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.

One of the most commonly used techniques in aerospace engineering is the RANS (Reynolds average Navier–Stokes) approach for calculating the transonic compressor flow field, where the accuracy of the computation is significantly affected by the turbulence model used. In this work, we use SA, SST, k-ɛ, and the PAFV turbulence model developed based on the side-biased mean fluctuations velocity and the mean strain rate tensor to numerically simulate the transonic compressor NASA Rotor 67 to evaluate the accuracy of turbulence modeling in numerical calculations of transonic compressors. The simulation results demonstrate that the four turbulence models are generally superior in the numerical computation of NASA Rotor 67, which essentially satisfies the requirements of the accuracy of engineering calculations; by comparing and analyzing the ability of the four turbulence models to predict the aerodynamic performance of transonic compressors and to capture the details of the flow inside the rotor. The errors of the Rotor 67 clogging flow rate calculated by the SA, SST, k-ɛ, and PAFV turbulence models with the experimental data are 0.9%, 0.8%, 0.7%, and 0.6%, respectively. The errors of the calculated peak efficiencies are 2.2%, 1.6%, 0.9%, and 4.9%. The SA and SST turbulence models were developed for the computational characteristics of the aerospace industry. Their computational stability is better and their outputs for Rotor 67 are comparable. The k-ɛ turbulence model calculates the pressure ratio and efficiency that are closest to the experimental data, but the computation of its details of the flow field near the wall surface is not ideal because the k-ɛ turbulence model cannot accurately capture the flow characteristics of the region of high shear stresses. The PAFV turbulence model has a better prediction of complex phenomena such as rotor internal shock wave location, shock–boundary layer interaction, etc., due to the use of a turbulent velocity scale in vector form, but the calculated rotor efficiency is small.

This study proposes a novel partial average fluctuation velocity (PAFV) turbulence based on the PAFV and the average strain rate tensor, which is used to calculate the shock wave boundary layer interaction flows, including cascade flow and transonic compressor flow. In order to illustrate the adequacy, the calculation results of several other turbulence models were also compared with PAFV, including k-ω, shear stress transport, SA-neg (negative Spalart-Allmaras), and stress-BSL (ω-based Reynolds stress model). The suitability of the PAFV turbulence model was initially tested by calculating the transonic flow in the L030-4 cascade. Subsequently, numerical computations were performed for the 3D (three-dimensional) National Aeronautics and Space Administration Rotor 67 transonic compressor rotor. In the numerical simulation, the flow control equations were transformed in a general curvilinear coordinate system for precision enhancement, and the spatial discretization of control equations was executed using the finite difference method. The convection term was processed using the Steger–Warming flux vector splitting method, the diffusion term was discretized using a second-order central difference scheme, and the time derivative term was discretized using the third-order Runge–Kutta method. A parallel computing strategy with multi-block partitioning was employed to speed up the calculations and facilitate faster convergence alongside a local time step method. All numerical computation procedures were written in Python, revealing the following: (1) The PAFV turbulence model aptly simulates the transonic flow within the cascade channel. The shock wave pattern in the cascade channel aligns well with the experimental schlieren images. (2) During the Rotor 67 transonic compressor rotor calculation, the flow–pressure ratio, flow efficiency, and inlet and outlet total temperatures and pressures align well with the experimental data. Furthermore, the resolution of the flow field structure related to the interaction between the tip leakage vortex and channel shock wave is high. (3) The turbulence model uses PAFV as the turbulence velocity scale, thereby suppressing the fluctuation velocity and turbulence viscosity near shock wave areas, preventing excessive turbulence viscosity. Moreover, PAFV inherently exhibits transport properties and anisotropic characteristics, making it well-suited for handling transonic compressor flows.