# Aerodynamic Characteristics of Coupled Twin Circular Bridge Hangers with Near Wake Interference
## 4 Flow Visualization  
In order to better understand the flow characteristics and wake interference between two cylinders, two-dimensional fluid computations using CFD (computational fluid dynamics) technology were also performed to visualize the flow regimes around cylinders. RANS (Reynolds Averaged Navier-Stokes) and LES (Large Eddy Simulation) are two most popular methods in CFD simulation. In recent decades, they have been widely used in the simulation of flow around cylinders, and the efficiency of them has been verified by many previous studies [29]. By contrast, RANS is much less computationally intensive than LES and is sufficient to describe the nature of the problem in this study. Therefore, RANS equations were chosen and solved with the SST k-\(\omega\) turbulence model in this study [8; 51]. Before formal simulation, a mesh convergence test for the numerical model was carried  
Figure 10: Lift coefficients of coupled twin cylinders with various spacings. Figure 9: Drag coefficients of coupled twin cylinders with various spacings. out on a single circular cylinder (as shown in Appendix A). The computational domain used for the numerical model with a height of 45D and width of 68D was discretized by about 250,000 cells, and the mesh near cylinders is shown in Figure 11. Furthermore, to validate both the present experimental and numerical method, the results of a single circular cylinder are compared with the data of other literatures in Table 1. It can be seen that the present results are in agreement with the literature to a certain extent, especially those of the experiment. Nevertheless, the drag coefficient by numerical simulation of this paper is about 16-25% smaller than those of the experiments, while the corresponding numerical result of [52] is about 13-27% smaller than the experiment results. Present Strouhal numbers (St) also agree well with those of the previous papers. To sum up, errors in this paper can be generally accepted. According to the discussion in Section 3, there are two typical flow patterns for twin cylinders both in tandem and staggered arrangements with various spacings. Therefore, two typical spacings of 2.5D and 4.3D are selected for numerical computation. Figure 12 shows the velocity contours for twin cylinders arranged in tandem. It can be seen that the flow regime around the twin cylinders shows two typical patterns. For W/D = 2.5, both shear layers from the upstream cylinder symmetrically reattached to the downstream one, and as outlined above, flow velocity is very low in the gap between cylinders. Meanwhile, the vortex formation of the downstream cylinder is not identifiable. In the other flow \begin{table}
\begin{tabular}{c c c c} \hline
**Reynolds Number** & **Case** & **C\({}_{\text{D}}\)** & **C\({}_{\text{L}}\)** & **St** \\ \hline \(1.08\times 10^{5}\) & Present experiment & 1.14 & 0.02 & 0.20 \\ \(1.08\times 10^{5}\) & Present numerical simulation & 0.92 & 0.00 & 0.21 \\ \(1.10\times 10^{5}\) & Experiment of [PERSON] [50] & 1.10 & - & 0.20 \\ \(1.40\times 10^{5}\) & Experiment of [PERSON] [53] & 1.24 & - & 0.18 \\ \(1.40\times 10^{5}\) & Numerical simulation of [PERSON] and Holde [52] & 1.40 & - & 0.18 \\ \hline \end{tabular}
\end{table} 
Table 1: Results comparison of a single cylinder. Figure 11: Mesh view of twin cylinder. pattern, for W/D = 4.3, small vortices were formed in the space between the cylinders and convected toward the downstream cylinder. In this case, evident vortices are formed in the wake of the downstream cylinder, indicating that the interference effect of the upstream cylinder is weak when compared with the other pattern. When twin cylinders are placed in a staggered arrangement, things become different. It is worth mentioning that in numerical simulation, the total lift coefficient of the twin cylinders at W/D = 2.5 comes to a peak at \(\alpha=10^{\circ}\), differing from the experiment result that the total lift coefficient comes to a peak at \(\alpha=9^{\circ}\).