Brief Communication: On the influence of vertical velocity profiles on the combined power output of two model wind turbines in yaw

The effect of vertical velocity gradients on the total power output of two aligned model wind turbines as a function of yaw misalignment of the upstream turbine is studied experimentally. It is shown that asymmetries of the power output of the downstream turbine and the combined power of both with respect to the upstream turbine’s yaw misalignment angle can be linked to the vertical velocity gradient of the inflow.

The experiments were performed at the University of Oldenburg. Two model wind turbines as described by Schottler et al. (2016b) were used in streamwise displacement. The turbines where separated by 3D, with D = 0.58 m being the rotor diameter.
The upstream turbine is placed on a turning table allowing a yaw misalignment, while the downstream turbine utilizes a partial load control and therewith adapts to the changing inflow conditions. Further details about the setup are described by Schottler 5 et al. (2016a). In order to isolate the effect of a vertical velocity gradient in the inflow, the horizontal axes of an active grid at the wind tunnel outlet were set statically to create two different inflow profiles, which were characterized prior to the experiments.
13 hot wire probes were used simultaneously in a vertical line arrangement with a distance of 75 mm separating two sensors.
For both settings of the grid, data were recorded for 120 s at a sampling frequency of 2 kHz. The downstream position of the hot wire array was 1 m from of the wind tunnel outlet, in agreement with the upstream turbine's rotor, which was installed 10 after characterizing the inflow. curves with respect to γ 1 become obvious. The minimum of the downstream turbine's power P 2 is shifted towards positive angles. The combined power P tot is maximal at γ 1 ≈ −18°, being approx. 4 % larger compared to the case with perfect yaw 5 alignment γ 1 = 0°. Also the combined power shows a distinct asymmetry with respect to γ 1 . While the power is maximal at γ 1 ≈ −18°, it further decreases for larger values of γ 1 . For positive yaw angles the total power output is smaller compared to the case of no yaw misalignment. The results support that the direction of a purposeful yaw misalignment is of great relevance regarding the application of this concept to wind farm control. Further, the general shape of the graphs is in good agreement with numeric simulations of full size turbines reported by Fleming et al. (2014).
10 Fig. 2(b) shows the results of the same experiment, whereas nothing but the inflow conditions was changed to profile 2. Since the reproducibility of results was proven by Schottler et al. (2016a), the effect of the changed inflow is isolated. As can be seen, asymmetric shapes of both graphs are still observed. More importantly, the direction of the asymmetry changed with the direction of the inflow's vertical velocity gradient. Now, in Fig. 2(b), the minimum of P 2 is located at negative yaw angles, γ 1 ≈ −4°. Also for the total power output, the sign of the maximum's location changed, being positive (γ 1 ≈ 12°) during inflow 15 profile 2. Our results suggest, that the reason for the asymmetric shapes of the graphs in Fig. 2 is related to the inflow velocity gradient, which is further discussed in Sec. 4.
In this study, we investigate the influence of vertical velocity gradients on the power output of two aligned model wind tur- bines. An asymmetry of the power output with respect to the upstream turbine's yaw angle was found in prior experiments on laboratory scale (Schottler et al., 2016a) as well as in full scale numeric simulations Vollmer et al., 2016), whereas the causes were not fully understood. With the present methods, we further investigate the reasons for the asymmetric 5 wake deflection and isolate the effect of a vertical inflow gradient's orientation on the power output of a two turbine array. A strong linkage between the asymmetry and the velocity gradient's orientation was found. For a potential application of active wake control by intentional yawing, the effect itself needs to be understood. If the reported asymmetry depends on boundary conditions of the surroundings, which our results suggest, than this drastically impacts the applicability to real world wind farm control scenarios. In this study, the downstream turbine is used and conclusions about the wake deflection of the upstream 10 turbine is based on power measurements. The interesting results regarding the asymmetry and its linkage to the inflow conditions motivate further examinations in detailed wake measurements during different inflow gradients and yaw errors. The vast majority of model wind turbine experiments face a Reynolds number mismatch between the laboratory and full scale case, which is nearly a factor of 170 in this study. However, due to the good agreement of the general shape of the turbines' normalized power comparing the present study and Schottler et al. (2016a) with simulations of a full scale case