# An Automated Framework for Streamlined CFD-Based Design and Optimization of Fixed-Wing UAV Wings
## 6 Optimization Case Study
### Conventional UAV Wing--RADERO  
The RADAERO platform (Figure 21), a conventional fixed-wing UAV with an inverted V-tail configuration, is selected as the reference configuration. The RADAERO platform is a platform that has been 100% designed and built by the Laboratory of Fluid Mechanics and Turbomachinery [70] and has successfully completed several hours of flight testing. The initial design variables for this case are given in Table 12. The wing's airfoil--NACA 2414--and dihedral angle are kept constant along the wing sections. The upper and lower bound of the design variables are constrained to a \(\pm\) 20% from the baseline configuration, ensuring a resemblance to the already designed aircraft. This minimizes the impact of the new wing on the overall performance of the UAV. Flight conditions  
Figure 20: Average iterative error for every angle of attack, for converged and non-converged wings. are fixed at a cruising speed of 25 m/s at sea level, with a reference Reynolds number of 200.000 and an angle of attack of 4\({}^{\circ}\). Since RADAERO already features a horizontal and vertical stabilizer, and in a hypothetical scenario of later-stage optimization it imposes a stability constraint on the wing, in order to ensure that the tail remains the same. The optimization problem formulation is displayed in Equation (14). \[ \begin{split} maximize\frac{L}{D}\\ \text{subject to}\left\{\begin{array}{c}C_{L}\geq 0.414\\ 0\leq\left|C_{M\frac{\zeta}{4}}\right|\leq\left|-0.0781\right|\end{array}\right. \end{split}  \tag{14}\]  
An initial DoE stage (Exploration) is performed, so as to explore the design space. In this phase, using LHS, random configurations are analyzed, thus providing information to the GPs, mapping the inputs to the outputs, and constructing the foundation of feasible and infeasible regions. According to [71; 72], the majority of the computational budget should be distributed to the exploitation stage i.e., the infill stage. Guided by the EI acquisition function, the optimizer specifically selects points in the design space that offer a high probability of improving the current best score of the quantity of interest. A total of 30 wing \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Design Variable** & **Baseline * ** & **Lower Bound** & **Upper Bound** \\ \hline \(c_{1}\) & - & & \\ \(c_{2}\) & - & & 0.10–0.50 m & \\ \(c_{3}\) & - & & & \\ \hline \(b_{1}\) & 0.24 m & 0.19 m & 0.29 m \\ \(b_{2}\) & 1.125 m & 0.9 m & 1.35 m \\ \hline \(\Lambda_{1}\) & 0\({}^{\circ}\) & 0\({}^{\circ}\) & 20\({}^{\circ}\) \\ \(\Lambda_{2}\) & 0\({}^{\circ}\) & 0\({}^{\circ}\) & 20\({}^{\circ}\) \\ \hline \(i_{1}\) & - & & \(-\)2.0–0.0 & \\ \(i_{2}\) & - & & \\ \hline \hline \end{tabular}
\end{table} 
Table 12: RADAERO wing planform design space. Figure 21: Top view of the RADAERO platform. designs are evaluated with a ratio of exploration-to-exploitation equal to 1:2. As illustrated in Figure 22, circles denote valid solutions that satisfy constraints, while crosses represent invalid solutions. The framework successfully identified a final optimal wing design with an 8% increase in \(L/D\), a 2% improvement in \(C_{L}\), and a modest reduction in \(C_{M_{c/4}}\), aligning with the constraint (Table 13). On the optimized wing, the average \(y^{+}\) value along the wing was kept below 1. This highlights the framework's effectiveness in navigating a constrained design space, as evidenced by the progressive improvements across iterations and the ability to maintain stability and aerodynamic performance, while also providing reliable and fully automated CFD results. The optimized wing planform is compared to the baseline in Figure 23. It is evident that the span of the wing increased leading along with its aspect ratio, which has an explicit effect on the reduction in induced drag [7].