# Influence of Porosity on Drag Coefficient of Perforated Road Signs
## 2 Computational Fluid Dynamics Analysis of Perforated Road Sign
The width of the inlet was set to five times the vertical length of the perforated road sign, and the width of the outlet and height of the domain were set to 10 times that. In the CFD analysis, boundary conditions were set to analyze the pure drag coefficient of the perforated road sign. In actual roads, road signs are fixed to the ground with posts; it is difficult to calculate the pure drag coefficient of perforated road signs considering the posts, due to wind pressure dispersion. [PERSON] et al. [18] performed a CFD analysis to analyze the wind load of traffic signs, and in the CFD analysis, elevated traffic signs installed away from the ground were modeled without posts. In the CFD analysis, the air flow and wind pressure around the perforated road sign are analyzed, so even if the perforated road sign is modeled away from the ground without post, it was confirmed that the CFD analysis is running properly. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Property** & **Unit** & **Value** \\ \hline Turbulence model & Two-equation k–\(\epsilon\) & - \\ Air density & kg/m\({}^{3}\) & 1.1845 \\ Viscosity & kg/(m-s) & 1.8444 \(\times\) 10\({}^{-5}\) \\ Turbulence intensity & \% & 5 \\ Turbulence length scale & m & 0.004 \\ Number of iterations & - & 1500 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Specific of fluid flow model. The parameters applied in the CFD analysis are the aspect ratio (\(B/S\)) and clearance ratio (\(S/H\)), which are the width/height ratio of the perforated road sign and the ratio of the height of the perforated road sign to its ground clearance, respectively. The parameters were set considering the aspect and clearance ratios of actual road signs. The aspect ratio was set to 1.0, 2.0, and 4.0 and the clearance ratio to 0.2, 0.3, and 0.5. In addition, five porosities (0, 5, 10, 20, and 30%) and six wind speeds ranging from 10 to 60 m/s were applied. Table 3 shows the parameters applied in the CFD analysis. [PERSON] et al. [26] calculated the drag coefficient using the difference in wind pressure between the front and rear surfaces of a structure. In this study, the drag coefficient of the perforated road sign was also calculated using the difference in wind pressure between the front and rear of the perforated road sign. The calculation formula is given by Equation (2). \[C_{D}=\frac{\Delta p}{p_{f}}=\frac{p_{f}-p_{r}}{p_{f}} \tag{2}\]  
where, \(p_{f}\) is the wind pressure on the front surface, and \(p_{r}\) is the wind pressure on the rear surface. In this study, the drag coefficient was calculated using the difference in wind pressure between the front and rear of the perforated road sign. Figure 2(a) shows the drag coefficient of road sign with 0% porosity and Figure 2(b) shows the drag coefficient of perforated road sign with 30% porosity. The drag coefficient of the perforated road sign with 30% porosity was lower than that of the road sign with 0% porosity. The drag coefficient of perforated road signs does not change significantly with the aspect ratio. The drag coefficient was high in perforated road signs with a low clearance ratio. To verify the validity of the CFD analysis conducted in this study, the drag coefficient of the road sign with 0% porosity calculated using the CFD analysis was compared with that obtained from the wind tunnel test in a study by [PERSON] [13]. The drag coefficient \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter Name** & **Aspect Ratio (A)** & **Clearance Ratio (C)** \\ \hline A2.0-C0.2 & 2.0 & 0.2 \\ A4.0-C0.2 & 4.0 & 0.2 \\ A1.0-C0.3 & 1.0 & \\ A2.0-C0.3 & 2.0 & 0.3 \\ A4.0-C0.3 & 4.0 & \\ A1.0-C0.5 & 1.0 & \\ A2.0-C0.5 & 2.0 & 0.5 \\ A4.0-C0.5 & 4.0 & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: CFD analysis parameters. Figure 2: Virtual wind tunnel domain. of the road sign calculated using the CFD analysis was found to be approximately 98% of that obtained in the wind tunnel test, as shown in Figure 4. This verified that the CFD environment of this study was properly implemented.