Artículos de revistas: "Volume of Fluid (VOF)"

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KUMAR, BIPIN, MARTIN CRANE y YAN DELAURÉ. "ON THE VOLUME OF FLUID METHOD FOR MULTIPHASE FLUID FLOW SIMULATION". International Journal of Modeling, Simulation, and Scientific Computing 04, n.º 02 (junio de 2013): 1350002. http://dx.doi.org/10.1142/s1793962313500025.

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Numerical study of multiphase fluid flows require mathematical methods for distinguishing interface between two fluids. The volume of fluid (VOF) method is one of such method which takes care of fluid shape in a local domain and reconstructs the interface from volume fraction of one fluid. Maintaining sharp interface during reconstruction is a challenging task and geometrical approach of VOF method better suits for incompressible fluids. This paper provides a complete mathematical discussion of extended form of VOF method using a approach known as piecewise linear interface calculation (PLIC). An analytical relation between volume fraction and interface position has been explored with the help of primitive geometrical shapes. The method with this analytical relation has been applied to multiphase fluid flow benchmark problems and found to be in good agreement.

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Ramamurthy, A. S., Junying Qu y Diep Vo. "Volume of fluid model for an open channel flow problem". Canadian Journal of Civil Engineering 32, n.º 5 (1 de octubre de 2005): 996–1001. http://dx.doi.org/10.1139/l05-038.

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In the past, the solutions to open flow problems were generally found on the basis of experimental data or through the development of theoretical expressions using simplified assumptions. The volume of fluid (VOF) turbulence model can be applied to obtain the flow parameters such as pressure head distributions, velocity distributions, and water surface profiles for flow in open channels. The free overfall in a rectangular open channel that serves as a discharge measuring structure is selected to apply to the VOF model. The predictions of the proposed VOF model are validated using existing experimental data for both subcritical and supercritical flow approach conditions. Based on the path followed by a fluid particle leaving the brink section, the equations for the nappe profiles in supercritical flows are obtained in terms of the end depth. The VOF turbulence model developed is used to predict the characteristics of a free overfall in a rectangular open channel.Key words: turbulence model, VOF model, numerical simulation, overfall characteristics, open channel flow.

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Ii, Satoshi, Xiaobo Gong, Kazuyasu Sugiyama, Jinbiao Wu, Huaxiong Huang y Shu Takagi. "A Full Eulerian Fluid-Membrane Coupling Method with a Smoothed Volume-of-Fluid Approach". Communications in Computational Physics 12, n.º 2 (agosto de 2012): 544–76. http://dx.doi.org/10.4208/cicp.141210.110811s.

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AbstractA novel full Eulerian fluid-elastic membrane coupling method on the fixed Cartesian coordinate mesh is proposed within the framework of the volume-of-fluid approach. The present method is based on a full Eulerian fluid-(bulk) structure coupling solver (Sugiyama et al., J. Comput. Phys., 230 (2011) 596-627), with the bulk structure replaced by elastic membranes. In this study, a closed membrane is consid-ered, and it is described by a volume-of-fluid or volume-fraction information generally called VOF function. A smoothed indicator (or characteristic) function is introduced as a phase indicator which results in a smoothed VOF function. This smoothed VOF function uses a smoothed delta function, and it enables a membrane singular force to be incorporated into a mixture momentum equation. In order to deal with a membrane deformation on the Eulerian mesh, a deformation tensor is introduced and updated within a compactly supported region near the interface. Both the neo-Hookean and the Skalak models are employed in the numerical simulations. A smoothed (and less dissipative) interface capturing method is employed for the advection of the VOF function and the quantities defined on the membrane. The stability restriction due to membrane stiffness is relaxed by using a quasi-implicit approach. The present method is validated by using the spherical membrane deformation problems, and is applied to a pressure-driven flow with the biconcave membrane capsules (red blood cells).

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Rossano, Viola y Giuliano De Stefano. "Hybrid VOF–Lagrangian CFD Modeling of Droplet Aerobreakup". Applied Sciences 12, n.º 16 (19 de agosto de 2022): 8302. http://dx.doi.org/10.3390/app12168302.

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A hybrid VOF–Lagrangian method for simulating the aerodynamic breakup of liquid droplets induced by a traveling shock wave is proposed and tested. The droplet deformation and fragmentation, together with the subsequent mist development, are predicted by using a fully three-dimensional computational fluid dynamics model following the unsteady Reynolds-averaged Navier–Stokes approach. The main characteristics of the aerobreakup process under the shear-induced entrainment regime are effectively reproduced by employing the scale-adaptive simulation method for unsteady turbulent flows. The hybrid two-phase method combines the volume-of-fluid technique for tracking the transient gas–liquid interface on the finite volume grid and the discrete phase model for following the dynamics of the smallest liquid fragments. The proposed computational approach for fluids engineering applications is demonstrated by making a comparison with reference experiments and high-fidelity numerical simulations, achieving acceptably accurate results without being computationally expensive.

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Cheng, Hongping. "Application of Motion Interface Tracking CVOFLS Method to Zalesak Disk Problem". Highlights in Science, Engineering and Technology 35 (11 de abril de 2023): 105–8. http://dx.doi.org/10.54097/hset.v35i.7041.

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The interface curvature calculation is not accurate in VOF method and the interface mass is not conserved in Level Set method, A new interface tracking method CVOFLS is proposed (Coupled Volume of Fluid and Level Set method). This method combines the advantages of VOF and Level Set, The VOF and Level Set functions are simultaneously solved according to the fluid velocity, The interface obtained by the VOF function is used to correct the fluid quality, The Level Set function is used to calculate the interface norma, The Level Set function reinitialization process is omitted, Thus, the deficiencies of the two methods are overcome effectively. An example of interface tracking numerical simulation shows that, this method can guarantee high precision of free interface tracking and good mass conservation, and it can improve the calculation efficiency.

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Shang, Zhi, Jing Lou y Hongying Li. "Simulations of Flow Transitions in a Vertical Pipe Using Coupled Level Set and VOF Method". International Journal of Computational Methods 14, n.º 02 (22 de febrero de 2017): 1750013. http://dx.doi.org/10.1142/s021987621750013x.

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The level set (LS) and volume-of-fluid (VOF) methods are usually employed to simulate the two-phase flow. However every single method of them will face the mass conservative or accurate issues during the simulation. The coupled level set and volume-of-fluid (CLSVOF) method was not only able to conquer the shortages of the LS and VOF methods but also simultaneously keep the merits of both of the methods. In CLSVOF method the geometry reconstruction technology was employed to realize the coupling between LS and VOF. After the validation of single bubble rising cases, the CLSVOF method was used to simulate the complex transitional two-phase flows in a vertical pipe and the simulation results were compared to experiments.

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Ketabdari, M. J. y H. Saghi. "A Novel Algorithm of Advection Procedure in Volume of Fluid Method to Model Free Surface Flows". ISRN Applied Mathematics 2012 (3 de abril de 2012): 1–16. http://dx.doi.org/10.5402/2012/521012.

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In this study, the developed procedure of advection in volume of fluid (VOF) method is presented for free surface modeling. The fluid is assumed to be incompressible and viscous and therefore, Navier-Stokes and continuity are considered as governing equations. Applying Youngs’ algorithm in staggered grids, it is assumed that fluid particles in the cell have the same velocity of the cell faces. Therefore, fluxes to neighboring cells are estimated based on cell face velocities. However, these particles can show different velocities between two adjacent cell faces. In developed model, the velocity in mass center of fluid cell is evaluated to calculate fluxes from cell faces. The performance of the model is evaluated using some alternative schemes such as translation, rotation, shear test, and dam break test. These tests showed that the developed procedure improves the results when using coarse grids. Therefore, the Modified Youngs-VOF (MYV) method is suggested as a new VOF algorithm which models the free surface problems more accurately.

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Chen, Gujun, Qiangqiang Wang y Shengping He. "Assessment of an Eulerian multi-fluid VOF model for simulation of multiphase flow in an industrial Ruhrstahl–Heraeus degasser". Metallurgical Research & Technology 116, n.º 6 (2019): 617. http://dx.doi.org/10.1051/metal/2019049.

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An Eulerian multi-fluid VOF model, the coupling of the Eulerian model and the “VOF” interface tracking method, offered by ANSYS Fluent has been first applied to investigate the complex multiphase flow in an industrial Ruhrstahl–Heraeus (RH) degasser. The idea of this study is to use the Eulerian model in the regions of the domain where the argon bubbles are dispersed in molten steel; in the regions of the domain where the sharp interfaces between the steel and slag or argon are of interest, the “VOF” method is adopted. The calculated flow characteristic, mixing time and circulation flow rate of molten steel in the RH degasser agree well with the observations reported in literature. Compared with the widely accepted Eulerian method and the discrete phase model–volume of fluid (DPM–VOF) coupled method, the Eulerian multi-fluid VOF model demonstrates the suitability for modeling the multiphase flow in the RH degasser where both dispersed and sharp interfaces are present.

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Zhang, Zheng Fu, Jun Wei Wang y Feng Bao. "Numerical Simulation of the Nozzle with Self-Oscillating Flow Using the VOF Model". Advanced Materials Research 479-481 (febrero de 2012): 2380–82. http://dx.doi.org/10.4028/www.scientific.net/amr.479-481.2380.

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The jet water shape of the nozzle will become a self-oscillating shape, if the triangle and U shape models are made into the normal nozzle. Using the VOF model , the jet shape of the nozzle will be simulated through a commercial CFD software 'FLUENT'. The VOF model (Volume of Fluid) is a surface-tracking technique applied to a fixed Eulerian mesh. It is designed for two or more immiscible fluids where the position of the interface between the fluids is of interest. The CFD simulation results shows that the jet shape of the nozzle is oscillate in a fixed period.

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Qiu, Ruofan, Anlin Wang, Qiwei Gong y Tao Jiang. "Simulation of two-phase fluid mixture flow in rectangular two-inlet cavity using lattice Boltzmann method". International Journal of Modern Physics C 25, n.º 04 (6 de marzo de 2014): 1450004. http://dx.doi.org/10.1142/s0129183114500041.

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In this paper, two-phase fluid mixture flow in rectangular two-inlet cavity is studied using lattice Boltzmann method (LBM). To simulate two-phase fluids with large viscosity difference, the pseudo-potential model is improved. The improved model is verified for surface tension through Laplace's law and shown much better performance in simulating fluids with large viscosity difference than pseudo-potential model. The multiple-relaxation-time (MRT) scheme is used to enhance numerical stability. Then the two-phase fluid mixture flow with same and different viscosity in two-inlet cavity is simulated by present lattice Boltzmann (LB) model, pseudo-potential LB model and volume-of-fluid (VOF) method, respectively. The comparison of these numerical results shows that LB model is more suitable for such kind of flow than VOF method, since it can reflect repulsive forces and transitional region of two-phase fluids in dynamic process. Moreover, it also shows that present LB model has better dynamic stability than pseudo-potential model. Furthermore, simulations of the two-phase fluid mixture flow with different fluid viscosities, inlet velocities, inlet heights and outlet positions using present LB model are presented, exhibiting their effect to contact area of fluids.

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Louis-Napoléon, Aurélie, Muriel Gerbault, Thomas Bonometti, Cédric Thieulot, Roland Martin y Olivier Vanderhaeghe. "3-D numerical modelling of crustal polydiapirs with volume-of-fluid methods". Geophysical Journal International 222, n.º 1 (20 de marzo de 2020): 474–506. http://dx.doi.org/10.1093/gji/ggaa141.

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SUMMARY Gravitational instabilities exert a crucial role on the Earth dynamics and in particular on its differentiation. The Earth’s crust can be considered as a multilayered fluid with different densities and viscosities, which may become unstable in particular with variations in temperature. With the specific aim to quantify crustal scale polydiapiric instabilities, we test here two codes, JADIM and OpenFOAM, which use a volume-of-fluid (VOF) method without interface reconstruction, and compare them with the geodynamics community code ASPECT, which uses a tracking algorithm based on compositional fields. The VOF method is well-known to preserve strongly deforming interfaces. Both JADIM and OpenFOAM are first tested against documented two and three-layer Rayleigh–Taylor instability configurations in 2-D and 3-D. 2-D and 3-D results show diapiric growth rates that fit the analytical theory and are found to be slightly more accurate than those obtained with ASPECT. We subsequently compare the results from VOF simulations with previously published Rayleigh–Bénard analogue and numerical experiments. We show that the VOF method is a robust method adapted to the study of diapirism and convection in the Earth’s crust, although it is not computationally as fast as ASPECT. OpenFOAM is found to run faster than, and conserve mass as well as JADIM. Finally, we provide a preliminary application to the polydiapiric dynamics of the orogenic crust of Naxos Island (Greece) at about 16 Myr, and propose a two-stages scenario of convection and diapirism. The timing and dimensions of the modelled gravitational instabilities not only corroborate previous estimates of timing and dimensions associated to the dynamics of this hot crustal domain, but also bring preliminary insight on its rheological and tectonic contexts.

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Cui, Liying, Yingge Yang y Cuiping Ren. "Application of CVOFLS method in multi vortex shear flow field". Journal of Physics: Conference Series 2441, n.º 1 (1 de marzo de 2023): 012034. http://dx.doi.org/10.1088/1742-6596/2441/1/012034.

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Abstract Coupled Volume of Fluid and Level Set method inherits the advantages of VOF and Level Set methods, takes VOF function as the main body to simulate the fluid motion interface, and corrects the normal direction of the interface through Level Set function, so as to effectively overcome the shortcomings of the two methods. The numerical simulation example of multi vortex shear flow field shows that this method can ensure better simulation accuracy of moving interface and higher calculation efficiency.

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Kranjčević, Lado, Luka Grbčić, Matija Mrazović y Siniša Družeta. "Rijeka Bay 3D VOF Costal Flow Model". Journal of Maritime & Transportation Science 3, n.º 3 (junio de 2020): 125–32. http://dx.doi.org/10.18048/2020.00.09.

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3D multiphase flow was analyzed in the area of Rijeka bay in the Adriatic Sea. The necessary morphology data in the range of interest of the coastal bottom area were collected and the spatial surface was created. The functionality of the 3D model was studied in the large area of the realistic stochastic structure of the bottom and the shore. The probability of meteorological conditions and wind impact in the model has been shown. The obtained results give a detailed view of the velocity fields in the horizontal plane of different depths. Numerical simulation was performed in open source program OpenFOAM with Volume of Fluid (VOF) method using the Eulerian approach. For solving this problem interFOAM solver for two incompressible, isothermal, immiscible fluids was used. The resulting simulations showed dominant flow from the western coast of the Krk island to the eastern coast of the Istrian peninsula. Seawater enters the bay through the Srednja Vrata and Tihi Kanal and exits the bay through the Vela Vrata. This research has shown that using a VOF method can be successfully implemented for describing fluid motion in large areas such as bays and oceans.

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Peng, Jian Jun, Yan Jun Liu, Yu Li y Xing Wang Sun. "Simulation of Numerical Wave Based on Fluid Volume Function". Advanced Materials Research 614-615 (diciembre de 2012): 541–45. http://dx.doi.org/10.4028/www.scientific.net/amr.614-615.541.

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This paper is based on the method of volume of fluid function (VOF) and founds numerical wave tank similar to real sea condition using business software CFD and its function of second development, proceeds numerical simulation of linear wave and second-order stokes and compares them with the theoretical value. The numerical result corresponds to the theoretical result, which lays the foundation for further research of interaction between wave and power generation device.

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Kumar, S. Senthil y Y. M. C. Delauré. "An Assessment of Suitability of a SIMPLE VOF/PLIC-CSF Multiphase Flow Model for Rising Bubble Dynamics". Journal of Computational Multiphase Flows 4, n.º 1 (marzo de 2012): 65–83. http://dx.doi.org/10.1260/1757-482x.4.1.65.

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A Volume of Fluid (VOF) – Youngs' model for the solution of an incompressible immiscible two-phase flows is presented. The solver computes the flow field by solving the family of Navier Stokes equations on a fixed (Eulerian) Staggered Cartesian grid using the Finite Volume formulation of Semi-Implicit Pressure Linked Equation (SIMPLE) method and tracks the position of interface between two fluids with different fluid properties by Piecewise Linear Interface Construction (PLIC) Method. The suitability of the SIMPLE type implementation is assessed by investigating the dynamics of free rising bubbles for different fluid properties and flow parameters. The results obtained with the present numerical method for rising bubbles in viscous liquids are compared with reported numerical and experimental results.

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Fayed, Hassan, Mustafa Bukhari y Saad Ragab. "Large-Eddy Simulation of a Hydrocyclone with an Air Core Using Two-Fluid and Volume-of-Fluid Models". Fluids 6, n.º 10 (14 de octubre de 2021): 364. http://dx.doi.org/10.3390/fluids6100364.

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Large-eddy simulations have been conducted for two-phase flow (water and air) in a hydrocyclone using Two-Fluid (Euler–Euler) and Volume-of-Fluid (VOF) models. Subgrid stresses are modeled using a dynamic eddy–viscosity model, and results are compared to those using the Smagorinsky model. The effects of grid resolutions on the mean flow and turbulence statistics have been thoroughly investigated. Five block-structured grids of 0.72, 1.47, 2.4, 3.81, and 7.38 million elements have been used for the simulations of Hsieh’s 75 mm hydrocyclone Mean velocity profiles and normal Reynolds stresses have been compared with experimental data. Results of the two-fluid model are in good agreement with those of the VOF model. A fine mesh in the axial and radial directions is necessary for capturing the turbulent vortical structure. Turbulence structures in the hydrocyclone are dominated by helical vortices around the air core. Energy spectra are analyzed at different points in the hydrocyclone, and regions of low turbulent kinetic energy are identified and attributed to stabilizing effects of the swirling velocity component.

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Fayed, Hassan, Mustafa Bukhari y Saad Ragab. "Large-Eddy Simulation of a Hydrocyclone with an Air Core Using Two-Fluid and Volume-of-Fluid Models". Fluids 6, n.º 10 (14 de octubre de 2021): 364. http://dx.doi.org/10.3390/fluids6100364.

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Large-eddy simulations have been conducted for two-phase flow (water and air) in a hydrocyclone using Two-Fluid (Euler–Euler) and Volume-of-Fluid (VOF) models. Subgrid stresses are modeled using a dynamic eddy–viscosity model, and results are compared to those using the Smagorinsky model. The effects of grid resolutions on the mean flow and turbulence statistics have been thoroughly investigated. Five block-structured grids of 0.72, 1.47, 2.4, 3.81, and 7.38 million elements have been used for the simulations of Hsieh’s 75 mm hydrocyclone Mean velocity profiles and normal Reynolds stresses have been compared with experimental data. Results of the two-fluid model are in good agreement with those of the VOF model. A fine mesh in the axial and radial directions is necessary for capturing the turbulent vortical structure. Turbulence structures in the hydrocyclone are dominated by helical vortices around the air core. Energy spectra are analyzed at different points in the hydrocyclone, and regions of low turbulent kinetic energy are identified and attributed to stabilizing effects of the swirling velocity component.

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Wang, Jiantao, Gang Liu, Xiong Jiang y Bin Mou. "ρ-VOF: An interface sharpening method for gas–liquid flow simulation". Modern Physics Letters B 32, n.º 12n13 (10 de mayo de 2018): 1840017. http://dx.doi.org/10.1142/s0217984918400171.

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The study on simulation of compressible gas–liquid flow remains open. Popular methods are either confined to incompressible flow regime, or inevitably induce smear of the free interface. A new finite volume method for compressible two-phase flow simulation is contributed for this subject. First, the “heterogeneous equilibrium” assumption is introduced to the control volume, by hiring free interface reconstruction technology, the distribution of each component in the control volume is achieved. Next, AUSM[Formula: see text]-up (advection upstream splitting method) scheme is employed to calculate the convective fluxes and pressure fluxes, with the contact discontinuity characteristic considered, followed by the update of the whole flow field. The new method features on density-based pattern and interface reconstruction technology from VOF (volume of fluid), thus we name it “[Formula: see text]-VOF method”. Inherited from AUSM families and VOF, [Formula: see text]-VOF behaves as an all-speed method, capable of simulating shock in gas–liquid flow, and preserving the sharpness of the free interface. Gas–liquid shock tube is simulated to evaluate the method, from which good agreement is obtained between the predicted results and those of the cited literature, meanwhile, sharper free interface is identified. Finally, the capability and validity of [Formula: see text]-VOF method can be concluded in compressible gas–liquid flow simulation.

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Tomescu, S. y I. O. Bucur. "Numerical Investigation of Oil Gas Separation with the Use of VOF CFD". Engineering, Technology & Applied Science Research 11, n.º 6 (11 de diciembre de 2021): 7841–45. http://dx.doi.org/10.48084/etasr.4446.

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In this research paper, a numerical study regarding gas-oil separation is presented. Employing the geometry of a classic separator used by the NRDI for Gas Turbines COMOTI and a Computer-Aided Design (CAD) software, the computational domain was defined. To perform the Computational Fluid Dynamics (CFD) investigation, the mesh was created with the ANSYS Meshing tool, and the ANSYS CFX was employed as a solver. The computational domain was split into 5 subdomains, 3 were fluid and 2 were defined as porous media. The volume porosity, loss model, and permeability were set up. In terms of turbulence flow, the standard k–ε model was adopted. The results of the numerical calculations in terms of oil volume fraction and streamline profiles were used to analyze the separator configuration. The results show that the numerical investigation with the VOF (Volume of Fluid Method) - CFD model is capable of analyzing the performance of a two-phase separator equipped with two demisters-porous media.

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von Boetticher, Albrecht, Jens M. Turowski, Brian W. McArdell, Dieter Rickenmann y James W. Kirchner. "DebrisInterMixing-2.3: a finite volume solver for three-dimensional debris-flow simulations with two calibration parameters – Part 1: Model description". Geoscientific Model Development 9, n.º 9 (31 de agosto de 2016): 2909–23. http://dx.doi.org/10.5194/gmd-9-2909-2016.

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Abstract. Here, we present a three-dimensional fluid dynamic solver that simulates debris flows as a mixture of two fluids (a Coulomb viscoplastic model of the gravel mixed with a Herschel–Bulkley representation of the fine material suspension) in combination with an additional unmixed phase representing the air and the free surface. We link all rheological parameters to the material composition, i.e., to water content, clay content, and mineral composition, content of sand and gravel, and the gravel's friction angle; the user must specify only two free model parameters. The volume-of-fluid (VoF) approach is used to combine the mixed phase and the air phase into a single cell-averaged Navier–Stokes equation for incompressible flow, based on code adapted from standard solvers of the open-source CFD software OpenFOAM. This effectively single-phase mixture VoF method saves computational costs compared to the more sophisticated drag-force-based multiphase models. Thus, complex three-dimensional flow structures can be simulated while accounting for the pressure- and shear-rate-dependent rheology.

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Yahyaee, Ali, Amir Sajjad Bahman y Henrik Sørensen. "A Benchmark Evaluation of the isoAdvection Interface Description Method for Thermally–Driven Phase Change Simulation". Nanomaterials 12, n.º 10 (13 de mayo de 2022): 1665. http://dx.doi.org/10.3390/nano12101665.

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A benchmark study is conducted using isoAdvection as the interface description method. In different studies for the simulation of the thermal phase change of nanofluids, the Volume of Fluid (VOF) method is a contemporary standard to locate the interface position. One of the main drawbacks of VOF is the smearing of the interface, leading to the generation of spurious flows. To solve this problem, the VOF method can be supplemented with a recently introduced geometric method called isoAdvection. We study four benchmark cases that show how isoAdvection affects the simulation results and expose its relative strengths and weaknesses in different scenarios. Comparisons are made with VOF employing the Multidimensional Universal Limiter for Explicit Solution (MULES) limiter and analytical data and experimental correlations. The impact of nanoparticles on the base fluid are considered using empirical equations from the literature. The benchmark cases are 1D and 2D boiling and condensation problems. Their results show that isoAdvection (with isoAlpha reconstruct scheme) delivers a faster solution than MULES while maintaining nearly the same accuracy and convergence rate in the majority of thermal phase change scenarios.

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Zou, Qingping, Zhong Peng y Pengzhi Lin. "EFFECTS OF WAVE BREAKING AND BEACH SLOPE ON TOE SCOUR IN FRONT OF A VERTICAL SEAWALL". Coastal Engineering Proceedings 1, n.º 33 (28 de diciembre de 2012): 122. http://dx.doi.org/10.9753/icce.v33.sediment.122.

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Scour in front of coastal structures is a major threat to structural stability and safety of properties behind. In this study, a Reynolds Averaged Navier-Stokes Solver (RANS) is combined with a Volume of Fluid (VOF) (RANS-VOF) surface capturing scheme to investigate the wave interactions with a Seawall and its adjacent sea bed. The main objective is to investigate the effects of wave breaking and beach slope on toe scour in front of a vertical wall.

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Qi, Fengsheng, Shuqi Zhou, Liangyu Zhang, Zhongqiu Liu, Sherman C. P. Cheung y Baokuan Li. "Numerical Study on Interfacial Structure and Mixing Characteristics in Converter Based on CLSVOF Method". Metals 13, n.º 5 (2 de mayo de 2023): 880. http://dx.doi.org/10.3390/met13050880.

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The blowing flow is a key factor in molten bath stirring to affects the steel-bath interface fluctuation and chemical reaction in the top-bottom-blowing converter. The Volume of Fluid (VOF) method is widely used to capture the gas-liquid interface. However, some limitations exist in dealing with the interface curvature and normal vectors of the complex deformed slag-bath interface. The Coupled Level-Set and Volume of Fluid (CLSVOF) method uses the VOF function to achieve mass conservation and capture interface smoothly by computing the curvature and normal vector using the Level-Set function to overcome the limitations in the VOF model. In the present work, a three-dimensional (3D) transient mathematical model coupled CLSVOF method has been developed to analyze the mixing process under different injection flow rates and bottom-blowing positions. The results show that when the bottom-blowing flow rate increases from 0.252 kg/s to 0.379 kg/s, the mixing time in the molten bath gradually decreases from 74 s to 66 s. When the bottom-blowing flow rate is 0.252 kg/s, it is recommended to distribute the outer bottom-blowing position on concentric circles with Dtuy,2/D2 = 0.33.

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Kolařík, Filip y Bořek Patzák. "IMPLEMENTATION OF 3D VOF TRACKING ALGORITHM BASED ON BINARY SPACE-PARTITIONING". Acta Polytechnica 57, n.º 2 (2 de mayo de 2017): 105. http://dx.doi.org/10.14311/ap.2017.57.0105.

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The paper focuses on modelling free surface flow. The interface is modelled using the Volume-Of-Fluid method, where the advection of volume fractions is treated by a purely geometrical method. The novelty of the work lies in the way that it incorporates Binary Space-Partitioning trees for computing the intersections of polyhedra. Volume-conserving properties and shape-preserving properties are presented on two benchmarks and on a simulation of the famous broken dam problem.

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Okagaki, Yuria, Taisuke Yonomoto, Masahiro Ishigaki y Yoshiyasu Hirose. "Numerical Study on an Interface Compression Method for the Volume of Fluid Approach". Fluids 6, n.º 2 (10 de febrero de 2021): 80. http://dx.doi.org/10.3390/fluids6020080.

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Many thermohydraulic issues about the safety of light water reactors are related to complicated two-phase flow phenomena. In these phenomena, computational fluid dynamics (CFD) analysis using the volume of fluid (VOF) method causes numerical diffusion generated by the first-order upwind scheme used in the convection term of the volume fraction equation. Thus, in this study, we focused on an interface compression (IC) method for such a VOF approach; this technique prevents numerical diffusion issues and maintains boundedness and conservation with negative diffusion. First, on a sufficiently high mesh resolution and without the IC method, the validation process was considered by comparing the amplitude growth of the interfacial wave between a two-dimensional gas sheet and a quiescent liquid using the linear theory. The disturbance growth rates were consistent with the linear theory, and the validation process was considered appropriate. Then, this validation process confirmed the effects of the IC method on numerical diffusion, and we derived the optimum value of the IC coefficient, which is the parameter that controls the numerical diffusion.

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Bahadar, Ali. "Volume of Fluid Computations of Gas Entrainment and Void Fraction for Plunging Liquid Jets to Aerate Wastewater". ChemEngineering 4, n.º 4 (18 de octubre de 2020): 56. http://dx.doi.org/10.3390/chemengineering4040056.

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Among various mechanisms for enhancing the interfacial area between gases and liquids, a vertical liquid jet striking a still liquid is considered an effective method. This method has vast industrial and environmental applications, where a significant application of this method is to aerate industrial effluents and wastewater treatment. Despite the huge interest and experimental and numerical efforts made by the academic and scientific community in this topic, there is still a need of further study to realize improved theoretical and computational schemes to narrow the gap between the measured and the computed entrained air. The present study is a numerical attempt to highlight the air being entrained by water jet when it intrudes into a still water surface in a tank by the application of a Volume of Fluid (VOF) scheme. The VOF scheme, along with a piecewise linear interface construction (PLIC) algorithm, is useful to follow the interface of the air and water bubbly plume and thus can provide an estimate of the volume fraction for the gas and the liquid. Dimensionless scaling derived from the Fronde number and Reynolds number along with geometric similarities due to the liquid jet’s length and nozzle diameter have been incorporated to validate the experimental data on air entrainment, penetration and void fraction. The VOF simulations for void fraction and air-water mixing and air jet’s penetration into the water were found more comparable to the measured values than those obtained using empirical and Euler-Euler methods. Although, small overestimates of air entrainment rate compared to the experiments have been found, however, VOF was found effective in reducing the gap between measurements and simulations.

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27

Palomino Solis, Daniel Angel y Federico Piscaglia. "Toward the Simulation of Flashing Cryogenic Liquids by a Fully Compressible Volume of Fluid Solver". Fluids 7, n.º 9 (30 de agosto de 2022): 289. http://dx.doi.org/10.3390/fluids7090289.

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We present a fully compressible single-fluid volume of fluid (VOF) solver with phase change for high-speed flows, where the atomization of the liquid can occur either by the aerodynamics or by the effect of the local pressure. The VOF approximation among a non-miscible phase (non-condensable gas) and a mixture of two fluids (liquid and vapor) represents the liquid core of the jet and its atomization. A barotropic model is used in combination with the equation of state (EoS) to link the mixture density to pressure and temperature. The solver is written with the aim to simulate high-pressure injection in gas–liquid systems, where the pressure of the liquid is great enough to cause significant compression of the surrounding gas. Being designed in an C++ object-oriented fashion, the solver is able to support any kind of EoS; the aim is to apply it to the simulation of the injection of liquid propellant in rocket engines. The present work includes the base development; a verification assessment of the code is provided by the solution of a set of numerical experiments to prove the boundedness, convergence and accuracy of the method. Experimental measurements of a cavitating microscopic in-nozzle flow, available in the literature, are finally used for a first validation with phase change.

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28

Liovic, Petar, Jong-Leng Liow y Murray Rudman. "A Volume of Fluid (VOF) Method for the Simulation of Metallurgical Flows". ISIJ International 41, n.º 3 (2001): 225–33. http://dx.doi.org/10.2355/isijinternational.41.225.

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29

Karimi-Sibaki, E., A. Kharicha, A. Vakhrushev, M. Wu, A. Ludwig y J. Bohacek. "A volume of fluid (VOF) method to model shape change during electrodeposition". Electrochemistry Communications 112 (marzo de 2020): 106675. http://dx.doi.org/10.1016/j.elecom.2020.106675.

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30

Li, Xiao-wei y Jun-fei Fan. "A stencil-like volume of fluid (VOF) method for tracking free interface". Applied Mathematics and Mechanics 29, n.º 7 (julio de 2008): 881–88. http://dx.doi.org/10.1007/s10483-008-0706-7.

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31

Kabdylkakov, Y. A. y A. S. Suraev. "APPLICATION OF THE VOLUME OF FLUID METHOD TO SIMULATE THE PROCESS OF MELTING AND MOVEMENT OF FUEL". NNC RK Bulletin, n.º 3 (7 de enero de 2022): 3–8. http://dx.doi.org/10.52676/1729-7885-2021-3-3-8.

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The article considers the possibility of using the method of multiphase fluid Volume of Fluid (VOF), the Ansys Fluent program, for numerical simulation of the melting process of the materials of the experimental device and their movement over the volume of the computational domain. For modeling the design of a typical experimental device tested in the reactor was selected, a two-dimensional computational model was developed, methods for solving the thermal problem were described, and the simulation results were presented.

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32

Taamneh, Yazan. "Influence of Jordanian zeolite on the performance of a solar still: experiments and CFD simulation studies". Water Supply 16, n.º 6 (2 de junio de 2016): 1700–1709. http://dx.doi.org/10.2166/ws.2016.091.

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Computational fluid dynamics (CFD) simulations were performed for experiments carried out with two identical pyramid-shaped solar stills. One was filled with Jordanian zeolite-seawater and the second was filled with seawater only. This work is focused on CFD analysis validation with experimental data conducted using a model of phase change interaction (evaporation-condensation model) inside the solar still. A volume-of-fluid (VOF) model was used to simulate the inter phase change through evaporation-condensation between zeolite-water and water vapor inside the two solar stills. The effect of the volume fraction of the zeolite particles (0 ≤ ϕ ≤ 0.05) on the heat and distillate yield inside the solar still was investigated. Based on the CFD simulation results, the hourly quantity of freshwater showed a good agreement with the corresponding experimental data. The present study has established the utility of using the VOF two phase flow model to provide a reasonable solution to the complicated inter phase mass transfer in a solar still.

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33

Adeniyi, A. A., H. P. Morvan y K. A. Simmons. "A coupled Euler-Lagrange CFD modelling of droplets-to-film". Aeronautical Journal 121, n.º 1246 (13 de octubre de 2017): 1897–918. http://dx.doi.org/10.1017/aer.2017.107.

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ABSTRACTIn this paper, a droplet to film interaction model technique is presented. In the proposed approach, the liquid and gas continua are modelled using an enhanced Volume-of-Fluid (VoF) technique while the droplets are tracked using a Lagrangian framework and are coupled to the Eulerian phases using source terms. The eventual target application is an aeroengine bearing chamber in which oil is found as droplets, shed from the bearings, splashing on impact, separated from wall surfaces at obstacles or simply re-entrained, and as a continuum oil film coating the bearing chamber outer walls which it also cools. In finite volume Computational Fluid Dynamics (CFD) techniques, a prohibitively large number of cells would be required to describe the details of the droplet impact phenomenon. Based on published correlations, the splashing droplets are created and tracked as Lagrangian particles. The flowing film and the gas continua are handled with an enhanced VoF technique.

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34

Bujor, Alexandra Madalina, Andreea Mandru y Florin Pacuraru. "Numerical simulation of the flow around kayak hull". Analele Universităţii "Dunărea de Jos" din Galaţi Fascicula XI Construcţii navale/ Annals of "Dunărea de Jos" of Galati Fascicle XI Shipbuilding 45 (3 de diciembre de 2022): 113–18. http://dx.doi.org/10.35219/annugalshipbuilding/2022.45.13.

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The purpose of this study was to determine the total resistance and investigate the flow around a full-scale kayak. Utilizing Computational Fluid Dynamics(CFD), it was deter-mined how the presence of a rudder affects the kayak hydrodynamic performance. To an-alyse the flow, computational fluid dynamics based on the RANS-VOF solver was em-ployed. The fluid volume approach and the k-ω turbulence model were used in two-phase steady flow simulations around the kayak hulls.

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35

Wei, W. L., X. J. Zhao y Y. L. Liu. "Simulation of of 3D Flood Waves by Gas-Liquid Two-Phase Model". Applied Mechanics and Materials 256-259 (diciembre de 2012): 2621–24. http://dx.doi.org/10.4028/www.scientific.net/amm.256-259.2621.

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This paper is concerned with a gas-liquid two-phase model combining with the k–ε turbulent model for numerical simulation of 3D flood waves due to complete or partial dam-break. The flow equations are solved with the finite volume method and solved by the pressure-correction algorithm of the SIMPLE-type. The free fluid surface is simulated by the the volume of fluid(VOF) method. The comparisons with other numerical results show that the proposed method is accurate, reliable and effective in simulation of dam-break flood waves.

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Viswanathan, Kumaran, Manu y Subba Rao. "Hydrodynamic performances of a wall type breakwater - a physical and numerical approach". Journal of Naval Architecture and Marine Engineering 18, n.º 2 (31 de diciembre de 2021): 141–54. http://dx.doi.org/10.3329/jname.v18i2.52134.

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In this paper, hydrodynamic characteristics of caisson type breakwater are investigated through physical model approach and a numerical model based on the Volume of Fluid (VOF) is validated. The investigations are carried out for varying wave characteristics and depth of water 0.50 m. In an experimental study, to understand the model and scale effects for the desired wave conditions is a critical task in all-time conditions. So, it is also necessary to develop an appropriate numerical model to understand the hydrodynamics of the selected test model. Using the Volume of Fluid (VOF) method and incompressible open channel fluid flow a 2D numerical wave flume is developed using ANSYS- Fluent platform. The wave boundary conditions are adopted by solving the Reynolds-Averaged Navier Stokes equations (RANS equation) and especially with k—ε model to examine the effects of turbulence on the numerical results. The wave forces, wave runup, and wave reflection characteristics on the test model are measured for different wave characteristics, and results obtained from the numerical investigations are comparable with the experimental results to evident the relevance of the developed numerical model.

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37

Missios, Konstantinos, Niels Jacobsen, Kasper Moeller y Johan Roenby. "Extending the isoAdvector Geometric VOF Method to Flows in Porous Media". OpenFOAM® Journal 3 (20 de mayo de 2023): 66–74. http://dx.doi.org/10.51560/ofj.v3.72.

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We consider the interfacial flow in and around porous structures in coastal and marine engineering.* During recent years, interfacial flow through porous media has been repeatedly simulated with Computational Fluid Dynamics (CFD) based on algebraic Volume Of Fluid (VOF) methods [1] [2]. Here, we present an implementation of a porous medium interfacial flow solver based on the geometric VOF method, isoAdvector [3] [4]. In our implementation, the porous medium is treated without resolving the actual pore geometry. Rather, the porous media, pores, and rigid structure are considered a continuum and the effects of porosity on the fluid flow are modelled through source terms in the Navier-Stokes equations, including Darcy-Forchheimer forces, added mass force and accounting for the part of mesh cells that are occupied by the solid material comprising the skeleton of the porous medium. The governing equations are adopted from the formulation by Jensen et al. [1]. For the interface advection using isoAdvector, we also account for the reduced cell volume available for fluid flow and for the increase in the interface front velocity caused by a cell being partially filled with solid material. The solver is implemented in the open source CFD library OpenFOAM®. It is validated using two case setups: 1) A pure passive advection test case to compare the isolated advection algorithm against a known analytical solution and 2) a porous dam break case by Liu et al. [5] where both numerical and experimental results are available for comparison. We find good agreement with numerical and experimental results. For both cases the interface sharpness, shape conservation as well as volume conservation and boundedness are demonstrated to be very good. The solver is released as open source for the benefit of the coastal and marine CFD community (code repository https://github.com/InterFlowers/porousInterIsoFoam) and as of OpenFOAM-v2112 the new functionality is integrated in the official interIsoFoam solver. * This article is an updated version of the conference paper Missios et al. 2022 [6] presented at the Marine2021 conference.

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38

Han, Shuang, Runhua Yang, Chaobo Li y Lixin Yang. "The Wettability and Numerical Model of Different Silicon Microstructural Surfaces". Applied Sciences 9, n.º 3 (8 de febrero de 2019): 566. http://dx.doi.org/10.3390/app9030566.

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Wettability is an important property of solid surfaces and is widely used in many industries. In this work, seven silicon microstructure surfaces were made by plasma immersion ion implantation (PIII) technology. The experimental contact angles and theoretical contact angles of various surfaces were compared, which indicated that the classical theory had great limitations in predicting the static contact angles of complex structures. A parameterized microstructure surface was established by computational fluid dynamics (CFD) with a volume-of-fluid (VOF) model to analyze the reasons for the differences between experimental and theoretical contact angles. Comparing the results of experiments and simulations, it was found that the VOF model can simulate the contact angle of these surfaces very well. The geometrical models of the different microstructures were simplified, and waveforms of the surfaces were obtained.

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39

Gao, Shian y Chimaobi Dennar. "Computational Simulation of Multi-Product Flow in an Oil Transportation Pipeline". Applied Mechanics and Materials 590 (junio de 2014): 161–65. http://dx.doi.org/10.4028/www.scientific.net/amm.590.161.

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This paper presents a predictive investigation using Computational Fluid Dynamic (CFD) techniques focusing on the study of contamination that occurs between different products in an oil pipeline under normal operating conditions. The use of CFD techniques yields detailed flow conditions including the velocity fields, phase distribution and interface evolution, which can provide valuable information to the oil industry especially in the distribution of oil products. The Volume of Fluid (VOF) model is used in this project in a pipe with two fluids. Simulation results show the interface evolution between the two fluids and how it is affected by properties such as viscosity ratio and pressure difference. Operational data from the Nigerian National Petroleum Corporation was obtained to validate the results from the simulations.

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40

Faroux, Dorian, Kimiaki Washino, Takuya Tsuji y Toshitsugu Tanaka. "Coupling non-local rheology and volume of fluid (VOF) method: a finite volume method (FVM) implementation". EPJ Web of Conferences 249 (2021): 03025. http://dx.doi.org/10.1051/epjconf/202124903025.

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Additional to a behavior switching between solid-like and liquid-like, dense granular flows also present propagating grain size-dependent effects also called non-local effects. Such behaviors cannot be efficiently modeled by standard rheologies such as µ(I)-rheology but have to be dealt with advanced non-local models. Unfortunately, these models are still new and cannot be used easily nor be used for various configurations. We propose in this work a FVM implementation of the recently popular NGF model coupled with the VOF method in order to both make non-local modeling more accessible to everyone and suitable not only for single-phase flows but also for two-phase flows. The proposed implementation has the advantage to be extremely straightforward and to only require a supplementary stabilization loop compared to the theoretical equations. We then applied our new framework to both single and two-phase flows for validation.

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41

El Baamrani, Hayat, Lahcen Bammou, Ahmed Aharoune y Abdallah Boukhris. "Volume of Fluid (VOF) Modeling of Liquid Film Evaporation in Mixed Convection Flow through a Vertical Channel". Mathematical Problems in Engineering 2021 (23 de mayo de 2021): 1–12. http://dx.doi.org/10.1155/2021/9934593.

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In this paper, the volume of fluid (VOF) method in the OpenFOAM open-source computational fluid dynamics (CFD) package is used to investigate the coupled heat and mass transfer by mixed convection during the evaporation of water-thin film. The liquid film is falling down on the left wall of a vertical channel and is subjected to a uniform heat flux density, whereas the right wall is assumed to be insulated and dry. The gas mixture consists of air and water vapor. The governing equations in the liquid and in the gas areas with the boundary conditions are solved by using the finite volume method. The results which include temperature, velocity, and vapor mass fraction are presented. The effect of heat flux density, liquid inlet temperature, and mass flow rate on the heat and mass transfer are also analyzed. Better liquid film evaporation is noted for the system with a higher heat flux density and inlet liquid temperature or a lower mass flow rate. Therefore, the VOF method describes well the thermal and dynamic behavior during the evaporation of the liquid film.

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42

Oomar, Muhammad Y., Arnaud G. Malan, Roy A. D. Horwitz, Bevan W. S. Jones y Genevieve S. Langdon. "An All-Mach Number HLLC-Based Scheme for Multi-Phase Flow with Surface Tension". Applied Sciences 11, n.º 8 (10 de abril de 2021): 3413. http://dx.doi.org/10.3390/app11083413.

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This paper presents an all-Mach method for two-phase inviscid flow in the presence of surface tension. A modified version of the Hartens–Lax–van Leer Contact (HLLC) solver is developed and combined for the first time with a widely used volume-of-fluid (VoF) method: the compressive interface capturing scheme for arbitrary meshes (CICSAM). This novel combination yields a scheme with both HLLC shock capturing as well as accurate liquid–gas interface tracking characteristics. It is achieved by reconstructing non-conservative (primitive) variables in a consistent manner to yield both robustness and accuracy. Liquid–gas interface curvature is computed via height functions and the convolution method. We emphasize the use of VoF in the interest of interface accuracy when modelling surface tension effects. The method is validated using a range of test-cases available in the literature. The results show flow features that are in sensible agreement with previous experimental and numerical work. In particular, the use of the HLLC-VoF combination leads to a sharp volume fraction and energy field with improved accuracy.

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43

Garoosi, Faroogh y Kamel Hooman. "Numerical simulation of multiphase flows using an enhanced Volume-of-Fluid (VOF) method". International Journal of Mechanical Sciences 215 (febrero de 2022): 106956. http://dx.doi.org/10.1016/j.ijmecsci.2021.106956.

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44

Passandideh-Fard, Mohammad y Ehsan Roohi. "Transient simulations of cavitating flows using a modified volume-of-fluid (VOF) technique". International Journal of Computational Fluid Dynamics 22, n.º 1-2 (enero de 2008): 97–114. http://dx.doi.org/10.1080/10618560701733657.

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45

Srinivasan, Vedanth, Abraham J. Salazar y Kozo Saito. "Modeling the disintegration of modulated liquid jets using volume-of-fluid (VOF) methodology". Applied Mathematical Modelling 35, n.º 8 (agosto de 2011): 3710–30. http://dx.doi.org/10.1016/j.apm.2011.01.040.

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46

Nguyen, Van-Tu y Warn-Gyu Park. "A volume-of-fluid (VOF) interface-sharpening method for two-phase incompressible flows". Computers & Fluids 152 (julio de 2017): 104–19. http://dx.doi.org/10.1016/j.compfluid.2017.04.018.

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47

von Boetticher, A., J. M. Turowski, B. W. McArdell, D. Rickenmann y J. W. Kirchner. "DebrisInterMixing-2.3: a Finite Volume solver for three dimensional debris flow simulations based on a single calibration parameter – Part 1: Model description". Geoscientific Model Development Discussions 8, n.º 8 (13 de agosto de 2015): 6349–78. http://dx.doi.org/10.5194/gmdd-8-6349-2015.

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Abstract. Here we present a three-dimensional fluid dynamic solver that simulates debris flows as a mixture of two phases (gravel and fine material suspension) with a third unmixed phase representing the air and the free surface. We link all rheological parameters to the material composition, i.e., to water content, clay content and mineral composition, content of sand and gravel, and the gravel's friction angle; the user must specify only a single free model parameter. The Volume-Of-Fluid (VOF) approach is used to combine the three phases into a single cell-averaged Navier–Stokes equation for incompressible flow, based on code adapted from standard solvers of the Open-Source CFD software OpenFOAM. We present a stable implementation of a Coulomb-Viscoplastic model that represents the pressure-dependent flow behavior of the granular phase, and a Herschel–Bulkley representation of the interstitial fluid. The VOF method saves computational costs compared to drag-force based multiphase models. Thus depth-averaging is not necessary and complex three-dimensional flow structures can be simulated.

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48

Cukrov, Alen, Yohei Sato, Ivanka Boras y Bojan Ničeno. "A SOLUTION TO STEFAN PROBLEM USING EULERIAN TWO FLUID VOF MODEL". Brodogradnja 72, n.º 4 (1 de octubre de 2021): 141–64. http://dx.doi.org/10.21278/brod72408.

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A novel approach for the solution of Stefan problem within the framework of the multi fluid model supplemented with Volume of Fluid (VOF) method, i.e. two-fluid VOF, is presented in this paper. The governing equation set is comprised of mass, momentum and energy conservation equations, written on a per phase basis and supplemented with closure models via the source terms. In our method, the heat and mass transfer is calculated from the heat transfer coefficient, which has a fictitious function and depends on the local cell size and the thermal conductivity, and the implementation is straightforward because of the usage of the local value instead of a global parameter. The interface sharpness is ensured by the application of the geometrical reconstruction scheme implemented in VOF. The model is verified for three types of computational meshes including triangular cells, and good agreement was obtained for the interface position and the temperature field. Although the developed method was validated only for Stefan problem, the application of the method to engineering problems is considered to be straightforward since it is implemented to a commercial CFD code only using a local value; especially in the field of naval hydrodynamics wherein the reduction of ship resistance using boiling flow can be computed efficiently since the method handles phase change processes using low resolution meshes.

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49

Zhang, Wei, You Hong Tang, Cheng Bi Zhao y Cheng Zhang. "A Two-Phase Flow Model with VOF for Free Surface Flow Problems". Applied Mechanics and Materials 232 (noviembre de 2012): 279–83. http://dx.doi.org/10.4028/www.scientific.net/amm.232.279.

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A numerical model based on the two-phase flow model for incompressible viscous fluid with a complex free surface has been developed in this study. The two-step projection method is employed to solve the Navier–Stokes equations in the numerical solutions, and finite difference method on a staggered grid is used throughout the computation. The two-order accurate volume of fluid (VOF) method is used to track the distorted and broken free surfaces. The two-phase model is first validated by simulating the dam break over a dry bed, in which the numerical results and experimental data agree well. Then 2-D fluid sloshing in a horizontally excited rectangular tank at different excitation frequencies is simulated using this two-phase model. The results of this study show that the two-phase flow model with VOF method is a potential tool for the simulation of nonlinear fluid sloshing. These studies demonstrate the capability of the two-phase model to simulate free surface flow problems with considering air movement effects.

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50

Wei, W. L., B. Lv, Y. L. Liu y X. F. Yang. "A Two-Fluid Model for Water Drop Falling". Applied Mechanics and Materials 170-173 (mayo de 2012): 2708–11. http://dx.doi.org/10.4028/www.scientific.net/amm.170-173.2708.

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In this paper, a numerical two-phase flow model combining with the Realizable k–ε turbulent model for compressible viscous fluid is presented for the computation of water drop falling characteristics; and the equations are solved with the finite volume method. The free fluid surface is simulated by the VOF method. A multigrid technique based on the full approximation storage (FAS) scheme is employed to accelerate the numerical convergence. The numerical results for water drop suggest that this basic model can be used to study violent aerated flows, especially by providing fast qualitative estimates.

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