# Flow-Induced Vibration of Cantilever Type Elastic Material in Straight Tricylinder
## 3 Results and Discussion  
### Lift Drag Coefficient  
The drag coefficient \(C_{D}\) and lift coefficient \(C_{L}\) are more effective in reflecting the primary stress on the cylinder for VIV. The lift and drag coefficient quantify the resistance experienced by the flexible cylinder in the direction of incoming flow (x-axis) and the lift force exerted on it in the lateral direction (z-axis). Figure 4 illustrates the time history curve of \(C_{D}\) and \(C_{L}\) at an L/D distance ratio ranging from 3 to 7. At L/D ratios of 3, 4, 5, and 6, upstream cylinder one exhibits a lower to \(C_{D}\) by approximately 16-27% compared to downstream cylinders two and three. Moreover, there is a drag difference between downstream cylinders two and three, amounting to around 4-8%. This phenomenon occurs due to the influence of a wake  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Mesh** & **Elements** & \(C_{D}\) & \(Y^{+}\) & \(S_{t}\) \\ \hline coarse & 626,726 & 1.6723 & 200 & 0.2238 \\ medium & 1,273,191 & 1.3137 & 120 & 0.2035 \\ fine & 3,729,179 & 1.2829 & 75 & 0.1925 \\ finer & 5,806,552 & 1.2818 & 50 & 0.1924 \\ [PERSON]’s and [PERSON] et al [20] & / & 1.28 & / & 0.19 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Mesh parameter.  
Figure 3: Meshing: (**a**) horizontal screenshot. (**b**) Mesh around the three cylinders.  
generated during VIV migration on downstream cylinders as they deform towards the middle O point. Consequently, upstream cylinder one becomes locked with a downstream cylinder, resulting in continuous deviation towards this particular cylinder while experiencing reduced resistance. This effect is particularly evident when considering spacing ratios L/D of either five or six. The coefficient \(C_{L}\) generally ranges between \(-0.1\) and \(+0.1\) without significant amplitude differences observed between upstream and downstream cylinders; however, occasional interference from downstream cylinders may cause fluctuations around zero for upstream cylinder motion primarily influenced by wake effects from upstream cylinder, it causing negative deformation along Z-axis direction by negative forces for downstream cylinder two, whereas an opposite trend can be observed for downstream cylinder three instead. When considering a spacing ratio L/D equal to seven, these interference phenomena between cylinders are significantly reduced, as clearly depicted in Figure 5.  
Figure 4: Lift and drag coefficients with L/D = 3–7.  
Note that some profiles exhibit a noticeable oscillation in Figure 4. In current transient structure-fluid coupling simulations, we use a relatively large time step yet still achieve  
Figure 5: Comparisons of the distribution of force coefficients on the cylinder surface at H/D = 30: (**a**) cylinder 1; (**b**) cylinder 2; (**c**) cylinder 3.  
convergent solutions for each case due to the computational resource required for such three-dimensional bidirectional interactions.  
The surface pressure coefficient of a cylinder with a spacing ratio of D/L = 3\(-\)7 is illustrated in Figure 5. It can be observed that the differences in pressure coefficients among different spacing ratios are relatively small; Figure 5 shows the pressure at the top section of the cylinder. After its integration, the component in the X direction is the cross-section resistance \(F_{D}\), and the component in the Z direction is the cross-section lift \(F_{L}\). The resistance is mainly obtained by subtracting the pressure near 0\({}^{\circ}\) from the pressure near \(\pm\)180\({}^{\circ}\). The lift force is mainly obtained by subtracting the pressure around \(-\)90\({}^{\circ}\) from the pressure around 90\({}^{\circ}\). Of course, this is just the force on the cross-section, and the resistance to lifting on the cylinder has to be integrated into the Y direction. We can briefly judge the force on the section according to the difference in pressure at different angles.