Wake structure in actuator disk models of wind turbines in yaw under uniform inflow conditions

Abstract

Reducing wake losses in wind farms by deflecting the wakes through turbine yawing has been shown to be a feasible wind farm controls approach. Nonetheless, the effectiveness of yawing depends not only on the degree of wake deflection but also on the resulting shape of the wake. In this work, the deflection and morphology of wakes behind a wind turbine operating in yawed conditions are studied using wind tunnel experiments of a wind turbine modeled as a porous disk in a uniform inflow. First, by measuring velocity distributions at various downstream positions and comparing with prior studies, we confirm that the non-rotating wind turbine model in yaw generates realistic wake deflections. Second, we characterize the wake shape and make first observations of what is termed a curled wake, displaying significant spanwise asymmetry. The wake curling observed in the experiments is also reproduced qualitatively in large eddy simulations using both actuator disk and actuator line models. When a wind turbine is yawed for the benefit of downstream turbines, the asymmetric shape of the wake must be taken into account since it affects how much of it intersects the downstream turbines.PREPRINT, submitted to the Journal of Renewable and Sustainable Energy (January 2016) Ref. [14] used two aligned turbines in a wind tunnel and tested varying the rotor yaw angle, tip speed ratio, and the blade pitch of the upstream wind turbine only. This study showed that varying the yaw angle of the wind turbine was of comparable benefit to increasing the streamwise spacing between turbines, with an optimal power output occurring at 30 • . Refs. [17,18] studied the effects of controlling yaw angle, tip speed ratio, and the blade pitch of the upstream turbine for scaled model wind turbines, with results also revealing the benefits of yawing the upstream turbine. Further, yaw misalignment has been shown to reduce the steady-state blade loading variations by up to 70%, which has lead to the use of yawing to increase operational life [19]. Ref.[20] studied a rotating wind turbine model in replicated atmospheric boundary layer conditions to discover a deflection of approximately 0.6D in the far wake.Refs. [9,[21][22][23] were computational studies of wake deflection using various yaw angles. Ref.[21] uses LES with an actuator disk model with turbulent inflow and shows that wake deflection can be reproduced in such simulations. They also propose a momentum-based model for the deflection which is compared to LES with reasonable validity in the far wake. Some experimental results are compared, but the authors cite a need for more experimental verification before a wake controller may be developed.Ref.[9] studied wake deflection under various conditions using the SOWFA Large Eddy Simulation (LES) code and using the NREL 5 MW turbine model [24]. When the yaw angle γ was γ = 30 • , the study found the maximum wake deflection to reach about 0.5D in the far wake, where D is the rotor diameter. Ref.[22] studied the near wake structure of a wind turbine unde...

A New Analytical Wake Model for Yawed Wind Turbines

“…k w is the wake expansion factor and the recommend values is k w = 0.4I a for the flat terrain under neutral conditions [39]. As shown by Gebraad et al [5] and Howland et al [40], the wake deflection was determined by integrating the skew angle θ in x and using y d(x=0) = 0:…”

“…Parkin et al [6] obtained the detailed velocity field from one to five rotor diameters downstream of a two-bladed wind turbine model under various yaw angles by using PIV and showed the initial skew angle of wakes. Medici and Alfredsson [7] and later Howland et al [8] performed the hot-wire measurement for a two-bladed and a porous disk model turbine, respectively, and quantified the velocity deficit and deflections in various yawed conditions. Note that these wind tunnel tests were carried out in a uniform flow.…”

“…However, experimental validation was not sufficient as the author mentioned. Gebraad et al [5] and Howland et al [8] derived the formula of yaw induced wake center trajectory by integrating the skew angle proposed by Jiménez et al [11]. However, the model of Jiménez et al [11] overestimates the wake deflection since the assumption of top-hat for the velocity deficit is not accurate as pointed out by Ishihara et al [18].…”

Comparative study on the wake deflection behind yawed wind turbine models

“…The model turbine, however, had a rotor diameter of D=0.90 m and thus was significantly larger. A slightly different wake deflection angle for γ = 30 • was found in an experimental PIV study by Bastankhah and Porté-Agel [3], who localized the wake center at z/D ≈ 0.16 for x/D=2 and at z/D ≈ 0.34 for x/D=6 downstream distance for a smaller wind turbine model of D=0.15 m. Howland et al [4] used a yawed drag disc of D=0.03 m and found a deflection between z/D ≈ 0.4 and z/D ≈ 0.5 at a distance of x/D = 6, dependent on the measurement technique and fitting method. All of these studies qualitatively showed consistent wake deflection effects, that can be generalized.…”

From wake steering to flow control

“…Further, the authors explain the change in shape by showing that the cross-flow wind of an aligned 20 turbine is largely due to counter-rotating vortices that appear in the flow behind a yawed turbine and generate this distortion. Howland et al (2016) studies the curled wake phenomenon experimentally using a porous actuator disk and with LES using an actuator disk and an actuator line model. The curled wake is observed in experiments and simulations.…”