# Wind Pressure Coefficient on a Multi-Storey Building with External Shading Louvers
## 3 CFD Simulation
### Result Validation  
Validation was performed by comparing the deviation between the numerical results of the reference case and the experimental data from [PERSON] et al. [44]. In that reference, research with experimental and numerical results, allowed the velocity value to be measured at some points along several lines, which was on the mid-surface of the cubic building and perpendicular to the ground in the wind tunnel, while wind pressure coefficients were investigated along three lines on the intersection between building surfaces and the mid-surface in CFD simulations. The normalized velocity \(U_{\text{n}}\) as shown in Equation (6) is to demonstrate the airflow velocity distribution:  
\[U_{n}(z)=\frac{U(z)}{U_{\text{ref}}} \tag{6}\]  
Figure 2 demonstrates the measurement locations to validate the numerical results. Figure 8 shows the normalized velocity \(U/U_{\text{ref}}\) distribution of the simulation data and the experimental results on vertical measurement locations. The average absolute deviation is 0.068 between simulation data and experimental data. Figure 9 shows \(C_{\text{P}}\) distribution for comparison of the data from the reference case and the data from [PERSON] et al. [44] along measurement lines on the windward, roof and leeward surfaces. The average absolute deviation is 0.046 between the two cases for wind pressure coefficient. The average values of \(U/U_{\text{ref}}\) and \(C_{\text{P}}\), as long as their deviation on each line, are shown in Table 1. The comparison results show that \(U\) and \(C_{\text{P}}\) in the reference case are in good agreement with results from the previous study. The \(U\) and \(C_{\text{P}}\) tendencies on these locations can be reproduced well by CFD technology. The maximum deviations occur beyond the roof for both, \(U\) and \(C_{\text{P}}\) distributions. This phenomenon seems to be that the realizable \(k\)-\(\varepsilon\) model with default parameters may provide airflow characteristics with overestimated reattachment lengths on the roof, and in the recirculating  
region at the corner between the ground and the leeward facade [32; 56; 57]. This over-estimation leads to the \(U\) near the roof and leeward facade and the smaller gradient for \(C_{\text{p}}\) along the roof line. Although, there are higher distortions in the reattachment region for the realizable \(k\)-\(\varepsilon\) model, the simulation accuracy is considered to be suitable enough to perform CFD simulations.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{2}{*}{**Value Type**} & \multicolumn{4}{c}{\(U/U_{\text{ref}}\)} & \multicolumn{4}{c}{\(C_{\text{p}}\)} \\ \cline{2-9}  & \(-0.5h_{0}\) & \(0.5h_{0}\) & \(1.5h_{0}\) & \(2.5h_{0}\) & **Windward** & **Roof** & **Leeward** \\ \hline Average value (reference case) & \(1.21\) & \(0.94\) & \(1.03\) & \(0.72\) & \(0.62\) & \(-0.45\) & \(-0.19\) \\ \hline Average value ([PERSON] et al.) & \(1.22\) & \(0.97\) & \(1.05\) & \(0.74\) & \(0.6\) & \(-0.45\) & \(-0.18\) \\ \hline Absolute deviation & \(0.08\) & \(0.05\) & \(0.04\) & \(0.1\) & \(0.03\) & \(0.09\) & \(0.02\) \\ \hline \end{tabular}
\end{table}
Table 1: Comparison of average value of normalized velocity \(U/U_{\text{ref}}\) and wind pressure coefficient \(C_{\text{p}}\) on measurement lines.  
Figure 8: Comparison of normalized velocity \(U/U_{\text{ref}}\) distribution around the building on the measurement line: (**a**) \(2.5h_{0}\). (**b**) \(1.5h_{0}\), (**c**) \(0.5h_{0}\) and (**d**) \(-0.5h_{0}\).