Accelerating hydrofoil optimization via U-Net surrogate coupled with the adjoint method

To overcome the computational bottleneck of traditional adjoint optimization methods, which relies heavily on time-consuming CFD simulations for the multi-objective optimization, this paper proposes a novel collaborative optimization strategy coupling machine learning with the adjoint method. Focusing on the NACA0015 hydrofoil, a multi-objective optimization framework is established. By analyzing the influence of weighting factors between the lift-to-drag ratio and the cavitation volume coefficient, the optimal weight combination is determined to construct an objective function, thereby enabling the simultaneous optimization of both parameters. To mitigate the considerable computational costs associated with traditional adjoint optimization methods in nonlinear flow field optimization, this study develops a predictive model based on an encoder-decoder convolutional neural network (U-Net). This approach enables rapid and accurate prediction of both the hydrofoil geometry and the pressure distribution. Building upon this, the predictive model is integrated into the optimization framework, using neural network predictions to replace the repetitive flow field simulations during the adjoint iterations. Consequently, the lift-to-drag ratio is increased by 8.87%, and the cavitation volume coefficient is improved by 23.84%. While preserving physical fidelity, this study achieved a simultaneous enhancement in both the hydrodynamic performance and cavitation suppression capability of the hydrofoil.