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

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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.
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