*4.2. Unsteady Aerodynamic Analysis under Pitch Motion*

#### 4.2.1. Total Performance Analysis

Figure 13 shows the overall power and thrust variation of the wind turbine with and without the tower. The pitch amplitude corresponds to the fluctuation of power and thrust values. For f = 0.05 Hz, Ap = 5◦, as shown in Figure 13a, the power of the wind turbine fluctuates violently due to the existence of the tower, and it decreases sharply three times in one rotation cycle of the wind turbine. As shown in Figure 13b, the maximum power of the wind turbine without the tower was 5.16 MW, while the wind turbine with the tower was 5.11 MW. The minimum power of the former was 5.01 MW, while that of the latter s 4.70 MW. It can be seen that pitch motion slightly increases the peak and valley values of power, but the extreme value of the wind turbine decreases due to the existence of the tower. The average power generation was 5.06 MW and 4.98 MW, respectively; the latter was reduced by 1.58%. It can be found that the pitch motion of the platform increases the power of the wind turbine, but under the combination of pitch and tower shadow effect, the power fluctuation is larger and the increase is smaller. As shown in Figure 13c,d, the fluctuation trend of axial thrust is similar to that of power. The peak thrust and valley thrust of the wind turbine without the tower are 780.7 KN and 771.6 KN, and those with the tower are 777.9 KN and 751.1 KN, respectively. The average thrust was 774.5 KN and

769.0 KN, separately; the latter was reduced by 0.71%. That is, in terms of numerical values, the tower shadow effect slightly reduces the average power, while the average thrust is almost unchanged under pitch motion.

**Figure 13.** Total aerodynamic comparison of pitch motion; (**a**) Power versus azimuth angle; (**b**) Extreme and average values of power; (**c**) Thrust versus azimuth angle; (**d**) Extreme and average values of thrust.

Figure 14 shows the induced velocity distribution of airfoil under pitch motion. The pitch motion of the platform changes the angle between the incoming wind speed and the rotating plane of the wind turbine and produces an additional induced velocity *Vind*. *Vind* can be decomposed into chord velocity *Vc* and radial velocity *Vr* on the rotating plane, in which the direction of chord velocity component *Vc* depends on the positive or negative angle of pitch motion, which changes the relative velocity and direction of the rotating plane of the airfoil, and the angle of attack changes correspondingly. It leads to the fluctuation of the overall aerodynamic performance of the wind turbine under pitch motion.

### 4.2.2. Distribution of Pressure on the Blade Surface

Figure 15 shows the pitch amplitude and angular velocity of the platform motion with reference to simulation time. The second period of stable pitch motion of the wind turbine was selected as the research object, and the two typical positions of the wind turbine moving forward and backward to the front of the tower were selected for further analysis.

Figure 16 shows the pressure distribution in each section of the blade with and without the tower at two typical positions in a pitch cycle. In terms of numerical values, the maximum pressure difference of the wind turbine without the tower at 0.32 R, 0.63 R and 0.94 R sections is 1711 Pa, 3630 Pa and 7030 Pa, respectively. It can be found that the pressure difference of each section of the blade under pitch motion is smaller than that of surge motion. Comparing the pressure difference distributions of different sections at two typical positions, it can be seen that the pressure difference distributions on the pressure surface and the suction surface are basically the same. The change of the pressure difference is not obvious under pitch motion. Besides, affected by the tower shadow effect, the absolute value of the maximum negative pressure difference at the leading edge of

suction in each section of the blade decreases by 9.02%, 7.31% and 4.93%, respectively. Compared with surge motion, it can be seen that under pitch motion, the interference of the tower shadow effect on each section of the blade is also mainly concentrated in the root and tip of the blade, but the degree of interference is less than that of surge motion.

**Figure 14.** Schematic diagram of airfoil-induced velocity under pitch motion.

**Figure 15.** The two typical positions during pitch motion.

**Figure 16.** Distribution of pressure in each section of blade at position 1 and position 2.

4.2.3. Near Flow Field of Each Section of Blade

Figure 17 shows the interaction between the different blade sections and the tower when the blade rotates to the shadow area of the tower under pitch motion. The pitch motion of the platform to the rear and the rotation of the wind turbine to position 1 directly in front of the tower are selected for further analysis.

Comparing the pressure field on different blade sections with or without the tower under pitch motion, it can be seen that the pressure difference distribution of the blade surface is still concentrated on the leading edge of the blade. Under the influence of the tower shadow effect, the range of the negative pressure field near the suction surface of 0.32 R section and 0.63 R section is reduced, and the absolute value of negative pressure is smaller, but the negative pressure field of the suction surface of 0.94 R section has no obvious change. This further shows that the influence of the tower shadow effect on the pressure field is mainly concentrated in the root and the middle of the blade.

**Figure 17.** Streamline and pressure contours on different blade sections under pitch motion.

Observing the streamline distribution shown in Figure 17, the main difference is still concentrated in the near wake flow field of the tower. It can be seen that the distribution of the streamline at 0.32 R section and 0.63 R section is similar under surge motion, but there is an obvious stall separation vortex under the pitch motion at 0.94 R section, because compared with the surge motion moving only in the horizontal direction, the pitch motion applies a relative partial velocity in the vertical direction to the wind turbine when the azimuth of the wind turbine changes. The angle between the direction of the incoming flow velocity and the rotating plane of the wind turbine is constantly changing, which makes the flow field more complex.

#### 4.2.4. Wake Field behind the Wind Turbine

Figure 18 shows the velocity distribution of the wake field under platform pitch motion. The two moments when the wind turbine is in the balanced position and pitches forward and backward, respectively, are selected for further analysis. It can be seen that when the wind turbine without the tower is in the equilibrium position, the mutual interference between the blade and the wake flow field is small, and the wake is more stable compared with surge motion. Nevertheless, the symmetry of the flow field behind the same wind turbine with the tower is affected, and there is an obvious low-speed disturbance zone behind the tower, which increases the complexity of the wake.

**Figure 18.** Velocity contours of wake field under pitch motion.

*4.3. Unsteady Aerodynamic Analysis under Yaw Motion* 4.3.1. Total Performance Analysis

Figure 19 shows the total power and thrust comparison with and without the tower under yaw motion. Similarly, the yaw amplitude corresponds to the fluctuation of power and thrust values. For f = 0.05 Hz, Ay = 15◦, as shown in Figure 19a, it can be seen that the power of the wind turbine with the tower is always lower than that of the wind turbine without the tower under the same azimuth, and the power rises after three sharp drops in a wind turbine rotation cycle, which is the result of the combined action of the tower shadow effect and yaw motion. As shown in Figure 19b, under the effect of tower shadow, the maximum, average and minimum power of wind turbines are reduced by 1.94%, 2.47% and 4.16%, respectively. It can be concluded that the tower shadow effect aggravates the change of power extremum under yaw motion. As shown in Figure 19c,d, the fluctuation of the axial thrust value is consistent with that of the power value similarly; that is, they reach their respective extremes at the same azimuth. Under the effect of tower shadow, the maximum, average and minimum thrust of the wind turbine is reduced by 0.76%, 1.1% and 1.86%, respectively. It can be deduced that under yaw motion, the amplitude of the power drop is obviously affected by the tower shadow effect, while the thrust decreases slightly.

**Figure 19.** Total aerodynamic comparison of yaw motion; (**a**) Power versus azimuth angle; (**b**) Extreme and average values of power; (**c**) Thrust versus azimuth angle; (**d**) Extreme and average values of thrust.

Figure 20 shows the induced velocity distribution of airfoil under yaw motion. The yaw motion of the platform produces an additional induced velocity perpendicular to the rotation plane, and the direction of the *Vind* can be determined according to the righthand rule. When the platform rotates to the left, the angle between the direction of the inflow velocity and the direction of *Vind* is an obtuse angle, and its relative inflow velocity increases; on the contrary, when the platform rotates to the right, the angle between the direction of the inflow velocity and the direction of *Vind* is an acute angle, and its relative inflow velocity decreases. *Vind* can also be decomposed into chord velocity *Vc* and radial velocity *Vr* on the rotating plane. *Vr* changes the rotation effect of the blade, and *Vc* causes periodic fluctuations in the angle of attack and the sectional load of the blade.
