## 5 Results and Discussions  
### Field Test Cases Selection  
The direct validation method is to compare the aerodynamic performance of blade section measured in the field with the 2D airfoil data measured in a wind tunnel. Thus, the testing conditions between field measurement and 2D wind tunnel measurement should be similar as much as possible. However, there exists some differences between field measurement on the 3D blade and wind tunnel measurement on the 2D airfoil. Firstly, tip and root vortices over a blade with finite length will have a 3D induction effect on the flow over the entire blade. Additionally, the airfoil and twist angle along the blade span are different, which will have another 3D effect. Secondly, for a rotating blade, stall delay effects [10] are remarkable, especially for the blade root. Finally, wind turbine usually operates in yaw and high turbulent density conditions due to the unsteady atmospheric inflow.  
Therefore, to minimize the 3D induction effect, aerodynamic data of DU93-W-210 airfoil, located at the mid-span in Table 3, were chosen to compare. In addition, for eliminating the stall delay effects, the aerodynamic data were sampled when the wind turbine was shutdown.  
The testing cases are shown in Table 7, where pitching angles are changed from 60\({}^{\circ}\) to 90\({}^{\circ}\) with interval of 5\({}^{\circ}\), sampling frequency is 50 Hz and sampling time is 60 s. In this paper, the pitching angle is 90\({}^{\circ}\) when the leading edge of the blade points to upstream of the inflow.  
Azimuth angle of rotor, \(\chi\), is the angle between pitch axis of the blade with pressure taps and tower axis. Yaw angle of wind turbine, \(\gamma\), is the angle between inflow direction and rotating axis of rotor. Yaw angle is positive when the freestream comes from left side of the wind turbine. The definitions are shown in Figure 12.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Case** & **Status of Turbine** & **Pitching Angle (\({}^{\circ}\))** & **Sampling Frequency (Hz)** & **Sampling Time (sec)** \\ \hline
1 & Stop & 60 & 50 & 60 \\
2 & Stop & 65 & 50 & 60 \\
3 & Stop & 70 & 50 & 60 \\
4 & Stop & 75 & 50 & 60 \\
5 & Stop & 80 & 50 & 60 \\
6 & Stop & 85 & 50 & 60 \\
7 & Stop & 90 & 50 & 60 \\ \hline \hline \end{tabular}
\end{table}
Table 7: The testing cases to compare with the 2D wind tunnel.  
Figure 11: Biot–Savart integral law.  
The inflow conditions at the nacelle are shown in Figure 13. It is observed that inflow speed varies in the 8 m/s to 12 m/s ranges, and yaw angle varies in the \(-20^{\circ}\) to \(0^{\circ}\). In the sampling time of 60 s, both magnitude and direction of inflow vary significantly, which is the third difference from the 2D wind tunnel measurement as is mentioned previously.  
When the wind turbine is shutdown, the rotor is still free to rotate, although rotor speed is very low. It is shown from Figure 14 that rotor speed increases with the decrease of pitching angle. The maximum rotor speed is about 9 rpm at a pitching angle of \(60^{\circ}\), which is much lower than rated rotor speed of 62 rpm. In these testing cases, rotor can be regarded as quasi-static, and stall delay effects due to rotating is weak enough to be ignored.  
Figure 12: Definitions of azimuth angle of rotor and yaw angle of wind turbine.  
Figure 13: Inflow speed (**a**) and yaw angle (**b**) at the nacelle in the testing cases.