In this paper, the effect of spatial configurations and quantities of fish school on the hydrodynamic characteristics of fish is numerically investigated by smoothed particle hydrodynamics, revealing the hydrodynamic mechanism of the fish school in terms of shedding vortices and channel effects. In this study, the spatial configuration of fish school includes three types, namely, side-by-side, triangle, and staggered; the number of fish varies from one to six. The pressure, velocity, and vortex contours are discussed to investigate the hydrodynamic parameters of fish school. The results show that the shedding vortex has a greater effect on the hydrodynamic characteristics of fish school than the channel effect; as the longitudinal distance increases, the channel effect rapidly declines while the shedding vortex still generates an effect on the hydrodynamic characteristics of fish school at a relatively big longitudinal distance; the inverted triangular configuration has a stronger channel effect than the positive triangle configuration; the number of fish has a greater impact on the hydrodynamic characteristics of fish located at the back of the fish school than on the hydrodynamic characteristics of fish located at the front of the fish school.

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.

Aircraft propellers produce relatively large in-plane loads, called propeller 1P loads, during maneuvers such as turning, diving, and lifting, and these loads can negatively affect the flight and control of the aircraft. In order to study the change rule of 1P aerodynamic loads, in this paper, a mathematical model of the propeller 1P aerodynamic loads has been developed based on the blade element momentum theory. This mathematical model was then corrected using the Pitt–Peters incoming flow correction method, the Prandtl tip correction method, and the propeller root flow correction method. Based on this mathematical model, a calculation procedure for the propeller 1P aerodynamic loads was developed using MATLAB software, and the accuracy of the procedure was verified by comparing the results with CFD simulation results. Numerical simulations show that the results calculated based on the proposed mathematical model for the coefficients of thrust, power, bending moment, and the tangential force of the propeller have an error of less than ±6.00% compared to the CFD simulation results. For a small inflow angle, the coefficients of bending moment and tangential force of the whole propeller fluctuate in a small range. But, as the inflow angle increases, the fluctuation range of the aerodynamic characteristic parameters of the propeller increases and the fluctuation becomes more complicated. Through numerical calculations, it has been shown that the mathematical model presented herein is reliable and accurate. In addition, it greatly shortens the calculation time and improves the calculation efficiency. It is expected that the proposed model can provide a certain help for the strength design of the propeller structure and the study of the aerodynamic performance of the whole aircraft.

To further develop a more effective turbulence model and to improve the calculation accuracy of the flow around airfoil, a new PAFV turbulence model has here been constructed by using a deformation rate tensor and the grouping of an average fluctuation velocity. To evaluate the applicability of the PAFV turbulence model, the numerical calculations of flow around the airfoil have here been implemented, which was based on the OpenFOAM calculation platform. On the basis of grid independence research, the model was used to calculate the low-speed flow-around problem for the plano-convex airfoil NACA4412 and the symmetric airfoil NACA0012. It was also compared with the S-A (Spalart-Allmaras) and SST (Shear Stress Transport) k-ω turbulence models. Firstly, the maximum lift angle-of-attack case of the NACA4412 airfoil was calculated. Thereafter, numerical calculations were performed for the flow around the airfoil in the multi-angle-of-attack case of the NACA0012 airfoil. The results showed that the NACA4412 airfoil had an obviously separated vortex at the trailing edge of the airfoil at the maximum lift angle of attack. Also, there was a certain velocity loss downstream of the trailing edge, which was calculated by all three models. However, the results of the PAFV turbulence model were found to be better than those of the S-A and SST turbulence models. The three turbulence models showed comparable accuracies for the calculations of the surface pressure coefficients of the NACA0012 airfoil. However, the S-A and SST k-ω turbulence models were slightly better for the calculations of the mean velocity profiles of the NACA0012 airfoil. Also, the PAFV turbulence model was more accurate for the calculations of the lift and drag coefficients. In conclusion, the PAFV model can make effective predictions of the airfoil low-speed flow around the problem at hand, which in turn preliminarily verifies the applicability of this turbulence model for the low-speed flow around the airfoil problems.

Sideslip maneuverability is a critical future requirement for hypersonic airbreathing vehicles. One of the main challenges is maintaining inlet performance under not only non-uniform inflow (NUF) but also varying inflow angles. This study systematically investigates the aerodynamic performance, sensitivity, and underlying flow mechanisms of four vector adaptive inward-turning inlets (VAIs) under angle of sideslip (AOS) conditions. In contrast to classical design methods, this study utilizes an originally developed methodology that integrates osculating flow theory and multi-objective optimization. A key advantage of this approach is its ability to design inlets for arbitrary NUFs. In this work, this method is applied to generate configurations for several representative NUFs. A high level of flow properties is achieved for all VAIs within AOS −3° to 3° (σex ≥ 0.534, φ ≥ 97.6%, and ηKE ≥ 0.966). A lateral flow mechanism is identified: as AOS increases, the lateral velocity component intensifies, leading to a significantly asymmetric flow structure. This evolution results in increased distortion and a gradual migration of low-kinetic flow in both circumferential and spatial directions, thereby reducing flow capture and energy conversion efficiency, while enhancing compressive capability. The findings provide critical insight into the lateral adaptability of such inlets, which is essential for designing maneuverable hypersonic vehicles.