4.3.2. Distribution of Pressure on the Blade Surface

Figure 21 shows the yaw amplitude and angular velocity of the platform motion with reference to simulation time. The second period of stable yaw motion of the wind turbine and two typical positions in front of the tower were selected for further analysis.

Figure 22 shows the pressure distribution in each section of the blade with and without the tower at two typical positions in a yaw cycle. The azimuth moment of 180◦ and 900◦ rotation of the wind turbine is selected to study when the wind turbine is at a certain yaw angle to both sides and the wind turbine is directly in front of the tower. In terms of numerical values, the maximum pressure difference of the wind turbine without the tower at 0.32 R, 0.63 R, 0.94 R sections is 1620 Pa, 3455 Pa and 6890 Pa, respectively. It can be found that the pressure difference of each section of the blade under yaw motion is smaller than that of pitch motion. Comparing the pressure distributions of the two kinds of wind turbines at two typical positions, it can be found that the distributions are consistent. The change of pressure difference at the different positions of yaw motion is also not obvious; however, 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 11.01%, 8.23% and 5.80%, respectively. It can be inferred that under yaw motion, the

interference degree of the tower shadow effect on the negative pressure on the suction surface of the blade is greater than that of surge motion.

**Figure 20.** Schematic diagram of airfoil-induced velocity under yaw motion.

**Figure 21.** The two typical positions during yaw motion.

4.3.3. Near Flow Field of Each Section of Blade

Figure 23 shows the interaction between the different blade sections and the tower when the blade rotates to the shadow area of the tower under yaw motion. Position 1 was selected for further analysis.

Under yaw motion, the distribution trend of the pressure field in each section of the blade with or without the tower is similar to that of surge and pitch motions; the maximum negative pressure is still concentrated near the leading edge of the suction of the blade, and the tower compresses the negative pressure field and reduces the absolute value of the maximum negative pressure. The main influence range of the tower shadow effect is in the root and middle of the blade. From a numerical point of view, the blade surface pressure difference of the same section under yaw motion is lower than that of surge and pitch motions, which further shows that the work capacity of the wind turbine under yaw motion is the worst among the three motions.

**Figure 22.** Distribution of pressure in each section of blade at position 1 and position 2.

By comparing the streamline of each section of the blade with or without the tower, the influence area of the tower shadow effect is still mainly concentrated in the wake flow field of the tower, and the streamline shifts behind the tower toward the trailing edge of the blade at 0.32 R section, which is mainly the interference of the tower. The streamline at 0.63 R section shifts in the opposite direction on both sides of the tower, which is the result of the joint action of the tower shadow effect and the enhanced rotation effect. At 0.94 R section, in addition to the weakening of the tower shadow effect and the enhancement of the rotation effect, the yaw motion changes the upwind area of the incoming flow and the rotating plane of the wind turbine, resulting in additional induced tangential velocity. The streamline behind the tower shifts to a greater extent along the rotation direction of the wind turbine.

**Figure 23.** Streamline and pressure contours on different blade sections under yaw motion.

4.3.4. Wake Field behind the Wind Turbine

Figure 24 shows the velocity distribution of the wake field under platform yaw motion. The two moments when the wind turbine is in the equilibrium position and begins to yaw to the left and right side was selected for further analysis. The wake area of the wind turbine without the tower shows a nearly symmetrical distribution under the balanced position of yaw motion. Meanwhile, the high-speed wake area near the hub is smaller than that under pitch motion; it can be concluded that the yaw motion could reduce the induced velocity behind the hub. Furthermore, under yaw motion, the tower shadow effect similarly leads to the asymmetric distribution of the wake field.

**Figure 24.** Velocity contours of wake field under yaw motion.

#### **5. Conclusions**

This paper investigated the aerodynamic performance of NREL 5 MW FOWT with a rigid blades turbine considering the tower shadow effect under surge, pitch and yaw motions, respectively. The motion form of the platform is equivalent to the change of relative velocity of the wind turbine. The dynamic inlet wind speed is compiled for unsteady numerical simulation using the UDF function. The accuracy of the numerical simulation was verified by proper computational grids. Three independent platform motions and two models with or without the tower were considered for calculation. The results illustrate the wind turbine's aerodynamics, including power, thrust, pressure distribution and flow field. The conclusions can be drawn as follows:

(1) The fluctuation frequency of power and thrust is always consistent with the motion frequency of the platform. The power is more obviously affected by the tower shadow effect than the thrust, in which the decrease of power is the largest under yaw motion, second-largest under surge motion, and smallest under pitch motion, with a decreased range of 1.58–2.47%.

(2) The influence of the tower shadow effect on the pressure difference of the wind turbine is mainly concentrated at the suction leading edge of the blade under different platform motions, and the interference ability of the tower from the root to the tip of the blade weakens along the blade-spreading direction. The pressure difference under yaw motion is most obviously interfered with by the tower, and the average maximum negative pressure is reduced by 8.35%, which is not conducive to the output power of FOWTs.

(3) For the pressure field, the tower shadow effect obviously compresses the range of the negative pressure field of the root and middle sections of the blade, while the negative pressure field of the tip section is less affected. For the near wake flow field, the wake of the tower at the root section is the most seriously interfered by the tower; the influence of the tower shadow effect decreases with the increase of the blade height and the additional induced velocity produced by yaw and pitch motions makes the near wake flow field of the tower more complicated.

(4) The wake field changes most violently under surge motion; the wake flow field is relatively stable under pitch and yaw motions. Besides, the tower shadow effect leads to the increase of the velocity gradient near the hub, and the influence range of the high-speed wake of the tower wind turbine hub is the farthest under surge motion.

In view of these findings, the platform motion and the tower shadow effect have a great impact on the steady operation of FOWTs, and the combination of the two causes greater interference to the flow field. However, this paper only considers the aerodynamic characteristics of FOWTs under single-degree-of-freedom (surge, pitch and yaw) motion, and future research on factors such as heave, roll, sway and multi-degree-of-freedom coupling motions are worthy of more in-depth discussion.

**Author Contributions:** Conceptualization, L.D. and L.Z.; Formal analysis, L.D.; Investigation, L.D. and L.Z.; Methodology, L.D.; Project administration, D.H.; Software, L.D.; Supervision, D.H.; Validation, L.D.; Writing—original draft, L.D.; Writing—review and editing, L.D. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Science and Technology Commission of Shanghai Municipality and the National Natural Science Foundation of China, grant number 18DZ1202302 and 50706025.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data are not publicly available.

**Acknowledgments:** This research work is sponsored by the Science and Technology Commission of Shanghai Municipality (18DZ1202302). Additionally, the support of the National Natural Science Foundation of China under project No. 50706025 is gratefully acknowledged.

**Conflicts of Interest:** The authors declare no conflict of interest.
