Showing papers on "Volume of fluid method published in 1994"
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TL;DR: In this article, the Navier-Stokes equation is solved using staggered finite differences on a MAC grid and a split-explicit time differencing scheme, while incompressibility is enforced using an iterative multigrid Poisson solver.
1,000 citations
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TL;DR: In this paper, the axisymmetric, dynamic breakup of a Newtonian liquid jet injected vertically into another immiscible liquid at various Reynolds numbers is investigated using an algorithm based on the Volume of Fluid (VOF) method.
Abstract: The axisymmetric, dynamic breakup of a Newtonian liquid jet injected vertically into another immiscible Newtonian liquid at various Reynolds numbers is investigated here The full transient from jet start‐up to breakup into drops was simulated numerically by solving the time‐dependent axisymmetric equations of motion and continuity using an algorithm based on the Volume of Fluid (VOF) method that was previously proven successful in simulations of steady‐state liquid jets (ie, of the jet region close to the nozzle before breakup) The algorithm has been further refined here based on its performance on transient problems such as the solution of the free liquid–liquid capillary jet breakup problem The comparison of the simulation results with previous experimental measurements of jet length under conditions where all forces, ie, viscous, inertial, buoyancy, and surface tension, are important, can be judged satisfactory given the sensitive dependence of the results on details of the experimental setup that are not available The comparison involves the jet length till breakup as well as the jet and drop shapes, often far from regular In comparison with experiment, the results of the present numerical method show a greater sensitivity of the jet length to the Reynolds number than the best predictions previously available based on the linear stability analysis of the free liquid–liquid capillary jet breakup problem
85 citations
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TL;DR: In this paper, the Lagrangian displacement of a fluid element can be either positive or negative, depending on the initial position of the fluid element and the velocity of the flow, where the velocity depends on the angle of the body to the plane of marked fluid.
Abstract: A body moves at uniform speed in an unbounded inviscid fluid. Initially, the body is infinitely far upstream of an infinite plane of marked fluid; later, the body moves through and distorts the plane and, finally, the body is infinitely far downstream of the marked plane. Darwin (1953) suggested that the volume between the initial and final positions of the surface of marked fluid (the drift volume) is equal to the volume of fluid associated with the ‘added-mass’ of the body. We re-examine Darwin's (1953) concept of drift and, as an illustration, we study flow around a sphere. Two lengthscales are introduced: ρmax, the radius of a circular plane of marked particles; and x0, the initial separation of the sphere and plane. Numerical solutions and asymptotic expansions are derived for the horizontal Lagrangian displacement of fluid elements. These calculations show that depending on its initial position, the Lagrangian displacement of a fluid element can be either positive – a Lagrangian drift – or negative – a Lagrangian reflux. By contrast, previous investigators have found only a positive horizontal Lagrangian displacement, because they only considered the case of infinite x0. For finite x0, the volume between the initial and final positions of the plane of marked fluid is defined to be the ‘partial drift volume’, which is calculated using a combination of the numerical solutions and the asymptotic expansions. Our analysis shows that in the limit corresponding to Darwin's study, namely that both x0 and ρmax become infinite, the partial drift volume is not well-defined: the ordering of the limit processes is important. This explains the difficulties Darwin and others noted in trying to prove his proposition as a mathematical theorem and indicates practical, as well as theoretical, criteria that must be satisfied for Darwin's result to hold. We generalize our results for a sphere by re-considering the general expressions for Lagrangian displacement and partial drift volume. It is shown that there are two contributions to the partial drift volume. The first contribution arises from a reflux of fluid and is related to the momentum of the flow; this part is spread over a large area. It is well-known that evaluating the momentum of an unbounded fluid is problematic since the integrals do not converge; it is this first term which prevented Darwin from proving his proposition as a theorem. The second contribution to the partial drift volume is related to the kinetic energy of the flow caused by the body: this part is Darwin's concept of drift and is localized near the centreline. Expressions for partial drift volume are generalized for flow around arbitrary-shaped two- and three-dimensional bodies. The partial drift volume is shown to depend on the solid angles the body subtends with the initial and final positions of the plane of marked fluid. This result explains why the proof of Darwin's proposition depends on the ratio ρmax/x0. An example of drift due to a sphere travelling at the centre of a square channel is used to illustrate the differences between drift in bounded and unbounded flows.
75 citations
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TL;DR: In this article, a new scheme for approximating the convective flux is introduced, which is smear free and is not subject to any time step restrictions, in the context of filling problems.
43 citations
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TL;DR: In this article, a computing method for water impact of arbitrary shaped bodies is proposed, which uses body-fitted coordinate system to model the arbitrary profile of the rigid body surface and the transient deformation of the free surface.
Abstract: In this paper, a computing method for water impact of arbitrary shaped bodies will be proposed. We use body-fitted coordinate system to model the arbitrary profile of the rigid body surface and the transient deformation of the free surface is solved by the fractional volume of fluid method. With this combination of the numerical techniques the rigid surface and the free surface boundary conditions are naturally treated at the intersection of both surfaces that improves remarkably the stability and accuracy of the numerical simulation.For the purpose of verifying the present computing method, classical problems of water impact of wedges and circular cylinders are studied. Moreover, water impact of a ship bow section is simulated to illustrate the applicability of the present computing method to practical ship design problems. In these basic studies, we considered the cases in which the body enters an initially calm water surface with a constant velocity. The results of the simulations are examined against the existing analytical theories and published experimental data.
40 citations
01 Jan 1994
TL;DR: In this article, a two-step non-oscillatory shape-preserving positive definite finite difference advection transport scheme was proposed, which merges the advantages of small dispersion error in simple first-order upstream scheme and small dissipation error in the simple second-order Lax-Wendroff scheme.
Abstract: This paper proposes a new two-step non-oscillatory shape-preserving positive definite finite difference advection transport scheme, which merges the advantages of small dispersion error in the simple first-order upstream scheme and small dissipation error in the simple second-order Lax-Wendroff scheme and is completely different from most of present positive definite advection schemes which are based on revising the upstream scheme results. The proposed scheme is much less time consuming than present shape-preserving or non-oscillatory advection transport schemes and produces results which are comparable to the results obtained from the present more complicated schemes. Elementary tests are also presented to examine the behavior of the scheme.
38 citations
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TL;DR: In this article, it is shown that at short times the flow solidifies completely only near the point of release where the flow is thinnest and at later times complete solidification also occurs near the nose of the flow where the cooling rates are greatest.
Abstract: The solidification of hot fluid flowing in a thin buoyancy-driven layer between cold solid boundaries is analysed in a series of two papers. As an approximation to flow in a crack in a weakly elastic solid or to free-surface flow beneath a thin solidified crust, the boundaries are considered to be flexible and to exert negligible resistance to lateral deformation. The resultant equations of continuity and motion reduce to a kinematic-wave equation with a loss term corresponding to the accumulation of solidified material at the boundaries. The Stefan problem for the solidification is coupled back to the flow through the advection of heat by the fluid, which competes with lateral heat loss by conduction to the solid. Heat and mass conservation are used to derive boundary conditions at the propagating nose of the flow. In this paper the two-dimensional flow produced by a line release of a given volume of fluid is investigated. It is shown that at short times the flow solidifies completely only near the point of release where the flow is thinnest, at later times complete solidification also occurs near the nose of the flow where the cooling rates are greatest and, eventually, the flow is completely solidified along its depth. Some transient melting of the boundaries can also occur if the fluid is initially above its solidification temperature. The dimensionless equations are parameterized only in terms of a Stefan number S and a dimensionless solidification temperature Θ. Asymptotic solutions for the flow at short times and near the source are derived by perturbation series and similarity arguments. The general evolution of the flow is calculated numerically, and the scaled time to final solidification, the length and the thickness of the solidified product are determined as functions of S and Θ. The theoretical solutions provide simple models of the release of a pulse of magma into a fissure in the Earth's lithosphere or of lava flow on the flanks of a volcano after a brief eruption. Other geological events are better modelled as flows fed by a continual supply of hot fluid. The solidification of such flows will be investigated in Part 2.
35 citations
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25 Nov 1994TL;DR: In this paper, an automated micro-valve assembly injects fluid into a destination stream, and a fixed volume of the injected fluid is injected into destination stream (26) by pressurizing injected fluid and opening valve.
Abstract: An automated micro-valve assembly injects fluid into a destination stream. The injected fluid is admitted into chamber (11) via valve (18). The injected fluid is retained in the chamber (11) by valves (13, 14, 17, 18). A fixed volume of the injected fluid is injected into destination stream (26) by pressurizing the injected fluid and opening valve (17). The fluid is pressurized by opening T-valve (14), which admits purge gas at a higher pressure than the injected fluid. The purge fluid flows toward the injection valve (17), forming a fluid-lock which establishes the fixed volume of fluid to be injected. The injected fluid between points (22) and (23) is thereby injected into destination stream (26).
28 citations
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3M1
TL;DR: In this paper, a method and apparatus for performing solid-phase extraction on a fluid that contains solubles and suspended solids is presented, which includes a conduit, an SPE medium located in the conduit, and a fluid flow direction altering mechanism or an SPE rotating mechanism.
Abstract: A method and apparatus for performing solid-phase extraction (SPE) on a fluid that contains solubles and suspended solids. The method includes: (a) providing a volume of fluid that contains solubles and suspended solids, (b) processing the volume of fluid to extract solubles therefrom by the steps comprising: (i) passing a first portion of the volume of fluid in a first direction through a solid phase extraction medium; and then (ii) passing a second portion of the volume of fluid through the solid phase extraction medium in a second direction opposite to the first direction; and (c) repeating step (b) a plurality of times such that no substantial amount of the suspended solids is removed from the processed volume of fluid. The apparatus includes a conduit, an SPE medium located in the conduit, and a fluid flow direction altering mechanism or an SPE rotating mechanism.
25 citations
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07 Jul 1994TL;DR: In this article, an isolation assembly is designed so that only a volume of fluid between the outside diameter of the isolation assembly and the inside diameter of a well over a fluid column height from the bottom of the well to the top of the active portion (lower annulus) is removed.
Abstract: The present invention specifically permits purging and/or sampling of a well but only removing, at most, about 25% of the fluid volume compared to conventional methods and, at a minimum, removing none of the fluid volume from the well. The invention is an isolation assembly that is inserted into the well. The isolation assembly is designed so that only a volume of fluid between the outside diameter of the isolation assembly and the inside diameter of the well over a fluid column height from the bottom of the well to the top of the active portion (lower annulus) is removed. A seal may be positioned above the active portion thereby sealing the well and preventing any mixing or contamination of inlet fluid with fluid above the packer. Purged well fluid is stored in a riser above the packer. Ports in the wall of the isolation assembly permit purging and sampling of the lower annulus along the height of the active portion.
15 citations
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TL;DR: In this article, a 3D detailed numerical simulation for flows with bubbles was conducted, based on the local instantaneous field equations of the gas liquid two-phase flow and on the interface tracking method of the volume of fluid method.
Abstract: A three-dimensional detailed numerical simulation for flows with bubbles was conducted in the present study. The simulation was based on the local instantaneous field equations of the gas liquid two-phase flow and on the interface tracking method of the volume of fluid method. The velocity and pressure fields were calculated using the modified SOLA method. The validity of the numerical method was confirmed by the comparison between measured and calculated terminal velocities and shapes of a single bubble in an infinite stagnant liquid for a wide range of the Morton number and the Eotvos number. Then, laminar bubbly flow in a vertical square duct was analyzed by making use of a periodic boundary condition. As a result, two typical void distributions, the wall peak and core peak, were obtained by varying the Eotvos number. This result agreed well with existing experimental data.
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17 May 1994
TL;DR: In this paper, the volumetric flow of the perfusion fluid extracted from the body aperture is measured, with real-time display of the volume difference between the supplied and extracted flow.
Abstract: The device supplies a perfusion fluid with a controlled pressure and flow to the body aperture, by detecting the volumetric flow in a pressure vessel (1.3), in which the fluid is held at a given pressure. The volumetric flow of the fluid extracted from the body aperture is measured, with real-time display of the volumetric difference between the supplied and extracted flow. Pref. separate displays are provided for indicating the volume of fluid within the body aperture and the volume of fluid extracted from the latter and fed to a reception container (1.9).
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TL;DR: In this paper, the feasibility of a detailed numerical simulation of a Taylor bubble in a stagnant liquid filling in a vertical pipe was examined, and the simulation was carried out using the volume of fluid method.
Abstract: The feasibility of a detailed numerical simulation of a Taylor bubble in a stagnant liquid filling in 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 the Eotvos number (Eo) and Morton number (M) were also conducted using sucrose solution and air at room temperature and atmospheric pressure. It was confirmed by the 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, Eo and M. Calculated terminal rising velocities and bubble shapes agreed fairly well with the measured ones, which indicates that the effects of drag force, buoyancy and surface tension force on the bubble were well predicted in the simulation.
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14 Jan 1994
TL;DR: In this article, a change in distance between wheel and chassis results in fluid being returned to the reservoir, and the volume of fluid is proportional to the gas pressure, where the vehicle is jacked up on one side and measured on the scale.
Abstract: A change in distance between wheel and chassis results in fluid being returned to the reservoir. The volume of fluid is proportional to the gas pressure. The connector (18) fits in the filler opening (2) of the reservoir (1). The manually-controlled valve (26) is closed. The return line (22) is disconnected from its pipe (8) and connected to the container input (20). The vehicle is jacked up on one side and the volume of returned fluid measured on the scale (34).
01 Jan 1994
TL;DR: In this article, the authors analyzed geotechnical and acoustic properties of sediments from Lau Basin backarc Sites 834, 835,838, and 839 to examine the large-scale heat and fluid circulation in the Lau Basin.
Abstract: We analyzed geotechnical and acoustic properties of sediments from Lau Basin backarc Sites 834, 835,838, and 839 to examine the large-scale heat and fluid circulation in the Lau Basin. We hypothesize that a feedback system exists in which sediment properties, particularly permeability, affect large-scale heat and fluid circulation and are, in turn, affected by the circulation of fluids. Sediments in the Lau backarc basin display none of the expected trends in physical and acoustic properties as a function of depth and are probably underconsolidated. The sediments can consolidate normally, however, as shown by measuring both compressional- and shear-wave velocity in a controlled laboratory triaxial setting. In-situ underconsolidation might occur because high sedimentation rates could prevent the sediments from dewatering and consolidating normally, or water lost during the consolidation process could be rapidly replaced by fluids circulating through the system convectively. Although initial sedimentation rates were extremely high in the Lau Basin, laboratory measurements indicate that the overlying clayey nannofossil oozes are sufficiently permeable to allow the passage of fluids through the sediments on the scale of several years; however, a comparison of vertical and horizontal components of flow indicates that horizontal fluid flow is 3 orders of magnitude greater than vertical flow. The highly permeable vitric silts and sands probably dominate the horizontal component of fluid flow. Measured vertical heat flow at these sites is much lower than would be predicted by a simple cooling model, suggesting that heat is flowing laterally. A large difference in measured heat flow exists between the lowermost stratigraphic units of Sites 834 and 835, indicating that lateral fluid flow may be occurring. The chemistry of pore fluids measured at Sites 834, 835, and 838 shows an increase and subsequent decrease in dissolved calcium with depth within the sediment column, again suggesting lateral fluid flow. The dissolved-calcium profile at Site 839 shows a seawater signature and no consistent trend downhole, indicating possible downwelling of bottom water throughout the entire sediment column. The volume of fluid required to (1) dissipate the excess heat expected but not measured and (2) prevent the sediments from consolidating normally in these Lau backarc sites is very small, about 8 m3 at Site 834. Very small gradients are required to replace this amount of fluid lost during the 5.5 m.y. of sediment deposition. In general, sites of downwelling are much more diffuse and cooler than sites of upwelling. Site 839 probably is a downwelling site. The remaining three sites possibly are located in a zone of lateral fluid flow within a large-scale, convective circulation cell.
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01 Feb 1994
TL;DR: In this paper, the Scalar Equation Algorithm (SEA) has been developed as an attachment to the PHOENICS and Harwell-FLOW3D CFD codes for this study.
Abstract: The research work presented herein addresses the problem of the mathematical modelling of the mould filling processes as encountered in the foundry industry.
The quality of castings, especially aerospace components, is primarily pre-determined at the stage of mould filling within the entire casting process. The entrapment of oxide films, air voids and other impurities into the cast, caused by waves and the breaking of the molten metal surface during filling must be avoided. Otherwise, substandard casting products will result which cost the foundry industry millions of pounds in lost revenue.
A three-dimensional control-volume, free surface flow technique known as the Scalar Equation Algorithm (SEA) has been developed as an attachment to the PHOENICS and Harwell-FLOW3D CFD codes for this study. The SEA technique uses a conserved scalar variable to represent the liquid, with an adaptation of the van Leer TVD scheme to define the instantaneous position of the interface. It is similar to the approach used by the well known Volume Of Fluid (VOF) method. However, the SEA technique deals with both air and liquid explicitly, whereas the VOF method does not.
A technique has also been developed to allow the liquid temperature to be determined from a conserved `mixture' enthalpy. The liquid temperature is subsequently used in a solidification algorithm to simulate the effect of phase change.
The filling model without heat transfer and solidification has been validated against experimental data in both water experiments and actual mould filling experiments. The capability of the SEA method in capturing convoluted waves and air voids has been successfully demonstrated in an example of filling part of a mould running system. It has also been compared against the predictions from the SOLution Algorithm-Volume Of Fluid (SOLA-VOF) and Marker And Cell (MAC) methods. Examples of the developed filling model coupled with heat transfer and solidification are also given.
To increase computational speed, the filling model has been implemented into a parallelised version of the Harwell-FLOWSD CFD code. A speed-up of up to 80% has been achieved by using a network of heterogeneous processing nodes. Each node consists of an Intel i860 vector processor and an Inmos T800 transputer.
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01 Jan 1994
TL;DR: Recent progress in the development of parallel algorithms for semi-Lagrangian advection is reviewed and a distributed MIMD implementation based on PVM is discussed, establishing that the code is scalable for reasonable sub-grid dimensions on each processor.
Abstract: The passive advection problem in computational fluid dynamics is examined. Eulerian methods are restricted by the Courant Friedrichs Lewy (CFL) condition and the semi-Lagrangian method is introduced as an alternative approach for taking longer time steps. Recent progress in the development of parallel algorithms for semi-Lagrangian advection is reviewed and a distributed MIMD implementation based on PVM is discussed. Parallel performance results on an Intel iPSC/860 are presented and it is established that the code is scalable for reasonable sub-grid dimensions on each processor.
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TL;DR: In this article, the authors used the simplified Hirt & Nichol method with the volume of fraction (VOF) method of treating the free surface for complex free-surface flows in the vicinity of an obstacle placed on the floor of a channel.
Abstract: Complex free-surface flows in the vicinity of an obstacle placed on the floor of a channel to generate a surface wave has been studied experimentally and numerically. The numerical method examined is the simplified MAC method of Hirt & Nichol with the volume of fraction (VOF) method of treating the free surface. This calculation method used with a third-order upwind differencing scheme gives results that agree very well with experiments for not too large waves with relatively small velocities. The experiments show that as the flow volume and the velocity increase, the disturbances appear on the free surface with significant air entrainment. The present calculation method, although does not reproduce the detailes of the experiment exactly, shows appearance similar disturbances.
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TL;DR: In this article, the numerical solution of advection dispersion equations using an Optimal Control,H1, least-squares formulation, associated with a quasi-Newton conjugate gradient algorithm was discussed.
Abstract: This paper discusses the numerical solution of advection dispersion equations using an Optimal control,H1, least-squares formulation, associated with a quasi-Newton conjugate gradient algorithm. The suggested algorithm represents an extension of the method proposed by Bristeauxet al., for the solution of nonlinear fluid flow problems.