Showing papers on "Fluid dynamics published in 1988"

Navier-Stokes equations

Abstract: Both an original contribution and a lucid introduction to mathematical aspects of fluid mechanics, Navier-Stokes Equations provides a compact and self-contained course on these classical, nonlinear, partial differential equations, which are used to describe and analyze fluid dynamics and the flow of gases.

Buoyancy-Induced Flows And Transport

Abstract: Contents: Introduction.- General Formulation of Buoyancy-Induced Flows.- External Vertical Thermally Induced Flows.- Vertical Axisymmetric Flows.- Other Than Vertical Flows.- Combined Mass and Thermal Transport.- Unsteady External Flows.- Effects of Variable Fluid Properties.- Transport in Cold Pure and Saline Water.- Mixed Convection.- Instability, Transition and Turbulence.- Turbulent Free-Boundary Buoyant Flows.- Unstably Stratified Fluid Layers.- Transport in Enclosures and Partial Enclosures.- Transport in Saturated Porous Media.- Non-Newtonian Transport.- Some Other Aspects.- Nomenclature.- Appendixes.- Additional References.- Author Index to Additional References.- Author Index.- Subject Index.

Immiscible cellular-automaton fluids

Abstract: We introduce a new deterministic collision rule for lattice-gas (cellular-automaton) hydrodynamics that yields immiscible two-phase flow. The rule is based on a minimization principle and the conservation of mass, momentum, and particle type. A numerical example demonstrates the spontaneous separation of two phases in two dimensions. Numerical studies show that the surface tension coefficient obeys Laplace's formula.

Hamiltonian fluid mechanics

Abstract: This paper reviews the relatively recent application of the methods of Hamiltonian mechanics to problems in fluid dynamics. By Hamiltonian mechanics I mean all of what is often called classical mechanics-the subject of the textbooks by Lanczos ( 1970), Goldstein ( 1 980), and Arnol'd (1978). Since the advent of quantum mechanics, Hamiltonian methods have played an increasingly important role in both the classical and quan­ tum mechanics of particles and fields. By comparison, the introduction of Hamiltonian methods into fluid mechanics has been tardy. Why is this so? In general mechanical systems, the Lagrangian or Hamiltonian equa­ tions of motion are coupled equations governing the locations and veloc­ ities of massive particles or rigid bodies. These coupled equations cannot generally be solved for any subset of the dependent variables without also finding all of the other dependent variables. By contrast, the conventional Eulerian fluid equations are closed equations in the velocity, density, and entropy (regarding pressure as a prescribed function of the density and entropy) that can (in principle) be solved without also finding the trajectory of every fluid particle. Once the velocity field is known, the particle tra­ jectories can always be reconstructed by solving the equations for three independent, passively advected tracers (such as the initial Cartesian com­ ponents), but these extra computations are not required if only the Eulerian fields are sought. In the special case of constant-density flow, the Eulerian equations are dramatically simpler than the general Lagrangian or Hamil­ tonian equations for the fluid. From the Hamiltonian perspective, the extraordinary simplicity of the Eulerian description derives from a symmetry property of the fluid

Closed multi-fluid delivery system and method

Abstract: A multiple fluid delivery system usable for the delivery of intravenous fluids to a patient from a plurality of fluid sources includes flexible tubing members for coupling the sources to a fluid junction member. The fluid junction member, wherein little or no interfluid mixing occurs, is coupled by an output conduit to a controllable pump. Output from the pump, via a further fluid flow conduit, can be coupled to the patient's catheter. The system can multiplex a plurality of different fluids. Spaced apart sequences of fluid quanta are injected into the output conduit from the fluid flow junction. The fluids are either mixed, or not, in the output conduit as desired. Operator interaction and control of the system can occur either through a display screen or by means of a bar code sensor. Hard copy records can be provided of fluid flow delivery schedules or other related information.

Effects of Capillary Pressure on Coalescence and Phase Mobilities in Foams Flowing Through Porous Media

Abstract: The stability of foam lamellae is limited by capillary pressure. Consequently, as the fractional flow of gas in a foam is raised at a fixed gas velocity, the capillary pressure in a porous medium at first increases and then approaches a characteristic value, here called the ''limiting capillary pressure.'' If the gas fractional flow is increased after the limiting capillary pressure has been attained, coalescence coarsens foam texture, the liquid saturation remains constant, and the relative gas mobility becomes proportional to the ratio of gas-to-liquid fractional flow. The limiting capillary pressure varies with the surfactant formulation, gas velocity, and permeability of the medium.

Flow and tracer transport in a single fracture: A stochastic model and its relation to some field observations

Abstract: Calculations for the flow and solute transport through a single rough-surfaced fracture were carried out. The fracture plane was discretized into a square mesh to which variable apertures were assigned. The spatially varying apertures of each single fracture were generated using geostatistical methods, based on a given aperture probability density distribution and a specified spatial correlation length. Constant head boundary conditions were assumed for the flow in the x direction of a single fracture with no flow boundaries in the y direction. The fluid potential at each node of the discretization mesh was computed and the steady state flow rates between all the nodes were obtained. Our calculations showed that fluid flow occurs predominantly in a few preferred paths. Hence, the large range of apertures in the single fracture gives rise to flow channeling. The solute transport was calculated using a particle tracking method. Both the spatial and time variations of tracer breakthrough results are presented. The spatial variation of tracer transport between a line of injection points and a line of observation points are displayed in contour plots which we labeled “transfer matrix.” Our results indicate that such plots can give information on the spatial correlation length of the heterogeneity in the fracture. The tracer breakthrough curve obtained from a line of point measurements is shown to be controlled by the aperture density distribution and is insensitive to statistical realization and spatial correlation length. These results suggest the importance of making line measurements in the laboratory and the field. Sensitivity of our results on parameter variations was also investigated.

Space conservation law in finite volume calculations of fluid flow

Abstract: In the numerical solutions of fluid flow problems in moving co-ordinates, an additional conservation equation, namely the space conservation law, has to be solved simultaneously with the mass, momentum and energy conservation equations. In this paper a method of incorporating the space conservation law into a finite volume procedure is proposed and applied to a number of test cases. The results show that the method is efficient and produces accurate results for all grid velocities and time steps for which temporal accuracy suffices. It is also demonstrated, by analysis and test calculations, that not satisfying the space conservation law in a numerical solution procedure introduces errors in the form of artificial mass sources. These errors can be made negligible only by choosing a sufficiently small time step, which sometimes may be smaller than required by the temporal discretization accuracy.

Linear stability of plane Poiseuille flow of two superposed fluids

Abstract: Stability of two superposed fluids of different viscosity in plane Poiseuille flow is studied numerically. Conditions for the growth of an interfacial wave are identified. The analysis extends Yih’s results [J. Fluid Mech. 27, 337 (1967)] for small wavenumbers to large wavenumbers and accounts for differences in density and thickness ratios, as well as the effects of interfacial tension and gravity. Neutral stability diagrams for the interfacial mode are reported for a wide range of the physical parameters describing the flow. The analysis shows also that the flow is linearly unstable to a shear mode instability. The dependence of the critical Reynolds number for the shear mode on the viscosity ratio is reported. Theoretical predictions of critical Reynolds numbers for both modes of instability are compared with available experimental data.

Cellular‐automaton fluids: A model for flow in porous media

Abstract: Numerical models of fluid flow through porous media can be developed from either microscopic or macroscopic properties. The large‐scale viewpoint is perhaps the most prevalent. Darcy’s law relates the chief macroscopic parameters of interest—flow rate, permeability, viscosity, and pressure gradient—and may be invoked to solve for any of these parameters when the others are known. In practical situations, however, this solution may not be possible. Attention is then typically focused on the estimation of permeability, and numerous numerical methods based on knowledge of the microscopic pore‐space geometry have been proposed. Because the intrinsic inhomogeneity of porous media makes the application of proper boundary conditions difficult, microscopic flow calculations have typically been achieved with idealized arrays of geometrically simple pores, throats, and cracks. I propose here an attractive alternative which can freely and accurately model fluid flow in grossly irregular geometries. This new method s...

Fluid flow due to a stretching cylinder

Abstract: The fluid flow outside of a stretching cylinder is studied. The problem is governed by a third‐order nonlinear ordinary differential equation that leads to exact similarity solutions of the Navier–Stokes equations. Because of algebraic decay, an exponential transform is used to facilitate numerical integration. Asymptotic solutions for large Reynolds numbers compare well with numerical results. The heat transfer is determined.

Deep fluid circulation in fault zones

Abstract: Massive fluid circulation in retrogressive ductile shear zones is a well-established but poorly understood phenomenon. In some cases, surface-derived fluids, which must initially have been at hydrostatic pressures, can be shown to have entered shear zones in which fluids would normally be expected to be at lithostatic pressure. In these circumstances, thermal convection is an unlikely driving force for fluid movement. Underthrusting of a surficial fluid reservoir beneath shear zones is a viable mechanism in some cases, but not for metasomatic shear zones in the Pyrenees where insufficient underthrusting has occurred. Seismic pumping provides an alternative mechanism to explain the paradox of fluid access into ductile shear zones; a kinematic analysis of a hypothetical fault zone shows that stress and dilatancy cycles will be out of phase above and below the frictional/quasiplastic transition. If this effect is sufficiently large, hydraulic gradients may force fluid downward across the transition immediately after earthquake rupture through highly permeable microcrack networks. Between earthquake cycles, plastic creep in mylonites will overprint microcrack networks, increase fluid pressure, and promote slow upward movement of fluid at low permeability. For smaller shear zones, such as those in the Pyrenees, seismic pumping could occur down a shallow decollement with subsequent upward fluid flow through shear zones in the hanging wall of the decollement.

Closure of the Reynolds stress and scalar flux equations

Abstract: A second‐order, single‐point closure model for calculating the transport of momentum and passive scalar quantities in turbulent flows is described. Of the unknown terms that appear in the Reynolds stress and scalar flux balance equations, it is those which involve the fluctuating pressure that exert a dominant influence in the majority of turbulent flows. A closure approximation (linear in the Reynolds stress) has been formulated for the velocity‐pressure gradient correlation appearing in the Reynolds stress equation. When this is used in conjunction with previous proposals for the other unknown terms in the stress equation, the proposed model closely simulates most of the data on high Reynolds number homogeneous turbulent flows. For the fluctuating scalar‐pressure gradient correlation appearing in the scalar flux equation, an approximation has been devised that satisfies the linear transformation properties of the exact equation. Additional characteristics of the fluctuating scalar field are obtained from the solution of modeled balance equations for the scalar variance and its ‘‘dissipation’’ rate. The resulting complete scalar field model is capable of reproducing measured data in decaying scalar grid turbulence and strongly sheared, nearly homogeneous flow in the presence of a mean scalar gradient. In addition, applications to the thermal mixing layer developing downstream from a partially heated grid and to a slightly heated plane jet issuing into stagnant surrounds result in calculated profiles in close agreement with those measured.

Mixed Convection in Stagnation Flows Adjacent to Vertical Surfaces

Abstract: Laminar mixed convection in two-dimensional stagnation flows around heated surfaces is analyzed for both cases of an arbitrary wall temperature and arbitrary surface heat flux variations. The two-dimensional Navier-Stokes equations and the energy equation governing the flow and thermal fields are reduced to a dimensionless form by appropriate transformations and the resulting system of ordinary differential equations is solved in the buoyancy assisting and opposing regions. Numerical results are obtained for the special cases for which locally similar solutions exist as a function of the buoyancy parameter. Local wall shear stress and heat transfer rates as well as velocity and temperature distributions are presented. It is found that the local Nusselt number and wall shear stress increase as the value of the buoyancy parameter increases in the buoyancy assisting flow region. A reverse flow region develops in the buoyancy opposing flow region, and dual solutions are found to exist in that flow regime for a certain range of the buoyancy parameter.

The Gasdynamics of Compact Relativistic Jets

Abstract: The gasdynamics of compact relativistic jets is explored by analyzing a specific idealized flow problem using the method of characteristics. The basic flow pattern of the gas and pressure waves within a jet experiencing a drop in external pressure is calculated, with analytic expressions given for many of the important parameters. Scaling laws which relate the intrinsic properties of the jet to the pressure of the surrounding medium are obtained and discussed. The physical properties of the jet depend critically on the value and abruptness of the decrease in external pressure, as well as on the initial Lorentz factor of the flow. A variety of the flow patterns can result, including jets of oscillating cross section, jets with standing shocks, and broad, nearly hollow beams which can break up into multiple jets. These results are discussed in relation to the observed characteristics of superluminal radio sources in general and the superluminal quasar 4C 39.25 in particular.

A continuum model for water movement in an unsaturated fractured rock mass

Abstract: The movement of fluids in a fractured, porous medium has been the subject of considerable study. This paper presents a continuum model that may be used to evaluate the isothermal movement of water in an unsaturated, fractured, porous medium under slowly changing conditions. This continuum model was developed for use in evaluating the unsaturated zone at the Yucca Mountain site as a potential repository for high-level nuclear waste. Thus its development has been influenced by the conditions thought to be present at Yucca Mountain. A macroscopic approach and a microscopic approach are used to develop a continuum model to evaluate water movement in a fractured rock mass. Both approaches assume that the pressure head in the fractures and the matrix are identical in a plane perpendicular to flow. Both approaches lead to a single-flow equation for a fractured rock mass. The two approaches are used to calculate unsaturated hydrologic properties, i.e., relative permeability and saturation as a function of pressure head, for several types of tuff underlying Yucca Mountain, using the best available hydrologic data for the matrix and the fractures. Rock mass properties calculated by both approaches are similar.

Natural convection in vertical enclosures containing simultaneously fluid and porous layers

Abstract: A numerical and experimental study is reported of natural convection in a vertical rectangular fluid enclosure that is partially filled with a fluid-saturated porous medium. Velocities, stresses, temperatures, and heat fluxes are assumed to be continuous across the fluid/porous-medium interface, and the conservation equations for the fluid and the porous regions are combined into a single set of equations for numerical solution. Thermocouples as well as a Mach-Zehnder interferometer are used to measure temperature distributions and infer fluid flow patterns within the fluid and the porous medium. For various test cells, porous-layer configurations and fluid-solid combinations, the model predictions show excellent agreement with the experimental measurements. It is found that the intensity of natural convection is always much stronger in the fluid regions, while the amount of fluid penetrating into the porous medium increases with increasing Darcy and Rayleigh numbers. The degree of penetration of fluid into the porous medium depends strongly on the porous-layer geometry and is less for a horizontal porous layer occupying the lower half of the test cell. If penetration takes place, the flow patterns in the fluid regions are significantly altered and the streamlines show cusps at the fluid/porous-medium interfaces. For a high effective-thermal-conductivity porous medium, natural convection in the medium is suppressed, while the isotherms bend sharply at the fluid/porous-medium interface.

Computational Fluid Dynamics: An Introduction

Abstract: This chapter provides an overview of computational fluid dynamics (CFD) with emphasis on its cost-effectiveness in design Some representative applications are described to indicate what CFD is capable of The typical structure of the equations governing fluid dynamics is highlighted and the way in which these equations are converted into computer-executable algorithms is illustrated Finally attention is drawn to some of the important sources of further information

Numerical simulation of Jupiter's Great Red Spot

Abstract: Jupiter's Great Red Spot is viewed as a vortex that arises naturally from the equations of motion of the jovian atmosphere. Here I solve numerically the equations governing fluid motion in a model of the jovian atmosphere for a variety of initial conditions. Large spots of vorticity form spontaneously in chaotic azimuthal flows and are stable if the vorticity of the spots has the same sign as the shear of the surrounding azimuthal flow. The Great Red Spot is compared with these solutions and a new prediction of its vertical structure is made.

Fluid percolation through single fractures

Abstract: Large deviations from "cubic-law" dependence of laminar fluid flow through fractures on the apparent mechanical aperture of a fracture can be explained by assuming: 1) cubic-law dependence of flow on the actual local aperture at the microscopic level; 2) conservation of rock volume when deforming the fracture; and 3) macroscopic flow properties are dominated by the critical neck (the smallest aperture along the path of highest aperture through the fracture).

Fluids in micropores. II. Self‐diffusion in a simple classical fluid in a slit pore

Abstract: Self‐diffusion coefficients D are computed for a model slit pore consisting of a rare‐gas fluid confined between two parallel face‐centered cubic (100) planes (walls) of rigidly fixed rare‐gas atoms. By means of an optimally vectorized molecular‐dynamics program for the CYBER 205, the dependence of D on the thermodynamic state (specified by the chemical potential μ, temperature T, and the pore width h) of the pore fluid has been explored. Diffusion is governed by Fick’s law, even in pores as narrow as 2 or 3 atomic diameters. The diffusion coefficient oscillates as a function of h with fixed μ and T, vanishing at critical values of h, where fluid–solid phase transitions occur. A shift of the pore walls relative to one another in directions parallel with the walls can radically alter the structure of the pore fluid and consequently the magnitude of D. Since the pore fluid forms distinct layers parallel to the walls, a local diffusion coefficient D(i)∥ associated with a given layer i can be defined. D(i)∥ is least for the contact layer, even for pores as wide as 30 atomic diameters (∼100 A). Moreover, D(i)∥ increases with increasing distance of the fluid layer from the wall and, for pore widths between 16 and 30 atomic diameters, D(i)∥ is larger in the center of the pore than in the bulk fluid that is in equilibrium with the pore fluid. The opposite behavior is observed in corresponding smooth‐wall pores, in which the discrete fluid–wall interactions have been averaged by smearing the wall atoms over the plane of the wall. The temperature dependence of D for fixed h is determined and the nature of melting of a pore solid is examined. It is found that the solid tends to melt first in the middle of the pore. All of the various results are related to the structural properties of the pore fluid, as manifested by the local density and pair correlation functions.

Ion collection by probes in strong magnetic fields with plasma flow.

Abstract: Fluid-theory calculations are presented of ion collection by electric probes in strongly magnetized plasmas with parallel flow In the first calculations the problem is treated in a one-dimensional approximation but the cross-field transport of momentum is included in such a way as to model different ratios of viscosity to diffusivity The results show that the flow deduced from probe measurements is not particularly sensitive to the assumed viscosity, provided it is finite However, results with zero viscosity are qualitatively different from those with nonzero viscous momentum transport The second set of calculations is two dimensional but only for fixed (unity) ratio of viscosity to diffusivity The results are in remarkably good agreement with the corresponding one-dimensional model

Fluid flow and sand production in heavy-oil reservoirs under solution-gas drive

Abstract: The production of heavy oil in Canada has led to a number of anomalous results, most of which have been excused as high-permeability channels resulting from sand production. The methods of soil mechanics predict gross formation failure resulting from high fluid compressability, small cohesion, and high viscosity. Gross failure results in excellent productivity but reduced in-situ stress (and fracture stress). Solution-gas drive in these reservoirs involves simultaneous-mixture flow of a gas as very tiny little bubbles entrained in heavy oil. Stress, geometry, and permeability alteration resulting from matrix deformation combined with peculiar pressure-depended multiphase-flow properties result in a new model of reservoir performance. A field observation of stress modification is discussed, as are the contributions of the four components discussed previously to the observed phenomena.

Fluid dynamics in bubble stirred ladles: Part II. Mathematical modeling

Abstract: A mathematical model which describes the fluid flow in a bubble stirred ladle is presented. The model predicts mean flow, turbulent characteristics, bubble dispersion, and gas-liquid interaction from fundamental principles. Numerical predictions for a water model of a ladle show very satisfactory quantitative agreement with experimental results for all regions of the ladle. The model is applied to the study of refractory wear and yields results that are in qualitative agreement with practical experience.

A tractable molecular theory of flow in strongly inhomogeneous fluids

Abstract: A recently introduced model is used to study several flows in fluids with large density variations over distances comparable to their molecular dimensions (strongly inhomogeneous fluids). According to our model, the local average density model (LADM), local viscosity coefficients can be assigned at each point in a strongly inhomogeneous fluid and the stress tensor retains its Newtonian form provided that the properly defined local viscosities are used. The model has been previously shown to agree with the results of molecular dynamics simulations on diffusion and flow properties in plane Couette flow. Application of this model requires determination of the molecular density profiles in the flow region. Using a successful closure for the pair distribution function, we solve the Yvon–Born–Green (YBG) equation of fluid structure in order to determine the density profiles of a fluid confined between planar micropore walls only a few molecular diameters apart. The fluid confinement produces a strongly inhomogeneous structure. Subsequently we apply LADM to set up the fluid mechanical equations for Couette flow, Poiseuille flow, and squeezing flow between parallel plates. With the use of the YBG theoretical density profiles we solve the flow equations and predict velocity profiles, stress distributions, and effective viscosities. The dependence of these quantities on the fluid inhomogeneity is described. The effective viscosity of strongly inhomogeneous fluids is found to be quite sensitive to the nature of the flow. Our squeezing flow analysis provides a first explanation of recent experimental findings on the effective viscosity of simple fluids confined in very narrow spaces.