Simulation of hindered settling in bidisperse suspensions of rigid spheres

Extensive progress has been made in using CFD tool in the simulation of multiphase flows in some gravity concentrators. Several case studies for calculation of multiphase flows by different numerical models in spiral, dense medium cyclone, water only cyclones, hindered-settling bed separator, heavy medium vessel and jig are reviewed. The Euler-Lagrange approach in calculation of the particle movement and particle-liquid coupling effect are also discussed. The limitation of Euler-Euler models in the treatment of the particles with a size distribution, and disadvantages of discrete element method (DEM) in description of the jigging processes will be presented. The successful two-dimensional simulation of the hindered-settling bed separator, heavy medium vessel and jig by Euler-Lagrange approach is also addressed.

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Sound waves in a periodic medium containing rigid spheres

The Journal of the Acoustical Society of America ◽

10.1121/1.395828 ◽

1987 ◽

Vol 82 (4) ◽

pp. 1436-1441 ◽

Cited By ~ 15

Author(s):

Dov Bai ◽

Joseph B. Keller

Keyword(s):

Periodic Medium ◽

Sound Waves ◽

Rigid Spheres

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A formulation of the linearized Boltzmann equations for a binary mixture of rigid spheres

European Journal of Mechanics - B/Fluids ◽

10.1016/j.euromechflu.2005.03.001 ◽

2005 ◽

Vol 24 (5) ◽

pp. 614-620 ◽

Cited By ~ 5

Author(s):

R.D.M. Garcia ◽

C.E. Siewert ◽

M.M.R. Williams

Keyword(s):

Binary Mixture ◽

Rigid Spheres ◽

Boltzmann Equations

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Asymmetric three-dimensional Stokes flows about two fused equal spheres

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2007.1872 ◽

2007 ◽

Vol 463 (2085) ◽

pp. 2329-2350 ◽

Cited By ~ 15

Author(s):

Michael Zabarankin

Keyword(s):

Meromorphic Functions ◽

Three Dimensional ◽

The Body ◽

Fredholm Integral Equations ◽

Rigid Spheres ◽

Riemann Boundary ◽

Fredholm Equations ◽

Flow Problems ◽

Toroidal Coordinates ◽

Class Of Functions

Exact solutions to three-dimensional Stokes flow problems for asymmetric translation and rotation of two fused rigid spheres of equal size have been obtained in toroidal coordinates. The problems have been reduced to three-contour equations for meromorphic functions from a certain class, and then the latter have been reduced to Fredholm integral equations of the second kind by the Mehler–Fock transform of order 1. For the specified class of functions, the equivalence of the corresponding three-contour and Fredholm equations has been established in the framework of Riemann boundary-value problems for analytic functions. As an illustration for the obtained solutions, the pressure has been calculated at the surface of the body for both problems, and resisting force and torque, experienced by the body in asymmetric translation and rotation, have been computed as functions of a geometrical parameter of the body.

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THE ABSORPTION OF HIGH-ENERGY RADIATION, A MONTE CARLO STUDY: II. SPHERICAL GEOMETRY

Canadian Journal of Physics ◽

10.1139/p63-066 ◽

1963 ◽

Vol 41 (4) ◽

pp. 651-663

Author(s):

N. R. Steenberg

Keyword(s):

Cross Section ◽

Spherical Geometry ◽

Monte Carlo Study ◽

Nuclear Data ◽

High Energy ◽

Rare Gas ◽

Nuclear Radius ◽

Rigid Spheres ◽

High Energy Radiation ◽

The Individual

The absorption of radiation in a spherical obstacle composed of rigid spheres has been studied. The result is the absorption cross section of such an obstacle as a function of the free cross section and the number A of the individual spheres and of packing density. It is found that the usual rare-gas formula represents the cross section adequately. The analysis is applied to nuclear data for the absorption of 25-Bev/c protons by nuclei. It is found that for a nuclear radius R = r0A1/3 + δ, where δ is the radius of the nucleon, r0 = 1.17 fermi, δ = 1.05 fermi, and an average nucleon transparency a2 = 0.30 is consistent with the data.

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