The airfoil is the foundation of an aircraft, and its characteristics have a significant impact on those of the aircraft. Conventional airfoil design mainly focuses on improving aerodynamic performance, while flying wing airfoil designs should also consider layout stability and stealth performance. The design requirements for an airfoil vary with its position on the flying wing layout aircraft based on corresponding spanwise flow field characteristics. By analyzing the spanwise flow characteristics of the flying wing, partition design models for flying wing airfoils were established in this study, and a series of flying wing airfoil designs that consider aerodynamics and aerodynamic/stealth were implemented. Then, the designed airfoils were configured on a three-dimensional X-47B layout for testing and verification. The results showed that the aerodynamic design and the aerodynamic/stealth design exhibited significant improvements in terms for aerodynamic and longitudinal trimming characteristics. However, the cruise drag performance of the aerodynamic/stealth design was slightly worse than that of the aerodynamic design, although the longitudinal moment trimming characteristics were basically the same. The stealth characteristics of the aerodynamic/stealth design had significant advantages, indicating that there were weak contradictions between the aerodynamic, stealth, and trimming requirements in the design of the flying wing.

For complicated aerodynamic design problems, the efficient global optimization method suffered from the defect of the incorrect portrayal of the design space, resulting in bad global convergence and efficiency performance. To this end, a Kriging-based global optimization method, named the Kriging-based space exploration method (KSE), was proposed in this paper. It selected multiple promising local minima and classified them into partially and fully explored minima in terms of the fitting quality of the surrogate model. Then, the partially explored minima would be furtherly exploited. During the local search, an enhanced trust-region method was adopted to make deep exploitation. By combining local and global searches, the proposed method could improve the fitting quality of the surrogate model and the optimization efficiency. The KSE was compared to other global surrogate-based optimization methods on 12 bound-constrained testing functions with 2 to 16 design variables and 2 aerodynamic optimization problems with 24 to 77 design variables. The results indicated that the KSE generally took fewer function evaluations to find the global optima or reach the target value in most test problems, holding better efficiency and robustness.

The design of the flying wing airfoil must consider aerodynamic stealth and trim requirements, with their coupling exacerbating the complexity of the design problem by introducing multiple local minimum points in design space. In addition, it would need a broad space with high dimensionality to obtain the ideal result, and expansion of design space could lead to more local minimum points, causing significant challenges to traditional optimization design methods. A Two-Stage Global–Local Constrained Optimization Method (TGLCOM) was proposed to address these issues. The parametric space was divided into a large-scale global space and a high-dimensional local space. A surrogate-based global constrained optimization method was applied in the large-scale global space, followed by a gradient-based algorithm in the high-dimensional local space to refine the design and obtain the global optima. The efficiency and robustness of the proposed TGLCOM were verified through the airfoil and flying wing layout aero/stealth design. The results indicated a minor conflict between the RCS drag and pitch moment performance. Moreover, the stealth design of the airfoil improved the stealth performance of the flying wing layout in both the yaw and pitch directions.