## 4 Results and Discussion
### Varying \(C_{\text{sep}}\) Coefficient
\begin{table}
\begin{tabular}{c c c c} \hline \hline \(C_{\text{sep}}\) & \(\Delta C_{La}\) & \(\Delta|\alpha_{0}|\) & \(\Delta C_{\text{D0}}\) **(Counts)** \\ \hline
0.7 & \(-0.0102\) & \(+0.30^{\circ}\) & \(-30\) \\
1 & \(-0.0060\) & \(+0.30^{\circ}\) & \(-20\) \\
1.75 & \(-0.0069\) & \(+0.53^{\circ}\) & \(+20\) \\
2 & \(-0.0072\) & \(+0.52^{\circ}\) & \(+15\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Errors for the predicted aerodynamic parameters, against the experimental data, for different values of \(C_{\text{sep}}\). Figure 7: Contours of surface skin-friction coefficient on the main wing suction-side, for \(C_{\text{sep}}=1\) **(top)** and 2 **(bottom)**, at three different incidences that are \(\alpha=17^{\circ}\) **(left)**, \(19^{\circ}\) **(middle)**, and \(21^{\circ}\) **(right)**. tion. On the contrary, fixing \(C_{\text{sep}}=1\) provided skin-friction contours that are practically indistinguishable from the higher-fidelity SBES solution (not reported for brevity). The quantitative analysis of the main wing aerodynamics was performed by examining the distributions of sectional pressure and skin-friction coefficients at four different spanwise locations. As depicted in Figure 8, the selected sections correspond to the semi-pan fractions: \(\eta=0.15\) (near the wing root), 0.40 (near the engine nacelle), 0.63, and 0.87 (near the wing tip). Unless otherwise indicated, the following data refer to the case \(\alpha=19^{\circ}\), while similar results obtained for the other two incidences are not reported for conciseness. Figure 9 shows the pressure coefficient distributions, with the corresponding skin-friction coefficient distributions being drawn in Figure 10, while making a comparison with the time-averaged SBES results. The aerodynamic loading coefficients are normalized by using the following reference data: \(C_{p,ref}=|C_{p,min}^{SBES}|\) and \(C_{f,ref}=C_{f,max}^{SBES}\). By inspection of these figures, the higher levels of \(C_{\text{sep}}\) (say \(C_{\text{sep}}>1\)) provide completely wrong or anticipated BL separations. Apparently, decreasing \(C_{\text{sep}}\) leads to more accurate predictions of pressure recovery regions while approaching the reference SBES solution. This is particularly evident for the wing sections where the BL separation is more important. For instance, Figure 11 shows the velocity profile at \(\eta=0.87\) and \(x/c=0.4\), normalized by the freestream velocity \(V_{\infty}\), along with the profile of the turbulent viscosity ratio that is \(\mu_{t}/\mu\). While the BL velocity field is practically not affected by the variation of \(C_{\text{sep}}\), the modeled eddy-viscosity increases with decreasing this parameter, leading to less sensitivity of the BL flows to the high adverse pressure gradients on the suction-side of the wing. Therefore, the separation onset is more correctly represented by the lowest levels of this parameter. However, for \(C_{\text{sep}}=0.7\), the eddy-viscosity was overly increased, and the accuracy of the solution was lost, with both pressure and skin-friction coefficients being overestimated. On the contrary, by increasing too much this parameter, the BL separation is anticipated, and the separated flow region is erroneously enlarged. This is particularly evident by looking at the skin-friction coefficient plots, where \(C_{f}\cong 0\) determines the separated flow zone. Overall, the prescription of \(C_{\text{sep}}=1\) resulted in being the optimal choice for the present aeronautical application (when keeping the other coefficients unchanged). Figure 8: Spanwise locations of the four main wing sections under consideration. Figure 9: _Cont._  
Figure 11: Normalized profiles of velocity (**left**) and turbulent viscosity (**right**) at \(\eta\,=\,0.87\) and \(x/c=0.4\). Figure 10: Normalized sectional skin-friction coefficient at \(\eta\,=\,0.15\) (**top left**), \(0.40\) (**top right**), \(0.63\) (**bottom left**), and \(0.87\) (**bottom right**) for different values of \(C_{\text{sep}}\) compared to SBES.