Free Surface Research Articles

Sloshing in a tank with elastic side walls and a membrane cover

The coupled problem of liquid sloshing in a tank with a membrane cover and elastic side walls is investigated. The velocity potential theory is used for the flow and the linear elastic theory for the cover and side walls. For the former, the vertical mode expansion is used, in which all the roots of the dispersion relationship are first found. The expansion automatically satisfies the governing equation, the tank bottom, and the tank cover conditions. The deflections of the side walls are expanded into a cosine series together with a four term polynomial, which is vital for the procedure to succeed. These expansions are then matched through the dynamic and kinematic equations of the plates, and the problem is completed by imposing the edge conditions of the plate and membrane. Through the combined matrix equation, the natural frequencies of the system are obtained. In addition, the nature of the dispersion relationship of the membrane is analyzed. Explicit solutions are obtained for some special cases, and the link with the free surface sloshing is established. Extensive numerical results are provided, and their physics is analyzed.

CFD simulations of the transition between non-aerated and aerated conditions in uncovered unbaffled stirred tanks

The transition between non-aerated and aerated regimes in uncovered unbaffled stirred tanks (UUSTs) was investigated using computational fluid dynamics (CFD). The Volume of Fluid (VOF) method was employed to model the free surface dynamics under various operational conditions. The simulations were able to predict the peculiar experimentally observed behavior of UUSTs and revealed that at velocities below a critical threshold (N_<_Ncrit), the system remains non-aerated, while exceeding this threshold (N_≥_Ncrit) induces bubble ingestion, leading to significant changes in power consumption and flow patterns. The CFD simulations accurately predicted the behaviour of the Power Number (Np) as well as the vortex shape inside the tank both in subcritical and supercritical regimes and showed good agreement with original experimental data and correlations from the literature. Additionally, the modeling of the aerated regime successfully predicted the vortex shape, the bubble dispersion within the tank, and the cavities formed behind the blades.

Experimental model of crushing coriander seeds

Seed crushing is one of the main technological operations [1] in the process of obtaining essential and fatty oils, on which their yield and quality depend [2]. Improving the process of preparation for the extraction of coriander seeds by selective cryodesintegration and creating technological lines of various productivity is of significant importance and relevance. However, modern methods and means of cryodesintegration of coriander seeds require research and improvement. The process of seed grinding is divided into three phases [3]: elastic deformation, which occurs from the beginning of the action of the applied force on the material being ground until the elastic limit is reached and is accompanied by compaction and compression of the structural aggregates of the seeds; plastic deformation, which occurs from the moment of the beginning of the shift of individual elements of the material relative to each other and is characterized by the relative displacement of the structural aggregates of the seed kernel, as a result of which the material is compacted and flattened; destruction of the material with the formation of a free surface of particles. The main parameter of the process of cryodesintegration of coriander seeds is subject to theoretical justification - normal pressure, leading to deformation, where the pressure on the seeds exceeds their tensile strength, but there is no appearance of oil on the surface of the opened seeds. This prevents oil loss and contamination of the working parts, especially with essential oils. Monitoring theoretical studies of the grinding process allows us to talk about the need to develop a mathematical description of this process.

Dynamics of a droplet on the surfactant-infested free surface of another liquid

The dynamics of liquid droplets surfing over the surfactant-infested free surface of another liquid have been explored experimentally. We analyze the motion of oil droplets that has been initiated through the creation of a surface tension gradient resulting from the deposition of a drop of surfactant at the water surface contained in the petri dish. The experiments reveal that the location of surfactant deposition with respect to the droplet position influences its motion. Due to the presence of a surface tension gradient, the footprint area of the droplet reduces and its shape changes. We have studied the temporal variation in the velocity (|vx|) of the droplets in relation to their proximity to a wall. Based on the evolution of droplet shape and change in droplet velocity, the drop dynamics can be experimentally divided into four distinct zones. Results indicate that in zone-1, |vx| grows with t as |vx|≈tn, where n is between 0.8 and 1.0. The scaling argument shows that in this zone, the surface tension force dominates the drag force, and thereby, |vx| of the droplets increases linearly with t expressed as |vx|∝t. The experimental investigation and the scaling law exhibit a reasonable agreement. In zone-2, |vx| remains more or less constant, as it is postulated that the surface tension force balances the drag force. In zone-3, a decrease in surface tension force results in a deceleration of the droplets. In zone-4, the deceleration becomes more prominent as the droplet approaches the petri dish wall.

Experimental and numerical analysis of the fluid flow behavior of a tank corner impacting a water surface

The interaction of a tank impacting a water surface is an extremely complex nonlinear multiphase flow phenomenon. In this study, experiments and numerical simulations are used to systematically investigate the flow physics and load characteristics of a tank corner impacting a water surface. Free surface flow at different fall heights (200–800 mm) and inclination angles (0°–15°) was obtained through free fall experiments. The volume of fluids method and overset grid technology were used to simulate the water impact process of a three-dimensional structure accurately. For typical bubble flows, the numerical and experimental results agree well. On the basis of the three-dimensional flow characteristics and pressure distribution, flow behaviors, such as fluid climbing, corrugation disturbances, and air cavity effects, are analyzed. Bubble flow has a significant effect on the behavior mode of the impact load. In particular, the bubbles at the upper wall play a key role in the load characteristics at different locations. In addition, the influences of corrugations inside the tank's corner and the impact velocity on fluid flow were investigated. These results provide beneficial references for an in-depth understanding of the fluid flow and load characteristics between a tank and fluid.

Determination of Submerged Breakwater Efficiency Using Computational Fluid Dynamics

Wind-induced waves can lead to the partial or complete wash-over of beaches, causing erosion that impacts both the landscape and tourist infrastructure. In some regions of the world, e.g., Croatia, this process, which usually occurs during a harsh winter, has a major impact on the environment and the economy, and preventing or reducing this process is highly desirable. One of the simplest methods to reduce or prevent beach erosion is the use of innovative underwater structures designed to decrease wave energy by reducing wave height. In this study, submerged breakwaters are numerically investigated using various topologies, positions, and angles relative to the free surface. Not only is the optimal topology determined, but the most efficient arrangement of multiple breakwaters is also determined. The advantage of newly developed submerged breakwaters over traditional ones (rock-fixed piers) is that they do not require complex construction, massive foundations, or high investment costs. Instead, they comprise simple floating bodies connected to the seabed by mooring lines. This design makes them not only cheap, adaptable, and easy to install but also environmentally friendly, as they have little impact on the seabed and the environment. To evaluate wave damping effectiveness, the incompressible computational fluid dynamics (ICFD) method is used, which enables the use of a turbulence model and the possibility of accurate wave modelling.

Hybrid numerical 3D model of electromagnetic levitation of molten metal

This paper introduces a new and efficient methodology for the numerical modeling of electromagnetic levitation. The model requires transferring the time-varying geometry of the molten metal from the hydrodynamic submodel to the electromagnetic submodel. The developed methodology combines a geometry transfer of the conductivity distribution of the metal/air system, and the accompanying conditional reconstruction of the electromagnetic submodel. The proposed solution strategy enables a computationally efficient simulation of the coupled process accounting for any evolution of the molten metal geometry. The developed methodology can be generalized to any magnetohydrodynamic process with the presence of a free surface of liquid metal. The method was applied to the 3D modeling of a classic example of low-scale levitation melting of aluminum.

Slot coating of time-dependent structured materials: Effects of thixotropy on the flow dynamics and operating limits

Some of the most common liquid-like formulations rooted in the coating industry consist of rheologically complex structured materials such as inks, paints, and slurries. Yet, the impact of time-dependent structuring effects due to thixotropy on thin film coating applications remains elusive and still unclear. Here, we present a computational study of the effects of thixotropy on slot coating of time-dependent structured materials. By coupling a recent fluidity-based constitutive model for thixotropic materials with a well-established finite element/elliptic mesh generation method for free surface flows, we assess the role of thixotropy by comparing the predictions from the thixotropic model with those from a simple Generalized Newtonian Fluid model that uses the same flow curve for the material steady-state equilibrium viscosity. We find that thixotropy can indeed have a major impact on slot coating applications, potentially bringing strong implications not only to the flow dynamics but also to the operating limits of the process. In conclusion, the results and discussions we present in this study underscore the importance of accounting for thixotropy to genuinely model and fundamentally understand the behavior of time-dependent structured materials with complex rheology in processing flows like those ubiquitous across the broad fields of coating science and engineering.

Experimental and numerical investigation on rock fracturing and fragmentation under coupled static pressure and blasting

The blasting technique is widely adopted to break rock in civil and mining engineering, and its operation is generally subjected to static pressure due to tectonic and gravitational stresses. In the present study, the rock fracturing and fragmentation under coupled static pressure (uniaxial pressure and confining pressure) and blasting are experimentally and numerically investigated. First, 11 blast tests with 100-mm cubic red sandstone samples are carried out based on a biaxial loading system. Then, the blast-produced rock fragmentation in blast testing is numerically modeled using finite element method with LS-DYNA, and the explosion pressure attenuation and fracture evolution in rock samples are numerically reproduced. The simulated rock fragmentation data are obtained by image processing in ImageJ, and the fragment size distribution of red sandstone under combined static stress and blasting is characterized using Weibull distribution. Accordingly, the effects of uniaxial pressure and confining pressure on blast-created rock fragmentation are quantitatively compared and analyzed, and the corresponding mechanisms are discussed and revealed. The current findings indicate that the static pressure plays a role in increasing blast-induced compressive stress and reducing tensile stress in both radial and hoop directions and thus results in a decrease in the length and number of fractures propagating vertically to the direction of applied pressure, further leading to the creation of coarser fragmentation. Blasting under confining pressure produces larger fragments than that under uniaxial pressure. The average fragment size increases quickly at first and then increases slowly with the increase of static stress, which can be well characterized using a logarithm equation. Based on current findings, increasing the free surface is crucial in practical blasting to improve rock fragmentation performance under blasting.

Crown control in a pair of cavitation bubbles close to a free surface: A numerical study

When a cavitation bubble re-expands near the surface of a liquid, an axisymmetric crown forms around the jet that is initially produced. Controlling this crown is essential if the first jet is to be used in engineering applications such as laser-induced transfer (LIT). Herein, we introduce a second cavitation bubble to control the formation and growth of the crown. Numerical simulations were performed using the compressibleInterIsoFoam solver within the open-source platform OpenFOAM, incorporating a geometric volume-of-fluid approach for tracking interfaces. Detailed analysis showed that a reversal in curvature across the concave interface indicates the moment of crown formation, and this is induced by flow focusing during bubble contraction or momentum transfer from a second expansion. In the presence of the second bubble, the crown type can be classified as either enhanced or inhibited in comparison with a single-bubble scenario. The velocity of crown formation, vcf, is defined to describe the crown type, and a parametric study of crown types was conducted based on the dimensionless stand-off distances, γ1 and γ2. The findings of this study offer new insights into the field of LIT.

Downstream Control on the Stability of River Bifurcations

AbstractRiver bifurcations are prevalent features in both gravel‐bed and sand‐bed fluvial systems, including braiding networks, anabranches and deltas. Therefore, gaining insight into their morphological evolution is important to understand the impact they have on the adjoining environment. While previous investigations have primarily focused on the influence on bifurcation morphodynamics by upstream channels, recent research has highlighted the importance of downstream controls. In particular, in the case of rivers, current linear stability analyses for a simple bifurcation are unable to capture the stabilizing effect of branches length unless a confluence is added downstream. In this work, we introduce a novel theoretical model that effectively accounts for the effects of downstream branch length in a single bifurcation. To substantiate our findings, a series of fully 2D numerical simulations are carried out to test different branches lengths. Results from linear stability analysis show that bifurcation stability increases as the branches length decreases. These results are confirmed by the numerical simulations, which also show that, as the branch length tends to vanish, bifurcations are invariably stable. Finally, our results interestingly reveal that when a source of asymmetry, such as a free surface gradient or channel area advantage, is present at the node, there are scenarios in which the less‐favored branch becomes dominant over the hydraulically favored branch.

Floating particles transport through the free surface vortex technique: A novel numerical study to assess the interaction among different scales of vortex structures

Fat, oil, and grease (FOG) floating particles in the sump of sewage pumping stations will accumulate together to form rigid layers, resulting in failure for pump device. To overcome this, the free surface vortex (FSV) technique has been considered and applied to transport floating particles toward the submerged suction pump inlet. This paper investigates the potential of vortices as a means of downward motion of FOG. The entrainment capacity of FSV is investigated by numerical simulations using a coupled level-set and volume-of-fluid method. Two coherent structures are decomposed by proper orthogonal decomposition: FSV represented by the first two orders with high energy content and spiral vortex bands represented by low energy and high order models. The extracted ridges of the finite-time Lyapunov exponent (FTLE) delineate different regions of the flow field and effectively capture the evolution of Lagrangian coherent structures. The floating particles in the sump are first caught by the dividing line formed by the FTLE ridges, mixed in the entrainment zone, and then merged into the vortex. The enstrophy production term dominates the development of vorticity. Subject to the influence of flow velocity gradients, both radial and tangential vortices undergo a transition into axial vortices. This transformation enhances the vortex's capacity to entrain particles within the vortex core area, leading to their rapid inward spiraling toward the vortex center and eventual expulsion due to the vortex's entrainment effect.

Stratified equatorial flows in cylindrical coordinates with surface tension

This paper considers a mathematical model of steady flows of an inviscid and incompressible fluid moving in the azimuthal direction. The water density varies with depth and the waves are propagating under the force of gravity, over a flat bed and with a free surface, on which acts a force of surface tension. Our solution pertains to large scale equatorial dynamics of a fluid with free surface expressed in cylindrical coordinates. We also prove a regularity result for the free surface.

Bluestein–Gulyaev(B-G) waves in a piezo-thermoelastic half-space in the context of modified multi-phase-lag theory

In the years 1968–69, Bluestein and Gulyaev discovered a new kind of surface wave in a piezoelectric material known as B-G wave after their name. Although it was discovered in few decades ago, but till now, no work has been done related to B-G wave propagation based on modified multi-phase-lag theory. In the present work, the authors have investigated the propagation behavior of Bluestein-Gulyaev-type waves in a piezo-thermoelastic half-space in the context of modified multi-phase-lag theory. The normal mode technique is employed to obtain the principal variables, for example, displacements, temperature, electric potential, electric displacements, and thermo-mechanical stresses. The boundary conditions are adopted in such a way that the upper surface of the piezo-thermoelastic half-space is stress free and the half-space is implicated by a perfectly conducting electrode that is grounded (i.e., electrically short conditions at the free surface). Based on these boundary conditions, secular equations are derived for the proposed model. Some special cases have also been discussed, and it is found that the secular equation is in well-agreement with the pre-established thermoelasticity theory. Moreover, some analyses are made to highlight the important peculiarities of the problem. The mathematical framework of the present study is momentous for both theoretical and practical expositions for temperature sensors and piezoelectric surface acoustic wave (SAW) devices. Also present study helps the researchers who are engaged on this domain.

Harnessing MBene termination for superior anode interfaces in Li/Ca-ion batteries

The elevation of two-dimensional (2D) transition metal borides, specifically MBenes, as anode materials for lithium-ion batteries (LIBs) and calcium-ion batteries (CIBs) can be achieved through strategic functionalization with appropriate groups. Utilizing a first-principles approach, we conducted an in-depth investigation into the electrochemical properties of chlorine-terminated V2B (V2BCl2) as a candidate anode material for LIBs and CIBs. V2BCl2 exhibits metallic behavior, as demonstrated by band structure analysis, which endows it with exceptional conductivity due to the free electron surface of the system, thereby embodying ideal anode characteristics. The dynamic and thermal stability of the system was assessed through comprehensive phonon dispersion analyses and ab-initio molecular dynamics (AIMD) calculations. High net charge transfer rates of Li/Ca ions towards the monolayer, augmented electron localization function (ELF) near system atoms, and the presence of ionic bonds between Ca/Li and the V2BCl2 monolayer contribute to the enhanced conductivity observed in these anode systems. This is corroborated by metrics such as the projected crystal orbital Hamiltonian population (-pCOHP), low diffusion energy barriers (< 0.35 eV) facilitating rapid charging mechanisms, and low open circuit voltages (< 0.32 V) ensuring robust battery performance stability. Furthermore, V2BCl2 exhibits notable specific storage capacities of 875.67 mAh g−1 for Ca ions and 1167.75 mAh g−1 for Li ions, surpassing the benchmarks set by recent MBene systems. These promising results strongly advocate for V2BCl2 as a viable candidate for anode material in both LIB and CIB applications, highlighting its potential significance in advancing battery technology.

АНАЛІЗ РІВНОВАГИ ТОНКИХ ОРТОТРОПНИХ ПЛИТА НА ТРИПАРАМЕТРИЧНИЙ ПРУЖНІЙ ОСНОВІ

The paper deals with the problem of studying the static equilibrium of thin orthotropic rectangular plates resting on a three-parameter elastic base. To solve this problem, a mathematical model of a thin reinforced concrete slab as a homogeneous orthotropic plate with an averaged Huber's modulus is constructed. A mathematical model of a three-parameter elastic foundation is proposed, taking into account the friction between the lower surface of the plate and the foundation. The developed method for analyzing the equilibrium of such plates allows obtaining an exact solution of the equilibrium equation, taking into account the boundary and surface conditions at individual nodes. During the numerical implementation of the developed approach, a procedure for generating such nodes is proposed. The solution of the equilibrium equation is presented as the sum of the deflection force functions and its shape functions multiplied by unknown parameters, which are interpreted as the degree of freedom of the plate. This approach made it possible to satisfy the boundary and surface conditions with high accuracy. On the basis of the obtained solutions, the stress-strain state of a thin homogeneous orthotropic square plate completely clamped along the contour is analyzed for the case when the plate is subjected to a distributed load on its upper part and rests on an elastic base. On the basis of the solutions obtained in this work and formulas obtained by other authors, a comparative analysis of the results for the case of three types of elastic bases is carried out: a three-parameter base, a Winkler base, and a plate with a free bottom surface. Based on numerical calculations, it was found that the elastic base significantly reduces the deflection, tilt and moment in the plate. The results obtained for the Winkler model and the three-parameter model differ by 3% and 1,5% for deflections and moments, respectively. It is established that the results obtained within the proposed model practically do not depend on the coefficient of friction between the lower surface of the plate and the foundation.

Buckets Instead of Umbrellas for Enhanced Sampling and Free Energy Calculations.

Umbrella sampling has been a workhorse for free energy calculations in molecular simulations for several decades. In conventional umbrella sampling, restraining bias potentials are strategically applied along one or several collective variables. Major drawbacks associated with this method are the requirement of a large number of bias windows and the poor sampling of the transverse coordinates. In this work, we propose an alternate formalism that departs from the traditional umbrella sampling to mitigate these issues, where we replace umbrella-type restraining bias potentials with bucket-type wall potentials. This modification permits one to formulate an efficient computational strategy leveraging wall potentials and metadynamics sampling. This new method, called "bucket sampling", can significantly reduce the computational cost of obtaining converged high-dimensional free energy surfaces. Extensions of the proposed method with temperature acceleration and replica exchange solute tempering are also demonstrated.

Sound‐Based Assembly of Magnetically Actuated Soft Robots Toward Enhanced Release of Extracellular Vesicles

Magnetic soft robots have emerged as promising tools in biomedicine due to their wireless actuation, rapid response, and compatibility with biological systems. Despite the various innovative strategies proposed for their fabrication, they suffer from complex processes and limited cellular compatibility. Therefore, there is an urgent need to explore alternative approaches that are fast, mild, and highly tunable. Herein, a novel fabrication strategy for contactless assembly of soft‐robots is introduced for the first time. This technology exploits hydrodynamic instabilities at the free surface of a fluid layer, thus enabling the fabrication of centimeter‐scale robots featuring diverse structural properties. These features show a wide range of deformation modes in response to magnetic fields, including folding, bending, and expanding. Furthermore, the design and assembly of novel actuators with customized shapes as fish‐ and butterfly‐like structures is shown. The fabricated patterns exhibit different modes of motion under the influence of uniform magnetic fields. As a proof of concept, an innovative application of this technology combined with the proposed soft robots is represented by the enhanced release of extracellular vesicles. Altogether, this novel fabrication method along with the newly developed magnetic soft robots enables the manufacturing of high‐performance, multifunctional, and cytocompatible intelligent systems.

In-Situ TEM study of microstructural evolution in proton irradiated single crystal UO2 under high-temperature annealing

Understanding microstructural changes in nuclear fuels under different irradiation conditions is important as it directly affects thermal, oxidation and mechanical properties and thereby reactor safety and longevity. This work focuses on the effect of temperature on the evolution of extended defects in uranium dioxide. In-situ transmission electron microscopy (TEM) annealing of proton irradiated UO2 was performed at different temperatures: 900 °C, 1100 °C and 1300 °C, 1 hour for each temperature. Microstructural evolution in terms of dislocation loops and voids were captured using in-situ TEM during annealing at different temperatures. Post-annealing at each temperature, detailed characterization using rel-rod dark field, bright field, and underfocus-overfocus imaging in TEM were used to identify faulted loops, perfect dislocation loops, and voids, respectively. Dislocation loops showed migration, disappearance, coalescence and loop-line interactions which significantly contributed to the recovery process during annealing at temperatures of 1100 °C and 1300 °C. Small voids were observed at 900 °C (diameter ∼ 0.5–1.5 nm) and grew rapidly during 1300 °C annealing (diameter ∼ 1–3 nm). Void growth was attributed to vacancy absorption, Ostwald ripening and void coalescence mechanisms. Extensive void growth was unique to in-situ TEM annealing due to free surface effect as ex-situ annealing confirmed negligible TEM resolvable (> 0.5 nm) voids at 1300 °C. The dislocation loops and voids behavior during in-situ TEM annealing were compared with rate theory and cluster dynamics predictions.

Generation of nonlinear gravity waves based on the harmonic polynomial cell method incorporated with a mass source

A nonlinear numerical wave tank is established using the Harmonic Polynomial Cell (HPC) method, which is incorporated with a mass source. The numerical wave tank consists of the mass source wave generation region and the working region, with sponge layers at both ends for wave absorption. In the mass source region, a generalized HPC method is applied to solve the inhomogeneous elliptic boundary value problems. The Poisson equation's special solution is represented by a bi-quadratic function. In the remaining domains, the HPC method is employed with harmonic polynomials to solve the problems governed by the Laplace equation in each grid cell. The free surface is tackled by the immersed boundary method (IB-HPC), and the kinematic and dynamic conditions of the free surface are described using a semi-Lagrangian approach. A variety of waves propagation are simulated, including Second-order Stokes wave, fifth-order Stokes wave, solitary wave, fifth-order Fenton stream function wave, random wave and the interaction with a straight vertical wall. The numerical solutions are compared with theoretical solutions. The numerical simulation results demonstrate that the present method can generate arbitrary two-dimensional wave fields by specifying an appropriate source function. Additionally, the reflected waves can propagate through the wave generation region, ensuring that the process of wave generation is not affected by the reflections.