Design space geometric filtering and manifold reconstruction-enhanced gradient optimization design method for laminar flow wing

The discrete adjoint-based gradient optimization method is one of the pivotal technical approaches for achieving laminar drag reduction optimization. However, the sensitivity of laminar wing transition location and aerodynamic performance of laminar wings to variations in pressure distribution makes the aerodynamic optimization problem under multiple constraints highly nonlinear and prone to prominent multimodality. These challenges significantly increase the optimization difficulty of gradient-based methods and compromise their robustness. This paper introduces a design space reconstruction method based on geometric smoothing and the geometric representation of Grassmann manifolds, which filters out high geometrical distorted configurations and maps the high-dimensional design space to a more compact low-dimensional design space without geometric constraints. Coupled with the discrete adjoint method, a design space geometric filtering and manifold reconstruction-enhanced gradient optimization design method for laminar flow wings has been developed. Aerodynamic optimization studies on the RAE2822 airfoil using different geometric parameterization forms demonstrate that the proposed method significantly reduces the dependence of optimization re -sults on specific parameterization schemes, and greatly improves algorithmic robustness compared to traditional gradient-based approaches. The gradient optimization method proposed in this paper is of significant importance for the development of efficient aerodynamic optimization technologies for full-aircraft laminar wings in practical engineering applications.