# Moving Surface Boundary-Layer Control on the Wake of Flow around a Square Cylinder
## 3 Results and Discussion
### Detailed Results and Analysis of \(D/L=0.3\) and \(h/D=1/4\)
#### 3.2.4 Wake Vortex Structure
the square cylinder reaches a positive maximum value at this time. The streamline at the downstream of the main vortex is obviously curved, indicating that the Karman vortex street with alternating shedding exists in the wake of the square cylinder. When \(k=1\), it can be seen from Figure 26b that the flow velocity around the small cylinders is increased, and the rotating cylinders started to inject momentum into the wake. At this time, there are still shedding main vortices and obviously curved streamlines in the square cylinder wake. Compared with Figure 26a, the low-velocity region in the wake begins to narrow, the scale of the main vortex is decreased, and the distance between the vortex center and the square cylinder is increased. The influence of the main vortex on the square cylinder begins to weaken, and the fluctuation of the lift coefficient is reduced to a certain extent, which is consistent with the result in Figure 18a. When \(k=2,\ 3\), as the velocity ratio increases gradually, the velocity around the small cylinders is increased gradually, and the momentum injected into the wake field is also increased gradually, as shown in Figure 26c,d. Meanwhile, two symmetrical small vortices appear in the near wake region of the square cylinder, and the alternating shedding main vortices are pushed farther downstream. The scale and energy of the main vortices are gradually decreased, and the fluctuation of the corresponding lift coefficient is also reduced significantly, as shown in Figure 18b,c. As shown in Figure 26e, the small circle cylinders rotating with high velocity ratio of \(k=4\) inject more momentum to the wake. The high momentum is mainly concentrated in the near wake range of one time of the side length of the square cylinder and symmetrically distributed on both sides of the centerline of the square cylinder wake. There is a pair of stable and symmetrical small vortices between the high-momentum region and the upper and lower shear layers separated from the corners of the leading edge of the square cylinder. The low-velocity region of the square cylinder wake becomes narrower, the separated shear layers are no longer curled, and the main vortex have entirely disappeared. The streamlines are symmetrically distributed on both sides of the wake centerline and became more and more straight as they move downstream. At this time, the fluctuation of the lift coefficient has disappeared, and the mean value of the drag coefficient is also decreased to its minimum. It can be seen that MSBC achieves the purpose of completely eliminating the alternating shedding vortices by inputting high momentum into the wake of the square cylinder. Figure 26: Cont. Figure 27 shows the vorticity contours of the flow field around the square cylinder for different \(k\) values, with an outward rotation, and for wind angles of \(30^{\circ}\) and \(120^{\circ}\). The momentum injected by the rotating cylinders significantly influences the wake field at \(\theta=30^{\circ}\). When \(k=2\) and \(k=4\), vortices of different scales appear in the flow field, and the vortex shedding patterns are very complex. As shown in Figure 27a, the vortex shedding pattern is obviously different from the regular vortex shedding model when \(k=0\); the drastic change in the shedding mode and the vortex scale cause a significant increase in the lift and drag coefficients. As shown in Figure 27b, the two small rotation cylinders on the upper side of the square cylinder cannot control the shear layer that has separated from lower side. When \(k=4\), the vortex street still exists, and the entire vortex street presents an inclined downward direction. This leads to a positive mean value of the lift coefficient, which increases with the increase in \(k\). Figure 28 shows the vorticity contours of the flow field around the square cylinder for different \(k\) values, with clockwise co-rotation, and for wind angles of \(60^{\circ}\) and \(90^{\circ}\).