# Moving Surface Boundary-Layer Control on the Wake of Flow around a Square Cylinder
## 3 Results and Discussion
### Analysis of Influence of \(D/L\) and \(h/D\) Parameters
When the two circular cylinders are rotating, the \(C_{l,c}\)/, \(\overline{C}_{d,c}\), and \(C_{d,c}\)/ of the controlled square cylinder are lower than those of the uncontrolled square cylinder, whereas the \(S_{t,c}\)  
Figure 6: Statistical values of lift and drag coefficients, Strouhal number, and control effects under different \(D/L\) values, (**a**) Statistical values of \(C_{l},\ C_{d}\), and \(S_{t}\), (**b**) Control effects of \(C_{l},\ C_{d}\). \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{_D/L_} & \multicolumn{6}{c}{_k=0_} & \multicolumn{6}{c}{_k=2_} \\ \cline{2-11}  & \(C_{l}^{{}^{\prime}}\) & \(C_{d}\) & \(C_{d}^{{}^{\prime}}\) & \(S_{t}\) & \(C_{L,c}^{{}^{\prime}}\) & \(C_{d,c}^{{}^{\prime}}\) & \(S_{t,c}\) & \(E_{C_{t}}\) (\%) & \(E_{C_{d}}\) (\%) \\ \hline
0.05 & 0.3466 & 1.2873 & 0.0186 & 0.15 & 0.2584 & 1.2255 & 0.0141 & 0.1625 & 25.45 & 4.80 \\
0.1 & 0.3433 & 1.2274 & 0.0180 & 0.15 & 0.1063 & 1.0828 & 0.0051 & 0.1786 & 69.04 & 11.78 \\
0.2 & 0.3309 & 1.1159 & 0.0155 & 0.15 & 0.0306 & 0.9144 & 0.0012 & 0.1961 & 90.75 & 18.06 \\
0.3 & 0.3238 & 1.0145 & 0.0128 & 0.15 & 0.0089 & 0.7927 & 0.0008 & 0.2000 & 97.25 & 21.86 \\
0.4 & 0.3189 & 0.9091 & 0.0093 & 0.15 & 0.0018 & 0.7027 & 0.0011 & 0.1832 & 99.44 & 22.70 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Lift and drag coefficient statistics, Strouhal number, and control effects of flow around an uncontrolled (\(k=0\)) and controlled (\(k=2\)) square cylinder with \(h/D=1/4\). of the controlled square cylinder is higher than that of the uncontrolled square cylinder. With the increasing \(D/L\), the control effect \(E_{C_{l}}\) on the RMS value of the lift coefficient is gradually increased from 25.45% to 99.44%, and the control effect \(E_{C_{d}}\) on the mean value of the drag coefficient is gradually increased from 4.8% to 22.7%. When \(D/L=0.3\), the RMS value of drag coefficient plummets to its minimum value, which is 93.7% lower than that of the uncontrolled square cylinder, and the \(E_{C_{l}}\) and \(E_{C_{d}}\) at this time are 97.25% and 21.86%, respectively. When \(D/L=0.05\,\sim 0.3\), the \(S_{l,c}\) is gradually increased from 0.1625 to 0.2; in turn, when the \(D/L\) is increased to 0.4, the \(S_{l,c}\) is decreased slightly to 0.1832. It can be seen that the rotating circular cylinders play the role of controlling the wake of the square cylinder. The mean value of the drag coefficient can be reduced by up to 22.7%, and the fluctuations of the lift and drag coefficients are basically completely suppressed, while the vortex shedding frequency in the wake of the square cylinder is increased from 8.3% to 33.3%. When \(D/L=0.3\), the aerodynamic statistical parameters, Strouhal number (\(S_{t}\) and \(S_{t,c}\)), and control effectiveness of flow around the uncontrolled (\(k=0\)) and controlled (\(k=2\)) square cylinder versus \(h/D\), the range of which varies from 1/8 to 3/8 with an interval of 1/16, are shown in the Figure 7 and Table 4. With gradually increasing \(h/D\), the \(C_{l}\) of the uncontrolled square cylinder does not change significantly between 0.3226 and 0.3388, and the \(S_{t}\) is also kept unchanged at 0.15, while \(\overline{C}_{d}\) and \(C_{d}\)' are decreased by 13% and 23%, respectively. When \(k=2\), the \(C_{l,c}\)' and \(\overline{C}_{d,c}\) of the controlled square cylinder are gradually increased with increase of \(h/D\), and the corresponding control effects of \(E_{C_{l}}\) and \(E_{C_{d}}\) are gradually decreased with the increasing \(h/D\). The \(C_{d,c}\)' of controlled square cylinder changes from 0.0006 to 0.0039, which is about 5.2% to 26% of the results of uncontrolled square cylinder, and the \(S_{t,c}\) of controlled square cylinder is between 0.18 and 0.2, which is still greater than the result of the uncontrolled square cylinder.