Showing papers on "Volume of fluid method published in 1993"

A numerical treatment of geodynamic : viscous flow problems involving the advection of material interfaces

Abstract: Effective numerical treatment of multicomponent viscous flow problems involving the advection of sharp interfaces between materials of differing physical properties requires correction techniques to prevent spurious diffusion and dispersion. We develop a particular algorithm, based on modern shock-capture techniques, employing a two-step nonlinear method. The first step involves the global application of a high-order upwind scheme to a hyperbolic advection equation used to model the distribution of distinct material components in a flow field. The second step is corrective and involves the application of a global filter designed to remove dispersion errors that result from the advection of discontinuities (e.g., material interfaces) by high-order, minimally dissipative schemes. The filter introduces no additional diffusion error. Nonuniform viscosity across a material interface is allowed for by the implementation of a compositionally weighted-inverse interface viscosity scheme. The combined method approaches the optimal accuracy of modern shock-capture techniques with a minimal increase in computational time and memory. A key advantage of this method is its simplicity to incorporate into preexisting codes be they finite difference, element, or volume of two or three dimensions.

Numerical Analysis of a Single Bubble by VOF Method.

Abstract: In order to examine the feasibility of direct simulation of bubbly flow, the applicability of the VOF (volume of fluid) method to analyses of a single rising bubble was examined in this study. Calculated bubble shapes and terminal velocities under wide ranges of Eotvos number and Morton number were compared with the experimental data summarized by Grace et al. Except for the cases in which bubble shapes were spherical-cap and skirted, the VOF method could predict them well by assigning only eight cells to the bubble diameter. Hence, it was confirmed that some modification of this method will enable us to simulate bubbly flow directly under a wide range of flow conditions. The relationship between bubble shape and velocity distribution was also examined within the ranges in which the VOF method is valid. It was found that the secondary vortex appearing in wobbling bubbles induces a velocity component normal to the bubble interface, and this velocity is one of the causes of the wobbling shape of the bubble.

Steady laminar flow of liquid–liquid jets at high Reynolds numbers*

Abstract: The axisymmetric steady‐state laminar flow of a Newtonian liquid jet injected vertically into another immiscible Newtonian liquid is investigated for various Reynolds numbers. The steady‐state solution was calculated by solving the axisymmetric transient equations of motion and continuity using a numerical scheme based on the volume of fluid (VOF) method combined with the new continuum surface force (CSF) algorithm. The analysis takes into account pressure, viscous, inertial, gravitational, and surface tension forces. Comparison with previous experimental measurements, performed on a xylene/water system, under conditions where all of these forces are important, shows good agreement over the entire range of conditions studied. Comparisons of the present numerical method with the numerical results of previous boundary‐layer methods help establish their range of validity.

Numerical simulation of wave motion on and in coastal structures

Abstract: A 2-dimensional program for simulation of wave motion on coastal structures is described. The program is based on the Volume Of Fluid method and is able to describe fully plunging waves on all kind of structures.

Cannula position detection

Abstract: Bidirectional flow patterns are induced in a fluid supply line and the reverse flow resistance and the forward flow resistance are measured and compared. A measure of the resistance to flow is made by normalizing a sum of the entire pressure response about a pressure baseline according to the volume of fluid in the bidirectional flow pattern. In the event that the cannula is positioned near or against the vessel wall, the resulting relatively large negative pressure response can indicate the positional irregularity. In one embodiment, a time period of zero flow is included between the positive and negative flow volumes to permit the system to stabilize.

Apparatus for heating or cooling of fluid including heating or cooling elements in a pair of counterflow fluid flow passages

Abstract: A heating or cooling vessel for heating or cooling a fluid as it flows through the vessel includes an outer tubular shell and an inner tubular member mounted to the outer tubular shell. The inner tubular member includes a central passage defining a first flow path, and a space between the inner tubular member and the outer shell defines a second flow path which communicates with the first flow path at one end of the inner tubular member. A seal member is provided toward the opposite end of the inner tubular member, for cutting off communication between the first flow path and the second flow path. An inlet provides cool fluid to the first flow path, and the fluid circulates through the first flow path and into the second flow path for discharge through an outlet in communication with the second flow path. Heating or cooling elements are disposed in both the first and second flow paths, and are arranged to provide optimal exposure of the fluid to the heating or cooling elements during flow of fluid through the vessel to maximize the velocity at which the fluid is capable of passing through the vessel and thereby the volume of fluid heated or cooled during flow of fluid through the vessel.

Apparatus and method for determining the measurement accuracy of electronic gas meters

Abstract: An apparatus and method for automatically determining the measurement accuracy of an uncalibrated field fluid flow meter by comparing its fluid flow volume, measurement, Vf, to a fluid flow volume measurement, Vm, of a master meter of known accuracy. The apparatus comprises fluid flow device operably coupled to the field and master meters for passing a common fluid stream through each of the meters at a predetermined flow rate until a predetermined volume of fluid has been registered by the field meter; a first measurement signalling device for a generating data representing the fluid volume registered by each of the meters; a second signalling device for generating data representing input temperatures and pressures to each of the meters; and a computer coupled to the fluid flow device for automatically controlling the flow rate and calculating the accuracy of the field meter.

A height-flux method for simulating free surface flows and interfaces

Abstract: A new technique for the numerical simulation of the free surface flows is developed. This technique is based on the finite element method with penalty formulation, and a flux method for surface advection. The advection part which is completely independent of the momentum solver is based on subdividing the fluid domain into small subvolumes along one of the co-ordinate axis. The subvolumes are then used to find the height function which will later describe the free surface. The free surface of the fluid in each subvolume is approximated by a line segment and its slope is calculated using the volume of the fluid in the two neighbouring subvolumes. Later, the unidirectional volume flux from one subvolume to its neighbouring one is calculated using the conservation laws, and the new surface line segments are reconstructed. This technique, referred to as the Height–Flux Method (HFM) is implemented to simulate the temporal instability of a capillary jet. The results of the numerical simulation well predict the experimental data. It is also shown that the HFM is computationally more efficient than the techniques which use a kinematic boundary condition for the surface advection.

Computation of wave breaking on sloping beach by vof method

Abstract: In this paper, the solitary wave deformation and breaking process along a sloping beach is investigated by suing the improved volume of fluid method. As the initial conditions of the incident wave, Laitone's second order formulas for the free surface profile, velocity and pressure fields of a solitary wave are employed. Comparisons with the laboratory experimental data of the wave height on the slope are presented. Numerical computations have been carried out for several configurations of beach slopes with m=1:2, 1:4, 1:8 and 1:20. Kinematics of the wave during propagation on a sloping beach is investigated. For a steep slope, the internal velocity field on the sloping beach is demonstrated in detail during run-up and run-down of the non-breaking wave. For a gentle slope, the phenomena of wave breaking such as wave steepening, overturning and bore formation have been successfully simulated by an improved VOF method.

Method for measuring the flow rate of a fluid in a pipe. Flow meter employing this method. As a corollary: meter

Abstract: The present invention relates to a method making it possible to measure the flow rate of a fluid in a pipe. It also relates to a device using this method for producing flow meters and, in corollary, meters for the volume of fluid which has flowed. It consists of a casing (1) which allows installation on the pipe in which the fluid flows. An electronic circuit (2) is connected to the sensors (3). Inside the flow meter, the fluid flows in a measurement chamber (4) which contains the flow meter device. The flow meter device is characterised by an obstacle (5) equipped with force sensors (3), by a mobile flap (valve) (6) which makes it possible to divert the flow and by a return device (7) of the flap which tends to return the flap into its initial position. In the absence of flow, the obstacle (5) and the flap (6) almost completely block the measurement chamber (4), the flap (6) is in its initial position. In the presence of a flow, the flap (6) is subjected to a system of forces, on the one hand those generated by the fluid which tends to open it and, on the other hand, those of the return device (7) which opposes the former.

Mass flow prover

Abstract: A mass flow prover suitable for calibrating flow meters for oil comprises volume proving means for receiving a defined volume of fluid defined by the positions of first and second signal means from a continuously flowing stream of fluid, said first and second signal means for generating start measurement and stop measurement signals corresponding to the fluid reaching first one and then the other measurement locations respectively as it flows into the volume proving means, means within the volume proving means for measuring the density of fluid therein, especially with means within the volume proving means for taking a representative sample of a fraction of the defined volume of fluid, means for isolating the sample from the flow of fluid, and means for determining the hydrostatic head between defined measurement locations in the isolated sample.

A volume-of-fluid computational technique for free surface flow problems

Abstract: The Volume of Fluid (VOF) method is a simple and robust technique for simulating free surface flows with large deformations and intersecting free surfaces. Earlier implementations used Laplace's equation for the normal stress boundary condition at the interface between the liquid and vapor phases. We have expanded the interfacial boundary conditions to include the viscous component of the normal stress in the liquid phase and, in a limited manner, to allow the pressure in the vapor phase to vary. Included are sample computations that show the accuracy of added third order accurate differencing schemes for the convective terms in the Navier-Stokes equations (NSE), the viscous terms in the normal stress at the interface, and the solution of potential flow in the vapor phase coupled with the solution of the NSE in the liquid phase. With these modifications we show that the VOF method can accurately predict the instability of a thin viscous sheet flowing through a stagnant vapor phase.

Development of an Atomization Methodology for Spray Combustion

Abstract: In liquid rocket propulsion, the knowledge and the understanding of liquid-gas interfacial phenomena are very important. This is important for predicting the onset of cavitation occurring in swirl injection elements used in STME, as well as atomization processes in shear-induced injectors (co-axial) and impinging injector elements. From the fact that all the physical processes including droplet size distribution, droplet dispersion, mixing and combustion are controlled by atomization processes, it is expected that the successful incorporation of the volume of fraction (VOF) will greatly enhance the analytical capability of predicting spray combustion processes in liquid-fueled engines. In this paper, a methodology is developed to define and track interfaces between two fluids in non-orthogonal, body-fitted grids using a single fractional volume of fluid (VOF) variable to describe the distribution of the liquid phase in a gas-liquid flow field. This method was implemented in a mature CFD code MAST (Multiphase All-Speed Transient) utilizing the general PISO-C algorithm. For the preliminary study on the analysis of spray combustion and tracking of the interface between two phases, we will report on the progress of the simulation of the instability on the liquid column; the surface wave instability and the droplet breakup from the liquid surface.

Steady flow of a viscous incompressible fluid between two co-axial circular cylinders with suction and injection

Abstract: In the present paper an attempt has been made to study the steady flow of a viscous incompressible fluid between two co-axial circular cylinders with small outward and inward normal suction on the outer and inner cylinders respectively with the assumption that the pressure is uniform over a cross-section. The expressions for axial velocity, the volume of fluid flowing per unit time across a cross-section and components of stress at any point of the fluid are derived.

Coating method and device

Abstract: PURPOSE: To provide a process and apparatus for uniformly coating discrete substrates by an application of a controlled volume of fluid per unit surface are of a substrate. CONSTITUTION: One embodiment is the coating method which prepares a fluid reservoir 24 and allows fluid to flow out of this fluid reservoir substantially without interruption via one or more fluid applicators 18 and 20 and the valve member 36 by manipulating the valve member, in which the controlled volume per unit surface area of the substrate is applied to the fluid. This coating apparatus fulfills these requirements.