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Multi-objective shape optimization of a hydraulic turbine runner using efficiency, strength and weight criteria


An approach for multi-discipline automatic optimization of the hydraulic turbine runner shape is presented. The approach accounts hydraulic efficiency, mechanical strength and the weight of the runner. In order to effectively control the strength and weight of the runner, a new parameterization of the blade thickness function is suggested. Turbine efficiency is evaluated through numerical solution of Reynolds-averaged Navier-Stokes equations, while the finite element method is used to evaluate the von Mises stress in the runner. An objective function, being the weighted sum of maximal stress and the blade volume, is suggested to account for both the strength and weight of the runner. Multi-objective genetic algorithm is used to solve the optimization problem. The suggested approach has been applied to automatic design of a Francis turbine runner. Series of three-objective optimization runs have been carried out. The obtained results clearly indicate that simultaneous account of stress and weight objectives accompanied by thickness variation allows obtaining high efficiency, light and durable turbine runners.

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  1. Bannikov DV, Yesipov DV, Cherny SG, Chirkov DV (2010) Optimization design of hydroturbine rotors according to the efficiency-strength criteria. Thermophys Aeromech 17(4):613–620.

    Article  Google Scholar 

  2. Cherny SG, Chirkov DV, Lapin VN, Lobareva IF, Sharov SV, Skorospelov VA (2006a) 3D Euler flow simulation in hydro turbines: unsteady analysis and automatic design. In: Shokin Y, Resch M, Shokina N, Danaev N, Orunkhanov M (eds) Advances in High Performance Computing and Computational Sciences. Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM), vol 93. p 33–51. Springer: Heidelberg.

  3. Cherny SG, Chirkov DV, Lapin VN, Skorospelov VA, Turuk PA (2006b) Numerical simulation of a turbulent flow in Francis hydroturbine. Russ J Numer Anal Math Model 21(5):425–446.

    MathSciNet  Article  MATH  Google Scholar 

  4. Cherny SG, Bannikov DV, Chirkov DV, Demianov VA, Pylev IM, Skorospelov VA, Stepanov VN (2008) Automatic optimal shape design of hydroturbine flow passage. In: Proceedings of Hydro 2008, Ljubljana, Slovenia

  5. Enomoto Y, Kurosawa S, Kawajiri H (2012) Design optimization of a high specific speed Francis turbine runner. IOP Conference Series: Earth and Environmental Science, vol 15. p 032010.

  6. Ferrando L (2005) Surface parameterization and optimum design methodology for hydraulic turbines. PhD Thesis EPFL No. 3448

  7. Flores E, Bornard L, Tomas L, Liu J, Couston M (2012) Design of large Francis turbine using optimal methods. IOP Conference Series: Earth and Environmental Science, vol 15. p 022023.

  8. Fonseca CM, Fleming PJ (1993) Genetic algorithms for multiobjective optimization: formulation, discussion and generalization. In: Proc. 5th Intern. Conf. on Genetic Algorithms. p 416-423.

  9. Georgopoulou HA, Kyriacou SA, Giannakoglou KC, Grafenberger P, Parkinson E (2008) Constrained multi-objective design optimization of hydraulic components using a hierarchical metamodel assisted evolutionary algorithm. Part 1: Theory. In: Proc. of 24th IAHR Symposium on hydraulic machinery and systems

  10. Horn J, Nafpliotis N (1993) Multiobjective optimization using niched Pareto algorithm. IlliGAL Rep. 93005. Urbana: University of Illinois.

  11. Hu W, Choi KK, Cho H (2016) Reliability-based design optimization of wind turbine blades for fatigue life under dynamic wind load uncertainty. Struct Multidiscip Optim 54:953–970.

    Article  Google Scholar 

  12. Joly MM, Verstraete T, Paniagua G (2014) Multidisciplinary design optimization of a compact highly loaded fan. Struct Multidiscip Optim 49:471–483.

    Article  Google Scholar 

  13. Kurosawa S, Nakamura K (2009) Design optimization of a high specific speed Francis turbine using multi-objective genetic algorithm. Int J Fluid Mach Syst 2(2):102–109.

    Article  Google Scholar 

  14. Liao CC, Zhao XL, Xu JZ (2012) Blade layers optimization of wind turbines using FAST and improved PSO. Renew Energy 42:227–233

    Article  Google Scholar 

  15. Lyutov AE, Chirkov DV, Skorospelov VA, Turuk PA, Cherny SG (2015) Coupled multipoint shape optimization of runner and draft tube of hydraulic turbines. J Fluids Eng 137:111302.

    Article  Google Scholar 

  16. Marjavaara B, Lundström T (2007) Hydraulic turbine diffuser shape optimization by multiple surrogate model approximations of Pareto fronts. ASME J Fluids Eng 129(9):1228–1240.

    Article  Google Scholar 

  17. Mazzouji F, Couston M, Ferrando L, Garsia F, Debeissat F (2004) Multicriteria optimization viscous fluid analysis – mechanical analysis. In: Proceedings of 22nd IAHR symposium on hydraulic machinery and systems, Stockholm

  18. Panov LV, Chirkov DV, Cherny SG, Pylev IM, Sotnikov AA (2012) Numerical simulation of steady cavitating flow of viscous fluid in a Francis hydroturbine. Thermophys Aeromech 19(3):415–427.

    Article  Google Scholar 

  19. Pierret S, Filomeno Coelho R, Kato H (2007) Multidisciplinary and multiple operating points shape optimization of three-dimensional compressor blades. Struct Multidiscip Optim 33:61–70.

    Article  Google Scholar 

  20. Risberg S, Jonassen M, Jonassen R (2008) Design of Francis turbine runners based on a surrogate model approach. Hydropower Dams 15(5)

  21. Rogers S, Kwak D, Kiris C (1991) Steady and unsteady solutions of the incompressible Navier-stokes equations. AIAA J 29(4):603–610

    Article  Google Scholar 

  22. Semenova A, Chirkov D, Lyutov A, Cherny S, Skorospelov V, Pylev I (2014) Multi-objective shape optimization of runner blade for Kaplan turbine. IOP conference series: earth and environmental science, vol 22. IOP Publishing, p 012025.

  23. Stadler D, Celic D (2015) Structure and fluid optimization of the guide vane blade with the decomposition of the optimization problem. Struct Multidiscip Optim 51:213–223.

    Article  Google Scholar 

  24. Wang L, Wang T, Luo Y (2011) Improved non-dominated sorting genetic algorithm (NSGA)-II in multi-objective optimization studies of wind turbine blades. Appl Math Mech 32:739–748.

    Article  MATH  Google Scholar 

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The work was done in the framework of state assignment for the Institute of Computational Technologies of Siberian Branch of Russian Academy of Sciences (topic No. 0316-2015-0001).

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Correspondence to Denis V. Chirkov.

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Chirkov, D.V., Ankudinova, A.S., Kryukov, A.E. et al. Multi-objective shape optimization of a hydraulic turbine runner using efficiency, strength and weight criteria. Struct Multidisc Optim 58, 627–640 (2018).

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  • Hydraulic turbine runner
  • Thickness function
  • Three-dimensional flow simulation
  • Finite element analysis
  • Genetic algorithm