# Aerodynamic Analysis of Simple Grider Bridges under Construction Phase
## 2 Materials and Methods
### Model Validation  
Model validation is performed through result comparisons with experimental data from the literature. Due to the lack of experimental data regarding single and double I-beams, the verification of the model was made with a similar geometry: a flat plate perpendicular to the flow. Both grid and time step convergence tests were conducted (Tables 2 and 3), and the validation was limited to the drag coefficient and the Strouhal number. The results are shown in the following tables. Err.Prev. refers to the change between a mesh and the previous one, whereas Err.Final. refers to the error with respect to the model with a greater number of elements; see Tables 2 and 3. Table 4 shows a comparison between the results from the model and experimental data from the published literature given by [PERSON] [9], [PERSON] and [PERSON] [20], [PERSON] and [PERSON] [27], and [PERSON] [31]. The comparison clearly shows that the drag coefficient is overestimated by 30-40%, while the Strouhal number was underestimated by 10-20%, however, the general trend was captured correctly. Considering the complexity of the problem, the domain size, and the limitations of the \(k\)-\(\epsilon\) turbulence model, the reported deviation falls within the acceptable margin of engineering applications, and therefore, the results were considered to be valid for a qualitative analysis. Figure 4: Mesh structure in the surroundings of the structure for a case with two beams (double column, B&W in the printed version). \begin{table}
\begin{tabular}{c c c c c c c} \hline  & \multicolumn{2}{c}{**[PERSON]**} & \multicolumn{2}{c}{**[PERSON] and**} & \multicolumn{2}{c}{**[PERSON] and**} & \multicolumn{2}{c}{**[PERSON]**} & \multicolumn{1}{c}{**Model**} \\  & **(1954)** & **[PERSON] (1996)** & **[PERSON] (1978)** & **(1992)** & **Model** \\ \hline \(St\) & 0.133–0.140 & 0.136 & 0.145 & - & 0.121 \\ \(C_{D}\) & - & - & 1.96–2.01 & 1.98 & 2.72 \\ \hline \end{tabular}
\end{table} 
Table 4: Values of the Strouhal number and drag coefficient of a flat plate normal to the flow given by [9; 20; 27; 31] in comparison with the results obtained from the model. \begin{table}
\begin{tabular}{c c c c c c c c} \hline  & \multicolumn{2}{c}{**N\({}^{\bullet}\) Elements**} & \multicolumn{2}{c}{**42,000**} & **55,000** & **68,000** & **81,000** & **94,000** & **107,000** \\ \hline \multirow{8}{*}{**Cond**} & \multirow{4}{*}{Strouhal number} & Value & 0.123 & 0.123 & 0.123 & 0.123 & 0.123 & 0.124 \\  & & Err. Prev. (\%) & & **0** & **0** & **0** & **0** & **0** \\  & & Err. Final (\%) & **0.81** & **0.81** & **0.81** & **0.81** & **0.81** & \\  & & Value & 2.7131 & 2.7144 & 2.7172 & 2.7124 & 2.709 & 2.7102 \\  & \multirow{2}{*}{Drag coefficient} & Err. Prev. (\%) & & **0.05** & **0** & **0** & **0** & **0** \\  & & Err. Final (\%) & **0.11** & **0.15** & **0.26** & **0.08** & **0.04** & \\  & & Value & 0.2202 & 0.2195 & 0.2212 & 0.2186 & 0.2166 & 0.2146 \\  & \multirow{2}{*}{RMS Drag coefficient} & Err. Prev. (\%) & & **0.32** & **0.77** & **1.18** & **0.91** & **0.92** \\  & & Err. Final (\%) & 2.61 & 2.28 & 3.08 & **1.86** & **0.93** & \\  & & Value & 0.121 & 0.121 & 0.122 & 0.122 & 0.122 & 0.122 \\  & \multirow{2}{*}{Strouhal number} & Err. Prev. (\%) & & **0** & **0** & **0** & **0** \\  & & Err. Final (\%) & **0.82** & **0.82** & **0** & **0** & \\  & & Value & 2.7094 & 2.7139 & 2.7189 & 2.7189 & 0.72 & 2.7237 \\  & \multirow{2}{*}{Drag coefficient} & Err. Prev. (\%) & & **0.17** & **0.18** & **0** & **0.04** & **0.14** \\  & & Err. Final (\%) & **0.53** & **0.36** & **0.18** & **0.18** & **0.14** & \\  & & Value & 0.224 & 0.223 & 0.2248 & 0.2213 & 0.2197 & 0.2182 \\  & \multirow{2}{*}{RMS Drag coefficient} & Err. Prev. (\%) & & **0.45** & **0.81** & **1.56** & **0.72** & **0.68** \\  & & Err. Final (\%) & 2.66 & 2.2 & 3.02 & 1.42 & 0.69 & \\ \hline \end{tabular}
\end{table} 
Table 2: Grid convergence tests were carried out for two different wind speeds of 5 m/s and 15 m/s. A mesh of 55,000 was finally chosen.