Showing papers on "Volume of fluid method published in 1998"
TL;DR: The method is tested by testing its ability to track interfaces through large, controlled topology changes, whereby an initially simple interface configuration is subjected to vortical flows, and numerical results for these strenuous test problems provide evidence for the algorithm's improved solution quality and accuracy.
1,552 citations
TL;DR: In this paper, a numerical technique (FGVT) for solving the time-dependent incompressible Navier-Stokes equations in fluid flows with large density variations is presented for staggered grids.
Abstract: A numerical technique (FGVT) for solving the time-dependent incompressible Navier-Stokes equations in fluid flows with large density variations is presented for staggered grids. Mass conservation is based on a volume tracking method and incorporates a piecewise-linear interface reconstruction on a grid twice as fine as the velocity pressure grid. It also uses a special flux-corrected transport algorithm for momentum advection, a multigrid algorithm for solving a pressure-correction equation and a surface tension algorithm that is robust and stable. In principle, the method conserves both mass and momentum exactly, and maintains extremely sharp fluid interfaces. Applications of the numerical method to prediction of two-dimensional bubble rise in an inclined channel and a bubble bursting through an interface are presented
357 citations
TL;DR: In this paper, an Arbitrary Lagrangian-Eulerian (ALE) finite element method for the simulation of fluid domains with moving structures is described, where the fluid is viscous, incompressible and unsteady and the fluid motion is solved by a fractional step discretization of the Navier-Stokes equations.
Abstract: This paper describes an Arbitrary Lagrangian- Eulerian (ALE) finite element method for the simulation of fluid domains with moving structures. The fluid is viscous, incompressible and unsteady and the fluid motion is solved by a fractional step discretization of the Navier-Stokes equations. The emphasis is on convection dominated flows, and a three-step method is used for the convection term. The moving structure causes the mesh of the fluid domain to move, and a new algorithm is proposed to solve the important and crucial problem of the calculation of the mesh velocities. Numerical calculations of the added mass and added damping of a vibrating two-dimensional circular cylinder in the frequency Reynolds number range Re
w
=20−2000 are performed to evaluate the proposed ALE finite element method. The numerically calculated added mass and added damping are compared to both analytical and numerical results. To further demonstrate the generality of the method, a numerical simulation of flow past an oscillating schematic sports car is presented.
343 citations
Book•
11 May 1998
TL;DR: The Navier-Stokes equation is derived from the advection-diffusion equation as discussed by the authors, and the Navier Stokes equation derived quantities are derived from weak operators some element matrices and projection methods.
Abstract: The advection-diffusion equation the Navier-Stokes equation derived quantities. Appendices: weak operators some element matrices and projection methods.
324 citations
Patent•
21 Jan 1998
TL;DR: In this paper, a system consisting of a volume of fluid and a temperature altering device in close proximity to the volume is described, and a transfer member is provided to transfer at least some of the fluid into the patient while at the desired temperature.
Abstract: The invention provides systems and methods for infusing a fluid into a patient. In one exemplary embodiment, a system comprises a volume of fluid (30) and a temperature altering device (32) in close proximity to the volume of fluid. The temperature altering device is employed to heat or cool the volume of fluid to a desired temperature. A positive pressure device (36, 46) is provided to place the volume of fluid under positive pressure while at the desired temperature. A transfer member (14) is further provided to transfer at least some of the fluid into the patient while at the desired temperature.
239 citations
TL;DR: In this paper, a simplified method for calculating advection of mixing ratios in a mass conservative and monotonic manner is presented, which employs a special treatment near local maxima and minima to preserve extremes very well.
173 citations
TL;DR: In this paper, the velocity distribution of fluid in the drop is computed numerically and the viscous flow and inertial force of a molten metal generated by the peak current are found to have significant effects on the metal transfer and drop detachment.
Abstract: The dynamic characteristics of metal transfer in the pulsed current gas metal arc welding are analysed using the volume of fluid method incorporating the electromagnetic force. The surface profile and the velocity distribution of fluid in the drop are computed numerically. The viscous flow and inertial force of a molten metal generated by the peak current are found to have significant effects on the metal transfer and drop detachment. The ranges of the pulsing frequency for which one drop is detached per current pulse are predicted and calculated results are in good agreement with the experimental data with some discrepancy for low load duty cycles.
93 citations
TL;DR: In this paper, the propagation at high Reynolds number of a heavy, two-dimensional gravity current of given initial volume at the base of a uniform flow is considered, and a simple box model for the motion of and deposit from the gravity current is constructed.
Abstract: The propagation at high Reynolds number of a heavy, two-dimensional gravity current of given initial volume at the base of a uniform flow is considered. An experimental setup is described for which a known volume of fluid is rapidly introduced halfway down a 9 m channel in which there is a uniform flow of water. The density excess of the released fluid is produced by either dissolving salt or suspending particles in water. The upstream and downstream propagation of the current was measured for dierent initial salt concentrations, particle sizes and concentrations. A simple box model for the motion of and deposit from the gravity current is constructed. The analytical results obtained compare well with our numerical solutions of one-layer and two-layer models incorporating the appropriate shallow-water equations. Both sets of results are in very good agreement with the experimental data.
85 citations
TL;DR: In this article, a self-consistent 1D finite-difference model was applied to the reaction of calcite + quartz to wollastonite in a 10m thick marble, in response to influx of H2O rich fluid, with fixed boundary conditions.
Abstract: Existing models of metasomatic flow do not allow for the effect that reaction has on the flow patterns. Instead, it is assumed that the volatiles produced are negligible in volume compared to those infiltrated and that reaction does not modify permeability. This is clearly unlikely to be true for infiltration-driven decarbonation reactions.
The rates of porosity creation by reaction and porosity loss by creep have been calculated for a representative volume of calcite –quartz-wollastonite marble, and it is found that, even for a weak calcite matrix, the rate of porosity generation by reaction is likely to outstrip the collapse of porosity, as long as the system is out of equilibrium.
We have applied a self-consistent 1D finite-difference model to the reaction of calcite + quartz to wollastonite in a 10m thick marble, in response to influx of H2O rich fluid, with fixed boundary conditions. The model allows us to evaluate the effect of reaction on the porosity structure and fluid pressure variation across the layer, from which local Darcy fluxes can be evaluated. The progress of reaction that we model is constrained by hydrological considerations, with the requisite parameters recalculated as reaction progresses, assuming creep compaction of rock under the stress difference between lithostatic and fluid pressures.
We fnd that the volume of fluid realised by decarbonation, driven by influx of H20, is sufficient to create a back-flow, so that further advancement of the reaction front is only possible as a result of diffusion of water against the Darcy flux. The effect of creep driven by differences between fluid pressure and lithostatic pressure is to reduce the permeability of the layer and especially reduce the secondary porosity developed in the zone at and behind the advancing reaction front. We predict that in a 3D situation, the porous zone of reacted marble becomes a conduit for layer-parallel flow, and the secondary porosity is infilled by calc-silicate minerals due to silica metasomatism.
77 citations
TL;DR: In this paper, a correction method is developed and applied to the piecewise parabolic method for use in multidimensional modeling, which is a time split, alternating direction method with a flux correction to account for diagonal advection.
Abstract: Meteorological and air quality models rely on accurately solving the advection equation in two and three dimensions. While a number of methods have been developed, all suffer from the formation and growth of errors during the solution procedure. Here, a correction method is developed and applied to the piecewise parabolic method for use in multidimensional modeling. This method is a time-split, alternating direction method with a flux correction to account for diagonal advection. The correction removes over- and undershooting while maintaining the method’s accuracy. The analysis also indicates that some methods will have errors that grow significantly in time, while the corrections developed minimize the problem. This analysis found that the buildup of errors was more pronounced in three-dimensional tests, suggesting that this is an import evaluation criteria for other advection algorithms as well.
65 citations
Journal Article•
TL;DR: In this paper, the effect of the welding arc is considered under the assumptions of a uniform and linear current density on the pendant drop surface, and free surface profiles, pressure and velocity distributions within the drop are calculated numerically.
Abstract: The dynamic characteristics of the globular and spray metal transfer modes are simulated by adopting the Volume of Fluid (VOF) method. The electromagnetic force due to the welding current is included in the formulation of the VOF algorithm. The effect of the welding arc is considered under the assumptions of a uniform and linear current density on the pendant drop surface. The free surface profiles, pressure and velocity distributions within the drop are calculated numerically. It is found that axial flow and radial pinch force promote drop detachment, and the taper of the elongated molten drop in the spray mode is maintained by the electromagnetic force. The current density distribution on the drop surface has significant effects on the molten drop profile, detaching drop volume and taper formation at the molten tip. Predicted results are in reasonably good agreement with the experimental data.
TL;DR: In this article, the fluid displacement associated with the injection and subsequent translation of high Reynolds number bubbles in a thin gap is examined experimentally, and compared with a theoretical model based on a two-dimensional inviscid flow calculation.
TL;DR: In this paper, the dynamics of a passive particle in a two-dimensional incompressible flow generated by three point vortices advected by their mutual interaction is considered as a periodically forced Hamiltonian system.
Abstract: The dynamics of a passive particle in a two-dimensional incompressible flow generated by three point vortices advected by their mutual interaction is considered as a periodically forced Hamiltonian system. The geometry of the background vortex flow determines the degree of chaotization of the tracer motion. Two extreme regimes, of strong and weak chaos, are specified and investigated analytically. Mappings are derived for both cases, and the border between the chaotic and regular advection is found by applying the stochasticity criterion. In the case of strong chaos, there exist coherent regular structures around vortices (vortex cores), which correspond to domains with $\mathrm{KAM}$ curves. An expression for the radius of the cores is obtained. The robust nature of vortex cores, demonstrated numerically, is explained. In the near-integrable case of weak chaotization, a separatrix map is used to find the width of the stochastic layer. Numerical simulations reveal a variety of structures in the pattern of advection, such as a hierarchy of island chains and sticky bands around the vortex cores.
TL;DR: In this article, the authors used Computational Fluid Dynamics (CFD) analysis to simulate fluid and dilute particulate flows on one operational spiral unit, and the model forms the basis for future examination of the two-way fluid-particle coupling processes and interparticle effects.
TL;DR: In this paper, the VOF method is adopted for finite element analysis of transient fluid flow with a free surface, and an adaptation technique for generating an adaptive grid is incorporated to capture a higher resolution of the free surface configuration.
Abstract: SUMMARY The VOF method is adopted for the finite element analysis of transient fluid flow with a free surface. In particular, an adaptation technique for generating an adaptive grid is incorporated to capture a higher resolution of the free surface configuration. An adaptive grid is created through the refinement and mergence of elements. In this domain the elements in the surface region are made finer than those in the remaining regions for more efficient computation. Also, three techniques based on the VOF method are newly developed to increase the accuracy of the analysis, namely the filling pattern, advection treatment and free surface smoothing techniques. Using the proposed numerical techniques, radial flow with a point source and the collapse of a dam are analysed. The numerical results agree well with the theoretical solutions as well as with the experimental results. Through comparisons with the numerical results of several cases using different grids, the efficiency of the proposed technique is verified. # 1998 by John Wiley & Sons, Ltd.
01 Sep 1998
TL;DR: In this paper, the authors present an analytical method for the computation of boundary shear stress distributions acting on the flow perimeter of prismatic open channels, based on the premise that the surplus energy of any arbitrary unit volume of fluid in a three-dimensional flow channel will be transported towards and dissipated at a unit area on the wetted perimeter.
Abstract: This paper presents an analytical method for the computation of boundary shear stress distributions acting on the flow perimeter of prismatic open channels. The approach is based on the premise that the surplus energy of any arbitrary unit volume of fluid in a three-dimensional flow channel will be transported towards and dissipated at a unit area on the wetted perimeter. This leads to a concept which states that the direction of energy transportation will define a minimum relative distance, Φ, between the source of energy in the flow field and the boundary. Based on this concept, a novel method is developed for the partitioning of the flow cross-sectional area into various parts corresponding to the channel shape and roughness composition on the wetted perimeter. The method enables the distribution of the boundary shear over the wetted perimeter to be assessed within each sub-flow area. This paper illustrates the application of the principle to steady and uniform flow in smooth rectangular open channels. Analytical equations governing the boundary shear stress distributions have been derived and are valid for all channel aspect ratios. The formulae have been verified using experimental shear data from published sources.
TL;DR: In this article, a numerical model for two-phase flows with varying density is presented, in which a modified volume of fluid (VOF) method is combined with a semi-implicit algorithm (simple ) and a higher-order advection scheme in a collocated grid.
Abstract: One of the challenges in modelling multiphase fluid systems is to capture accurately the discontinuous-interface phenomenon. In this paper a numerical model for two-phase flows with a varying density is presented, in which a modified volume of fluid (VOF) method is combined with a semi-implicit algorithm ( simple ) and a higher-order advection scheme in a collocated grid. The improved volume tracking method allows interfaces to be captured and maintained compactly in one cell, without imposing restrictions on the topological complexity or the number of interfaces that can be represented. The surface tension force is modelled by a continuum surface force approximation. An efficient solver is used for the resulting system of the linear equations. Example problems simulated in this paper are the buoyancy-driven motion of multiple bubbles in a viscous liquid, and bubble-rise towards an interface. The complex topological changes that occur during bubble rise are well predicted. The result is verified by experimental data in the literature.
TL;DR: In this paper, a numerical procedure for simulating two-fluid flows is presented, based on the Volume of Fluid (VOF) method proposed by Hirt and Nichols and the continuum surface force (CSF) model developed by Brackbill, et al.
Abstract: In this paper a numerical procedure for simulating two-fluid flows is presented. This procedure is based on the Volume of Fluid (VOF) method proposed by Hirt and Nichols and the continuum surface force (CSF) model developed by Brackbill, et al. In the VOF method fluids of different properties are identified through the use of a continuous field variable (color function). The color function assigns a unique constant (color) to each fluid. The interfaces between different fluids are distinct due to sharp gradients of the color function. The evolution of the interfaces is captured by solving the convective equation of the color function. The CSF model is used as a means to treat surface tension effect at the interfaces. Here a modified version of the CSF model, proposed by Jacqmin, is used to calculate the tension force. In the modified version, the force term is obtained by calculating the divergence of a stress tensor defined by the gradient of the color function. In its analytical form, this stress formulation is equivalent to the original CSF model. Numerically, however, the use of the stress formulation has some advantages over the original CSF model, as it bypasses the difficulty in approximating the curvatures of the interfaces. The least-squares finite element method (LSFEM) is used to discretize the governing equation systems. The LSFEM has proven to be effective in solving incompressible Navier-Stokes equations and pure convection equations, making it an ideal candidate for the present applications. The LSFEM handles all the equations in a unified manner without any additional special treatment such as upwinding or artificial dissipation. Various bench mark tests have been carried out for both two dimensional planar and axisymmetric flows, including a dam breaking, oscillating and stationary bubbles and a conical liquid sheet in a pressure swirl atomizer.
TL;DR: In this article, a finite element algorithm is presented for filling of moulds which also models the solidification effects such as the formation of cold shuts during the process, and the incompressible Navier-Stokes equations are solved using the Galerkin finite element method.
Journal Article•
TL;DR: In this paper, the effects of welding current, drop volume, contact area, and wire feed rate on metal transfer are analyzed through variations of the pinch radius and break-up time, and a current waveform on the characteristics of the metal transfer also are simulated.
Abstract: Short-circuit transfer is simulated dynamically by adopting the Volume of Fluid (VOF) method to analyze the effects of welding parameters on metal transfer. Appropriate initial and boundary conditions are imposed to simulate short-circuit transfer. The free surface profiles, pressure and velocity distributions are computed numerically during short-circuit transfer. The effects of the welding current, drop volume, contact area and wire feed rate on metal transfer are analyzed through variations of the pinch radius and break-up time. In the early stage of transfer, the molten metal in the bridge is transferred to the weld pool mainly due to the capillary pressure. The electromagnetic force becomes a dominant factor in the later stages of transfer. The effects of a current waveform on the characteristics of the metal transfer also are simulated.
TL;DR: In this paper, the transport properties of dipolar vortices propagating on an f-plane are studied experimentally by examining the distortion of a series of material surfaces, and the results are applied to give new insight to the effect of Vortices in enhancing diffusion, and to the secondary flow generated by the transport of ambient potential vorticity.
TL;DR: In this paper, both first and second-order algorithms were developed based on the volume-of-fluid method to improve the numerical analysis of free surface convection and interface reconstruction.
Abstract: SUMMARY To improve the numerical analysis of free surface convection and interface reconstruction, both first- and secondorder algorithms are developed based on the volume-of-fluid method. The methodology applied to the secondorder model is to define the second-order linear curve having both face slopes as near horizontal as possible while satisfying the cell’s defined volume fraction. The second-order method is compared with the FLAIR method and the first-order method through simulation of the convection for various sizes of circular liquid shapes and solitary waves. For small curvature of the free surface, e.g. circles with large diameter, linear methods such as the FLAIR method and the first-order method show relatively good predictions. However, for large-curvature configurations, e.g. circles with relatively small diameter or solitary waves, the linear approach shows large distortion of the free surface. In contrast, the secondorder model always shows powerful prediction capabilities of free surface convection. # 1998 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Fluids, 26: 79‐100 (1998)
TL;DR: Methods used to track the free surface in numerical flow simulations, typically during the casting of metals into moulds are examined, and a method for the numerical simulation of flow where thefree surface boundary conditions are important is proposed.
Abstract: Methods used to track the free surface in numerical flow simulations, typically during the casting of metals into moulds are examined in this paper. The algorithm employed makes use of a mixed interpolation formulation to approximate the discretised governing equations for elimination on a Langrangian type moving mesh. Significant savings in CPU time are realised by virtue of the the air domain not being considered in the finite element analysis. The advantages and drawbacks of commonly used methods are discussed, and a method proposed for the numerical simulation of flow where the free surface boundary conditions are important. The effectiveness of the proposed algorithm in solving typical industrial flow problems is demonstrated using numerical examples. The results obtained are compared with analytical and numerical data with a view to validating the algorithm.
TL;DR: In this article, a volume of fluid finite difference method based computer code was developed to simulate the heat transfer and squeezing flow in the hot-plate welding process and the simulation results include melt displacement, temperature distribution, and stress build-up and relaxation.
Abstract: A volume of fluid finite difference method based computer code was developed to simulate the heat transfer and squeezing flow in the hot-plate welding process. The simulation results include melt displacement, temperature distribution, and stress build-up and relaxation. By implementing the crystallization kinetic model developed in Part I, the formation of stress-induced crystal structure in the heat affected zone can be revealed.
01 Jan 1998
TL;DR: In this paper, a volume tracking model based on Youngs' VOF is proposed to track the motion of a gas- liquid interface subject to appreciable changes in its topology, embedded in a flow field with significant vorticity.
Abstract: This paper presents a Volume Tracking model developed with the specific objective of studying the time – dependent behavior of multiple, “large” gas bubbles rising in an initially quiescent liquid. The model, based on the Volume – Of – Fluid concept, employs an advanced interface tracking scheme known as Youngs’ VOF to advance the gas – liquid interface through the Eulerian mesh. Additionally, the model solves the incompressible Navier – Stokes equations to obtain the flow field. Results obtained for four different cases will be discussed: the formation and rise of a skirted bubble and of a spherical cap bubble, the coalescence of two identical gas bubbles and the behavior of two gas bubbles emanating from two adjacent orifices. It could be concluded that the Volume Tracking model is able to track the motion of a gas – liquid interface, subject to appreciable changes in its topology, embedded in a flow field with significant vorticity.
Patent•
17 Jul 1998TL;DR: In this article, the authors present a container (11) in the form of a single housing for holding fluid, including a first collapsible reservoir (13C) having a first valve (25).
Abstract: The present invention is a container (11) in the form of a single housing for holding fluid, including a first collapsible reservoir (13C) having a first valve (25). The first reservoir initially contains a volume of fluid. The container also includes a second reservoir (13W), initially empty (or substantially empty), expandable to a second volume. The second reservoir has a second valve (25). As the volume of said first reservoir decreases, the volume of the second reservoir proportionally increases.
TL;DR: In this article, a fully-analytical design sensitivity formulation for transient, turbulent, free surface flows is derived and implemented in the context of finite element analysis, and the design of the runner and gating system of a simple block casting is presented as an example application for using sensitivity information in design.
Abstract: A novel, fully-analytical design sensitivity formulation for transient, turbulent, free surface flows is derived and implemented in the context of finite element analysis. The time-averaged, turbulent form of the Navier–Stokes equations are solved using a mixing length model, in conjunction with the volume of fluid (VOF) method to model the free surface movement. The design derivatives of these governing equations are computed and solved to find the analytical sensitivities of the fluid position, velocity and pressure fields with respect to shape design variables. The computational efficiency produced by evaluating the sensitivities analytically is demonstrated. The design of the runner and gating system of a simple block casting is presented as an example application for using sensitivity information in design. The analytical sensitivity routine is coupled to a numerical optimizer to yield an automated method for optimal design of the casting rigging system. The results produce runner shapes which eliminate mold-gas aspiration. © 1998 John Wiley & Sons, Ltd.
TL;DR: In this paper, a code using a finite volume approach on the thin gap Hele-Shaw flow equations to simulate the filling stage of the injection molding process has been developed which requires a suitable algorithm for the free front tracking.
Abstract: With free surface flow problems the position of the free front at a particular time step needs to be predicted. When simulating the flow of hot molten polymer in injection moulds this position is essential for the prediction of the position of the weld lines on the final product. Weld lines are important in that they indicate positions of diminished strength and spoil the aesthetics of the product. A code using a finite volume approach on the thin gap Hele–Shaw flow equations to simulate the filling stage of the injection moulding process has been developed which requires a suitable algorithm for the free-front tracking. The Volume of Fluid (VOF) method was implemented in this study for the tracking of the free front. The discretization and various formulations of the VOF equation are presented as well as the results obtained. The impact on the existing equations is also investigated as well as the development of a packing routine that is used to eliminate the diffusive nature of the VOF equation. © 1998 John Wiley & Sons, Ltd.
TL;DR: In this article, the authors used primitive variables on a staggered grid system for solving incompressible Navier-Stokes equations, which are subjected to the distortion of free surface.
Abstract: The sloshing dynamics in a tank partially filled with liquid oil was simulated in this study. The formulation uses primitive variables on a staggered grid system for solving incompressible Navier-Stokes equations, which are subjected to the distortion of free surface. We made use of a volume of fluid technique to resolve numerical difficulties in association with nonlinear free-surface boundary conditions while a two-dimensional quadratic upwind advection scheme to deal with flux nonlinearities. Two problems, namely the free oscillation and the solitary wave propagation, have been chosen for benchmarking the method presented here. The liquid oscillations under conditions of resonance or nonresonance frequency in an oil tanker containing a perforated baffle plate have been studied extensively for two different liquid levels. Through this simulation, we have found that the degree of sloshing can be mitigated by these baffle plates.
01 May 1998
TL;DR: In this article, a modified version of the free-surface Navier-Stokes solver RIPPLE was used to compute the time development of an oil drop on a surface under a simulated air boundary layer.
Abstract: The fringe-imaging skin friction (FISF) technique, which was originally developed by D J Monson and G G Mateer at Ames Research Center and recently extended to 3-D flows, is the most accurate skin friction measurement technique currently available The principle of this technique is that the skin friction at a point on an aerodynamic surface can be determined by measuring the time-rate-of-change of the thickness of an oil drop placed on the surface under the influence of the external air boundary layer Lubrication theory is used to relate the oil-patch thickness variation to shear stress The uncertainty of FISF measurements is estimated to be as low as 4 percent, yet little is known about the effects of surface tension and wall adhesion forces on the measured results A modified version of the free-surface Navier-Stokes solver RIPPLE, developed at Los Alamos National Laboratories, was used to compute the time development of an oil drop on a surface under a simulated air boundary layer RIPPLE uses the volume of fluid method to track the surface and the continuum surface force approach to model surface tension and wall adhesion effects The development of an oil drop, over a time period of approximately 4 seconds, was studied Under the influence of shear imposed by an air boundary layer, the computed profile of the drop rapidly changes from its initial circular-arc shape to a wedge-like shape Comparison of the time-varying oil-thickness distributions computed using RIPPLE and also computed using a greatly simplified numerical model of an oil drop equation which does not include surface tension and wall adhesion effects) was used to evaluate the effects of surface tension on FISF measurement results The effects of surface tension were found to be small but not necessarily negligible in some cases