# Experimental Assessment of RANS Models for Wind Load Estimation over Solar-Panel Arrays
## 4 Results
### Turbulence Kinetic Energy \(k\)  
Planar PIV measures only the in-plane velocity components \((u,v)\). The transversal velocity fluctuations of the flow are here neglected when compared with the ones in the tangential plane. The final value of the turbulence kinetic energy \(k\) is computed as:  
\[k=\frac{1}{2}\left(\overline{u^{\prime 2}}+\overline{v^{\prime 2}}\right), \tag{2}\]  
where \(u^{\prime}\) and \(v^{\prime}\) are the velocity fluctuations in the streamwise and vertical direction, respectively. Figure 6 shows the vertical profile of \(k\) between (a) 1 st and 2 nd panel (\(x/c=1.5\)), (b) 2 nd and the 3 rd panel (\(x/c=3.5\)), (c) 3 rd and 4 th panel (\(x/c=5.5\)), and (d) after the 4 th panel (\(x/c=7.5\)). In addition, it is also shown the Reynolds stress \(\overline{u^{\prime 2}}\). In Figure 6a transition SST and SST \(k\)-\(\omega\) models produces a \(k\) very similar to the measured Reynolds stress \(\overline{u^{\prime 2}}\) than to \(k\), specially at \(y/c=0.5\) and \(1.5\), where the flow leaves the 1 st panel at the bottom and top corners respectively. In this condition the flow is highly anisotropic, nevertheless due to the Boussinesq hypothesis \(k\) is often found to be in simulations larger than in experiments [40]. In any case, none of the numerical model fits perfectly with the experiment in the region inside the turbulent wake of the panel. It is remarkable that \(k\)-\(e\) predicts no \(k\) at \(y/c=1\), a region with a fully turbulent flow. Figure 5: Pressure coefficient \(C_{p}\) distribution for (**a**) 1 st panel, (**b**) 2 nd panel, (**c**) 3 rd panel, and (**d**) 4 th panel. Lines refers to numerical results for the different turbulent models: \(k\)-\(\epsilon\) (); SST \(k\)-\(\omega\) (); transition SST (); and RSM (). Experimental measurements are shown as (e). In Figure 6b the measured \(\overline{u^{\prime 2}}\) shows a more similar shape to the numerical \(k\) than the experimental one. \(k\)-\(\epsilon\), SST \(k\)-\(\omega\) and transition SST predict the same \(k\) in the region inside the turbulent wake after the 2 nd panel, while RSM prediction is slightly different from the other simulations. The RSM profile is more similar to the \(\overline{u^{\prime 2}}\) profile than the other methods, with a more intense fluctuation of the flow passing below the panels than of the one passing above. However, the numerical results are underestimated with respect to \(\overline{u^{\prime 2}}\) and \(k\) in this region. There is also difference between the measured \(\overline{u^{\prime 2}}\) and \(k\) in this region, which implies that the cross-wise fluctuations are strongly contributing to \(k\). The region below the turbulent wake shows also a significant difference between the experimental and numerical \(k\). The simulation predict that there is almost no \(k\) is this region. In the numerical fields for the mean horizontal velocity it was seen that, after the acceleration when leaving the 1 st panel, the flow did not reduce its streamwise mean velocity as much as seen in the experiment. This could be possibly justified by the fact that no simulation is able to correctly predict the streamwise fluctuations of the flow passing below the panels, thus overestimating its momentum. In Figure 6c the \(k\) predicted by \(k\)-\(\epsilon\) is the most similar to the measured \(\overline{u^{\prime 2}}\) in the region above \(y/c=1.5\). However, none of the numerical model gets to simulate neither \(k\) or \(\overline{u^{\prime 2}}\) in the turbulent wake after the 3 rd panel. The region of larger \(k\) is thinner in the transition SST model than in the other three. This was expected behaviour after seen the thinner turbulent wake in the velocity fields of this model. The same difference in experimental and numerical \(k\) in the flow below the panels can be seen in this profile. Figure 6: Turbulent kinetic energy \(k\) profiles at (**a**) \(x/c=1.5\), (**b**) \(x/c=3.5\), (**c**) \(x/c=5.5\), and (**d**) \(x/c=7.5\).