# The Effects of Aerodynamic Interference on the Aerodynamic Characteristics of a Twin-Box Grider
## 3 Results and Discussions
### Modulation of Aerodynamic Forces by Leading Circular Cylinders  
Figures 15-20 show the mean and fluctuating aerodynamic force coefficients of the twin-box girder under the aerodynamic interference by leading circular cylinders at different spacing ratios. Figure 15 shows that the time-averaged drag force coefficient of the twin-box girder with cylinder interference decreased significantly compared with the original force coefficient without interference, because the shedding vortices in the wake of the circular cylinder destroyed the original laminar boundary layers; hence, the laminar boundary layers transition to turbulence at the windward corner, and the turbulent boundary layers can be maintained throughout the girder section. Thus, the boundary layer is composed of many small vortices, which effectively reduce the contact area between the fluid boundary layer and the twin-box girder, leading to a decrease in the friction between the turbulent boundary layer and the model. Meanwhile, when the vortices contact the girder, the velocity direction is generally opposite to the incoming flow. In this way, the vortices generate a force that is opposite to the streamwise direction, and the force generated by the interaction between the vortices and the girder reduces the total drag force of the bridge deck. Meanwhile, when the diameter of the cylinder is 3 mm, it clearly shows that the time-averaged drag force coefficient exhibits a periodic trend at different locations from the model, as shown in Figure 15, which indicates that the vortex scale is closer to the diameter. In addition, the time-averaged drag force with cylinder interference at low Re achieves a similar characteristic of undisturbed drag force at high Re. Figure 15: (**a–d**) The relationship between the time-averaged drag force coefficient and the Reynolds number at different spacing ratios and cylinder diameters. Figure 16: (**a–d**) The relationship between the fluctuating drag force coefficient and the Reynolds number at different spacing ratios and cylinder diameters. Figure 17: (**a–d**) The relationship between the time-averaged lift force coefficient and the Reynolds number at different spacing ratios and cylinder diameters. Figure 19: (**a–d**) The relationship between the time-averaged moment force coefficient and the Reynolds number at different spacing ratios and cylinder diameters. Figure 18: (**a–d**) The relationship between the fluctuating lift force coefficient and the Reynolds number at different spacing ratios and cylinder diameters. Figure 16 shows that the fluctuating drag force coefficient of the twin-box girder with cylinder interference is much smaller than that of the twin-box girder without interference at \(\text{Re}\leq 9.0\,\times 10^{3}\). Moreover, the fluctuating drag force is insensitive to the Reynolds number, and the disturbed fluctuating drag force at low Re is closer to that of the undisturbed fluctuating force at high Re. Furthermore, the fluctuating drag force is independent of the spacing ratio \(\varepsilon\). Figure 17 shows that the time-averaged lift force coefficient of the girder with cylinder interference also decreased sharply compared with that of the bare twin-box girder. It should be noted that with the increase in distance between the cylinder and the twin-box girder, the \(C_{L\,\,mean}\) shows less sensitivity to the Reynolds number, because the turbulence in the wake of cylinder has been fully developed, which causes the boundary layer of the body surface to transition to turbulence. When the cylinder is close to the twin-box girder, the wake of the cylinder cannot fully develop into turbulence to change the boundary layer, which explains why the Reynolds number effect still exists. In conclusion, when the spacing ratio \(\varepsilon>2\), the turbulence generated by the wake of the cylinder effectively eliminates the Reynolds number effects on the time-averaged lift force.