# Influence of Porosity on Drag Coefficient of Perforated Road Signs
## 2 Computational Fluid Dynamics Analysis of Perforated Road Sign  
In the CFD analysis, the width of the analyzed perforated road sign is denoted by \(B\), and its height by \(S\). The height of the installed perforated road sign from the ground is marked by \(H\). The analysis model followed the Road Sign Standard, which is a standard for actual road signs. The aspect ratio (\(B/S\)) ranged from 1.0 to 4.0, and the clearance ratio (\(S/H\)) from 0.2 to 0.5. Figure 1 shows the geometry of the perforated road sign model analyzed in the CFD analysis. For the perforated road sign model, the hole spacing was adjusted according to the porosity by applying the appropriate 6 mm diameter hole derived in consideration of readability and retro-reflection in the previous study [2]. The material used in actual road signs was used as the material of the perforated road sign model applied in the analysis, as shown in Table 1.  
The \"Midas NFX\" software was used for the CFD analysis of this study [23]. In addition, the \"Two-equation k-\(\varepsilon\)\" turbulence model capable of implementing realistic fluid \begin{table}
\begin{tabular}{c c c} \hline \hline
**Property** & **Unit** & **Value** \\ \hline Material & Alloy steel & - \\ Elastic modulus & N/mm\({}^{2}\) & 210 \\ Poisson’s ratio & - & 0.28 \\ Tensile strength & N/mm\({}^{2}\) & 730 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material of perforated road sign. Figure 1: CFD analysis model of perforated road sign. turbulence was applied to analyze the airflow pattern around the perforated road sign [24]. The k-\(\epsilon\) turbulence model is commonly used in turbulence analysis because it effectively models the kinetic energy of turbulence. The turbulence intensity and length applied to the model was 0.05 and 0.004 m, respectively. The fluid loaded on the analysis model was air at 25 \({}^{\circ}\)C. In addition, it was set as incompressible. In the analysis, 1500 iterations were applied for sufficient convergence to an approximate value. Table 2 shows the conditions of the applied turbulence model. In the CFD analysis, many parameter analyses were performed, considering the aspect ratio, clearance ratio and porosity of the perforated road sign. Among the turbulence analysis models, the Reynolds-averaged Navier-Stokes (RANS) model calculates the average value of the change in turbulence occurring within a period of time. Accordingly, in the CFD analysis, the most efficient RANS model was applied in various parameter analyses. The formula for calculating the turbulent flow in the RANS model is the Navier-Stokes equation, which is given in Equation (1). \[\rho\bigg{(}\frac{\partial u}{\partial t}+(u\cdot\
abla)u\bigg{)}=-\
abla p+ \rho g+\mu\
abla^{2}u \tag{1}\]  
where, \(u\) is the wind speed, \(p\) is the wind pressure, \(\rho\) is the air density, \(g\) is the gravity, and \(\mu\) is the viscosity of wind. In the CFD analysis, a virtual wind tunnel test domain is required to apply a fluid to the target structures. Figure 2 shows the geometry of the CFD analysis wind tunnel test domain. A study of turbulence CFD analysis of windbreaks was performed by [PERSON] et al. [25]. For the virtual wind tunnel test domain applied in this study, the methodology of the previous literature was applied. Figure 2a shows the conditions of the wind tunnel domain. The virtual wind tunnel test domain applied in the CFD analysis was set to the form of a hexahedral box to include the inlet and outlet of the fluid. Wall boundary conditions were applied to the ground, top and side walls of the domain, and to remove the influence on the fluid, all the walls were set in a no-slip condition. The top and side walls of the domain set the wind speed in the vertical direction to 0 m/s, the dimensions of which were set to prevent interference with the fluid flow inside the domain. Figure 2b shows the aspect of the wind tunnel domain.