# 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 \(h/D=1/4\)
#### 3.2.1 Aerodynamic Statistics and Frequency Characteristics  
Figures 8-10 show the variations in the lift and drag coefficient statistics of the square cylinder for the wind angle (\(\theta\)) and the velocity ratio (\(k\)) for each of the three rotation directions, respectively. The results include the mean value \(\overline{C}_{l}\) and the fluctuating value \(C_{l}\prime\) of the lift coefficient, as well as the mean value \(\overline{C}_{d}\) and the fluctuating value \(C_{d}\prime\) of the drag coefficient. When \(k>0\), the small rotating cylinders transfer the momentum into the flow field. The results for \(k=0\) given in the abovementioned figures correspond to the results from the flow around a standard square cylinder. As shown in Figure 8a, when \(\theta=0^{{}^{\circ}}\) and \(\theta=180^{{}^{\circ}}\), the square cylinder is symmetrically placed in the flow direction. Therefore, the value of \(\overline{C}_{l}\) is near zero for different \(k\) values at these two wind angles. When \(15^{{}^{\circ}}<\theta<90^{{}^{\circ}}\) and \(k>0\), the absolute value of \(\overline{C}_{l}\) is greater than the absolute value of \(\overline{C}_{l}\) when \(k=0\). When \(\theta=15^{{}^{\circ}}\) and \(k=4\), the value of \(\overline{C}_{l}\) increases \(5.36\) times compared with its value when  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{D/\(L\)} & \multicolumn{4}{c}{\(k\)=0} & \multicolumn{4}{c}{\(k\)=2} \\ \cline{2-13}  & \(C_{l}^{{}^{\prime}}\) & \(-\) & \(C_{d}\) & \(C_{d}^{{}^{\prime}}\) & \(S_{t}\) & \(C_{l,c}^{{}^{\prime}}\) & \(-\) & \(C_{d,c}^{{}^{\prime}}\) & \(S_{t,e}\) & \(E_{C  
\(k=0\). When \(\theta\geq 120^{\circ}\), the values of \(\overline{C}_{l}\) are similar among them for various \(k\) values. As illustrated in Figure 8b, when \(\theta\leq 60^{\circ}\) and \(k>0\), \(C_{l}\prime\) is lower than the value of \(C_{l}\prime\) when \(k=0\). It may be observed that for smaller wind angles, the rate of decrease of \(C_{l}\prime\) becomes more obvious. The alternate shedding vortex behind the square cylinder is responsible for the lift coefficient fluctuation; the results show that the vortex shedding of the square cylinder should be suppressed at small wind angles. When \(k=4\) and \(\theta\) increases from \(0^{\circ}\) to \(15^{\circ}\), \(C_{l}\prime\) decreases by \(98\%\) and \(87\%\), respectively, compared with the value of \(C_{l}\prime\) when \(k=0\). When \(\theta=60^{\circ}\) and \(k=4\), the value of \(C_{l}\prime\) is slightly higher than the value of \(C_{l}\prime\) when \(k=2\). This instance suggests that the increment of momentum that is transferred to the flow field may lead to the diminution of the control effect. When \(\theta>60^{\circ}\), \(C_{l}\prime\) increases with the increase in \(k\); this means that the MSBC is involved in the enhancement of the wake. As shown in Figure 8c, the variation of \(\overline{C}_{d}\) at \(k=0\) is similar to that of \(C_{l}\prime\) at \(k=0\) in Figure 8b. When \(k=4\) and \(\theta\) increases from \(0^{\circ}\) to \(15^{\circ}\) and then increases to \(30^{\circ}\), the values of \(\overline{C}_{d}\) decrease by \(36\%\), \(54\%\), and \(47\%\), respectively, compared with the value of \(\overline{C}_{d}\) when \(k=0\). When \(\theta=60^{\circ}\), the value of \(\overline{C}_{d}\) at \(k=2\) decreases to the lowest point. When \(\theta=90^{\circ}\) and \(\theta=120^{\circ}\), the values of \(\overline{C}_{d}\) at \(k=4\) are \(1.94\) and \(1.38\) times the values of \(\overline{C}_{d}\) when \(k=0\), respectively. When \(\theta=150^{\circ}\) and \(k>0\), the values of \(\overline{C}_{d}\) are near the value that corresponds to \(k=0\). When \(\theta=180^{\circ}\), the values of \(\overline{C}_{d}\) at \(k=2,\ 4\) increase by \(37\%\) and \(44\%\), respectively. As shown in Figure 8d, when \(\theta\geq 30^{\circ}\), \(C_{d}\prime\) increases with the increase in \(k\), and the change is similar to the results when \(k=0\).