Volume Of Fluid Function Research Articles

Study on the dynamic characteristics of rising bubbles under the influence of viscosity based on VOF method

Abstract In order to study the buoyancy-driven rising bubbles in liquids in various types of problems such as oil pipeline transportation, combustible ice mining, ship drag reduction, and the use of bubbles to deliver drugs in blood, this paper establishes a model for the rising bubbles in liquids based on the Volume of Fluid Function (VOF) method, and investigates the change rule of the larger-size bubbles under the influence of viscosity in different viscous silicone oils. It provides theoretical and technical support for various natural and industrial processes such as deep-sea oil extraction and metal smelting.

Numerical Analysis of Flood Invasion Path and Mass Flow Rate in Subway Stations under Heavy Rainfall Conditions

The occurrence of extreme weather, such as heavy rainfall and sudden increases in precipitation, has led to a notable rise in the frequency of flooding in subway stations. By conducting numerical simulations of flood disasters in subway stations under heavy rainfall conditions and gaining insights into the patterns of flood invasion inside the stations, it is possible to develop practical and feasible drainage designs for the stations. This paper employs the computational fluid dynamics (CFD) method, utilising the volume of fluid function (VOF) method and the renormalization k-ε group model within the vortex viscosity model. The complete process of flood invasion into subway stations with varying water levels (1500 mm, 2000 mm, and 2450 mm) is modelled, and the distribution of floods at different times under varying operational conditions is analysed to identify the evolutionary patterns of station flood history. The simulation calculations yielded the mass flow rate time history curve at the tunnel entrance and exit, which was then subjected to an analysis of its development trend over time. The total accumulated water in the subway station is calculated by integrating the difference in mass flow rate between the entrance and the tunnel exit, using the mass flow rate curve. In conclusion, the paper proposes drainage measures that provide valuable insights into pumping strategies when floodwaters infiltrate subway stations. The results indicate that the speed of flood spreading in subway stations increases with higher groundwater levels, and that the mass flow rate of floodwater entering the tunnels increases over time, eventually reaching a stable state. It was observed that, at certain times, the mass flow rate of floodwater into the tunnels exhibited a linear relationship with time.

A coupled level-set and tangent of hyperbola interface capturing (THINC) scheme with a single-step time integration for incompressible flows

In this paper, we present a concise and efficient interface capturing scheme on polyhedral unstructured mesh with its numerical implementation for incompressible fluid simulation with surface tension. The so-called coupled Level-Set and Tangent of Hyperbola INterface Capturing scheme with a Consistent Single-step time integration (THINC/CSLS) updates both the volume-of-fluid (VOF) and level-set function simultaneously from a THINC reconstruction function. The proposed scheme has the potential to integrate the positive aspects of mass conservation from the VOF method and the accurate geometric representation from the level-set method. Other innovative and noteworthy aspects of the present scheme are listed as (1) an adaptive THINC reconstruction strategy is applied to ensure the boundness of the VOF function for various Courant–Friedrichs–Lewy (CFL) numbers and the high quality of the level-set function for surface tension; (2) a single-step update procedure for both VOF and level-set function is implemented for better algorithmic consistency and efficiency; (3) a well-adapted numerical model is developed for incompressible simulation with free surface for both structured and unstructured grids. A comprehensive numerical procedure is introduced and validated by various well-received benchmark tests. Convincing evidence suggests that the present scheme is both accurate and efficient compared with other most advanced methods.

Numerical Study on Interfacial Structure and Mixing Characteristics in Converter Based on CLSVOF Method

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.

Effects of spanwise length and side-wall boundary condition on plunging breaking waves

A systematic study of the effect of the spanwise length and the sidewall boundary condition of a numerical wave flume (NWF) on direct numerical simulation of a plunging breaking wave is performed. To deal with the topological changes of free surfaces, a high-fidelity numerical model is employed to solve the Navier–Stokes equations together with the volume of fluid function. After verification by two-dimensional (2D) simulations of a plunging breaker on a sloping beach, ten NWFs with different spanwise extents and sidewall boundary conditions are studied. Special attention is devoted to the three-dimensionality of the plunging breaker. Compared with three-dimensional (3D) models, the 2D model accurately reproduces the dynamics of a breaking solitary wave in the early stage, but it is inadequate for the study of the post-breaking process. For a 3D NWF with nonslip sidewall boundary condition, the wave domain can be divided into two regions with different physical properties. In the near-wall region, the nonslip boundary condition on the sidewall plays a crucial role in the wave hydrodynamics, while in the central region, the properties of the breaking wave are similar to those for the periodic boundary condition, which provide a closer representation of the real sea environment. The spanwise length of the NWF plays only a minor role in simulations under the periodic boundary condition. Furthermore, lateral boundaries and spanwise length show more influences on a plunging breaker with larger incident wave steepness. This study provides valuable support for the design of numerical simulations of wave breaking.

A hybrid volume of fluid and level set interface capturing scheme with quartic surface representation for unstructured meshes

AbstractIn this article, we developed a hybrid volume of fluid (VOF) and level set interface capturing scheme with quartic surface representation for unstructured meshes. The so‐called tangent of hyperbola interface capturing‐scaling scheme with quartic surface representation (THINC‐scaling/QSR) preserves the merits of the mass/volume conservativeness from the VOF scheme along with the geometric faithfulness from the level set scheme. Compared with linear/quadratic surface representation used in many other interface capturing schemes, the fluid interface is defined more precisely as a quartic polynomial surface of the THINC function which synchronize the interface between the VOF and level set functions in a straightforward solution procedure. We update the VOF function using a finite volume formulation. The level set function is first locally updated via a semi‐Lagrangian method for interface cells and then reinitialized within each time step. Two‐dimensional algorithm has been developed and verified by some benchmark tests on unstructured meshes. Convincing evidence suggests that the present scheme, with quartic surface representation, can provide high‐fidelity solution with more pronounced sub‐grid interface capturing capability than other most advanced methods.

Volume‐of‐fluid based two‐phase flow methods on structured multiblock and overset grids

AbstractA geometric volume‐of‐fluid (VOF) method is implemented on the static/dynamic overset grids with a new VOF interpolation algorithm developed. The VOF value cannot be directly interpolated through the overset grid boundaries since the VOF function is a discontinuous step function. In the present study, the interface is reconstructed in the fringe cells of the overset grids using the interpolated distance function and normal vector. The VOF value in the fringe cells is calculated geometrically based on the reconstructed interface on the physical domain. The gravity and surface tension forces are implemented using a VOF based ghost fluid method, where a ghost pressure interpolation scheme is developed to handle the pressure jump across the interface due to the density changes and surface tension effect. Numerical tests and application examples have been performed for the verification and validation of the numerical methods developed in the present study. The advection tests show that the effect of the VOF overset interpolation on the accuracy of the VOF method is small. The numerical test for the static pressure shows that the present VOF based ghost fluid method can greatly reduce the spurious velocity observed in the body force method. The sharp pressure profile due to the surface tension effects can be preserved across the interface. Application examples demonstrate the capability and superiority of the VOF based numerical methods for the prediction of the violent ship flows involving strong air water interface interactions and complex geometries.

Numerical investigation of interface capturing method by the Rayleigh-Taylor instability, dambreak and solitary wave problems

Free surface simulation always plays an important role among the problems in ship and ocean engineering. In the research described herein, an interface capturing method, combined with the level set (LS) and volume of fluid (VOF) method (CLSVOF), was developed and verified detailedly on the basis of the Rayleigh-Taylor instability (RTI), dambreak and solitary wave problems numerically in two-dimensional (2D) situation. According to CLSVOF approach, the LS function but not the VOF function can estimate the interface normal vector in the reconstruction procedure of interface. The numerical solver was first verified by solving the single-mode RTI. After that, the shape of the interface, the evolution process of vortices and the relationship between penetration depth and time were obtained. Simultaneously, this article separately discussed the effects of surface tension, density ratio and viscosity ratio on the RTI. Next, for the multi-mode RTI, the complicate interface evolution process was finely simulated to verify the mass conservation property during simulation. Eventually, this paper shows dambreak and solitary wave problems to demonstrate that CLSVOF solver is capable of handling a large density difference situation, as well as wave profile evolution in ocean engineering application.

Experimental and numerical simulation of bidirectional propagation of an air cavity

This study numerically and experimentally investigates the transient flow associated with a so-called Benjamin bubble, but, in contrast to previous studies, the approach permits bidirectional flow. Two experiments investigated the bidirectional propagation of an air cavity in a square tank; these two events were also simulated using a three-dimensional numerical model. An exactly conservative semi-Lagrangian scheme was employed to solve both the advection term in the momentum equation and the advection equation of the volume of fluid function. The model was compared with previous one-dimensional Benjamin bubble experimental data and a one-dimensional Boussinesq model. For the one-dimensional Benjamin bubble experiments, the three-dimensional model showed good agreement with both published data and a one-dimensional non-hydrostatic model. After modelling the advance of a one-dimensional cavity, a bidirectional Benjamin bubble was simulated using the three-dimensional model. The numerical results are in reasonable agreement with observations of the free surface and pressurized regions and reasonably predict the shape of the air–water interface.

A volume of fluid method algorithm for simulation of surface tension dominant two-phase flows

In this article, a two-phase flow algorithm that uses an explicit Adams–Bashforth scheme coupled with volume of fluid (VOF) method in a uniform staggered Cartesian grid for surface tension dominant simulation is presented. The interface reconstruction procedure is implemented using the Weighed Linear Interface Calculation (WLIC) algorithm. The level set (LS) function instead of VOF function is adopted for calculation of not only the interface normal vectors in the WLIC algorithm but also the surface tension terms in the Navier–Stokes equations. This VOF method is compared with LS method and other experiment results in the literature for vortex deforming, milk crown, droplet impacting into deep liquid pool and bubble bursting at a free surface problems to show whether mass can be well conserved and breaking and merging phenomena can be accurately simulated.

Numerical simulation of a laser-induced cavitation bubble near a solid boundary considering phase change

ABSTRACTThis paper documents the numerical investigation of the flow surrounding a collapsing laser-induced cavitation bubble with an initial radius of 1.45 mm. The three-dimensional laminar flow was captured by solving the Navier–Stokes equations. To account for the multiphase flow (water and vapour), the Volume of Fluid (VoF) method was used. The source term of the transport equation of the VoF function was based on the simplified Rayleigh–Plesset equation. The distance of the bubble from a solid surface wall was varied according to the dimensionless parameter D/Rmax ranging from 0.3 to 3.0, where Rmax is maximum bubble radius and D is the distance between bubble centre and solid surface. Computed collapse derivatives, impact velocity, impact pressure, and visual characteristics, such as toroidal shapes of oval impacts, agreed favourably to experimental measurements.

A Coupled Level Set and Volume of Fluid method with multi-directional advection algorithms for two-phase flows with and without phase change

A Coupled Level Set and Volume of Fluid (CLSVOF) interface capturing method using a multi-dimensional advection algorithm for non-uniform grids has been developed for two phase flows with and without phase change for two-dimensional problems. A finite volume method with a collocated grid arrangement is used for solving the governing equations. The SIMPLE algorithm is used for velocity and pressure coupling. The piecewise linear interface calculation (PLIC) based geometrical reconstruction procedure and an Edge Matched Flux Polygon Advection (EMFPA) multi-dimensional algorithm have been implemented for the Volume of Fluid (VOF) method. For the Level Set (LS) advection equation, the convective terms are discretized using the second order accurate essentially non-oscillating (ENO) scheme. The proposed multi-dimensional advection of CLSVOF method requires interface reconstruction for the advection of VOF function and the Level Set function re-initialization only once compared to the requirement of twice interface reconstruction and Level Set re-initialization in the operator-splitting method for 2D problems. The performance of proposed CLSVOF method is evaluated for accurate mass conservation, surface tension force and interface mass transfer through various standard benchmark problems. The numerical study of two-dimensional saturated film boiling flow over a horizontal plane surface was carried out for different constant wall superheats in order to validate the implementation of boiling flow model. The present numerical results of boiling flows show better agreement with the experimental correlations.

Estimates of surface normal and curvature, reconstruction of continuum surface force model, and elimination of spurious currents

SUMMARYA reconstructed continuum surface force (CSF) model is presented for the volume‐of‐fluid (VOF) method in numerical simulations of surface tension‐driven flow. The gradient of VOF function yielded by the one‐direction difference (ODD) algorithm has second‐order accuracy in one direction and exhibits unit pulse function in the other direction. Use of our ODD algorithm for surface normal and curvature improves the accuracy of surface tension force estimate and meets the necessary condition of a circular droplet free of spurious currents. The immersed length, a physical depth of grid cell center introduced in this paper, is computed from VOF function and surface orientation. It is chosen instead of VOF function as weight parameters in the evaluations of density and volumetric surface tension force between interfacial grid cells. Grid cells and control cells are classified into interfacial, sublayer, and interior cells according to their distances to interface. Surface tension is thus constructed within interfacial or sublayer cells. The numerical approach is modified so that flow pressure solutions are sought only at those immersed grid cell centers. The transitional region from one fluid to the other is compressed. Spurious currents by no means grow on free surface in the numerical simulations using our algorithms and reconstructed CSF model. The simulation results agree with the Laplace pressure jump across a static circular free surface or experimental observations. Copyright © 2014 John Wiley & Sons, Ltd.

A mass-conserving volume-of-fluid method: Volume tracking and droplet surface-tension in incompressible isotropic turbulence

We have developed a volume of fluid (VoF)/projection method for simulating droplet-laden incompressible turbulent flows with uniform density and viscosity. The method is mass-conserving, wisp-free, and consistent (i.e., the VoF function, C, satisfies the condition 0⩽C⩽1).First, we present the results of the VoF method for tracking volumes of initially spherical shape and with zero surface tension in analytical velocity fields (linear translation, solid-body rotation, single-vortex flow, and Taylor–Green vortex) and in incompressible isotropic turbulence at Reλ0=75 and 190. These numerical tests show that (i) our VoF method is mass-conserving, consistent, and wisp-free; (ii) for a CFL number of 0.1, the VoF geometrical error has almost a second-order convergence rate for a mesh resolution with more than 10 grid points per diameter; (iii) in the isotropic turbulence case, a resolution of about 32 grid points per diameter of the sphere is required in order to limit the VoF geometrical error below 1%. Then, in order to simulate droplet-laden flows, we have adopted the continuum surface force (CSF) model to compute the surface tension force. We have modified the sequence of the VoF advection sweeps, and show that, in the case of droplet in a translating reference frame, the r.m.s. of the spurious currents is about 1% of the translating velocity. Finally, we present DNS results of fully-resolved droplet-laden incompressible isotropic turbulence at Reλ0=75 using a computational mesh of 10243 grid points and 7000 droplets of Weber number Werms=0.5, and initial droplet diameter equal to the Taylor length-scale of turbulence.

Computational Modelling of Liquid Sloshing in Rectangular Tank

Liquid sloshing inside a partially filled rectangular tank has been investigated. The fluid is assumed to be water and the tank is forced to move along x axis to simulate the actual tank excitation. The volume of fluid technique is used to track the free surface and the model solves Navier_Stokes equations by the use of the finite difference estimation. At each time step, a donar-acceptor method is used to transport the volume of fluid function and locations of the free surface. In this paper the location and transport of the free surface in the tank have been investigated using a CFD code (FLUENT) for 3D configuration. The use of a numerical tool has resulted in a detailed investigation of these characteristics, which have not been available in the literature previously.

Simulation of Numerical Wave Based on Fluid Volume Function

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.

A Coupled Level Set-Moment of Fluid Method for Incompressible Two-Phase Flows

A coupled level set and moment of fluid method (CLSMOF) is described for computing solutions to incompressible two-phase flows. The local piecewise linear interface reconstruction (the CLSMOF reconstruction) uses information from the level set function, volume of fluid function, and reference centroid, in order to produce a slope and an intercept for the local reconstruction. The level set function is coupled to the volume-of-fluid function and reference centroid by being maintained as the signed distance to the CLSMOF piecewise linear reconstructed interface. The nonlinear terms in the momentum equations are solved using the sharp interface approach recently developed by Raessi and Pitsch (Annual Research Brief, 2009). We have modified the algorithm of Raessi and Pitsch from a staggered grid method to a collocated grid method and we combine their treatment for the nonlinear terms with the variable density, collocated, pressure projection algorithm developed by Kwatra et al. (J. Comput. Phys. 228:4146---4161, 2009). A collocated grid method makes it convenient for using block structured adaptive mesh refinement (AMR) grids. Many 2D and 3D numerical simulations of bubbles, jets, drops, and waves on a block structured adaptive grid are presented in order to demonstrate the capabilities of our new method.

Multiphase Fluid Simulations on a Multiple GPGPU PC Using Unsplit Time Integration VSIAM3

This talk presents the implementation of simulations on multiphase fluid dynamics on hardware of multiple GPGPU architecture by using robust and efficient numerical methods. An unsplit formulation for the advection computation is proposed to take the place of the original split formulation in the so-called VSIAM3 method. The new formulation improves dimensional symmetry of numerical results without losing the advantages of the original formulation. We also devised a numerical scheme named STAA to capture the moving interface between different fluids. The volume of fluid function is transported by the above advection scheme, and then modified by an anti-diffusion step based on a well designed numerical flux that rigorously conserves the mass and effectively eliminate the numerical smearing around the interface. Our experiments show that it is able to maintain the VOF function in a well-regulated shape with compact transition layer between different fluids. We have developed a 3D numerical model for multi-fluid simulations with above methods incorporated, and implemented it on a multiple GPGPU computer. It is shown that the present model is able to adequately make use of the advantage of the GPGPU architecture. Through this research, we have built a numerical tool with adequate reliability for sanitary ware product design. Computational efficiency which is of particular importance for real-case design process is achieved by implementing the code on a multiple GPGPU hardware.

A Level Set Method Coupled With a Volume of Fluid Method for Modeling of Gas-Liquid Interface in Bubbly Flow

This paper describes the implementation of a 3D parallel and Cartesian level set (LS) method coupled with a volume of fluid (VOF) method into the commercial CFD code FLUENT for modeling the gas-liquid interface in bubbly flow. Both level set and volume of fluid methods belong to the so called “one” fluid methods, where a single set of conservation equations is solved and the interface is captured via a scalar function. Since both LS and VOF have advantages and disadvantages, our aim is to couple these two methods to obtain a method, which is superior to both standalone LS and VOF and verify it versus a selection of test cases. VOF is already available in FLUENT, so we implemented an LS method into FLUENT via user defined functions. The level set function is used to compute the surface tension contribution to the momentum equations, via curvature and its normal to the interface, using the Brackbill method while the volume of fluid function is used to capture the interface itself. A re-initialization equation is implemented and solved at every time step using a fifth-order weighted essentially nonoscillatory scheme for the spatial derivative, and a first-order Euler method for time integration. The coupling effect is introduced by solving at the end of each time step an equation, which connects the volume fractions with the level set function. The verification of parasitic currents and interfacial deformation due to numerical error is assessed in comparison to original VOF scheme. Validation is presented for free rising bubbles of different diameters for Morton numbers ranging from 102 to 10−11.

Numerical modeling of wave overtopping a levee during Hurricane Katrina

In this paper, a numerical wave model based on the incompressible Reynolds equations and k– ε equations has been applied to estimate the impact of overtopping on levee during storm surge. The free surface locations are represented by volume of fluid function (VOF). The model was satisfactorily tested against empirical equation of overflow discharge at a vertical seawall, and experimental data of overtopping discharge at a sloping seawall. The validated model was used to simulate wave overtopping of the levee system during storm surge of Hurricane Katrina. The time history of wave profiles and velocity magnitude field in the vicinity of the levee are demonstrated and analyzed. It is concluded that the failure of parts of the levee system was caused by erosion during wave overtopping.