Showing papers on "Volume of fluid method published in 2001"

Modeling and computation of unsteady cavitation flows in injection nozzles

Abstract: This paper deals with the numerical simulation of cavitation phenomena inside injector nozzles. The numerical approach combines the Volume-of-Fluid technique (VOF) with a model predicting the growth and collapse of bubbles. To model the turbulence effect a k–ω model is introduced for the two-phase flow. Calculations show that the numerical method is able to reproduce complex cavitation phenomena as observed in injection nozzle experiments.

A new volume of fluid advection algorithm: the defined donating region scheme

Abstract: This paper presents a new volume of fluid (VOF) advection algorithm, termed the defined donating region (DDR) scheme. The algorithm uses a linear piecewise method of free surface reconstruction, coupled to a fully multi-dimensional method of cell boundary flux integration. The performance of the new scheme has been compared with the performance of a number of alternative schemes using translation, rotation and shear advection tests. The DDR scheme is shown to be generally more accurate than linear constant and flux limited schemes, and comparable with an alternative linear piecewise scheme. The DDR scheme conserves fluid volume rigorously without local redistribution algorithms, and generates no fluid ‘flotsam’ or other debris, making it ideal in applications where stability of the free surface interface is paramount. Copyright © 2001 John Wiley & Sons, Ltd.

Two-dimensional viscous gravity currents flowing over a deep porous medium

Abstract: The spreading of a two-dimensional, viscous gravity current propagating over and draining into a deep porous substrate is considered both theoretically and experimentally. We first determine analytically the rate of drainage of a one-dimensional layer of fluid into a porous bed and find that the theoretical predictions for the downward rate of migration of the fluid front are in excellent agreement with our laboratory experiments. The experiments suggest a rapid and simple technique for the determination of the permeability of a porous medium. We then combine the relationships for the drainage of liquid from the current through the underlying medium with a formalism for its forward motion driven by the pressure gradient arising from the slope of its free surface. For the situation in which the volume of fluid V fed to the current increases at a rate proportional to t 3 , where t is the time since its initiation, the shape of the current takes a self-similar form for all time and its length is proportional to t 2 . When the volume increases less rapidly, in particular for a constant volume, the front of the gravity current comes to rest in finite time as the effects of fluid drainage into the underlying porous medium become dominant. In this case, the runout length is independent of the coefficient of viscosity of the current, which sets the time scale of the motion. We present numerical solutions of the governing partial differential equations for the constant-volume case and find good agreement with our experimental data obtained from the flow of glycerine over a deep layer of spherical beads in air.

On a fundamental problem in implementing flux‐form advection schemes for tracer transport in 3‐dimensional general circulation and chemistry transport models

Abstract: A fundamental difficulty in 3-D models is addressed which can arise due to inconsistencies between advection schemes and winds. It is shown that a model will fail to meet certain basic criteria, desired of 3-D transport models, when the density field computed by the advection scheme from the winds differs from the implied density field based on the surface pressure and the sigma (or hybrid) coordinates. To allow a rigorous mathematical formulation, the focus is on the example of a mass flux advection scheme in a model where the winds and surface pressure are derived from different advection schemes (e.g. a spectral scheme in a climate model or a weather centre model); however, in principle the discussion applies to nearly any situation in which the pressure levels change in a model. To illustrate the potential severity of such problems, a mass conserving grid-to-grid transformation scheme is constructed which only uses the current tracer mass mixing-ratio distribution. It is shown that only one solution exists that is comprehensively valid for any arbitrary tracer distribution, and that this type of correction introduces an additional undesired artificial vertical diffusion component into the model transport that increases with increasing tracer mass mixing-ratio gradients and may exceed the physical vertical transport itself. It is demonstrated that the results of any supplementary fix, either mass fixer or grid-to-grid transformation, are generally unacceptable for global modelling applications. From this, it is concluded that the only alternative which can produce reliable results for any arbitrary tracer is to maintain a consistent grid throughout the entire model time step, where all changes in pressure levels due to modelled advection exactly match the changes implied by the surface pressure at the next time step. Although this is already done in some models, this would require significant changes in the structure of the advection scheme or its input wind fields in several other contemporary general circulation and chemistry transport models.

Simulation of Bubble Motion under Gravity by Lattice Boltzmann Method

Abstract: We describe the numerical simulation results of bubble motion under gravity by the lattice Boltzmann method(LBM), which assumes that a fluid consists of mesoscopic fluid particles repeating collision and translation and a multiphase interface is reproduced in a self-organizing way by repulsive interaction between different kinds of particles. The purposes in this study are to examine the applicability of LBM to the numerical analysis of bubble motions, and to develop a three-dimensional version of the binary fluid model that introduces a free energy function. We included the buoyancy terms due to the density difference in the lattice Boltzmann equations, and simulated single- and two-bubble motions, setting flow conditions according to the Eotvos and Morton numbers. The two-dimensional results by LBM agree with those by the Volume of Fluid method based on the Navier-Stokes equations. The three-dimensional model possesses the surface tension satisfying the Laplace's law, and reproduces the motion of single...

Fluid manipulating system for therapy apparatus

Abstract: The invention concerns a fluid manipulating system, comprising a reservoir of fluid (7), a bubble trap (9) connected to the reservoir, a heat-exchanger (11) and an appliance (21) forming with the bubble trap a closed circuit of fluid, and a pump (21) circulating the fluid in the closed circuit, thereby enabling to control easily the volume of fluid in the apparatus and the temperature of said fluid. The invention is useful for manipulating coupling and cooling fluid of rectal tubes in ultrasound therapy.

Solitary wave breaking on sloping beaches: 2-D two phase flow numerical simulation by SL-VOF method

Abstract: This paper describes the development of a computational method for simulating breaking and post-breaking of solitary waves over sloping bottoms. The Navier–Stokes equations are solved in air and water with respect to the real density ratio between the two fluids using a pseudo-compressibility method. The interface tracking is achieved by a new method, called Segment Lagrangian-Volume Of Fluid (SL-VOF), using the well known concepts of VOF, Piecewise Linear Interface Calculation (PLIC) and adding Lagrangian advection of the segments representing the interface. The verification of this method is made through various simple test cases. Results concerning wave shoaling are compared with those of Boundary Integral Element Method (BIEM) simulations, that are known to be very accurate up to breaking. The SL-VOF method is able to simulate the flow beyond the point at which the interface impacts on itself. Simulations of the breaking stage are compared with experiments. In both cases a very good agreement is observed.

Capillary Blocking in Forced Convective Condensation in Horizontal Miniature Channels

Abstract: Forced convective condensation in miniature channels is investigated numerically. Capillary blocking that occurs due to condensation in a horizontal miniature tube and between parallel plates is simulated by using the Volume of Fluid (VOF) method. The effects of vapor inlet velocity, saturation temperature, surface tension, and diameter on effective condensation length, film thickness, and heat transfer coefficient are investigated. The film thickness and the condensation length decrease as the hydraulic diameter or the distance between parallel plates decreases. When the total mass flow rate drops, the condensation length decreases significantly.

Numerical calculation of submerged hydraulic jumps

Abstract: The turbulence characteristics of submerged hydraulic jumps have been investigated numerically by means of the standard k-e turbulence model. The concept of a fractional volume of fluid (VOF) is employed to track the moving free surface. Numerical predictions include surface profiles, hydrodynamic pressures, mean velocities, turbulence intensities and shear stresses, maximum horizontal velocities and friction coefficients along the channel bed. Computational results are presented for Froude numbers ranging from 3.2 to 8.2 and submergence factors ranging from 0.24 to 0.85. The results are compared with available experimental data. They provide insights into both the macroscopic structure and the turbulent structure of submerged hydraulic jumps.

A volume of fluid (VOF) method for the simulation of metallurgical flows

Abstract: A finite difference numerical method, based on the VOF approach for tracking interface distortions, is presented. It is capable of accurately simulating the fluid flow of multiple immiscible fluids for metallurgical applications. This volume tracking method is based on piecewise linear reconstructions of interfaces, density distributions based on a shifted grid approach, and a fully kernel-based CSF method for surface force modelling. Second order temporal and spatial accuracy are achieved using improved Euler time-stepping enhancement of a two-step projection algorithm, supported by a multigrid-preconditioned GMRES solver that enabled large density ratios (1 : 30 000) between the fluids and fine scale flow phenomena to be resolved. The code was used to simulate the rise of an air bubble in water and in liquid pig iron and was able to capture the time dependent oscillation of the bubble. The bubble velocity varied with the instantaneous shape of the bubble. The averaged terminal velocity of the gas bubble in water was in good agreement with published experimental data. Splash formation from a top submerged gas injection lance was simulated to illustrate the capability of the code in resolving the break up and fragmentation of liquid drops for possible use in the study of bath smelting processes.

Anti-Roll Tank Simulations with a Volume of Fluid (VOF) Based Navier-Stokes Solver

Abstract: Results of computer simulations of the water motion in ship anti-roll tanks are compared with experimental data. The numerical computations are done with a Volume of Fluid (VOF) based Navier-Stokes solver. Both free-surface anti-roll tanks and U-tube anti-roll tanks are considered. Calculated and measured results for the local wave heights, the sway force and roll moment are presented for both regular and irregular tank motions. A simple but effective simulation model for the active control of U-tube anti-roll tanks is introduced. Finally, the fully nonlinear time-domain coupling of the ship motion and the tank water motion is established.

Angle independent ultrasound volume flow measurement

Abstract: The volume of fluid flow within a vessel (VE) is measured by an ultrasound system. Ultrasound waves backscattered from the fluid within the vessel generate data from which velocity values representing components of velocity (V x and V y ) of the fluid flow in the scan plane (IP) are calculated. Grayscale data is correlated and the rate of decorrelation of the data is calculated. The volume flow of the fluid is estimated in response to the velocity signals and the rate of decorrelation.

Properties of Advection Algorithms in the Context of Variational Data Assimilation

Abstract: The influence of numerical advection algorithm properties on variational data assimilation results are investigated. Nonlinear and linear advection algorithms are tested in a 2D idealized scalar advection framework in which the true solution was known. The accuracy of the optimal solutions after the data assimilation was positively correlated with the accuracy of numerical approximations used in both the forward and adjoint advection models. The accuracy of the optimal solutions was significantly smaller in the experiments in which linearized versions of the nonlinear advection algorithm were used. This property was the consequence of the optimization convergence to a local minimum in the cost function. The local minimum was avoided in the experiments in which the adjoint equation was solved by the original nonlinear advection algorithm. The results presented here suggest application of the exact same scalar advection algorithm in forward and adjoint computations in order to obtain, at lower cost, an optimal solution accuracy that is consistent with the forward model accuracy.

Numerical simulation of condensation on a capillary grooved structure

Abstract: Condensation in a capillary groove is investigated using the volume of fluid (VOF) model. The governing equations are written in a generalized form and are applicable to both liquid and vapor phases. Condensation on the fin top and at the meniscus is modeled by introducing additional source terms in the continuity, VOF, and energy equations. The effects of temperature drop, contact angle, surface tension, and fin thickness on the condensation heat transfer are also investigated.

Conservative semi-Lagrangian finite volume schemes

Abstract: Semi-Lagrangian finite volume schemes for the numerical approximation of linear advection equations are presented. These schemes are constructed so that the conservation properties are preserved by the numerical approximation. This is achieved using an interpolation procedure based on area-weighting. Numerical results are presented illustrating some of the features of these schemes.

Numerical Study on a Sliding Bubble During Nucleate Boiling

Abstract: A numerical method for simulating bubble motion during nucleate boiling is presented. The vapor-liquid interface is captured by a level set method which can easily handle breaking and merging of the interface and can calculate an interfacial curvature more accurately than the VOF method using a step function. The level set method is modified to include the effects of phase change at the interface and contact angle at the wall as well to achieve mass conservation during the whole calculation procedure. Also, a simplified model to predict the heat flux in a thin liquid microlayer is developed. The method is applied for simulation of a sliding bubble on a vertical surface to further understand the physics of partial nucleate boiling. Based on the computed results, the effects of contact angle, wall superheat and phase caange on a sliding bubble are quantified.

Volume-averaged conservation equations for volume-of-fluid interface tracking

Abstract: We derive local volume-averaged single-field conservation equations, called the VA-VOF equations, for a two-phase system consisting of two immiscible incompressible components. These equations are suitable for numerical simulations of dynamic interface evolutions with the Volumeof-Fluid (VOF) method, where the boundary layer at the interface is not fully resolved by the grid. As compared to the local equations currently used within the customary VOF-method, the newly derived mass and momentum conservation equations contain additional terms, which depend on the local phase-space-averaged relative velocity. For very fine grids, this relative velocity vanishes and the local form of the VOF equations is recovered. The additional terms in the VA-VOF equations are discussed and shown to render the VA-VOF equations incomplete. To close the VA-VOF equations, a local uniform relative velocity (LURV) model is presented. For a benchmark problem depicting a two-dimensional circular interface between two liquids in static equilibrium, the LURVmodel is shown to reduce appreciably the negative effects of the spurious currents that numerically distort the interface.

Numerical study of flows with multiple free surfaces

Abstract: This paper demonstrates that a numerical method based on the generalized simplified marker and cell (GENSMAC) flow solver and Youngs' volume of fluid (Y-VOF) surface-tracking technique is an effective tool for studying the basic mechanics of hydraulic engineering problems with multiple free surfaces and non-hydrostatic pressure distributions. Two-dimensional flow equations in a vertical plane are solved numerically for this purpose. The numerical results are compared with experimental data and earlier numerical results based on a higher-order depth-averaged flow model available in the literature. Two classical problems, (i) flow in a free overfall and (ii) flow past a floor slot, are considered. The numerical results correspond very well with the experimental data for both sub-critical and supercritical flows. Copyright © 2001 John Wiley & Sons, Ltd.

Method for measuring flow rate of a continuous fluid flow

Abstract: A method for measuring flow rate of a continuous fluid flow is shown. The method comprises the steps of generating a first signal representing a height of the fluid flow having a known cross-sectional area at the first predetermined location and for generating a second signal at a second predetermined location located in a selected direction and at a known distance from the first predetermined location; generating a third signal representing the conductivity of the fluid; receiving the signals and creating a data stream therefrom; calculating an elapsed time for the fluid flow to traverse the known distance; calculating the average conductivity of the fluid; deriving the cross-sectional area of the selected section and compensating the cross-sectional area for variance in conductivity; calculating the volume of fluid flow; and generating an output signal representing the calculated volume of fluid flow.

Fluid clutch fill detection system and method

Abstract: A method of controlling a transmission is provided. A command is received to engage a clutch having a chamber. A control valve is opened to allow pressurized fluid to flow from a fluid supply line into the clutch chamber. The pressure of the fluid within the fluid supply line is monitored as fluid flows through the control valve to enter the clutch chamber. A rate of change in the volume of fluid entering the chamber is determined based on the sensed pressure of the fluid within the fluid supply line. A fill point of the clutch chamber is detected when the rate of change in the volume of fluid entering the chamber is less than a volume differential threshold.