## 4 Vortex Shedding Characteristics by Numerical Simulations
### Accuracy Verification of Calculation Results  
Truss girders have a continuously changing cross-section with the length direction of the bridge, resulting mainly from the web member position changes. To investigate the impact of web member position on the calculation results, three cross-sections were selected for CFD simulations, with web members located at 0.25D, 0.5D, and 0.75D from the upper chord, as shown in Figure 16. The simulations were performed using wind angles of attack of +3\({}^{\circ}\) and +5\({}^{\circ}\), and a wind speed of 2.23 m/s (equivalent to an actual wind speed of 10.0 m/s, consistent with the wind speed used in the force tests conducted in the wind tunnel). The aerodynamic coefficients were averaged over 5 s after the calculation converged, and the results are presented in Table 5. The findings indicate that the differences between the aerodynamic coefficients of the three cross-sections are within 5%. Moreover, the web member position does not produce significant differences in the calculation results. Consequently, subsequent calculations were conducted using 2-2 cross-sections.  
To validate the model's reliability, five different wind angles of attack were used to calculate the aerodynamic coefficients at a wind speed of 2.23 m/s (equivalent to an actual wind speed of 10.0 m/s, consistent with the wind speed used in the force tests conducted in the wind tunnel). The calculated results were compared with the wind tunnel test results, and the findings are presented in Table 6.  
Figure 14: The computational domain boundary conditions.  
Figure 15: The computational domain mesh division.  
Table 6 shows that the maximum error between the simulation and test values is 9.14%, while the minimum error is 0.34%. The drag coefficient has an average error of 3.51%, the lift coefficient has an average error of 3.85%, and the moment coefficient has an average error of 6.15%. The overall average error is 4.50%, indicating that the simulation results have a small error. Therefore, the chosen algorithm and the mesh division of the CFD simulation are feasible and can be used to analyze the flow characteristics near the girder cross-section.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Wind Angle of Attack**} & \(-\mathbf{5}^{\circ}\) & \(-\mathbf{3}^{\circ}\) & \(\mathbf{0}^{\circ}\) & \(+\mathbf{3}^{\circ}\) & \(+\mathbf{5}^{\circ}\) \\ \hline \multirow{3}{*}{\(\bar{\mathcal{C}}_{D}\)} & Test value & 0.6404 & 0.6374 & 0.6531 & 0.6398 & 0.6672 \\  & Simulation value & 0.6233 & 0.6291 & 0.6509 & 0.5813 & 0.6391 \\  & Error & 2.67\% & 1.20\% & 0.34\% & 9.14\% & 4.21\% \\ \hline \multirow{3}{*}{\(\bar{\mathcal{C}}_{L}\)} & Test value & \(-0.8520\) & \(-0.4276\) & 0.2989 & 0.8948 & 1.1012 \\  & Simulation value & \(-0.8184\) & \(-0.4128\) & 0.2890 & 0.8622 & 1.0472 \\  & Error & 3.94\% & 3.46\% & 3.31\% & 3.64\% & 4.90\% \\ \hline \multirow{3}{*}{\(\bar{\mathcal{C}}_{M}\)} & Test value & \(-0.1039\) & \(-0.0889\) & \(-0.0153\) & 0.0310 & 0.0451 \\  & Simulation value & \(-0.0998\) & \(-0.0841\) & \(-0.0145\) & 0.0285 & 0.0419 \\ \cline{1-1}  & Error & 3.95\% & 5.40\% & 5.23\% & 9.08\% & 7.09\% \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparisons of test and simulation values of aerodynamic coefficients.  
Figure 16: Three cross-sections of the truss girder for the trial calculation.