**4. Conclusions**

This paper has presented the results of unsteady numerical simulations investigating the static and dynamic aerodynamic performances of a NREL 5-MW HAWT under yawed and yawing conditions. The blades were considered rigid for cases with a prescribed motion, and the tower was not included in the computational domain. The numerical simulation results based on the T-SST turbulent model were consistent with the BEM data. Fluctuating and alternative loads were observed for the yawed case, resulting in the retreating and advancing effect. As the yawing angle decreased, overall performance also decreased according to the cosine law. The results sugges<sup>t</sup> larger variations in power for the dynamic yaw case, compared to yawed cases. The wind turbine suffers from the coupled effects of the rotational axes (yawing axis and rotating axis). For maximum loading of rotor, the combined effects of the yawed condition and yawing resulted in an azimuth around the first periodic, which became larger as the yaw angle increased.

In the simulations of two different yawing start-stop durations (2-s and 4-s), the faster shift of yaw angle (2-s duration) resulted in a larger torque than the 4-s duration, owing to the additional velocity induced by the yawing effect of different sinusoidal frequency and yaw velocity magnitude. Interestingly, the torque of the rotor and blade was much higher in forward yawing compared to backward yawing, caused by reversing the direction of the yaw velocity. The wake deflection occurs in the near wake flow structure and expands more than in the yawed case. The different start-stop durations under dynamic yawing have little influence on the near wake velocity contour. The next step will be to include deformation of the blade in the simulation of multiple axial angular motions.

**Author Contributions:** S.K. and H.H. contributed to the conception of the study. X.W. and Z.Y. contributed significantly to analysis and manuscript preparation; Z.Y. performed the data analyses and wrote the manuscript; X.W. helped perform the analysis with constructive discussions.

**Funding:** This research was supported by National Natural Science Foundation of China (51576065), and the Fundamental Research Funds for the Central Universities (2015RCY05, 2018ZD09).

**Conflicts of Interest:** The authors declare no conflict of interest.
