# Wind Loads on Overhead Sign Structures: A Comparative Study
## 3 Methodology
### Panels  
Panels with porosity will affect the vortex region on the leeward side. Incorporating porosity does not eliminate the vortex region in the wake; however, porosity can reduce the overall vortex size while moving it farther downstream, away from the leeward face of the panel. With an introduction of a porosity factor, \(K_{p}\), which is dependent on the solidity of the plate, \(\delta\), being the ratio of the solid area, the drag coefficient for that of a panel with porous qualities can be represented as follows [20]. \[C_{D,\delta}=C_{D}\;K_{p} \tag{1}\]  
Figure 1: Computational domain: (**a**) domain dimensions for an object with height H, (**b**) wall and symmetric boundary conditions, and (**c**) inlet and outlet boundary conditions. when the panel has a porous quality that is not linearly related to the solidity of the plate, \(\delta\), an approximate expression for the porosity factor, \(K_{p}\), can be obtained by the following equation [20]. \[K_{p}=1-\left(1-\delta\right)^{2} \tag{2}\]  
The above equation is best for bluff bodies with a height-to-width ratio between 0.2 to 5 [20]. The first set of geometry to be made is the standard, solid sign panel. The sign panel is the first because the height and width of the object influence the geometry of the domain that surrounds it. The geometry of the standard sign panel in this study represents a commonly used overhead sign structure. The sign panel in this study is 11 feet in height and 22 feet in width, giving it a height-to-width ratio of 1:2. The thickness has an arbitrary value of 2 inches (50 mm). There are five cases to be examined: a single case of a standard sign panel, three panels with porous characteristics, and a single case of a curved panel (Figure 2). All sign panels have similar outer dimensions. Panels with porous characteristics were given a porosity value of 25% but with different geometric variations of how the porosity is applied. Given that the size of the standard panel is 11 ft \(\times\) 22 ft, with a surface area of 242 ft\({}^{2}\), each porous panel will have a solid area of 181.5 ft\({}^{2}\) and a porous area of 60.5 ft\({}^{2}\). The variations of the porous cases are as follows: the first case has 28 large staggered holes with a radius of 0.83 feet or 10 inches; the second case has 200 uniform square holes with a height and width of 0.55 feet; the last case has 10 rectangular slots at 0.3025 feet or 3\({}^{\tfrac{2}{3}}_{3}\) inches in height and spans across the panel at 20 feet in width with equal spacing of 0.7 feet or 8 \({}^{\tfrac{2}{5}}_{3}\) inches. The last panel geometry to discuss is one with a curvature applied to it. Since sign panels need to be read and easily seen by motorists, introducing curvature to the sign panel should not affect the legibility of the information displayed. Like the other sign panels, this panel has a width and height of 11 feet by 22 feet like the other panels in this study, but with a radius of 11 feet applied to the entire panel. A radius of 11 feet is a realistic and applicable curvature based on the panel's height. Figure 2: Panel with different geometric configurations in a porosity value of 25%: (**a**) 28 staggered holes, (**b**) 200 uniform square holes, (**c**) 10 rectangular slots, and (**d**) curved (solid). Grid-Independence Study  
Because the mesh quality impacts the accuracy of the simulation results, creating the mesh for the CFD simulation is often the most time-consuming step. There are several approaches to creating a mesh, depending on the type of CFD simulation. A mesh breaks down the surfaces of a 2-D model or the faces and the volume of a 3-D model into a large grid where each small part of the grid combines to make the physical model. These small parts of the model are known as elements. For this study, the surfaces of the enclosure and the sign panel will be meshed, as well as the volume within the domain surrounding the sign panel.