Wake scaling of actuator discs in different aspect ratios

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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.