## 4 Analyses and Discussions  
### The Dynamic Stall Characteristics of Airfoil Under 3D Conditions  
Aiming at researching the dynamic stall characteristics of rotor airfoil with OFV under actual rotor working conditions, a two-blade untwisted rotor model with a rectangular planform is designed based on the OA209 airfoil, and the aspect ratio of the rotor blade is 15.0. The blade grids with \(356\times 70\times 90\) points are generated based on the 2D airfoil grids, and the background grids are \(176\times 99\times 156\). The numerical simulation is performed at an advance ratio of 0.3 with blade tip, Mach number of 0.6, and the pitch angle is \(\alpha=10.0^{{}^{\circ}}-6.0^{{}^{\circ}}\sin(\omega t)\). In this case, two different spanwise sections of blade, 0.6 R and 0.7 R (R is the radius of rotor), are selected to compare the numerical results under the 2D conditions, where the steady Mach numbers are 0.36 and 0.42, the unsteady Mach numbers are verified based on the steady Mach number with \(\lambda\) of 0.5 and 0.43, respectively. The corresponding airflow information of different spanwise sections is shown in Table 1.  
In order to verify the accuracy of the present CFD method used in the 3D rotor condition, a case of SA349/2 rotor with an advance ratio of 0.26 is present in this section, just as shown in Figures 6 and 7. The comparisons of normal force (Cn) and Cp distributions (0.75 r/R) are correlated well with the test data [37]. It is illustrated that the present CFD method can effectively simulate the unsteady aerodynamic characteristics of a rotor.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Blade Section** & \(M_{\mathbf{B}}\) & \(\Lambda\) & \(\mathbf{k}\) \\ \hline
**0.6 R** & 0.36 & 0.5 & 0.0556 \\
**0.7 R** & 0.42 & 0.43 & 0.0476 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Airflow information at different blade sections.  
Figure 5: Comparison of simulated results with [PERSON]’s theory under the oscillating freestream velocity (OFV) condition.  
The comparisons of dynamic stall characteristics of the OA209 airfoil between the 2D and 3D conditions are shown in Figure 8. It is illustrated that the simulated \(C_{l}\) under the OFV condition is much closer to that simulated under the 3D rotor condition compared with the simulated results under SFV conditions at sections of 0.6 R and 0.7 R. Meanwhile, it can be noticed that the simulated results under the 2D OFV conditions are smaller than that of the 3D simulation between the azimuth  
Figure 6: Comparison of normal force between the test data and numerical data. (a) r/R = 0.75. (b) r/R = 0.97.  
Figure 7: Comparison of Cp between the test data and numerical data. (a) \(\psi\) = 90\({}^{\circ}\). (b) \(\psi\) = 180\({}^{\circ}\). (c) \(\psi\) = 270\({}^{\circ}\). (d) \(\psi\) = 360\({}^{\circ}\).  
of 240.0\({}^{\circ}\) to 360.0\({}^{\circ}\), because the airflow separation is restricted by the spanwise flow under the 3D condition [38]. Therefore, the lift stall would be postponed. From this case, it is illustrated that the dynamic stall characteristics of an airfoil under the OFV condition could reflect the actual unsteady aerodynamic characteristics of rotor airfoil in forward flight more accurately. Therefore, the dynamic stall characteristics of rotor airfoil need to be researched under the OFV conditions more deeply.