## 3 Results and Discussion
### Equivalence Analysis between Pitch Oscillation and Oscillating Freestream  
The aforementioned theoretical analysis indicates an opposite effect of PO and OF on the effective airfoil camber. Figure 11 shows the variations of the lift and the drag coefficients along one cycle. Notice that the difference in the nonlinear air loads (where \(\phi\) is from \(30^{\circ}\) to \(180^{\circ}\)) is relatively negligible. A clear difference in the linear lift coefficient can be observed with a higher value under PO during upstroke and a higher value under OF during downstroke; the CFD results agree well with the thin-airfoil theory. From the vorticity contours in Figure 12, flow is attached to the airfoil and there is no obvious difference between the two motions from \(\phi=270^{\circ}\) to \(\phi=360^{\circ}\). When the AOA reaches the maximum at \(\phi=90^{\circ}\), the flow separation is apparent under both PO and OF. The separated flow under PO is more persistent. In contrast, the vortex under OF rolls up and then sheds into wake. Despite a great difference in separated flow structure between the two motions, the associated aerodynamic  
Figure 10: Comparison of aerodynamic coefficients under oscillating freestream. \(\alpha_{m}=8^{\circ}\), \(A=10^{\circ}\) and \(k=0.026\). (**a**) The lift coefficient; (**b**) The drag coefficient; (**c**) The pitching moment coefficient. Figure 9: Comparison between the inflow angle and the local angle. loads do not show great differences. The possible reason is that the pressure distribution under PO possesses a sharp leading-edge suction peak, while the pressure distribution under OF experiences an elevated pressure on the suction side due to the separated vortex. These two factors may lead to an almost equal value in calculation. Figure 13 shows the unsteady pressure variations at different chordwise locations at \(\alpha_{m}=2^{\circ}\), \(A=8^{\circ}\), and \(k=0.078\). It is obvious that there is a stronger suction peak under PO than under OF. However, the pressure coefficient under OF decreases with a time lag. Because the difference between the two motions focuses on the linear part of the aerodynamic loads, the unsteady aerodynamic effect only at the low AOA is assessed. The mean AOA, AOA amplitude, and oscillation frequency are chosen as parameters to evaluate the difference. The deviation of the normal coefficient along one cycle between the two motions is defined as follows:  
Figure 11: Comparison of lift coefficient and drag coefficient between pitch oscillation and oscillating freestream. \(\alpha_{m}=8^{\circ}\), \(A=10^{\circ}\), and \(k=0.026\). (**a**) The lift coefficient; (**b**) The drag coefficient. Figure 12: Vorticity contours of pitch oscillation and oscillating freestream at different phase angles. \(\alpha_{m}=8^{\circ}\), \(A=10^{\circ}\) and \(k=0.026\). \[Dev.=\frac{max(|C_{n,pO}(\varnothing)-C_{n,OF}(\varnothing)|)}{C_{n,qs}} \tag{20}\]  
where \(C_{n,qs}\) is the quasi-steady normal coefficient at the mean AOA. Figure 14 indicates that the oscillation frequency \(f\) and the AOA amplitude \(A\) affect the deviation more strongly than the mean AOA. From the thin-airfoil theory, the key is the pitch rate \(\dot{\alpha}=2\pi fA\cos(2\pi f)\). Because \(f\) and \(A\) are factors of the pitch rate, the deviation becomes great when \(f\) and \(A\) are high. Under yawed inflow, the oscillation frequency is directly determined by the rotor speed, and the AOA amplitude is seriously affected by the yaw angle. Consequently, it is necessary to consider the effects of PO and OF separately. Figure 14: Effects of the oscillation frequency, the mean AOA and the AOA amplitude on the deviation between pitch oscillation and oscillating freestream. (**a**) Effect of the oscillation frequency; (**b**) Effect of the mean AOA; (**c**) Effect of the AOA amplitude. Figure 13: Comparison of unsteady pressures at different chordwise locations on the upper surface between pitch oscillation and oscillating freestream. \(\alpha_{m}=2^{\circ}\), \(A=8^{\circ}\), and \(k=0.078\).