Abstract
The wake recovery from planar porous actuators that surrogate the effect of wind turbines is investigated, focusing on rectangular shapes for vertical axis wind turbines (VAWTs). We proposed an effective mixing diameter D∗ to scale the streamwise momentum recovery for actuators of arbitrary shape. The length-scale D∗ is given by the ratio between frontal area and disc perimeter characterising the wake-freestream interface, whereby the momentum loss and the turbulent exchange of momentum take place. Wind tunnel experiments of planar actuators from porous plates are presented. The three-dimensional development of the wake is surveyed up to six widths/diameters downstream of the actuators making use of robotic particle image velocimetry with helium-filled soap bubbles as flow tracers. The recovery rate analysis is performed using D∗ for wake normalisation. The scaled wake data agrees well among actuators in different shapes. And it is significantly improved for rectangular actuators, comparing with existing scaling lengths. The flow behaviour is confirmed with numerical simulations of VAWT wakes with different aspect ratios, indicating the validity of this scaling concept for wind turbine wake modelling.
Highlights
Porous plates have become prevailing representatives of horizontal axis wind turbines (HAWTs) to efficiently simulate wind farm behaviour by experiments [1]
Deq is essentially an extrapolation of the momentum thickness concept for planar wakes, where the vertical axis wind turbines (VAWTs)'s momentum deficit is redistributed to an equivalent circular disc
Their results indicate that the momentum recovery normalised by Deq exhibits a limited degree of match for large values of aspect ratio (AR), within the typical inter-turbine separation distances of wind farms
Summary
Porous plates have become prevailing representatives of horizontal axis wind turbines (HAWTs) to efficiently simulate wind farm behaviour by experiments [1]. Deq is essentially an extrapolation of the momentum thickness concept for planar wakes, where the VAWT's momentum deficit is redistributed to an equivalent circular disc Their results indicate that the momentum recovery normalised by Deq exhibits a limited degree of match for large values of AR, within the typical inter-turbine separation distances of wind farms The aim of the present analysis is to account for the cross-sectional momentum deficit that occurs within the frontal area, and introduce the momentum transport across the wake interface as a main driver for the process of momentum recovery By this approach, a normalisation length can be obtained whereby the streamwise development of the momentum in the wake becomes independent of the actuator shape. The experimental data is used to compare the use of D* with the traditional choices of length scale such as width W and a characteristic length l alongside the recently introduced Deq
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