# Numerical Study of Flow Separation Control over a Hump Airfoil Using a Novel Sweeping Jet Actuator
## 3 Results
By T* = 1/3T, the size of V2 has mostly disappeared. At T* = 1/2T, at this point, the jet is fully attached to the upper surface, generating a newly separated vortex V3 at the exit. Simultaneously, the size of V1 reaches its maximum and moves downstream. At T* = 5/6T, the size of V3 does not increase significantly, and V1 continues to move downstream while its size decreases. At T* = T, the jet attaches to the lower surface, V4 appears, and V1 keeps moving downstream. At this point, one cycle is completed. Throughout the entire cycle, V1 initially grows from a small size to form a large separation vortex, accompanied by a gradual reduction in the size of V2. When V1 reaches its maximum size, V2 disappears. Subsequently, with the appearance of V3, the development process of V1 is similar to that of V2, moving downstream and decreasing in size. When the new V1 emerges (i.e., V4), the entire cycle concludes. The motion of V1 is also the reason behind maintaining consistency between the flow field frequency at the two monitoring points and the oscillation frequency. At F+ = 0.375, the periodic behavior is essentially akin to F+ = 1. During the transition of the oscillating jet from the lower wall to the upper wall, V1 increases in size continuously, yet due to the longer cycle time, V1 achieves a larger size. During the phase where the oscillating jet moves from the upper wall to the lower wall, V3 maintains a constant size and the slower downstream motion of V1 results in the existence of two separation regions within the average flow field. As shown in Figure 18, the periodic flow field for F+ = 10 exhibits similarities to the flow field for F+ = 1, but there are also some differences. From T* = 0 to T* = 1/3T, the size of V1 gradually increases; however, it remains relatively small. V2 moves downstream, but due to the shorter cycle, the movement is less pronounced. At T* = 1/2T, V1 replaces the V3 from the F+ = 1 case, and at T* = 5/6T, it merges with V2 to form a new V2. Throughout the entire cycle, the size of V2 does not exhibit as significant variations as in other F+. It essentially represents the size of the separation region. The subtle motion of V2 is the reason for the lower frequency observed at monitoring point 2. Figure 18: _Cont._  
Furthermore, the presence of V1 exhibits an entrainment effect, as it can assist in directing the outflow from the SWJ actuator and the incoming external flow along the direction of the airfoil. This results in more momentum being applied to flow control. However, at this VR, the SWJ actuator provides limited entrainment energy, and V1 dissipates too quickly, resulting in poor flow control effectiveness. With an increase in the VR, V1 can entrain more energy, which reduces the size of V2. When VR = 3.1, V2 almost disappears, achieving complete flow separation. In the periodic flow fields described above, studies were conducted on the cyclic flow patterns for F\({}^{+}\) = 1 and 10, elucidating the operational mechanisms of the SWJ actuator under different F\({}^{+}\) conditions. However, at VR = 3.1, a suppressive effect on flow control was observed specifically for F\({}^{+}\) = 1. In response to this phenomenon, an investigation was conducted on the flow field at VR = 3.1 with F\({}^{+}\) = 1. In Figure 19, it was found that throughout the entire cycle, the developmental trend of V1 remained consistent with previous observations. However, the size of V3 noticeably increased during this process, with its dimensions essentially matching the size of the separation vortex in the average streamwise velocity field. This finding suggests that the inhibitory effect on flow control is attributed to the growth of V3. Figure 18: Periodic flow field of the HUMP airfoil under F\({}^{+}\) = 10 and VR = 1.8 control.