Machine learning-based multipoint optimisation for improving aerodynamics of symmetrically cambered wing sails in wind-assisted ship propulsion

• New hybrid geometry parametrisation method for symmetrically cambered wing sails. • A rapid optimisation algorithm with a Gaussian process based surrogate model. • Optimised wing sail achieves 8% increased thrust over benchmark configuration. • Insights in thrust increase mechanisms through IDDES simulations. • Larger LE/TE radii and reduced maximum thickness can improve thrust production. The threat of climate change has renewed interest in sailing as a carbon-neutral propulsion method, with rigid wing sails emerging as promising auxiliary systems. A new class of wing sails that is symmetric about the half chord (also termed crescent-shape in the literature) has enabled the introduction of camber to enhance thrust production. They are particularly suited for wind-assisted ship propulsion, where performance across a wide range of apparent wind angles is critical. However, their aerodynamic shape remains largely unoptimised. To address this, an efficient aerodynamic optimisation method was developed by integrating a neural network-based aerofoil simulation tool and a Bayesian optimisation framework. The optimisation strategy guided the search for maximum average thrust across apparent wind angles from 10 ∘ to 150 ∘ , using a Gaussian Process surrogate model to balance exploration and exploitation. Aerofoil profiles were sampled through hybrid geometry parametrisation that combines Bézier curve-specified camber and modified NACA 4-digit thickness distribution. Sensitivity analysis revealed that larger tip radii and reduced maximum thickness can improve thrust production. The optimised geometry, termed BN4, was adopted to construct a full-size wing sail configuration. This configuration together with a benchmark configuration were simulated using the Improved Delayed Detached Eddy Simulation (IDDES). The simulation results indicated that the optimisation alleviates flow separation and increases pressure magnitudes on the suction side of the profile. This work demonstrates a path for the use of machine learning techniques in aerodynamic optimisation for wing sails, and sheds light on geometric parameters dominating the specific thrust production.