# An Automated Framework for Streamlined CFD-Based Design and Optimization of Fixed-Wing UAV Wings
## 4 Evaluation Metrics
### Solution Confidence  
Unlike global error estimates, key simulation quality indicators provide a practical and immediate assessment of grid and solution reliability. The confidence metrics utilized in this study are systematically implemented as part of the automated process, providing a quick and actionable diagnostic tool to assess simulation quality. By flagging runs that deviate from established thresholds, this method empowers engineers to either proceed with confidence or refine their setup, thus safeguarding the integrity of the design process. According to widely accepted guidelines for the subsonic regime, as well as experimental validations [58], proper resolution of turbulence effects--particularly when using the low-Reynolds variant of the k-omega SST turbulence model adopted in this study--requires careful treatment of the boundary layer grid. For accurate turbulence modeling and wall shear stress prediction, an average \(y^{+}\) value of less than 1 and a maximum \(y^{+}\) value of 2 should be enforced across the wing surface. While a maximum \(y^{+}\) value strictly below 1 is suggested by some researchers (see Table 5) as an ideal target, it is often unrealistic to achieve this consistently in automated frameworks, especially when considering the broad design space and flow conditions investigated in this work. Nevertheless, it should be noted that this practical guideline is applied to ensure that the low-Reynolds modeling will consider the phenomena encountered within the viscous sublayer, which appears at a \(y^{+}\) smaller than 5 [46]. Several studies have attempted to quantify the sensitivity of aerodynamic quantities to variations in \(y^{+}\) values across a range of geometries and flow conditions [58; 59]. However, these efforts remain limited, both in scope and applicability, as they do not comprehensively cover the design space or operational conditions explored in this study. As such, relying solely on \(y^{+}\) values for a quantified grid-resolution error remains impractical and, in many cases, misleading. In addition to satisfying the first layer height requirements near wall boundaries, an accurate boundary layer resolution also demands a sufficient number of prism layers within the boundary layer to properly capture the flow phenomena starting from the near-wall region of the viscous sublayer and moving on to the buffer zone and logarithmic region. Existing studies have established that 20 to 40 prism layers are typically required to discretize the boundary layer accurately and ensure numerical fidelity (see Table 5). This ensures that steep gradients, particularly in the near-wall regions, are resolved with an adequate grid density. By combining the guidelines for \(y^{+}\) and the boundary layer discretization, a systematic confidence assessment system is suggested in the current study, indicatively using color coding to flag deviations from established thresholds. This system allows for a rapid visual evaluation of simulation reliability, as illustrated in Figure 9. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Study** & **Proposed \(y^{+}\)** & **Proposed Prism Layers** \\ \hline [PERSON] et al., 1994 [38] & 3 & N/A \\ [PERSON] et al., 1995 [58] & 2 & N/A \\ [PERSON] et al., 2015 [59] & 1 & 30 \\ [PERSON] et al., 2019 [41] & N/A & 20–40 \\ [PERSON] et al., 2003 [60] & 2 & N/A \\ ANSYS–[PERSON] 2021 [48] & 1 & 30–40 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Proposed \(y^{+}\) values and prism layers in boundary layers in different studies. The green color represents the best-case scenario according to most guidelines, the orange color (left cross pattern) represents a type of grey zone where some studies agree, and the red color (right cross pattern) indicates poor confidence about the results of the analysis. In this framework, the \(y^{+}\) values (both average and maximum) are extracted using the solver module and the functionality provided by PyFluent, utilizing built-in methods.