Aerodynamic Design Optimization of Transonic Natural-Laminar-Flow Airfoil at Low Reynolds Number

The position and size of laminar separation bubble on airfoil surfaces exert a profound impact on the efficiency of transonic natural-laminar-flow airfoil at low Reynolds number. Based on the particle swarm algorithm, an optimization methodology in the current work would be established with the aim of designing a high and robust performance transonic natural-laminar-flow airfoil at low Reynolds number. This methodology primarily includes two design processes: a traditional deterministic optimization at on-design point and a multi-objective of uncertainty-based optimization. First, a multigroup cooperative particle swarm optimization was used to obtain the optimal deterministic solution. The crowing distance multi-objective particle swarm optimization and the non-intrusive polynomial chaos expansion method were then adopted to determinate the Pareto-optimal front of uncertainty-based optimization. Additionally, the transition model was employed to predict the laminar-turbulent transition. Regarding to the established optimization methodology, a propeller tip airfoil of solar energy unmanned aerial vehicle was finally designed. During optimization processes, the minimized pressure drag was particularly chosen as the optimization objective, while the friction drag increment served as a constraint condition. The deterministic results indicate that the optimized airfoil has a good ability to control the separation and reattachment positions, and the pressure drag can be greatly reduced when the laminar separation bubble is weakened. The multi-objective results show that the uncertainty-based optimized airfoil possesses a significant robust performance by considering the uncertainty of Mach number. The findings evidently demonstrate that the proposed optimization methodology and mathematical model are valuable tools to design a high-efficiency airfoil for the propeller tip.