# Numerical Study on the Yaw Control for Two Wind Turbines under Different Spacings
## 4 Results
### Wake Time-Averaged Velocity  
For all points in the calculation domain, the quasi-periodic stable velocities in the last 200 s of wake simulations are averaged. Figure 10 shows the time-averaged wake velocity deficit profiles normalized by the hub-height average speed. It can be found from Figure 10 that the characteristics of the wake velocity of WT1 are only related to the yaw angle. As shown in Figure 10a, when the yaw angle is 0, the wake velocity profiles on the left and right sides of the turbine present a high degree of symmetry. The average velocity profiles become more chaotic as the yaw angle increases, as shown in Figure 10b-d. However, a comprehensive comparison of Figure 10 shows that with the increase in yaw angle, the velocity deficit behind WT2 decreases. It can be seen that the increase in yaw angle can significantly increase the inflow velocity of WT2, and the position of bimodal shape of WT1 gradually shifts away from the centerline where y/D = 0. Clearly, the wake velocity profiles under different turbine spacing are different only after WT2, and the difference becomes more evident with the increase in yaw angle. As shown in Figure 10a, for the 0\({}^{\circ}\) yaw angle, there is little difference in the velocity deficit profiles at 10D downstream of WT1. Generally speaking, the recovery of the wake velocity deficit is closely related to the yaw angle. Yaw control will lead to the offset of the wake centerline. The greater the yaw angle is, the greater the offset of the wake centerline in front of WT2 will be. This situation will change after passing through the downstream turbine. In addition, the larger the spacing between two turbines is, the greater the inflow wind speed of WT2 will be, because the impact of WT1's wake on WT2 is relatively weakened. The contours of time-averaged velocity are shown in Figure 11 in a horizontal plane at hub height. The change in spacing from 5-8D has no obvious effect on the velocity deficit of WT1 wake under uniform inflow. However, the yaw control can obviously change the wake direction of WT1. Wake redirection makes the wake of WT2 present an asymmetrical distribution, and the wake velocity deficit decreases. Under the conditions with large yaw and spacing, the range of low velocity region in the downstream wake has shrunk obviously. In addition, it can be found that when the yaw angle of WT1 is as large as 30\({}^{\circ}\), the maximum wake velocity deficit will not appear immediately on the left side (opposite to the wake deflection induced by the yaw control) behind WT2 but after some distance, and then it slowly recovers. From Figure 11, we can find that when the yaw angle reaches 20\({}^{\circ}\), WT2 is still under strong wake effects because the spacing between two turbines is relatively small under 5D, 6D and 7D conditions. Moreover, the power rise of WT2 is greater than the power loss of WT1 when yaw changes to 30\({}^{\circ}\), so total power is still rising. For 8D situations, the influence of WT1 on the wake field of WT2 has been weakened when the yaw angle is 20\({}^{\circ}\), so the change of the total output power is not evident under yaw control from 20\({}^{\circ}\) to 30\({}^{\circ}\). In the working condition with the yaw angle of 30\({}^{\circ}\) and spacing of 7D, the overall performance of two wind turbines is relatively optimal. The wake velocity contours of two  
Figure 10: Time\(-\)averaged wake velocity deficit profiles normalized by the hub\(-\)height average speed of 11.4 m/s. The velocity deficit scale for each profile ranges from 0 to 1. Each consecutive profile is taken 1D downwind: (**a**) yaw = 0\({}^{\circ}\); (**b**) yaw = 10\({}^{\circ}\); (**c**) yaw = 20\({}^{\circ}\); (**d**) yaw = 30\({}^{\circ}\). turbines in yz slices at different locations downstream of two wind turbines corresponding to this case, as shown in Figure 12, are chosen to be analyzed. Figure 12a shows the velocity contour in yz slices at 1D downstream of WT1.