Showing papers on "Volume of fluid method published in 1996"

Volume tracking of interfaces having surface tension in two and three dimensions

Abstract: Solution algorithms are presented for tracking interfaces with piecewise linear (PLIC) volume-of-fluid (VOF) methods on fixed (Eulerian) two-dimensional (2-D) structured and three-dimensional (3-D) structured and unstructured grids. We review the theory of volume tracking methods, derive appropriate volume evolution equations, identify and present solutions to the basic geometric functions needed for interface reconstruction and volume fluxing, and provide detailed algorithm templates for modern 2-D and 3-D PLIC VOF interface tracking methods. We discuss some key outstanding issues for PLIC VOF methods, namely the method used for time integration of fluid volumes (operator splitting, unsplit, Runge-Kutta, etc.) and the estimation of interface normals. We also present our latest developments in the continuum surface force (CSF) model for surface tension, namely extension to 3-D and variable surface tension effects. We identify and focus on key outstanding CSF model issues that become especially critical on fine meshes with high density ratio interfacial flows, namely the surface delta function approximation, the estimation of interfacial curvature, and the continuum surface force scaling and/or smoothing model. Numerical results in two and three dimensions are used to illustrate the properties of these methods.

Entrainment into two-dimensional and axisymmetric turbulent gravity currents

Abstract: Entrainment of ambient fluid into both two-dimensional and axisymmetric gravity currents is investigated experimentally using a novel neutralization technique. The technique involves the titrative neutralization of an alkaline gravity current which intrudes into and entrains an acidic ambient, and is visualized using a pH indicator solution. Using this technique, we can determine quantitative results for the amount of dilution in the head of the current. The head of the current is able to entrain ambient fluid both by shear instabilities on the current/ambient interface and by over-riding (relatively light) ambient fluid. Guided by our experimental observations, we present two slightly different theoretical models to determine the entrainment into the head of the current as a function of distance from the source for the instantaneous release of a constant volume of fluid in a two-dimensional geometry. By dimensional analysis, we determine from both models that the dimensionless entrainment or dilution ratio, E, defined as the ratio of the volumes of ambient and original fluid in the head, is independent of the initial reduced gravity of the current ; and this result is confirmed by our experiments in Boussinesq situations. Our theoretical evaluation of E in terms of the initial cross-sectional area of the current agrees very well with our experimental measurements on the incorporation of an entrainment coefficient a, evaluated experimentally to be 0.063 ± 0.003. We also obtain experimental results for constant-volume gravity currents moving over horizontal surfaces of varying roughness. A particularly surprising result from all the experiments, which is reflected in the theoretical models, is that the head remains essentially unmixed - the entrainment is negligible - in the slumping phase. Thus the heads of gravity currents with identical initial cross-sectional areas but different initial aspect ratios (lock lengths) will begin to be diluted by ambient fluid at different positions and hence propagate at different rates. A range of similar results is determined, both theoretically and experimentally, for the instantaneous release of a fixed volume of (heavy) fluid in an axisymmetric geometry. By contrast, the results of our experiments with gravity currents fed by a constant flux exhibit markedly different entrainment dynamics due to the continual replenishment of the fluid in the head by the constant input of undiluted fluid from the tail.

Quantitative analysis and computation of two‐dimensional bubble columns

Abstract: Experiments conducted quantify the macroscopic hydrodynamic characteristics of various scale 2-D bubble columns, which include dispersed and coalesced bubble regimes characterized by two flow conditions (4- and 3-region flow) with coherent flow structures. Hydrodynamic behavior is analyzed based on flow visualization and a particle image velocimetry (PIV) system. Columns operated in the 4-region flow condition comprise descending, vortical, fast bubble and central plume regions. The fast bubble flow region moves in a wavelike manner, and thus the flow in the vicinity of this region is characterized macroscopically in terms of wave properties. In columns greater than 20 cm in width, the transition from the dispersed bubble flow regime to the 4- and then to 3-region flow in the coalesced bubble regime occurs progressively with gas velocities at 1 and 3 cm/s, respectively. The demarcation of flow regimes is directly related to measurable coherent flow structures. The instantaneous and time-averaged liquid velocity and holdup profiles provided by the PIV system are presented in light of the macroscopic flow structure in various 2-D bubble columns. Numerical simulations demonstrate that the volume of fluid method can provide the time-dependent behavior of dispersed bubbling flows and account for the coupling effects of pressure field and the liquid velocity on the bubble motion. Comparison of computational results with PIV results for two different bubble injector arrangements is satisfactory.

Method of compensating for changes in flow characteristics of a dispensed fluid

Abstract: A fluid dispensing control for controlling the dispensing of a fluid by a metering valve through a nozzle onto a workpiece. An initial value of a flow characteristic of the fluid is determined that is correlated to the relationship between the flow rate of the fluid and nozzle pressure. Desired nozzle pressure values are periodically determined by evaluating a model of flow rate of the fluid through nozzle in response to the initial value of the flow characteristic and a desired flow rate value. Thereafter, the control provides command signals to the metering valve as a function of the desired nozzle pressures. A new value of the flow characteristic is determined as a function of the measured volume of fluid dispensed during the dispensing cycle to the measured nozzle pressure. During a subsequent dispensing cycle, the control determines the desired nozzle pressures by evaluating the model of flow rate of the fluid through the nozzle as a function of the new value of the flow characteristic. The process of reevaluating the flow characteristic over successive dispensing cycles as a function of measured volumes of fluid dispensed and measured nozzle pressures, and using those updated values to reevaluate the model of flow rate of fluid through the nozzle, is repeated.

Formation fluid flow rate determination method and apparatus for electric wireline formation testing tools

Abstract: A method of determining the volume of a fluid sample withdrawn from an earth formation penetrated by a wellbore is disclosed. The method includes the step of positioning a formation testing tool adjacent to the earth formation. The tool includes a probe which can be selectively placed in hydraulic communication with the formation and excluded from hydraulic communication with the wellbore. The probe can be in hydraulic communication with a pressure transducer. The tool includes a sample chamber selectively placed in hydraulic communication with the probe. The chamber includes means for measuring the volume of the chamber and means for selectively controlling the volume of the chamber. The method further includes the steps of placing the probe in hydraulic communication with the formation, placing the sample chamber in hydraulic communication with the probe and selectively increasing the volume of the chamber while measuring the volume of the chamber and the pressure, determining the volume of the chamber when a fluid from the wellbore disposed within the probe at the start of withdrawal of the sample ceases to expand, by determining an expansion volume at which the pressure decreases less rapidly with respect to an increase in chamber volume, and determining the volume of the fluid sample by subtracting the expansion volume from a total volume of fluid withdrawn into the sample chamber.

Method and apparatus for computational fluid dynamic analysis with error estimation functions

Abstract: A method of and apparatus for performing error estimation for a computational fluid dynamic analysis, which quantitatively indicates an error involved in the computational solutions. Virtual substance advection calculation means performs an advection computation, assuming that a virtual substance whose diffusion coefficient is substantially zero is mixed in the fluid, wherein the behavior of the fluid is given by flow field data that is previously obtained as a result of the computational fluid dynamic analysis. Through the advection computation, the virtual substance advection calculation means obtains concentration data of the virtual substance, thus allowing an error in the flow field data to be estimated by comparing the concentration value after advection of the virtual substance with its initial value. If the flow field data perfectly satisfies the primitive equations of fluid dynamics, the concentration value of the virtual substance will not vary with advection. In contrast, if the flow field data violated the primitive equations, the concentration value obtained by the advection computation would show some variation. This variation enables the error in the flow field data to be quantified.

Vortex fluid meter including a profiled pipe

Abstract: A vortex fluid meter (1) includes a pipe (2) having a maximum inside diameter D in which the fluid flows and having an internal profile comprising from the upstream end to the downstream end: a first pipe portion (4) progressively reducing the inside diameter of said pipe to a value D1 and having an inside wall (4a, 4b, 4c, 4d) at a continuously varying angle to the general direction of flow of the fluid; a second pipe portion (6) of constant diameter D1 in which is disposed at least one obstacle (8) adapted to generate oscillating fluid vortices; and a third pipe portion (20) returning the inside diameter of the pipe (2) to its original value D and adapted to separate the boundary layer of the fluid flow at a downstream end (6a) of said second pipe portion (6), and means (10, 12, 14, 16, 18, 200-221) for detecting the signal corresponding to the oscillations of the vortices and deducing the volume of fluid therefrom.

CFD studies of flow in screw and scroll compressors.

Abstract: An analysis of flow in rotary positive displacement machines has been carried out using a standard CFD package by separating out the motions of the fluid and the instantaneous volume in which it is contained. Examples are given of both twin screw and scroll compressors. Pressure-volume diagrams obtained from such analyses are compared with experimental results and good agreement shown. Longer term aims of such studies are to obtain a better understanding of the internal flow processes, especially where two component flow, such as oil/air mixtures are involved. INTRODUCTION This paper describes the first stages of a longer term project to obtain greater understanding of the nature of fluid flow within rotary positive displacement machines such as those of the screw and scroll type. The greatest need for such improved understanding is where there is more than one flow component as in oil injected compressors. In such cases, the assumptions normally made on oil and gas separation within the machines may thus be checked. Flow of fluid in a rotary positive displacement compressor is unsteady, three-dimensional, turbulent and compressible. Its analysis may be simplified if a grid is defined to describe the instantaneous volume of fluid trapped in the machine and the motion is described first in terms of the fluid relative to the grid and then of the grid itself. By this means fluid motion through all compressors of this type may be analysed with standard numerical procedures. The flow of the fluid relative to the grid may be calculated using a numerical procedure, but with the grid motion replaced by external body forces on the fluid. Although the grid is continuously in motion and changing in shape, its geometry may be defined at all times and its motion described

Numerical Simulation of a Taylor Bubble in a Stagnant Liquid inside a Vertical Pipe

Abstract: The feasibility of a detailed numerical simulation of a Taylor bubble in a stagnant liquid filling a vertical pipe was examined in the present study. The simulation was carried out using the volume of fluid method. Since there have been few quantitative experiments on Taylor bubble shape, physical experiments under a wide range of Eotvos and Morton numbers were also conducted using sucrose solution and air at room temperature and atmospheric pressure. It was confirmed by experiments that the bluntness of the nose of the bubble, the flatness of the tail and the liquid film thickness around the bubble are strongly affected by the two dimensionless numbers. Calculated terminal rising velocities and bubble shapes agreed fairly well with all the measured ones, which indicates that the effects of drag force, buoyancy and surface tension force on the bubble were well predicted by the simulation.

A mass-conservative, positive-definite, and efficient Eulerian advection scheme in spherical geometry and on a nonuniform grid system

Abstract: The flux-form advection scheme of Bott is modified for the spherical coordinates, combined with the expanded-polar-zone (EPZ) technique to improve the overall performance of the advection calculations. With the EPZ technique, this Eulerian scheme has comparable efficiency as semi-Lagrangian methods for advection of nonreactive tracers on a sphere but with somewhat better overall numerical accuracy. The conservation of global tracer mass and the, positive definiteness of the algorithm are achieved to machine precision. For the test problem of solid body rotations on a sphere, this scheme shows small numerical diffusion, almost undetectable phase errors, and very little artificial deformation of the test shape even for cross-polar transport. In comparison with some semi-Lagrangian schemes and other high-order Eulerian methods, it shows very competitive performance. Numerical tests also indicate that, without any modifications, it performs just as well on slightly nonuniform Gaussian grid as on unif...

Numerical analysis of fluid flow with free surface and phase change under electromagnetic force

Abstract: In this study, fluid flow of liquid metal with free surface and melting of metal under electromagnetic force was investigated numerically. The computational code was developed by the authors based upon a finite difference method to simulate the free surface flow and the eddy current simultaneously. The VOF method was introduced to treat the free surface, and magnetic vector potential was used for eddy current analysis. The free surface shape predicted by the code agreed with that obtained experimentally. Furthermore, the code was improved to calculate the phase change (melting) of solid metal by Joule heating due to eddy current. Numerical results of melting of metal were also demonstrated.

Displacement of inviscid fluid by a sphere moving away from a wall

Abstract: We develop a theoretical analysis of the displacement of inviscid fluid particles and material surfaces caused by the unsteady flow around a solid body that is moving away from a wall. The body starts at position hs from the wall, and the material surface is initially parallel to the wall and at distance hL from it. A volume of fluid Df+ is displaced away from the wall and a volume Df- towards the wall. Df+ and Df- are found to be sensitive to the ratio hL/hs. The results of our specific calculations for a sphere can be extended in general to other shapes of bodies. When the sphere moves perpendicular to the wall the fluid displacement and drift volume Df+ are calculated numerically by computing the flow around the sphere. These numerical results are compared with analytical expressions calculated by approximating the flow around the sphere as a dipole moving away from the wall. The two methods agree well because displacement is an integrated effect of the fluid flow and the largest contribution to displacement is produced when the sphere is more than two radii away from the wall, i.e. when the dipole approximation adequately describes the flow. Analytic expressions for fluid displacement are used to calculate Df+ when the sphere moves at an acute angle α away from the wall. In general the presence of the wall reduces the volume displaced forward and this effect is still significant when the sphere starts 100 radii from the wall. A sphere travelling perpendicular to the wall, α = 0, displaces forward a volume Df+(0) = 4πa3hL/33/2hS when the marked surface starts downstream, or behind the sphere, and displaces a volume Df+(0) [similar] 2πa3/3 forward when it is marked upstream or in front of the body. A sphere travelling at an acute angle away from the wall displaces a volume Df+(α) [similar] Df+(0) cos α forward when the surface starts downstream of the sphere. When the marked surface is initially upstream of the sphere, there are two separate regions displaced forward and a simple cosine dependence on α is not found. These results can all be generalized to calculate material surfaces when the sphere moves at variable speed, displacements no longer being expressed in terms of time, but in relation to the distance travelled by the sphere.

Flows with Interfaces: dealing with surface tension and reconnection

Abstract: In this lecture, we discuss the numerical simulation of 3D flows with interfaces. We briefly review the Volume of Fluid approach to interface simulation and the conservative modeling of surface tension. Applications to falling droplets are shown.

Combined eulerian-vof-lagrangian method for general gas-liquid flow applications

Abstract: This article summarizes the technical development and validation of a multiphase computational fluid dynamics (CFD) numerical method using a combined volume-of-fluid (VOF)/Lagrangian tracking model to analyze general dispersed multiphase-flow problems with free surfaces. The gas-liquid interfacial mass, momentum, and energy transfer are modeled by continuum surface mechanisms. A high-order TVD scheme is also implemented for capturing sharp interfaces between immiscible phases. The objectives of the present study are to develop and verify the fractional volume-of-fluid cell partitioning approach into a predictor-corrector algorithm, which is suitable for solving fluid flows at all speeds regimes, and to demonstrate the effectiveness of the present approach by simulating benchmark problems including coaxial jet atomization.

Analysis of bubble rise using the VOF method. 2: Bubble interactions, wall effects and evaporation

Abstract: The motion of single and multiple gas bubbles in an otherwise stationary liquid contained in a closed, right vertical cylinder is investigated using a modified Volume-of-Fluid (VOF) method incorporating surface tension stresses. The theoretical background and the motion of an isolated bubble was considered in a separate paper (Chen et al., 1996) where the initial bubble radius was small compared to that of the cylinder and wall-effects were negligible. In this work, the focus is on the interference effects during the motion of two initially spherical bubbles in a gravitational field, as well as the influence of the container wall on the bubble motion: the initial bubble diameter in the present study is more than half the cylinder diameter. The bubble size is also much larger than that required to satisfy the condition in which the gas can be treated as incompressible. In addition, the effect on bubble motion of the inclusion of evaporation at the gas-liquid interface is considered.

Numerical and experimental research for wave damping over a submerged porous breakwater

Abstract: In this paper, wave motion coupled with porous flow within a submerged porous breakwater is studied. Based on Volume-of-Fluid (VOF) technique a Synchro-Linking method (SLM) is developed to simulate waves and porous flow, which are respectively governed by Navier-Stokes' and Forchheimer's equations. Dynamic pressure inside the porous breakwater and wave dissipation over it are obtained through calculation. It is discovered that both the results are significantly affected by breakwater dimensions, as well as the parameters of incident waves. Experiments are also carried out to verify numerical models and results. Comparison between them shows good agreement.

The study of flow pattern and phase-change problem in die casting process

Abstract: The flow pattern and solidification phenomena in die casting process have been investigated in the first phase study. The flow pattern in filling process is predicted by using a VOF (volume of fluid) method. A good agreement with experimental observation is obtained for filling the water into a die cavity with different gate geometry and with an obstacle in the cavity. An enthalpy method has been applied to solve the solidification problem. By treating the latent heat implicitly into the enthalpy instead of explicitly into the source term, the CPU time can be reduced at least 20 times. The effect of material properties on solidification fronts is tested. It concludes that the dependence of properties on temperature is significant. The influence of the natural convection over the diffusion has also been studied. The result shows that the liquid metal solidification phenomena is diffusion dominant, and the natural convection can affect the shape of the interface. In the second phase study, the filling and solidification processes will be considered simultaneously.

VOF法の改良 : Donor-Accepor法と表面張力計算法の改良

Abstract: A new donor-acceptor method and a calculation technique for estimating the surface tension force term have been developed in order to improve VOF (volume of fluid) method. The improved VOF consists of (1) calculation of liquid quantity transferred from donor to acceptor cell by grouped into 11 interface patterns, (2) correction of liquid transfer rate by considering movement in oblique direction, (3) correction of inner cells with defects under conservation of total liquid quantity, (4) highly accurate calculation technique for estimating the surface tension force term by approximating the liquid-vapor interface to a circle. We applied the improved VOF method to a simulation of oscillating liquid drop in which the surface tension force is dominant and the obtained frequency agrees well with the theoretical one.

Simulation of slide-coating flows using a fixed grid and a volume-of- fluid front-tracking technique: Startup and bead breakup

Abstract: Slide coating flow is a workhorse process for manufacturing precision film-coating products. Properly starting up a slide coating process is very important in reducing wastage during startup and ensuring that the process operates within the desired `coating window.` A two-phase flow analysis of slide-coating startup was performed by Palmquist and Scriven (1994) using Galerkin`s method with finite-element basis functions and an elliptic mesh generation scheme. As reported by Chen (1992) from flow visualization experiments, a continuously coated liquid film breaks up into rivulets, which are coating stripes with dry lanes in between, when the coated film becomes thinner and thinner due to either the increase in substrate speed or the reduction in pre-metered feed-liquid pump speed. It was observed that the coated-film breakup process originated from the coating bead, thus the name of bead breakup. Understanding the bead-breakup phenomena and elucidating mechanisms involved will provide guidance for manufacturing thinner coating, an industrial trend for better product performance. In this paper we present simulation results of slide-coating flows obtained from a computational method capable of describing arbitrary, three-dimensional and time-dependent deformations. The method, which is available in a commercial code, uses a fixed grid through which fluid interfaces are tracked by a Volume-of-Fluid technique (Hirt and Nichols, 1981). Surface tension, wall adhesion, and viscous stresses are fully accounted for in our analysis. We illustrate our computational approach by application to startup and the bead-breakup problems. As will be shown, for rapid processes our approach offers the computational efficiency and robustness that are difficult o achieve in conventional finite-element-based methods.

Analysis of electrically induced flows in DC electric arc furnace

Abstract: Limitations of natural resources and environmental pollution problems have forced people to consider seriously about recycling of materials. As a means of recycling, DC arc furnaces can be used to recycle scrap materials and already some industries have started to use them in small scale production. An in depth understanding of the process involved is essential for optimal design and efficient control. Therefore, in order to have a better understanding of the process, the authors developed a mathematical model and the model equations are numerically solved. Volume of fluid method is used to treat the free surface. Numerical results show that a single vortical region is generated within the melt when the bottom electrode diameter is large. When the bottom electrode diameter is small, two vortical regions are found with opposite rotation. It is also found that the volume of fluid method can give a more detailed picture of the flow near the surface below the top electrode.

Design optimization of the STS external LOX tank using a coupled fluid-structures dynamics code with free surface tracking

Abstract: A hybrid structures-computational fluid dynamics code is developed in support of a proposed Space Shuttle External Oxygen Tank baffle redesign. The code is created by incorporating a finite element structure solver and the Volume of Fluid free surface tracking technique into a multi-purpose CFD code. The result is a hybrid numerical code capable of modeling the coupled fluid-structural dynamics for generic axisymmetric tanks. A preliminary test of the model is conducted for the Shuttle LOX Tank using both a four and eight baffle configuration. The results are compared with flight data and the recommended model improvements identified.

Numerical analysis of bubble growth under electric field

Abstract: Numerical analysis has been performed on bubble growth and deformation under an electric field in order to elucidate the mechanisms of boiling heat transfer enhancement by EHD (Electro- Hydrodynamic) effects. Transient Navier-Stokes and Maxwell's equations were solved simultaneously for liquid and vapor phases in a two-dimensional cylindrical co-ordinate system making use of the VOF (Volume of Fluid) method. Bubble growth in liquid R113 under atmospheric pressure has been simulated. First, elongation of a single bubble under uniform electric field is simulated and the final shapes of the bubble are found to be in good agreement with Garton's analytical and experimental results. Second, the bubble deformation process under non-uniform electric field was simulated. A bubble initially attached to the lower electrode starts to deform and finally detaches from the lower electrode. The shape of bubble depends on the intensity of the electric field. The behavior of bubbles, the velocity vectors, and the contours of electric field are also shown and compared with experiment.

Formation fluid flow rate determination

Abstract: A method of determining the volume of a fluid sample withdrawn from an earth formation penetrated by a wellbore is disclosed. The method includes the step of positioning a formation testing tool 13 adjacent to the earth formation 11. The tool includes a probe 18 which can be selectively placed in hydraulic communication with the formation and excluded from hydraulic communication with the wellbore. The probe is in hydraulic communication with a pressure transducer (108 Fig. 3). The tool includes a sample chamber (62, 64) selectively placed in hydraulic communication with the probe. The chamber includes means (111) for measuring the volume of the chamber and means (108) for selectively controlling the volume of the chamber. The method further includes the steps of placing the probe in hydraulic communication with the formation, placing the sample chamber in hydraulic communication with the probe and selectively increasing the volume of the chamber while measuring the volume of the chamber and the pressure, determining the volume of the chamber when a fluid from the wellbore disposed within the probe at the start of withdrawal of the sample ceases to expand, by determining an expansion volume at which the pressure decreases less rapidly with respect to an increase in chamber volume, and determining the volume of the fluid sample by subtracting the expansion volume from a total volume of fluid withdrawn into the sample chamber (62, 64).

Computer modelling of solidification of pure metals and alloys

Abstract: Two numerical models have been developed to describe the volumetric changes during solidification in pure metals and alloys and to predict shrinkage defects in the castings of general three-dimensional configuration. The first model is based on the full system of the Continuity, Navier-Stokes and Enthalpy Equations. Volumetric changes are described by introducing a source term in the Continuity Equation which is a function of the rate of local phase transformation. The model is capable of simulating both volumetric shrinkage and expansion. The second simplified shrinkage model involves the solution of only the Enthalpy Equation. Simplifying assumptions that the feeding flow is governed only by gravity and solidification rate and that phase transformation proceeds only from liquid to solid allowed the fluid flow equations to be excluded from consideration. The numerical implementation of both models is based on an existing proprietary general purpose CFD code, FLOW-3D, which already contains a numerical algorithm for incompressible fluid flow with heat transfer and phase transformation. An important part of the code is. the Volume Of Fluid (VOF) algorithm for tracking multiple free surfaces. The VOF function is employed in both shrinkage models to describe shrinkage cavity formation. Several modifications to FLOW-3D have been made to improve the accuracy and efficiency of the metal/mould heat transfer and solidification algorithms. As part of the development of the upwind differencing advection algorithm used in the simulations, the Leith's method is incorporated into the public domain twodimensional SOLA code. It is shown that the resulting scheme is unconditionally stable despite being explicit.

Numerical simulation of the sloshing of liquids in tanks

Abstract: This thesis presents the development and implementation of a Finite Volume Method (FVM) to simulate the sloshing behaviour of incompressible, constant density liquids in a two- dimensional, rigid rectangular tank. The phenomenon of sloshing is of importance to engineers involved in the design of all types of vehicles which transport confined liquids. This paper reports on the research conducted in the context of the transport of liquids on the ocean surface. The method presented has two immediate applications in this context: the transport of petroleum products, and roll stabilization systems for ocean-going vessels. -- The FVM is used to discretize the governing momentum and mass conservation equations using primitive variables in a fully Eulerian approach. The method is formulated by integrating the governing equations over appropriate control volumes, and assembling systems of linear equations. A fixed rectangular grid with variable spacing is utilized, and momentum control volumes (CVs) are staggered relative to the continuity CVs. The inertial accelerations caused by a specified tank motion are applied to the fluid by the inclusion of additional source terms in the momentum equations. The method can accommodate the simultaneous translation and rotation of the tank relative to an absolute reference frame, and rotation of the tank about a frame attached to it. -- The free surface boundary is handled using the Volume of Fluid (VOF) method, which permits arbitrary movement of the surface, including the possibility of overlapping and smaller regions breaking away. The VOF method is based on the assignment of a variable Ffor each continuity CV, where F represents the average fraction of the cell volume which is occupied by fluid. The VOF method, therefore, defines the shape of the fluid-occupied calculation domain, and the free surface. -- Results were obtained in the form of the free surface configuration, and velocity and pressure distributions throughout the fluid domain. Results are presented for various prescribed tank motions, chosen to verify the method's stability, reliability, and conformance to behaviour predicted by other established means. Prescribed tank motions were; (i) rotation to a constant angle of inclination; (ii) excitation with the predicted natural period; (iii) excitation near the natural period (producing a surface wave with a beating behaviour ); (iv) impulsive translation; (v) continuous rotation; and (vi) arbitrary simultaneous rotation and translation. All input tank motions are of a sinusoidal form. The method generated results in good agreement with expected physical behaviour. In particular, the wave period characteristics has been verified, and the ability of the method to accommodate a combined rotational and translational tank motion (representing ship roll and sway) lias been proven. -- To fully develop and define the capabilities of the proposed method, it is necessary to conduct further testing of the method to verify the surface heights calculated, and to optimize the use of various calculation parameters. In addition, testing with general tank motion (i.e. roll, sway, and heave), and with motions extreme in nature, is recommended. It is also recommended that a version of this method be developed to model a three-dimensional rectangular tank, thus ensuring its applicability to the widest possible range of practical design problems.

Time-Dependent 3D Numerical Simulation of Oldroyd-B Fluid Using Finite Volume Method

Abstract: A three-dimensional numerical simulation of an Oldroyd-B fluid through a 4:1 planar contraction was performed using a time-dependent finite volume method on a staggered grid. The forward Euler scheme was employed to march in time. The non-linear terms in the momentum equations were discretized using a quadratic upstream interpolation. The program was validated on the start-up Couette flow at Reynolds number 1 and different Deborah numbers from 0.5 to 900, and the 2D 4:1 planar contraction of a Newtonian fluid. The time-dependent nature of these flows is analysed taking the solution at various times, from the initial condition to the steady-state, as frames in a motion picture. Results for vortex formation and growth are presented, then the differences between the simulated 2D and 3D planar contractions are discussed. To our knowledge, this is the first time-dependent numerical simulation of a viscoelastic fluid through a three-dimensional 4:1 contraction.

High order accurate, semi-implicit free surface tracking algorithm for aerospace and material processing applications

Abstract: The paper describes a numerical method to predict the dynamics of a free boundary within the flow domain. An algorithm based on the volume of fluid approach is developed for tracking the material, e.g. liquid/gas, interface. The interface is approximated by a set of line (2D) or plane (3D) segments over each computational cell. This piecewise linear approximation of the interface provides the opportunity to evaluate the volumetric fluxes with higher order accuracy. A new scheme for estimating the convective fluxes at cell interfaces is proposed to update the volume fraction field. Using this scheme along with an semi-implicit finite volume discretization coupled with a structure finite element approximation, an efficient numerical algorithm for treating fluid problems with interfaces is developed. Assistant Professor " Senior Engineer/Research *** Graduate Research Assistant Copyright © 1996 by the American Institute for Aeronautics and Astronautics, Inc. All rights reserved. 1 American Institute for Aeronautics and Astronautics

Two-Dimensional Navier-Stokes Simulation of Breaking Waves

Abstract: Numerical simulations describing plunging breakers including the splash-up phenomenon are presented. The motion is governed by the classical, incompressible, two-dimensional Navier-Stokes equation. The numerical modelling of this two-phase flow is based on a piecewise linear version of the volume of fluid method. Preliminary results concerning the time evolution of the liquid-gas interface and the vorticity field are given for short waves, showing how an initial steep wave undergoes breaking and successive splash-up cycles.