## 3 Results and Discussion
### Validations of Numerical Modeling Methods  
The pitch-oscillation case in the deep stall regime is selected for analyses of the grid independence and time step independence, where \(\alpha_{m}=14^{\circ}\), \(A=10^{\circ}\), and \(k=0.078\). Different grid resolutions are obtained by changing the numbers of wrap-around points on the airfoil and normal layers; then, three types of grids are generated with total numbers of 37,850, 51,090, and 70,525, respectively. Three different time steps of 0.002 s, 0.001 s, and 0.0005 s are used with the steps per cycle being 273, 546, and 1092, respectively. However, there is no clear difference in the lift coefficient among the test cases. The streamwise velocity profile is used to estimate the capability of capturing flow structures; this velocity profile is at mid-chord at the phase angle of \(90^{\circ}\) (i.e., \(\phi=90^{\circ}\), where \(\phi=2\pi\theta\)). The coarsen grid and large time step can yield clear deviation (Figure 7). Finally, the grid in the size of 51,090 and the time step of 0.001 s are chosen as the computational settings.  
In light stall, the numerical results agree well with the experimental data [40] as shown in Figure 8. An improvement over [PERSON], [PERSON], and [PERSON]'s CFD results [17] can be observed due to the consideration of the transition effect. The B-L model shows a reasonable representation of unsteady aerodynamics. Because of a lack of measurements under OF, the CFD results are compared with those of [PERSON] et al. in the same conditions [41]. First and foremost, it is necessary to clarify the determination of the AOA under OF. In steady flow, the AOA is defined as the angle between the chord and freestream velocity, and this instantaneous AOA (denoted as 'inflow angle') is assured at same value for both motions in the computations. Actually, the true AOA (denoted as 'local angle') is different, because the relative velocity direction to the airfoil can be influenced by the freestream time lag and flow disturbance of the airfoil. To obtain the local angle and compare it with the inflow  
Figure 5: Schematic of a wind turbine in the yawed condition. (**a**) Top view; (**b**) Front view.  
Figure 6: The variation of the angle of attack (AOA) and relative velocity with the azimuth at different spans. Wind speed is 13 m/s, and yaw angle is \(30^{\circ}\). (**a**) AOA; (**b**) Relative velocity.  
angle, we extract the unsteady relative velocity vector at the location of \(3\)\(c\) before the airfoil stagnation point (Figure 9). An apparent lag between the two types of AOAs can be observed during downstroke. The variation amplitude of the local angle becomes slightly larger. Both the trend and the shape of the hysteresis loop agree well with the results of [PERSON] et al. (2018), as shown in Figure 10. A notable feature is that the hysteresis loop is more apparent with respect to the inflow angle than to the local angle. To avoid ambiguity, the phase angle will replace the AOA as an independent variable afterwards.  
Figure 8: Comparison of aerodynamic coefficients under pitch oscillation. \(\alpha_{m}=8^{\circ}\), \(A=10^{\circ}\), and \(k=0.026\). (**a**) The lift coefficient; (**b**) The drag coefficient; (**c**) The pitching moment coefficient.  
Figure 7: Effects of grid resolution and time steps on streamwise velocity profile at mid-chord at \(\phi=90^{\circ}\). \(S_{n}\) is a normal distance away from the mid-chord, and \(u_{e}\) is the streamwise velocity of external flow. (**a**) Effect of grid resolution; (**b**) Effect of time steps.