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

Denis V. Chirkov, Anna S. Ankudinova, Artem E. Kryukov, Sergey G. Cherny, Vladimir A. Skorospelov

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)627-640
Number of pages14
JournalStructural and Multidisciplinary Optimization
Issue number2
Publication statusPublished - Aug 2018


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


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