Skip to main content
SpringerLink
Log in

Robust design of natural laminar flow supercritical airfoil by multi-objective evolution method

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

A transonic, high Reynolds number natural laminar flow airfoil is designed and studied. The γ-θ transition model is combined with the shear stress transport (SST) k-w turbulence model to predict the transition region for a laminar-turbulent boundary layer. The non-uniform free-form deformation (NFFD) method based on the non-uniform rational B-spline (NURBS) basis function is introduced to the airfoil parameterization. The non-dominated sorting genetic algorithm-II (NSGA-II) is used as the search algorithm, and the surrogate model based on the Kriging models is introduced to improve the efficiency of the optimization system. The optimization system is set up based on the above technologies, and the robust design about the uncertainty of the Mach number is carried out for NASA0412 airfoil. The optimized airfoil is analyzed and compared with the original airfoil. The results show that natural laminar flow can be achieved on a supercritical airfoil to improve the aerodynamic characteristic of airfoils.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Eggleston, B., Poole, R. J. D., Jones, D. J., and Khalid, M. Thick supercritical airfoils with low drag and natural laminar flow. Journal of Aircraft, 24, 405–411 (1987)

    Article  Google Scholar 

  2. Viken, J. and Wagner, R. D. Design limits of compressible NLF airfoils. 29th Aerospace Sciences Meeting, AIAA Press, Nevada, 1–32 (1991)

    Google Scholar 

  3. Qiao, Z. D. Design of supercritical airfoils with natural laminar flow (in Chinese). Experiments and Measurements in Fluid Mechanics, 12, 23–30 (1998)

    Google Scholar 

  4. Langtry, R. B. A Correlation Based Transition Model Using Local Variables for Unstructured Parallelized CFD Codes, Ph. D. dissertation, Stuttgart University, 34–57 (2006)

    Google Scholar 

  5. Langtry, R. B. and Menter, F. R. Correlation-based transition modeling for unstructured parallelized computational fluid dynamics codes. AIAA Journal, 47, 2894–2906 (2009)

    Article  Google Scholar 

  6. Menter, F. R. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA Journal, 32, 1598–1605 (1994)

    Article  Google Scholar 

  7. Benini, E. Laminar to turbulent boundary layer transition investigation on a supercritical airfoil using the γ-θ transitional model. 40th Fluid Dynamics Conference and Exhibit, AIAA Press, Chicago, 1–12 (2010)

    Google Scholar 

  8. Sederberg, T. W. and Parry, S. R. Freeform deformation of solid geometric models. Computer Graphics, 22, 151–160 (1986)

    Article  Google Scholar 

  9. Zhu, X. X. Free Curve and Surface Modeling Techniques (in Chinese), Science Press, Beijing, 236–248 (2000)

    Google Scholar 

  10. Huang, J. T. Research on Aerodynamic Configuration Optimization Design Method and Applications (in Chinese), Ph. D. dissertation, Northwestern Polytechnical University, 123–130 (2012)

    Google Scholar 

  11. Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T. A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Transaction on Evolutionary Computation, 6, 181–197 (2002)

    Article  Google Scholar 

  12. Jeong, S., Murayama, M., and Yamamoto, K. Efficient optimization design method using Kriging model. Journal of Aircraft, 42, 413–420 (2005)

    Article  Google Scholar 

  13. Simpson, T. W., Mauery, T. M., Korte, J. J., and Mistree, F. Kriging models for global approximation in simulation-based multidisciplinary design optimization. AIAA Journal, 39, 2233–2241 (2001)

    Article  Google Scholar 

  14. Ding, J. F., Li, W. J., Zang, Y., and Tang, W. Robust airfoil optimization based on response surface method (in Chinese). Acta Aerodynamica Sinica, 25, 19–22 (2007)

    Google Scholar 

  15. Hung, J. T., Gao, Z. H., Zhao, K., and Bai, J. Q. Robust design of supercritical wing aerodynamic optimization considering fuselage interfering. Chinese Journal of Aeronautics, 13, 523–528 (2010)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Key Laboratory of Aerodynamic Design and Research, Northwestern Polytechnical University, Xi’an, 710072, P. R. China

    Ke Zhao  (赵 轲), Zheng-hong Gao  (高正红) & Jiang-tao Huang  (黄江涛)

  2. China Aerodynamics Research & Development Center, Mianyang, 621000, Sichuan Province, P. R. China

    Jiang-tao Huang  (黄江涛)

Authors
  1. Ke Zhao  (赵 轲)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zheng-hong Gao  (高正红)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jiang-tao Huang  (黄江涛)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ke Zhao  (赵 轲).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhao, K., Gao, Zh. & Huang, Jt. Robust design of natural laminar flow supercritical airfoil by multi-objective evolution method. Appl. Math. Mech.-Engl. Ed. 35, 191–202 (2014). https://doi.org/10.1007/s10483-014-1783-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-014-1783-6

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

Search

Navigation