## 5 Propeller Design for HAPS Operation
### Recent Development on Propeller Design Methodology
Another type of approach, in order to include CFD in the design process, is proposed in [94]; the authors present a high-fidelity multi-level optimization framework for the propeller, which is characterized by direct optimization using CFD. They propose a series of criteria to quantify the influence of shape changes on the viscosity loss and induced loss of the propeller, which can avoid the consumption of computing power at unnecessary design points and thus keep the computational cost within an acceptable range without sacrificing the computational accuracy. First of all, the optimization result, based on a variable-fidelity model based on BEMT and CFD, is taken as the baseline propeller [145; 146; 147]. Subsequently, the discrete adjoint method is used to optimize the airfoil cluster in a three-dimensional state. Next, parametric perturbation and flow pattern reconstruction techniques are employed to refine the chord length distribution and twist angle. To assess viscosity losses, the concepts of perturbation loss and additional efficiency are introduced, enabling a more precise evaluation of chord length optimization at each blade section. The optimization accuracy is verified through CFD simulations, which closely align with experimental data. By effectively balancing high accuracy with low computational costs, this approach optimizes the propeller shape while accounting for complex three-dimensional aerodynamic effects. Ultimately, the methodology provides valuable insights for designing efficient propellers for high-altitude, long-endurance UAVs. In this study, the operational conditions considered are an altitude of 15 km, a constant undisturbed flow velocity of 17 m/s, and a thrust of approximately 13 N per propeller. The characteristics of the propeller are as follows: \(D~{}=~{}1.4\) m, \(N_{b}~{}=~{}2\), rpm = 1150. The optimization resulted in a total propeller efficiency of 79.29%, 2% higher than that of a baseline propeller designed, under the same conditions, using the conventional variable-fidelity methods described before. In propeller design, both efficiency and weight are critical factors in improving the endurance or payload capacity of a HAPS. This topic is investigated in [97], where a parallel multi-fidelity, multi-objective optimization framework is developed. The framework combines advanced metamodeling techniques and acquisition functions to efficiently handle large datasets while balancing computational cost and accuracy, aiming to optimize propellers for high-altitude operations. The framework targets two main objectives: the aerodynamic performance of the propeller and the weight of the propeller blades, specifically their total volume, without specifying the material. Both objectives significantly influence the endurance of unmanned aerial vehicles. A notable innovation is the Deep Mean Subset of Data (DMSoD), a novel Kriging-based model that surpasses traditional Sparse Gaussian Process models in processing high-dimensional datasets. For acquisition, the framework employs the Variable Fidelity Expected Improvement Matrix (VFEIM), which effectively selects designs by optimizing the trade-off between cost and accuracy across various fidelity levels. This approach proves particularly beneficial when fidelity cost ratios are high, such as those between Vortex Theory and 3D RANS simulations. Additionally, a three-level Hierarchical Kriging model integrates evaluations from Vortex Theory and two types of 3D RANS simulations (first- and second-order upwind schemes), enhancing optimization robustness. Figure 14: Comparison between the efficiency curve of a propeller, evaluated with low-fidelity and high-fidelity methods. A batch-based infill strategy outperforms sequential design selection, accelerating the identification of high-performance solutions. Nevertheless, challenges occur in high-fidelity simulations, as many designs fail to converge using the second-order upwind scheme.