Scaling Analysis of the Swirling Wake of a Porous Disc: Application to Wind Turbines

TL;DR

This study develops and validates new scaling laws for the swirling wake of porous discs, demonstrating their relevance to wind turbine wake modeling and recovery, through experimental and theoretical analysis.

Contribution

It introduces a new swirl number and scaling laws for porous disc wakes, linking swirl dynamics to wake recovery and wind turbine wake characteristics.

Findings

Swirling motion creates a low-pressure core affecting velocity deficit.

Experimental data supports the new scaling laws for wake properties.

Swirling wake profiles resemble those of actual wind turbines.

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) momentums 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. 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 lab-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.