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Scaling analysis of the swirling wake of a porous disc: application to wind turbines

Published online by Cambridge University Press:  24 January 2025

E. Fuentes Noriega Open the ORCID record for E. Fuentes Noriega [Opens in a new window]  and
N. Mazellier Open the ORCID record for N. Mazellier [Opens in a new window]
E. Fuentes Noriega
Affiliation:
University of Orléans, INSA-CVL, PRISME, EA 4229, 45072 Orléans, France
N. Mazellier*
Affiliation:
University of Orléans, INSA-CVL, PRISME, EA 4229, 45072 Orléans, France
*
†Email address for correspondence: [email protected]
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Abstract

We report a comprehensive study of the wake of a porous disc, the design of which has been modified to incorporate a swirling motion at an inexpensive cost. The swirl intensity is passively controlled by varying the internal disc geometry, i.e. the pitch angle of the blades. A swirl number is introduced to characterise the competition between the linear (drag) and the azimuthal (swirl) momenta on the wake recovery. Assuming that swirl dominates the near wake and non-equilibrium turbulence theory applies, new scaling laws of the mean wake properties are derived. To assess these theoretical predictions, an in-depth analysis of the aerodynamics of these original porous discs has been conducted experimentally. It is found that, at the early stage of wake recovery, the swirling motion induces a low-pressure core, which controls the mean velocity deficit properties and the onset of self-similarity. The measurements collected in the swirling wake of the porous discs support the new scaling laws proposed in this work. Finally, it is shown that, as far as swirl is injected in the wake, the characteristics of the mean velocity deficit profiles match very well those of both laboratory-scale and real-scale wind-turbine data extracted from the literature. Overall, our results emphasise that, by setting the initial conditions of the wake recovery, swirl is a key ingredient to be taken into account in order to faithfully replicate the mean wake of wind turbines.

JFM classification

Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1003 , 25 January 2025 , A34
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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