# Wind Vulnerability of Flexible Outdoor Single-Post Billboards
## 2 Methodology
### Description of Fluid Model  
Simulations to determine the pressures generated by the wind on the billboard were carried out using ANSYS CFX 16.2 commercial fluid dynamics software. In the fluid model, tetrahedral solid elements with 4 nodes identified as MESH200 were used to simulate the air volume used in computational fluid dynamics, CFD, analysis as depicted in Figure 6. This volume considered as a continuous flow of air was an ideal gas at 25 \({}^{\circ}\)C at a reference pressure of 1 atm and initial speeds in u, v and w of 0 km/h with a relative pressure of 0 Pa. The dimensions of the volume (80 m \(\times\) 70 m \(\times\) 318 m) guarantee the development of the fluid and avoid interference between the walls and the billboard. In the numerical model, the Z and X axes were parallel to the westerly and southerly wind directions, respectively.  
The analysis was defined as steady-state isothermal using the shear stress transport (SST) turbulence model and the convergence criterion was defined as 1 \(\times\) 10\({}^{-4}\). The three walls (top and sides) of the control volume were considered as free slip walls and the floor and all the surfaces that make up the geometry of the billboard and the area that the floor represents were considered as non-slip walls. To represent the variable wind speed at the domain input fluid, the power law was considered (Equation (3))  
\[u(y)=u_{ref}\Bigg{(}\frac{y}{y_{ref}}\Bigg{)}^{\alpha} \tag{3}\]  
where \(u_{ref}\) and \(y_{ref}\) represent the reference speed and the reference height, respectively. To depict the most severe scenario, it was considered that the billboard was in a flat terrain without sudden topography changes and with obstacles less than 5 m height, and located in the Port of Veracruz, one of the cities with the most severe high intensity winds in Mexico. With these characteristics, the reference speed was set to 180 km/h, and the reference height was set to 10 m (CFE, [6]). For its part, the exponent \(\alpha\) represents the stability of the atmosphere and for the study cases where the billboard is located near the coast, it was considered as 0.14 [21], whilst the volume outlet was considered as an outlet type and a relative pressure was assigned of 0 Pa.  
To determine the vulnerability of the billboard, as an example, several wind reference speeds were adopted. Wind references along the Mexican coast can vary between 160 up to 220 km/h (CFE, [6]). Therefore, it is interesting to know how variations of the initial reference speed of 180 km/h causes changes in the safety levels of the structure. Here, wind reference speeds ranged from 160 to 220 km/h with increments of 10 km/h, to capture variations and trends of the safety levels, were considered for further analyses. Moreover, to take into account the dynamic interaction between the billboard structure and the wind, a gust load factor, GLF, was determined according to specifications given in CFE [6]. Table 3 indicates the wind reference speeds, and their gust loading factors (GLF) used in the computational fluid dynamics model. GLF indicates how many times the wind static response calculated with the CFD analysis needs to be incremented. From Table 3, it can be deduced that an important dynamic interaction, bigger than 2.0, is obtained for all wind reference speeds with higher values of GLF when wind reference speed increases.  
Figure 6: CFD model: (**a**) air volume, boundary conditions, geometry of the billboard and wind directions; (**b**) longitudinal section; (**c**) cross section.