Free Surface Deformation Research Articles

Interactions between a toroidal bubble and a free surface

Toroidal bubbles (TBs) represent cases of vortex rings with a gas–liquid interface where a gas vortex ring is encased within a liquid vortex ring, and can serve as effective media for mass conveyance, process mixing, noise reduction and reaction regulation. In this study, we carry out a systematic study on the interaction between a TB and a free surface. According to the high-speed photographic images from the experiments, we identify strong and weak interactions in terms of the normalized maximum free surface deformation $h_{max}^*$ . Then, we perform numerical simulations based on the volume of fluid (VOF) method in the OpenFOAM platform. Based on both the experimental and the numerical results, we conclude that the Froude number, $Fr$ , determines the main characteristics during the interaction process. The TB–free surface interaction is essentially the interaction between the liquid vortex ring enveloping the TB and the free surface, supplemented by the TB's complex behaviour. Next, we establish the scaling law of $h_{max}^*$ based on the energy balance condition. Based on this, we provide the critical $Fr$ and the slenderness of the TB, $\eta$ , for identifying the strong and weak interactions, and a parametric plot of the interactions in terms of $Fr$ and $\eta$ .

The influence of water turbulence on surface deformations and the gas transfer rate across an air–water interface

We present experimental results of a study on oxygen transfer rates in a water channel facility with varying turbulence inflow conditions set by an active grid. We compare the change in gas transfer rate with different turbulence characteristics of the flow set by four different water channel and grid configurations. It was found that the change in gas transfer rate correlates best with the turbulence intensity in the vertical direction. The most turbulent cases increased the gas transfer rate by 30% compared to the low turbulence reference case. Between the two most turbulent cases studied here, the streamwise turbulence and largest length scales in the flow change, while the gas transfer rate is relatively unchanged. In contrast, for the two less turbulent cases where the magnitude of the fluctuations normal to the free surface are also smaller, the gas transfer rate is significantly reduced. Since the air–water interface plays an important role in the gas transfer process, special attention is given to the free-surface deformations. Despite taking measures to minimise it, the active grid also leaves a direct imprint on the free surface, and the majority of the waves on the surface originate from the grid itself. Surface deformations were, however, ruled out as a main driver for the increase in gas transfer because the increase in surface area is < 0.25%, which is two orders of magnitude smaller than the measured change in the gas transfer rate.

Improved diffuse interface-immersed boundary method for three-dimensional multiphase fluids–structure interaction with moving contact lines

In the realm of numerical algorithms for investigating interactions between multiphase fluids and structure, the accurate computation of moving contact lines (MCLs) dynamics and the substantial computational resource demands bring challenges in three-dimensional simulations. In this study, an improved diffuse interface-immersed boundary method is proposed to efficiently investigate three-dimensional multiphase fluids–structure interactions. The present work commences with the development of the explicit correction scheme and the simplified Dirac function coefficient, designed to efficiently implement the immersed boundary technique. To validate the effectiveness and accuracy of the proposed method, the simulations of water entry and exit for a half-buoyant sphere are carried out, which conclusively demonstrate that the proposed method offers significant advantages in terms of both efficiency and accuracy, faithfully capturing the dynamic response of solid structures and the substantial deformation of free surfaces at the three-dimensional scale. Additionally, a comparative analysis of the results obtained using the proposed method for the free water exit of a hollow sphere against previous experimental data is conducted, highlighting the promising potential of the proposed method for applications.

Anti-slosh effect of baffle configurations and air pressure on liquid sloshing in partially filled tank trucks

Abstract The phenomenon of liquid sloshing inside partially filled tank trucks adversely affects the stability of the tanktrucks. In order to mitigate the negative effects of liquid sloshing inside the tank, this study proposes several baffle configurations and investigates their anti-slosh effect on liquid sloshing. First, a numerical model of liquid sloshing is established. Then, the effectiveness of the numerical model is validated by comparing the results of free surface deformation, wall pressure, and sloshing frequency obtained from simulations and experiments under identical conditions. During the research process, it was found that the air pressure formed in locally sealed spaces within the tank also plays a positive role in suppressing liquid sloshing. The research results indicate that, under low fill volumes, baffles fixed at the bottom of the tank are more effective in suppressing liquid sloshing inside the tank, while under high fill volumes, baffles fixed at the top of the tank are more effective. Considering the tank’s airtightness, the air pressure formed in locally sealed spaces within the tank plays an important role in suppressing liquid sloshing when baffles are fixed at the top of the tank and the fill volume is high.&amp;#xD;

Numerical simulation of the influence of wave parameters on the horizontal cylinder in the nonlinear coupling of the wave–current

Considering that marine structures are frequently subjected to the combined effects of waves and currents, the wave–current coupling environment largely determines the structural load and the surrounding water–air mixed flow, which is a typical feature of offshore structures, such as ships and offshore platforms. This study focuses on the interaction between a horizontal cylinder and a free surface in a wave–current nonlinear coupled environment using numerical simulations. The numerical method is based on the incompressible Navier–Stokes equation, with the volume-of-fluid method used to capture the free surface. Based on the second-order Stokes wave theory, we studied the impact of wave height and steepness on the cylinder force, vorticity field, free-surface deformation, and spatial–temporal distribution characteristics of entrainment bubbles. The results showed that the wave height and wave steepness have opposite effects on the root mean square (RMS) value of the force and influence the amplitude and period of the force curve. The stretching of the negative vortex led to varying degrees of double-frequency oscillation modes in the force curves. The main sources of bubbles in the wake are the breaking of the free surface and the entrainment caused by the cylinder vortex, and the bubbles caused by the former account for the majority. Compared with the wave height, an increase in wave steepness can cause a more severe interface breaking, resulting in more entrainment bubbles.

A coupled smoothed particle hydrodynamics–peridynamics model for two-dimensional hydroelastic water entry

In this paper, a numerical model coupling the smoothed particle hydrodynamics (SPH) with peridynamics (PD) is developed to solve the problem of the hydroelastic water entry. By combining the geometric nonlinear peridynamics with the weakly compressible SPH, the proposed model can efficiently simulate the nonlinear deformation of the structure and the deformation of a fluid free surface. The transmission of information between the fluid and solid phases is implemented by a dummy particle boundary treatment method. By simulating benchmark tests, the ability of the proposed model to solve nonlinear fluid–structure coupling problems is verified. In order to improve the computational efficiency, the graphics processing unit parallel acceleration scheme is applied to the SPH-PD model. Compared with the serial scheme, the speedup effect of the parallel scheme in large-scale computation is verified. As an application of the numerical model, the water entry of the flexible panel at a constant entry velocity is studied. The mechanism of hydroelastic effect is explained by analyzing the variations in the fluid pressure field, slamming force, and panel deformation during water entry. In addition, the influences of plate rigidity, impact velocity, and deadrise angle on the hydroelastic effect are investigated.

Study on Water Entry of a 3D Torpedo Based on the Improved Smoothed Particle Hydrodynamics Method

The water entry of a torpedo is a complex nonlinear problem, involving transient impact, free surface deformation, droplet splashing, and fluid–structure coupling, which poses severe challenges to traditional mesh methods. The meshless smoothed particle hydrodynamics (SPH) method shows unique advantages in capturing the complex features of the water entry of the torpedo at different entry angles. However, it still suffers from some inherent shortcomings, such as low surface discretization accuracy, poor discretization flexibility, and low calculation efficiency. In this study, an improved adaptive SPH algorithm is proposed to investigate the water entry of the torpedo accurately and efficiently. This method integrates meshless point generation and adaptive techniques simultaneously. The numerical results demonstrate that when the torpedo vertically enters the water at different velocities, the induced impact loads acting on the head of the torpedo fluctuate significantly with two peak values in the initial stage and thereafter stabilize in a later stage. The impact load acting on the torpedo, the entry depth of the torpedo, the splash height of the droplets, and the size of the cavity generated around the torpedo increase with the increment in the entry velocity. When the torpedo enters the water at different entry angles under the same initial entry velocity, both the vertical and the horizontal movements of the torpedo are observed, which results in more complex variations in parameters along the x- and y-axes. The findings and the corresponding numerical method in this study can provide a certain basis for the future designs of the entry trajectory and the structural bearing capacity of torpedoes.

Air-Water Flow Properties In Highly Unsteady Flows

Recent catastrophic events caused by tsunamis, storm surges, flood waves, and the failure of dams (e.g. in Ukraine and Libya) have shown to be a significant threat to densely populated coastal communities. Interactions with built environments can lead to violent wave impacts that may have severe consequences, including significant infrastructural damage and potential loss of life. The frequency of these water-related disasters is increasing globally due to climate change and sea level rise, resulting in a rising demand for deeper knowledge related to the physical processes of such hazards. The dynamic behaviour of these type of wave phenomena is described by long-period, high translatory waves, where the on-shore propagation or inland inundation is associated with sudden free-surface deformations. This results in a steeping of the slope at the leading edge, causing non-linear flow behaviour to prevail and inducing the wave to collapse. The breaking process generates a breaking roller at the wave front, containing a rapidly fluctuating mixture of air and water, associated with a strong recirculation. The high degree of air-water interaction in these unsteady flows has a significant impact on the flow properties as it influences many dynamic processes, including viscous and surface tension effects at air-bubble level, as well as larger scale gravitational effects associated with the turbulent flow and eddy formation (Brocchini and Peregrine, 2001). New innovative measurement techniques have allowed experimental studies to more precisely quantify the air-water interactions in multiphase flows. However, most experimental research focused on air-water flow properties in hydraulic jumps and other steady flows (e.g. spillway flows, plunging jets). Currently, limited research is available for unsteady flows and mostly based on small datasets and limited flow conditions. This lack of availability and diversity of experimental data restricts the understanding of how these multi-phase flows behave under different conditions, hence the need for future research.

Free surface oscillation driven by rotating stirrer

To gain insights into the mechanisms of free surface oscillation in a rotating mixing container, we observe the free surface deformation and measure the torque acting on the bar. The container was half-filled with liquids. Periodic surface oscillation occurs. At the rotational speed where the amplitude of the oscillation reaches its maximum, the time-averaged torque also takes the local maximum values. To account for the sloshing mechanism, an equation of motion is derived using the Lagrangian mechanics; we found that the sloshing occurs when the collision frequency of bar on the surface is consistent with the natural frequency of the system and the damping coefficient is sufficiently smaller than unity. The time-averaged torque increases when the sloshing becomes violent. We conclude that the hydrodynamics of oscillation is successfully modeled using point-mass mechanics, and thus we can reasonably capture the rotation speed at which violent oscillation occurs.Graphical Free surface deformation driven by the rotating arm in the cylindrical container which is half-filled with liquids

THE ONSET OF LONG-WAVELENGTH MARANGONI CONVECTION IN A BINARY FLUID MIXTURE UNDER HEAT FLUX MODULATION

The Marangoni instability of a horizontal binary mixture layer with a deformable free surface and a solid substrate is investigated under the action of a modulated heat flux. In contrast to a homogeneous liquid, due to thermal diffusion (Soret effect), the modulation of the heat flux creates not only a temperature wave but also a concentration wave, which changes the surface tension. Two cases of the modulation of the heat flux with a zero mean value are considered: (i) on a free surface and (ii) on a rigid substrate. In both cases, the long-wave instability exists within the established frequency intervals. The dependences of the critical Marangoni number and the corresponding modulation frequency on the separation ratio and the Lewis number are obtained for long-wave disturbances. The fundamental features of case (i), as compared to case (ii), are as follows: the instability domains are located in the lower frequency ranges and the minimum Marangoni number is several times smaller.

Advanced Hydrodynamic Modelling of Flow at a River Bridge: Insights from 3D Computational Fluid Dynamics

Failure of river bridges is often due to hydraulic reasons, such as the development of severe scouring around piers and abutments. In many cases, the presence of bridge structures produces complex flow fields, which are difficult to predict using standard hydraulic models. This entails difficulties in estimating the hydrodynamic actions on the structure and the potential scour on the riverbed. A three-dimensional Computational Fluid Dynamics (3D CFD) model is used to analyze the flow field and the bed shear stresses at an existing bridge. The Volume of Fluid (VoF) method allows resolving the deformable free-surface, and the Detached Eddy Simulation (DES) approach allows resolving the dynamics of the energetically important turbulent eddies in the flow. The analysis deals with modeling the flow around a realistic, full-scale, multi-pier bridge in the Po River. Simulations considered different hydrodynamic regimes, i.e., the free-surface flow regime and the hypothetical pressure-flow regime which would occur when water levels are higher than the low chord of the bridge deck. The numerical application highlights the potential of the DES technique for analyzing the hydrodynamics of flow at bridges in natural river channels. Besides the turbulent flow fields and the description of the vortical structures, relevant results include the time-varying spatial distribution of the hydrodynamic forces acting on the different parts of the bridge and the time-varying distribution of the shear stress on the bed. This aspect is of particular interest because i) the estimation of drag forces on the structure components may be oversimplified using canonical, averaged formulas, and ii) the fluctuations in time of the bed shear stresses play a key role in determining the removal of sediments from the bed and the scour hole close to the bridge piers.

Hydrodynamic design of the Separate Effect test facility for Flow-Accelerated Corrosion and Erosion (SEFACE) studies in liquid lead

Flow-accelerated corrosion and erosion (FACE) phenomena can be crucial for performance of structural elements in heavy liquid metal (HLM) cooled reactor systems. Existing experimental observations indicate that turbulent flow characteristic can affect FACE, but there is no quantitative data that can be used for model development and validation. Main recirculation pump impellers, which operate at high relative velocities and rotational flow conditions can be especially vulnerable to FACE. For comparison, the core internals operate at lower velocities and in axial flow conditions, but at higher temperatures and neutron fluence. Hence, systematic experimental data is needed to improve our knowledge on FACE phenomena. The Separate Effect Test Facility for Flow-Accelerated Corrosion and Erosion (SEFACE) is designed to obtain such experimental data including high relative velocities (up 20 ms−1) and high temperatures (400 to 550 °C) of liquid lead. This article focuses on the hydrodynamic design of SEFACE. The aim of the design is to achieve well defined flow conditions for experiments and ensure safe operation of the facility. First, we examine three design concepts (i.e., forced convection loop, rotating cylinder, and rotating disk) and motivate the choice of the rotating disk approach for SEFACE. Second, we discuss different design options, i.e., a confined rotor–stator test chamber and the unconfined rotating disk configuration. We used Reynolds-Averaged Navier Stokes (RANS) calculations to identify and solve the issues stemming from the high rotational speed. These include, for instance, lead free surface deformation, radial pressure buildup, and axial bending forces due to asymmetric test chamber. The CFD-derived torque and power predictions in rotor–stator and rotating disk systems are verified with selected empirical turbulent friction factor correlations or/and DNS calculations. We demonstrate that the developed hydrodynamic design of SEFACE solves identified issues and enables obtaining experimental data under well-defined flow conditions. The findings are deemed to also be applicable to the design of rotating disk-type FACE installations for other liquid mediums.

Numerical study of liquid sloshing using smoothed particle hydrodynamics with adaptive spatial resolution

Liquid sloshing is a typical problem of free surface flow in a number of engineering applications. The efficient simulation of liquid sloshing, particularly the large deformation and breakup of free surface, is a challenge for numerical methods. This paper presents a numerical method based on smoothed particle hydrodynamics with adaptive spatial resolution (SPH-ASR) for liquid sloshing. The SPH-ASR method can adaptively adjust the spatial resolution based on the distance to the free surface and the moving boundary. The numerical method was validated against experimental results from literature. Then the SPH-ASR method was applied to study the liquid sloshing problem in a prismatic tank and a rectangular tank. The effects of liquid fill level, external excitation frequency and amplitude on liquid sloshing were investigated. The pressure at different points on the tank wall and the total moment on the rotating shaft of the tank were compared and analyzed.

Melt pool electromagnetic force model extended to account for free surface deformation – Application to gas metal arc

Computational fluid dynamics models with free surface tracking intended to simulate the melt pool produced by an electric arc usually model the electromagnetic force ignoring the deformation of the free surface. However, with an arc heat source, the electromagnetic force is known to be among the leading-order forces, especially at high currents. In addition, the free surface can undergo significant deformations, especially in the presence of metal transfer. In the present study, a generalization of the electromagnetic force model that accounts for the deformation of the free surface is therefore proposed. Test cases with a pulsed gas-metal arc that transfers one metal drop per pulse were investigated experimentally at three different travel speeds to provide validation data. The cases were simulated with both the proposed and the earlier model to assess the influence of the new developments. The results showed that, in the regions where both models determine the force, the discrepancy between the models' results can reach up to an order of magnitude. Especially, the earlier model overestimates the electromagnetic force deep into the melt pool. On the other hand, it neglects it in the liquid metal that is located at an elevation above the original upper surface of the workpiece, while the proposed model showed that in this area the intensity of the electromagnetic force is the largest. These significant discrepancies result in non-negligible differences in the predicted melt pool thermal flow and geometry. Especially, the proposed extended model provides an improved prediction of the fingertip-shaped fusion boundary.

Unsteady ship–bank interaction: a comparison between experimental and computational predictions

ABSTRACT A collaborative exercise is presented where different numerical methods were used to recreate the forces acting on a ship model while executing captive model tests along a channel which has an unsteady cross section (dock opening). Such a layout is typical for a harbour environment. The unsteady nature of the cross section leads to peak values in forces, sinkage and free surface deformations. Experimental tests were conducted by Flanders Hydraulics (with the co-operation of Ghent University). Numerical contributions involve three potential flow methods (Strathclyde University and Pinkster Marine Hydrodynamics) and one RANS method (Federal Waterways Engineering and Research Institute of Germany). All methods are capable of qualitatively predicting the water level variations and sinkage and trim of the vessel. RANS has a better capability of predicting the unsteady sway force and yaw moment acting on the ship including sinkage and trim, but it comes at a much higher computational cost.

A comprehensive investigation on liquid sloshing of rectangular water tank with vertical baffles

Although numerical method is used to analyze the liquid sloshing-induced wave height and control force, it is worth noting that the effects of vertical baffle on liquid sloshing of rectangular water tanks have not been thoroughly explored. Further research in this domain would be invaluable for gaining a more profound understanding of liquid sloshing in such tanks. Therefore, the CFD method and finite volume model are employed in this paper, and the effects of vertical baffle on the liquid sloshing behaviors are comprehensively investigated, including wave height of free surface, horizontal control force, damping ratio of liquid sloshing, natural frequency, and free surface deformation. Then, the influences of excitation amplitude, water depth, number of baffles, baffle position, and baffle height are extensively explored. The accuracy of the modeling is confirmed through rigorous comparisons with existing experimental results. The number of baffles has a considerable influence on the behaviors of liquid sloshing. The effectiveness of the baffle in reducing liquid sloshing is closely tied to its position. Exceeding the baffle height beyond the water depth causes a transformation of the working mechanism and inherent properties of the rectangular water tank. The natural frequency is generally overestimated by linear potential flow theory.

Marangoni stability of a thin liquid film falling down above or below an inclined thick wall with slip

AbstractThe linear and nonlinear instability of a thin liquid film flowing down above or below (Rayleigh-Taylor instability) an inclined thick wall with finite thermal conductivity are investigated in the presence of slip at the wall-liquid interface. A nonlinear evolution equation for the free surface deformation is obtained under the lubrication approximation. The curves of linear growth rate, maximum growth rate and critical Marangoni number are calculated. When the film flows below the wall it will be subjected to destabilizing and stabilizing Marangoni numbers. It is found that from the point of view of the linear growth rate the flow destabilizes with slip in a wavenumber range. However slip stabilizes for larger wavenumbers up to the critical (cutoff) wavenumber. From the point of view of the maximum growth rate flow slip may stabilize or destabilize increasing the slip parameter depending on the magnitude of the Marangoni and Galilei numbers. Explicit formulas were derived for the intersections (the wavenumber for the growth rate and the Marangoni number for the maximum growth rate) where slip changes its stabilizing and destabilizing properties. From the numerical solution of the nonlinear evolution equation of the free surface profiles, it is found that slip may suppress or stimulate the appearance of subharmonics depending on the magnitudes of the selected parameters. In the same way, it is found that slip may increase or decrease the nonlinear amplitude of the free surface deformation. The effect of the thickness and finite thermal conductivity of the wall is also investigated.

APPLICATION OF THE METHOD OF DISCRETE SINGULARITIES TO THE CALCULATION OF THE EVOLUTION OF SURFACE GRAVITY WAVES OVER BOTTOM IRREGULARITIES

The numerical technique for simulation of viscous non-linear interactions between a solitary wave and a non-regular bottom was developed. It couples the boundary integral method used to determine the free surface deformations and the vortex scheme for integrating the fluid dynamic equations. To verify the model, a series of test calculations was carried out, where the obtained results were compared with our own experimental data and results known from similar studies by other authors. A good coincidence of the free surface elevation, as well as the velocity fields during the passage of a solitary wave over a thin submerged plate, was obtained. Systematic calculations of the interaction of a solitary wave with a submerged step in a wide range of wave amplitudes and step heights were performed. It is shown that when a wave emerges from deep water into the shallows, its evolution is determined by energy losses due to reflection, dispersion effects, and the generation of a vortex field. The dynamics of the wave on the submerged step depends on the coefficient of interaction, which is the ratio of the wave amplitude to the water depth above the step. Four types of wave behavior are possible above the step. Those are the weak interaction, when the wave gently splits into transmitted and reflected solitons; fission with development of two solitons behind the irregularity; fission with the generation of a dispersion chain of waves in the shallow water; and the collapse of a wave. The obtained critical value of the coefficient of interaction, at which the solitary wave is always breaking, is about 0.8, which is in congruence with the experimental data. Studies of patterns of vorticity generated by a solitary wave at the edge of a submerged step revealed two oppositely directed vortices with a horizontal axis, the scale of which is proportional to the water depth in a shallow channel. Their dynamics causes intensive exchange processes between deep water and shallows, as well as water flows from the bottom to the top and water mixing. The obtained data make it possible to predict in advance the development of processes and dangers caused by long nonlinear waves reaching the shelf.

Coupling SPH with a mesh-based Eulerian approach for simulation of incompressible free-surface flows

This paper presents a coupling algorithm for the simulation of incompressible free-surface flows over the near and far fields by solving the Navier-Stokes equations. The coupling combines the Smoothed Particle Hydrodynamics (SPH) with the Finite Difference (FD) method implemented on structured Eulerian grids. Based on the domain decomposition, the SPH is applied to the near-field core region for modeling with high-fidelity the severe free-surface deformation and even fragmentation of flow, while the FD method is used to resolve the remaining far-field region with relatively high efficiency. The primary purpose of the hybrid approach is to mitigate the computational load of SPH applications through combination with a mesh-based Eulerian method while maintaining high accuracy for both the near-field and far-field simulations. Two-way coupling between the FD and SPH models is achieved by the overlapping region between the computational subdomains, in which the Eulerian solutions and the Lagrangian solutions are coupled with each other through interpolation in the overlapping region for the fluid transfer and free-surface movement between the near-field and far-field regions. The proposed algorithm is validated by several test cases, showing favorable accuracy, convergence, and applicability in the simulation of wave interactions with complex bathymetry and structures.

Simulation of fallpipe rock dumping utilizing a multi-phase particle-in-cell (MPPIC)-Discrete Element Method (DEM) model. Part I: Concepts and formulation

Dumping blasted rock fragments into water bodies through vertical fallpipes can be a challenging engineering activity due to the concerns of dispersion of fine contents (suspended sediments). This study aims to provide better understanding of the fallpipe rock dumping processes through numerical simulation approaches. We propose a modified multiphase particle-in-cell (MPPIC) method to simulate the fluid–solid mixture flows, and an advection–diffusion model for handling the fine contents. The modifications to the MPPIC method include: (i) changing the pure Eulerian fluid model to a hybrid Eulerian–Lagrangian model for numerical flexibility in handling large free-surface deformations, and (ii) replacing the empirical interparticle stress model with the Discrete Element Method (DEM) for numerical stability when dealing with large-size solids. The numerical model is first validated via two physical experiments: (i) wave generation by a granular collapse and (ii) sand dumping from a split hopper. The simulations generally agree well with the experimental findings, reflecting both the fluid–solid interaction and propagation of suspended sediments. Fallpipe rock dumping is then simulated with a consideration of the effects of fallpipe size on the dynamic interactions between the DEM solid particles, the fluid, and, hence, the fine contents. The results show that long narrow fallpipes perform better in terms of containing the fine contents and limiting the spreading range of the DEM solid particles on the seabed. The time-varying distribution of the fines concentration and the fluid velocity within the fallpipe are also discussed based on the simulation results.