Flexible Formulation of Spatial Integration Constraints in Aerodynamic Shape Optimization

In aircraft design, spatial integration places limits on aerodynamic and structural performance. While the outer mold line shape largely determines aircraft aerodynamic characteristics, aircraft systems and passengers or payloads must fit inside. Emerging categories of aircraft, such as electric aircraft, are likely to experience new and critical spatial integration challenges. Existing aerodynamic shape optimization tools can accept a narrowly defined set of geometric constraints. However, no known aerodynamic optimization framework can handle spatial integration constraints derived directly from 3D geometry. We propose a general geometric constraint formulation based on triangulated 3D geometry of both the outer mold line surface and the “object(s) to fit.” The constraint consists of two metrics: the length of the intersection curve(s) between any two objects, and the Kreisselmeier–Steinhauser function aggregated minimum distance. Our implementation of the intersection and distance calculations is fast and analytically differentiable with respect to geometric design variables, making it suitable for efficient gradient-based optimization. We validate our constraint formulation on three RANS-based aerodynamic shape optimization problems: a 2D fairing design problem, a 3D fairing design problem, and the design of an aeroshell to surround a human avatar. We show that this approach is robust and efficient, which enables the aerodynamic optimization of bodies containing objects with arbitrary shapes.