基于离散伴随的梯度优化方法是实现层流减阻优化设计的重要技术途径之一。层流翼转捩位置及气动性能对压力分布形态特征变化的敏感性，使得多约束下层流翼气动优化问题非线性较强、多极值特性较突出，显著增大了梯度优化方法的寻优难度及优化效能的鲁棒性。本文引入基于几何光顺与基于格拉斯曼流形几何表征的设计空间重构方法，滤除设计空间中的高几何畸变构型，并将高维设计空间映射到更紧致的低维无几何约束设计空间，耦合离散伴随方法，发展了设计空间几何过滤与流形重构增强的层流翼梯度优化设计方法。针对RAE2822翼型，基于不同几何参数化形式开展了气动优化设计。优化结果显示，相比传统层流翼梯度优化方法，优化效果对几何参数化形式的依赖性显著降低，算法寻优鲁棒性极大提高。本文提出的层流翼梯度优化方法对于发展工程实用的整机级层流翼高效气动优化技术具有重要意义。
The discrete adjoint-based gradient optimization method is one of the pivotal technical approaches for achieving laminar drag reduction optimization. The sensitivity of laminar wing transition location and aerodynamic performance to changes 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 results on specific parameterization schemes, while greatly improving 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.
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