Showing papers on "Fluid dynamics published in 2005"

Thermo-Fluid Dynamics of Two-Phase Flow

Abstract: Part I Fundamental of two-phase flow.- Introduction.- Local Instant Formulation.- Part II Two-phase field equations based on time average.- Basic Relations in Time Average.- Time Averaged Balance Equation.- Connection to Other Statistical Averages.- Part III. Three-dimensional model based on time average.- Kinematics of Averaged Fields.- Interfacial Transport.- Two-fluid Model.- Interfacial Area Transport.- Constitutive Modeling of Interfacial Area Transport.- Hydrodynamic Constitutive Relations for Interfacial Transfer.- Drift Flux Model.- Part IV: One-dimensional model based on time average.- One-dimensional Drift-flux Model.- One-dimensional Two-fluid Model.- Two-Fluid Model Considering Structural Materials in a Control Volume.

The Finite Element Method for Fluid Dynamics

Abstract: The Finite Element Method for Fluid Dynamics offers a complete introduction the application of the finite element method to fluid mechanics. The book begins with a useful summary of all relevant partial differential equations before moving on to discuss convection stabilization procedures, steady and transient state equations, and numerical solution of fluid dynamic equations. The character-based split (CBS) scheme is introduced and discussed in detail, followed by thorough coverage of incompressible and compressible fluid dynamics, flow through porous media, shallow water flow, and the numerical treatment of long and short waves. Updated throughout, this new edition includes new chapters on: * Fluid-structure interaction, including discussion of one-dimensional and multidimensional problems. * Biofluid dynamics, covering flow throughout the human arterial system. Focusing on the core knowledge, mathematical and analytical tools needed for successful computational fluid dynamics (CFD), The Finite Element Method for Fluid Dynamics is the authoritative introduction of choice for graduate level students, researchers and professional engineers. * A proven keystone reference in the library of any engineer needing to understand and apply the finite element method to fluid mechanics. * Founded by an influential pioneer in the field and updated in this seventh edition by leading academics who worked closely with Olgierd C. Zienkiewicz. * Features new chapters on fluid-structure interaction and biofluid dynamics, including coverage of one-dimensional flow in flexible pipes and challenges in modeling systemic arterial circulation.

Lattice-Boltzmann simulations of low-Reynolds-number flow past mono- and bidisperse arrays of spheres: results for the permeability and drag force

Abstract: We report on lattice-Boltzmann simulations of slow fluid flow past mono- and bidisperse random arrays of spheres. We have measured the drag force on the spheres for a range of diameter ratios, mass fractions and packing fractions; in total, we studied 58 different parameter sets. Our simulation data for the permeability agrees well with previous simulation results and the experimental findings. On the basis of our data for the individual drag force, we have formulated new drag force relations for both monodisperse and polydisperse systems, based on the Carman?Kozeny equations; the average deviation of our binary simulation data with the new relation is less than 5%. We expect that these new relations will significantly improve the numerical modelling of gas?solid systems with polydisperse particles, in particular with respect to mixing and segregation phenomena. For binary systems with large diameter ratios (1:4), the individual drag force on a particle, as calculated from our relations, can differ by up to a factor of five compared with predictions presently favoured in chemical engineering.

Three-dimensional mixed-wet random pore-scale network modeling of two- and three-phase flow in porous media. I. Model description

Abstract: We present a three-dimensional network model to simulate two- and three-phase capillary dominated processes at the pore level. The displacement mechanisms incorporated in the model are based on the physics of multiphase flow observed in micromodel experiments. All the important features of immiscible fluid flow at the pore scale, such as wetting layers, spreading layers of the intermediate-wet phase, hysteresis, and wettability alteration are implemented in the model. Wettability alteration allows any values for the advancing and receding oil-water, gas-water, and gas-oil contact angles to be assigned. Multiple phases can be present in each pore or throat (element), in wetting and spreading layers, as well as occupying the center of the pore space. In all, some 30 different generic fluid configurations for two- and three-phase flow are analyzed. Double displacement and layer formation are implemented as well as direct two-phase displacement and layer collapse events. Every element has a circular, square, or triangular cross section. A random network that represents the pore space in Berea sandstone is used in this study. The model computes relative permeabilities, saturation paths, and capillary pressures for any displacement sequence. A methodology to track a given three-phase saturation path is presented that enables us to compare predicted and measured relative permeabilities on a point-by-point basis. A robust displacement-based clustering algorithm is also presented.

Recent progress in understanding the transition to turbulence in a pipe

Abstract: The problem of understanding the nature of fluid flow through a circular straight pipe remains one of the oldest problems in fluid mechanics. So far no explanation has been substantiated to rationalize the transition process by which the steady unidirectional laminar flow state gives way to a temporally and spatially disordered three-dimensional (turbulent) solution as the flow rate increases. Recently, new travelling wave solutions have been discovered which are saddle points in phase space. These plausibly represent the lowest level in a hierarchy of spatio-temporal periodic flow solutions which may be used to construct a cycle expansion theory of turbulent pipe flows. We summarize this success against the backdrop of past work and discuss its implications for future research.

A mathematical model for blood flow in magnetic field

Abstract: In the present study a mathematical model of biomagnetic fluid dynamics (BFD), suitable for the description of the Newtonian blood flow under the action of an applied magnetic field, is proposed. This model is consistent with the principles of ferrohydrodynamics and magnetohydrodynamics and takes into account both magnetization and electrical conductivity of blood. As a representative application the laminar, incompressible, three-dimensional, fully developed viscous flow of a Newtonian biomagnetic fluid (blood) in a straight rectangular duct is numerically studied under the action of a uniform or a spatially varying magnetic field. The numerical results are obtained using a finite differences numerical technique based on a pressure-linked pseudotransient method on a collocated grid. The flow is appreciably influenced by the application of the magnetic field and in particularly by the strength and the magnetic field gradient. A comparison of the derived results is also made with those obtained using the existing BFD model indicating the necessity of taking into account the electrical conductivity of blood.

Coupling between Deformation, Fluid Pressures, and Fluid Flow in Ore-Producing Hydrothermal Systems at Depth in the Crust

Abstract: At depths greater than several kilometers in the crust, elevated temperature, elevated confining pressure, and the presence of reactive pore fluids typically drive rapid destruction of permeability in fractured and porous rock. Ongoing deformation is required to regenerate permeability and facilitate the high fluid flux necessary to produce hydrothermal ore systems. A dominant influence on the development of fluid pathways in hydrothermal systems is provided by stress states, fluid pressures, and reactions that drive permeability enhancement and compete with permeability destruction processes. Fluid redistribution within hydrothermal systems at depth in the crust is governed largely by hydraulic gradients between upstream fluid reservoirs and the downstream regions of permeable networks of active faults, shear zones, and related structures that drain reservoirs. Pressure-driven flow leads to generally upward migration of fluids, although permeability anisotropy and tortuous flow paths may cause a significant along-strike component to fluid migration. Devolatilization reactions in prograding metamorphic regimes play a key role, not only in fluid production but also in generating transitory elevated permeability in deep crustal reservoirs. Active deformation and the development of high pore-fluid factors (the ratio of fluid pressure to vertical stress) in fluid reservoirs also drive permeability enhancement via grain-scale microfracturing and pervasive development of mesoto macroscale hydraulic fracture arrays. In the upstream, high-temperature parts of hydrothermal systems, pervasive fluid flow through the crust may occur via episodic migration of fluid-pressure pulses. Recent observations suggest that propagating fluid-pressure pulses may create transient permeabilities as high as 10–13m2 in the deep crust. Flow focusing occurs wherever networks of active, high-permeability shear zones, faults, or other permeable structures, penetrate pressurized fluid reservoirs. These structures drain reservoirs and provide pathways for fluid redistribution to higher crustal levels. Contrasting styles of flow are expected between flow pathways in the aseismically deforming lower half of the crust and pathways within the seismogenic regime in the upper half of the crust. Below the seismic-aseismic transition, steady-state creep processes favor near-constant permeabilities and continuous fluid flow. In the seismogenic regime, large changes in fault permeability during the seismic cycle produce episodic flow regimes. In particular, large earthquake ruptures that propagate down from the upper crust into deeper level fluid reservoirs generate major, transitory perturbations to fluid pressure gradients. Episodic fluid redistribution from breached, overpressured (i.e., suprahydrostatic) reservoirs has the potential to generate large fluid discharge and high fluid/rock ratios around the downstream parts of fault systems after large rupture events. Hydrothermal self-sealing of faults, together with drainage of the hydraulically accessible parts of reservoirs between earthquakes, progressively shuts off flow along fault ruptures. Permeability enhancement due to rupture events may also drive transitory flow of fluids, derived from shallow crustal reservoirs, deep into fault zones after earthquakes. As earthquakes migrate around fault systems in the upper, seismogenic part of the crust, permeability distribution and fluid pathways can evolve in complex ways. To achieve the necessary time-integrated fluid fluxes, the formation of large ore systems in this regime requires redistribution of fluid batches predominantly through small segments of fault systems during numerous rupture cycles. Sustained localized flow at the ore field scale is favored by development of long-lived, actively deforming, high-permeability structures such as fault jogs or fault intersections on high displacement faults. These structures can produce pipelike pathways linking deep reservoirs and shallower crustal levels. The generation of aftershock networks also influences fluid redistribution and discharge around the downstream ends of main-shock rupture zones. The distribution of these networks, and their repeated reactivation, is influenced by stress changes caused by main-shock rupture and by postseismic migration of fluid-pressure pulses away from the downstream ends of main-shock rupture zones. At the deposit scale, in fracture-controlled hydrothermal systems, the highest fluid flux occurs where the apertures, densities, and connectivities of fractures are greatest. The locations and geometries of these sites are governed by fluid-driven permeability enhancement in structurally controlled sites such as jogs, bends, and terminal splays, typically in low displacement faults and shear zones, as well as by fault intersections, competence contrasts, and fold-related dilation. Permeability anisotropy in structural pathways can influence deposit-scale flow directions and shapes of ore shoots. † E-mail, Stephen.Cox@anu.edu.au ©2005 Society of Economic Geologists, Inc. Economic Geology 100th Anniversary Volume pp. 39–75

Modeling of Bubble Column Reactors: Progress and Limitations

Abstract: Bubble columns are widely used for carrying out gas−liquid and gas−liquid−solid reactions in a variety of industrial applications. The dispersion and interfacial heat- and mass-transfer fluxes, which often limit the overall chemical reaction rates, are closely related to the fluid dynamics of the system through the liquid−gas contact area and the turbulence properties of the flow. There is thus considerable interest, within both academia and industry, to improve the limited understanding of the complex multiphase flow phenomena involved, which is preventing optimal scale-up and design of these reactors. In this paper, the progress reported in the literature during the past decade regarding the use of averaged Eulerian multifluid models and computational fluid dynamics (CFD) to model vertical bubble-driven flows is reviewed. The limiting steps in the model derivation are the formulation of proper boundary conditions, closure laws determining turbulent effects, interfacial transfer fluxes, and the bubble co...

Computational study of turbulent laminar patterns in couette flow.

Abstract: Turbulent-laminar patterns near transition are simulated in plane Couette flow using an extension of the minimal-flow-unit methodology. Computational domains are of minimal size in two directions but large in the third. The long direction can be tilted at any prescribed angle to the streamwise direction. Three types of patterned states are found and studied: periodic, localized, and intermittent. These correspond closely to observations in large-aspect-ratio experiments.

Locomotion of articulated bodies in a perfect fluid

Abstract: This paper is concerned with modeling the dynamics of N articulated solid bodies submerged in an ideal fluid. The model is used to analyze the locomotion of aquatic animals due to the coupling between their shape changes and the fluid dynamics in their environment. The equations of motion are obtained by making use of a two-stage reduction process which leads to significant mathematical and computational simplifications. The first reduction exploits particle relabeling symmetry: that is, the symmetry associated with the conservation of circulation for ideal, incompressible fluids. As a result, the equations of motion for the submerged solid bodies can be formulated without explicitly incorporating the fluid variables. This reduction by the fluid variables is a key difference with earlier methods, and it is appropriate since one is mainly interested in the location of the bodies, not the fluid particles. The second reduction is associated with the invariance of the dynamics under superimposed rigid motions. This invariance corresponds to the conservation of total momentum of the solid-fluid system. Due to this symmetry, the net locomotion of the solid system is realized as the sum of geometric and dynamic phases over the shape space consisting of allowable relative motions, or deformations, of the solids. In particular, reconstruction equations that govern the net locomotion at zero momentum, that is, the geometric phases, are obtained. As an illustrative example, a planar three-link mechanism is shown to propel and steer itself at zero momentum by periodically changing its shape. Two solutions are presented: one corresponds to a hydrodynamically decoupled mechanism and one is based on accurately computing the added inertias using a boundary element method. The hydrodynamically decoupled model produces smaller net motion than the more accurate model, indicating that it is important to consider the hydrodynamic interaction of the links.

Modeling fluid flow in oil reservoirs

Abstract: ▪ Abstract Efficiently and accurately solving the equations governing fluid flow in oil reservoirs is very challenging because of the complex geological environment and the intricate properties of crude oil and gas at high pressure. We present these challenges and review successful and promising solution approaches. We discuss in detail the modeling of fluid flow in reservoirs with strongly varying rock properties. This requires subgrid-scale models that accurately represent the flow physics due to fine-scale fluctuations. A second focus is on the complex multiphase, multicomponent systems that describe miscible gas injection processes for enhanced oil recovery and CO2 sequestration.

Finite element methods and their applications

Abstract: Elementary Finite Elements.- Nonconforming Finite Elements.- Mixed Finite Elements.- Discontinuous Finite Elements.- Characteristic Finite Elements.- Adaptive Finite Elements.- Solid Mechanics.- Fluid Mechanics.- Fluid Flow in Porous Media.- Semiconductor Modeling.

Fast fluid dynamics simulation on the GPU

Abstract: This chapter describes a method for fast, stable fluid simulation that runs entirely on the GPU. It introduces fluid dynamics and the associated mathematics, and it describes in detail the techniques to perform the simulation on the GPU. After reading this chapter, you should have a basic understanding of fluid dynamics and know how to simulate fluids using the GPU. The source code accompanying this book demonstrates the techniques described in this chapter.

Multicomponent fluid flow by discontinuous Galerkin and mixed methods in unfractured and fractured media

Abstract: [1] A discrete fracture model for the flow of compressible, multicomponent fluids in homogeneous, heterogeneous, and fractured media is presented in single phase In the numerical model we combine the mixed finite element (MFE) and the discontinuous Galerkin (DG) methods We use the cross-flow equilibrium concept to approximate the fractured matrix mass transfer The discrete fracture model is numerically superior to the single-porosity model and overcomes limitations of the dual-porosity models including the use of a shape factor The MFE method provides a direct and accurate approximation for the velocity field, which is crucial for the convective terms in the flow equations The DG method associated with a slope limiter is used to approximate the species balance equations This method can capture the sharp moving fronts The calculation of the fracture-fracture flux across three and higher intersecting fracture branches is a challenge In this work, we provide an accurate approximation of these fluxes by using the MFE formulation Numerical examples in unfractured and fractured media illustrate the efficiency and robustness of the proposed numerical model

Discontinuous Finite Elements in Fluid Dynamics and Heat Transfer

Abstract: Discontinuous Finite Element Procedures.- Shape Functions and Elemental Calculations.- Conduction Heat Transfer and Potential Flows.- Convection-dominated Problems.- Incompressible Flows.- Compressible Fluid Flows.- External Radiative Heat Transfer.- Radiative Transfer in Participating Media.- Free and Moving Boundary Problems.- Micro and Nanoscale Fluid Flow and Heat Transfer.- Fluid Flow and Heat Transfer in Electromagnetic Fields.

Pumping of liquids with traveling-wave electroosmosis

Abstract: Net flow of electrolyte induced by a traveling-wave electric potential applied to an array of microelectrodes is reported. Two fluid flow regimes have been observed: at small-voltage amplitudes the fluid flow follows the direction of the traveling wave, and at higher-voltage amplitudes the fluid flow is reversed. In both cases, the flow seems to be driven at the level of the electrodes. The experiments have been analyzed with a linear electroosmotic model based upon the Debye–Huckel theory of the double layer. The electrical problem for the experimental interdigitated electrode array is solved numerically using a truncated Fourier series. The observations at low voltages are in qualitative accordance with the electroosmotic model.

Mixing and dissipation in particle-driven gravity currents

Abstract: Results are presented from a high-resolution computational study of particle-driven gravity currents in a plane channel. The investigation was conducted in order to obtain better insight into the energy budget and the mixing behaviour of such flows. Two- and three-dimensional simulations are discussed, and the effects of different factors influencing the flow are examined in detail. Among these are the aspect ratio of the initial suspension reservoir, the settling speed of the particles, and the initial level of turbulence in the suspension. While most of the study is concerned with the lock-exchange configuration, where the initial height of the suspension layer is equal to the height of the channel, part of the analysis is also done for a deeply submerged case. Here, the suspension layer is only one-tenth of the full channel height. Concerning the energy budget, a careful analysis is undertaken of dissipative losses in the flow. Dissipative losses arising from the macroscopic fluid motion are distinguished from those due to the microscopic flow around each sedimenting particle. It is found that over a large range of settling velocities and suspension reservoir aspect ratios, sedimentation accounts for roughly half of all dissipative losses. The analysis of the mixing behaviour of the flow concentrates on the mixing between interstitial and ambient fluid, which are taken to be of identical density. The former is assumed to carry a passive contaminant, whose dispersion with time is analysed qualitatively and quantitatively by means of Lagrangian markers. The simulations show the mixing between interstitial and ambient fluid to be more intense for larger values of the particle settling velocity. Finally, the question is addressed of whether or not initial turbulence in the suspension may exert a significant effect on the flow evolution. To this end, results from three simulations with widely different levels of initial kinetic energy are compared. While the initial turbulence level strongly affects the mixing within the current, it has only a small influence on the front velocity and the overall sedimentation rate.

Fluctuating lattice Boltzmann

Abstract: The lattice Boltzmann algorithm efficiently simulates the Navier-Stokes equation of isothermal fluid flow, but ignores thermal fluctuations of the fluid, important in mesoscopic flows. We show how to adapt the algorithm to include noise, satisfying a fluctuation-dissipation theorem (FDT) directly at lattice level: this gives correct fluctuations for mass and momentum densities, and for stresses, at all wave vectors k. Unlike previous work, which recovers FDT only as k → 0, our algorithm offers full statistical mechanical consistency in mesoscale simulations of, e.g., fluctuating colloidal hydrodynamics.

Colloquium : Physically based fluid modeling of collisionally dominated low-temperature plasmas

Abstract: This colloquium examines the theoretical modeling of nonequilibrium low-temperature (tens of thousands of degrees) plasmas, which involves a juxtaposition of three distinct fields: atomic and molecular physics, for the input of scattering cross sections; statistical mechanics, for the kinetic modeling; and electromagnetic theory, for the simultaneous solution of Maxwell's equations. Cross sections come either from single-scattering beam experiments or, at very low energies (<0.5 eV), from multiple-scattering experiments on "swarms" in gases—the free diffusion or large Debye length limit of a plasma, where they are embedded in transport coefficient data. The same Boltzmann kinetic theory that has been developed to a high level of sophistication over the past 50 years, specifically for the purpose of unfolding these transport data, can be employed for low-temperature plasmas with appropriate modification to allow for self-consistent rather than externally prescribed fields. A full kinetic treatment of low-temperature plasmas is, however, a daunting task and remains at the developmental level. Fortunately, since the accuracy requirements for modeling plasmas are generally much less stringent than for swarms, such a sophisticated phase-space treatment is not always necessary or desirable, and a computationally more efficient but correspondingly less accurate macroscopic theoretical model in configuration space at the fluid level is often considered sufficient. There has been a proliferation of such fluid modeling in recent times and this approach is now routinely used in the design and development of a large variety of plasma technologies, ranging from plasma display panels to plasma etching reactors for microelectronic device fabrication. However, many of these models have been developed empirically with specific applications in mind, and rigor and sophistication vary accordingly. In this colloquium, starting from the governing Boltzmann kinetic equation, a unified, general formulation of fluid equations is given for both ions and electrons in gaseous media with transparent and internally consistent approximations, all benchmarked against established results. Thereby a fluid model is obtained that is appropriate for practical application but at the same time is based on a firmer physical foundation.

Ludwig Prandtl’s Boundary Layer

Abstract: In 1904 a little-known physicist revolutionized fluid dynamics with his notion that the effects of friction are experienced only very near an object moving through a fluid.

Computational study of a single-phase flow in packed beds of spheres

Abstract: Packed-bed reactors are widely used in petrochemical, fine chemical, and pharmaceutical industries. Detailed knowledge of interstitial flow in the void space of such packed-bed reactors is essential for understanding the heat and mass transfer characteristics. In this paper, fluid flow through the array of spheres was studied using the unit-cell approach, in which different periodically repeating arrangements of particles such as simple cubical, 1-D rhombohedral, 3-D rhombohedral, and face-centered cubical geometries were considered. Single-phase flow through these geometries was simulated using computational fluid dynamics (CFD). The model was first validated by comparing predicted results with published experimental and computational results. The validated model was further used to study the effect of particle arrangement/orientation on velocity distribution and heat transfer characteristics. The simulated results were also used to understand and to quantify relative contributions of surface drag and form drag in overall resistance to the flow through packed-bed reactors. The model and the results presented here would be useful in elucidating the role of microscopic flow structure on mixing and other transport processes occurring in packed-bed reactors.

Three-dimensional filling flow into a model left ventricle

Abstract: A numerical study of the three-dimensional fluid dynamics inside a model left ventricle during diastole is presented. The ventricle is modelled as a portion of a prolate spheroid with a moving wall, whose dynamics is externally forced to agree with a simplified waveform of the entering flow. The flow equations are written in the meridian body-fitted system of coordinates, and expanded in the azimuthal direction using the Fourier representation. The harmonics of the dependent variables are normalized in such a way that they automatically satisfy the high-order regularity conditions of the solution at the singular axis of the system of coordinates. The resulting equations are solved numerically using a mixed spectral–finite differences technique. The flow dynamics is analysed by varying the governing parameters, in order to understand the main fluid phenomena in an expanding ventricle, and to obtain some insight into the physiological pattern commonly detected. The flow is characterized by a well-defined structure of vorticity that is found to be the same for all values of the parameters, until, at low values of the Strouhal number, the flow develops weak turbulence.