Actuator disk is one of the most used theories in wake modeling of wind turbines [1]. Experimental and numerical study on the wake of planar actuator disks is conducted to compare the three-dimensional flow developments. In the experimental study, circular, square and rectangular actuators are realized by porous plates with a solidity of 56%. The experimental apparatuses are shown in figure 1. The measurement of the flow field from 1 diameter upstream up to 6 diameters downstream of the actuator are conducted using robotic particle image velocimetry (robotic PIV [2]). As for the numerical study, this research further develops comparing the present experiments with computational fluid dynamics (CFD) simulations of the actuator surface model. The actuator surfaces are numerically realized by force fields distributed in different planar shapes.

The study shows that the presence of corner vortices for the square actuator, shaping the cross-section of shear layers into diamond-like in the far-field (figure 2). The development of the vortex sheet features a clover-leaf shape, as depicted in figure 3. The momentum deficit imparted at the actuator surface and its recovery are examined and compared among the different actuator surfaces, a similar recovery length is observed for circular and square actuators.

[1] W. Yu, V.W. Hong, C. Ferreira, G.A.M. van Kuik, Experimental analysis on the dynamic wake of an actuator disc undergoing transient loads, Exp. Fluids. 58 (2017).

[2] C. Jux, A. Sciacchitano, J.F.G. Schneiders, F. Scarano, Robotic volumetric PIV of a full-scale cyclist, Exp. Fluids. 59 (2018)