Fast S-shape CFX Method

S-shape calculation time reduction


Using the same efficient physical models, a fast numerical method has been developed to compute the S-shape of pump-turbine designs. This method uses criteria based on flow parameters calculated from steady CFX calculations which require relatively few computational resources. These criteria make it possible to correctly select the position of certain important operating points in the S-shape, such as the point of maximum reduced speed n11. Then the selected points are calculated thanks to the adequate unsteady simulations, making it possible to get the accurate position of the characteristic. Computational time is optimised and unsteady CFX simulations are only focused on the essential operating points of the S-shape.
Compared to the complete unsteady calculation approach, the differences between simulations and experimental results increase slightly but still allow for all relative studies.

With this new method, the time needed to estimate the S-shape is divided by around 3. A quick comparison between different hydraulic designs (runner, guide vanes, etc.) is now possible before the scaled model tests in order to pre-select the design with the least pronounced S-shape. Finally, to further optimise time, the method has been automated with a user interface software (Scilab).




  • Faster S-shape estimation
  • Runner comparison and classification
  • Money saving


  • Pump-turbine runner design


  • User Interface Software
  • Technical reports
  • Technical training upon request
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