scholarly journals Transient and asymptotic dispersion in confined sphere packings with cylindrical and non-cylindrical conduit geometries

2011 ◽  
Vol 369 (1945) ◽  
pp. 2485-2493 ◽  
Author(s):  
Siarhei Khirevich ◽  
Alexandra Höltzel ◽  
Ulrich Tallarek
Keyword(s):  
Velocity Field ◽  
Hydrodynamic Dispersion ◽  
Sphere Diameter ◽  
Sphere Packings ◽  
Length Scales ◽  
Bed Porosity ◽  
Long Time ◽  
Boltzmann Method ◽  
Random Walk Particle Tracking ◽  
Asymptotic Dispersion

We study the time and length scales of hydrodynamic dispersion in confined monodisperse sphere packings as a function of the conduit geometry. By a modified Jodrey–Tory algorithm, we generated packings at a bed porosity (interstitial void fraction) of ε =0.40 in conduits with circular, rectangular, or semicircular cross section of area 100 πd 2 p (where d p is the sphere diameter) and dimensions of about 20 d p (cylinder diameter) by 6553.6 d p (length), 25 d p by 12.5 d p (rectangle sides) by 8192 d p or 14.1 d p (radius of semicircle) by 8192 d p , respectively. The fluid-flow velocity field in the generated packings was calculated by the lattice Boltzmann method for Péclet numbers of up to 500, and convective–diffusive mass transport of 4×10 6 inert tracers was modelled with a random-walk particle-tracking technique. We present lateral porosity and velocity distributions for all packings and monitor the time evolution of longitudinal dispersion up to the asymptotic (long-time) limit. The characteristic length scales for asymptotic behaviour are explained from the symmetry of each conduit’s velocity field. Finally, we quantify the influence of the confinement and of a specific conduit geometry on the velocity dependence of the asymptotic dispersion coefficients.

Validation of Pore-Scale Simulations of Hydrodynamic Dispersion in Random Sphere Packings

2013 ◽  
Vol 13 (3) ◽  
pp. 801-822 ◽  
Author(s):  
Siarhei Khirevich ◽  
Alexandra Höltzel ◽  
Ulrich Tallarek
Keyword(s):  
Dispersion Coefficient ◽  
Finite Size ◽  
Grid Resolution ◽  
Space Distribution ◽  
Hydrodynamic Dispersion ◽  
Sphere Diameter ◽  
Sphere Packings ◽  
Void Space ◽  
Longitudinal Dispersion Coefficient ◽  
Loose Packing

AbstractWe employ the lattice Boltzmann method and random walk particle tracking to simulate the time evolution of hydrodynamic dispersion in bulk, random, monodisperse, hard-sphere packings with bed porosities (interparticle void volume fractions) between the random-close and the random-loose packing limit. Using Jodrey-Tory and Monte Carlo-based algorithms and a systematic variation of the packing protocols we generate a portfolio of packings, whose microstructures differ in their degree of heterogeneity (DoH). Because the DoH quantifies the heterogeneity of the void space distribution in a packing, the asymptotic longitudinal dispersion coefficient calculated for the packings increases with the packings’ DoH. We investigate the influence of packing length (up to 150 dp, where dp is the sphere diameter) and grid resolution (up to 90 nodes per dp) on the simulated hydrodynamic dispersion coefficient, and demonstrate that the chosen packing dimensions of 10 dpx 10 dpx 70 dp and the employed grid resolution of 60 nodes per dp are sufficient to observe asymptotic behavior of the dispersion coefficient and to minimize finite size effects. Asymptotic values of the dispersion coefficients calculated for the generated packings are compared with simulated as well as experimental data from the literature and yield good to excellent agreement.

scholarly journals The Effects of Periodicity Assumptions in Porous Media Modelling

2021 ◽  
Author(s):  
T. O. M. Forslund ◽  
I. A. S. Larsson ◽  
J. G. I. Hellström ◽  
T. S. Lundström
Keyword(s):  
Fluid Flow ◽  
Lattice Boltzmann ◽  
Single Unit ◽  
Unsteady Flows ◽  
Unit Cell ◽  
Porous Bed ◽  
Bed Porosity ◽  
Macroscopic Properties ◽  
Boltzmann Method ◽  
Method Model

AbstractThe effects of periodicity assumptions on the macroscopic properties of packed porous beds are evaluated using a cascaded Lattice-Boltzmann method model. The porous bed is modelled as cubic and staggered packings of mono-radii circular obstructions where the bed porosity is varied by altering the circle radii. The results for the macroscopic properties are validated using previously published results. For unsteady flows, it is found that one unit cell is not enough to represent all structures of the fluid flow which substantially impacts the permeability and dispersive properties of the porous bed. In the steady region, a single unit cell is shown to accurately represent the fluid flow across all cases studied

Relationship between temporal and spatial averages in grid turbulence

2013 ◽  
Vol 730 ◽  
pp. 593-606 ◽  
Author(s):  
L. Djenidi ◽  
S. F. Tardu ◽  
R. A. Antonia
Keyword(s):  
Strong Support ◽  
Statistical Properties ◽  
Grid Turbulence ◽  
Mean Flow ◽  
Lateral Direction ◽  
Ergodic Hypothesis ◽  
Long Time ◽  
The Mean ◽  
Temporal And Spatial ◽  
Boltzmann Method

AbstractA long-time direct numerical simulation (DNS) based on the lattice Boltzmann method is carried out for grid turbulence with the view to compare spatially averaged statistical properties in planes perpendicular to the mean flow with their temporal counterparts. The results show that the two averages become equal a short distance downstream of the grid. This equality indicates that the flow has become homogeneous in a plane perpendicular to the mean flow. This is an important result, since it confirms that hot-wire measurements are appropriate for testing theoretical results based on spatially averaged statistics. It is equally important in the context of DNS of grid turbulence, since it justifies the use of spatial averaging along a lateral direction and over several realizations for determining various statistical properties. Finally, the very good agreement between temporal and spatial averages validates the comparison between temporal (experiments) and spatial (DNS) statistical properties. The results are also interesting because, since the flow is stationary in time and spatially homogeneous along lateral directions, the equality between the two types of averaging provides strong support for the ergodic hypothesis in grid turbulence in planes perpendicular to the mean flow.

Numerical Simulation of Surface Roughness Effects in Laminar Lubrication Using the Lattice-Boltzmann Method

2007 ◽  
Vol 129 (3) ◽  
pp. 603-610 ◽  
Author(s):  
Gunther Brenner ◽  
Ahmad Al-Zoubi ◽  
Merim Mukinovic ◽  
Hubert Schwarze ◽  
Stefan Swoboda
Keyword(s):  
Velocity Field ◽  
Surface Texture ◽  
Lattice Boltzmann ◽  
Load Capacity ◽  
Three Dimensional ◽  
Hydrodynamic Characteristics ◽  
Real Surface ◽  
Roughness Effects ◽  
Lattice Boltzmann Simulations ◽  
Boltzmann Method

The effect of surface texture and roughness on shear and pressure forces in tribological applications in the lubrication regime is analyzed by means of lattice-Boltzmann simulations that take the geometry of real surface elements into account. Topographic data on representative surface structures are obtained with high spatial resolution with the application of an optical interference technique. The three-dimensional velocity field past these surfaces is computed for laminar flow of Newtonian fluids in the continuum regime. Subsequently, pressure and shear flow factors are obtained by evaluating the velocity field in accordance with the extended Reynolds equation of Patir and Cheng (1978, ASME J. Tribol., 100, pp. 12–17). The approach allows an efficient determination of the hydrodynamic characteristics of microstructured surfaces in lubrication. Especially, the influence of anisotropy of surface texture on the hydrodynamic load capacity and friction is determined. The numerical method used in the present work is verified for a simplified model configuration, the flow past a channel with sinusoidal walls. The results obtained indicate that full numerical simulations should be used to accurately and efficiently compute the characteristic properties of film flows past rough surfaces and may therefore contribute to a better understanding and prediction of tribological problems.

Simulating Oxide Interfaces and Heterointerfaces

2002 ◽  
Vol 751 ◽  
Author(s):  
John H. Harding ◽  
Dorothy M. Duffy ◽  
Duncan J. Harris
Keyword(s):  
Grain Boundaries ◽  
Continuum Mechanics ◽  
Atomistic Simulation ◽  
Geometric Constraints ◽  
Length Scales ◽  
Oxide Interfaces ◽  
Local Ordering ◽  
Dielectric Interfaces ◽  
Long Time ◽  
Large Length

ABSTRACTInterfaces can be considered at a variety of length scales. All interfaces except grain boundaries are dielectric interfaces. In many cases, the geometric constraints of matching two lattices must be considered, together with the misfit strains that are often present. Continuum mechanics is useful for tackling such problems. In many cases, however, the local ordering of ions must also be considered. Atomistic simulation is therefore necessary, together with the problems associated with large length scales and long time scales. We discuss a number of examples to illustrate the issues involved and the compromises between different approaches that must be made.

Flow Dynamics Characteristics in Micro and Nano Length Scale Devices With the Lattice-Boltzmann Method: The Air Bearing Problem

2008 ◽  
Author(s):  
Alvaro J. Ramirez ◽  
Amador M. Guzman ◽  
Rodrigo A. Escobar
Keyword(s):  
Poiseuille Flow ◽  
Lattice Boltzmann ◽  
Numerical Results ◽  
Flow Dynamics ◽  
Length Scale ◽  
Air Bearing ◽  
Small Length ◽  
Length Scales ◽  
Boltzmann Method ◽  
Acceptable Agreement

The Lattice-Boltzmann Method (LBM) has been used for investigating flow behavior and characteristics in mini, micro and nano channels with the objective of describing the transition among different length scales. In particular, we have used the LBM to describe the air bearing lubrication problem at very small scales. For doing this, first we simulate and characterize the Poiseuille flow through different length scale and compare the LBM numerical results to existing experimental and numerical results. We put special attention on the application of the slip boundary condition on the channel wall for very small length scales. Our numerical results for the Poiseuille flow show an acceptable agreement with the Fukui & Kaneko numerical solution for continuous and slip-velocity regimes. For both, the rarified flow regime and the free molecular flow regime our solutions do not show an acceptable agreement with the Fukui & Kaneko Model. Then, we focus on the Couette flow characterization at very small length scales. The pressure distribution on both walls for different Knudsen numbers is obtained and compared to existing numerical results. Last, we concentrate in the air bearing problem. We have looked at the best simulation parameters for successfully describing this device flow dynamics, and particularly, for determining the pressure distribution and the net force with a good accuracy.

Influence of Bed Size on the Flow Characteristics and Porosity of Randomly Packed Beds of Spheres

1973 ◽  
Vol 40 (3) ◽  
pp. 655-660 ◽  
Author(s):  
G. S. Beavers ◽  
E. M. Sparrow ◽  
D. E. Rodenz
Keyword(s):  
Rectangular Cross Section ◽  
Flow Characteristics ◽  
Operating Conditions ◽  
Darcy Law ◽  
Equivalent Diameter ◽  
Packed Beds ◽  
Sphere Diameter ◽  
Number Range ◽  
Inertia Term ◽  
Bed Porosity

Experiments were performed to investigate the flow characteristics and porosity of randomly packed beds of glass spheres for conditions where the bed size cannot be regarded as infinitely large compared with the sphere size. The operating conditions of the flow experiments extended over a Reynolds number range for which the flow was governed by the Forchheimer extension of the linear Darcy law. The influence of the bed bounding walls on the permeability, on the coefficient of the Forchheimer inertia term, and on the porosity, was studied by using beds of rectangular cross section. It was found that the permeability was not apparently influenced by the bounding walls when the equivalent diameter of the bed was greater than 12 times the sphere diameter, whereas the coefficient of the inertia term was affected by the presence of the walls for bed equivalent diameters as high as 40 sphere diameters. The porosity of the beds was not influenced by the bed size for values of the bed equivalent diameter greater than 15 sphere diameters. When the large-bed porosity value was used with the Carman-Kozeny relationship for the permeability as a function of sphere diameter, an excellent representation of accumulated experimental data was attained.

scholarly journals On the spectrum of mid-latitude sporadic-<i>E</i> irregularities

2000 ◽  
Vol 18 (10) ◽  
pp. 1283-1292
Author(s):  
Yu. V. Kyzyurov
Keyword(s):  
Velocity Field ◽  
Power Law ◽  
Space Plasma ◽  
Density Fluctuations ◽  
Neutral Atmosphere ◽  
Space Plasma Physics ◽  
Length Scales ◽  
Plasma Irregularities ◽  
Atmosphere Turbulence ◽  
Sporadic E

Abstract. We discuss the creation of mid-latitude sporadic-E plasma irregularities (with length-scales smaller than sporadic layer thickness) by the neutral atmosphere turbulence. Using fluid equations, the relation between plasma density fluctuations and the velocity field of neutrals is derived. After a brief discussion of the relevant neutral turbulence, the analytical expression for the power spectrum of plasma irregularities is obtained. This expression allows a power-law type of experimental irregularity spectra (the spectral index depends on sporadic-E characteristics) and possible departures in detail of the irregularity spectra from the power-law form to be explained. In addition, it allows us to make estimates of length-scales at which such departures must occur.Key words: Ionosphere (ionospheric irregularities; mid-latitude ionosphere) – Space plasma physics (turbulence)

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