*2.4. Design and Validation Cases of Wind Turbine Blade*

Three load cases are considered in this work, viz.:

(1) DLC-1 (Worst working case)

According to the IEC 61400-1 standard [39], the reference wind turbine is in the 1A IWC wind class, which means it can only withstand wind gusts up to 21% of its rated speed. Therefore, the first load case is when the wind turbine is operating under rated case in severe gusts, in which the gusts suddenly occur so that the blades do not have enough time to change pitch. As it is of great importance for the safety of turbine, this case is also used as the design condition for topology optimization in this work. The related parameters are given in Table 2.

**Table 2.** Operation parameters in different load cases.


Note: In DLC-1 case, wind speed = Rated wind speed + maximum allowable gust (11.4 + 21% × 11.4); in DLC-2 case, wind speed = cut-out wind speed; in DLC-3 case, wind speed = speed of typhoon.

(2) DLC-2 (Cut-out wind speed working case)

This case is the cut-out wind speed condition. This is the highest wind speed that the wind turbine can reach before opening the propeller to the downwind position and shutting it down. In this case, blade tip deflection is relatively small. The tip deflection acceleration is even less than that in DLC-1, and therefore the inertial load can be ignored in this case. In this work, this case was used as a verification design case, and the related parameters are listed in Table 2.

#### (3) DLC-3 (Shutdown working case)

This case is the parking brake condition, at which the blade is in the downwind position and the incoming wind is typhoon speed (37.5 m/s). Here, the downwind position is the pitch angle of the blade that is not affected by any torque. In this work, this case was also adopted as a verification design case, and the relevant parameters are shown in Table 2.

#### **3. Results**

### *3.1. CFD Simulation of Wind Turbine Blade*

In this work, two turbulence models, viz. k-*ω* SST and k-*ε*, were adopted to elaborate the rationality of CFD simulation. Furthermore, the rationality analyses in terms of output torque and power were compared with the results obtained from the FAST software. Figure 2a illustrates the output torque curves based on the k-*ω* SST and k-*ε* models and FAST as the increase in wind speed, and the corresponding data are also listed in Table 3. It can be seen from Figure 2a and Table 3 that the predicted torque values of turbine blade based on the k-*ω* SST and k-*ε* turbulence models under the different wind speeds were close to the values based on the FAST. The k-*ω* SST model had a higher prediction accuracy in comparison with the k-*ε* model. Compared to the values obtained from the FAST, the errors of output torque based on the k-*ω* SST model in the wind speed range of 7–25 m/s were less than 7%. The predicted values for the k-*ε* turbulence model at high wind speeds were relatively low, and the related errors in the wind speed range of 15–25 m/s were within 7–12%.


**Table 3.** Output torques based on the k-*ω* SST and k-*ε* models and FAST.

Apart from the output torque performance, the output power performance of the turbine blade based on the k-*ω* SST and k-*ε* models and FAST was also evaluated. The output power can be calculated as the following formula:

$$P = M\omega \tag{6}$$

where *M* is the torque of blade; *ω* is rotation speed. Figure 2b and Table 4 show the output power values of the turbine blade based on the k-*ω* SST and k-*ε* models and FAST, respectively. It can be noted that both the models simulated the output power performance relatively well, and the maximum errors were basically within 10%. However, the error based on the k-*ε* model at the wind speed of 25 m/s was 11.16%, probably resulting in a relatively dangerous result. Consequently, the k-*ω* SST turbulence model was adopted in this work.


**Table 4.** Output power based on the k-*ω* SST and k-*ε* models and FAST.

#### *3.2. Structural Responses of Wind Pressure on the Surface of Wind Turbine Blade*

According to the design case shown in Table 2 where the pitch angle of the wind turbine blade was adjusted to 0◦ and the meshing strategy discussed in Section 2.2.2, the structural responses of wind pressure on the surface of blade were obtained based on the k-*ω* SST turbulence model (Section 3.1). Figure 3 illustrates the pressure surface and suction surface contours of turbine blade under the aerodynamic external load. From Figure 2, the pressure was mainly concentrated in the blade root and trailing edge, while the suction force in the middle of the blade was mainly focused on the blade edge. The maximum pressure and suction force were 2723 and 5729 Pa, respectively.

**Figure 3.** (**a**) Pressure surface contour. (**b**) Suction surface contour.
