The analysis of the relations between porosity and tortuosity in granular beds

2017 ◽  
Vol 1 (20) ◽  
pp. 75-85 ◽  
Author(s):  
Wojciech Sobieski ◽  
Seweryn Lipiński
Keyword(s):  
Lattice Boltzmann ◽  
Creeping Flow ◽  
Spherical Particles ◽  
Particle Sizes ◽  
Granular Bed ◽  
Tracking Method ◽  
Bed Porosity ◽  
Relative Errors ◽  
Boltzmann Method ◽  
Path Tracking Method

In the paper, functions describing different porosity-tortuosity relations were collected, and then the tortuosity values were calculated for a one granular bed consisting of spherical particles with normal distribution of diameters. Information about the bed porosity and particle sizes was obtained from measurements conducted for an artificial granular bed, consisting of glass marbles. The results of calculations were compared with the results of two other methods of tortuosity determination, performed for the same case (details are not described in this paper): the first of them uses the Path Tracking Method, the second one - information about the velocity components in a creeping flow (the Lattice-Boltzmann Method was applied to obtain the velocity field in the flow). The main aim of our article was to test whether the functions linking tortuosity with porosity, which are available in the literature, give similar results as the methods described above. To achieve this aim, the relative errors between results of calculations for the collected formulas and values from the both previous mentioned methods were calculated.

scholarly journals Influence of walls on the migration of non-Brownian spherical particles in creeping flow: a lattice Boltzmann study

2011 ◽  
Vol 369 (1945) ◽  
pp. 2387-2395 ◽  
Author(s):  
Ernesto Monaco ◽  
Gunther Brenner
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Creeping Flow ◽  
Spherical Particles ◽  
Particle Displacement ◽  
Initial Particle ◽  
Preliminary Results ◽  
Monodisperse Suspensions ◽  
Different Diameters ◽  
Boltzmann Method

The influence of walls on binary encounters of spherical particles under creeping flow is studied by means of the lattice Boltzmann method. Depending on the initial particle displacement different behaviours can be observed, including the ‘swapping’ trajectories. The domain of the swapping trajectories is identified for interacting spheres with the same diameter; some preliminary results are given for the case of two spheres with different diameters. Finally, the influence of particle swapping on the dynamics of monodisperse suspensions is also described.

scholarly journals Calculating the Binary Tortuosity in DEM-Generated Granular Beds

Processes ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1105 ◽  
Author(s):  
Wojciech Sobieski
Keyword(s):  
Discrete Element Method ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Three Dimensional ◽  
Path Tracking ◽  
Empirical Formulas ◽  
Tracking Method ◽  
Value Range ◽  
Boltzmann Method ◽  
Path Tracking Method

In this paper, a methodology of calculating the tortuosity in three-dimensional granular beds saved in a form of binary geometry with the application of the A-Star Algorithm and the Path Searching Algorithm is presented. The virtual beds serving as examples are prepared with the use of the Discrete Element Method based on data of real, existing samples. The obtained results are compared with the results described in other papers (obtained by the use of the Lattice Boltzmann Method and the Path Tracking Method) as well as with the selected empirical formulas found in the literature. It was stated in the paper that the A-Star Algorithm gives values similar (but always slightly underestimated) to the values obtained via approaches based on the Lattice Boltzmann Method or the Path Tracking Method. In turn, the Path Searching Algorithm gives results in the same value range as popular empirical formulas and additionally it is approximately two times faster than the A-Star Algorithm.

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

Lattice-Boltzmann simulations of particles in non-zero-Reynolds-number flows

1999 ◽  
Vol 385 ◽  
pp. 41-62 ◽  
Author(s):  
DEWEI QI
Keyword(s):  
Reynolds Number ◽  
Cross Section ◽  
Lattice Boltzmann ◽  
Three Dimensional ◽  
Spherical Particles ◽  
Computational Results ◽  
Two Dimensional ◽  
Lattice Boltzmann Simulations ◽  
Boltzmann Method ◽  
Reynolds Number Flows

A lattice-Boltzmann method has been developed to simulate suspensions of both spherical and non-spherical particles in finite-Reynolds-number flows. The results for sedimentation of a single elliptical particle are shown to be in excellent agreement with the results of Huang, Hu & Joseph (1998) who used a finite-element method. Sedimentation of two-dimensional circular and rectangular particles in a two-dimensional channel and three-dimensional spherical particles in a tube with square cross-section is simulated. Computational results are consistent with experimentally observed phenomena, such as drafting, kissing and tumbling.

scholarly journals Lattice Boltzmann method used to simulate particle motion in a conduit

2017 ◽  
Vol 65 (2) ◽  
pp. 105-113 ◽  
Author(s):  
Jindřich Dolanský ◽  
Zdeněk Chára ◽  
Pavel Vlasák ◽  
Bohuš Kysela
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Particle Motion ◽  
Three Dimensional ◽  
Hydrodynamic Forces ◽  
Spherical Particles ◽  
Momentum Exchange ◽  
Carrier Liquid ◽  
Particle Tracking Method ◽  
Boltzmann Method

AbstractA three-dimensional numerical simulation of particle motion in a pipe with a rough bed is presented. The simulation based on the Lattice Boltzmann Method (LBM) employs the hybrid diffuse bounce-back approach to model moving boundaries. The bed of the pipe is formed by stationary spherical particles of the same size as the moving particles. Particle movements are induced by gravitational and hydrodynamic forces. To evaluate the hydrodynamic forces, the Momentum Exchange Algorithm is used. The LBM unified computational frame makes it possible to simulate both the particle motion and the fluid flow and to study mutual interactions of the carrier liquid flow and particles and the particle–bed and particle–particle collisions. The trajectories of simulated and experimental particles are compared. The Particle Tracking method is used to track particle motion. The correctness of the applied approach is assessed.

scholarly journals Lattice Boltzmann Method Simulation of 3-D Melting Using Double MRT Model With Interfacial Tracking Method

2016 ◽  
Author(s):  
Zheng Li ◽  
Mo Yang ◽  
Yuwen Zhang
Keyword(s):  
Lattice Boltzmann Method ◽  
Numerical Method ◽  
Lattice Boltzmann ◽  
Liquid Fraction ◽  
Melting Process ◽  
Distribution Functions ◽  
Collision Term ◽  
Melting Front ◽  
Tracking Method ◽  
Boltzmann Method

Three-dimensional melting problems are investigated numerically with Lattice Boltzmann method (LBM). Regarding algorithm’s accuracy and stability, Multiple-Relaxation-Time (MRT) models are employed to simplify the collision term in LBM. Temperature and velocity fields are solved with double distribution functions, respectively. 3-D melting problems are solved with double MRT models for the first time in this article. The key point for the numerical simulation of a melting problem is the methods to obtain the location of the melting front and this article uses interfacial tracking method. The interfacial tracking method combines advantages of both deforming and fixed grid approaches. The location of the melting front was obtained by calculating the energy balance at the solid-liquid interface. Various 3-D conduction controlled melting problems are solved firstly to verify the numerical method. Liquid fraction tendency and temperature distribution obtained from numerical methods agree with the analytical results well. The proposed double MRT model with interfacial tracking method is valid to solve 3-D melting problems. Different 3-D convection controlled melting problems are then solved with the proposed numerical method. Various locations of the heat surface have different melting front moving velocities, due to the natural convection effects. Rayleigh number’s effects to the 3-D melting process is discussed.

Model of fluidized bed expansion

1979 ◽  
Vol 44 (1) ◽  
pp. 50-55
Author(s):  
Benitto Mayrhofer ◽  
Lubomír Neužil ◽  
František Procháska
Keyword(s):  
Experimental Data ◽  
Fluidized Bed ◽  
Fixed Bed ◽  
Theoretical Models ◽  
Creeping Flow ◽  
Spherical Particles ◽  
Bed Porosity ◽  
Porosity Dependence ◽  
Bed Expansion ◽  
Better Than

Theoretical relations have been derived for the superficial velocity of fluidization under the creeping flow regime for cubic, monoclinic and tetrahedron configurations of spherical particles. The models proposed have been compared with theoretical models published up to the present and with the power-law correlations recommended. The configuration fitting the best was found to be the tetrahedron one. All configurations examined in this work gave correct trend of the velocity of fluidization versus porosity dependence. Experimental data indicate that for the bed porosity ranging between 0.45 and 0.68 our models are better than other so far published. However theoretical models of other authors based on the analysis of the behavior of a fixed bed give better results.

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