RANS and LES computations of the tip-leakage vortex for different gap widths

Abstract

In hydraulic turbines, the tip-leakage vortex is responsible for flow instabilities and for promoting erosion due to cavitation. To better understand the tip vortex flow, Reynolds-averaged Navier–Stokes (RANS) and large eddy simulation (LES) computations are carried out to simulate the flow around a NACA0009 blade including the gap between the tip and the wall. The main focus of the study is to understand the influence of the gap width on the development of the tip vortex, as for instance its trajectory. The RANS computations are performed using the open source solver OpenFOAM 2.1.0, two incidences and five gaps are considered. The LESs are achieved using the YALES2 solver for one incidence and two gaps.

The validation of the results is performed by comparisons with experimental data available downstream the trailing edge. The position of the vortex core, the mean velocity and the mean axial vorticity fields are compared at three different downstream locations. The results show that the mean behaviour of the tip vortex is well captured by the RANS and LES computations compared to the experiment. The LES results are also analysed to bring out the influence of the gap width on the development of the tip-leakage vortex. Finally, a law that matches the vortex trajectory from the leading edge to the mid-chord is proposed. Such a law can be helpful to determine, in case of cavitation, if the tip vortex will interact with the walls and cause erosion.

Keywords:

• tip-leakage vortex
• dynamic Smagorinsky model
• k − ω SST
• YALES2
• OpenFOAM
• vortex trajectory

Acknowledgements

Vincent Moureau and Ghislain Lartigue from the CORIA lab, and the SUCCESS scientific group are acknowledged for providing the YALES2 code.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors are very grateful to the Competence Center in Energy and Mobility (CCEM), Swisselectric Research and the foundation The Ark through the programme The Ark Energy for their financial support. A part of this work was performed using HPC resources from GENCI-IDRIS [grant number 2012-020611].