Multi-point design optimization of hydrofoil for marine current turbine


The comprehensive performance of the marine current turbine is an important issue in the ocean energy development. Its key is the performance of the hydrofoil, which is used to form the turbine blade. A multi-point optimization method of the hydrofoil is proposed in this paper. In this method, the Bezier curve is used to parameterize the hydrofoil. The geometrical parameters are used as variables while the lift-drag ratio and the cavitation performance of the hydrofoil are used as the objective functions. The Nsga-Ii algorithm is chosen as the optimization algorithm. In order to resolve the difficulty of this high-dimensional multi-objective optimization problem, the conception of the distance metric in the metric space is introduced to unify the lift-drag ratio and the cavitation performance under different working conditions. And then, the above optimization method is applied in the NACA63-815 hydrofoil’s optimal design under three typical conditions. Finally, the results from the performance comparison of the original and optimized hydrofoils obtained by using the CFD simulation are analyzed in detail. It is indicated that the optimized hydrofoils enjoy a better hydrodynamic performance than the original ones under the three conditions. The feasibility and the theoretical validity of this optimization method are confirmed by the results.

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


  1. [1]

    XU Chao. Research on hydrodynamics of marine current turbine’s hydrofoil blades based on lattice Boltzmann method[D]. Master Thesis, Qingdao, China: Ocean University of China, 2010(in Chinese).

    Google Scholar 

  2. [2]

    WANG Ying-ying, Research on lattice Boltzmann simulation on high Reynolds number flow around marine current turbine[D]. Master Thesis, Qingdao, China: Ocean University of China, 2011(in Chinese).

    Google Scholar 

  3. [3]

    HYUN B.-S., CHOI D.-H. and HAN J.-S. et al. Performance analysis and design of vertical axis tidal stream turbine[J]. Journal of Shipping and Ocean Engineering, 2012, 4(2): 191–200.

    Google Scholar 

  4. [4]

    LUZNIK L., FLACK K. A. and LUST E. E. et al. The effect of surface waves on the performance characteristics of a model tidal turbine[J]. Renewable Energy, 2012, 58: 108–114.

    Article  Google Scholar 

  5. [5]

    ZHAO Guang, YANG Ran-sheng and LIU Yan et al. Hydrodynamic performance of a vertical-axis tidal-current turbine with different preset angles of attack[J]. Journal of Hydrodynamics, 2013, 25(2): 280–287.

    Article  Google Scholar 

  6. [6]

    MA Sun, LI Wei and LIU Hong-wei et al. Experimental investigation of a horizontal axial tidal current energy conversion system[C]. International Ocean Energy Symposium 2009. Harbin, China, 2009, 32–36.

    Google Scholar 

  7. [7]

    GOUNDAR J. N., AHMED M. R. and LEE Y.-H. Numerical and experimental studies on hydrofoils for ma-rine current turbines[J]. Renewable Energy, 2012, 42: 173–179.

    Article  Google Scholar 

  8. [8]

    MOLLAND A. F., BAHAJ A. S. and CHAPLIN J. R. et al. Measurements and predictions of forces, pressures and cavitation on 2-D sections suitable for marine cur-rent turbines[J]. Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment, 2004, 218(2): 127–138.

    Google Scholar 

  9. [9]

    BAHAJ A. S., MOLLAND A. F. and CHAPLIN J. R. et al. Power and thrust measurements of marine current turbines under various hydrodynamic flow conditions in a cavitation tunnel and a towing tank[J]. Renewable Energy, 2007, 32(3): 407–426.

    Article  Google Scholar 

  10. [10]

    BATTEN W. M. J., BAHAJ A. S. and MOLLAND A. F. et al. The prediction of the hydrodynamic performance of marine current turbines[J]. Renewable Energy, 2008, 33(5): 1085–1096.

    Article  Google Scholar 

  11. [11]

    BATTEN W. M. J., BAHAJ A. S. and MOLLAND A. F. et al. Experimentally validated numerical method for the hydrodynamic design of horizontal axis tidal turbines[J]. Ocean Energy, 2007, 34(7): 1013–1020.

    Article  Google Scholar 

  12. [12]

    BAHAJ A. S., BATTEN W. M. J. and MCCANN G. Experimental verifications of numerical predictions for the hydrodynamic performance of horizontal axis marine current turbines[J]. Renewable Energy, 2007, 32(15): 2479–2490.

    Article  Google Scholar 

  13. [13]

    GRASSO F. Design and optimization of tidal turbine airfoil[C]. 29th Aiaa Applied Aerodynamics Con-ference. Honolulu, Hawaii, USA, 2011.

    Google Scholar 

  14. [14]

    YANG B., SHU X. W. Hydrofoil optimization and ex-perimental validation in helical vertical axis turbine for power generation from marine current[J]. Ocean Engineering, 2012, 42: 35–46.

    Article  Google Scholar 

  15. [15]

    COCKE T., MOSCICKI Z. and AGARWAL R. Optimization of hydrofoils using a genetic algorithm[C]. 30th Aiaa Applied Aerodynamics Conference. New Orleans, USA, 2012.

    Google Scholar 

  16. [16]

    GONG Mao-guo, JIAO Li-cheng and YANG Dongdong et al. Research on evolutionary multi-objective optimization algorithms[J]. Journal of Software, 2009, 20(2): 271–289(in Chinese).

    MathSciNet  Article  Google Scholar 

  17. [17]

    XUE Xiao-ping, SUN Li-min and WU Li-zhong. Applied functional analysis[M]. Beijing, China: Publishing House of Electronics Industry, 2006, 42–43(in Chinese).

    Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Xing-qi Luo 罗兴锜.

Additional information

Project supported by the Key Program of National Natural Science Foundation of China (Grant No. 51339005), the National Natural Science Foundation of China (Grant Nos. 51379174, 51279160) and the Doctoral Fund of Ministry of Education of China (Grant No. 20126118130002).

Biography: LUO Xing-qi (1962- ), Male, Ph. D., Professor

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Luo, X., Zhu, G. & Feng, J. Multi-point design optimization of hydrofoil for marine current turbine. J Hydrodyn 26, 807–817 (2014).

Download citation

Key words

  • marine current turbine
  • hydrofoil
  • multi-point optimization
  • metric space
  • NSGA-II algorithm