An improved formula for determination of secondary energy losses in the runner of Kaplan turbine


Secondary losses have impacts on the overall efficiency of a Kaplan turbine.

Runner radial gaps and blade-to-blade complex flow induce secondary losses.

The existing semi empirical formula for the loss determination was improved.

The formerly proposed constant coefficient is introduced as a variable one.

The novel coefficient depends on blade opening angles and turbine operating modes.


Secondary losses, which occur during the energy transfer process in axial turbomachinery, have been the subject of investigation for a long time. So far, much more attention has been naturally paid to the research of the phenomenon in gas and steam turbines than in hydraulic turbines. In the paper, the profile and secondary energy losses in the Kaplan turbine runner were considered by the comprehensive numerical simulations using two turbulence models and by the available experimental data of the blade profiles’ characteristics. The performed research provides a contribution to better determination of secondary losses in the engineering practice, its distributions and participations in the total turbine losses for a wide range of on-cam operating modes. According to the proposed methodology and the obtained results, the improvement of the existing formula has been done thus enabling more accurate quantifying of secondary losses in the runner of the axial hydraulic turbine.


  • Secondary losses;
  • Runner;
  • Kaplan turbine;
  • Numerical simulations

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