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

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Abstract

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.

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Abbreviations

\(c\) :

Hydrofoil chord

\(h\) :

Maximum foil thickness

\(W_{\infty }\) :

Inlet velocity

\(p_{\infty }\) :

Inlet pressure

\(x,y,z\) :

Cartesian coordinates

\(u,v,w\) :

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

\(\alpha\) :

Incidence angle

\(\tau\) :

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

\(\omega\) :

Vorticity

\(\varGamma\) :

Circulation

\(\varGamma ^*\) :

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 \(\left(\frac{p(r\,=\,0)\,-\,p_{\infty }}{\frac{1}{2}\rho W_{\infty }^2}\right)\)

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Acknowledgments

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

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Authors and Affiliations

  1. Laboratory for Hydraulic Machines, Ecole polytechnique fédérale de Lausanne, Av. de Cour 33 bis, 1007, Lausanne, Switzerland

    Matthieu Dreyer & Mohamed Farhat

  2. Institut Systèmes industriels, HES-SO Valais-Wallis, Route du Rawyl 47, 1950, Sion, Switzerland

    Jean Decaix & Cécile Münch-Alligné

Authors
  1. Matthieu Dreyer
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  2. Jean Decaix
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  3. Cécile Münch-Alligné
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  4. Mohamed Farhat
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Correspondence to Matthieu Dreyer.

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Dreyer, M., Decaix, J., Münch-Alligné, C. et al. Mind the gap: a new insight into the tip leakage vortex using stereo-PIV. Exp Fluids 55, 1849 (2014). https://doi.org/10.1007/s00348-014-1849-7

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