# The Effects of Aerodynamic Interference on the Aerodynamic Characteristics of a Twin-Box Grider
## 3 Results and Discussions
### Modulation of Aerodynamic Forces by Leading Body-Height Grids  
Figure 14 shows the distribution of the mean and fluctuating aerodynamic force coefficients in the phase plane of the Reynolds number and turbulence intensity, and the aerodynamic forces show strong sensitivity to the Reynolds number and turbulence intensity.  
As shown in Figure 14a, the distribution of the time-averaged drag force coefficient shows different characteristics at different turbulence intensities. At low turbulence intensity (\(I\leq 5\%\)), the \(C_{D\ mean}\) is sensitive to the Reynolds number when \(\text{Re}\leq 1.0\times 10^{4}\). Moreover, the hypotenuse of the contour at the corner indicates that the turbulence intensity can reduce the Reynolds number effects of \(C_{D\ mean}\). When the Reynolds number is further increased, the \(C_{D\ mean}\) shows slight Reynolds number sensitivity, which is consistent with the bare deck (see Figure 9a). At moderate turbulence intensity (\(5\%\leq I\leq 20\%\)), the \(C_{D\ mean}\) is enhanced, and the \(C_{D\ mean}\) presents slight Reynolds number dependence. It should be noted that there exists a lock-up region of \(C_{D\ mean}\). At high turbulence intensity (\(I>20\%\)), the \(C_{D\ mean}\) is further promoted, and is only associated with the turbulence intensity.  
The time-averaged lift force coefficient shows strong sensitivity to the turbulence intensity when \(\text{Re}\leq 1.0\times 10^{4}\) (see Figure 14b), and with the increase in turbulence intensity, the lift force is enhanced, which implies that the strength of turbulent flow can effectively promote the lift force. Meanwhile, at \(\text{Re}>1\text{e}4\), the lift force is insensitive to both Reynolds number and turbulence intensity, because the boundary layer transitions to full turbulence.  
Figure 13: The time-averaged surface pressure distributions of the twin-box girder with circular cylinder interference at different Reynolds numbers with the same spacing ratio.  
As for the fluctuating forces, \(C_{D\,rms}\) and \(C_{L\,rms}\) show different distribution characteristics. At low turbulence intensity (\(I\) < 2.5%), \(C_{D\,rms}\) shows Reynolds number dependence at low Re, i.e., Re < 1.0 \(\times\) 10\({}^{4}\). With the increase in turbulence intensity, the \(C_{D\,rms}\) is enhanced by the strong fluctuating component of incoming flow, and the Reynolds number sensitivity of the \(C_{D\,rms}\) is eliminated (see Figure 14d). However, the \(C_{L\,rms}\) depends on the Reynolds number and turbulence intensity, because the increase in Re or turbulence intensity can enhance the vertical fluctuating force.  
As shown in Figure 14c,f, when Re \(\leq\) 1.0 \(\times\) 10\({}^{4}\) and turbulence intensity \(I\)\(\leq\) 12.5%, the mean moment force coefficient increases significantly with the turbulence intensity, which may be due to the increase in the vertical and horizontal fluctuating velocity of the flow field caused by the turbulence. However, in other regions, the mean moment force  
Figure 14: (**a–c**) The distributions of the time-averaged drag, lift, and moment, respectively, in the phase plane of Reynolds number and turbulence intensity. (**d–f**) The distributions of the fluctuating drag, lift, and moment, respectively, in the phase plane of Reynolds number and turbulence intensity.  
coefficient does not show strong turbulence intensity sensitivity, because the turbulence mainly affects and increases the horizontal and vertical velocities, but has a small impact on the moment force. The fluctuating moment force coefficient and the fluctuating lift force coefficient exhibit similar trends, indicating that the fluctuating lift force is the dominant component of the fluctuating moment force.