An integrated data-driven and experimental methodology for toroidal propeller design improvement

This study presents a data-driven hydrodynamic optimization framework for toroidal propellers. As a representative engineering application of artificial intelligence (AI), the framework offers an efficient route toward the advanced design of underwater propulsion systems. The framework is based on an experimentally validated high-fidelity Computational Fluid Dynamics (CFD) model, where open-water test data are used to validate the numerical methodology. A high-precision parametric modeling approach using the Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) expands the design space while ensuring geometric smoothness. To improve search efficiency, an Adaptive Radial Basis Function-Evolutionary Sampling Assisted Optimization (AR-ESAO) method is proposed. Its novelty lies in an online Leave-One-Out Cross-Validation (LOOCV) strategy to dynamically tune the Radial Basis Function (RBF) kernel hyperparameters during the optimization. Fourteen key design variables are optimized to minimize toroidal propeller power subject to thrust and geometric constraints. Compared with the prototype, the optimized design achieves a 7.26% power reduction while meeting thrust requirements. Flow field analysis reveals a more uniform pressure distribution and smoother gradient at the key section. Further vortex analysis shows that the optimized propeller accelerates vortex breakdown, with primary vortices dissipating within 3–4 rotational cycles (versus 7–8 for the best of sampling), thereby shortening coherence lifetime. Acoustic directivity analysis indicates that the optimized configuration yields the lowest sound pressure levels across most directions, with a reduction of 1.74 dB. Within a limited computational budget, this framework successfully coordinates the toroidal propeller's geometric interaction between fore and aft blades, significantly enhancing both hydrodynamic performance and underwater noise reduction.