Gradient-Based Aerodynamic Shape Optimization Subject to Flow Separation

Abstract

Aerodynamic shape optimization is an established tool for improving aircraft performance, yet the integration of separation-related constraints into gradient-based optimization frameworks remains challenging for three-dimensional transonic wing configurations. In such cases, separation phenomena manifest locally and require cell-wise evaluation over large surface regions, leading to a substantial number of constraint functions. This work develops a surface-force-based separation constraint formulation that enables control of separated flow regions within a predefined region of interest on the wing suction side. The proposed methodology extracts tangential surface force components and projects them into a sweep-aligned local reference frame. A directional flow-angle threshold of 70° is introduced as an indicator of separated flow. Sensitivities are computed using forward mode algorithmic differentiation, ensuring that the computational effort scales primarily with the number of design variables rather than with the number of locally evaluated constraints. The optimization is performed using a sequential quadratic programming (SQP) algorithm and applied to a modified simple transonic wing configuration. The study is conducted in two stages. First, an unconstrained aerodynamic shape optimization is performed to establish a reference design. Subsequently, the separation constraint is activated and the constrained optimization is carried out for two elevated lift conditions, CL = 0.72 and CL = 0.75, in order to assess the robustness of the proposed formulation under off-design operating points. The unconstrained optimization reduces cruise drag by 4.58% and significantly decreases the extent of separated surface regions under elevated lift conditions, although separation is not fully eliminated. When activating the separation constraint at CL = 0.72 and CL = 0.75, separated regions are completely removed according to the applied criterion, while only minor increases in cruise drag of 0.056% and 0.36%, respectively, are observed. The additional computational time required for the constrained cases remains moderate due to the applied differentiation strategy.