## 5 Propeller Design for HAPS Operation
### Recent Development on Propeller Design Methodology
Specifically, the authors report that 50% of the cases evaluated with second-order discretization exhibited numerical instabilities or divergence issues, highlighting the practical limitations of high-fidelity methods in large-scale design exploration. Despite these difficulties, the framework successfully identifies propeller designs with efficiencies between 80% and 85%, illustrating the benefits of multi-fidelity modeling in optimizing aerodynamic performance while managing computational costs. The optimization is conducted under design conditions representative of high-altitude cruise, namely a flight altitude of 16 km, a freestream velocity of 55 km, and shaft power availability ranging from 11 to 30 kW. The resulting designs span diameters up to 3.0 m, with rotational speeds constrained according to a maximum tip Mach number of 0.8. The integration of DMSOoD, VFEIM, and Hierarchical Kriging increases the reliability and efficiency of the optimization process, providing a powerful tool for the development of high-altitude propellers. An innovative method that integrates Bayesian optimization, Vortex Theory, and 3D RANS simulations is presented in [141] to maximize efficiency during cruise (i.e., minimize energy consumption for the required thrust) while simultaneously minimizing volume to reduce weight and aerodynamic drag. The study considers operational conditions at altitudes of 16 km and 20 km, with a constant undisturbed flow velocity of 55 km and shaft power availability ranging from 11 to 30 kW. The proposed method identified blade designs achieving up to 86% cruise efficiency at 16 km and 83% at 20 km, which are highly promising results for the design of stratospheric propellers. The efficiency curves, as a function of the advance ratio, of the optimized propeller, derived from CFD simulations using 3D RANS with the \(\gamma\)-\(Re_{\theta}\) transition model, are presented in Figure 15.  
With the advent of artificial intelligence and neural network-based techniques, modern design methodologies are increasingly leveraging these technologies to optimize complex aerodynamic components such as propellers. One such example, although not originally developed for HAPS, is a recently proposed methodology based on Multi-Fidelity Neural Networks (MFNNs), which integrates low-fidelity BEMT data with high-fidelity CFD aerodynamic data [95]. In particular, the methodology was applied for the design of a propeller for an electric aircraft operating at 28 m/s, with a thrust of 190 N under cruise conditions. A comparison between a baseline propeller, obtained using BEMT, and the optimized propeller is presented through the efficiency trends shown in Figure 16. These trends clearly indicate that the MFNN model effectively captures the nonlinear relationship between low-fidelity BEMT and high-fidelity CFD, improving aerodynamic predictions with minimal computational cost. As a result, the optimized propeller features increased chord length at the root and tip, along with a reduced pitch angle. This configuration helps to minimize tip vortex intensity and enhances efficiency both at cruise conditions (design point) and at higher rotational speeds. Furthermore, the MFNN model demonstrates significantly higher accuracy compared to single-fidelity surrogate models. Performance predictions were derived using CFD with a 3D RANS \(k-\omega\) SST turbulence model. At the design point, the propeller thrust is 190 N. When the advance ratio falls below 0.32, corresponding to relatively high rotational speeds, the optimized propeller exhibits higher efficiency over a wide range of operating conditions, accompanied by a slight increase in thrust. Some common findings from the optimizations methodologies for HAPS propellers illustrated before are as follows: the diameter in every optimization consistently converges toward the maximum allowable value, so once clearances are determined, it is recommended to use the largest possible diameter.