Showing papers on "Fluid dynamics published in 1969"

An Introduction to Fluid Dynamics.

Abstract: Keywords: dynamique des : fluides Reference Record created on 2005-11-18, modified on 2016-08-08

The deformation of a drop in a general time-dependent fluid flow

Abstract: A theoretical method is given for the determination of the shape of a fluid drop in steady and unsteady flows by making an expansion in terms of the drop deformation. Effects of fluid viscosity and interfacial tension are taken into account. Examples given include the determination of the shape of a drop in shear and in hyperbolic flow when each is started impulsively from rest.

Viscous flow in a cylindrical tube containing a line of spherical particles.

Abstract: Viscous flow in a circular cylindrical tube containing an infinite line of rigid spheroidal particles equally spaced along the axis of the tube is considered for (a) uniform axial translation of the spheroids (b) flow past a line of stationary spheriods and (c) flow of the suspending fluid and spheroids under an imposed pressure gradient. The fluid is assumed to be incompressible and Newtonian. The Reynolds number is assumed to be small and the equations of creeping flow are used.

Turbulence phenomena in drag reducing systems

Abstract: An analysis based on the Townsend-Bakewell model of the eddies in the wall regions of turbulent shear flows shows that viscoelastic fluid properties must lead to significant reductions in the rate of production of turbulent energy. This analysis in turn leads to the proper form of the similarity laws for drag reducing fluids, heretofore deduced empirically. Measurements of the axial and radial turbulence intensities for flow through smooth round tubes are reported, as are measurements of the time-averaged velocity profiles and the drag coefficients. These indicate that for solutions exhibiting drag reduction at all Reynolds numbers the flow may be transitional to Reynolds numbers of the order of 105. This transitional flow consists of alternating patches of laminar and turbulent fluid, within each of which the flow characteristics are approximately similar to those of Newtonian fluids. At high Reynolds number conditions with the turbulent field fully developed the velocity profile in the core is flatter under drag-reducing conditions than for turbulent Newtonian fluids, a change dependent on the increased isotropy of the turbulent field of the drag-reducing fluid. These effects appear to be a result of increases in the time scales of the radial fluctuations caused by the fluid properties. Design calculations based upon the present results suggest that in large diameter pipelines, or in boundary layers on large objects, drag reduction may not be attainable under conditions of practical interest until fluids having relaxation times an order of magnitude larger than those presently available, but with comparable viscosity levels, are developed or, alternately, until fluids exhibiting Weissenberg numbers which do not change with deformation rate, can be found.

A Method of Analyzing Transient Fluid Flow in Multilayered Aquifers

Abstract: A new approach to transient fluid flow in multilayered aquifers has been developed using the finite element method. This is a numeric technique in which an initial boundary value problem is converted to a variational problem and applied to a descretized system of elements. Details for the case of isotropic systems have been presented elsewhere. This paper extends the treatment to anisotropic systems. The method has been used to investigate potential distributions in multilayered aquifers of finite radial extent being pumped at constant rate using completely penetrating wells. An analysis of two-layer systems with permeability contrasts of up to 100:1 indicates that at early time the drawdown behavior can vary significantly from the Theis solution, depending on where observations are made. As time increases, however, the results eventually converge on the Theis solution regardless of the permeability contrast. A 13-layer aquifer containing either isotropic or anisotropic layers has been examined, and the results are in general agreement with the behavior for two-layer systems.

Mechanics of Red-Cell Motion through Very Narrow Capillaries

Abstract: In a recent paper, Lighthill (1968) has formulated a model of compressible pellet movement through narrow, fluid-filled, elastic tubes; the model involves a thin lubricating layer of fluid between the pellet and the wall, and the results obtained are expressed in the form of relationships between various velocity, resistance, clearance, and lubrication-film thickness parameters. An important biological motivation for this work was the problem of the movement of red blood cells through narrow capillaries. The present paper examines in detail the approximations and assumptions of Lighthill's model, and extends the investigation in several directions. First, the elastic behaviour of the pellet is discussed with particular relevance to the red cell, which is considered to consist of a fluid-filled flexible membrane. It is shown, in particular, that as the velocity of such a red cell in a capillary increases, the consequent increase in viscous drag on the rim tends to 'bow' the cell, and allow it to fit more easily into a capillary of given diameter. Further, the modulus of elastic response to the non-uniform lubrication pressures around the rim is shown to depend on the membrane's 'resistance to deformation' and the geometry of the cell. Next, a model of axisymmetric pellet flow through a tube is set up. Results are expressed in terms of clearance and resistance experienced by the pellet, for various velocities and film thicknesses typical of capillary flows. Much greater resistances than those estimated by Lighthill are obtained; for normal flow in capillaries of 5 to 7 $\mu $m diameter, these range from 4.5 to 7 times that expected for a corresponding Poiseuille fluid flow with whole-blood viscosity. It is not suggested that these results are true of all capillaries, or of a capillary network, but only of those very narrow capillaries in the diameter range being considered. Of equal importance is the nonlinear dependence of resistance on velocity. The red cell velocity falls off very rapidly as the pressure gradient is reduced; this is discussed in detail with reference to the phenomenon of auto-regulation. Finally, the effects of asymmetry and tube porosity are considered. It is shown that deviations from axisymmetry tend to be reduced by pressures developed in the fluid; this is due to the compressible nature of the pellets, and means that the results obtained for capillary flow are reasonably valid even for configurations in which the red cells may not be axisymmetric. Leakage of plasma through the walls of the capillary is shown not to affect the flow characteristics of a capillary to any great extent, or to significantly increase the possibility of 'seizing-up' of the flow due to failure of lubrication at small film thicknesses.

The Effect of Hall Currents on the Magnetohydrodynamic Boundary Layer Flow past a Semi-Infinite Flat Plate

Abstract: This paper concerns with the numerical investigation of the effect of Hall currents on the steady boundary layer flow of an incompressible, viscous and electrically conducting fluid past a semi-infinite flat plate in the presence of a transverse magnetic field on the assumption of small magnetic Reynolds number. The numerical solutions of boundary layer equations are obtained by the difference-differential method originated by Hartree and Womersley with an iterative method in solving resulting differential equations. The velocity profiles and the skin friction on the flat plate are computed for various values of the Hall parameter. Hall currents induce the flow and the skin friction in the cross direction. The effect of Hall currents especially on the skin friction is examined in detail.

Effects of surfactants on mass transfer inside drops

Abstract: A model is presented to account for reduced mass transfer to drops falling through a continuous phase which contains a surface active agent. The fluid flow patterns are essentially laminar. The reduction in mass transfer is said to be due to a reduction in available interfacial transfer area and to changes in both velocity and pattern of internal circulation. These are shown to be functions of contact time and can be characterized. Experimental values agreed with the theoretically predicted ones with a deviation of less than 10%.

Importance of Boundary Conditions in the Numerical Treatment of Hyperbolic Equations

Abstract: Many of the existing computations of initial‐ and boundary‐value problems in fluid mechanics suffer from unrealistic treatment of boundary points. Three categories of boundaries are discussed briefly: rigid walls, arbitrary boundaries of a computational region in a subsonic flow, and shock waves. An attempt is made to show in what sense the numerical treatment of such boundaries may be physically wrong and what can be done instead. Examples from the blunt body problem, the transonic flow in a nozzle, the incompressible inviscid flow past a circle, and the quasi‐one‐dimensional flow in a Laval nozzle, are shown.

HYDRODYNAMICS AND THIRD SOUND IN THIN He II FILMS.

Abstract: The linearized hydrodynamic equations of motion for a thin, flat, superfluid helium film are derived in some detail from standard two-fluid hydrodynamics. Interactions of the film with both the He vapor and the substrate which are in contract with it are included and discussed in detail. Boundary conditions for both the film-substrate and film-gas interfaces are derived. It is indicated how one may construct the equations of motion for the entire coupled system (gas-film-substrate). The equations are actually constructed and solved for the case when a certain parameter is small, which includes all the third-sound experiments on unsaturated films. A dispersion equation is found which is exact in the limit of vanishing frequency, and which is eminently suited to describe both the velocity and the attenuation of third sound in the regime of unsaturated films. No hydrodynamic instability is found. Results for the attenuation are shown to be in good agreement with preliminary experiments on unsaturated He films.

Experiments on the Flow Around a Sphere at High Reynolds Numbers

Abstract: Fluid flow around sphere at high Reynolds number by measuring pressure distribution, considering boundary layer separation, tunnel blockage, etc

Experimental Study of Thermal Convection in a Vertical Cylinder of Mercury Heated from Below

Abstract: Very precise temperature measurements have been made on a vertical circular column of liquid mercury, and also a mercury‐zinc alloy, heated from below In both pure mercury and the alloy, two types of temperature oscillations, indicating two modes of time‐dependent fluid flow, were observed The first oscillatory mode appeared at a Rayleigh number 10% higher than the critical Rayleigh number for the onset of fluid flow predicted by linear stability theory At higher Rayleigh numbers this mode disappeared and the second oscillatory mode, having a shorter period, began at Rayleigh numbers 30% above the critical value Both types of temperature oscillations are consistent with a pulsed mode of fluid flow Attempts to detect the predicted, steady, antisymmetric flow at the onset of fluid motion by means of lateral temperature measurements were unsuccessful

Well Test Interpretation of Vertically Fractured Gas Wells

Abstract: A mathematical model was developed to generate simulated drawdown tests for fractured gas wells. The model includes the effects of real gas properties, well bore storage, and turbulence. A special coordinate transformation is used to obtain better accuracy for turbulent flow near the well bore. The results show that the slope of the drawdown curve is affected by the nonlinearity of real gas flow.

On the Geometry of Current Ripples in Relation to Stability of Fluid Flow

Abstract: Very commonly small-scale current ripples display wave-like changes of elevation in a direction transverse as well as parallel to current flow. It is shown theoretically. and confirmed experimental...

A Study of Immiscible Fingering in Linear Models

Abstract: Studies of immiscible fingering in linear Hele-Shaw and bead-packed models are described. Immiscible fingers were readily initiated in all models. However, the fingers were damped out before traveling very far in the uniform bead packs that contained connate water. The damping mechanism is believed due to movement of the 2 phases in a direction transverse to the direction of gross flow. To study the transverse flow phenomenon under controlled conditions, oil and water were injected simultaneously and side-by side in linear models. Transition zones were formed that grew broader as the distance from the inlet increased. The saturation distribution in the transition zones could be described mathematically by an immiscible dispersion coefficient and the well-known error-function solution of the dispersion equation. The immiscible dispersion coefficients were found to be proportional to the interstitial velocity and proportional to the product of the bead diameter and packing inhomogeneity factor. (12 refs.)

Vibration correlation for maximum fuel-element displacement in parallel turbulent flow.

Abstract: Fuel elements have been observed to vibrate in turbulent parallel flow. Available data describing the fluctuating pressure in a turbulent boundary layer is used to calculate fuel-element response t...

Ultimate heat-pipe performance

Abstract: Ultimate heat-transfer limitations imposed by sonic vapor flow were determined in heat pipes for sodium, potassium, and cesium working fluids. Each fluid was investigated in a heat pipe consisting of an inner porous tube, an annulus for liquid return, and an outer container tube. Thin, rigid tubes with very small pores were obtained by compressing several layers of fine-mesh screen. These tubes allowed large capillary forces to develop so that sonic vapor flow could be achieved at several operating temperatures. The results of the investigation showed that sonic limitations were influenced strongly by the temperature and the working fluid. Reasonable agreement was found between the experimental results and existing theory. It was also found that the theory could be used to predict evaporator pressure and temperature gradients when the heat pipes were operated at various fractions of their ultimate heat-transfer capability.

Numerical studies of steady, viscous, incompressible flow in a channel with a step

Abstract: For many years one of the major criticisms of mathematics was that it provided no methods for solving nonlinear problems. With the development of the high speed computer and related numerical methods, this criticism is now being answered. In this paper we present a numerical method for solving a fundamental nonlinear problem in fluid dynamics. That the numbers presented actually do represent a numerical solution can be verified easily by direct substitution into the difference equations. Why the method converges is a difficult matter and is at present under study.

Design and physical characteristics of a multistage, continuous tower fermentor

Abstract: A multistage tower laboratory fermentor has been constructed consisting of eight compartments separated by sieve plates. Flow of substrate and air is concurrent from the bottom to the top of the column. It, was hoped that this system could be used to reproduce, simultaneously on a continuous basis, eight distinct phases of a batch growth curve. It was believed that the extent of batch curve simulation would depend upon the character of hydraulic mean residence time of broth in the column and in the individual compartments. The expected relationship did not occur. Rather it was found that growth in the column involved residence time characteristics not only for the fluid but also for the microorganisms, and for the growth limiting substrate. Depending upon the column operation, these could be distinct and different. The purpose of this investigation was to study the residence time distribution (RTD) of the continous (fluid) and dispersed (microorganisms) phases for model systems as well as for a yeast fermentation. Various degrees of flow nonideality, i.e., fluid blackflow and dispersed phase sedimentation, were noticed. The former seems to be due to interaction of the concurrent gas and liquid flow; it is particularly dependent upon void area of the sieve plate holes. Sedimentation is probably a function of plate design as well as cell size and density. It wa concluded that for a particular plate design the gas hold-up wass controlled by superficial air velocity and was the main parameter governing the differences between dispersed and continous phase(Rt1). This conclusion was supported by a computeraided styudy utilizing a mathematical model of fluid flow to fit the growth kinetics and cell distribution observed experimentally throughout the fermentor. Some advantages of foam control in the tower fermentor by surface active compounds are mentioned. Also, suggestions are made for carrying out fermentations that have two liquid phases, such as a hydrocarbon fermentation. The possibility of closely approximating plug-flow conditions in the multistage tower fermentor, a necessary condition for batch growth simulation, is discussed from a practical point of view.

Steady-State and Unsteady-State Flow of Non~Newtonian Fluids Through Porous Media

Abstract: Non-Newtonian fluids may be injected into a reservoir during secondary recovery operations. The non-Newtonian fluid used in this work is a power-law type of fluid; that is, the viscosity of the fluid decreases as the flow rate or rate of shear increases. Equations are presented for steady-state linear and radial flow of such fluids, transient behavior results from a finite difference model of a radial system, and transient behavior results from a field test. The equations that describe the flow of a non-Newtonian fluid are non-linear and are solved numerically. Finite difference solutions are presented as curves of dimensionless pressure drop at the well bore vs. dimensionless time for a constant injection rate. Solutions were obtained for 5%, 10%, and 100% PV of a non-Newtonian fluid for injection rates of 1, 10, 100, and 1,000 cc/sec and for a 5% PV of non-Newtonian fluid located at r = rDwU, 3, 10, 20, 50, and 100 ft for a flow rate of 1 cc/sec. The buildup curves do not exhibit a straight-line portion as is the case for Newtonian flow through porous media. Correlations also are shown for the productivity index vs. rate for the computer model study and the fieldmore » tests.« less

Numerical, Three-Phase Simulation of the Linear Steamflood Process

Abstract: A numerical mathematical model is described on the steam-flood process which depends on fewer restrictive assumptions than models previously reported, but the solution of which is economically obtained. Example calculations are presented which, on comparison with experimental results, tend to validate the model. Results which expose certain process mechanics are discussed. The model describes the simultaneous flow of 3 phases--oil, water, and gas--in one dimension. It includes the effects of 3-phase relative permeabilities, capillary pressure, and temperature- and pressure-dependent fluid properties. Interphase mass transfer of water-steam is allowed, but the oil is assumed nonvolatile and the hydrocarbon gas insoluble in the liquid phases. The model allows heat convection in one dimensional and 2-dimensional heat conduction in a vertical cross section spanning the oil sand and adjacent strata. The hydrocarbon-steam gas composition is tracked, but the effect of gas composition on water-steam phase behavior is neglected. The model is solved numerically in 3 separate stages. (12 refs.)

Measurement of the Axial Pressure Distribution of Molten Polymers in Flow through a Rectangular Duct

Abstract: The authors have experimentally determined the axial pressure distributions for the flow of polyethylene and polypropylene melts through a rectangular duct having an aspect ratio of 2. “Exit pressures,” which were found by extrapolating the pressure profiles to the duct exit, were found to correlate well with the volumetric flow rate. This result is quite understandable in light of previous results regarding the flow of melts through circular capillaries, because the nature of fluid flow through a capillary is the same as that of the flow through a rectangular duct having a very large aspect ratio (i.e., simple shearing flow). Thus, the rheological implication of the “exit pressure” is the same for both of these geometries. The analysis of flow through a rectangular duct having a very large aspect ratio shows that the normal stress difference is approximately equal to the “exit pressure” for polymer melts. A preliminary analysis of flow through a rectangular duct having a small aspect ratio is presented, and it gives a clear direction to future experiment.

A finite-difference approximation of the primitive equations for a hexagonal grid on a plane

Abstract: The hexagonal grid based on a partition of the icosahedron has distinct geometrical qualities for the mapping of a sphere and also presents some indexing difficulties. The applicability of this grid to the primitive equations of fluid dynamics is demonstrated, and a finite-difference approximation of these equations is proposed. The basic variables are the mass fluxes from one hexagonal cell to the next through their common boundary. This scheme conserves the total mass, the total momentum, and the total kinetic energy of the fluid as well as the total squared vorticity of a nondivergent flow. A computational test was performed using a hexagonal grid to describe space periodic waves on a nonrotating plane. The systematic variation of total kinetic and potential energy is less than 10−5 after 1,000 time steps.

Magnetohydrodynamic flow between rotating coaxial disks.

Abstract: This is a study of the magnetohydrodynamic flow of an incompressible viscous fluid between coaxial disks, with a uniform axial magnetic field B. The fluid has density ρ, viseosity η and electrical conductivity σ. The flow is assumed to be steady, and to be similar in the sense that the radial and tangential components of velocity increase linearly with radial distance from the axis of rotation. Most of the work is concerned with disks which are electrical insulators, one of which rotates while the other remains stationary. The imposed conditions can then be represented by the Reynolds number R = ρΩad2/η and the Hartmann number M2 = σB2d2/η, where Ωa is the angular velocity of the rotating disk and d is the gap between the disks. Asymptotic solutions are given for R [Lt ] M2, and numerical solutions are obtained for values of R and M2 up to 512. Experimental measurements are presented which are in general agreement with the theoretical flows, and the results for small values of the Hartmann number provide the first known experimental support for the purely hydrodynamic solutions in the range 100 < R < 800.