# An Automated Framework for Streamlined CFD-Based Design and Optimization of Fixed-Wing UAV Wings
## 5 Framework Performance
### Large Scale Deployment
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Type of Value** & **Mesh Generation [s]** & \begin{tabular}{c} **Writing Mesh to** \\ **Disk [s]** \\ \end{tabular} & \begin{tabular}{c} **Loading Mesh in** \\ **FLUENT [s]** \\ \end{tabular} & \
\begin{tabular}{c} **Initializing Solution** \\ **in FLUENT [s]** \\ \end{tabular} &
\begin{tabular}{c} **Analysis Execution** \\ **in FLUENT [s]** \\ \end{tabular} \\ \hline Minimum Value & 54 & 0.5 & 1 & 8 & 38 \\ Maximum Value & 3385 & 89 & 115 & 56 & 1150 \\ Mean Value & 255 & 36 & 50 & 19 & 259 \\ Median Value & 232 & 33 & 45 & 17 & 212 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Summary statistics of required execution time for 1165 wings (rounded). Figure 18: Distribution of the two most time-consuming phases of the framework for 1165 wings. (**a**) Mesh generation time, which is mostly centered around 250–300 s. (**b**) Simulation execution time, which is mostly centered around 150 s.  
values exceeding two orders of magnitude above the quality threshold, are excluded from the analysis. Table 11 provides summary statistics for the \(y^{+}\) values of the valid cases. To further analyze the distribution of \(y^{+}\) values, Figure 19 provides scatter plots of the average and maximum \(y^{+}\) values for all cases. Figure 19a presents the full dataset, excluding the extreme outliers, and highlights the strong clustering of cases that meet the quality criteria, shown by the green diamond points. The presence of a small subset of extreme values, where \(y^{+}_{max}\) exceeds 10, indicates specific challenges in grid resolution for certain geometries or flow conditions. These cases, although rare, suggest areas for localized adjustments to boundary layer refinement settings. Figure 19b focuses on cases that satisfy or marginally exceed the quality thresholds, offering a clearer view of the robust performance achieved by the framework. The tightly clustered data points illustrate the consistency of the automated meshing process, particularly for the majority of sampled wings. Overall, these visualizations confirm that the framework maintains a high degree of mesh quality across a diverse range of wing configurations, with only minor deviations requiring further attention. Regarding the iterative error, the same batch of wings is used to investigate the total uncertainty from either non-converged or prematurely converged cases. Solutions are either converged fully or stopped at 2000 iterations (maximum iterations) to assess the impact of incomplete convergence. Figure 20 illustrates the average iterative error (for both forces in X and Z axis) for converged and non-converged wings across the sampled angles of attack. Non-converged wings exhibit significantly higher iterative errors, particularly at low angles of attack, where the error reaches its peak. In contrast, converged wings demonstrate negligible iterative errors across the entire range, underscoring the importance of convergence in achieving reliable results. This comparison emphasizes the role of iterative errors as a diagnostic tool for assessing the solution quality and the reliability of early terminated simulations. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Type of Value** & \(y^{+}_{average}\) & \(y^{+}_{maximum}\) \\ \hline Minimum & 0.32 & 0.79 \\ Maximum & 9.18 & 29.53 \\ Mean & 0.48 & 1.55 \\ Median & 0.46 & 1.40 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Summary statistics of the results for grid resolution. Figure 19: Scatter plot of the average and maximum \(y^{+}\) values for all the cases. (**a**) All cases without the extreme outliers. (**b**) Focused scatter plot around \(y^{+}_{mean}<1\) and \(y^{+}_{max}<5\).