## 3 Results and Discussions
### Flow Development and Separation Points on the Suction Surface of the Airfoil  
The reason for the variation of forces and lift-to-drag ratio can be found in flow field contours. One case was selected to investigate the characteristics as an example. The pressure fields and corresponding streamlines at different angles of attack through a full pitching cycle in the case with \(k=0.052\), \(\alpha_{0}=10^{\circ}\), \(\alpha_{amp}=10^{\circ}\) are demonstrated in Figure 8. It was observed that the development trend of flow field structures of the DU 91-W2-250 was qualitatively in good agreement with the conclusions of other papers with different shapes of airfoils [15; 45; 46]. The flow was fully attached to the airfoil from the angles of attack \(\alpha_{t}=0^{\circ}\)\(\sim\)10.31\({}^{\circ}\). The hysteresis of stall angles of attack in lift curves, which is the most obvious feature of dynamic stall, is observed clearly here. The lift dropped suddenly at about 14\({}^{\circ}\) in the hysteresis loop, while the static stall angle was 12\({}^{\circ}\) in the experiment. It was manifested as reversed flow generated near the trailing edge, as shown in Figure 8c. The reverse flow was due to the adverse pressure gradient caused by the rapid movement of the airfoil surface. As the angle of attack increased, the clockwise-rotating vortex on the suction surface moved forward to the leading edge, and the strength of the recirculation increased. There was a small counterclockwise-rotating vortex behind the trailing edge vortex in Figure 8c, implying that the vortex near the trailing edge started to move downstream slowly. This would lead to a decrease in the lift coefficient compared with the lift coefficient curves in Figure 7a. The effects of vortices rotating in two opposite directions on the lift coefficient are shown in Figure 9 in more detail. At Point A in Figure 9a, the clockwise-rotating vortex appeared. With the growth of the vortex, the lift coefficient was still increasing. The growing vortex increased the slope of the lift curves until the maximum value of \(C_{l}\) when the angle of attack was 14.07\({}^{\circ}\) at Point B; see Figure 9b. The reason that \(C_{l}\) decreased was the generation of the counterclockwise-rotating vortex, as shown in Figure 9c. \(C_{l}\) decreased with the growth of the counterclockwise-rotating vortex until the counterclockwise-rotating vortex traveled into the wake and the clockwise-rotating vortex appeared again; see Figure 9e. This process would repeat until the trend of the lift coefficient curve became flat when \(\alpha_{t}=10.31^{\circ}\) in the downstroke process. The counterclockwise-rotating vortex did not appear from this moment. In other words, the growth and shedding of vortices in opposite directions led to the fluctuations of the lift coefficient curve. The lift coefficient \(C_{l}\) increased with the growth of the vortex, and it decreased with the shedding of the vortex. What needs to be noted here is that the range of the angles of attack in this case was from 0\({}^{\circ}\)-20\({}^{\circ}\), so the airfoil did not experience a deep stall. Vortices on the suction surface of airfoil did not develop to reach the leading edge, but only reached 30% of the chord from the leading edge. Therefore, in this case with \(k=0.052\), \(\alpha_{0}=10^{\circ}\), \(\alpha_{amp}=10^{\circ}\), the LEV observed in other papers [15] did not appear, but it appeared when \(k=0.052\), \(\alpha_{0}=15^{\circ}\), \(\alpha_{amp}=10^{\circ}\). After the maximum angle of 20\({}^{\circ}\), the airfoil was performing the downstroke motion. It is known that the lift coefficient of the downstroke process was much smaller than the upstroke process from Section 3.1. This is because the vortex still existed near the trailing edge and the pressure of pressure surface was lower at the same angle of attack by comparing Figure 8b,h and Figure 8c,g. As the airfoil attack angle became smaller, vortices eventually moved into the wake.