New insight in Francis turbine cavitation vortex rope: role of the runner outlet flow swirl number

Arthur Favrel*, Joao Gomes Pereira Junior, Christian Landry, Andres Müller, Christophe Nicolet, François Avellan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

52 Citations (Scopus)


At part load operation, Francis turbines experience the development of a cavitation vortex rope in the draft tube, whose precession acts as a pressure excitation source. In case of resonance, the resulting pressure pulsations lead to unacceptable torque and power fluctuations on the prototype machine, putting at risk the system stability. However, the accurate prediction of resonance conditions at the prototype scale remains challenging since it requires a proper hydro-acoustic modelling of the draft tube cavitation flow. Furthermore, both the head and discharge values have an impact on the precession frequency of the vortex and the natural frequency of the system. The present paper demonstrates for the first time that the influence of both parameters on the frequencies of interest can be represented by a single parameter, the swirl number. Its analytical expression is derived as a function of the operating parameters of the machine. It is used to establish empirical laws enabling the determination of both frequencies and finally the operating parameters in resonance conditions on the complete part load operating range at the model scale. The methodology presented in this paper represents a decisive step towards the prediction of resonances on the complete part load operating range of the prototype.

Original languageEnglish
Pages (from-to)367-379
Number of pages13
JournalJournal of Hydraulic Research
Issue number3
Publication statusPublished - 2018 May 4
Externally publishedYes


  • Cavitation
  • Francis turbine
  • hydro-acoustic resonance
  • part load
  • swirl number
  • vortex rope

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Water Science and Technology


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