# Wind Loads on a Solar Panel at High Tilt Angles
## 3 Results and Discussion
### The Uplift Coefficient  
The value of \(C_{L}\) is calculated by integrating \(\Delta C_{p}\). Examples of \(C_{p}\) distributions on the upper and lower surface (\(\alpha=30^{\circ}\) and \(\beta=0^{\circ}\)) are shown in Figure 11. There is a symmetrical spanwise pressure distribution with respect to \(y/W=0.5\). The flow expansion and corner vortices on the first half of the panel result in a relatively large negative value of \(C_{p}\) for the upper surface. A positive value of \(C_{p}\) is observed on the lower surface. Near the front and rear edges, a more positive value for \(C_{p}\) corresponds to the blocking effect of the tilted panel. The variation in \(C_{L}\) with respect to \(\alpha\) and \(\beta\) is shown in Figure 12. The value of \(C_{L}\) (uplift force) is negative for \(\beta<90^{\circ}\), and is relatively small for \(\beta=90^{\circ}\). The lowest value for \(C_{L}\) is for \(\alpha=30^{\circ}\) to \(40^{\circ}\). This is similar to the observation by [PERSON] et al., who noted that peak suction occurs at \(\alpha=45^{\circ}\)[9]. The positive value for \(C_{L}\) for \(\beta\geq 105^{\circ}\) represents a downward force. A kink is also observed at \(\alpha=50^{\circ}\)  
Figure 10: Mean spanwise pressure distributions at \(x/L=0.5\); \(\beta=135^{\circ}\). Figure 9: Mean spanwise pressure distributions at \(x/L=0.5\); \(\beta=45^{\circ}\). For a specific value of \(\beta\), the effect of \(\alpha\) on \(C_{L}\) is shown in Figure 13. For \(\beta\leq 75^{\circ}\), \(C_{L}\) decreases linearly as \(\alpha\) increases (\(\leq\)30\({}^{\circ}\)), following an increase for \(\alpha\) = 50\({}^{\circ}\). The value of \(C_{L}\) at high \(\alpha\) (60\({}^{\circ}\) to 80\({}^{\circ}\)) is approximately the same as that at \(\alpha\) = 30\({}^{\circ}\) and 40\({}^{\circ}\). Wind loads on a tilted panel at lower \(\beta\) require caution at the design stage. An opposite effect is observed for \(\beta\geq 90^{\circ}\). The variation of \(C_{L}\) with \(\alpha\) (\(\geq\)60\({}^{\circ}\)) is minimal. The value of \(C_{L}\) also varies linearly with \(\alpha\) (\(\leq\)30\({}^{\circ}\)) for a specific value of \(\beta\). Figure 14 shows that the value of \(C_{L}\) increases as the value of \(\alpha\) increases. The value of \(dC_{L}/d\alpha\) increases from a negative to a positive value when there is an increase in \(\beta\). Therefore, the uplift force is more significant at lower values of \(\beta\), so \(dC_{L}/d\alpha=-0.0542+7.376\times 10^{-4}\beta-1.67\times 10^{-6}\beta^{2}\). Figure 15 shows the effect of \(\beta\) on \(C_{L}\) for a specific value of \(\alpha\). For \(\alpha\) = 10\({}^{\circ}\) and 20\({}^{\circ}\), the value of \(C_{L}\) decreases initially and the lowest value of \(C_{L}\) is for \(\beta\) = 30\({}^{\circ}\), following an increase in \(C_{L}\) with \(\beta\). There is a smaller variation in \(C_{L}\) for \(\beta\geq 120^{\circ}\). For \(\alpha\) \(\geq\) 30\({}^{\circ}\), the value of \(C_{L}\) increases as the value of \(\beta\) increases. Figure 11: Pressure coefficient contours for \(\alpha\) = 30\({}^{\circ}\) and \(\beta\) = 0\({}^{\circ}\) for (**a**) the upper surface and (**b**) the lower surface. Figure 12: Uplift coefficient. For the numerical study, 3D incompressible RANS simulations of wind flow over a stand-alone PV panel in full scale were performed using a steady finite volume solver of second-order accuracy (ANSYS Fluent 13) for the value of \(\alpha\) of 10\({}^{\circ}\) to 40\({}^{\circ}\) (in increments of 10\({}^{\circ}\)) and the value of \(\beta\) of 0\({}^{\circ}\) to 180\({}^{\circ}\) (in increments of 45\({}^{\circ}\)). The semi-implicit method for the pressure-linked equation (SIMPLE) is used. The SST \(\kappa\)-\(\alpha\) turbulence model [27] models flows with separation reasonably well. However, it is necessary to mesh down (wall spacing; \(y^{+}\sim\) 1).