Fulong Shi

Energy-harvesting performance and wake–foil interaction mechanisms of two tandem flapping foils operating within a moderately confined channel are investigated numerically. The numerical model solves the two-dimensional unsteady Reynolds-averaged Navier–Stokes equations on overset grids and is validated against published single-foil ground-effect and tandem-foil benchmark data. A wide parametric range is considered with the streamwise spacing (L* = 2.5–4.5), inter-foil phase difference (Φ = 0°–180°), and non-dimensional flapping frequency (f * = 0.10–0.30). Two favorable operating regimes with different dominant wake–foil interaction signatures are identified where the downstream foil achieves slightly better energy-harvesting performance compared to the upstream foil. In the compact-spacing regime (L* = 2.5, f * = 0.22–0.25, Φ = 0°), the upstream-shed vorticity is transported toward the suction surface of the downstream foil and overlaps with the locally generated leading-edge vorticity region. This interaction coincides with a mid-chord suction hump that contributes to the downstream-foil lift and efficiency. In the anti-phase large-spacing regime (L* = 4.5, Φ = 180°, f * = 0.2), the upstream-wake vortex passes along the vicinity of the downstream-foil surface and produces a localized pressure perturbation, amplifying lift with minimal pitching-power costs. Moreover, the peak cycle-averaged efficiency of both foils consistently exceeds 60% across all cases near the optimal frequency, markedly above the ceiling reported for unbounded configurations. The findings supply mechanistic guidance for the design of compact, near-wall tandem flapping-foil energy converters in rivers, tidal channels, and other confined hydrodynamic environments.

This paper numerically investigates the synchronous water entry of two-dimensional, variable-curvature twin wedges, representative of marine engineering catamaran structures. It aims to extend conventional flat-wedge studies to water entry behavior of complex curved geometries. A Cartesian grid multiphase flow framework is employed, integrating the radial basis function ghost cell method and the gradient augmented level set method for accurate treatment of moving boundaries and violent free-surface deformations. A systematic parametric study is conducted, encompassing five local curvature configurations (C1–C5), five inter-body spacings (G0 = 0.2–2.0), and two water entry velocities (2.77 and 13.85 m/s). Results reveal that geometric curvature is a dominant parameter influencing pressure distribution. For wedges with higher curvature (i.e., blunter configurations), the peak slamming pressure increases significantly due to stronger fluid accumulation and reduced flow separation. In contrast, wedges with sharper profiles tend to promote earlier flow separation, leading to lower, pressure peaks. Moreover, the spacing between the twin hulls modulates the hydrodynamic interaction. At small spacing, the interference between the two wedges leads to pronounced pressure amplification and increased load fluctuations, whereas larger spacing tends to decouple the flow fields, making the water entry process resemble that of single-wedge cases. The present model also captures transient phenomena such as spray jets, splash formation, and free-surface fragmentation. These conclusions provide a basis for the design and optimization of curved twin bodies, such as high-speed ship bows/bottoms and seaplane floats.

Oblique inflow fundamentally reorganizes the wakes of dense fish schools, generating deflected reverse Kármán jets and multiscale vortex-bridging interactions that govern the propulsion and energetics at the group level. Using a Graphics Processing Unit (GPU)-accelerated ghost-cell immersed boundary solver, we conducted two-dimensional simulations of dense bioinspired fish schools, systematically varying the Strouhal number (St), Reynolds number (Re), and lateral spacing (ds). Force decomposition in body-tangential and normal coordinates, together with wake-topology analysis, revealed a unifying mechanism: propulsion efficiency peaks when the convective transit time of the shed vortices matches the undulation period, resulting in constructive phase locking among neighbors. This condition emerges within a moderate St window and at transitional Re, where coherent reverse Kármán jets remain compact. At higher St, resonance amplifies force fluctuations and dissipates power, whereas at higher Re, additional small-scale content disrupts phase coherence, reducing school-level gains. Spacing governs the coupling strength: an intermediate, dense but non-contact arrangement (ds = 0.6L) yields the broadest efficiency maximum and increases the school-averaged efficiency by approximately 12%–15% relative to both tighter and wider spacings. Furthermore, the benefits of interaction converge as the wakes diffuse. Energetic advantages are spatially selective across the formation: individuals directly exposed to the inflow incur greater drag, whereas shielded interior or trailing positions benefit from phase locking. These results provide a macroscale framework linking inflow obliquity, wake coherence, and array geometry, thereby offering design guidance for bioinspired multivehicle formations that adapt spacing and phasing to maximize collective propulsion while minimizing energy loss.

The flow structures surrounding a school of fish in an oblique flow environment are subject to mutual interference, resulting in complex turbulent formations. This leads to a significantly uneven distribution of efficiency experienced by different parts of the school. To investigate the impact of complex turbulent formations in oblique flow environments on fish interactions and to explore the swimming efficiency of a school of biomimetic underwater robots, this study focuses on analyzing the effects of inter-fish spacing, swimming angle of attack, and Strouhal number on the swimming efficiency of the school. A self-developed Central Processing Unit/Graphics Processing Unit heterogeneous parallel accelerated Ghost Cell Method was employed to numerically simulate the swimming of four fish arranged in a diamond formation. The effects of the angle of attack, inter-fish spacing, Strouhal number, and other factors on the swimming efficiency and turbulent structure of a school of fish were analyzed. The study revealed that at a low angle of attack (10°), the school of fish exhibited a significant flow synergistic optimization effect, with the amplitudes of fluctuations in the normal force coefficient (CN) and the tangential force coefficient (CT) being significantly reduced. As the angle of attack increased to 20° and 30°, the flow separation effect intensified. However, the schooling fish effectively suppressed the main fluctuation components of the normal force and enhanced the modulating effect of high-frequency vortex shedding on the surface pressure through vortex-phase interference and vortex redistribution mechanisms. Inter-fish spacing significantly influenced the synergistic effect and propulsion efficiency of schooling fish. At a medium spacing (ds = 0.6L), the schooling fish exhibited an optimal synergistic effect, with the smallest amplitude of fluctuations in the tangential and normal force coefficients and the highest propulsion efficiency among all the spacings. This study not only revealed the synergistic mechanisms of multiple fish swimming in oblique flow but also provided a theoretical basis for the design and optimization of a biomimetic underwater robot swarm. By optimizing parameters such as the angle of attack, Strouhal number, and inter-fish spacing, the synergistic effect and propulsion efficiency of schooling fish can be significantly enhanced. Future research can further explore the swimming characteristics of fish schools under more parameter combinations and optimization strategies for practical application.

Understanding the water entry in waves is crucial for the structural safety and stability of vehicles. This study numerically investigates the dynamics of the high-speed water entry of a slender, truncated-cone-shaped projectile under varying wave conditions. The numerical model employs the Reynolds-averaged Navier–Stokes method with an overlapping grid. The focus is put on the influence of the wave phases, speeds, and entry angles on the motion trajectory and associated flow field evolution. Wave presence significantly affects cavity formation compared with static water, with pronounced asymmetry observed during vertical water entry at zero-crossing points, leading to asymmetric hydrodynamic forces and pitch deviations. Substantial transient radial forces are generated, raising concerns regarding the structural integrity under adverse sea conditions. At wave crests or troughs, increased wave forces result in higher peak drag forces, particularly during the crest entry. The entry angle significantly influences hydrodynamic performance. A larger entry angle generally increases the drag and alters the lift, thereby affecting the stability and trajectory of the projectile. As the entry angle increased, a greater asymmetry between the left and right cavities appeared, particularly at 25°, where the left cavity was smaller. Moreover, higher entry angles often resulted in increased surface splashing and spray generation. This can affect the aerodynamic characteristics of the projectile and lead to additional drag forces that should be considered in the design. The results can help understand the dynamic loads of vehicles under wave conditions, thereby enhancing their trajectory stability and optimizing the structural design.

This study presents a gate-assisted flapping-foil system to enhance energy-extraction performance. A two-dimensional (2D) numerical model is established to investigate the energy-extraction performance and efficiency-enhancing mechanism under different flapping frequencies and clearance spacings between the gate and the foil. The intention is to maximize the energy-extraction performance by determining the appropriate gate size and flapping frequency of the foil. The results show that the energy-extraction efficiency exhibits a single peak pattern with the flapping frequency, and there exists an optimal frequency corresponding to the maximum efficiency. The optimal frequency and maximum energy-extraction performance increased with narrowing of the clearance spacing. Compared to the wall-free case, a narrow clearance spacing significantly enhances the energy-extraction efficiency by 116.01%. The lift variation due to the confinement effect is the primary contributor. The two walls promote flow separation and the rolling-up of wall vortices by redirecting and accelerating the vortex flow, leading to the merging and pairing of the vortices. The pressure differences across the foil are amplified, especially when the foil strokes near the wall, which is beneficial for lift generation and energy harvesting. This study enhances the understanding of the energy-extraction mechanism and provides inspiration for innovative energy-harvesting systems.

The water-entry dynamics of catamarans are critical in marine engineering due to their complex hydrodynamic behavior and potential for severe slamming loads. This paper investigates the hydrodynamic mechanisms of two-dimensional asymmetric catamarans during both synchronous and asynchronous water-entry situations. The numerical model is based on an immersed boundary ghost cell method combined with the gradient augmented level-set approach. The aim is to analyze the effects of key parameters such as hull spacing, bottom deadrise angle, and drop height on the slamming loads and free-surface evolution. The interaction between the two hulls significantly impacts the pressure distribution. A maximum pressure difference of 7% is observed at certain spacings. When the spacing reaches s/h = 2, the pressure interaction between the hulls is minimal, indicating that the hulls operate almost independently. The pressure at the starboard demi-hull increases by 70% with rising drop heights during synchronous entry, exhibiting pronounced Wagner-type impacts. In asynchronous entry, a 20% pressure increase is observed at the starboard demi-hull with a height difference, showing distinct impact patterns. As the deadrise angle increases from 7° to 20°, the peak pressure at the starboard demi-hull during synchronous water entry decreases by 60%. Increasing the bottom deadrise angle reduces pressure peaks and alters the pressure curve patterns. This research provides valuable insights for optimizing catamaran design and enhancing its operational safety and efficiency.

The hydrodynamic performance and wake structures of three-dimensional (3D) fish are distinct from those of two-dimensional (2D) models. To reveal the hydrodynamic interaction and energy-saving mechanism of 3D fish school, this study numerically simulated swimming of two 3D parallel fish, using a robust ghost cell method. The hydrodynamic benefits and wake structures were examined under different transverse spacings, Strouhal numbers, and phase differences. The results showed that the swimming efficiency at a narrow spacing was enhanced by 33.8% compared with the single-fish case. It can be further enhanced by 15.4% in the anti-phase undulation compared to the in-phase state. The critical spacing where the apparent hydrodynamic benefit occurs is wider than that obtained in 2D simulations because the vortex row induced by transverse velocity can obliquely approach that generated by the adjacent fish. The thrust enhancement can be attributed to the channeling effect in the general synchronous and asynchronous undulations. This channeling effect occurs in the wake centerline instead of in the gap between the two fish bodies in the 2D simulations. The wake is redirected downstream in the streamwise direction owing to the transverse obstruction, which strengthens the thrust. Additionally, vertical expansion with vorticity dissipation can be induced, compromising the channeling effect. Both the channeling effect and vertical expansion are more significant at narrower spacings and higher Strouhal numbers. Notably, the wall effect contributes to the thrust enhancement in the antiphase undulation. Also, the disorderly small-scale vortex contrails appearing in other phase states are not observed, further improving thrust.

This study numerically simulated oblique flows around an undulating fish using a ghost cell method with general processing unit (GPU) acceleration to investigate the hydrodynamic mechanism of swimming fish at an angle to the flow direction. The hydrodynamic performance and wake patterns of swimming fish were assessed under different attack angles (α) and Reynolds numbers (Re) over a wide range of Strouhal numbers (St). The results indicate that a higher St for the nonzero α yields a larger lift-to-drag ratio and thrust, which benefits propulsion and maneuverability. As the α grows, the fish can obtain a higher thrust along the tangential direction with reduced energy consumption. Additionally, the force coefficients shift from the nearly periodic variation to the multiple-period oscillations due to the modulation of several harmonic components. Similarly, increasing Re also enhances the propulsive performance, although to a lesser extent than α and St. Correspondingly, the force pattern becomes increasingly unstable and irregular as the viscous force diminishes. A high St can amplify the effects of α and Re. Diverse wake modes are captured, depending on the α, St, and Re including the von Kármán (VK) vortex modes, the interaction of the leading-edge vortex and trailing-edge vortex, and the multiscale vortex pattern. Thrust is not necessarily induced by the reverse von Kármán (RVK) mode, and it can be generated in both the VK and RVK modes. Furthermore, a higher Re intensifies vortex interactions and wake deflection.