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.

Viscous liquid sloshing damping in cylindrical container using a volume of fluid method

Liquid sloshing is a kind of very complicated free surface flow and exists widely in many fields.In order to calculate liquid sloshing damping precisely a volume of fluid method based on finite volume scheme is used to simulate free surface flows in partly filled cylindrical containers.A numerical method is pre-sented to simulate the movement of the free surface flow,in which a piecewise linear interface con-struction scheme and an unsplit Lagrangian advection scheme instead of Eulerian advection scheme are used.The damping performance of liquid sloshing in cylindrical containers under fundamental sloshing mode is investigated.There are four factors determining the surface-wave damping:free surface,boundary-layer,interior fluid and contact line.In order to study different contributions from these four factors to whole damping,several examples are simulated.No-slip and slip wall boundary conditions on both side wall and bottom wall of the cylindrical containers are studied to compare with the published results obtained by solving Stokes equations.In the present method the first three main factors can be considered.The simulation results show that the boundary-layer damping contribution increases while the interior fluid damping contribution decreases with increase of Reynolds number.

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.

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.

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.

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.

CFD-Based Load Calculation Method for Monopile Support Configuration of Offshore Wind Turbine

An unsteady load calculation method for the support configuration of a monopile-supported offshore wind turbine is developed based on the Fluent software platform.Firstly,the water wave is generated by imposing the inlet boundary conditions according to the exact potential flow solution.Then the wave evolution is simulated by solving the unsteady incompressible Navier-Stokes(N-S)equations coupled with the volume of fluid method.For the small amplitude wave with reasonable wave parameters,the numerical wave result agrees well with that of the given wave model.Finally,a monopile support configuration is introduced and a CFD-based load calculation method is established to accurately calculate the unsteady load under the combined action of wave and wind.The computed unsteady wave load on a small-size monopile support located in the small amplitude wave flow coincides with that of the Morison formula.The load calculations are also performed on a large-size monopile support and a monopile-supported offshore wind turbine under the combined action of small amplitude wave and wind.

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.

A VOF-based numerical model for breaking waves in surf zone

This paper introduces a numerical model for studying the evolution of a periodic wave train, shoaling, and breaking in surf zone. The model can solve the Reynolds averaged Navier-Stokes （RANS） equations for a mean flow, and the k-ε equations for turbulence kinetic energy k and turbulence dissipation rate ε. To track a free surface, the volume of fluid （VOF） function, satisfying the advection equation was introduced. In the numerical treatment, third-order upwind difference scheme was applied to the convection terms of the RANS equations in order to reduce the effect of numerical viscosity. The shoaling and breaking processes of a periodic wave train on gently sloping beaches were modeled. The computed wave heights of a sloping beach and the distribution of breaking wave pressure on a vertical wall were compared with laboratory data.

A comparative study of interface reconstruction algorithms in molten metal flow

In the present research,two numerical schemes for improving the accuracy of the solution in the flow simulation of molten metal were applied.One method is the Piecewise Linear Interface Calculation(PLIC) method and the other is the Donor-Acceptor(D-A) method.To verify the module of the interface reconstruction algorithms,simple problems were tested.After these validations,the accuracy and efficiency of these two methods were compared by simulating various real products.On the numerical simulation of free surface flow,it is possible for the PLIC method to track very accurately the interface between phases.The PLIC method,however,has the weak point in that a lot of computational time is required,though it shows the more accurate interface reconstruction.The Donor-Acceptor method has enough effectiveness in the macro-observation of a mold filling sequence though it shows inferior accuracy.Therefore,for the problems that need the accurate solution,PLIC is more appropriate than D-A.More accuracy may cause less efficiency in numerical analysis.Which method between D-A method and PLIC method should be chosen depends on the product.

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.

Asymmetric breakup of a droplet in an axisymmetric extensional flow

The asymmetric breakups of a droplet in an axisymmetric cross-like microfluidic device are investigated by using a three-dimensional volume of fluid(VOF) multiphase numerical model. Two kinds of asymmetries(droplet location deviation from the symmetric geometry center and different flow rates at two symmetric outlets) generate asymmetric flow fields near the droplet, which results in the asymmetric breakup of the latter. Four typical breakup regimes(no breakup, one-side breakup, retraction breakup and direct breakup) have been observed.Two regime maps are plotted to describe the transition from one regime to another for the two types of different asymmetries, respectively. A power law model, which is based on the three critical factors(the capillary number,the asymmetry of flow fields and the initial volume ratio), is employed to predict the volume ratio of the two unequal daughter droplets generated in the direct breakup. The influences of capillary numbers and the asymmetries have been studied systematically in this paper. The larger the asymmetry is, the bigger the oneside breakup zone is. The larger the capillary number is, the more possible the breakup is in the direct breakup zone. When the radius of the initial droplet is 20 μm, the critical capillary numbers are 0.122, 0.128, 0.145,0.165, 0.192 and 0.226 for flow asymmetry factor AS= 0.05, 0.1, 0.2, 0.3, 0.4 and 0.5, respectively, in the flow system whose asymmetry is generated by location deviations. In the flow system whose asymmetry is generated by two different flow rates at two outlets, the critical capillary numbers are 0.121, 0.133, 0.145, 0.156 and 0.167 for AS= 1/21, 3/23, 1/5, 7/27 and 9/29, respectively.

Implementation and validation of a volume-of-fluid and discrete-element-method combined solver in OpenFOAM

Numerous gas-liquid-solid flows exist in chemical engineering and metallurgical processes. Numerical modeling is an important topic that can be used to improve the design and investigate the operating conditions of these processes. The complicated interphase interaction within such three-phase systems, which include free surfaces and discrete phases, poses challenges in the existing methods. We imple- mented a volume-of-fluid （VOF） and discrete-element-method （DEM） combined solver, which should be useful for modeling the gas-liquid-solid systems, within the OpenFOAM framework. The Du Plessis and Masliyah drag force, added mass force, and capillary force were considered for fluid-particle coupling. The VOF-DEM solver was tested in three different cases, namely, particles in pure gas, particle collision in water, and gas-liquid-solid three-phase dam break. The results were validated against previous experi- ments and good agreement was obtained between the simulations and the experiments, which indicates the accuracy and suitability of this VOF-DEM solver for gas-liquid-solid systems.

Numerical simulation on partial coalescence of a droplet with different impact velocities

Partial coalescence is a complicated flow phenomenon.In the present study,the coalescence process is simulated with the volume of fluid(VOF)method.The numerical results reveal that a downward high-velocity region plays a significant role in partial coalescence.The high-velocity region pulls the droplet downward continuously which is an important factor for the droplet turning into a prolate shape and the final pinch-off.The shift from partial coalescence to full coalescence is explained based on the droplet shape before the pinch-off.With the droplet impact velocity increasing,the droplet shape will get close to a sphere before the pinch-off.When the shape gets close enough to a sphere,the partial coalescence shifts to full coalescence.The effect of film thickness on the coalescence process is also investigated.With large film thickness,partial coalescence happens,while with small film thickness,full coalescence happens.In addition,the results indicate that the critical droplet impact velocity increases with the increase of surface tension coefficient but decreases with the increase of viscosity and initial droplet diameter.And there is a maximum critical Weber number with the increase of surface tension coefficient and initial droplet diameter.

Surface tension effects on the behaviour of a rising bubble driven by buoyancy force

In the inviscid and incompressible fluid flow regime,surface tension effects on the behaviour of an initially spherical buoyancy-driven bubble rising in an infinite and initially stationary liquid are investigated numerically by a volume of fluid （VOF） method. The ratio of the gas density to the liquid density is 0.001, which is close to the case of an air bubble rising in water. It is found by numerical experiment that there exist four critical Weber numbers We1,~We2,~We3 and We4, which distinguish five different kinds of bubble behaviours. It is also found that when 1≤We2, the bubble will finally reach a steady shape, and in this case after it rises acceleratedly for a moment, it will rise with an almost constant speed, and the lower the Weber number is, the higher the speed is. When We 〉We2, the bubble will not reach a steady shape, and in this case it will not rise with a constant speed. The mechanism of the above phenomena has been analysed theoretically and numerically.

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 on Interaction Between Two Bubbles Rising Side by Side in CMC Solution

A numerical simulation was performed to investigate the interaction of two bubbles rising side by side in shear-thinning fluid using volume of fluid （VOF） method coupled with continuous surface force （CSF） method. By considering rheological characteristics of fluid, this approach was able to accurately capture the deformation of bubble interface, and validated by comparing with the experimental results. The rising of bubble pairs with different configurations, including horizontal alignment and oblique alignment, was simulated by the method. The influences of the bubble initial distance and the bubble alignment were studied by analyzing the bubble deformation, rising paths and flow fields surrounding bubbles. The results indicate that within certam mltlal bubble spacing of S = 3.3 （S＊ = SI/D, SI initial distance between bubbles, and D bubble diameter）, the dynamic interaction between two bub- bles aligned horizontally shows repulsive effect that decreases with the increase of initial bubble spacing, but weakens to certain degree by the shear-thinning properties of fluid. However, the interaction between two bubbles aligned obliquely presents a repulsive effect for the small angle involved but an attractive impact for the large one, which is vet strengthened by the rheological characteristics of fluid.

Optimal Evacuation Scheme Based on Dam-Break Flood Numerical Simulation

The optimal evacuation scheme is studied based on the dam-break flood numerical simulation. A three- dimensional dam-break mathematical model combined with the volume of fluid （VOF） method is adopted. According to the hydraulic information obtained from numerical simulation and selecting principles of evacuation emergency scheme, evacuation route analysis model is proposed, which consists of the road right model and random degree model. The road right model is used to calculate the consumption time in roads, and the random degree model is used to judge whether the roads are blocked. Then the shortest evacuation route is obtained based on Dijstra algorithm. Gongming Reservoir located in Shenzhen is taken as a case to study. The results show that industrial area I is flooded at 2 500 s, and after 5 500 s, most of industrial area II is submerged. The Hushan, Loucun Forest and Chaishan are not flooded around industrial area I and II. Based on the above analysis, the optimal evacuation scheme is determined.

Research on theoretical and numerical methods of single bubble oscillation

A comparison of theoretical investigation and numerical simulation of a single bubble oscillation is carried out in this paper.The theoretical research is based on solving Rayleigh-Plesset(R-P)equation and Keller-Miksis(K-M)equation using Runge-Kutta method.The numerical method focuses on the two discrete methods in the volume of fluid(VOF)method,geometric reconstruction(GR)and modified high resolution interface capturing(MHRIC).The results show that the interface captured by MHRIC in the collapse stage is more stable,and the evolution of bubble radius agrees better with the theoretical solution.The R-P equation and K-M equation,which omit the effect of the energy equation,have limitations when the bubble collapses under ultra-high pressure.