Skip to main content
Skip to article control options
No AccessFull-Length Paper

Efficient Global Optimization of Vortex Generators on a Supercritical Infinite Wing

Published Online:

Multi-objective optimization of vortex generators on a transonic infinite wing is performed using computational fluid dynamics and a multi-objective genetic algorithm coupled with surrogate models. Vortex generator arrangements are defined by five design variables: height, length, incidence angle, chord location, and spacing. The objective functions are to maximize the lift-to-drag ratio at low angle of attack, to maximize lift coefficient at high angle of attack, and to the shift chordwise separation location downstream at high angle of attack. To evaluate these objective functions of each individual in the multi-objective genetic algorithm, the ordinary kriging surrogate model and the radial-basis-function/kriging hybrid surrogate model are employed because numerical analysis of the wing with vortex generators requires a large amount of computational time. Nondominated solutions are classified into five clusters with different aerodynamic characteristics. Comparison of the five clusters revealed that the balance among three objective functions is controlled mainly by vortex generator height, spacing, and their ratio. The solutions in each cluster have specific values of these three parameters, which identify the aerodynamic characteristics. In addition, appropriate values of design variables for generating the vortex most effectively are investigated.


  • [1] Wik E. and Shaw S. T., “Numerical Simulation of Micro Vortex Generators,” 2nd AIAA Flow Control Conference, AIAA Paper  2004-2697, June–July 2004. LinkGoogle Scholar

  • [2] Spalart P. R. and Allmaras S. R., “A One-Equation Turbulence Model for Aerodynamic Flows,” Recherche Aerospatiale, Vol. 1, 1994, pp. 5–21. REARAU Google Scholar

  • [3] Dacles-Mariani J., Zilliac G. G., Chow J. S. and Bradshaw P., “Numerical/Experimental Study of a Wingtip Vortex in the Near Field,” AIAA Journal, Vol. 33, No. 9, 1995, pp. 1561–1568. doi: AIAJAH 0001-1452 LinkGoogle Scholar

  • [4] Menter F. R., “Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications,” AIAA Journal, Vol. 32, No. 8, 1994, pp. 1598–1605. doi: AIAJAH 0001-1452 LinkGoogle Scholar

  • [5] Bur R., Coponet D. and Carpels Y., “Separation Control by Vortex Generator Devices in a Transonic Channel,” Shock Waves, Vol. 19, No. 6, 2009, pp. 521–530. doi: SHWAEN 0938-1287 CrossrefGoogle Scholar

  • [6] Huang J., Fu S., Xiao Z. and Zhang M., “Study of Separation Control of Vortex Generators on Transonic Wings,” Journal of Fluid Science and Technology, Vol. 6, No. 1, 2011, pp. 85–97. doi: CrossrefGoogle Scholar

  • [7] Dandois J., Brunet V., Molton P., Abart J.-C. and Lepage A., “Buffet Control by Means of Mechanical and Fluidic Vortex Generators,” 5th AIAA Flow Control Conference, AIAA Paper  2010-4975, June–July 2010. LinkGoogle Scholar

  • [8] Bender E. E., Anderson B. H. and Yagle P. J., “Vortex Generator Modeling for Navier–Stokes Codes,” Proceedings of the 3rd Joint ASME/JSME Fluids Engineering Conference, ASME Paper FEDSM99-6919, New York, July 1999. Google Scholar

  • [9] Lee B. J., Kumano T. and Liou M. S., “Design Exploration for Vortex Generators for Boundary-Layer-Ingesting Inlet,” 13th AIAA/ISSMO Multidisciplinary Analysis Optimization Conference, AIAA Paper  2010-9399, Sept. 2010. LinkGoogle Scholar

  • [10] Namura N. and Jeong S., “Parametric Study of Vortex Generators on a Super Critical Infinite-Wing to Alleviate Shock-Induced Separation,” Transactions of the Japan Society for Aeronautical and Space Sciences, Vol. 56, No. 5, 2013, pp. 293–302. doi: TJASAM 0549-3811 CrossrefGoogle Scholar

  • [11] Ito Y., Murayama M. and Yamamoto K., “High-Quality Unstructured Hybrid Mesh Generation for Capturing Effects of Vortex Generators,” 51st AIAA Aerospace Sciences Meeting, AIAA Paper  2013-0554, Jan. 2013. LinkGoogle Scholar

  • [12] Koike S., Sato M., Kanda H., Nakajima T., Nakakita K., Kusunose K., Murayama M., Ito Y. and Yamamoto K., “Experiment of Vortex Generators on NASA SC(2)-0518 Two Dimensional Wing for Buffet Reduction,” Proceedings of the 2013 Asia-Pacific International Symposium on Aerospace Technology, The Japan Soc. for Aeronautical and Space Sciences, Tokyo, Japan, 2013. Google Scholar

  • [13] Koike S., Nakakita K., Nakajima T., Koga S., Sato M., Kanda H., Kusunose K., Murayama M., Ito Y. and Yamamoto K., “Experimental Investigation of Vortex Generator Effect on Two- and Three-Dimensional NASA Common Research Models,” 53rd AIAA Aerospace Sciences Meeting, AIAA Paper  2015-1237, 2015. LinkGoogle Scholar

  • [14] Deb K., Multi-Objective Optimization Using Evolutionary Algorithms, Wiley, Chichester, U.K., 2001, pp. 245–247. Google Scholar

  • [15] Jones D. R., Schonlau M. and Welch W. J., “Efficient Global Optimization of Expensive Black-Box Function,” Journal of Global Optimization, Vol. 13, Dec. 1998, pp. 455–492. doi: JGOPEO 0925-5001 CrossrefGoogle Scholar

  • [16] Namura N., Shimoyama K., Jeong S. and Obayashi S., “Kriging/RBF-Hybrid Response Surface Methodology for Highly Nonlinear Functions,” Journal of Computational Science and Technology, Vol. 6, No. 3, 2012, pp. 81–96. doi: CrossrefGoogle Scholar

  • [17] Baker J. E., “Adaptive Selection Methods for Genetic Algorithms,” Proceedings of the International Conference on Genetic Algorithms and Their Applications, Lawrence Erlbaum Associates, Inc., Hillsdale, NJ, 1985, pp. 101–111. Google Scholar

  • [18] Deb K. and Agrawal R. B., “Simulated Binary Crossover for Continuous Search Space,” Complex Systems, Vol. 9, No. 2, 1995, pp. 114–148. CPSYEN 0891-2513 Google Scholar

  • [19] Deb K. and Goyal M., “A Combined Genetic Adaptive Search (GeneAS) for Engineering Design,” Computer Science and Informatics, Vol. 26, No. 4, 1996, pp. 30–45. CSINET Google Scholar

  • [20] Deb K., Pratap A., Agarwal S. and Meyarivan T., “A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II,” IEEE Transactions on Evolutionary Computation, Vol. 6, No. 2, 2002, pp. 182–197. doi: ITEVF5 1089-778X CrossrefGoogle Scholar

  • [21] Obayashi S. and Guruswamy G. P., “Convergence Acceleration of an Aeroelastic Navier–Stokes Solver,” AIAA Journal, Vol. 33, No. 6, 1994, pp. 1134–1141. AIAJAH 0001-1452 LinkGoogle Scholar

  • [22] Venkatakrishnan V., “Convergence to Steady State Solutions of the Euler Equations on Unstructured Grids with Limiters,” Journal of Computational Physics, Vol. 118, No. 1, 1995, pp. 120–130. doi: CrossrefGoogle Scholar

  • [23] Sharov D. and Nakahashi K., “Reordering of Hybrid Unstructured Grids for Lower–Upper Symmetric Gauss–Seidel Computations,” AIAA Journal, Vol. 36, No. 3, 1998, pp. 484–486. doi: AIAJAH 0001-1452 LinkGoogle Scholar

  • [24] Aupoix B. and Spalart P. R., “Extensions of the Spalart–Allmaras Turbulence Model to Account for Wall Roughness,” International Journal of Heat and Fluid Flow, Vol. 24, No. 4, 2003, pp. 454–462. doi: IJHFD2 0142-727X CrossrefGoogle Scholar

  • [25] Vassberg J., Dehaan M., Rivers M. and Wahls R., “Development of a Common Research Model for Applied CFD Validation Studies,” 26th AIAA Applied Aerodynamics Conference, AIAA Paper  2008-6919, Aug. 2008. LinkGoogle Scholar

  • [26] CRM.65.Airfoil Sections,” NASA, [retrieved 24 Jan. 2016]. Google Scholar

  • [27] Ito Y. and Nakahashi K., “Direct Surface Triangulation Using Stereolithography Data,” AIAA Journal, Vol. 40, No. 3, 2002, pp. 490–496. doi: AIAJAH 0001-1452 LinkGoogle Scholar

  • [28] Sharov D. and Nakahashi K., “Hybrid Prismatic/Tetrahedral Grid Generation for Viscous Flow Applications,” AIAA Journal, Vol. 36, No. 2, 1998, pp. 157–162. doi: AIAJAH 0001-1452 LinkGoogle Scholar

  • [29] Ito Y. and Nakahashi K., “Unstructured Mesh Generation for Viscous Flow Computations,” Proceedings of the 11th International Meshing Roundtable, Springer–Verlag, Berlin, Sept. 2002, pp. 367–378. Google Scholar

  • [30] Ito Y. and Nakahashi K., “Surface Triangulation for Polygonal Models Based on CAD Data,” International Journal for Numerical Methods in Fluids, Vol. 39, No. 1, 2002, pp. 75–96. doi: IJNFDW 0271-2091 CrossrefGoogle Scholar

  • [31] Vortex Generators for Control of Shock-Induced Separation. Part 1: Introduction and Aerodynamics,” Engineering Sciences and Data Unit, Rept.  93024, London, U.K., 1993. Google Scholar

  • [32] Vortex Generators for Control of Shock-Induced Separation. Part 2: Guide to Use of Vane Vortex Generators,” Engineering Sciences and Data Unit, Rept.  93025, London, U.K., 1994. Google Scholar

  • [33] Vortex Generators for Control of Shock-Induced Separation. Part 3: Example of Applications of Vortex Generators to Aircraft,” Engineering Sciences and Data Unit, Rept.  93026, London, U.K., 1995. Google Scholar

  • [34] McKay M. D., Beckman R. J. and Conover W. J., “A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code,” Technometrics, Vol. 21, No. 2, 1979, pp. 239–245. doi: TCMTA2 0040-1706 CrossrefGoogle Scholar

  • [35] Jain A. K., Murty M. N. and Flynn P. J., “Data Clustering: A Review,” ACM Computing Surveys, Vol. 31, No. 3, 1999, pp. 264–323. doi: ACSUEY 0360-0300 CrossrefGoogle Scholar

  • [36] Kohonen T., Self-Organizing Maps, Springer, Berlin, 1995, pp. 1–261. CrossrefGoogle Scholar