## 2 Numerical Model
### Computational Domain and Yaved Flow  
In the numerical simulation, a realistic wind field was simulated using the rectangular computational domain, as illustrated in Figure 3. The length, width, and height of the calculation domain were 15D, 8D, and 6D, respectively. The wind turbine rotation domain \begin{table}
\begin{tabular}{l c c} \hline \hline
**Geometric Parameter** & **Symbol** & **Value** \\ \hline Aerofoil profile & – & NACA 4415 \\ Rotor orientation & – & Upwind \\ Blade number & \(N\) & 3 \\ Wind speed (m\(\cdot\)s\({}^{-1}\)) & \(U\) & 8 \\ Rotor diameter (m) & \(D\) & 1.4 \\ Material & – & Wood composite \\ Elasticity modulus (GPa) & \(E\) & 4.8 \\ Poisson’s ratio & \(\mu\) & 0.33 \\ Density (kg m\({}^{-3}\)) & \(\rho\) & 625 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Structural parameters of the wind turbine used in this study. Figure 1: The stress–strain curve of a wind turbine blade. Figure 2: Azimuth angle and number of blades. \(\psi\) is the blade azimuth angle. was nested within the cylinder's yaw rotation domain, which was used to define the wind turbine rotation motion, and the built-in encryption cylinder yaw rotation domain was used to define the yaw dynamic rotation rules. The wind turbine rotated clockwise. The geometric center of the rotational axis of the wind turbine was defined as the coordinate origin. The flow direction was in the positive direction of the \(y\) axis, the yaw axis of rotation was the \(z\) axis, and the width of the computational domain was the \(x\) axis. When blade 1 was turned to the downward position in the \(z\) axis, the azimuth angles of blades 1, 2, and 3 were 0\({}^{\circ}\), 120\({}^{\circ}\), and 240\({}^{\circ}\), respectively. The data on wind turbine blade rotation to this position under various yaw angles was extracted for the average wind load and minimum fatigue load on the blades being minimized in this \"shutdown\" position [6]. Dynamic yaw motion is developed using a proprietary approach that combines user-defined functions to replicate the motion of wind turbine blades. The periodic variation in yaw angle over time is defined using the trigonometric function. This method of simulation calculation is supported by the literature [18], although the author of that study only provided a research conclusion regarding the aerodynamic properties of a wind turbine with a dynamic deflection of 30\({}^{\circ}\). In order to make the rotation of the wind turbine relatively stable and to more effectively examine the stress on the wind turbine blades during the yaw process, the original method was modified in this study by using multiple phases of reciprocating motion. Specifically, as shown in Figure 3, by designating the rotation plane when the wind turbine rotor is not yawing as the dividing line, the positive yaw time (rotating along the axis of the wind turbine tower to the counterclockwise position) can be defined as ranging from 0 T to 0.5 T. Furthermore, the negative yaw time (rotating along the axis of the wind turbine tower to the clockwise position) can be defined as ranging from 0.5 T to 1.0 T.  
In accordance with International Electrotechnical Commission standards, the wind direction is set to deflect 30\({}^{\circ}\) in 6 s, and the deflection period of periodic dynamic yaw is set as T = 24 s. The initial yaw angle is 0\({}^{\circ}\), where the axis of rotation of the wind turbine at the initial position is consistent with the actual incoming wind direction. The changes in yaw angle and yaw velocity with time are shown in Figure 4. The trigonometric function describing yaw change with time can be expressed as  
\[\theta=30\sin\biggl{(}\frac{\pi t}{12}\biggr{)} \tag{1}\]  
Figure 3: Three–dimensional view of the computational domain with sizes and boundary conditions. where \(t\) is the yaw time. The induced velocities of the blades change with the azimuth angle when the wind turbine is operating in a yawing mode.