiple surrogate models. In: ASME 2006, 2nd joint U.S.-European fluids engineering summer meeting collocated with the 14th internation conference on nuclear engineering, Miami, FL, 17–20 July, pp. 827–836.

11.

Samad

Kim

. Application of surrogate modeling to design of a compressor blade to optimize staking and thickness. Int J Fluid Mach Syst 2009; 2(1): 1–12.

12.

Marinus BG, Roger M and Van den Braembussche RA. Aeroacoustic and aerodynamic optimization of aircraft propeller blades. In: 16th AIAA/CEAS aeroacoustics conference, Stockholm, Sweden, 7–9 June 2010.

13.

Massaro

Benini

. Multi-objective optimization of helicopter airfoils using surrogate-assisted memetic algorithms. J Aircraft 2012; 49(2): 375–383.

14.

Jin

Chen

Simpson

. Comparative studies of meta-modeling techniques under multiple modeling criteria. Struct Multidisc Optim 2001; 23: 1–13.

15.

Laurenceau

Sagaut

. Building efficient response surfaces of aerodynamic functions with Kriging and Cokriging. AIAA J 2008; 46(2): 498–507.

16.

Hardy

. Multiquadric equations of topography and other irregular surfaces. J Geophys Res 1971; 76: 1905–1915.

17.

Dyn

Interpolation of scattered data by radial function. In: Chui

Schumaker

Utreras

(eds). Topics in multivariate approximation, New York: Academic Press, 1987, pp. 47–61.

18.

Haykin

. Neural networks: a comprehensive foundation, Englewood Cliffs, NJ: Prentice-Hall, 1999.

19.

Dale

McDonald Walter

Grantham Wayne

Tabor . Global and local optimization using radial basis function response surface models. Appl Math Model 2007; 31: 2095–2110.

20.

Fang

Winker

. Uniform design: theory and application. Technometrics 2000; 42(3): 237–248.

21.

Simpson

Lin

DKJ

Chen

. Sampling strategies for computer experiments: design and analysis. Int J Reliabil Appl 2001; 2(3): 209–240.

22.

Beiqing Huang Xiaoping Du . Analytical robustness assessment for robust design. Struct Multidisc Optim 2007; 34: 123–137.

23.

Mckay

Beckman

Conover

. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 1979; 21: 239–245.

24.

Iman

Conover

. Small sensitivity analysis techniques for computer models with an application to risk assessment. Commun Stat Theory Methods 1980; A9(17): 1749–1842.

25.

Gary Wang

. Adaptive response surface method using inherited Latin hypercube design points. J Mech Des 2003; 125: 210–220.

26.

Sacks

Welch

Mitchell

. Design and analysis of computer experiments. Stat Sci 1989; 4(4): 409–423.

27.

Manteufel RD. Distributed hypercube sampling algorithm. In: 42nd structures, structural dynamics, and materials conference, Seattle, WA, 16–19 April 2001, paper no. AIAA-2001-1673.

28.

Pleming JB and Manteufel RD. Replicated Latin hypercube sampling. In: 46th AIAA/ASME/ASCE/AHS/ASC, structures, structural dynamics and materials conference, Austin, Texas, 16–21 April 2005.

29.

Ramu

Prabhu Raja

Thyla

. Design optimization of complex structures using meta-models. Jordan J Mech Indus Eng Des 2010; 4(5): 653–664.

30.

Beachkofski B and Grandhi R. Improved distributed hypercube sampling. AIAA-paper no. 2002-1274, 2002.

31.

Gambit 2.4.6. Fluent Inc, 1988-2012.

32.

ANSYS-CFX. Release 12.0. ANSYS, Inc.

33.

Nemec M, Aftosmis M and Pulliam T. CAD-based aerodynamic design of complex conﬁgurations using a Cartesian method. In: 42nd AIAA aerospace sciences meeting, Reno, NV, 5–8 January 2004, pp. 82–86.

34.

Vanderplaats GN. CONMIN FORTRAN program for constrained function minimization, NASA TM X-62,282 reprint 1991.

35.

Deb

Pratap

Agarwal

. A fast elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 2002; 6(2): 182–197.

36.

Sheldahl RE and Klimas PC. Aerodynamic characteristics of seven airfoil sections through 180 degrees angle of attack for use in aerodynamic analysis of vertical axis wind turbines, SAND80-2114. Albuquerque, New Mexico: Sandia National Laboratories, March 1981.

37.

Mellen

Fröhlich

Rodi

. Lessons from LESFOIL project on large-eddy simulation of flow around an airfoil. AIAA J 2003; 41(4): 573–581.