Showing papers on "Volume of fluid method published in 2003"

Interface reconstruction with least-square fit and split Eulerian–Lagrangian advection

Abstract: Two new volume-of-fluid (VOF) reconstruction algorithms, which are based on a least-square fit technique, are presented. Their performance is tested for several standard shapes and is compared to a few other VOF/PLIC reconstruction techniques, showing in general a better convergence rate. The geometric nature of Lagrangian and Eulerian split advection algorithms is investigated in detail and a new mixed split Eulerian implicit–Lagrangian explicit (EI–LE) scheme is presented. This method conserves the mass to machine error, performs better than split Eulerian and Lagrangian algorithms, and it is only slightly worse than unsplit schemes. However, the combination of the interface reconstruction with the least-square fit and its advection with the EI–LE scheme appears superior to other existing approaches. Copyright © 2003 John Wiley & Sons, Ltd.

Efficient implementation of a coupled level-set and volume-of-fluid method for three-dimensional incompressible two-phase flows

Abstract: A level-set method is combined with the volume-of-fluid method for computing incompressible two-phase flows in three dimensions, where the interface configurations are much more diverse and complicated. For efficient implementation of the coupled method, we propose geometric formulations necessary for interface reconstruction, advection of the volume fraction, and reinitialization of the level-set function. The calculation procedures are based on an explicit relation between the interface configuration and the volume fraction. This allows us to reduce the number of iterations required for reconstructing the interface. The coupled method is applied for computations of bubbles rising in a liquid and droplets adhering to a vertical wall.

Numerical simulation of unsteady multidimensional free surface motions by level set method

Abstract: This paper presents a numerical method that couples the incompressible Navier–Stokes equations with the level set method in a curvilinear co-ordinate system for study of free surface flows. The finite volume method is used to discretize the governing equations on a non-staggered grid with a four-step fractional step method. The free surface flow problem is converted into a two-phase flow system on a fixed grid in which the free surface is implicitly captured by the zero level set. We compare different numerical schemes for advection of the level set function in a generalized curvilinear format, including the third order quadratic upwind interpolation for convective kinematics (QUICK) scheme, and the second and third order essentially non-oscillatory (ENO) schemes. The level set equations of evolution and reinitialization are validated with benchmark cases, e.g. a stationary circle, a rotating slotted disk and stretching of a circular fluid element. The coupled system is then applied to a travelling solitary wave, and two- and three-dimensional dam breaking problems. Some interesting free surface phenomena are revealed by the computational results, such as, the large free surface vortices, air entrapment and splashing of the water surge front. The computational results are in excellent agreement with theoretical predictions and experimental data, where they are available. Copyright © 2003 John Wiley & Sons, Ltd.

Short Note A geometrical area-preserving Volume-of-Fluid advection method

Abstract: A new class of algorithms that preserve mass exactly for incompressible flows on a Cartesian mesh are presented. They amount to piecewise-linear, area-preserving mappings of tessellations of the plane. They are equivalent to Volume-of-Fluid (VOF) advection methods which are decomposed into an Eulerian implicit scheme in one direction followed by a Lagrangian explicit step in the other one. It is demonstrated that mass conservation is exact for incompressible flows and that there are no undershoots or overshoots of the volume fraction which thus always remains constrained between 0 and 1. 2003 Elsevier B.V. All rights reserved. AMS: 65M05; 76M20; 76T99

A new VOF-based numerical scheme for the simulation of fluid flow with free surface. Part I: New free surface-tracking algorithm and its verification

Abstract: Numerical simulation of fluid flow with moving free surface has been performed. For the free surface flow, a volume of fluid (VOF)-based algorithm utilizing a fixed grid system has been investigated. In order to reduce numerical smearing at the free surface represented on a fixed grid system, a new free surface-tracking algorithm based on the donor–acceptor scheme has been proposed. Novel features of the proposed algorithm are characterized by two numerical tools; the orientation vector to represent the free surface orientation in each cell and the baby-cell to determine the fluid volume flux at each cell boundary. The proposed algorithm can be easily implemented in any irregular non-uniform grid systems usually encountered in the finite element method (FEM). Moreover, the proposed algorithm can be extended and applied to the 3D free surface flow problems without additional efforts. For computation of unsteady incompressible flow, a finite element approximation based on the explicit fractional step method has been adopted. In addition, the streamline upwind/Petrov–Galerkin (SUPG) method has been implemented to deal with convection dominated flows. Combination of the proposed free surface-tracking scheme and the explicit fractional step formulation resulted in an efficient solution algorithm. Validity of the present solution algorithm was demonstrated from its application to the broken dam and the solitary wave propagation problems. Copyright © 2003 John Wiley & Sons, Ltd.

A mass conserving level set (MCLS) method for modeling of multi-phase flows

Abstract: The Mass-Conserving Level-Set (MCLS) method is proposed to model multi-phase flows. The aim is to model high density-ratio flows with complex interface topologies, such as mixtures of bubbles and droplets. Aspects which are taken into account are: a sharp front (density changes rapidly), arbitrary shaped interfaces, surface tension, buoyancy and co-alescence of drops/bubbles. Attention is paid to mass-conservation and integrity of the interface. A survey of available computational methods is performed in [1]. The proposed computational method is a combination of Level-Set and Volume-of-Fluid methods. The flow is computed with a pressure correction method with a Marker-and-Cell layout. Interface conditions are satised by means of the continuous surface force/stress (CSF/CSS) methodology and the GhostFluid method for incompressible flows. The Level-Set method is an elegant method. The major disadvantage is that it is not rigorously mass-conserving. This means that additional effort is necessary to conserve mass. The MCLS method introduces a Volume-of-Fluid function, which is advected without the necessity to reconstruct the interface. There is a strong relationship between the Volume-of-Fluid function and the Level-Set function. In the spirit of the Level-Set methodology, the advection of the VOF-function is, unlike other VOF methods, purely implicit at every time. This makes the method straightforward to apply to arbitrarily shaped interfaces, which may collide and break up.

Numerical analysis of metal transfer in gas metal arc welding

Abstract: The present article describes a numerical procedure to simulate metal transfer and the model will be used to analyze the transport processes involved in gas metal arc welding (GMAW). Advanced Computational fluid dynamics (CFD) techniques used in this model include a two-step projection method for solving the incompressible fluid flow; a volume of fluid (VOF) method for capturing free surface; and a continuum surface force (CSF) model for calculating surface tension. The electromagnetic force due to the welding current is estimated by assuming several different types of current density distribution on the free surface of the drop. The simulations based on the assumption of Gaussian current density distribution show that the transition from globular to spray transfer mode occurs over a narrow current range and the size of detached drops is nonuniform in this transition zone. The analysis of the calculation results gives a better understanding of this physical procedure. Comparisons between calculated results and experimental results are presented. It is found that the results computed from the Gaussian assumption agree well with those observed in experiments.

VOF-Simulations of Mass Transfer From Single Bubbles and Bubble Chains Rising in Aqueous Solutions

Abstract: This paper presents numerical simulations of two-phase flow with high-density ratio, taking into account mass transport of a soluble component and its interfacial mass transfer. The mathematical model and the numerical method allow for different solubility of the species in the respective fluid phases, while volume changes due to mass transfer are neglected. The discontinuous changes in species concentrations at the interface are modeled by means of Henry’s law. Simulations are carried out with an extended version of the highly parallelized code FS3D, which employs an advanced Volume-Of-Fluid (VOF) method. Transfer and transport of oxygen is examined in case of single bubbles as well as bubble chains rising in aqueous solutions. Numerical simulations show good qualitative agreement with experimental data and render the observed mass transfer phenomena correctly.Copyright © 2003 by ASME

Modeling of Breaking and Post-breaking Waves on Slopes by Coupling of BEM and VOF Methods

Abstract: We study the shoaling, breaking, and post-breaking of waves, in two dimensions, using a model, i.e., a Numerical Wave Tank, based on coupling a Boundary Element Model, solving potential flow equations, to a Volume Of Fluid model, solving Navier-Stokes equations. We apply the model to calculating the transformation of solitary waves over plane slopes. We compare results to existing laboratory experiments. The agreement is quite good between computations and measurements. Finally, we compute properties of waves breaking over various slopes, such as shape, internal velocities and type of breaking.

An Efficient Method for Capturing Free Boundaries in Multi-Fluid Simulations

Abstract: An easy-to-use front capturing method is devised by directly solving the transport equation for a volume of fluid (VOF) function. The key to this method is a semi-Lagrangian conservative scheme, namely CIP_CSL3, recently proposed by the author. In the CIP_CSL3 scheme, the first-order derivative of the interpolation polynomial at each cell centre is used to control the shape of the reconstructed profile. We show in the present paper that the first-order derivative, which plays a crucial role in reconstructing the interpolation profile, can also be used to eliminate numerical diffusion. The resulting algorithm can be directly used to compute the VOF-like function and retain the compact thickness of the moving interface in multi-fluid simulations. No surface reconstruction based on the value of VOF function is required in the method, which makes it quite economical and easy to use. The presented method has been tested with various interfacial flows including pure rotation, vortex shearing, multi-vortex deformation and the moving boundaries in real fluid as well. The method gives promising results to all computed problems. Copyright © 2003 John Wiley & Sons, Ltd.

Numerical and Physical Simulation of Tundish Fluid Flow Phenomena

Abstract: The fluid flow in a continuous casting tundish is numerically and physically simulated by means of water models. Results of residence time distribution (RTD) measurements and laser-optical measurements (Laser Doppler Anemometry - LDA, Digital Particle Image Velocimetry - DPIV) are used to validate the numerical results for water before the numerical simulation is transferred to the steel melt. The investigations are focused on both steady-state and transient casting conditions. To reduce vortexing and turbulence in the tundish different types of turbo-stoppers are installed in the water models and their influence on the spacious flow structure is discussed. The turbo-stopper produces higher turbulence in the inlet region of the tundish, but this region is spatially more limited in relation to the flow without turbo-stopper. Thereby a more homogeneous flow is created at the outlet of the tundish with better conditions for particle separation. Basic design criteria for the geometry of a turbo-stopper are developed. Moreover, the processes of first tundish filling and ladle change are simulated at a downscaled water model and these results are compared with numerical simulations using a Volume of Fluid (VoF) model. This multiphase model is able to reproduce the motion of gas bubbles and waves at the free surface.

A new VOF‐based numerical scheme for the simulation of fluid flow with free surface. Part II: application to the cavity filling and sloshing problems

Abstract: Finite element analysis of fluid flow with moving free surface has been performed in 2-D and 3-D. The new VOF-based numerical algorithm that has been proposed by the present authors (Int. J. Numer. Meth. Fluids, submitted) was applied to several 2-D and 3-D free surface flow problems. The proposed free surface tracking scheme is based on two numerical tools; the orientation vector to represent the free surface orientation in each cell and the baby-cell to determine the fluid volume flux at each cell boundary. The proposed numerical algorithm has been applied to 2-D and 3-D cavity filling and sloshing problems in order to demonstrate the versatility and effectiveness of the scheme. The proposed numerical algorithm resolved successfully the free surfaces interacting with each other. The simulated results demonstrated applicability of the proposed numerical algorithm to the practical problems of large free surface motion. It has been also demonstrated that the proposed free surface tracking scheme can be easily implemented in any irregular non-uniform grid systems and can be extended to 3-D free surface flow problems without additional efforts. Copyright © 2003 John Wiley & Sons, Ltd.

Numerical simulation of three-dimensional free surface flows

Abstract: A numerical model is presented for the simulation of complex fluid flows with free surfaces in three space dimensions. The model described in Maronnier et al. (J. Comput. Phys. 1999; 155(2):439) is extended to three dimensional situations. The mathematical formulation of the model is similar to that of the volume of fluid (VOF) method, but the numerical procedures are different. A splitting method is used for the time discretization. At each time step, two advection problems-one for the predicted velocity field and the other for the volume fraction of liquid-are to be solved. Then, a generalized Stokes problem is solved and the velocity field is corrected. Two different grids are used for the space discretization. The two advection problems are solved on a fixed, structured grid made out of small cubic cells, using a forward characteristic method. The generalized Stokes problem is solved using continuous, piecewise linear stabilized finite elements on a fixed, unstructured mesh of tetrahedrons. The three-dimensional implementation is discussed. Efficient postprocessing algorithms enhance the quality of the numerical solution. A hierarchical data structure reduces memory requirements. Numerical results are presented for complex geometries arising in mold filling. Copyright (C) 2003 John Wiley Sons, Ltd.

Natural element meshless simulation of flows involving short fiber suspensions

Abstract: Numerical modeling of non-Newtonian flows typically involves the coupling between the equations of motion characterized by an elliptic character, and the fluid constitutive equation, which is an advection equation linked to the fluid history. Thus, the numerical modeling of short fiber suspensions flows requires a description of the microstructural evolution (fiber orientation) which affects the flow kinematics and that is itself governed by this kinematics (coupled problem). Some industrial flows involve moving or free boundaries (injection, extrusion, …). Lagrangian descriptions allow an accurate description of the flow front tracking as well as an accurate integration of transport equations along the flow trajectories. However, Lagrangian techniques in the context of finite elements have the important drawback of requiring frequent remeshing in order to avoid large elements distortions. The natural element method (NEM) has the capabilities of Lagrangian models to describe the flow front tracking as well as to treat the convection terms related to the fiber orientation equation without the mesh quality requirement characteristics of the standard finite elements method.

Numerical analysis of the internal kinematics and dynamics of three-dimensional breaking waves on slopes

Abstract: In this paper, we describe the breaking and post-breaking in a threedimensional numerical wave tank of a solitary wave over a sloping ridge. The numerical model is based on coupling a higher-order Boundary Element Method (BEM) solution of fully nonlinear potential flow equations to a Volume Of Fluid (VOF) method solving NavierStokes equations, in three-dimensions (3D). Analysis of wave profiles and kinematics (velocity, vorticity, pressure) are carried out.

Fluid displacement by Stokes flow past a spherical droplet

Abstract: The concept of 'drift', which has been exploited in many high Reynolds number and inviscid flow problems, is here applied to examine transport by a spherical viscous droplet (of radius a) moving in a Stokes flowIn an unbounded flow, the velocity in the direction of translation of a spherical droplet is positive everywhere because streamlines, in the fluid frame of reference, 'close' at infinity Fluid particles are displaced a positive distance, X, forward, which is expressed in terms of the initial distance from the stagnation streamline rho(0) Asymptotic expressions are developed for X in the limits of rho(0)/a much less than 1 and much greater than 1 The nature of the singularity of the centreline displacement changes from O(-a log(rho(0)/a)) to O(a(2)/rho(0)) as the viscosity of the droplet, compared to the ambient fluid, increases By employing a mass-conservation argument, asymptotic expressions are calculated for the partial drift volume, D-p, associated with a circular material surface of radius rho(m) which starts far in front of a droplet that translates a finite distance Since the velocity perturbation decays slowly with distance from the droplet, D-p tends to become unbounded as rho(m) increases, in contrast to inviscid flowsThe presence of a rigid wall ensures that the velocity perturbation decays sufficiently rapidly that fluid particles, which do not lie on the stagnation streamline, are displaced a finite distance away from the wall The distortion of a material surface lying a distance h(L) above a wall, by the droplet, starting a distance h(S) from the wall and moving away, is studied The volume transported away from the wall, calculated using a multipolar flow approximation, is D-p = pih(L)(2)a(3lambda + 2)/(lambda + 1), and is weakly dependent on the starting position of the droplet, in accordance with numerical results When the material surface is close to the wall (h(L)/a < 1), the volume transported away from a wall is significantly smaller than for inviscid flows because the no-slip condition on the rigid wall tends to inhibit 'scouring' When the material surface is far from the wall (h(L)/a much greater than 1), the viscously dominated flow transports a larger volume of fluid away from the wall because the flow decays slowly with distance from the dropletThese results can be generalized to arbitrarily shaped bodies, since the transport processes are dominated by the strength of the Stokeslet The effect of boundaries and inertia on fluid transport processes is briefly discussed

Method and device for numerical analysis of flow field of incompressible viscous fluid, directly using V-CAD data

Abstract: A method for numerical analysis of flow field of non-compressive viscous fluid includes: a division step (A) for dividing external data (12) consisting of boundary data on the object in contact with a non-compressive viscous fluid into a plurality of cells (13) to which the boundary is orthogonal; a cell grouping step (B) for grouping the divided cells into internal cells (13a) positioned inside the object and boundary cells (13b) including boundary data; a cut point decision step (C) for obtaining cut points of the edge line of the boundary cells (13b) by the boundary data; a boundary decision step (D) for treating a polygon obtained by connecting the cut points as boundary cell internal data; and an analysis step (E) for applying the cut cell finite volume method together with the VOF method to the boundary of the flow field.

Numerical Simulations of Three-dimensional Wave Breaking by Coupling of a VOF Method and a Boundary Element Method

Abstract: In this paper, we describe the development and validation of a numerical model based on coupling a higher-order Boundary Element Method (BEM) solution of fully nonlinear potential flow equations to a Volume Of Fluid (VOF) solution of Euler equations, in threedimensions (3-D). In the model, the BEM solution is used to initialize the VOF/Euler computations. Numerical simulations of breaking waves on sloping beaches for 2-D (using an earlier model) and 3-D flows are carried out.

Direct Numerical Simulation of Air Bubbles in Water/Glycerol Mixtures: Shapes and Velocity Fields

Abstract: In this paper results of direct numerical simulation (DNS) of bubbles rising in viscous Newtonian liquids with high-density ratio are presented. The simulations are carried out with the highly parallelized code FS3D, which employs the Volume-of-Fluid (VOF) method. The high degree of parallization of the code allows high resolution of the computational domain, such that the Kolmogorov length scale inside the liquid phase is resolved for the simulations. For validation of the numerical results the terminal rise velocities, bubble shapes and flow fields are compared to experimental data as well as to approximate analytical solutions. For high Morton numbers terminal rise velocities and aspect ratios agree very well with experimental values. For lower Morton numbers there is an increasing difference between experimental and numerical rise velocities. The aspect ratios of ellipsoidal bubbles match both with experimental measurements and with theoretical values of Taylor and Acrivos. At very low Reynolds numbers (ReB < 1) the velocity fields in and outside of the bubble show good semi-quantitative agreement with the analytical creeping flow solution of Hadamard and Rybczynski.Copyright © 2003 by ASME

On the Critical Plunger Speed and Three-Dimensional Effects in High-Pressure Die Casting Injection Chambers

Abstract: During the initial slow stage of the injection process in high-pressure die casting machines with horizontal cold chamber, a plunger pushes the molten metal which partially fills the injection chamber, causing the formation of a gravity wave. The evolution of the wave surface profile, which depends on the plunger acceleration law, may trap air in the molten metal, causing porosity when the metal solidifies. In this work, a one-dimensional shallow-water model, which is solved numerically using the method of characteristics, and a three-dimensional numerical model, based on a finite element formulation and the volume of fluid (VOF) method for treating the free surface, are used to analyze the flow of molten metal in an injection chamber of circular cross section. The results for the evolution of the free surface obtained from both models for different plunger motion laws and initial filling fractions of the injection chamber were in good agreement for broad ranges of operating conditions. The existence of a critical plunger speed, above which the reflection of the wave of molten metal against the chamber ceiling might appreciably increase air entrapment effects, is investigated. The results for the wave profiles in chambers of circular cross section are compared with those obtained in an equivalent two-dimensional configuration of the injection chamber, for which the shallow-water model is solved analytically. It is shown how the results obtained by applying the one-dimensional model to a two-dimensional chamber configuration can be used to reproduce, with an acceptable degree of accuracy, the salient characteristics of the flow of molten metal in a real injection chamber of circular cross section.

Three-Dimensional Numerical Simulation of the Inverse Problem of Thermal Convection

Abstract: Both forward and inverse (time-reversed) three-dimensional simulations of slow thermocon- vective flow are considered for a highly viscous fluid with temperature-dependent density and viscosity. The model is described by the equations of quasi-steady viscous inhomogeneous incompressible flow, advection equations for density and viscosity, and a heat equation. The numerical solution is based on the introduction of a two-component vector velocity potential and on the application of a finite element method with a tricubic-spline basis for computing the potential. The advection equations were solved by the method of characteristics. The heat equation was solved forward in time by a finite-difference method based on a tridiagonal algorithm with the Crank-Nicolson scheme employed in each direction. It was solved backwards in time by a variational method essentially based on a solution of a series of forward problems. The numerical algorithms were designed to be implemented on parallel computers. The principal results of the study are summarized as follows: a numerical method is developed for simul- taneous solution of the Stokes flow equation, heat equation, and advection equations for physical param- eters of the fluid both forward and backwards in time. Substantial progress in these problems was achieved by using a special representation of the vector velocity potential and choosing a special basis in the finite element method, which resulted in a considerable reduction of numerical complexity. Char- acteristic examples were computed.