Showing papers on "Volume of fluid method published in 2002"

A coupled level set and volume-of-fluid method for the buoyancy-driven motion of fluid particles

Abstract: A level set method is combined with the volume-of-fluid method so that the coupled method not only can calculate an interfacial curvature accurately but also can achieve mass conservation well. The coupled level set and volume-of-fluid (CLSVOF) method is applied to the buoyancy-driven motion of fluid particles. For its easy and efficient implementation, we develop a complete and efficient interface reconstruction algorithm which is based on the explicit relationship between the interface configuration and the fluid volume function. Also, a cubic-interpolated propagation (CIP) scheme is combined with the CLSVOF method to calculate the advection terms of the momentum equation accurately. The improved CLSVOF method is applied for numerical simulation of bubbles and drops rising or falling in a quiescent fluid. The numerical results are found to preserve mass conservation and to be in good agreement with the data reported in the literature.

Volume of fluid interface reconstruction methods for multi-material problems

Abstract: Butadiene polymers containing 70% or more of 1,2-structure and a relatively low melting point are produced by polymerizing 1,3-butadiene in the presence of a catalyst which has been prepared by admixing (A) an organic solvent solution containing 1,3-butadiene, a cobalt compound and an organoaluminium compound; (B) an amide compound of the formula (2) or (3): (2) or (3) wherein R1, R2 and R3 are respectively an H atom, aliphatic hydrocarbon radical of 1 to 7 carbon atoms or aromatic hydrocarbon radical of 6 or 7 carbon atoms, R3 is H or an aliphatic hydrocarbon radical of 1 to 3 carbon atoms and n is 2 to 5, and; (C) carbon disulfide.

A new volume-of-fluid formulation for surfactants and simulations of drop deformation under shear at a low viscosity ratio

Abstract: A numerical algorithm for the linear equation of state is developed for the volume-of-fluid interface-tracking code SURFER++, using the continuous surface stress formulation for the description of interfacial tension. This is applied to deformation under simple shear for a liquid drop in a much more viscous matrix liquid. We choose a Reynolds number and capillary number at which the drop settles to an ellipsoidal steady state, when there is no surfactant. The viscosity ratio is selected in a range where experiments have shown tip streaming when surfactants are added. Our calculations show that surfactant is advected by the flow and moves to the tips of the drop. There is a threshhold surfactant level, above which the drop develops pointed tips, which are due to surfactant accumulating at the ends of the drop. Fragments emitted from these tips are on the scale of the mesh size, pointing to a shortcoming of the linear equation of state, namely that it does not provide a lower bound on interfacial tension. One outcome is the possibility of an unphysical negative surface tension on the emitted drops.

Volume-of-fluid calculation of heat or mass transfer across deforming interfaces in two-fluid flow

Abstract: A new volume-of-fluid (VOF)-based numerical method for calculating heat transfer or mass transfer of a species within and between fluids with deforming interfaces is described. The algorithm is tested first against an analytical solution for diffusion from a sphere, and good agreement between theory and calculation is shown. The method is then demonstrated by predicting (a) heat transfer from a rising bubble when the bubble forms a toroidal shape, and (b) mass transfer from a rising drop when the drop phase controls diffusion. The method is shown to be a viable approach for complex interfacial heat/mass transfer.

Experimental validation of 3-D Lagrangian VOF model : bubble shape and rise velocity

Abstract: A novel 3-D computational fluid dynamics model using an advanced Lagrangian interface tracking scheme was studied to find the time-dependent behavior of gas bubbles rising in an initially quiescent liquid. A novel least-square approach is used to determine the normal behavior at the interface for an accurate reconstruction and advection of the interface based on mollification of the color function by convolution. The incompressible Navier–Stokes equations are solved using an accurate discretization scheme to obtain the flow field of the gas and liquid phase. Detailed experiments of single rising bubbles of different sizes were performed to compare the shape, rise velocity and pressure signal of the bubble with the performed simulations. The developed Lagrangian volume-of-fluid model could accurately track the motion and shape of the gas–liquid interface embedded in a flow field with significant vorticity.

Modification of fluid flow about bodies and surfaces through virtual aero-shaping of airfoils with synthetic jet actuators

Abstract: The present invention involves a system for altering the aerodynamic shape and/or fluid flow about a solid body. The preferred embodiment comprises an obstruction disposed on the solid body and extending outwardly from the solid body into the fluid flowing over the solid body and a synthetic jet actuator embedded in the solid body such that said fluid flowing over the solid body encounters the obstruction before the synthetic jet actuator. The synthetic jet actuator includes a jet housing defined by walls, the jet housing having an internal chamber with a volume of fluid and an opening in the jet housing connecting the chamber to an external environment having the fluid, and a volume changing means for periodically changing the volume within the internal chamber so that a series of fluid vortices are generated and projected in the external environment out from the opening of the jet housing. A synthetic jet stream is formed by the fluid vortices entraining the fluid of the external environment and is projected outwardly from the solid body. The fluid flowing over the solid body contacts the synthetic jet stream forming a recirculation region, thereby modifying both the flow field and the pressure distribution and similarly modifying both the lift and drag characteristics of the solid body.

Airway closure: surface-tension-driven non-axisymmetric instabilities of liquid-lined elastic rings

Abstract: This paper investigates the stability and large-displacement post-buckling behaviour of liquid-lined elastic rings. The fluid flow and the wall deformation are described by the free-surface Navier–Stokes equations and by geometrically nonlinear shell theory, respectively. The fluid–structure interaction problem is solved numerically by a finite element method. The compressive load on the ring is a combination of the external pressure and the effect of surface tension. Once this combined load exceeds a critical value, the subsequent non-axisymmetric collapse of the ring is controlled by the dynamics of the surface-tension-driven redistribution of fluid in the liquid lining. It is shown that, for sufficiently large surface tension, the ring can undergo a catastrophic collapse which leads to a complete occlusion of its lumen. A novel lubrication theory model, which ensures exact volume conservation for flows on strongly curved substrates, is developed and found to be capable of accurately describing the motion of the air–liquid interface and the fluid–structure interaction in the large-displacement regime, even in cases where the film thickness is large.The findings have important implications for the occurrence of airway closure in lung diseases (such as oedema) which cause an increase in the thickness of the airways' liquid lining. It is shown that under such conditions, airways can become occluded even if the volume of fluid in their liquid lining is much smaller than that required to occlude them in their axisymmetric state.

Numerical computation of film boiling including conjugate heat transfer

Abstract: This article presents a numerical method and simulations of film boiling including conjugate heat transfer. A volume-of-fluid (VOF) interface tracking method is augmented with a mass transfer model and a model for surface tension. The bulk fluids are viscous, conducting, and incompressible. We explore film boiling on a horizontal surface and we consider the effect of the energy exchange between a solid wall and the boiling fluid during saturated horizontal film boiling.

A General Fluid Dynamic Analysis of Drop Ejection in Drop-on-Demand Ink Jet Devices

Abstract: Drop-on-demand devices are the heart of most modern ink jet printers. The fluid dynamic process during drop ejection is complex with time-dependent fluid interface disruptions. Based on computations with a generic problem configuration, the present work attempts to provide an insight into the drop ejection behavior for establishing general design rules in device development. The computational results show that the volume of ejected drop is very close to the volume of fluid pushed through the nozzle by an actuation pulse. The speed of the ejected drop is typically between one third and two thirds of the average velocity of the fluid pushed through the nozzle during actuation. The conditions for obtaining various (desirable or undesirable) drop shapes immediately after ejection are examined. The cases when drops may not be successfully ejected are also discussed.

Numerical errors of the volume‐of‐fluid interface tracking algorithm

Abstract: One of the important limitations of the interface tracking algorithms is that they can be used only as long as the local computational grid density allows surface tracking. In a dispersed flow, where the dimensions of the particular fluid parts are comparable or smaller than the grid spacing, several numerical and reconstruction errors become considerable. In this paper the analysis of the interface tracking errors is performed for the volume-of-fluid method with the least squares volume of fluid interface reconstruction algorithm. A few simple two-fluid benchmarks are proposed for the investigation of the interface tracking grid dependence. The expression based on the gradient of the volume fraction variable is introduced for the estimation of the reconstruction correctness and can be used for the activation of an adaptive mesh refinement algorithm. Copyright © 2002 John Wiley & Sons, Ltd.

Dispensing method and apparatus for dispensing very small quantities of fluid

Abstract: A fluid dispensing system and method includes a pump to aspirate and expel sample fluid, a fluid dispensing tip, and a metering station. The fluid dispensing tip includes a working fluid and an air gap where the air gap separates the working fluid from the sample fluid. The metering station receives a drop of sample fluid that is at least twice as large as the predetermined volume to ultimately be dispensed. The fluid dispensing tip then withdraws the predetermined volume of fluid from the sample fluid. Precise volumes are ascertained by prior knowledge of the geometry of the fluid dispensing tip and by using an imaging device to monitor an interface of either the sample fluid or working fluid with the air gap within the fluid dispensing tip. The system and method are capable of accurately dispensing very small volumes of sample fluid on the order of 10 picoliters. In addition, the system and method do not require large volumes of sample fluid to prime a pump mechanism.

A Compressible Model for Separated Two-Phase Flows Computations

Abstract: In order to simulate numerically the physical behaviour of a free surface between two fluids, we have developped a compressible model, able to correctly reproduce sloshing at high Bond number (capillary forces neglectible). We will first present the model. It is composed of four equations in two space dimensions : two for each fluid mass conservation, and two for momemtum conservation. The gas and liquid phases are supposed to be compressible fluids following an isothermal linearized equation of state. A mechanical equilibrium relation closes the model (the equilibrium model). Relaxing this relation, we obtain a new model (the relaxation model) that is more adapted for numerical treatment. The second part of the paper is dedicated to the presentation of the numerical method that we used. We explain why it does not need a scheme for the volume fraction. In particular, there is no specific algorithm to localize the interface, as in VOF, Level-Set or Front Tracking methods. The last part of the paper is devoted to some validation results, compared to analytical solution or experimental data.Copyright © 2002 by ASME

Investigations of mixing in a fluid Jet agitated tank

Abstract: Mixing can be achieved in a variety of ways including mechanical agitation, agitation by a fluid jet impingement or by static mixers. This article is concerned with mixing by a fluid jet impingement. Jet mixing can be described as a fast-moving stream of liquid being injected into a slow-moving or stationary liquid. In this study, computational fluid dynamics (CFD) is used to investigate the performance of a jet mixer. The degree of mixing has been evaluated by monitoring mixing of a hot volume of fluid in the larger tank until criteria for 95% mixing are met at a number of monitoring points. A wide range of jet injection rates has been investigated. Good agreement was shown between numerical and published experimental results. Moreover, the need to monitor mixing at more than one point, and especially at points in zones with little liquid motion, is shown to be necessary. Numerical results provided detailed plots of velocity and temperature fields and clearly showed the locations of zones with very low v...

Acoustic control of the composition and/or volume of fluid in a reservoir

Abstract: The invention provides a device for controlling the composition and/or volume of a fluid within a reservoir. The device includes a reservoir adapted to contain at least one fluid, a means for monitoring a characteristic of the fluid contained in the reservoir, and a means for introducing additional fluid into the reservoir according to the fluid characteristic monitored by the monitoring means. The device also includes an acoustic generator for generating acoustic radiation. A dispensing means may be provided as well. Other devices and methods that use acoustic radiation to control the composition and/or volume of a fluid within a reservoir are included.

Fluid mechanics of Taylor bubbles and slug flows in vertical channels

Abstract: Fluid mechanics of Taylor bubbles and slug flows is investigated in vertical, circular channels using detailed, three-dimensional computational fluid dynamics simulations. The Volume of Fluid model with the interface-sharpening algorithm, implemented in the commercial CFX4 code, is used to predict the shape and velocity of Taylor bubbles moving along a vertical channel. Several cases are investigated, including both a single Taylor bubble and a train of bubbles rising in water. It is shown that the potential flow solution underpredicts the water film thickness around Taylor bubbles. Furthermore, the computer simulations that are performed reveal the importance of properly modeling the three-dimensional nature of phenomena governing the motion of Taylor bubbles. Based on the present results, a new formula for the evaluation of bubble shape is derived. Both the shape of Taylor bubbles and the bubble rise velocity predicted by the proposed model agree well with experimental observations. Furthermore, the present model shows good promise in predicting the coalescence of Taylor bubbles.

Prediction of Green Water and Wave Loading Using a Navier-Stokes Based Simulation Tool

Abstract: Results of computer simulation of wave and green water loading on floating offshore structures are presented. The simulation program used is a CFD code which solves the Navier-Stokes equations that describe flow of incompressible viscous fluids. The Navier-Stokes equations are discretised using a Finite Volume method on a Cartesian grid with staggered variables. The free surface is displaced using a Volume Of Fluid based algorithm combined with a local height function. In this paper results of validation and sensitivity tests of simulation of green water on the foredeck of an FPSO are presented. Here, the waves are modeled as a dam of water around the deck which is suddenly released. Furthermore, wave loading from impact of regular waves on a SPAR platform is computed and compared with experimental results. The program is found to be robust and the computational results show good agreement with the experiments.Copyright © 2002 by ASME

Simulation of hydrodynamic dispersion in gas/liquid microreactors

Abstract: Dispersion and spreading of concentration signals in gas/liquid microreactors is studied with methods of computational fluid dynamics (CFD). It is shown that conventional reactor designs exhibit a broad residence-time distribution due to convective signal dispersion. This result is supported by experiments monitoring the transport of a liquid plug introduced into the microreactor by a microdispenser. A new reactor design is proposed which exhibits a more favorable velocity profile by guiding the liquid stream over alternating platelets. With simulations based on the volume-of-fluid (VOF) method it is shown that a thin, continuous liquid film forms inside the reactor. Subsequently, the transport of concentration fields described by a convection-diffusion equation is studied. It is found that, due to the approximate plug-flow character of fluid motion within this film, concentration signals experience significantly lower dispersion than in the conventional design. The new reactor design will provide the basis of a new class of gas/liquid microreactors to be developed at the Institute of Microtechnology Mainz.

3D Direct Numerical Simulation of Air Bubbles in Water at High Reynolds Number

Abstract: This article presents direct numerical simulations of single air bubbles and bubble pairs in water (with log Mo = −10.6) with a highly parallelized code based on the Volume Of Fluid method (VOF). Systematical simulations of terminal velocity of single bubbles with a diameter ranging from 0.5–15 mm (ReB = 200–3750) show good agreement with experimental data from Clift et al. Bubbles with a diameter of 8 mm show strong realistic surface deformations. Initial white noise has been added to all simulations to create realistic starting conditions. Rise paths of the bubbles depend strongly on the boundary conditions and the wall distance. Small wall distances reduce the path radii of the bubbles leading to an increased wake shedding frequency. For bubble pairs with wobbling surfaces the phenomenon of shedding of vortices from the edges of the bubbles is observed.Copyright © 2002 by ASME

The effect of non-newtonian flow behaviour on binary droplet collisions: vof-simulation and experimental analysis

Abstract: Experimental investigations and numerical simulations of binary droplet collisions using Newtonian and nonNewtonian fluids have been performed. This provides a validation of the employed numerical methods and simulation software as well as a first insight into the basic phenomenon of binary droplet collision with nonNewtonian fluids. The Newtonian, respectively non-Newtonian fluids used were glycerol/water and shear-thinning water/carboxymethylcellulose (CMC). The non-Newtonian behaviour was modelled by means of a generalized Newtonian constitutive equation using a modified power law viscosity function. A shear-thinning liquid shows its lowered viscosity during the droplets collision by a larger maximum diameter of the generated collision complex, compared to a Newtonian collision with similar values of the characteristic dimensionless groups. This behaviour can be simulated and quantitatively reproduced by the three-dimensional CFD code FS3D (University of Stuttgart, ITLR), which has been extended in the present investigation towards non-Newtonian fluids. The code uses the Volume-of-Fluid (VOF) method for the description of the free fluid surface. The obtained results increase confidence in the selected generalized Newtonian modelling for the experimental fluid. The dimensionless time until the collision complex attains its maximum expansion is found to be independent of the viscosity characteristics; it is only a function of the Weber number. Therefore, the absolute time for reaching the maximum complex diameter for a given Weber number is merely proportional to the ratio of droplet diameter to droplet velocity. The simulated velocity fields show that at all stages of the collision process there are areas in which the velocity gradients for shear are larger than the elongational ones, and vice versa. Overall, elongational flow dominates.

Use of the particle level set method for enhanced resolution of free surface flows

Abstract: A new numerical method for improving the mass conservation properties of the level set method when the interface is passively advected in a flow field is proposed. The method, a hybrid “Particle Level Set Method”, uses Lagrangian marker particles to rebuild a level set representation of the interface in regions which are under-resolved. This is often the case for flows undergoing stretching and tearing. A level set only approach towards maintaining small-scale interface features is subject to excessive amounts of numerical regularization. This numerical regularization artificially alters or destroy these features. By combining a simple Lagrangian method, massless marker particles, with the level set method, the ability to smoothly represent both large and small scale geometrical features is obtained while maintaining the implementation simplicity characteristic of the level set method. A variety of interface tracking tests, including a newly proposed three dimensional deformation flow test case, are performed to demonstrate that the method compares favorably with volume of fluid methods in the conservation of mass and purely Lagrangian schemes for interface resolution. The robustness of the method in representing complex, three dimensional free surface fluid flows is illustrated through its use in producing physically based animations of the pouring of a glass of water; the splash generated by the impact of a ball thrown into a tank of water; and the breaking of a wave on a submerged beach. The behavior of the water is calculated by a three dimensional Navier-Stokes free surface fluid simulation. A novel application of a level set based velocity extrapolation technique is used to provide a smooth, physically based velocity field away from the liquid at the interface. This velocity field satisfies the physical boundary conditions at the interface and provides a plausible velocity field for use by Lagrangian particles outside the liquid as required by the “Particle Level Set Method”. Selected frames from each of the animations are provided.

Feed channels of a fluid ejection device

Abstract: Volume of fluid feed channels is adjusted for drop generators that are staggered with respect to a feed edge. In one embodiment, barrier islands are positioned, sized, and/or shaped to adjust the volume. In another embodiment, protrusions or walls thereof are positioned to adjust the volume.