# Aerodynamic Characteristics of Coupled Twin Circular Bridge Hangers with Near Wake Interference
## 3 Results and Discussion  
### Time-Mean Pressure  
Experimental results of time-mean pressure distribution on twin cylinders for various cylinder spacings at \(\alpha=0^{\circ}\) and \(\alpha=9^{\circ}\) are shown in Figures 4 and 5, respectively. According to Figure 4a, it is shown that the upstream cylinder has an obvious different mean pressure  
Figure 3: Layout of section model and apparatus in the wind tunnel. Figure 2: Relative position of twin cylinders and definition of force coefficients. distribution compared to the single isolated case, especially at \(60^{\circ}<\theta<300^{\circ}\). The mean pressure coefficient of upstream cylinders increases at various spacings compared to that of the single isolated one due to the aerodynamic interaction. At W/D > 3.8, the mean pressure of the upstream cylinder has an almost constant value of \(-1\), while at W/D \(\leq\) 3.8, mean pressure increases with an increase in W/D at \(60^{\circ}<\theta<300^{\circ}\) and reaches a maximum value at W/D = 3.8. The mean pressure coefficient of the upstream cylinder is \(-0.86\) and \(-0.69\) at W/D = 2.5 and 3.8, respectively. Overall, no apparent changes in the characteristics of mean pressure distribution were observed. Figure 4: Distributions of time–mean pressure coefficients on cylinders at \(\alpha\) = 0\({}^{\circ}\): (**a**) upstream cylinder; (**b**) downstream cylinder. Compared to the upstream cylinder, the downstream cylinder has a more obvious variation of pressure distribution with respect to various spacings. According to Figure 4b, there are two different flow regimes around the twin cylinders with various spacings, and the critical spacing for these two regimes is in the range of 3.8D-4.3D. When W/D > 3.8, the mean pressure distribution of the downstream changes to another pattern compared to that at W/D \(\leq\) 3.8. Due to the shelter of the upstream cylinder, the mean pressure coefficient of the front stagnation point is significantly smaller than that of the upstream cylinder, but increases with increasing W/D. At W/D > 3.8, the mean pressure coefficient of the downstream cylinder has a peak value at the front stagnation point. There are two symmetrical peaks on the pressure distribution curve at \(\theta\) = 75\({}^{\circ}\) and \(\theta\) = 285\({}^{\circ}\), which are caused by the shear layers of the upstream cylinder, which attaches to the surface of the downstream cylinder. The mean pressure coefficient of the upstream cylinder is \(-\)1.02 and 0.22 at W/D = 2.5 and 11, respectively. At W/D = 6.5, the mean pressure coefficient at the stagnation point is 0. It is worth mentioning that at W/D \(\leq\) 3.8, the mean pressure of the downstream cylinder at the front stagnation point is almost equal to the pressure of the upstream cylinder at \(\theta\) = 180\({}^{\circ}\), indicating that there is no obvious flow in the gap of the twin cylinders. Figure 5: Distributions of time–mean pressure coefficients on cylinders at \(\alpha\) = 9\({}^{\circ}\): (**a**) upstream cylinder; (**b**) downstream cylinder. Figure 5 indicates that the flow around cylinders shows two completely different patterns with various spacings at \(\alpha=9^{\circ}\), and the critical spacing is in the range of 3.5D-3.8D. For the upstream cylinder, the mean pressure distribution at different spacings falls in the range between those at 3.5D and 3.8D, which is distinctly different from the pressure distribution of the upstream cylinder in tandem. At \(\theta=180^{\circ}\), the mean pressure coefficient reaches a maximum value of \(-0.79\) when W/D = 3.5, and the pressure distribution on the trailing edge of the cylinder is almost constant. Meanwhile, the mean pressure coefficient reaches a minimum value of \(-1.27\) when W/D = 3.8, and the minimum value is smaller than that of the single isolated cylinder, which illustrates that the gap flow between cylinders has a significant influence on the upstream cylinder at \(\alpha=9^{\circ}\).