# Aerodynamic Characteristics of Coupled Twin Circular Bridge Hangers with Near Wake Interference
## 3 Results and Discussion
### Fluctuating Pressure  
The fluctuating pressure distribution of cylinders at \(\alpha=0^{\circ}\) is illustrated in Figure 6. According to the curve shapes, there exist two distinct flow patterns while the cylinder spacing varies, which is consistent with the results of mean pressure distribution. For the upstream cylinder, when W/D \(\leq\) 3.8, the fluctuating pressure coefficient is almost constant with respect to \(\theta\) and they are all less than 0.07. This is because the shear layer separated from the upstream cylinder is reattached to the downstream cylinder, with vortex shedding suppressed. However, at W/D > 3.8, the fluctuating pressures change drastically with respect to \(\theta\) and show two obvious peaks at \(\theta=75^{\circ}\) and \(\theta=285^{\circ}\), respectively. This indicates that the shear layer of the upstream cylinder is separated at \(\theta=75^{\circ}\) and \(\theta=285^{\circ}\) and vortex shedding occurs. For the downstream cylinder, the fluctuating pressure varies violently at various spacings and displays obvious symmetry with respect to \(\theta\). One can see that the magnitude of the fluctuating pressure at a cylinder spacing of 4.3D is greatly larger than other spacings. In order to facilitate the description, only the fluctuating pressure distribution at \(\theta=0^{\circ}\)-\(180^{\circ}\) is discussed in the following. At W/D > 3.8, there are two peaks of the fluctuating pressure, with one peak at \(\theta=30^{\circ}\)-\(60^{\circ}\) and another nearly at \(\theta=110^{\circ}\). The first peak is due to the vortex generated from the upstream cylinder impacting on the downstream cylinder, resulting in a maximum value of C\({}_{\rm p^{\prime}}\) = 0.8, while the peak value decreases with rising spacing, indicating that the eddy energy and the impact are gradually weakened. The second peak is due to the point of vortex shedding for the downstream cylinder. When W/D \(\leq\) 3.8, there are also two peaks: the first peak is nearly at \(\theta=70^{\circ}\), and the second peak is nearly at \(\theta=110^{\circ}\). The first peak is due to the reattachment of the shear layer separated by the upstream cylinder, and the second peak is due to the point of vortex shedding for the downstream cylinder. To sum up, the corresponding position for the first peak of fluctuating pressure on the downstream cylinder varies with W, while that for the second peak is invariant. Figure 7 shows the fluctuating pressure distribution of cylinders at \(\alpha=9^{\circ}\). The curve shapes in Figure 7 indicate that there exist two distinct flow patterns while the spacing varies, and the critical spacing is in the range of 3.5D-3.8D. For the upstream cylinder, the fluctuating pressure distribution is similar to that at \(\alpha=0^{\circ}\), but the critical spacing changes. At W/D \(\leq\) 3.5, the fluctuating wind pressure almost keeps constant with a small value less than 0.05. When W/D > 3.8, the fluctuating pressure distribution is similar to that of a single cylinder, and there are two prominent peaks at the separation points. For W/D = 3.8, the fluctuating pressure fluctuates drastically versus \(\theta\) with multiple peaks, and the maximum fluctuating pressure coefficient C\({}_{\text{p}}\)' = 0.45. It may be concluded that the critical spacing is about 3.8D. Figure 6: Distributions of fluctuating pressure coefficients on cylinders at \(\alpha=0^{\circ}\): (**a**) upstream cylinder; (**b**) downstream cylinder. For the downstream cylinder, the fluctuating pressure distribution is obviously different from that at \(\alpha\) = 0\({}^{\circ}\), and the fluctuating pressure distribution is not symmetrical versus \(\theta\). Such an asymmetrical distribution is peculiar to the twin cylinders with staggered arrangement [47]. At W/D \(\leq\) 3.5, the fluctuating wind pressure almost keeps constant at \(\theta\) = 0\({}^{\circ}\)-180\({}^{\circ}\) with a small value less than 0.1.