## 4 Results
### Wind Turbine Rotor Results
#### 4.1.2 Yawed Uniform Free-Stream Flow  
Figures 23 and 24 depict the out-of-plane bending moment of the blade root at 8 and 11 m/s wind speed and for yaw angles of \(\pm\)15\({}^{\circ}\) and \(\pm\)30\({}^{\circ}\), respectively. A mean value difference is observed between BEM and the two higher fidelity models that increases with yaw angle (\(\approx\)3.5% at \(\pm\)15\({}^{\circ}\) and \(\approx\)8.5% at \(\pm\)30\({}^{\circ}\)). Mean wind speed has a smaller impact. Nevertheless, the amplitude of the variation changes similarly for all three methods. Moreover, a phase difference in the range 35\({}^{\circ}\)-45\({}^{\circ}\) between BEM and the other two models exists in all cases. The corresponding deflections at the blade tip are depicted in Figures 25 and 26, presenting qualitatively similar results with those moments. Figure 21: Circulation radial distribution at 8 m/s axial wind speed. Averaging over the final revolution of the simulation. Figure 22: Angle of attack radial distribution at 8 m/s axial wind speed. Averaging over the final revolution of the simulation. Figure 23: Out-of-plane bending moment of blade root at 15\({}^{\circ}\) yawed wind speed at 8 and 11 m/s. Figure 24: Out-of-plane bending moment of blade root at 30\({}^{\circ}\) yawed wind speed at 8 and 11 m/s. Figure 26: Out-of-plane deflection of blade tip at 30\({}^{\circ}\) yawed wind speed at 8 and 11 m/s. Figures 27 and 28 show the twisting moment of the blade root at 8 and 11 m/s wind speed and for yaw angles of \(\pm 15^{\circ}\) and \(\pm 30^{\circ}\). The corresponding torsion angles at the blade tip are depicted in Figures 29 and 30. Very good agreement is observed both for the mean values, as well as for the amplitudes of the variations. The phase differences of BEM encountered in the out-of-plane signals are not present, or at least are much less pronounced herein. The torsion angle is not only driven by the aerodynamic twisting moment but also by the out-of-plane bending loads as a result of very high flapwise deflection. This is also justified by the phase difference of the torsion angle signals, comparing positive and negative yaw angles, which agrees with the corresponding phase difference of the out-of-plane deflection and load signals. In summary, the main differences between the three models are concentrated in the out-of-plane moments (Figures 23 and 24) and deflections (Figures 25 and 26). A small difference ranging from 4% to 10% is observed in the mean value, alongside with a phase difference of about 35\({}^{\circ}\) to 45\({}^{\circ}\). This can be attributed to the differences encountered in the axial induction factor seen in Figures 31 and 32. Clearly, AL and LL predict lower mean values compared to BEM, which explains the level difference of moments and deflections (lower induction results in higher inflow velocity and therefore in higher loads). This difference grows as the yaw angle increases. Furthermore, AL and LL predict higher variation amplitude of induction than BEM at all wind speeds and yaw angles. Moreover, a phase difference of about 20\({}^{\circ}\) to 45\({}^{\circ}\) is encountered, which is close to the one seen in the out-of-plane moments and deflections. The phase difference in loads and deformations is significant and needs deeper investigation. At positive yaw angles, both at a wind speed of 8 and 11 m/s, all aerodynamic models predict the maximum loading around the azimuth angle of 180\({}^{\circ}\). The reason for that is the increased relative velocity seen by the blade at this azimuth position, due to its clockwise rotation. In this position, the in-plane component of the wind is superimposed to the rotational speed of the blade. Apart from that, the effect of the wake skewness is important. It is the origin of the differences between the different aerodynamic models.