This paper researched into the harmonic and anharmonic underwater flapping foil propulsion systems to improve the efficiency of these bioinspired propulsors. The angle of attack, the pitching angle, the heaving amplitude, and the phase difference are parametrically investigated in this paper. A rigid two-dimensional NACA (National Advisory Committee for Aeronautics) 0012 airfoil is modeled with the aid of a commercial computational fluid dynamics software, FINE™/Marine. Unsteady Reynolds Average Navier-Stokes (URANS) equation is solved together with dynamic mesh to simulate the foil motion. The investigation first verifies the reliability of the developed modeling method against the benchmark data. Then, the systematic investigation is conducted and identifies that the heaving amplitude is most influential factor for the propulsion efficiency. Secondly, phase difference also has a significant influence on efficiency, but this effect is related to the reference working condition, which needs further study. Then, the pitching amplitude has little effect on the maximum efficiency value of flapping foil, while it will affect its optimal speed range. When the heaving amplitude ratio reaches 3 and the corresponding maximum angle of attack is about 9°, the maximum efficiency can reach 87%. The effect of anharmonic motion on the efficiency is very small and varies with the St number, but in summary, it can maintain the peak efficiency over a wider range of operations. In addition, the force and flow field characteristics of different efficiency points are compared and analyzed to distinguish their corresponding relationship with the propulsion efficiency.

The semi-active flapping foil driven by the swing arm is a simple structure to realize the propulsion of the flapping foil. The motion trajectory of this semi-active flapping foil mechanism is a circular arc, and its hydrodynamic characteristics are not clear. This paper systematically investigates the working characteristics and hydrodynamic performance of this semi-active flapping foil with a circular arc track. Compared with the traditional flapping foil structure, the special design parameters of the semi-active flapping foil driven by the swing arm mainly include the length of the swing arm and the stiffness of the torsion spring. In this paper, the three-dimensional fluid-structure coupling method is used by solving the fluid dynamics equation and the structural dynamics equation, and the working characteristics of the structure with different motion and geometric parameters are analyzed. From the results, increasing the swing arm length is beneficial to improving the peak efficiency of the flapping foil, and also to improving the thrust coefficient corresponding to the peak efficiency point. Under a certain swing arm length, reducing the spring stiffness is also conducive to improving the peak efficiency of the propulsion system, but it is adverse to the thrust coefficient. Further analysis shows that the maximum angle of attack is the key factor affecting the efficiency of this flapping foil propulsion. For the flapping foil described in this paper, its peak efficiency is usually concentrated near ${\alpha }_{max}=0.2 \mathrm{rad}$. However, for the thrust coefficient of this kind of flapping foil propulsion, the influencing factors are relatively complex, including swinging arm, the spring stiffness, and the advance coefficient. The maximum angle of attack remains the key factor affecting the peak thrust in the range of advance coefficient far from the starting state.

Recent studies indicate that bow foil biomimetic systems can significantly improve ship propulsion in waves. In this paper, the DTMB 5415 ship model is taken as the object and a semi-active elastic flapping foil is proposed to install at its bow underwater position. When a ship sails in head wave, heave and pitch motion will occur, which will drive the bow foil to form heave motion. According to the working characteristics of elastic foil, bow foil can generate forward thrust under drive of given heave motion. At first, co-simulation of the ship with self-pitching bow foil in head waves is realized by ISIS-CFD solver and preliminarily realizes drag reduction and thrust increase effect of the bow foil. At the same time, it is found that the effect of bow foil on hull drag reduction is reflected in two aspects, one is the additional thrust generated by the bow foil and the other is that suppression of the bow foil on hull motion also reduces hull resistance in waves. Then, in order to optimize the working characteristics of elastic bow foil, the influence of spring stiffness and span length of the bow foil on drag reduction and thrust increase effect is discussed. A preliminary spring optimization result is obtained, as well as the influence of the span length of the bow foil on the system.

Taking the rigid NACA0012 airfoil as the object, the key structural parameters of the spring–mass system that govern the dynamics of the double-elastic-constrained flapping hydrofoil are numerically studied in this paper. A two-dimensional numerical model, based on the CFD software FINE/Marine, is established to investigate the influence of the spring stiffness coefficient, frequency ratio, and damping coefficient on the motion and performance of the flapping hydrofoil. This study demonstrates that when the structural parameters are adequately adjusted, the power factor exceeding 1.0 has been achieved, and the corresponding efficiency is up to 37.8%. Moreover, this system can start and work within a wide range of damping coefficients. However, the hydraulic efficiency and power coefficient are sensitive to the change in damping coefficient, so it is very necessary to design an appropriate power output. Lastly, the most obvious parameter affecting the energy acquisition performance is the spring stiffness coefficients. Frequency ratios in the two directions have little influence on the peak value of the power coefficient, but they will cause the change of damping coefficients of the peak point. The key structural parameters studied in this paper provide a useful guideline for an optimized design of this interesting system through searching for the best performance.

Numerous studies indicate that a flapping-foil thruster installed at a ship’s bow can convert wave energy into propulsive power and reduce added wave resistance while improving dynamic stability. Based on the preliminary exploration of the drag reduction mechanism of an elastic bow-flapping-foil system in waves, this paper further compares the effects and universality of this system on the resistance and motion response of different ship types under similar operating conditions, using three classic ship types (DTMB 5415, KCS, and Wigley) as research objects. Using the ISIS-CFD solver in NUMECA software, the study simulates the ship coupled with a semi-active elastic flapping foil in head waves, analyzing the influences of spring stiffness, foil size, installation position, and encounter phase on system performance. Numerical results show effective wave energy harvesting, boosting propulsion and stability. Under optimized parameters, ship pitch and heave amplitudes decrease by up to 20.14%, resistance reduction reaches 9.60%, and DTMB 5415 achieves a comprehensive drag-reduction and thrust-increase ratio of 31.39%. Further analysis reveals that thrust performance does not rise proportionally with spring stiffness, whereas drag and heaving reduction improve with increasing stiffness. The system performs best at a wavelength-to-ship-length ratio of 1.2 and a foil encounter phase of −90°. This work supports parameter optimization for such systems based on practical application scenarios and requirements.