# The Influence of Tilt Angle on the Aerodynamic Performance of a Wind Turbine
## 3 Results and Discussion  
### Validations  
The 1/75 scale model of a DTU 10 MW reference wind turbine was used for the mesh independence test. In the numerical verification, the tilt angle of the wind turbine was not considered. The main parameters of the scale model are given in Table 1. A detailed introduction of the blade parameters at 40 different blade sections is provided by [14]. Figure 3 shows the wind turbine geometric model and the surface grid. After scaling according to the scale factor, the boundary layers near the blade and hub surface have five layers of refined grid with the total layer thickness of 0.004 m and a progression factor of 1.2. The blade surface mesh size includes the maximum mesh size and the minimum mesh size. The number of meshes corresponding to different mesh sizes is shown in Table 2. According to previous study, the time-step size corresponding to \(1^{\circ}\) increment of azimuth angle of the wind turbine per time-step was applied in all simulations [15]. Moreover, the simulation was run under unsteady conditions. The comparison of thrust and torque for different grid resolutions with the same wind speed of 5.53 m/s, rotor speed of 330 rpm and time-step size of \(5\times 10^{-4}\) s is presented in Tables 3 and 4. It can be observed from Tables 3 and 4 that the grid resolution of Case 3 is sufficient to solve the unsteady aerodynamics of the wind turbine. Therefore, the grid resolution of Case 3 was used in subsequent simulations. \begin{table}
\begin{tabular}{c c} \hline \hline
**Specifications** & **DTU Down-Scaled** \\ \hline Number of Blades & 3 \\ Rotor Diameter (m) & 2.37 \\ Hub Diameter (m) & 0.178 \\ Rated Wind Speed (m/s) & 5.53 \\ Rated Rotor Speed (rpm) & 330 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Principal dimensions of the scale model. Figure 3: Geometric model and surface grid: (**a**) the rotor geometric model; (**b**) the blade surface grid. Simulations at different wind speeds were performed, and the simulation results were compared with wind tunnel experiment data, as presented in Figure 4. In this paper, we always keep the pitch angle at 0\({}^{\circ}\), so we have not considered the working conditions above the rated wind speed. When the wind speed is close to the rated wind speed, the thrust and torque of the CFD simulation are lower than those of the wind tunnel experiment, but the maximum error is not more than 10%. This means that STAR-CCM+ can accurately simulate the aerodynamic performance of the wind turbine under rotating motion. In order to ensure the reliability of the NREL 5 MW real-scale wind turbine simulation, the NREL 5 MW real-scale wind turbine was used for grid convergence analysis. Major properties of the NREL 5 MW reference wind turbine are given in Table 5[16]. Figure 5 shows the blade alone geometric model and full configuration geometric model with the tower. The blade alone model was used for numerical verification, and the full configuration model was used to investigate the effect of tilt angle on the aerodynamic performance of the wind turbine. Near the wall surface of the blades and hub, the boundary layers have 10 layers of refined grid with the total layer thickness of 0.03 m and a \begin{table}
\begin{tabular}{c c c c} \hline \hline
**CFD Mesh Type** & **LIFES50+Wind Tunnel Data (N-M), [14]** & **Present Study (N-M)** & **Error (\%)** \\ \hline Case 1 & & 5,690 & 8.700 \\ Case 2 & & 5.850 & 6.100 \\ Case 3 & & 5.900 & 5.300 \\ Case 4 & & 5.920 & 5.000 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of torque between experiment and CFD simulation at different grid densities. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**CFD Mesh Type** & **Case 1** & **Case 2** & **Case 3** & **Case 4** \\ \hline Maximum Size (mm) & 3.000 & 2.000 & 1.500 & 1.100 \\ Minimum Size (mm) & 0.500 & 0.350 & 0.250 & 0.180 \\ Total Mesh Number (million) & 1.850 & 3.240 & 4.630 & 9.400 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mesh size of blade surface.