# An Automated Framework for Streamlined CFD-Based Design and Optimization of Fixed-Wing UAV Wings
## 5 Framework Performance
### Grid Independence Studies and Error Quantification  
This section focuses on performing grid independence studies within the framework, ensuring that the solution converges under mesh refinement using previously established practices [39]. Because these studies are performed by the framework automatically, the simulation setup, including model and solution scheme selection, matches the setup detailed in Algorithm for Convergence Detection section. The ONERA M6 wing is selected for the grid independence studies due to its simplicity, public availability, and frequent use in benchmarking studies [65]. This well-documented geometry, depicted in Figure 12 is a staple in aerodynamic validation, offering established reference data for comparison. Although the ONERA M6 wing is commonly validated in high-speed subsonic and transonic flow regimes, this study is focused on subsonic incompressible flow conditions. Transonic regimes demand more intricate grid setups and solver configurations, which are outside the framework's intended operational domain [66]. The ONERA M6 model, along with the corresponding design space parametrization, is illustrated in Figure 12 and Table 7. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Component** & **Quantity** & **Specification** \\ \hline CPU Cores & 16 & AMD EPYC 7742 \\ GPU & 1 & NVIDIA A100 40 GB \\ RAM & 128 & Gb of DDR4 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: AUTh’s system cluster specifications. The studies are conducted under sea-level atmospheric properties, with a freestream velocity of 25 m/s. Two angles of attack (AoAs) are selected: a moderate 4\({}^{\circ}\) and a higher 12\({}^{\circ}\). The latter is commonly more demanding in terms of convergence, requiring more iterations due to the possible flow separation on the suction surface. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **ONERA M6** \\ \hline \(c_{1}\) & 805.9 mm \\ \(c_{2}\) & 629.5 mm \\ \(c_{3}\) & 451.3 mm \\ \hline \(b_{1}\) & 598.2 mm \\ \(b_{2}\) & 1196.3 mm \\ \hline \(\Lambda_{1}\) & 26.7\({}^{\circ}\) \\ \(\Lambda_{2}\) & 26.7\({}^{\circ}\) \\ \hline \(i_{1}\) & 0\({}^{\circ}\) \\ \(i_{2}\) & 0\({}^{\circ}\) \\ \hline \(\gamma_{1}\) & 0\({}^{\circ}\) \\ \(\gamma_{2}\) & 0\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Parametrization of the ONERA M6 wing. Figure 12: ONERA M6 wing planform. The study is executed by progressively increasing the number of grid elements using a scale factor that affects the hyper-parameters of the meshing algorithm. In Figure 13, the lift and drag forces on the ONERA M6 wing are illustrated for both AoAs. The results highlight that for both cases, the lift and drag forces converge to stable values as the mesh density increases. This also validates the usage of a universal grid per wing and the importance of the BOIs in the proposed framework. Beyond a certain number, which in this case is for approximately 7.5 million grid elements, further refinement provides diminishing returns in accuracy. Thus, the appropriate parameters are being fine-tuned for the meshing module in order to reliably provide computational grids with this refinement. Using these parameters as the baseline, further investigation is being conducted into the determination of the discretization error as per the methodology described in Section 4.1. Three wings are chosen for this phase: the ONERA M6 wing, the RADAERO conventional wing (details are present in Section 6), and a wing belonging to the EURRICA BWB UAV [62]. The planform of the EURRICA wing is illustrated in Figure 14, along with the parametrization in Table 8.  
Figure 14: EURRICA wing planform. Figure 13: Grid independence study for ONERA M6 wing. (a) Lift and drag at 4\({}^{\text{o}}\) AoA for a varying number of grid elements; (b) lift and drag at 12\({}^{\text{o}}\) AoA for a varying number of grid elements. Red points indicates the selected refinement that satisfies the study.