In this paper, the cavity dynamics of a grooved slender body during vertical water entry is numerically investigated. Six distinct configurations are established to evaluate the effects of groove quantity and position on cavity enhancement. By analyzing cavity morphology, cavity dimensions, pressure distribution, and the surrounding flow-field vortex structures, the results indicate that grooves near the head apex promote cavity generation via shear, while those near the cylindrical section suppress collapse. Increasing the contact angle significantly enlarges cavity sizes. For case 6 at t = 0.05 s, the cavity on the 160° surface measures 0.129 m in length and 0.056 m in width, which are significantly larger than those in other wettability cases. Differences in enhancement induced by groove structures are observed only on hydrophilic surfaces, with case 6 demonstrating the optimal performance within the parameters studied. This research elucidates the influence of surface structure on cavity formation during water entry, providing theoretical insights to enhance cavity generation during water entry.

In this paper, an efficient high-order gas-kinetic scheme for compressible flow simulation is presented. It combines the fifth-order targeted essentially non-oscillatory (TENO) reconstruction with a circular-function-based gas kinetic flux solver (C-GKFS), which enhances the resolution of flow field details while maintaining stability and high accuracy. To further improve the efficiency of time advancement, this work introduces two-derivative, multi-step or multi-stage time discretization schemes with strong stability preserving time coefficients. These schemes are combined with the Lax-Wendroff spatio-temporal coupling strategy, which effectively reduce the number of function evaluations, lowers the computational complexity, and improves the overall robustness. The numerical results of several typical examples verify the advantages of the proposed method in terms of resolution, stability and efficiency, especially in the simulations of the shock-bubble interaction and the inviscid 3D Taylor-Green vortex, which show good potential for applications in complex flows.

Droplets impact is widely present in numerous fields such as agriculture, aerospace, and chemical engineering. Time-varying wettability technology has been proven to be an effective means of droplet manipulation, and its application to heterogeneous surfaces is of significant interest. In this paper, we combine the temporal control of wettability with the spatial configuration of patterned surfaces to achieve semi-active regulation. Specifically, the impact of droplets on hydrophobic substrates decorated with a time-varying wettability stripe are investigated numerically and theoretically. A validated diffuse interface method is adopted for interface capture. The dynamic behaviours and rebound performance of droplets are studied on three typical forms of time-varying wettability surfaces. Special attention is paid to the aspects of controllable rebound, satellite droplets, and residual liquid. Subsequently, the effects of multiple parameters on droplet lateral motion are investigated systematically, including the contact angle, action time and offset distance of stripe, and the Weber number. The numerical results show that the normalized lateral velocity obeys some simple scaling laws. Moreover, the theoretical analysis of droplets impact is performed, and the similar relationship between the droplet motion and impact conditions is derived. Our research further enriches the theoretical framework of droplets impact, and may provide new insights into improving droplet manipulation from predictable to controllable rebound.

The influence of hydrodynamic interactions on the schooling behaviour of fish is still poorly understood. This paper numerically investigates the collective motion of two parallel fish that move freely in both the longitudinal and lateral directions, focusing on the effects of wavelength and phase difference on their stable formations, swimming speed and energy efficiency. It is found that two parallel fish can achieve stable formations in both longitudinal and lateral directions, only via the hydrodynamic interactions. Three distinct modes are classified based on the cycle-averaged longitudinal speed, i.e. the steady slow mode, the steady fast mode and the fluctuating fast mode; which mode occurs depends on the wavelength and phase difference. Compared to a single fish, two fish in the steady slow mode swim slower, whereas they swim faster in both the steady fast and fluctuating fast modes, with a maximum speed increase of 12 % observed in the latter mode. Moreover, the fish school exhibits higher propulsive efficiency than a single fish in most cases. Furthermore, the power consumption and propulsive efficiency of each fish in different modes are discussed in detail. Finally, the mechanism behind the stable formations has been analysed. These results may shed some light on understanding the underlying mechanisms of fish schooling behaviour.

Droplet impact on solid surfaces is ubiquitous in agricultural, energy, and chemical engineering applications. Electrowetting-on-dielectric (EWOD) has been demonstrated to be an effective method for droplet manipulation, and its integration with spatial heterogeneity represents a promising direction. In this work, a locally addressable EWOD strategy is proposed by embedding multiple parallel electrodes within a hydrophobic substrate, where only the voltage-applied electrode region undergoes wettability switching. A validated diffuse interface method is adopted for interface capture. The effects of the activated electrode position, the Weber number, and the amplitude and duration of the applied voltage on droplet lateral motion are examined systematically. The numerical results reveal several scaling laws for the normalized lateral velocity. Moreover, the theoretical analysis based on unbalanced surface tension forces and momentum accumulation is conducted. A unified relationship between the droplet deflection and compound parameter ω (We−1S*U*Δt*) is obtained, which is well validated by all simulation data. This work establishes a prediction framework for controlled droplet rebound and offers a robust pathway toward active and precise droplet manipulation.

A numerical study was conducted on the flow induced vibration of an eight-spined cactus-shaped cylinder under subcritical Reynolds numbers. The influence of porous spines with different Darcy numbers $(D_a=10^{–4} to 10^{–2})$ and different arrangements (W1, W2, L1, L2) on the vibration control performance of the cactus cylinder was investigated. The results indicate that the arrangement significantly impacts the control effectiveness. The cactus cylinder configuration W1, featuring five porous spines arranged on the windward side and a Darcy number of $10^{–2}$, effectively suppressed VIV, achieving reductions of 73.1% in amplitude, 31.3% in mean drag, and 84.8% in root mean square lift. However, improper arrangements, such as the L1 configura tion with five porous spines arranged on the leeward side, induced galloping in the cylinder structure, leading to further divergence and amplification of the vibration amplitude.

After droplet impact, asymmetric retraction is beneficial for reducing contact time. This work conducts numerical simulations to investigate the morphological evolution and contact time of droplets on a single-triangular-ridge superhydrophobic surface following off-centered impact. Based on the observed morphological evolution, droplet behaviors are categorized into five types according to the off-centered distance. A theoretical classification model is proposed to predict the ranges of off-centered distances for different types. The effects of the Weber number and off-centered distance on the contact time, along with the underlying reasons, are explored. The resultant spreading, contraction, and splitting processes are analyzed, and the potential mechanisms for contact time reduction are elucidated by quantifying droplet shape and characteristic time. A theoretical model for predicting the contact time of a subdroplet under splitting conditions is explained. Off-centered-induced asymmetry and ridge compression significantly alter the droplet velocity distribution. At small off-centered distances, ridge compression directs a larger portion of the droplet to spread along it, greatly affecting the spreading duration. Contact time is primarily determined by retraction time. These findings are expected to clarify the basics of asymmetric bouncing on a ridge and provide useful guidance for self-cleaning and anti-icing strategies.

This paper presents an enthalpy-based lattice Boltzmann flux solver for simulating droplet freezing in a uniform electric field. The solver is validated against the three-phase Stefan problem, droplet freezing on a cold surface, and droplet deformation in a uniform electric field, demonstrating its accuracy and robustness for electrofreezing applications. It is then employed to investigate the effects of the conductivity and permittivity ratios (Cr and Pr) on droplet freezing dynamics. The results show that Cr and Pr markedly modify the distribution interfacial free charges, thereby reshaping the droplet, altering the contact-line length, and regulating heat transfer. Although Cr and Pr are varied independently, their influence fundamentally arises from their combined effect on the charge relaxation time ratio tau(rel)= Pr/Cr. A transition in freezing behavior occurs when the charge relaxation times of the droplet and the surrounding medium become comparable (tau(rel) =1), which corresponds Cr = Pr = 2 for the material parameters used in this study. For tau(rel)< 1, positive-charge accumulation compresses the droplet, enlarges the contact line, enhances heat flux into the cold substrate, and shortens the freezing time. In contrast, for tau(rel) > 1, negative charges dominate, stretching the droplet, reducing the contact line, weakening heat transfer, and prolonging the freezing process. These findings indicate that the electrical properties regulate freezing primarily through charge-relaxation-controlled interfacial electrohydrodynamics, with the freezing time governed by the resulting changes in droplet morphology rather than by modifications to the underlying freezing mechanism.

High-order gas-kinetic schemes with targeted essentially non-oscillatory (TENO) spatial reconstruction have demonstrated their accuracy, efficiency, and robustness through numerous numerical studies. However, when very high-order spatial reconstructions are coupled with low-order Runge-Kutta time discretization, overall order degradation and efficiency losses often occur. In this paper, we propose an arbitrary high-order numerical framework for compressible flows with space-time consistent accuracy. Within the finite-volume semi-discrete formulation, the method couples TENO reconstruction with deferred correction (DeC) time discretization of matching order, enabling the high-order spatial accuracy to be fully realized throughout the temporal evolution and eliminating the accuracy deterioration associated with lower-order time discretization. Systematic numerical experiments are conducted by combining TENO reconstructions up to seventh order with both DeC and Runge-Kutta time discretization. The results demonstrate that the proposed high-order space-time consistent framework achieves higher accuracy and superior robustness in simulating complex compressible flows, including shock capturing, multi-component interactions, and viscous structures.

Droplet impact is ubiquitous in industry, agriculture, and daily life. Flexible surfaces have recently attracted increasing attention, yet how fluid-structure interaction affects the dependence of contact time on substrate stiffness remains unclear. In this paper, the impact of a droplet on a flexible rectangular substrate with fixed edges is investigated numerically and theoretically using the volume of fluid (VOF) method and linear elasticity theory. The main focus is on the droplet morphology, contact time, impact force, and energy conversion. The three-dimensional (3D) simulation results reveal a “double-dip” phenomenon of the substrate, which is characterized by two successive downward deflections at moderate stiffness. This behaviour is caused by a downward jet that emerges from momentum redistribution during the late retraction stage. Interestingly, the contact time first decreases and then increases with decreasing bending stiffness, and the minimum contact time also occurs at moderate stiffness. A theoretical analysis of energy transfer shows a pathway from kinetic energy to surface energy and then to elastic potential energy. It further demonstrates that the efficient storage and rapid release of elastic potential energy at moderate stiffness facilitate the reduction of contact time. These findings clarify the mechanism underlying contact-time minimization on the fully clamped flexible plate and provide mechanistic insight into droplet rebound on flexible surfaces.

An enthalpy-based unified lattice Boltzmann flux solver (EULBFS) is proposed in this paper for simulating liquid solidification, incorporating the effects of volume expansion and shrinkage caused by density differences between liquid and solid phases. The proposed solver first establishes the relationships between the macroscopic governing equations and mesoscopic formal equations that describe the temperature, flow, and phase fields. The macroscopic governing equations are then discretized by the finite volume method (FVM), with the corresponding fluxes calculated based on the established relationships. In this way, it enables a unified and coherent solution framework for all fields. In contrast to the conventional lattice Boltzmann methods, the present approach handles additional terms directly via finite volume discretization, offering a more straightforward and flexible formulation. Furthermore, the use of the total enthalpy equation to couple the temperature field with the phase fraction allows for efficient modeling of phase change processes, significantly reducing the computational complexity associated with interface tracking. The accuracy and robustness of the proposed solver are demonstrated by a series of benchmark tests, including the conductive freezing problem, the three-phase Stefan problem, the freezing of a liquid film in a two-dimensional container, the solidification of a static droplet on a cold surface, and the freezing of a droplet upon impact with a cold surface.

The impact of ferrofluid droplets on hydrophobic cylindrical surfaces under magnetic fields has attracted increasing attention due to its potential applications in water repellence, anti-icing, and drag reduction. In this work, the anisotropic spreading dynamics of a ferrofluid droplet impacting an asymmetric geometric structure are systematically investigated through combined experimental, numerical, and theoretical analyses. The results show that the spreading behaviour of the ferrofluid droplet is primarily governed by the magnetic field strength, impact Weber number, and surface curvature ratio. As magnetic flux density increases, the axial spreading diameter decreases, while the time required to reach the maximum spreading grows correspondingly. A theoretical model is further developed to predict the maximum spreading diameter of ferrofluid droplets under the influence of magnetic fields, showing good agreement with experimental results.

The present study examines the impact behavior of air-in-liquid compound droplets on curved surfaces using a numerical approach. By integrating the lattice Boltzmann method (LBM) for multiphase flow modeling and the immersed boundary method (IBM) for fluid-substrate interactions, we systematically investigate the influence of surface diameter and inner bubble size on the dynamics of droplet impact. Key parameters analyzed include liquid film thickness, bubble deformation, splash morphology, rupture mechanisms, impact force and pressure. Our findings reveal several significant conclusions: (1) Surface diameter and inner bubble size exhibit opposing effects on splash length and cavity formation. (2) The splashing angle at rupture is correlated with single-phase droplet behavior and surface diameter, showing minimal dependence on bubble size. (3) Three distinct rupture mechanisms emerge during the spreading phase, influenced by interactions between surface diameter and inner bubble size, with potential hybrid manifestations observed. (4) The maximum impact force is primarily determined by inner bubble size, with smaller bubbles demonstrating enhanced impact buffering capabilities. (5) The developed models for maximum impact force and pressure show excellent agreement with numerical simulations. These findings provide valuable insights into the control of droplet dynamics, offering practical applications in fields ranging from spray coating to biomedical engineering.

In this study, an enthalpy-based lattice Boltzmann flux solver is developed to simulate the freezing dynamics of a ferrofluid droplet under a uniform magnetic field. The accuracy and robustness of the solver are first validated through three benchmark tests: conductive freezing, static droplet freezing, and ferrofluid droplet deformation. The solver is then employed to investigate the influence of a uniform magnetic field on the freezing behavior of ferrofluid droplets, focusing on the overall freezing process, heat transfer characteristics, and freezing duration. The results reveal that the uniform magnetic field affects the freezing dynamics primarily by altering the droplet morphology. Under a vertically oriented magnetic field, the droplet elongates along the field direction, which increases the thermal resistance and consequently prolongs the freezing time. Conversely, a horizontally uniform magnetic field flattens the droplet, reducing the thermal resistance and thus shortening the freezing time. These findings provide new physical insight into magnetic-field-induced modulation of the freezing process in ferrofluid systems.

In this paper, a unified magnetic multiphase lattice Boltzmann flux solver (UMMLBFS) is developed for simulating ferrofluid multiphase flows. The method begins by establishing consistent relationships between the macroscopic governing equations and the corresponding mesoscopic equations for the flow field, the phase field, and the magnetic field. The fluxes in the macroscopic governing equations are then derived from the mesoscopic distribution functions. These macroscopic governing equations are discretized using the finite volume method, with the fluxes at the cell interface computed based on the established mesoscopic-macroscopic relationships. In this way, it enables a unified and coherent solution strategy for coupling the flow field, the phase field, and the magnetic field. To evaluate the stability and accuracy of the proposed solver, five test examples, including a static cylinder in a magnetic field, the deformation of a ferrofluid droplet, the merging of two bubbles in a ferrofluid under a magnetic field, the Rosensweig instability of ferrofluid on a smooth surface, and the spreading of a ferrofluid droplet on a flat surface under a magnetic field, are simulated. The results indicate that the UMMLBFS achieves enhanced stability and accuracy in simulating ferrofluid multiphase flows compared to the non-unified method. Additionally, it performs robustly across a wide range of density ratios (1.975-850.7) and viscosity ratios (20-279.3), with excellent mass conservation properties.

The fluid mechanism underlying the remarkable swimming capabilities of fish remains incompletely understood. In this paper, fish swimming is simplified as the two-degree-of-freedom self-propulsion of an undulating swimmer, and the combined effects of frequency and wavelength on its performance are numerically studied. It is found that the optimal wavelength is approximately lambda = 1.25, at which the maximum cruising speed is achieved. Moreover, some simple scaling laws with respect to frequency and wavelength are established to predict the propulsive performance of the undulating swimmer. On the other hand, the hydrodynamic mechanism underlying thrust generation of the undulating swimmer is analyzed in detail. It is shown that the net thrust is primarily generated by its posterior body, and its head contributes positively only when the wavelength is large enough. The findings may contribute to a deeper understanding of fish swimming and the optimization of bio-inspired underwater robots.

The tandem dual-wings/fins of natural flyers/swimmers exhibit superior propulsive performance. However, the fluid mechanism behind it remains uncertain. In this paper, the self-propulsion of compact tandem flapping foils with a fixed gap is numerically studied. It is found that as compared with a single foil, the compact tandem-foil system has significant speed enhancement and efficiency augmentation. When the phase difference and gap distance are appropriate, the maximum increase in speed can reach up to 54 %, and increase in efficiency can reach up to 72 %. Subsequently, some simple scaling laws are proposed for the propulsive speed and power consumption of the compact tandem-foil system. Furthermore, the fluid-structure interactions between the two foils are analyzed, and it is found that the speed enhancement primarily results from the thrust increase of the hind foil. The results obtained here may shed some light on understanding the propulsion mechanisms of the dual-wings/fins of natural flyers/swimmers.

The self-propulsion of tandem flapping foils, which can self-propel identically and maintain a fixed gap distance, is numerically studied in this paper. It is found that there is a sudden alteration in the self-propulsion of tandem flapping foils, in which the speed of the tandem-foil system dramatically changes from the highest to the lowest. Moreover, the emergence of the sudden alteration is determined by the gap distance and phase difference between tandem foils. This can be described as the equivalent distance G. The critical points at which the sudden alteration occurs are located at G = (2N − 1)/2, where N = 1, 2, 3…. In the interval between two adjacent critical points, the propulsive speed, power consumption, and propulsive efficiency of the tandem-foil system increase monotonically with the rise of G. Additionally, compared with the isolated flapping foil, the tandem-foil system shows performance enhancement at every interval where G = 0.5. Furthermore, the mechanism behind the sudden alteration is analyzed, and it is found that this sudden alteration is associated with the potential landscape. Finally, the hydrodynamics of each foil are discussed in detail. The results obtained here may shed some light on understanding the performance of dual-flipper/wings in nature.

This study employs a combined k–ε turbulence model, integrating the Launder–Sharma with porous production terms and renormalization group model to simulate vortex-induced vibration (VIV) control of a square cylinder with porous splitter plates. The numerical framework addresses two-dimensional incompressible turbulent flow over a square cylinder system with three Darcy numbers (Da = 10−2, 10−3, and 10−4) and a solid splitter plate. Key parameters, including vibration amplitude, mean drag coefficient, and root mean square lift coefficient, are analyzed across reduced velocities (Ur) and Reynolds number. Vorticity and pressure fields at Ur = 8 are examined to elucidate suppression mechanisms. The calculation results show that all porous plates suppress VIV effectively at low Ur (<8), with Da = 10−4 configuration achieving a 43% amplitude reduction. At a higher Ur (>10), control efficacy diminishes for Da = 10−2 and 10−3, while Da = 10−4 retains partial suppression capability. Vorticity and pressure field analyses at Ur = 8 demonstrate that the Da = 10−4 plate balances upper and lower vortex shedding, minimizing lift fluctuations.

A high-order TENO scheme for compressible multi-phase flows is developed within the lattice Boltzmann flux solver (LBFS) framework, incorporating level-set based interface-tracking methods. The proposed method leverages the advantages of both TENO and LBFS, resulting in improved overall performance. Specifically, the high-order TENO scheme enhances robustness, minimizes numerical dissipation, and excels in capturing sharp discontinuities. In parallel, the LBFS maintains low dissipation and accounts for real physical effects in the lattice Boltzmann method, ensuring the preservation of positive density and pressure even in the presence of strong shocks and discontinuities. To evaluate the capability of the current method in handling multiphase flow problems, several benchmark tests are simulated. The simulation of air-helium shock tube problem demonstrates that the TENO-LBFS method yields results closer to the exact solution compared to other approximate Riemann solvers, attributed to the excellent dissipation adjustment capability of the LBFS. The remaining three test cases further evaluate the accuracy and robustness of the proposed methodology, encompassing multi-phase flows that account for viscosity, surface tension, and shock effects.