## 2 Computational Framework
### Specifications of Validation Cases  
A three-dimensional Zimmerman wing planform was selected for the validation purposes, and the geometry was investigated by [PERSON] and [PERSON] experimentally [9]. It has a zero camber and the aspect ratio (AR) is two, and the aerodynamic mean chord is 0.1725 m which gives a corresponding Reynolds number of 100,000. The model has a thickness-to-chord ratio of 1.96% and 5-to-1 elliptical leading- and trailing-edges. The aerodynamic center was assumed to be at the 25% point of the mean aerodynamic chord. To minimize the boundary condition effects, two different types of boundary settings were tested, and results were compared with the experiment data. Model 1 had an H-type mesh topology and the boundary conditions were set as velocity-inlet, pressure-outlet, and a non-slip wall boundary was applied on the wing. The farfield boundary condition was applied for the outer boundary. On the other hand, Model 2 was set as wing tunnel model boundaries. It has a velocity-inlet, pressure-outlet, and a wall boundary was applied for the wing and the outer domain faces, respectively (listed in Table 1). Model 2 was set as the wing tunnel model which had a contraction ratio of 20.6 to 1 and a rectangular inlet contraction cone. The freestream turbulence intensity in the test section was measured to be less than 0.05%. The test section was 182 cm long with a square cross-sectional area of 61 cm \(\times\) 61 cm [9]. An O-grid mesh topology was applied around the wing planform to capture the detailed flow field near the boundary layer for Model 1 and Model 2 configurations. Therefore, the grid points were concentrated near the wing planform edge, as shown in Figure 2d. For the wind tunnel setting case, a symmetric boundary condition was applied at the wing root plane, as shown in Figure 2c. The no-slip wall boundary condition was enforced on the wing surface. To minimize the farfield boundary condition effects, Model 1 had the domain which is set at 25\(\overline{c}\) upstream, 35\(\overline{c}\) downstream, and the upper and lower boundaries were placed at 25\(\overline{c}\) away from the airfoil leading-edge. However, Model 2 was set as wing tunnel model boundaries which had exactly same dimensions as the real wind tunnel. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Case** & **Grid Size** & **C\({}_{\text{L}}\)** & **C\({}_{\text{D}}\)** \\ \hline \multirow{4}{*}{Model 1} & G1 & 190 \(\times\) 135 \(\times\) 60 & 0.1744 & 0.01913 \\  & G2 & 220 \(\times\) 165 \(\times\) 90 & 0.1775 & 0.02068 \\  & G3 & 250 \(\times\) 195 \(\times\) 120 & 0.1781 & 0.02052 \\  & G1 & 190 \(\times\) 135 \(\times\) 60 & 0.1899 & 0.01890 \\ \multirow{2}{*}{Model 2} & G2 & 220 \(\times\) 165 \(\times\) 90 & 0.1900 & 0.01877 \\  & G3 & 250 \(\times\) 195 \(\times\) 120 & 0.1901 & 0.01879 \\ \multirow{2}{*}{Model 1} & Experiment [1] & NA & 0.1906 \(\pm\) 0.02 & 0.0220 \(\pm\) 0.003 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Grid-sensitivity analysis for \(\alpha=4^{\circ}\). The mesh sensitivity was studied for the three-dimensional cases for \(\alpha\) = 4\({}^{\circ}\) and the results are shown in Table 1. The baseline mesh (G1) had about 1.5 million mesh elements and model with a fine mesh (G2) had a doubled size of 3 million. Close to the wall, there were about 60 grid points within the boundary layer, and in the turbulent region, the y\({}^{+}\) value of the first cell distance was ensured to be in the order of O(1). The stretching ratio for the mesh was less than or equal to 1.2. Validation results are summarized in Table 1. The aerodynamic results comparisons, in Figure 2e,f, showed that Model 2 (wind tunnel settings) gave a better lift coefficient as compared with the experimental data. The results from Model 1 were close to the experimental data at low incidences but under-predicted at high incidences. The drag values showed a similar conclusion, showing potentially the stronger wall interference at higher incidences ([PERSON] [9]).