## 4 Results
### Wind Turbine Rotor Results
#### 4.1.1 Axial Uniform Free-Stream Flow  
Figure 16 depicts the out-of-plane bending moment (\(M_{flap}\)) of the blade root and the out-of-plane deflection at the blade tip (\(U_{flap}\)) for axial wind speed at 8 m/s. The 1/_rev_ variation is brought about by the 5\({}^{\circ}\) tilt angle of the rotor that shifts the maximum loading towards the azimuth position of 180\({}^{\circ}\). Good agreement is observed in the mean values (maximum difference 1.8%). Furthermore, all the models predict a small amplitude of the 1/_rev_ variation (\(\leq\)3.25% of the mean load). Nevertheless, BEM appears to have a phase difference of approximately 35\({}^{\circ}\), while the AL and LL results match perfectly with each other. Results for the predicted by the different models mean load, amplitude, and phase are tabulated in Table 10. The phase difference in BEM results can be attributed to disregarding the wake skewness effect induced by the tilt angle of the rotor in BEM model. The quality of agreement is similar between the different models in the out-of-plane deflection. In Figure 17, the in-plane bending moment (\(M_{edge}\)) of blade root and the in-plane deflection of blade tip (\(U_{edge}\)) is shown for the same free-stream flow velocity. Nearly total agreement is achieved between the different aerodynamic models. In-plain loads and deflections are mainly driven by gravitational loads. Consequently, deviations between different aerodynamic analysis methodologies are not expected to have significant effect. This conclusion is valid in yaw misalignment cases as well. For this reason, the corresponding figures of \(M_{edge}\) and \(U_{edge}\) are omitted in the yaw misalignment section. As Figure 18 shows, the different aerodynamic models are in good agreement regarding the twisting moment (\(M_{tw}\)) of blade root. Very small differences are predicted in the mean value of the tip torsion angle (about 0.02\({}^{\circ}\)). The phase differences seen in \(M_{flap}\) and \(U_{flap}\) have vanished herein. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Mode** & **hGAST** & **NEREA** & **Cp-Lambda** & **HAWC2** & **NISA** \\ \hline
1 st \(flap\) & 0.62 & 0.62 & 0.62 & 0.61 & 0.64 \\
1 st \(edge\) & 0.94 & 0.94 & 0.94 & 0.93 & 0.96 \\
2 nd \(flap\) & 1.76 & 1.74 & 1.76 & 1.74 & 1.85 \\
2 nd \(edge\) & 2.80 & 2.79 & 2.80 & 2.77 & 2.86 \\
3 rd \(flap\) & 3.59 & 3.52 & 3.60 & 3.57 & 3.76 \\
1 st \(torsion\) & 5.40 & 5.36 & — & 6.60 & 6.01 \\
3 rd \(edge\) & 5.73 & 5.61 & 5.74 & 5.70 & 5.82 \\
4 th \(flap\) & 6.09 & 6.03 & 6.11 & 6.11 & — \\ \hline \hline \end{tabular}
\end{table} 
Table 9: DTU 10 MW blades natural frequencies. Comparison between different structural models used in WP2 of the INNWIND.EU project. Figure 15: Mode shape of 1 st flapwise mode. Figure 16: Out-of-plane root bending moment and tip deflection at 8 m/s axial wind speed. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Mean Value [MNm]** & **Amplitude [MNm]** & **Phase [\({}^{\circ}\)]** \\ \hline BEM & 17.004 & 0.434 & 124 \\ LL & 17.307 & 0.560 & 160 \\ AL & 17.151 & 0.559 & 156 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Out-of-plane bending moment of blade root at 8 m/s axial wind speed. Comparison between different aerodynamic models. Figure 17: In-plane root bending moment and tip deflection at 8 m/s axial wind speed. Comparison of the Aerodynamic Models  
It needs to be stressed that in LL and AL models, the blade \"perceives\" the wake-induced velocity in a different way compared to BEM. This is attributed to the detailed description of the 3D flow field by the Free Vortex Wake and the CFD methodologies respectively. Figure 19 verifies the correct effect of the tip correction model used in BEM [20], as the aerodynamic forces are effectively reduced close to the tip. As depicted in Figure 20 however, axial induction factor computed by BEM has a constant level difference and an increase towards the tip. This is the result of applying [PERSON]'s tip correction formula directly on the thrust coefficient \(C_{T}\).