# Numerical Study on Dynamic-Stall Characteristics of Finite Wing and Rotor
## 3 Analyses and Discussion
### Rotor-Blade Dynamic Stall  
Helicopter rotors usually have the dynamic-stall phenomenon appear in the retreating side in forward flight due to the cyclic pitch movement of the rotor blade. In order to research rotational influence on dynamic-stall characteristics, a simplified case was performed based on finite-wing research. The used rotor in this study had two rectangular blades, and the shape of the rotor blade was the same as the finite wing. In this case, numerical simulation was performed at an advance ratio of 0.3 with blade-tip Mach number of 0.6. To dismiss the interaction of the subordinate influence factor on rotor dynamic stall, the cyclic pitch of the rotor blade was simplified as \(\alpha=10.0^{\circ}-8.0^{\circ}\sin(\omega t)\). Streamline and vorticity contour distributions at \(\alpha=18.00^{\circ}\) on the surface of the rotor blade at an azimuth of \(270^{\circ}\) are shown in Figure 14. It can be seen that a small airflow-separation region appeared on the upper surface from r/R = 0.7 to 0.9. It can also be seen that streamlines inclined to the blade tip. This may be attributed to the rotational motion of the blade, because airflow near the blade surface would follow with blade rotation due to airflow stickiness. Therefore, airflow convects to the blade tip due to centrifugal force. From the vorticity contours of the dynamic-stall vortex at different blades, it can be seen that vorticity basically concentrates on the blade surface. This means that no obvious LEV forms and sheds under this condition, which is very different from the finite-wing case. As a result, it is indicated that the dynamic stall of the rotor blade would be restricted. In order to analyze spanwise velocity characteristics, spanwise velocities (normalized by blade-tip velocity) at different chord positions are shown in Figure 15 (\(\alpha=18.00^{\circ}\)), and these data were calculated at a normal distance of 0.001 c from the blade surface, where c represents the chord length of the blade. It can be seen that spanwise velocity is basically enlarged with the increase of blade radius. This variation can be attributed to centrifugal force being larger when radius increases. As a result, airflow would more obviously be accelerated, and spanwise velocity would be larger. Moreover, it could be seen that spanwise velocity is also enlarged with the increase of chord position at the same blade radius. This is due to airflow acceleration time along the blade surface increasing as chord position  
Figure 12: Pressure and streamline distributions of a finite wing on upper and lower surfaces. The comparison of \(C_{l}\) curves between the different blade sections and the 2D airfoil is shown in Figure 16. The dynamic-stall characteristics under a 2D condition are simulated under variational freestream velocity, i.e., \(Ma=0.6\cdot\lambda-0.18\cdot\sin(\omega t)\), where \(\lambda\) represents blade section. AoA variations are the same as those of the rotor blade, i.e., \(\alpha=10.0^{\circ}-8.0^{\circ}\sin(\omega t)\). By comparing the simulated rotor results with \(\mu=0.0\) and \(\mu=0.3\), it can be seen that rotor \(C_{l}\) with \(\mu=0.3\) is larger than that of \(\mu=0.0\) at different blade sections, because downwash airflow in forward flight is smaller than that in hovering flight. As a result, effective AoA decrement is smaller in forward flight. It can also be seen in the figure that the deviation between the two rotor conditions is decreased with the increase of the blade radius, because downwash airflow would be reduced near the blade tip. Another observation is that dynamic stall occurs on the 2D airfoil. However, dynamic stall is not obviously on the rotor blade. One of the reasons is that airflow in the boundary layer of the blade surface would receive additional force due to Coriolis force, as shown in Figure 17. It can be seen that  
Figure 16: Lift coefficients vary with azimuth at different blade sections. (**a**) r/R = 0.5, (**b**) r/R = 0.7, (**c**) r/R = 0.9, (**d**) r/R = 0.95.