# The Influence of Tilt Angle on the Aerodynamic Performance of a Wind Turbine
## 3 Results and Discussion
### Validations
Figure 4: Comparison of thrust and torque between wind tunnel experiment and CFD simulation at different wind speeds (Case 3). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**CFD Mesh Type** & **LIFES50+ Wind Tunnel Data (N), [14]** & **Present Study (N)** & **Error (\%)** \\ \hline Case 1 & & 70.010 & 2.000 \\ Case 2 & & 69.660 & 1.500 \\ Case 3 & & 69.520 & 1.300 \\ Case 4 & & 69.500 & 1.300 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of thrust between experiment and CFD simulation at different grid densities. progression factor of 1.2. The same wind speed of 11.4 m/s and rotor speed of 12.1 rpm were applied in all simulations. Meanwhile, in all simulations, the time step is the time taken by the wind turbine to increase the azimuth angle by 1\({}^{\circ}\). The number of meshes corresponding to different mesh sizes is shown in Table 6. The comparison of power for different grid resolutions with the same wind speed of 11.4 m/s and rotor speed of 12.1 rpm is presented in Table 7. It can be observed from Table 7 that the grid resolution of Case 2 is sufficient to solve the unsteady aerodynamics of the wind turbine. Therefore, the grid of Case 2 was used for the simulation of NREL 5 MW real-scale wind turbines at different wind speeds. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**CFD Mesh Type** & **Case 1** & **Case 2** & **Case 3** \\ \hline Maximum Size (m) & 0.20 & 0.10 & 0.05 \\ Minimum Size (m) & 0.04 & 0.02 & 0.01 \\ Total Mesh Number (Million) & 1.52 & 4.80 & 9.53 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Mesh size of blade surface. \begin{table}
\begin{tabular}{c c} \hline \hline
**Specifications** & \\ \hline Rated Power (MW) & 5 \\ Rotor Orientation, Configuration & Upwind, 3 blades \\ Rated Wind Speed (m/s) & 11.4 \\ Rated Rotor Speed (rpm) & 12.1 \\ Rotor Diameter (m) & 126 \\ Hub Diameter (m) & 3 \\ Hub Height (m) & 90 \\ Tower Base Diameter (m) & 6 \\ Tower Top Diameter (m) & 3.87 \\ Pre-cone (\({}^{\circ}\)) & 2.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Principal dimensions of the NREL 5 MW reference wind turbine. Figure 5: Geometric model of a 5 MW reference wind turbine: (**a**) the rotor geometric model; (**b**) the full configuration model. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**CFD Mesh Type** & **NREL Data (MW), [16]** & **Present Study (N)** & **Error (\%)** \\ \hline Case 1 & & 4.767 & 4.700 \\ Case 2 & 5.000 & 4.981 & 0.380 \\ Case 3 & & 5.020 & 0.400 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of power between NREL data and CFD simulation at different grid densities. Aerodynamic simulations of a wind turbine with various wind speeds were tested and compared with the FAST results. The obtained thrust and power were compared with the corresponding NREL data calculated by FAST V8, as presented in Figure 6. The power agrees well with the NREL data, but the thrust tends to be smaller than that from NREL data. The reason for the difference between the CFD method and the FAST can be summarized as follows: (a) the FAST does not consider the three-dimensional flow effects around blades; (b) in the BEM method, in order to calculate a rotor with a limited number of blades, a tip loss correction model needs to be added. The results obtained by different tip loss correction models are also quite different [17]. FAST uses a Prandtl tip loss correction model [16]. Therefore, the CFD result of the thrust is significantly lower than the FAST result. A similar phenomenon appeared in [18]. However, at the rated wind speed, compared with FAST data, the errors of the thrust and power obtained by CFD are less than 5% Through the above analysis, the grid of Case 2 can accurately simulate the aerodynamic performance of NREL 5 MW real-scale wind turbines. Therefore, the grid of Case 2 was used to simulate the effect of tilt angle on the aerodynamic performance of the wind turbine.