Showing papers on "Fluid dynamics published in 1992"

Lattice BGK Models for Navier-Stokes Equation

Abstract: We propose the lattice BGK models, as an alternative to lattice gases or the lattice Boltzmann equation, to obtain an efficient numerical scheme for the simulation of fluid dynamics. With a properly chosen equilibrium distribution, the Navier-Stokes equation is obtained from the kinetic BGK equation at the second-order of approximation. Compared to lattice gases, the present model is noise-free, has Galileian invariance and a velocity-independent pressure. It involves a relaxation parameter that influences the stability of the new scheme. Numerical simulations are shown to confirm the speed of sound and the shear viscosity.

Bubbles, Drops, and Particles in Non-Newtonian Fluids

Abstract: Preface Preface to the First Edition Acknowledgements About the Author INTRODUCTION, SCOPE, AND ORGANIZATION NON-NEWTONIAN FLUID BEHAVIOR Definition of a Newtonian Fluid Non-Newtonian Fluids: Definition, Examples of Different Types, Mathematical Models Dimensional Considerations in the Mechanics of Viscoelastic Fluids Experimental Techniques: Rheometry RIGID PARTICLES IN TIME-INDEPENDENT FLUIDS WITHOUT A YIELD STRESS Governing Equations for a Sphere Spherical Particles in Newtonian Fluids Spheres in Shear-thinning Fluids Spheres in Shear-thickening Fluids Light Spheres Rising in Pseudoplastic Media Pressure Drop due to a Settling Sphere Non-Spherical Particles RIGID PARTICLES IN VISCOPLASTIC FLUIDS Static Equilibrium of Particles Flow Field: Shape and size of flow zones Drag Force Role of Values of Yield stress used in correlations Time Effects RIGID PARTICLES IN VISCOELASTIC FLUIDS Flow over a sphere Flow over a cylinder Other Studies Involving Interactions Between Non-Newtonian Characteristics, Particle Shape, Flow Field, etc. FLUID PARTICLES IN NON-NEWTONIAN MEDIA Formation of Fluid Particles Shapes of Bubbles and Drops in Free Rise or Fall Terminal Velocity-Volume Behavior in Free Motion Drag Behavior of Single Particles Bubble and Drops Ensembles in Free Motion Coalescence of Bubbles and Drops Breakage of Drops Motion and Deformation of Bubbles and Drops in Confined Flows NON-NEWTONIAN FLUID FLOW IN POROUS MEDIA AND PACKED BEDS Porous Medium Definition, Examples and Characterization Flow of Newtonian Fluids Flow of Non-Newtonian Fluids Miscellaneous Effects Two Phase Gas/Liquid Flow FLUIDIZATION AND HINDERED SETTLING Two-Phase Fluidization Sedimentation or Hindered Settling Three Phase Fluidized Beds MOMENTUM, HEAT AND MASS TRANSFER IN BOUNDARY LAYER FLOWS Boundary Layer Flows Viscoelastic Effects in Boundary Layers Mass Transfer from Bubbles Mass Transfer from Drops Mass Transfer from Ensembles of Bubbles and Drops Heat and Mass Transfer in Fixed Beds Heat and Mass Transfer in Fluidized Beds Heat and Mass Transfer in Three Phase Fluidized Beds Heat Transfer from Tube Bundles WALL EFFECTS Definition For Rigid Spheres For Non-Spherical Particles For Drops and Bubbles FALLING OBJECT RHEOMETRY Falling Ball Method Rolling Ball Method Rotating Sphere Viscometer Falling Cylinder Viscometer *All Chapters contain Introduction, Summary and Nomenclature sections References Subject index Author index

Semi-implicit finite difference methods for three-dimensional shallow water flow

Abstract: A semi-implicit finite difference method for the numerical solution of three-dimensional shallow water flows is presented and discussed. The governing equations are the primitive three-dimensional turbulent mean flow equations where the pressure distribution in the vertical has been assumed to be hydrostatic. In the method of solution a minimal degree of implicitness has been adopted in such a fashion that the resulting algorithm is stable and gives a maximal computational efficiency at a minimal computational cost. At each time step the numerical method requires the solution of one large linear system which can be formally decomposed into a set of small three-diagonal systems coupled with one five-diagonal system. All these linear systems are symmetric and positive definite. Thus the existence and uniquencess of the numerical solution are assured. When only one vertical layer is specified, this method reduces as a special case to a semi-implicit scheme for solving the corresponding two-dimensional shallow water equations. The resulting two- and three-dimensional algorithm has been shown to be fast, accurate and mass-conservative and can also be applied to simulate flooding and drying of tidal mud-flats in conjunction with three-dimensional flows. Furthermore, the resulting algorithm is fully vectorizable for an efficient implementation on modern vector computers.

A Three-Dimensional Environmental Fluid Dynamics Computer Code : Theoretical and computational aspects

Abstract: This report describes and documents the theoretical and computational aspects of a three-dimensional computer code for environmental fluid flows. The code solves the three-dimensional primitive variable v1ertically hydrostatic equations of motion for turbulent flow in a coordinate system which is curvilinear and orthogonal in the horizontal plane and stretched to follow bottom topography and free surface displacement in the vertical direction which is aligned with the gravitational vector. A second moment turbulence closure scheme relates turbulent viscosity and diffusivity to the turbulence intensity and a turbulence length scale. Transport equations for the turbulence intensity and length scale as well as transport equations for and a dye tracer are also to pressure, salinity, concentration. salinity, temperature, suspended sediment solved. An equation of state relates density temperature and suspended sediment The computational scheme utilizes an external-internal mode splitting to solve the horizontal momentum equations and the continuity equation on a staggered grid. The external mode, associated with barotropic long wave motion, is solved using a semiimplicit three time level scheme with a periodic two time level correction. A multi-c:olor successive over relaxation scheme is used to solve the resulting system of equations for the free surface displacement. The internal mode, associated with vertical shear of the horizontal velocity components is solved using a fractional step scheme combining an implicit step for the vertical shear terms, with an explicit step for all other terms. The transport equations for the turbulence intensity, turbulence length scale, salinity, temperature, suspended sediment and dye tracer are also solved using a fractional step scheme with implicit vertical diffusion and explicit advection and horizontal diffusion. A number of alternate advection schemes are implemented in th1e code.

Fluids in accretionary prisms

Abstract: Accretionary prisms are composed of initially saturated sediments caught in subduction zone tectonism. As sediments deform, fluid pressures rise and fluid is expelled, resembling a saturated sponge being tectonically squeezed. Fluid flow from the accretionary prism feeds surface biological cases, precipitates and dissolves minerals, and causes temperature and geochemical anomalies. Structural and metamorphic features are affected at all scales by fluid pressures or fluid flow in accretionary prisms. Accordingly, this dynamic tectonic environment provides an accessible model for fluid/rock interactions occurring at greater crustal depths. Porosity reduction and to a lesser degree mineral dehydration and the breakdown of sedimentary organic matter provide the fluids expelled from accretionary prisms. Mature hydrocarbons expulsed along prism faults indicate deep sources and many tens of kilometers of lateral transport of fluids. Many faults cutting accretionary prisms expel fluids fresher than seawater, presumably generated by dehydration of clay minerals at depth. Models of fluid flow from accretionary prisms use Darcy's law with matrix and fractures/faults being assigned different permeabilities. Fluid pressures in accretionary prisms are commonly high but range from hydrostatic to lithostatic. Matrix or intergranular permeability ranges from less than 10−20 m² to 10−13 m². Fracture permeability probably exceeds 10−12 m². A global estimate of fluid flux into accretionary prisms suggests they recycle the oceans every 500 m.y. Fluid flow out of accretionary prisms occurs by distributed flow through intergranular permeability and along zones of focused flow, typically faults. Focused fluid flow is 3 to 4 orders of magnitude faster than distributed flow, probably representing the mean differences in permeability along these respective expulsion paths. During the geological evolution of accretionary prisms, distributed flow through pore spaces decreases as a result of consolidation and cementation, whereas flow along fracture systems becomes dominant. Although thrust faults are most common in the compressional environment of accretionary prisms, normal and strike-slip faults are efficient fluid drains, because they are easier to dilate. Observations from both modern and ancient prisms suggest episodic fluid flow which is probably coupled to episodic fault displacement and ultimately to the earthquake cycle.

MHD flow of a viscoelastic fluid past a stretching surface

Abstract: The flow of a viscoelastic fluid past a stretching sheet in the presence of a transverse magnetic field is considered. An exact analytical solution of the governing non-linear boundary layer equation is obtained, showing that an external magnetic field has the same effect on the flow as the viscoelasticity.

Boundary Layer Analysis

Abstract: Notation. 1. Introduction to Viscous Flows. 2. Integral Equations and Solutions for Laminar Flow. 3. Differential Equations of Motion for Laminar Flow. 4. Exact and Numerical Solutions for Laminar Constant-Property Incompressible Flows. 5. Compressible Laminar Boundary Layers. 6. Transition to Turbulent Flow. 7. Wall-Bounded, Incompressible Turbulent Flows. 8. Internal Flows. 9. Free Shear Flows. 10. Wall-Bounded Turbulent Flows with Variable Density and Heat and Mass Transfer. 11. Three-Dimensional External Boundary Layer Flows. Appendix A: Laminar Thermophysical Properties for Selected Fluids. Appendix B: Computer Codes for Students. References. Index.

Dense, vertical gas‐solid flow in a pipe

Abstract: The hydrodynamics of gas-solid flow, usually referred to as circulating fluidizedbed flow, was studied in a 7.5-cm clear acrylic riser with 75-μm FCC catalyst particles. Data were obtained for three central sections as a function of gas and solids flow rates. Fluxes were measured by means of an extraction probe. Particle concentrations were measured with an X-ray densitometer. In agreement with previous investigators, these data showed the flow to be in the core-annular regime, with a dilute rising core and a dense descending annular region. However, unlike the previous studies conducted worldwide, the data obtained in this investigation allowed us to determine the viscosity of the suspension. The viscosity was a linear function of the volume fraction of solids. It extrapolates to the high bubbling-bed viscosities.

Multidimensional modeling of turbulent two‐phase flows in stirred vessels

Abstract: This article outlines a computational procedure for the prediction of dispersed two-phase, solid-liquid and gas-liquid, turbulent flows in baffled, impeller-stirred vessles common in the chemical industries. A two-flow Eulerian model is employed, based on the main assumption of interpenetrating coexisting continua. Mean momentum and mass conservation equations are solved for each phase and turbulent closure is effected by extending the single phase k- epsilon turbulence model to two-phase flows. The resulting set of highly coupled equations is solved by a two-phase implicit algorithm, PISO-2P, which allows calculation for a wide range of phase fraction, particle size and phase density ratios. Predictions are presented for solid-liquid and gas-liquid (bubbly) flows. Comparisons are made with experimental data for the mean phase velocities and volume fraction, mean slip velocity and turbulence quantities. (from Authors)

Numerical calculation of wall‐to‐bed heat‐transfer coefficients in gas‐fluidized beds

Abstract: A computer model for a hot gas-fluidized bed has been developed. The theoretical description is based on a two-fluid model (TFM) approach in which both phases are considered to be continuous and fully interpenetrating. Local wall-to-bed heat-transfer coefficients have been calculated by the simultaneous solution of the TFM conservation of mass, momentum and thermal energy equations. Preliminary calculations suggest that the experimentally observed large wall-to-bed heat-transfer coefficients, frequently reported in literature, can be computed from the present hydrodynamic model with no turbulence. This implies that there is no need to explain these high transfer rates by additional heat transport mechanisms (by turbulence). The calculations clearly show the enhancement of the wall-to-bed heat-transfer process due to the bubble-induced bed-material refreshment along the heated wall. By providing detailed information on the local behavior of the wall-to-bed heat-transfer coefficients, the model distinguishes itself advantageously from previous theoretical models. Due to the vigorous solids circulation in the bubble wake, the local wall-to-bed heat-transfer coefficient is relatively large in the wake of the bubbles rising along a heated wall.

A Class of Semi-Lagrangian Approximations for Fluids

Abstract: This paper discusses a class of finite-difference approximations to the evolution equations of fluid dynamics These approximations derive from elementary properties of differential forms Values of a fluid variable ψ at any two points of a space-time continuum are related through the integral of the space-time gradient of ψ along an arbitrary contour connecting these two points (Stokes' theorem) Noting that spatial and temporal components of the gradient are related through the fluid equations, and selecting the contour composed of a parcel trajectory and an appropriate residual, leads to the integral form of the fluid equations, which is particularly convenient for finite-difference approximations In these equations, the inertial and forcing terms are separated such that forces are integrated along a parcel trajectory (the Lagrangian aspect), whereas advection of the variable is evaluated along the residual contour (the Eulerian aspect) The virtue of this method is an extreme simplicity of t

A Unified Model for Predicting Flowing Temperature Distribution in Wellbores and Pipelines

Abstract: This paper presents a general and unified equation for flowing temperature prediction that is applicable for the entire range of inclination angles. The equation degenerates into Ramey's equations for ideal gas or incompressible liquid and into the Coulter and Bardon equation, with the appropriate assumptions. This work also proposes an approximate method for calculating the Joule- Thomson coefficient for black-oil models

Geological Applications of Capillary Pressure: A Review

Abstract: Capillary pressure concepts can be used to evaluate reservoir rock quality, expected reservoir fluid saturations and depths of fluid contacts, thickness of transition zone, seal capacity, and pay versus nonpay, and to approximate recovery efficiency. Mercury-injection capillary pressure is typically favored for geological applications, such as inferring the size and sorting of pore throats. The differences between mercury injection and withdrawal curves can provide information on recovery efficiency. The height above free water level can be determined by comparing capillary pressure data to hydrocarbon shows and measured fluid saturations. Capillary pressure data can also be used to distinguish reservoir from nonreservoir rocks and pay from nonpay on the basis of nonwetti g-phase saturations. Other applications of capillary pressure data include relating capillary pressure to absolute and relative permeabilities, and using porosimetry to investigate pore-level heterogeneity. This paper reviews geological applications and interpretation of capillary pressure in reservoir studies.

Relaxation in two dimensions and the "sinh-Poisson" equation

Abstract: Long‐time states of a turbulent, decaying, two‐dimensional, Navier–Stokes flow are shown numerically to relax toward maximum‐entropy configurations, as defined by the ‘‘sinh‐Poisson’’ equation. The large‐scale Reynolds number is about 14 000, the spatial resolution is (512)2, the boundary conditions are spatially periodic, and the evolution takes place over nearly 400 large‐scale eddy‐turnover times.

Metasomatism and fluid flow in ductile fault zones

Abstract: Observed major element metasomatism in 5 amphibolite facies ductile fault zones can be explained as the inevitable consequence of aqueous fluid flow along normal temperature gradients under conditions of local chemical equilibrium. The metasomatism does not require the infiltration of chemically exotic fluids. Calculations suggest that metasomatized ductile fault zones are typically infiltrated by ∼105 moles H2O/cm2, fluid flow is in the direction of decreasing temperature, and fluids contain about 1.0 molal total chloride. Where available, stable isotopic alteration data confirm both flow direction and fluid fluxes calculated from major element metasomatism. The fluid fluxes inferred from metasomatism do not require large-scale fluid recirculation or mantle sources if significant lateral fluid flow occurs in the deep crust. Time-integrated fluid fluxes are combined with estimates of flow duration to constrain average flow rates and average permeabilities. Rocks in ductile fault zones are probably much more permeable during metasomatism (average permeabilities of 10-17 to 10-15 m2) than rocks normally are during regional metamorphism (10-21 to 10-18 m2). Estimated average fluid flow rates (3.5×10-3 to 0.35 m/yr) are insufficient, however, to significantly elevate ambient temperatures within ductile faults. Fluid flow in the direction of decreasing temperature may increase the ductility of silicate rocks by adding K to the rocks and thereby driving mica-forming reactions.

Relaxation towards a statistical equilibrium state in two-dimensional perfect fluid dynamics.

Abstract: In previous works we have defined statistical equilibrium states for two-dimensional incompressible Euler equations. We establish here evolution equations governing the relaxation of the system towards these equilibrium states.

Topological aspects of the dynamics of fluids and plasmas

Abstract: I Introductory Lectures- Relaxation under Topological Constraints- Knot Theory, Jones' Polynomials, Invariants of 3-Manifolds, and the Topological Theory of Fluid Dynamics- Topology of Knots- Stretching and Alignment in General Flow Fields: Classical Trajectories from Reynolds Number Zero to Infinity- Fast Dynamo Theory- II Relaxation and Minimum Energy States- Relaxation and Topology in Plasma Experiments- Taylor's Relaxation in an Unbounded Domain of Space- Force-Free Magnetic Fields with Constant Alpha- Minimum Energy Magnetic Fields with Toroidal Topology- Research Announcement on the "Energy" of Knots- III Helicity, Linkage, and Flow Topology- The Helicity of a Knotted Vortex Filament- A Heirarchy of Linking Integrals- Borromeanism and Bordism- Topology of Steady Fluid Flows- IV The Euler Equations: Extremal Properties and Finite Time Singularities- Extremal Properties and Hamiltonian Structure of the Euler Equations- Blow Up in Axisymmetric Euler Flows- Is There a Finite-Time Singularity in Axisymmetric Euler Flows?- Evidence for a Singularity of the Three-Dimensional Incompressible Euler Equations- Singularity Formation on Vortex Sheets: The Raleigh-Taylor Problem- V Vortex Interactions and the Structure of Turbulence- 2D Turbulence: New Results for Re ? ?- On Vortex Reconnection and Turbulence- New Aspects of Vortex Dynamics: Helical Waves, Core Dynamics, Viscous Helicity Generation, and Interaction with Turbulence- Intermittency Growth in 3D Turbulence- Dynamical Mechanisms for Intermittency Effects in Fully Developed Turbulence- The Multispiral Model of Turbulence and Intermittency- Measurements of Local Scaling of Turbulent Velocity Fields at High Reynolds Numbers- On the Determination of Universal Multifractal Parameters in Turbulence- VI Chaos, Instability and Dynamo Theory- Anomolous Transport and Fractal Kinectics- Kinematical Instability and Line-Stretching in Relation to the Geodesics of Fluid Motion- The Behavior of Active and Passive Particles in a Chaotic Flow- Chaos Associated with Fluid Inertia- Instability Criteria in Fluid Dynamics- Localized Instabilities in Fluids- Kinematic Fast Dynamo Action in a Time-Periodic Chaotic Flow- An Exact Turbulent Closure for the Hydromagnetic Dynamo- Author Index

Turbulent deposition and trapping of aerosols at a wall

Abstract: The trajectories of aerosols are computed in a high‐resolution direct numerical simulation of turbulent flow in a vertical channel. The aerosol equation of motion includes only a Stokes drag force and the influence of the aerosols on the gas flow is assumed to be negligible. Since the flow is vertical, aerosols deposit as a consequence of the turbulent fluctuations and their own inertia. It is shown that the eddies which are responsible for aerosol deposition are the same eddies that control turbulence production. Typical aerosol trajectories are shown and related to eddy structure. A free‐flight theory suggested by Friedlander and Johnstone [Ind. Eng. Chem. 49, 1151 (1957)] is found to be based on reasonable assumptions about typical velocities of depositing aerosols as they pass through the viscous sublayer, but the theory is shown to be deficient in other respects. The distribution of normal velocities of the aerosols that deposit is compared to the distribution of fluid particle velocities in the visc...

Nonlinear gyrofluid description of turbulent magnetized plasmas

Abstract: Nonlinear gyrofluid equations are obtained from the gyrocenter‐fluid moments of the nonlinear gyrokinetic Vlasov equation, which describes an equilibrium magnetized nonuniform plasma perturbed by electromagnetic field fluctuations (δφ,δA∥,δB∥), whose space‐time scales satisfy the gyrokinetic ordering: ω≪Ωi, ‖k∥‖/k⊥≪1, and e⊥≡(k⊥ρi)2≂O(1). These low‐frequency (reduced) fluid equations contain terms of arbitrary order in e⊥ and take into account the nonuniformity in the equilibrium density and temperature of the ion and electron species, as well as the nonuniformity in the equilibrium magnetic field. From the gyrofluid equations, one can systematically derive nonlinear reduced fluid equations with finite‐Larmor‐radius (FLR) corrections, which contain linear and nonlinear terms of O(e⊥), by expressing the gyrocenter‐fluid moments appearing in the gyrofluid equations in terms of the particle‐fluid moments, and then keeping terms up to O(e⊥) in the e⊥ expansion of the gyrofluid equations. By using gyrocenter‐fluid moments, this new gyrofluid approach effectively bypasses the issue of the gyroviscous cancellations, while retaining all the important diamagnetic effects and the gyroviscous corrections. From the present FLR‐corrected reduced fluid equations, the reduced Braginskii equations are recoverd for the ion and electron species (without collisional dissipation) and the ideal reduced magnetohydrodynamic (MHD) equations (in the absence of FLR effects).

Stationary transonic solutions of a one—dimensional hydrodynamic model for semiconductors

Abstract: We study a hydrodynamic model for semiconductors where the energy equation is replaced by a pressure-density relationship. We construct artificial viscosity solutions, prove BV estimates independent of the viscosity coefficient and study the transonic weak limit. We also study the behavior of the limiting solution at the boundary for subsonic data. We find that a boundary layer can be formed on each side of the boundary and has a condition that determines the possible range of discontinuities for the density.

Turbulence transport equations for variable-density turbulence and their relationship to two-field models

Abstract: This study gives an updated account of our current ability to describe multimaterial compressible turbulent flows by means of a one-point transport model. Evolution equations are developed for a number of second-order correlations of turbulent data, and approximations of the gradient type are applied to additional correlations to close the system of equations. The principal fields of interest are the one- point Reynolds tensor for variable-density flow, the turbulent energy dissipation rate, and correlations for density-velocity and density- density fluctuations. This single-field description of turbulent flows is compared in some detail to two-field flow equations for nonturbulent, highly dispersed flow with separate variables for each field. This comparison suggests means for improved modeling of some correlations not subjected to evolution equations.