Numerical simulations have been used in this paper to study the propulsion device of a wave glider based on an oscillating hydrofoil, in which the profile of the pitching and heaving motion have been prescribed for the sake of simplicity. A grid model for a two-dimensional NACA0012 hydrofoil was built by using the dynamic and moving mesh technology of the Computational Fluid Dynamics (CFD) software FLUENT and the corresponding mathematical model has also been established. First, for the sinusoidal pitching, the effects of the pitching amplitude and the reduced frequency were investigated. As the reduced frequency increased, both the mean output power coefficient and the optimal pitching amplitude increased. Then non-sinusoidal pitching was studied, with a gradual change from a sinusoid to a square wave as the value of β was increased from 1. It was found that when the pitching amplitude was small, the trapezoidal pitching profile could indeed improve the mean output power coefficient of the flapping foil. However, when the pitching amplitude was larger than the optimal value, the non-sinusoidal pitching motion negatively contributed to the propulsion performance. Finally, the overall results suggested that a trapezoidal-like pitching profile was effective for the oscillating foil of a wave glider when the pitching amplitude was less than the optimal value.

A numerical investigation is conducted to study the propulsive performance of the semi-active flapping foil of the wave glider, where the heaving smotion is fully prescribed, and the pitching motion is determined by the hydrodynamic force and torsion spring. A mesh for two-dimensional NACA0012 foil with the Reynolds number Re = 42000 is produced, and a dynamic mesh and sliding interface are used in the computation. The influences of reduced frequency, spring stiffness, and critical pitching amplitude on the hydrodynamic characteristics of semi-active flapping foil are systematically investigated. We find that there is a critical reduced frequency: When the reduced frequency is lower than the critical value, the propulsive performance of flapping foil can be improved exponentially, and when the reduced frequency is higher than the critical value, the semi-active flapping foil cannot provide an effective thrust. For a greater reduced frequency, there is an optimal spring stiffness value, which corresponds to the maximum value of the output power coefficient. For a lower reduced frequency, the mean value of the output power coefficient monotonically decreases as the spring stiffness increases. We also notice that the propulsive efficiency of flapping foil monotonically decreases as the spring stiffness increases. Finally, we find that the appropriate critical pitching amplitude can improve the propulsive performance of semi-active flapping foil, especially for greater heaving amplitudes.

A numerical investigation on the propulsion performance of the semi-active flapping foil of the wave glider with different mass ratio and damping coefficient is investigated. The commercial CFD software Fluent is used to solve the URANS equations around the flapping foil by the Finite Volume Method. A mesh of 2D NACA0012 foil with the Reynolds number Re = 42,000 is used in all simulations. We first analyze the effect of the mass ratio on the mean output power coefficient and propulsion efficiency and note that with the variation of the mass ratio, the propulsion efficiency decreases slightly. Besides, we find that the mass ratio has a noticeable influence on the mean output power coefficient, and the influence is determined by the reduced frequency. For high reduced frequency, with the increase of the mass ratio, the propulsion performance of the flapping foil decreases monotonously. For low reduced frequency, the mean output power increases slightly. For critically reduced frequency, the mean output power coefficient of the foil firstly increases and then decreases via the mass ratio increase. Then, we examine the influence of the damping coefficient on the propulsion performance of the flapping foil and find that the damping coefficient has a severe adverse effect on the output power and propulsion efficiency. We conclude that the influence of the damping coefficient should be considered first when we design the propulsion device of the semi-active flapping foil. Meanwhile, we should also consider the sea conditions to choose the mass ratio to optimize the flapping foil.

A numerical investigation of the propulsion performance and hydrodynamic characters of the full-active flapping foil under time-varying freestream is conducted. The finite volume method is used to calculate the unsteady Reynolds averaged Navier–Stokes by commercial Computational Fluid Dynamics (CFD) software Fluent. A mesh of two-dimensional (2D) NACA0012 foil with the Reynolds number Re = 42,000 is used in all simulations. We first investigate the propulsion performance of the flapping foil in the parameter space of reduced frequency and pitching amplitude at a uniform flow velocity. We define the time-varying freestream as a superposition of steady flow and sinusoidal pulsating flow. Then, we study the influence of time-varying flow velocity on the propulsion performance of flapping foil and note that the influence of the time-varying flow is time dependent. For one period, we find that the oscillating amplitude and the oscillating frequency coefficient of the time-varying flow have a significant influence on the propulsion performance of the flapping foil. The influence of the time-varying flow is related to the motion parameters (reduced frequency and pitching amplitude) of the flapping foil. The larger the motion parameters, the more significant the impact of propulsion performance of the flapping foil. For multiple periods, we note that the time-varying freestream has little effect on the propulsion performance of the full-active flapping foil at different pitching amplitudes and reduced frequency. In summary, we conclude that the time-varying incoming flow has little effect on the flapping propulsion performance for multiple periods. We can simplify the time-varying flow to a steady flow field to a certain extent for numerical simulation.

We numerically investigate the propulsion performance of a flapping foil operating near a free surface, focusing on the effects of submergence depth, Strouhal number, pitching amplitude, and surface features. A two-dimensional flapping foil of a National Advisory Committee for Aeronautics (NACA) section 0015, subjected to coupled pitching and heaving motions, is simulated using the Volume of Fluid (VOF) method and overset grid techniques at a Reynolds number of 1 × 105. Results show that submergence depth critically affects the hydrodynamic performance of the flapping foil by modulating the ground effect. At small submergence depths, interactions between the free surface and flapping foil induce energy dissipation and reduce thrust generation, particularly on the upper surface of the foil during its ascending phase. However, as submergence depth increases beyond a threshold, i.e., more than five times the flapping chord length, the ground effect diminishes rapidly. Further, the Strouhal number exhibits a positive correlation with the thrust generation of the flapping foil, enhancing propulsion through intensified dipole structures and jet-like wake effects. In contrast, pitching amplitude shows a negative correlation, as excessive amplitudes decrease propulsion performance. Moreover, the comparative analysis of free and rigid surfaces highlighted that the free surface introduces energy dissipation and slightly degrades propulsion performance at small submergence depths.