## 3 Theoretical Formulation and Numerical Modeling
### Effect of the Locations of Strips  
In order to investigate the influence of the locations of strips on the wake flow, a pair of rectangular strips with a thickness of 0.5 mm was selected. Six different installation locations were discussed: \(\alpha=0^{\circ}\), \(\alpha=20^{\circ}\), \(\alpha=60^{\circ}\), \(\alpha=90^{\circ}\), \(\alpha=120^{\circ}\) and \(\alpha=150^{\circ}\). The cylinder with a diameter of 50 mm (\(\delta/D=0.01\)) has a starting speed of 1.1 m/s, and the starting is almost instantaneous. The focus of this paper is on the initial stage of transient flow behind the cylinder, so only the results before the dimensionless time, T = 3, are given. The effect of the locations of strips on the drag coefficient, the lift coefficient, the pressure coefficient, the velocity distribution on the axis and the vorticity contours for the wake flow were analyzed. Figure 7 depicts the comparison of the drag coefficients between the smooth cylinder and cylinder with strips. It can be seen that the drag coefficient of the smooth cylinder is gradually increasing. When the strips are mounted on the cylinder, the drag coefficient increased initially and then decreased  
Figure 5: The comparison of the velocity distribution on the axis between the present solutions and the results of Reference [43] for Re = 550. Figure 6: The comparison of the length of the wake and the coordinate of the eddy center between the present results and the results of Reference [43] for Re = 550.  
with the placement angle of strips increased. In the cases of \(\alpha=0^{\circ}\) and \(\alpha=20^{\circ}\), the trends of the results are the same. When the dimensionless time, T, is less than 1, the drag coefficient is almost the same as that of the smooth cylinder. However, as time goes on, the results of these two cases become stable, indicating that installing strips near the forward stagnation point will reduce the drag acting on the cylinder. In the case of \(\alpha=60^{\circ}\), the drag coefficient is four times as large as that of the cylinder without strips when T = 3. A new phenomenon that a peak appears in the curve of the drag coefficient has emerged at the case of \(\alpha=90^{\circ}\). The results of \(\alpha=120^{\circ}\) are much smaller than that of \(\alpha=90^{\circ}\), indicating that the local peak value and the dimensionless time corresponding to the peak are sensitive to the arrangement angle of the strips. It can be concluded from the results that the installation of strips near the stagnation point can reduce the drag, while the installation of strips near the separation point can increase the drag. We can find an explanation from the vorticity contours of the wake. After the strips are installed near the separation point, the rotational speed of the vortex center increases, and more kinetic energy is transferred from the cylinder to the fluid. Figure 7: \(Cont.\)  
Figure 8 shows the comparison of the lift coefficients between the smooth cylinder and cylinder with strips. It can be seen that the lift coefficient of the smooth cylinder remains near zero. When the strips are mounted on the cylinder, the lift coefficient increased first and then decreased as the arrangement angle of strips increased. When \(\alpha=0^{\circ}\) and \(\alpha=20^{\circ}\), the variation trend of the lift coefficient is similar. It is equal to the smooth cylinder before the dimensionless time is less than 1.5. As time goes on, it keeps growing. When the dimensionless time, T, is equal to 3, the lift coefficient is 0.05 and 0.2, respectively, which is much larger than that of the cylinder without strips. As the placement angle of strips increases, the oscillation of the lift coefficient is suppressed. When \(\alpha=150^{\circ}\), a peak-to-valley appears in the lift coefficient curve at T = 2.5. In summary, the influence on the lift coefficient is large when the strips are moved near the stagnation point. Figure 8: _Cont._  
Figure 7: The comparison of the drag coefficients between the smooth cylinder and cylinder with strips for Re = 55,000.