The toroidal propeller, as a high-performance propulsor with a unique geometric configuration, presents challenges in parameterizing its complex geometry and conducting design optimization. This paper proposes a hybrid Free-Form Deformation (FFD) based parametric method, which integrates global FFD control with local parameters to achieve flexible and efficient description of the complex surfaces of toroidal propellers. Building upon this, an automated design framework integrating Computational Fluid Dynamics (CFD), a Kriging surrogate model, and a data-driven optimization algorithm is constructed to explore a high-dimensional design space comprising 14 variables. The goal is to minimize torque while satisfying thrust and geometric constraints. Optimization results show that the optimized propeller achieves approximately 3.63% higher propulsive efficiency at the design condition and requires about 4.32% less power for the required thrust, compared with the best design from Design of Experiments (DOE) sampling. Further flow field analysis reveals that the optimized design achieves a more gradual pressure distribution, which effectively suppresses flow separation and cavitation risk, thereby maintaining better performance across a wider operational range. This study provides a systematic parametric modeling method and optimization strategy for the efficient design of toroidal propellers, demonstrating clear engineering application value.

This research applied a data-driven hydrodynamic optimization design method for toroidal propellers based on experimental validation. First, open-water performance tests of the toroidal propeller were conducted, and the results were used to calibrate the high-fidelity numerical simulation. Second, a high-precision parametric geometry modeling approach was developed by the PCHIP method for spline curves, effectively expanding the design space while ensuring geometric smoothness. Subsequently, a surrogate model-assisted optimization algorithm (ESAO) was employed to optimize the toroidal propeller with 14 key design variables, and the objective was to minimize power under thrust and thickness constraints at the design condition. A total of 150 numerical evaluations were performed. The optimal design reduces the power by 7.26%, compared to the prototype while meeting thrust requirements. Furthermore, the optimized propeller demonstrated better performance in off-design condition, achieving an efficiency of 71% at an advance coefficient of J=1.3. Finally, a detailed flow field comparison among the original, the best from random sampling, and the optimized design was conducted. The results revealed that the optimized propeller exhibits a more uniform pressure distribution and a significantly smoother pressure gradient at the 0.6r/R section. This effectively suppresses flow separation and reduces energy loss. With limited computational resources and intervention, the proposed data-driven optimization framework coordinates the geometric interaction between the fore and aft blades of the toroidal propeller, significantly enhances its overall hydrodynamic performance.