Experiments in Fluids

, 55:1849 | Cite as

Mind the gap: a new insight into the tip leakage vortex using stereo-PIV

  • Matthieu DreyerEmail author
  • Jean Decaix
  • Cécile Münch-Alligné
  • Mohamed Farhat
Research Article


The tip leakage vortex (TLV), which develops in the clearance between the rotor and the stator of axial hydro turbines, has been studied for decades. Yet, many associated phenomena are still not understood. For instance, it remains unclear how the clearance size is related to the occurrence of cavitation in the vortex, which can lead to severe erosion. Experiments are here carried out on the influence of the clearance size on the tip vortex structure in a simplified case study. A NACA0009 hydrofoil is used as a generic blade in a water tunnel while the clearance between the blade tip and the wall is varied. The 3D velocity fields are measured using Stereo Particle Image Velocimetry (SPIV) in three planes located downstream of the hydrofoil for different values of the upstream velocity, the incidence angle and a large number of tip clearances. The influence of the flow conditions on the structure of the TLV is described through changes in the vortex intensity, core axial flow, vortex center position and wandering motion amplitude. Moreover, high-speed visualizations are used to highlight the vortex core trajectory and clearance flow alteration, turning into a wall jet as the tip clearance is reduced. The measurements clearly reveal the existence of a specific tip clearance for which the vortex strength is maximum and most prone to generating cavitation.


Vortex Cavitation Vortex Core Inlet Velocity Vortex Center 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols


Hydrofoil chord


Maximum foil thickness

\(W_{\infty }\)

Inlet velocity

\(p_{\infty }\)

Inlet pressure


Cartesian coordinates


Spanwise, transverse and axial velocity

\(x_\text {c}, y_\text {c}\)

Vortex center coordinates

\(r_{\rm c}\)

Vortex core radius

\(Re_\text {c}\)

Reynolds number \(({W_{\infty }c}/{\nu })\)


Incidence angle


Normalized tip clearance \((gap/h)\)





\(\varGamma ^*\)

Normalized circulation \((\varGamma /W_{\infty } r_{\rm c})\)

\(\varGamma ^*_{\infty }\)

\(\varGamma ^*\) at \(\tau\) = 2

\(C_{\rm p_{\rm min}}\)

Pressure coefficient in the vortex center \(\left(\frac{p(r\,=\,0)\,-\,p_{\infty }}{\frac{1}{2}\rho W_{\infty }^2}\right)\)



The present study was performed within the framework of the HydroNet project ( The authors would like to thank the Competence Center of Energy and Mobility (CCEM) and swisselectric research for their financial support.

Supplementary material

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Matthieu Dreyer
    • 1
    Email author
  • Jean Decaix
    • 2
  • Cécile Münch-Alligné
    • 2
  • Mohamed Farhat
    • 1
  1. 1.Laboratory for Hydraulic MachinesEcole polytechnique fédérale de LausanneLausanneSwitzerland
  2. 2.Institut Systèmes industrielsHES-SO Valais-WallisSionSwitzerland

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