A stencil-like volume of fluid (VOF)method for tracking free interface

A stencil-like volume of fluid （VOF） method is proposed for tracking free interface. A stencil on a grid cell is worked out according to the normal direction of the interface, in which only three interface positions are possible in 2D cases, and the interface can be reconstructed by only requiring the known local volume fraction information. On the other hand, the fluid-occupying-length is defined on each side of the stencil, through which a unified fluid-occupying volume model and a unified algorithm can be obtained to solve the interface advection equation. The method is suitable for the arbitrary geometry of the grid cell, and is extendible to 3D cases. Typical numerical examples show that the current method can give ＂sharp＂ results for tracking free interface.

Volume of fluid simulation of single argon bubble dynamics in liquid steel under RH vacuum conditions

Single argon bubble dynamics in liquid steel under Ruhrstahl-Heraeus(RH)vacuum conditions were simulated using the volume of fluid method,and the ideal gas law was used to consider bubble growth due to heat transfer and pressure drop.Additional simulation with a constant bubble density was also performed to validate the numerical method,and the predicted terminal bubble shape and velocity were found to agree with those presented in the Grace diagram and calculated by drag correlation,respectively.The simulation results under RH conditions indicate that the terminal bubble shape and velocity cannot be reached.The primary bubble growth occurs within a rising distance of 0.3 m owing to heating by the high-temperature liquid steel;subsequently,the bubble continues to grow under equilibrium with the hydrostatic pressure.When the initial diameter is 8-32 mm,the bubble diameter and rising velocity near the liquid surface are 80-200 mm and 0.5-0.8 m/s,respectively.The bubble rises rectilinearly with an axisymmetric shape,and the shape evolution history includes an initial sphere,(dimpled)ellipsoid,and spherical cap with satellite bubbles.

CFD Simulation of a container ship in random waves using a coupled level-set and volume of fluid method

The coupled level-set and volume of fluid(CLSVOF)method is an advanced interface-capturing method that has been extended to handle overset grid systems.However,artificial uneven interface may be observed across block boundaries of different sizes and geometries.We present an improved inter-grid VOF interpolation and mass correction scheme to address the issue.To demonstrate the capability of the improved CLSVOF method,it is applied to the simulation of a container ship in pitch and heave motions under both head sea and following sea irregular wave conditions.Our simulation proves that the improved CLSVOF method is capable of revealing detailed physics difficult to see with other methods.Those phenomena simulated in our work include the extensive greenwater propagation on the ship deck,the breakup of overtopping waves into small droplets,and the formation and collapse of air pockets in sudden bow and stern slamming which cause strong and highly localized impacts on the ship bow,stern,and rudder.

NUMERICAL SIMULATION OF HYDRODYNAMIC CHARACTERISTICS ON AN ARC CROWN WALL USING VOLUME OF FLUID METHOD BASED ON BFC

In the present study, a new algorithm based on the Volume Of Fluid （VOF） method is developed to simulate the hydrodynamic characteristics on an arc crown wall. Structured grids are generated by the coordinate transform method in an arbitrary complex region. The Navier-Stokes equations for two-dimensional incompressible viscous flows are discretized in the Body Fitted Coordinate （BFC） system. The transformed SIMPLE algorithm is proposed to modify the pressure-velocity field and a transformed VOF method is used to trace the free surface. Hydrodynamic characteristics on an arc crown wall are obtained by the improved numerical model based on the BFC system （BFC model）. The velocity field, the pressure field and the time profiles of the water surface near the arc crown wall obtained by using the BFC model and the Cartesian model are compared. The BFC model is verified by experimental results.

AN UNSPLIT LAGRANGIAN ADVECTION SCHEME FOR VOLUME OF FLUID METHOD

An Unsplit Lagrangian Advection （ULA） scheme for Volume Of Fluid （VOF） method is presented in this article. The ULA scheme is developed based on an algorithm of Piecewise Linear Interface Construction （PLIC）. The volume fluxes between cells are calculated through solving the new equation of the linear interfaces in cells in the ULA scheme. The fluxes flowing out from one cell is the inflow fluxes for another cell. In this way the whole fluid volume is conserved strictly without using any redistribution algorithms. The ULA scheme is based on two-dimensional structured rectangular mesh and may be extended to three-dimensional structured mesh with more geometrical efforts. The results from three widely-used benchmark tests show that the ULA scheme can achieve the accuracy higher than Split Lagaragian Advection （SLA） scheme and the Flux-Corrected Transport （FCT） algorithm.

Modeling droplet vaporization and combustion with the volume of fluid method at a small Reynolds number

The volume of fluid(VOF) formulation is applied to model the combustion process of a single droplet in a hightemperature convective air free stream environment.The calculations solve the flow field for both phases,and consider the droplet deformation based on an axisymmetrical model.The chemical reaction is modeled with one-step finite-rate mechanism and the thermo-physical properties for the gas mixture are species and temperature dependence.A mass transfer model applicable to the VOF calculations due to vaporization of the liquid phases is developed in consideration with the fluctuation of the liquid surface.The model is validated by examining the burning rate constants at different convective air temperatures,which accord well with experimental data of previous studies.Other phenomena from the simulations,such as the transient history of droplet deformation and flame structure,are also qualitatively accordant with the descriptions of other numerical results.However,a different droplet deformation mechanism for the low Reynolds number is explained compared with that for the high Reynolds number.The calculations verified the feasibility of the VOF computational fluid dynamics(CFD) formulation as well as the mass transfer model due to vaporization.

A three-dimensional robust volume-of-fluid solver based on the adaptive mesh refinement

The present study provides a three-dimensional volume-of-fluid method based on the adaptive mesh refinement technique.The projection method on the adaptive mesh is introduced for solving the incompressible Navier-Stokes equations.The octree structure mesh is employed to solve the flow velocities and the pressure.The developed solver is applied to simulate the deformation of the cubic droplet driven by the surface tension without the effect of the gravity.The numerical results well predict the shape evolution of the droplet.

Application of volume of fluid method for simulation of a droplet impacting a fiber

In the present work,impact of a Newtonian drop on horizontal thin fibers withcircular cross section is simulated in 2D views.The numerical simulations of the phenomenaare carried out using volume of fluid(VOF)method for tracking the free surface motion.Impacting of a Newtonian droplet on a circular thin fiber(350 um radius)investigatednumerically.The main focus of this simulation is to acquire threshold radius and velocity of adrop which is entirely captured by the fiber.The model agrees well with the experiments anddemonstrates the threshold radius decreased generally with the increase of impact velocity.Inother words,for velocity larger than threshold velocity of capture perhaps only a small portionof fluid is stuck on the solid and the rest of the drop is ejected for impact velocity smaller thancritical velocity the drop is totally captured.This threshold velocity has been determined whenthe impact is centered.

Numerical investigation of sinusoidal pulsating gas intake to intensify the gas-slag momentum transfer in the top-blown smelting furnace

The variation characteristics of bubble morphology and the thermal-physical properties of bubble boundary in the top-blown smelting furnace were explored by means of the computational fluid dynamics method.The essential aspects of the fluid phase(e.g.,splashing volume,dead zone of copper slag,and gas penetration depth)were explored together with the effect of sinusoidal pulsating gas intake on the momentum-transfer performance between phases.The results illustrated that two relatively larger vortices and two smaller vortices appear in the bubble waist and below the lance,respectively.The expansion of larger ones as well as the shrinking of smaller ones combine to cause the contraction of the bubble waist.Compared to the results of the case with a fixed gas injection velocity(V_(g)=58 m/s),the splashing volume and dead zone volume of the slag under the V_(g)=58+10sin(2πt)condition are reduced by 24.9%and 23.5%,respectively,where t represents the instant time.Gas penetration depth and slag motion velocity of the latter are 1.03 and 1.31 times high-er than those of the former,respectively.

Three-dimensional computational fluid dynamics （volume of fluid） modelling coupled with a stochastic discrete phase model for the performance analysis of an invert trap experimentally validated using field sewer solids

Invert traps are used to trap sewer solids flowing into a sewer drainage system, The performance of the invert trap in an open rectangular channel was experimentally and numerically analysed using field sewer solids collected from a sewer drain. Experiments showed that the free water surface rises over the central opening （slot） of the invert trap, which reduces the velocity near the slot and allows more sediment to be trapped in comparison with the case for the fixed-lid model （assuming closed conduit flow with a shear-free top wall） used by earlier investigators. This phenomenon cannot be modelled using a closed conduit model as no extra space is provided for the fluctuation of the water surface, whereas this space is provided in the volume of fluid （VOF） model in the form of air space in ANSYS Fluent 14.0 software. Additionally, the zero atmospheric pressure at the free water surface cannot be modelled in a fixed-lid model. In the present study, experimental trap efflciencies of the invert trap using field sewer solids were fairly validated using a three-dimensional computational fluid dynamics model （VOF model） coupled with a stochastic discrete phase model. The flow field （i.e., velocities） predicted by the VOF model were compared with experimental velocities obtained employing particle image velocimetry. The water surface profile above the invert trap predicted by the VOF model was found to be in good agreement with the experimentally measured profile. The present study thus showed that the VOF model can be used with the stochastic discrete phase model to well predict the performance of invert traps.

Cavitation Evolution Around a Twist Hydrofoil by Large Eddy Simulation(LES)with Mesh Adaption

The cavitating flow around a Delft Twist-11 hydrofoil is simulated using the large eddy simulation approach.The volume-of-fluid method incorporated with the Schnerr-Sauer cavitation model is utilized to track the water-vapor interface.Adaptive mesh refinement(AMR)is also applied to improve the simulation accuracy automatically.Two refinement levels are conducted to verify the dominance of AMR in predicting cavitating flows.Results show that cavitation features,including the U-type structure of shedding clouds,are consistent with experimental observations.Even a coarse mesh can precisely capture the phase field without increasing the total cell number significantly using mesh adaption.The predicted shedding frequency agrees fairly well with the experimental data under refinement level 2.This study illustrates that AMR is a promising approach to achieve accurate simulations for multiscale cavitating flows within limited computational costs.Finally,the force element method is currently adopted to investigate the lift and drag fluctuations during the evolution of cavitation structure.The mechanisms of lift and drag fluctuations due to cavitation and the interaction between vorticity forces and cavitation are explicitly revealed.

基于STAR-CCM+的船体周围流体流动数值分析及验证结果

In this paper,numerical analyses of fluid flow around the ship hulls such as Series 60,the Kriso Container Ship(KCS),and catamaran advancing in calm water,are presented.A commercial computational fluid dynamic(CFD)code,STAR-CCM+is used to analyze total resistance,sinkage,trim,wave profile,and wave pattern for a range of Froude numbers.The governing RANS equations of fluid flow are discretized using the finite volume method(FVM),and the pressure-velocity coupling equations are solved using the SIMPLE(semi-implicit method for pressure linked equations)algorithm.Volume of fluid(VOF)method is employed to capture the interface between air and water phases.A fine discretization is performed in between these two phases to get a higher mesh resolution.The fluid-structure interaction(FSI)is modeled with the dynamic fluid-body interaction(DFBI)module within the STAR-CCM+.The numerical results are verified using the results available in the literatures.Grid convergence studies are also carried out to determine the dependence of results on the grid quality.In comparison to previous findings,the current CFD analysis shows the satisfactory results.

Numerical simulation of fluid flow and free surface fluctuations during wheel and belt casting process

The unstable fluid flow and severe free surface fluctuations in the wheel and belt caster can affect the quality of the cast bar.The lower level height tends to entrap inclusions in the molten metal.On the other hand,the higher level height makes the production process more dangerous due to the overflow of high temperature fluid from the mold.A computational model of the molten metal pouring process was established.The transient fluid flow and free surface fluctuations behavior were calculated using the three-dimensional large eddy simulation model and the volume of fluid model.The results show that the flow velocity of the main jet gradually decreases under the influence of the low kinetic energy fluid in the mold.There is an obvious oscillation in the tail of the jet,while the flow field is asymmetric in space.The jet is closer to the inside radius side due to the Coanda effect,and there is a recirculation zone on the inside radius and the outside radius respectively,according to the 10 s time-averaged results.Compared with the industrial observation and simulation results,the shape of the free surface is a wave that varies with time.In addition,the free surface height is lowest and the flow velocity is highest in the region near the jet.

Numerical Investigation on Dynamic Response Characteristics of Fluid-Structure Interaction of Gas-Liquid Two-Phase Flow in Horizontal Pipe

Fluid-structure interaction(FSI)of gas-liquid two-phase fow in the horizontal pipe is investigated numerically in the present study.The volume of fluid model and standard k-e turbulence model are integrated to simulate the typical gas-liquid two-phase fow patterns.First,validation of the numerical model is conducted and the typical fow patterns are consistent with the Baker chart.Then,the FSI framework is established to investigate the dynamic responses of the interaction between the horizontal pipe and gas-liquid two-phase fow.The results show that the dynamic response under stratified fow condition is relatively flat and the maximum pipe deformation and equivalent stress are 1.8 mm and 7.5 MPa respectively.Meanwhile,the dynamic responses induced by slug fow,wave fow and annular fow show obvious periodic fuctuations.Furthermore,the dynamic response characteristics under slug flow condition are maximum;the maximum pipe deformation and equivalent stress can reach 4mm and 17.5 MPa,respectively.The principal direction of total deformation is different under various flow patterns.Therefore,the periodic equivalent stress will form the cyclic impact on the pipe wall and affect the fatigue life of the horizontal pipe.The present study may serve as a reference for FSI simulation under gas-liquid two-phase transport conditions.

Numerical simulations of sloshing and suppressing sloshing using the optimization technology method

Sloshing is a common phenomenon in nature and industry, and it is important in many fields, such as marine engineering and aerospace engineering. To reduce the sloshing load on the side walls, the topology optimization and optimal control methods are used to design the shape of the board, which is fixed in the middle of the tank. The results show that the new board shape, which is designed via topology optimization, can significantly reduce the sloshing load on the side wall.

In-Situ Test and Numerical Analysis of Bore Pressure on Sheet-Pile Groin

An in-situ test of bore pressure on a sheet-pile groin is carried out to investigate the characteristics of the bore pressure of fide in the Qian-tang River. The histories of bore pressure and the rule of the distribution of bore pressure on the sheet-pile groin are obtained through the test, which shows that the bore pressure on the sheet-pile groin are varies with time and space. The peak value of bore pressure on sheet-pile groin at different heights occurs almost at the same time. vertical distribution of bore pressure on the sheet-pile groin is linear above the still water level. The maximum bore pressure on the sheet-pile groin occurs at the still water level. Then a numerical method is also used to further study the characteristics of bore pressure. The standard k - ε turbulence model and VOF （volume of fluid） method for surface tracking are used to simulate the bore against the sheet-pile groin. The numerical results show flow fields, the position of free surface and time history and spatial distribution of bore pressure on the sheet-pile groin. The numerical and test resuits show good agreement.

Simulation of Gravity Currents Using VOF Model

By the Volume of Fluid (VOF) multiphase flow model two-dimensional gravity currents with three phases including air are numerically simulated in this article. The necessity of consideration of turbulence effect for high Reynolds numbers is demonstrated quantitatively by LES (the Large Eddy Simulation) turbulence model. The gravity currents are simulated for h not equal H as well as h = H, where h is the depth of the gravity current before the release and H is the depth of the intruded fluid. Uprising of swell occurs when a current flows horizontally into another lighter one for h not equal H. The problems under what condition the uprising of swell occurs and how long it takes are considered in this article. All the simulated results are in reasonable agreement with the experimental results available.

Very Large Eddy Simulation of Cavitation from Inception to Sheet/Cloud Regimes by A Multiscale Model

The cavitating flow in different regimes has the intricate flow structure with multiple time and space scales.The present work develops a multiscale model by coupling the volume of fluid(VOF)method and a discrete bubble model(DBM),to simulate the cavitating flow in a convergent-divergent test section.The Schnerr-Sauer cavitation model is used to calculate the mass transfer rate to obtain the macroscale phase structure,and the simplified Rayleigh-Plesset equation is applied to simulate the growing and collapsing of discrete bubbles.An algorithm for bridging between the macroscale cavities and microscale bubbles is also developed to achieve the multiscale simulation.For the flow field,the very large eddy simulation(VLES)approach is applied.Conditions from inception to sheet/cloud cavitation regimes are taken into account and simulations are conducted.Compared with the experimental observations,it is shown that the cavitation inception,bubble clouds formation and glass cavity generation are all well represented,indicating that the proposed VOF-DBM model is a promising approach to accurately and comprehensively reveal the multiscale phase field induced by cavitation.

Effect of viscosity on motion of splashing crown in high speed drop impact

A splashing crown is commonly observed when a high-speed drop impacts a liquid film. The influence of the liquid viscosity on the crown＇s evolution is not yet clear. We review several existing theories of this problem, and carry out a series of numerical simulations. We find that a three-segment model can describe the crown＇s motion. In the very early stage when the crown is barely visible, the influence of viscosity is small. Later, a shallow water approach used in most existing models is applicable as long as the initial conditions are formulated properly. They depend on viscous dissipation in the intermediate period. Preliminary estimation based on a dissipation function is proposed to characterize the influence of viscosity in this problem.

Numerical Study of Interactions between Regular Water Waves and a Submerged Obstacle

The interaction between regular water waves and a submerged obstacle in a channel is studied numerically. The fluid viscosity is taken into account and the volume of fluid method is used to deal with the free surface. The incident regular waves are generated by use of numerical absorbing wave maker paddle. The present method can be used to predict the nonlinear deformations of the transmitted regular waves, and to simulate the vortex flow near the obstacle and the shear flows beneath the free surface.