Flapping foils are studied to achieve an efficient propeller. The performance of the flapping foil is influenced by many factors such as oncoming vortices, heaving amplitude, and geometrical parameters. In this paper, investigations are performed on flapping foils to assess its performance in the wake of a D-section cylinder located half a diameter in front of the foil. The effects of heaving amplitude and foil thickness are examined. The results indicate that oncoming vortices facilitate the flapping motion. Although the thrust increases with the increasing heaving amplitude, the propelling efficiency decreases with it. Moreover, increasing thickness results in higher efficiency. The highest propelling efficiency is achieved when the heaving amplitude equals ten percent of the chord length with a symmetric foil type of NACA0050 foil. When the heaving amplitude is small, the influence of the thickness tends to be more remarkable. The propelling efficiency exceeds 100% and the heaving amplitude is 10% of the chord length when the commonly used equation is adopted. This result demonstrates that the flapping motion extracts some energy from the oncoming vortices. Based on the numerical results, a new parameter, the energy transforming ratio (R_ET), is applied to explicate the energy transforming procedure. The R_ET represents that the flapping foil is driven by the engine or both the engines and the oncoming vortices with the range of R_ET being (0, Infini) and (−1, 0), respectively. With what has been discussed in this paper, the oncoming wake of the D-section cylinder benefits the flapping motion which indicates that the macro underwater vehicle performs better following a bluff body.

Multi-fidelity surrogate-based methods play an important role in modern engineering design applications, aiming to improve model accuracy while reducing computational cost. One of the widely adopted approaches is the calibration-based method, which calibrates the low-fidelity model through a discrepancy model between low-fidelity and high-fidelity models. Since discrepancies between models exhibit varying characteristics across different problems, using a single surrogate for discrepancy approximation may lack stability. In practical engineering design problems, it is often hard for designers to select optimal surrogate models. To this end, a hybrid-surrogate-calibration-assisted multi-fidelity modeling (HSC-MFM) approach is proposed in this paper. Specifically, this approach integrates three representative surrogate models, including the polynomial response surface, Kriging model, and radial basis function, to comprehensively capture the discrepancy characteristics between different fidelity models. Furthermore, an adaptive weight calculation method is developed to improve the modeling accuracy. Testing results demonstrate that HSC-MFM achieves enhanced stability compared to most existing methods while maintaining good prediction accuracy. Finally, the proposed method is applied to predict the strength of the frame for a blended-wing-body underwater glider, which verifies its engineering applicability.

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.

Leading-edge tubercles provide a bio-inspired modification for regulating the hydrodynamic performance of marine propellers, but their controllable generation on complex three-dimensional blades remains insufficiently studied. This study develops a parametric modeling method for tubercled leading-edge propellers based on the David Taylor Model Basin (DTMB) 4383 geometry. The method combines B-spline smooth reconstruction with a Gaussian envelope function to control tubercle radial peak position and height. After validation with publicly available open-water experimental data, the computational fluid dynamics (CFD) method is applied to uniform and locally targeted tubercled models. The results show that leading-edge tubercles modify the suction-side low-pressure region and redistribute local blade loading. The radial peak position mainly controls the concentration region of the pressure disturbance, whereas peak height affects its intensity. At the design advance coefficient, moving the target peak from r/R = 0.26 to r/R = 0.92 decreased the thrust coefficient by 0.77% and increased the torque coefficient by 1.75%. For a fixed target position, increasing the maximum amplitude ratio from 0.05 to 0.80 increased the thrust and torque coefficients by 0.25% and 0.88%, respectively. These findings indicate that tubercle design should balance radial position and protrusion height.

Rapid surrogate prediction of ducted propeller performance is challenging when only a limited number of independent geometries are available and operating points belonging to the same geometry are strongly correlated. This study proposes a sensitivity-informed physics-regularized backpropagation neural network (SIPR-BP) for simultaneous prediction of the thrust coefficient K_T and the scaled torque coefficient 10K_Q. A CFD database comprising 20 Ka4-70-derived parameterized geometries, each evaluated at five advance ratios, provides 100 observations and 20 complete performance curves. The framework combines three main strategies. First, two-component multi-output partial least-squares (PLS) curve surrogates are reconstructed exclusively from the training geometries of each outer fold to generate leakage-controlled conditional Sobol gate priors. Second, the operating coordinate J is separated from geometric gating and represented by five ordered curve nodes, which guarantee non-increasing K_T and 10K_Q responses over the investigated interval. Third, training-only physics-consistency reliability weighting and a three-member ensemble improve robustness to locally irregular CFD responses and initialization variability. Under a ten-round geometry-grouped holdout protocol, SIPR-BP achieves a geometry-balanced MAPE of 2.65%, RMSE of 0.0112, MAE of 0.00911, and pooled R² of 0.951. When evaluated under the same outer partitions, a two-component PLS baseline yields a MAPE of 4.38%. Across the evaluated PLS, Extra Trees, GPR, and SVR baselines, SIPR-BP reduces geometry-balanced MAPE by approximately 39.6–79.2%. The results indicate that the proposed framework improves unseen-geometry prediction while preserving the prescribed response-curve structure.