Showing papers on "Fluid dynamics published in 1968"

Variational Principles in Continuum Mechanics

Abstract: Variational principles for problems in fluid dynamics, plasma dynamics and elasticity are discussed in the context of the general problem of finding a variational principle for a given system of equations. In continuum mechanics, the difficulties arise when the Eulerian description is used; the extension of Hamilton’s principle is straightforward in the Lagrangian description. It is found that the solution to these difficulties is to represent the Eulerian velocity v by expressions of the type v = ∇ X + λ∇ μ introduced by Clebsch (1859) for the case of isentropic fluid flow. The relation with Hamilton’s principle is elucidated following work by Lin (1963). It is also shown that the potential representation of electromagnetic fields and the variational principle for Maxwell’s equations can be fitted into the same overall scheme. The equations for water waves, waves in rotating and stratified fluids, Rossby waves, and plasma waves are given particular attention since the need for variational formulations of these equations has arisen in recent work on wave propagation (Whitham 1967). The idea of solving some of the equations by ‘potential representations’ (such as the Clebsch representation in continuum mechanics and the scalar and vector potentials in electromagnetism), and then finding a variational principle for the remaining equations, seems to be the crucial one for the general problem. An analogy with Pfaff’s problem in differential forms is given to support this idea.

On the Maintenance of Anomalous Fluid Pressures: I. Thick Sedimentary Sequences

Abstract: Various physical and chemical processes may be envisioned which will cause anomalous pressures on an underground fluid. In order to consider the maintenance of anomalous pressure, it is necessary to consider the problem as one of nonsteady fluid flow. The time rate of pressure change and maintenance depends upon the hydrodynamics of flow through porous media and the particular boundary conditions. This paper presents a series of general solutions to hydrodynamic models which are germane to the problem of creating and maintaining excess-fluid pressures in a thick sedimentary sequence. The creation and maintenance of fluid pressures approaching lithostatic pressure through a process of continuous sedimentation was evaluated. Our results indicate that a sedimentation rate of 500 m/106 yr (reasonable for the Gulf Coast) will create fluid pressures approaching lithostatic in a sedimentary column that has a hydraulic conductivity of 10−8 cm sec−1, or lower. It is apparent that the creation of anomalous pressure and its maintenance depends, to a large degree, upon the hydraulic conductivity and, to a lesser extent, upon the specific storage of clay layers within the system.

Steady fluid flow in a precessing spheroidal shell

Abstract: The linear boundary-layer analysis by Stewartson & Roberts (1963) and by Roberts & Stewartson (1965) for the motion of a viscous fluid inside the spheroidal cavity of a precessing rigid body is extended to include effects due to the nonlinear terms in the boundary-layer equation. The most significant consequence is a differential rotation super-imposed on the constant vorticity flow given by the linear theory. In addition it is shown that a tidal bulge of the cavity forces a fluid motion similar to that caused by the precessional torque. The relevance of both effects for the liquid core of the earth is briefly discussed.

Fluid flow through woven screens

Abstract: A packed bed model has been adopted to develop a general correlation applicable to the flow of Newtonian fluids through all types of woven metal screens. Both of the main theoretical approaches to studying pressure drop in packed systems have been used by visualizing the screen as a collection of submerged objects with surface area to unit volume ratio a for laminar flow, and as a bundle of tubes of diameter D for turbulent flow. In the usual manner viscous and inertial energy losses are added to give an expression for the total pressure loss. Rearrangement of the general equation to the form of a friction factor yields a unique definition of the Reynolds number for screens NRe = ρu/μa2D. Procedures are described for collection of pressure drop-velocity data for the flow of nitrogen and helium through plain square, full twill, fourdrinier, plain dutch, and twilled dutch weaves. The data are used to derive a viscous resistance coefficient α = 8.61 and an inertial resistance coefficient β = 0.52. The validity of the correlation equation is tested by using additional data from the literature. The correlation successfully predicts pressure drop for a Reynolds number range of 0.1 to 1,000, void fractions from 0.35 to 0.76, screen pore diameters from 5 to 550 μ, mesh sizes from 30 to 2,400 wires/in., and surface area to unit volume ratios from 1,200 to 29,000 ft.−1.

Nonlinear shallow fluid flow over an isolated ridge

Abstract: The shallow water theory is applied to the study of one dimensional fluid flows over an isolated ridge. The work was motivated by the desire to investigate the phenomenon called the chinook which occurs on the eastern side of the Rockies and is characterized by extremely strong winds which blow from the mountains. The motion that arises from an initially uniform flow involves the formation of hydraulic jumps both on the windward and leeward sides of a ridge. Special emphasis is put on determining analytically the asymptotic structure of such flows with jumps by solving the appropriate "steady" state equations. The presence of the hydraulic jumps and a rarefaction wave was revealed by preliminary numerical solutions of the time dependent problems. These numerical results demonstrate the evolution in time of the various features of the flow found in the asymptotic solutions.

On the Maintenance of Anomalous Fluid Pressures: II. Source Layer at Depth

Abstract: Physico-chemical mechanisms have been suggested to account for anomalous fluid pressures in the geologic environment which require a fluid source at depth. The persistence of anomalous pressure is a problem that involves nonsteady fluid flow. The hydrodynamics and particular boundary conditions control the time rate of pressure change and its maintenance. A series of mathematical solutions germane to the maintenance of anomalous pressure caused by the injection of fluids into the system from a source layer are presented. The phase change, gypsum to anhydrite plus water, is used as an example of a fluid source at depth. The thermodynamics of the gypsum-dehydration reaction indicates that conversion will probably occur at shallow depths and produce fluid at a constant rate. The dehydration of montmorillonite will also produce fluids at a constant rate under geologic conditions where the reaction can occur. If horizons of material of low permeability are missing or scarce, it is doubtful that anomalous pore pressures can be maintained for more than a geologic instant. The creation and continuation of anomalous pressure depend largely upon the hydraulic conductivity and, to a lesser extent, upon the specific storage of clay layers within the system.

Measurement of fluid flow

Abstract: An electric signal is produced which is dependent on fluid flow, by producing a magnetic field which changes with fluid flow and by positioning in the changing magnetic field a semiconductor detector whose electrical characteristics change in accordance with the changes in the field and which produces the electric signal in response to those changes.

Electroconvective Instability with a Stabilizing Temperature Gradient. I. Theory

Abstract: A uniform vertical electric field produces an instability in a poorly conducting liquid subject to a vertical temperature gradient A gradient in conductivity resulting from the temperature gradient causes free charge to accumulate in the fluid when an electric field is applied For the cases considered, the gradient in dielectric constant can be neglected with the significant electric force being that due to the free charge The threshold conditions for the instability are predicted using linear perturbation theory Approximations are made which allow the equations with space‐varying coefficients to be solved The analysis shows that, for liquids with short or moderate electrical relaxation times, the electric field causes the internal gravity wave propagating downward to become unstable

Metering of steam--water two-phase flow by sharp-edged orifices.

Abstract: This paper describes work conducted on the passage of steam-water mixtures through standard sharp-edged orifices for the prediction of flow conditions.When the stagnation enthalpy or alternatively ...

Influence of an Axial Magnetic Field on the Steady Linear Ekman Boundary Layer

Abstract: A hydromagnetic version of the Ekman boundary layer is developed in a simple form in order to study how the geophysically important Ekman suction velocity is affected by magnetic fields. The problem treated consists of a viscous, incompressible, conducting fluid in the presence of an infinite, flat, insulating boundary which rotates at speed Ω0. Outside the boundary layer, the fluid rotates uniformly with speed Ω1 = Ω0 (1 + e), and there is a uniform magnetic field aligned with the rotation axis. An expansion in powers of e, the Rossby number, together with von Karman similarity, leads to an exact solution which to first order in e, describes a continuous transition between pure Ekman flow and a rotating analog of Hartmann flow. The magnetic field is found to inhibit Ekman suction; yet, such a boundary layer may still exert a strong influence on the outer flow because of a new feature that replaces the suction, namely an induced axial current outside the boundary layer. This “Hartmann current,” not presen...

Exact solutions of the hydromagnetic dynamo problem

Abstract: Exact solutions of the steady-state hydromagnetic equations with a solenoidal velocity field are derived for appropriate boundary conditions in a helical geometry.

Miscible Displacement in an Unsaturated Glass Bead Medium

Abstract: A series of miscible displacement experiments was conducted in an unsaturated glass bead medium maintained at a constant average water content during each displacement. The variation in the form of the breakthrough curve with decreasing water content was not large and was not related in a simple way to the water content; however, there was consistent shift of the breakthrough curve to the left of the relative concentration value of 0.5 and 1 pore volume and a lone tail or slow approach to the final relative concentration of 1.0. Some of these effects may be attributed to the presence of stagnant liquid in the pores. (11 refs.)

Flow properties for the continuum viewpoint of a non-equilibrium gas-particle mixture

Abstract: Flow properties for the non-equilibrium two-phase flow of a gas-particle mixture are formulated from the theoretical standpoint. A quasi-one-dimensional flow containing an arbitrary volume of particles is considered, and mass transfer between the phases is allowed. It is shown that meaningful definitions of the flow properties of each phase can be constructed as area-averages of (time-averaged local flow-field properties). Special definitions of averages overcome the difficulties introduced by the fact that one phase does not occupy the entire region at all times. Conservation equations for the newly defined properties are given and criteria for their validity determined. The results give fresh interpretation to several aspects of two-phase flow: the particle-phase pressure is associated with the internal particle pressure, whereas Reynolds-stress terms are introduced by fluctuations in particle velocity. Reynolds stresses for both phases are important in laminar as well as turbulent flow and provide a significant particlephase viscous effect. The interphase momentum transfer because of condensation or vaporization is shown to be characterized by the particle-phase velocity irrespective of the direction of the mass transfer.

Transient rocket-engine gas flow in soil

Abstract: As a result of an examination of the behavior of soils subjected to rocket and jet exhaust gases. it was concluded that the gas pressure in the pores of the soil played an important part in the process of soil removal which occurred. Consequently, a numerical study of axially symmetric isothermal nonlinear gas flow ill a porous medium was undertaken. The paper presents the results and interpretations of the calculations for the particular boundary pressure conditions developed by a Surveyor spacecraft vernier engine mounted 12 in, above a granular material.

Three-dimensional MHD duct flows with strong transverse magnetic fields Part 1. Obstacles in a constant area channel

Abstract: This paper is an analysis of incompressible three-dimensional flows of electrically conducting fluids under the action of transverse magnetic fields which are assumed to be sufficiently strong that the interaction parameter N (= M2/R) [Gt ] 1, where M is the Hartmann number and R is the Reynolds number. We also assume that R [Gt ] 1 and Rm (magnetic Reynolds number) [Lt ] 1, so that experimental verification of the theory may be possible.The main results are: (i) when a thick body is placed in a parallel-sided channel with non-conducting walls the flow over it is highly dependent on the conductivity of the body, in a surprising way. If the body is non-conducting, there is no flow within that cylinder which circumscribes the body and is parallel to the magnetic field; outside the cylinder the flow is plane and potential and enters or leaves the surface shear layer of this cylinder at right angles. If the body is conducting, flow over it is possible and is of a different nature outside and inside the cylinder. (ii) When a non-conducting flat plate is placed in such a channel no blocking of the flow occurs. If the plate is elongated in the flow direction, the flow over it becomes identical to that calculated by Hasimoto (1960) and, if elongated at right angles to the flow, becomes identical to that calculated by Dix (1963).Of particular interest in our analysis are the two types of layer which occur in these flows, the first being the Hartmann boundary layer, which is shown to have a controlling influence on the vorticity of the core flow in three-dimensional situations analogous to that of the Eckman layer in rotating-fluid flows. The second type, the free shear layer at the circumscribing cylinder, is of interest because of its internal structure and effect on the external flow.

Formulation of the Theory of Turbulence

Abstract: A theory of homogeneous, isotropic turbulence in an incompressible fluid is formulated. This theory provides a basis for the dynamics of fully developed turbulence. A hierarchy of equations to determine the time evolution of single‐time moments of the velocity field is derived. Various properties of this hierarchy are exhibited, such as positivity of the dynamically determined energy density. The theory is applied to the study of the inertial range, where the Kolmogoroff theory is justified. A generalized inertial‐range theory is formulated. This “semilocal” theory is characterized by local energy transfer and nonlocal relaxation of triple moments. The generalized theory is applied to the study of hydromagnetic turbulence, which is shown to possess a semilocal inertial range.

Creeping flow of power‐law fluid over newtonian fluid sphere

Abstract: A technique which is a combination of Galerkin's method and variational principle was developed and used for the approximate solution of creeping flow of power-law fluid over a Newtonian fluid sphere. The stream functions (both internal and external) and drag coefficient are expressed in terms of three parameters: the flow behavior index of the power law fluid, the external Reynolds number, and a viscosity ratio parameter . Comparisons with existing experimental data are also given.

Effects of Couple Stresses in Fluids on Hydromagnetic Channel Flows

Abstract: Two boundary value problems have been solved. It has been shown, that for large Hartmann numbers, the effects of couple stresses are quite large for Poiseuille flow between two parallel plates subjected to a transverse magnetic field.

Double rate flow controller

Abstract: A double rate flow controller including a means for permitting fluid flow at a first high flow rate, a means for reducing the first flow rate to a second lower flow rate and a means for regulating the volume of water passing through the flow controller during the high flow condition before the high flow rate is terminated and the low flow rate begins.

Unsteady momentum fluxes in two-phase flow and the vibration of nuclear reactor components

Abstract: The steady and unsteady components of the momentum flux in a twophase flow have been measured at the exit of a vertical pipe. Measured momentum flux data has been machine processed by standard random vibration techniques to obtain the power spectral density curves. From these curves, the predominant frequency and the rms value of the unsteady momentum flux have been obtained. The effects of the average flow velocity, volumetric quality, system pressure, flow channel size and geometry on the unsteady momentum fluxes have been observed. It has been found that the fluctuation of momentum fluxes is important only in the low frequency range. The maximum values of unsteady momentum fluxes appeared in either the high void slug flow or the low void annular flow regime. The experimental results have been correlated and suggestions have been made for constructing the power spectral density curve of momentum fluxes under untested conditions. In the sample problems, using the experimental results, the effect of the unsteady momentum fluxes on a steam generator U-tube and a reactor fuel rod has been studied. The amplitudes of the structural vibrations resulting from the two-phase excitation have been found. In addition, it has also been found that there is a possibility of unstable vibrations owing to a nonlinear restoring force on the mechanical system. This nonlinearity is due to the unsteady component of the momentum flux in the flow past the system. In both examples, the major vibrations occurred in a narrow frequency band around the natural frequency of the mechanical system.

Experimental studies in magneto-fluid dynamics - Pressure distribution measurements around a sphere.

Abstract: Measurements of the pressure distribution around a sphere placed in aligned magnetic and velocity fields show that an increase in drag is mainly due to a decrease in the pressure on the base of the body. When magnetic forces are large compared to inertia forces, this decrease is due to a loss in total pressure along streamlines just outside the surface boundary layer and an acceleration of the flow to a velocity much larger than the reference velocity. Separation of a viscous boundary layer takes place behind the equator and still, to a large extent, controls the magnitude of the base pressure and the drag experienced by the sphere. A model consistent with these findings is presented.