Free surface intake vortices: scale effects due to surface tension and viscosity

ABSTRACT

Engineers frequently use physical scale models of hydropower intakes to assess and minimize the occurrence of harmful free surface vortices. The impact of surface tension, viscosity and turbulence on the scaling behaviour of the vortices is examined here using an analytical free surface vortex model developed from measurements in a laboratory-scale hydropower intake. First, the effect of surface tension on the free surface depression is computed using a finite-difference model over a wide range of depression scales and shapes. The impact and scaling behaviour of surface tension are found to be qualitatively different depending on whether the depression is dimple- or funnel-shaped. The influence of viscosity on scaling predicted by the analytical vortex model contradicts trends recorded by previous authors, which suggests that additional processes such as turbulent diffusion may play a significant role at larger scales. Scale effects due to the interplay of viscosity and turbulence require further investigation, whereas those due to surface tension are fairly easily quantified and predicted.

Keywords:

• Hydraulic models
• hydropower intake
• similarity (scaling) theory
• surface tension
• turbulence in rotating flow
• turbulent diffusion
• vortex dynamics

Acknowledgements

We would like to acknowledge the advice and contributions of David Morissette, Pierre Tadeo, Tristan Aubel, Maryse Page, Anne-Marie Giroux and Sébastien Houde.

Funding

This work was supported by the National Sciences and Engineering Research Council of Canada (Postgraduate Scholarship B), the Fonds Québécois pour les Sciences et les Technologies (Bourse de recherche au doctorat) and Hydro-Québec's research centre.

Notation

The underlying research materials for this article can be accessed at http://digitool.library.mcgill.ca/thesisfile119367.pdf (Ph.D. Thesis)