# The Effects of Aerodynamic Interference on the Aerodynamic Characteristics of a Twin-Box Grider
## 2 Experimental Setup
### Section Model Geometrical Information and Surface Pressure Measurements  
The detailed geometrical information of the prototype bridge deck is shown in Figure 1. The twin-box girder has two parallel box girders with a gap of length \(L\) = 6 m and width \(B\) = 36 m, and the center height of the deck \(H\) = 3.51 m. The spanwise length of the section model is \(L_{s}\) = 480 mm, and the geometric scale ratio of the section model is 1:120. Figure 2a shows a 3D sketch of the twin-box girder used in the present study. To obtain the surface pressure distributions, 46 pressure taps with a 0.5 mm radius were installed in the slice, which is 230 mm away from the right end of the bridge deck, as shown in Figure 2b. It should be noted that the experiments on the twin-box girder were stationary in this paper. Figure 1: Geometric information of the twin-box girder (unit: m). The distribution of these taps around the section circumference is illustrated in Figure 3. The pressure taps are connected to three pressure scanners (DSA3217, 16 channels for each scanner) with a measuring range of \(\pm\)2.5 kPa by using connecting tubes (independent polyvinyl chloride (PVC) tubes, internal diameter of 1 mm) with a full length of 500 mm. This system is adopted to measure and record the instantaneous pressure distributions. The Scanivalve system monitors the surface pressure data at a sampling rate of 312.5 Hz, and the time length of one sampling period is 32 s. Based on the correction algorithm [19], the distortion effects brought by the connecting tubes--such as amplification factor and phase shift [20]--are quite small and negligible in the surface pressure measurements of this study. The time-averaged pressure coefficient \(C_{p}\) can be calculated by nondimensionalization of the time-averaged pressure \(p_{m}\), which can be written as:  
\[C_{p}=\frac{p_{m}}{\frac{1}{2}p_{air}U_{\infty}^{2}}, \tag{3}\]  
\[p_{m}=\frac{1}{T}\int_{0}^{T}\left(p_{i}-p_{\infty}\right)dt, \tag{4}\]  
where \(p_{i}\) denotes the instantaneous pressure, \(p_{\infty}\) is the pressure of the free stream, \(p_{air}\) is the density of air, \(U_{\infty}\) is the flow velocity of the free stream, and \(T\) is the sample period. In the present study, the Reynolds number is high (Re \(>\) 5 \(\times\) 10\({}^{3}\)); hence, the boundary layer around the solid structure becomes turbulent and the pressure drag force dominates the skin drag force [21]. Thus, the pressure drag force is the dominant component of total drag, and the skin friction drag can be neglected. Once the instantaneous pressure distributions are obtained, the corresponding aerodynamic forces of the bridge girder can be calculated by standard integration, which can be expressed as follows:  
\[F_{D}=\int\mathbf{P}_{xi}\,ds_{i}, \tag{5}\]  
\[F_{L}=\int\mathbf{P}_{zi}\,ds_{i}, \tag{6}\]  
\[F_{m}=\int\mathbf{P}_{i}\zeta_{i}\,ds_{i}, \tag{7}\]  
where \(\mathbf{P}_{i}\) is the pressure force, \(\mathbf{P}_{xi}\) and \(\mathbf{P}_{zi}\) are the pressure force components along the \(x\) and \(z\) directions, respectively, \(ds_{i}\) denotes the element area, and \(\zeta_{i}\) is the moment arm. Figure 3: Location of the pressure taps in the section circumference. Figure 2: Schematic diagrams of the section model: (**a**) 3D sketch of the twin-box girder, and (**b**) spanwise location of the pressure tap (unit: mm). It should be noted that, when the gap exists, the pressure forces at pressure taps 9-11 and 32-34 should be considered. The drag force coefficient \(C_{D}\), the lift force coefficient \(C_{L}\), and the moment force coefficient \(C_{m}\) are defined as:  
Figure 1:0  
Figure 1:1  
Figure 1:2  
where \(F_{D}\), \(F_{L}\), and \(F_{m}\) are the drag, lift, and moment forces, respectively, and \(B\) is the width of the twin-box girder.