Showing papers on "Fluid dynamics published in 1980"

Numerical heat transfer and fluid flow

Abstract: This book focuses on heat and mass transfer, fluid flow, chemical reaction, and other related processes that occur in engineering equipment, the natural environment, and living organisms. Using simple algebra and elementary calculus, the author develops numerical methods for predicting these processes mainly based on physical considerations. Through this approach, readers will develop a deeper understanding of the underlying physical aspects of heat transfer and fluid flow as well as improve their ability to analyze and interpret computed results.

Validity of Cubic Law for fluid flow in a deformable rock fracture

Abstract: The validity of the cubic law for laminar flow of fluids through open fractures consisting of parallel planar plates has been established by others over a wide range of conditions with apertures ranging down to a minimum of 0.2 µm. The law may be given in simplified form by Q/Δh = C(2b)3, where Q is the flow rate, Δh is the difference in hydraulic head, C is a constant that depends on the flow geometry and fluid properties, and 2b is the fracture aperture. The validity of this law for flow in a closed fracture where the surfaces are in contact and the aperture is being decreased under stress has been investigated at room temperature by using homogeneous samples of granite, basalt, and marble. Tension fractures were artificially induced, and the laboratory setup used radial as well as straight flow geometries. Apertures ranged from 250 down to 4µm, which was the minimum size that could be attained under a normal stress of 20 MPa. The cubic law was found to be valid whether the fracture surfaces were held open or were being closed under stress, and the results are not dependent on rock type. Permeability was uniquely defined by fracture aperture and was independent of the stress history used in these investigations. The effects of deviations from the ideal parallel plate concept only cause an apparent reduction in flow and may be incorporated into the cubic law by replacing C by C/ƒ. The factor ƒ varied from 1.04 to 1.65 in these investigations. The model of a fracture that is being closed under normal stress is visualized as being controlled by the strength of the asperities that are in contact. These contact areas are able to withstand significant stresses while maintaining space for fluids to continue to flow as the fracture aperture decreases. The controlling factor is the magnitude of the aperture, and since flow depends on (2b)3, a slight change in aperture evidently can easily dominate any other change in the geometry of the flow field. Thus one does not see any noticeable shift in the correlations of our experimental results in passing from a condition where the fracture surfaces were held open to one where the surfaces were being closed under stress.

Two-dimensional turbulence

Abstract: The theory of two-dimensional turbulence is reviewed and unified, and some hydrodynamic and plasma applications are considered. The topics covered include some equations of incompressible hydrodynamics, absolute statistical equilibrium, spectral transport of energy and enstrophy, turbulence on the surface of a rotating sphere, turbulent diffusion, MHD turbulence, and two-dimensional superflow. Finally, an attempt is made to assess the status and future of the principal research topics which have been discussed.

The slumping of gravity currents

Abstract: Experimental results for the release of a fixed volume of one homogeneous fluid into another of slightly different density are presented, From these results and those obtained by previous experiments, it is argued that the resulting gravity current can pass through three states. There is first a slumping phase, during which the current is retarded by the counterflow in the fluidinto which it is issuing. The current remains in this slumping phase until the depth ratio of current to intruded fluid is reduced to less than about 0,075. This may be followed by a (previously investigated) purely inertial phase, wherein the buoyancy force of the intruding fluid is balanced by the inertial force. Motion in the surrounding fluid plays a negligible role in this phase. There then follows a viscous phase, wherein the buoyancy force is balanced by viscous forces. It is argued and confirmed by experiment that the inertial phase is absent if viscous effects become important before the slumping phase has been completed. R’elationships between spreading distance and time for each phase are obtained for all three phases for both two-dimensional and axisymmetric geometries. Some consequences of the retardation of the gravity current during the slumping phase are discussed.

SOLA-VOF: a solution algorithm for transient fluid flow with multiple free boundaries

Abstract: In this report a simple, but powerful, computer program is presented for the solution of two-dimensional transient fluid flow with free boundaries The SOLA-VOF program, which is based on the concept of a fractional volume of fluid (VOF), is more flexible and efficient than other methods for treating arbitrary free boundaries SOLA-VOF has a variety of user options that provide capabilities for a wide range of applications Its basic mode of operation is for single fluid calculations having multiple free surfaces However, SOLA-VOF can also be used for calculations involving two fluids separated by a sharp interface In either case, the fluids may be treated as incompressible or as having limited compressibility Surface tension forces with wall adhesion are permitted in both cases Internal obstacles may be defined by blocking out any desired combination of cells in the mesh, which is composed of rectangular cells of variable size SOLA-VOF is an easy-to-use program Its logical parts are isolated in separate subroutines, and numerous special features have been included to simplify its operation, such as an automatic time-step control, a flexible mesh generator, extensive output capabilities, a variety of optional boundary conditions, and instructive internal documentation

Convection in a compressible fluid with infinite Prandtl number

Abstract: An approximate set of equations is derived for a compressible liquid of infinite Prandtl number. These are referred to as the anelastic-liquid equations. The approximation requires the product of absolute temperature and volume coefficient of thermal expansion to be small compared to one. A single parameter defined as the ratio of the depth of the convecting layer, d, to the temperature scale height of the liquid, HT, governs the importance of the non-Boussinesq effects of compressibility, viscous dissipation, variable adiabatic temperature gradients and non-hydrostatic pressure gradients. When d/HT [Lt ] 1 the Boussinesq equations result, but when d/HT is O(1) the non-Boussinesq terms become important. Using a time-dependent numerical model, the anelastic-liquid equations are solved in two dimensions and a systematic investigation of compressible convection is presented in which d/HT is varied from 0·1 to 1·5. Both marginal stability and finite-amplitude convection are studied. For d/HT [les ] 1·0 the effect of density variations is primarily geometric; descending parcels of liquid contract and ascending parcels expand, resulting in an increase in vorticity with depth. When d/HT > 1·0 the density stratification significantly stabilizes the lower regions of the marginal state solutions. At all values of d/HT [ges ] 0·25, an adiabatic temperature gradient proportional to temperature has a noticeable stabilizing effect on the lower regions. For d/HT [ges ] 0·5, marginal solutions are completely stabilized at the bottom of the layer and penetrative convection occurs for a finite range of supercritical Rayleigh numbers. In the finite-amplitude solutions adiabatic heating and cooling produces an isentropic central region. Viscous dissipation acts to redistribute buoyancy sources and intense frictional heating influences flow solutions locally in a time-dependent manner. The ratio of the total viscous heating in the convecting system, ϕ, to the heat flux across the upper surface, Fu, has an upper limit equal to d/HT. This limit is achieved at high Rayleigh numbers, when heating is entirely from below, and, for sufficiently large values of d/HT, Φ/Fu is greater than 1·00.

On the calculation of turbulent heat transport downstream from an abrupt pipe expansion

Abstract: A numerical study is reported of flow and heat transfer in the separated flow region created by an abrupt pipe expansion Computations employed an adaptation of the TEACH-2E computer program with the standard model of turbulence Emphasis is given to the simulation, from both a physical and numerical viewpoint, of the region in the immediate vicinity of the wall where turbulent transport gives way to molecular conduction and diffusion Wall resistance laws or wall functions used to bridge this near-wall region are based on the idea that, beyond the viscous sublayer, the turbulent length scale is universal, increasing linearly with distance from the wall Predictions of expermental data for a diameter ratio of 054 show generally encouraging agreement with experiment At a diameter of 043 different trends are discernible between measurement and calculation though this appears to be due to effects unconnected with the wall region studied

Convection in a rotating layer: a simple case of turbulence.

Abstract: Convection in a layer heated from below and rotating about a vertical axis exhibits a unique phenomenon in fluid dynamics in that the small-amplitude motion is governed by random effects in both its spatial and its time dependence. A simple theoretical description of the phenomenon is compared with laboratory observations. A more detailed mathematical description appears to be feasible because of the weakly nonlinear nature of the problem.

Fluid mechanics for chemical engineers

Abstract: 1 Introduction Part I Preliminaries 2 Fluid Statics 3 The Balance Equation and the Mass Balance 4 The First Law of Thermodynamics Part II Flows which are Practically One-Dimensional or can be Treated as Such 5 Bernoulli's Equation 6 Fluid Friction in Steady One-Dimensional Flow 7 The Momentum Balance 8 One-Dimensional High-Velocity Gas Flow Part III Some Other Topics, Which can be Viewed by the Methods of One-Dimensional Fluid Mechanics 9 Model Studies, Dimensional Analysis, and Similitude 10 Pumps, Compressors, and Turbines 11 Flow Through Porous Media 12 Gas-Liquid Flow 13 Non-Newtonian Fluid Flow in Circular Pipes 14 Surface Forces Part IV Two- and Three-Dimensional Fluid Mechanics 15 Two- and Three-Dimensional Fluid Mechanics 16 Potential Flow 17 The Boundary Layer 18 Turbulence 19 Mixing 20 Computational Fluid Dynamics, (CFD) Appendix A Tables and Charts of Fluid Properties, Pipe Dimensions and Flows, and High-Velocity Gas Flows Appendix B Derivations and Proofs Appendix C Equations for Two- and Three-Dimensional Fluid Mechanics Appendix D Answers to Selected Problems

Shock-wave structure via nonequilibrium molecular dynamics and Navier-Stokes continuum mechanics

Abstract: A strong steady dense-fluid shock wave is simulated with 4800-atom nonequilibrium molecular dynamics. The resulting density, stress, energy, and temperature profiles are compared with corresponding macroscopic profiles we derive from Navier-Stokes continuum mechanics. The differences found are relatively small.

A Simple Theory on the Dynamical Effects of a Stratified Fluid Core upon Nutational Motion of the Earth

Abstract: The theory of Molodensky (1961) on dynamical effects of a stratified fluid outer core upon nutations and diurnal Earth tides is reconstructed on a new and probably much simpler ground. A theory equivalent to Molodensky’s is well represented on the basis of two linear equations for angular-momentum balance of the whole Earth and the fluid outer core, which differ from the well-known equations of Poincare (1910) only in the existence of products of inertia due to deformations of the whole Earth and fluid outer core. The products of inertia are characterized by four parameters which are easily computed for every Earth model by the usual Earth tide equations. A reciprocity relation exists between two of the parameters. The Adams-Wiliamson condition is not a necessary premise of the theory. Amplitudes of nutations and tidal gravity factors are computed for three Earth models. A dissipative core-mantle coupling is introduced into the theory qualitatively. The resulting equations are expressed in the same form as those of Sasao, Okamoto and Sakai (1977). Formulae for secular changes in the Earth-Moon system due to the core-mantle friction are derived as evidences of internal consistency of the theory.

Debris Flow on Prismatic Open Channel

Abstract: Reviews on the yield strength and viscosity of the interstitial clay slurry in debris flow prove that ordinary debris flow may be modeled as a dilatant fluid in which the intergranular forces dominate. Theoretical velocity distributions in dilatant fluid compare well with the experimental results when the value of a numerical constant is appropriately selected. The longitudinal profile of the lobate snout is satisfactorily analyzed by applying the theory of one-dimensional translation wave on an open channel, where the resistance coefficient is a function of concentration, depth, and grain diameter. A remarkable segregation of particles, in which the larger ones move upwards, occurs in debris flow due to the effects of collisions of particles. The accumulation of boulders in the front part of debris flow is a result of the faster transportation of the larger particles in the upper layer of the flow than that of the smaller ones in the lower layer.

Internal Fluid Flow: The Fluid Dynamics of Flow in Pipes and Ducts

Abstract: Keywords: ecoulement : interne ; theorie ; applications Reference Record created on 2005-11-18, modified on 2016-08-08

An adaptive grid method for problems in fluid mechanics and heat transfer

Abstract: A new method for generating adaptive grids for time-dependent and steady problems in multidimensional fluid mechanics and heat transfer has been developed. The method can be used with many existing grid generation schemes or can be used as an independent grid generation technique. The present adaptive method is based upon the placement of grid points in proportion to the gradients that appear in the dependent variable. The multidimensional results presented in the paper are for the unsteady heat conduction equation and have included steep gradients due to geometry and unsteady boundary conditions. The method has performed in an impressive fashion, although there is a need to control grid skewness better. A study of one-dimensional problems associated with combustion and cell Reynolds number has demonstrated the technique's accuracy and versitility. The paper also discusses the relationship of the method to other grid generation techniques, as well as extensions of the new method.

Study of two-fluid model and interfacial area

Abstract: The interfacial transfer terms are the weakest link in a two-fluid-model formulation, because of considerable difficulties in terms of experimentation as well as modeling. However, these terms are of supreme importance for a two-fluid model in determining phase interactions between liquid and vapor. In view of these, the interfacial transfer terms have been studied in detail and new constitutive relations have been developed. The interfacial terms are proportional to the interfacial area and driving force; therefore these two effects are modeled separately. In addition, new flow-regime criteria that are appropriate for a two-fluid model are proposed.

Boundary effects in fluid flow. Application to quantum liquids

Abstract: The effect of boundaries on the flow of rarefied gases is considered. For an excitation gas of arbitrary statistics and energy-momentum relationship we determine the magnitude of the slip length and the flow between parallel plates mostly by variational methods. Our approximate method avoids the need to solve integral equations numerically and yields in the stationary case better than 1% agreement with known exact results for the classical Maxwell-Boltzmann gas. Our general results are primarily applied to normal and superfluid Fermi liquids. We calculate the surface impedance of an oscillating plate and determine the frequency-dependent slip length for frequencies ranging from the hydrodynamic to the collisionless limit. Our results are applied to the analysis of viscosity measurements based on a torsional oscillator or a vibrating wire. The slip effects are shown to be very important for realistic experimental parameters, especially at low temperatures in the superfluid B phase of liquid 3He.

Stokeslets and Eddies in Creeping Flow

Abstract: Flow at low Reynolds number Re = pUL//1 is characterized by the small­ ness of representative quantities in the flow, i.e. the density p, the velocity U, and the length L, as well as by large values of the viscosity J.l. If we let Re --+ 0 and neglect the molecular structure of the fluid that is studied in rarefied fluid dynamics as well as the Brownian motions that appear for extremely small p and L, we are led to a universal feature of a real fluid. We have a perfectly laminar creeping flow governed by the Stokes equations of motion, which are linear and reversible, and contain no parameters to complicate the structure of the flow field. The most essential factor is the geometry of the flow. As is well known, the Stokes equations are not uniformly valid in an unbounded fluid, leading to various paradoxes, which however are remedied by matching to an outer region where the neglected inertia terms are dominant. Further, in real situations, the flow is usually bounded and is dominated by the so-called Stokes regions if we let pU //1 be sufficiently small. In this review certain limited aspects of creeping flow will be surveyed, since extensive surveys before 1964 are found in Happel & Brenner's treatise (1965) and in several articles in the Annual Review of Fluid Mechanics (Cox & Mason 1971, Brennen & Winet 1977). First, we neglect unsteady effects on the assumption that the typical frequency is not larger than U /L, as well as the effect of free surfaces such as bubbles and suspensions. In Section 2 Stokes flow and various singularities are introduced as factors as free of geometries as possible, leading to general solutions of the Stokes equations proposed by Imai (1973). In Section 3 two-dimensional solutions of the Stokes equations are discussed as the inner solutions near a cyiindrical body. The complex velocity at a distance is characterized by the logarithmic term and constants depend­ ing on the size and ellipticity of the cylinder. In Section 4 typical stokeslet constants depending on the geometry of a particle, i.e. the

A mathematical model for fluid flow in a weld pool at high currents

Abstract: In order to determine the heat transfer inside a TIG (tungsten/inert gas) weld pool, it is necessary to have a good understanding of the flow patterns of the liquid metal. The principal force driving the fluid motion is the electromagnetic j × B force due to the current from the welding arc and its self-magnetic field. In this paper we consider the flow of a viscous incompressible conducting fluid in a hemispherical container due to various distributions of the electric current. The problem is posed as a time-dependent problem and is solved numerically using the Du Fort–Frankel leap-frog method. Results are presented for currents of 100 A flowing through the weld pool. This is a typical current for TIG welding, and corresponds to a Reynolds number in the range 200 < Re < 600. Previous solutions of the problem were restricted to low Reynolds numbers, i.e. low currents.

Onsager's pancake approximation for the fluid dynamics of a gas centrifuge

Abstract: A previously unpublished theory for describing the internal flow in a gas centrifuge is presented. The theory is based on boundary layer type arguments on the side walls of the centrifuge with the additional approximation of neglecting radial diffusion of radial momentum. The effects of the top and bottom end caps are incorporated through Ekman layer solutions. The results are presented in a form amenable to numerical calculations. Some sample calculations are presented for the special case of a centrifuge with a linear temperature profile on the wall and the top and bottom of the centrifuge at the same temperature as the corresponding end of the side wall.

Thermodynamic and transport properties of fluids

Abstract: Computer program subroutine FLUID calculates thermodynamic and transport properties of pure fluids in liquid, gas, or two-phase (liquid/gas) conditions. Program determines thermodynamic state from assigned values for temperature and density, pressure and density, temperature and pressure, pressure and entropy, or pressure and enthalpy.

Darcy's Law for Flow in Porous Media and the Two-Space Method,

Abstract: A common problem in engineering and science is to derive simple equations governing complicated phenomena. Often complicated governing equations are known, but they are too difficult to analyze. An example of a simplified equation is Darcy’s law, which describes flow of a viscous fluid through a porous medium. The more complicated equation for the same phenomenon is the Navier-Stokes equation. As an example of a general method for simplifying equations, This chapter shows how to derive Darcy’s law from the Navier-Stokes equation. Simplified equations are often called “homogenized equations,” and the procedure of replacing the original equations by them is often called “homogenization.” The chapter discusses the two-space method for deriving simplified equations by using an example of the flow of a compressible viscous fluid through a rigid porous medium.

One- and Two-Phase Nozzle Flows

Abstract: A time-dependent technique, in conjunction with the boundary-fitted coordinates system, is applied to solve a gas-only one-phase flow and a fully-coupled, gas-particle two-phase flow inside nozzles with small throat radii of curvature, steep wall gradients, and submerged configurations. The emphasis of the study has been placed on one- and two-phase flow in the transonic region. Various particle sizes and particle mass fractions have been investigated in the two-phase flow. The salient features associated with the two-phase nozzle flow compared with those of the one-phase flow are illustrated through the calculations of the JPL nozzle, the Titan III solid rocket motor, and the submerged nozzle configuration found in the Inertial Upper Stage (IUS) solid rocket motor.

Automatic controlling valve for maintaining the rate of fluid flow at a constant value

Abstract: An automatic fluid control valve for maintaining a substantially constant fluid flow includes a valve stem movable linearly within a casing and having valve means thereon cooperable with a valve port to regulate the flow of fluids therethrough in response to changes in fluid pressure differential, diaphragm means operatively connected to the valve stem and separating a region within the valve casing into a pair of pressure-differential chambers, a fluids passageway of variable cross-sectional area settable to establish a predetermined fluid flow rate through the control valve located intermediate the fluid inlet and the outlet and thereby establishing first and second fluid pressures respectively on the upstream and downstream sides of the fluids passageway, and means communicating the fluid pressure on the upstream side of the fluids passageway to one of the pressure differential chambers and the fluid pressure on the downstream side of the fluids passageway to the other of the pressure differential chambers

Method and apparatus utilizing the weight of moving traffic to produce useful work

Abstract: A method and apparatus which includes locating a compressible chamber filled with a non-compressible fluid confined in a closed circuit in the path of moving traffic so that the weight of the traffic passing over the chamber will affect a displacement of the incompressible fluid to create a fluid flow through the circuit. The circuit includes unidirectional flow control valves for directing the flow of displaced fluid through a fluid motor connected in circuit with the compressible chamber. Disposed in the circuit is a rectifier for rectifying the intermittent displacement of the fluid into a generally uniform fluid flow to affect the drive of the fluid motor with the output of the fluid motor being translated into useful work.