## 3 Modeling and Validation
### CFD Validation  
The diameter of the wind wheel of NREL 5 MW wind turbine is D = 126 m, and to take into account the rotation of the blade, two areas need to be divided: background area and rotation area, and the flow field information between the two areas is transmitted through the slip grid. The dimensions of the background domain are 5D \(\times\) 5D \(\times\) 8D, and the diameter and width of the rotation domain are 170 m and 30 m, respectively. The fan is 2.5D away from the upstream inlet and 5.5D away from the downstream outlet. Figure 4 shows the setting of boundary conditions: the upstream boundary of the wind turbine is the velocity inlet, the downstream boundary of the wind turbine is the pressure outlet, and the other four surfaces are symmetric planes, which can effectively reduce the blocking effect and ensure the accuracy of calculation. The blockage ratio of the model turbines, defined as the rotor swept area divided by the wind tunnel cross-section area, was about 3.14%. As suggested, the upper limit to prevent the wind tunnel wall interference was 10% [20; 21], the current blockage ratio achieved well. The surface of the wind turbine blade is the non-slip wall, and the turbulence model chooses the SST \(k-\omega\) turbulence model. Due to the complex shape of wind turbine blades but the need to capture the flow on the blade surface, this paper adopts the technique of cut volume meshing to generate 10 layers of prismatic layer meshes on the blade and hub surfaces simultaneously, with a total thickness of 0.04 m, 10 layers in total, and a growth rate of 1.2. Figure 5 shows the meshing of the blade surface and the surrounding flow field, as well as the boundary layer meshes of the blade cross-section. In order to verify the rationality and accuracy of the meshing, the convergence of the meshing is verified in the following. At the wind speed of 11.4 m/s, the mesh size of the flow field in the outer domain is kept constant, and the meshes of the rotating domain and the blade surface are scaled to different degrees to achieve mesh encapsulation. The mesh size of the outer domain is 8 m. The mesh size of the rotating domain, the mesh size of the blade surface and the mesh number of the whole computational domain are shown in Table 1. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Case 1** & **Case 2** & **Case 3** & **Case 4** \\ \hline Rotation domain grid size (m) & 2 & 2 & 2 & 1 \\ Maximum mesh size of blade surface (m) & 0.8 & 0.4 & 0.2 & 0.2 \\ Minimum mesh size of blade surface (m) & 0.08 & 0.04 & 0.02 & 0.02 \\ Total number of grids (million) & 3.70 & 4.67 & 6.70 & 8.02 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Grid size of wind turbine blade surface. Figure 4: Setting of boundary conditions. After grid division is completed, the wind speed at rated working condition is selected as 11.4 m/s, the wind turbine blade speed is 12.10 rpm, and the time step is selected as the wind turbine rotation time of one degree of 0.0138 s. The calculation results of wind turbine thrust and torque under different grid sizes are shown in Table 2, and Figure 6 shows the relationship between the number of grids and blade thrust, torque and relative error. The following conclusions can be drawn from the contents shown in Table 2 and Figure 6: with the reduction in the rotation domain and blade surface mesh size, the thrust and torque of the wind turbine are closer and closer to the values reported by NREL official FAST calculation. At the same time, the relative errors between adjacent examples are gradually reduced, and the convergence of the mesh is guaranteed. In order to ensure the accuracy of simulation and improve the computational efficiency as much as possible, the grid size of case3 will be selected for the subsequent calculation in this paper to simulate the aerodynamic performance under different wind speeds and compare with various numerical simulation methods to further ensure the reliability and accuracy of the grid.