Numerical simulation of particle sedimentation in 3D rectangular channel

The 3D lattice Boltzmann method is used to simulate particle sedimentation in a rectangular channel. The results of single particle sedimentation indicate that the last position of the particle is along the center line of the channel regardless of the initial position, the particle diameter, and the particle Reynolds number. The wall effect on the terminal velocity is in good agreement with experimental results quantitatively. The drafting, kissing, and tumbling (DKT) process is reproduced and analyzed by simulating two-particle cluster sedimentation. The effects of the diameter ratio, initial position, and wall on the DKT process are investigated. When the two particles have equal diameter sediment in the rectangular channel, a periodical DKT process and the spiraling trajectory are found. The last equilibrium configuration is obtained from the simulation results. The interesting regular sedimentation phenomena are found when 49 particles fall down under gravity.     

Numerical simulation of fluid–particle hydrodynamics in a rectangular spouted vessel

A three-dimensional, Eulerian simulation was developed to describe isothermal, two-phase flow of the continuous (water) and dispersed (solid particles) phases in a rectangular spouted vessel. The mass and momentum conservation equations for each phase were solved using the finite volume technique, which treats each phase separately, while coupling them through drag, turbulence, and energy dissipation due to particle fluctuations. Particle–particle interactions via friction were also included.     

Numerical simulation of sedimentation of microparticles using the discrete particle method

A mathematical model has been formulated based on the combined continuous and discrete particle method for investigating the sedimentation behaviour of microparticles in aqueous suspensions, by treating the fluid phase as continuous and the particles phase as discrete, thus allowing the behaviour of individual particles to be followed and the evolution of the structure of the particle phase to be investigated as a function of time. The model takes into account most of the prevailing forces acting on individual particles including van der Waals attractive, electrostatic repulsive, gravitational, Brownian, depletion, steric, contact and drag forces. A code has also been developed based on the model. This paper reports some preliminary modelling results of mono-dispersed microparticles settling in aqueous suspensions under various conditions. The results show the short time dynamics of the fluid phase, which has a similar order of magnitude to the particle phase. Such short time dynamics could bear significance to processes such as particle aggregation when their size becomes very small. Preliminary analyses of the results have also been carried out on the evolution of particle settling based on a newly proposed parameter, local normalised volume fraction （LNVF）.     

Newtonian and Power-Law fluid flow in a T-junction of rectangular ducts

The aim of the present study is the numerical investigation of the shear-thinning and shear-thickening effects of flow in a T-junction of rectangular ducts. The employed CFD code incorporates the SIMPLE scheme in conjunction with the finite volume method with collocated arrangement of variables. The code enables multi-block computations in domains with multiple apertures, thus coping with the two-block, two-outlet layout of the current 3D computational domain. The shear-thinning and shear-thickening behaviours of the flow are covered by changing the index n of the Power-Law model within a range from 0.20 to 1.25, and the subsequent effects are investigated by means of different flow parameters namely the Reynolds (Re) number and the boundary conditions at the outlets. Results exhibit the extent of the effect of the Re number on the velocity profiles at different positions in the domain for both Newtonian and non-Newtonian cases. Similarly, the trend of the effect of shear-thinning and shear-thickening behaviours on the flow rate ratio between inlet and outlets, in the case of equal pressure imposed on outlets, is shown.     

Numerical simulation of the sedimentation of an elliptic body in an incompressible viscous fluid

In this note we discuss the application of a methodology combining distributed Lagrange multiplier based fictitious domain techniques, finite element approximations and operator splitting, to the numerical simulation of the motion of an elliptic body falling in a Newtonian incompressible viscous fluid. The motion of the body is driven by the hydrodynamical forces and gravity. As qualitatively expected, the elliptic body rotates so that its broad side tends to be perpendicular to the flow direction.     

Numerical simulation of the motion of neutrally buoyant particles in the plane Poiseuille flow of a Newtonian fluid

In this note we discuss the generalization of a Lagrange multiplier based fictitious domain method to the simulation of migration of neutrally buoyant particles in plane Poiseuille flow of a Newtonian fluid. The migration away from the center of the channel is believed to be an effect of the curvature of the velocity profile. We found this effect is not weakened by the presence of many particles, but instead by the collisions among the particles. Experiments and simulations show that the particles concentrate in the central region where the shear rate is low.     

Numerical study of the wall effect on particle sedimentation

ABSTRACT

In this article, we investigate the abnormal settling of two-disk systems and elliptical shaped particles in infinite two-dimensional channels filled with an incompressible viscous fluid. We apply a distributed Lagrange multiplier/fictitious domain method (DLM/FDM) for the direct numerical simulation of these particulate flows. Due to the wall effect, the two-disk systems can form chains which settle stably instead of having the particles moving apart. Also, sedimentation with the long axis moving to vertical positions in the middle of the infinite channel has been observed for the elliptic shaped particles. The critical Reynolds number for having such an abnormal settling behaviour decreases as the width of the channel increases.     

Numerical simulation of rarefied suspension sedimentation in a container

The evolution of the large-scale velocity perturbations in a homogeneous suspension sedimenting in a rectangular container with rigid horizontal walls and periodic conditions on the vertical boundaries is considered. Numerical simulation of the point-particle motion showed that the density and velocity fluctuations decrease with time. The perturbations are damped due to reshaping of the sedimentation front and the nonlinear interaction of the different modes.     

Direct simulation of fluid particle motions

Continuum models of two-phase flows of solids and liquids use constitutive assumptions to close the equations. A more fundamental approach is a molecular dynamic simulation of flowing big particles based on reliable macroscopic equations for both solid and liquid. We developed a package that simulates the unsteady two-dimensional solid-liquid two-phase flows using the Navier-Stokes equations for the liquid and Newton's equations of motion for the solid particles. The Navier-Stokes equations are solved using a finite-element formulation and Newton's equations of motion are solved using an explicit-implicit scheme. We show that the simplest fully explicit scheme to update the particle motion using Newton's equations is unstable. To correct this instability we propose and implement and Explicit-Implicit Scheme in which, at each time step, the positions of the particles are updated explicitly, the computational domain is remeshed, the solution at the previous time is mapped onto the new mesh, and finally the nonlinear Navier-Stokes equation and the implicitly discretized Newton's equations for particle velocities are solved on the new mesh iteratively. The numerical simulation reveals the effect of vortex shedding on the motion of the cylinders and reproduces the drafting, kissing, and tumbling scenario which is the dominant rearrangement mechanism in two-phase flow of solids and liquids in beds of spheres which are constrained to move in only two dimensions.This work was supported by the National Science Foundation, the Department of Energy, and the Army Research Office, Mathematics.     

Unsteady sedimentation of a spherical solid particle in a viscous fluid

Sedimentation of spherical heavy solid particles from a state of rest in a highly viscous incompressible fluid is studied. With account of the Basset force, the problem is reduced to Cauchy’s problem for a linear integro-differential equation. An exact solution of this problem is found in the form of single-valued functions of a real variable, and simple asymptotic formulas are obtained. The sedimentation law determined is verified experimentally.     

Numerical simulation of the extrusion of strongly compressible Newtonian liquids

The axisymmetric and plane extrusion flows of a liquid foam are simulated assuming that the foam is a homogeneous compressible Newtonian fluid that slips along the walls. Compressibility effects are investigated using both a linear and an exponential equation of state. The numerical results confirm previous reports that the swelling of the extrudate decreases initially as the compressibility of the fluid is increased and then increases considerably. The latter increase is sharper in the case of the exponential equation of state. In the case of non-zero inertia, high compressibility was found to lead to a contraction of the extrudate after the initial expansion, similar to that observed experimentally with liquid foams and to decaying oscillations of the extrudate surface. The time-dependent calculations show that the oscillatory steady-state solutions are stable. These steady-state oscillatory solutions are not affected by the length of the extrudate region nor by the boundary condition along the wall.     

Dynamic simulation of sedimentation of solid particles in an Oldroyd-B fluid

In this paper we present a two-dimensional numerical study of the viscoelastic effects on the sedimentation of particles in the presence of solid walls or another particle. The Navier-Stokes equations coupled with an Oldroyd-B model are solved using a finite-element method with the EVSS formalism, and the particles are moved according to their equations of motion. In a vertical channel filled with a viscoelastic fluid, a particle settling very close to one side wall experiences a repulsion from the wall; a particle farther away from the wall is attracted toward it. Thus a settling particle will approach an eccentric equilibrium position, which depends on the Reynolds and Deborah numbers. Two particles settling one on top of the other attract and form a doublet if their initial separation is not too large. Two particles settling side by side approach each other and the doublet also rotates till the line of centers is aligned with the direction of sedimentation. The particle-particle interactions are in qualitative agreement with experimental observations, while the wall repulsion has not been documented in experiments. The driving force for lateral migrations is shown to correlate with the pressure distribution on the particle's surface. As a rule, viscoelasticity affects the motion of particles by modifying the pressure distribution on their surface. The direct contribution of viscoelastic normal stresses to the force and torque is not important.     

Shear flow of a Newtonian fluid over a quiescent generalized Newtonian fluid

The flow of an upper shear-driven Newtonian fluid above an otherwise still non-Newtonian fluid is considered. The lower fluid is modelled as a generalized Newtonian fluid and set into motion by interfacial shear. By means of similarity transformations, the governing partial differential equations for the two-fluid problem transform exactly into two sets of ordinary differential equations coupled only at the interface. The successful transformation of the two-fluid problem is applied to the particular case when the lower fluid obeys power-law rheology. The resulting three-parameter problem is solved numerically for some different parameter combinations by means of a direct integration approach with the density ratio fixed to unity. We observed that the interfacial velocities decreased with increasing values of the power-law index n in the range from 0.6 to 1.4 whereas the shear-induced motion of the lower fluid penetrates far deeper into a shear-thinning (n < 1) than into a shear-thickening (n > 1) fluid. This phenomenon is ascribed to a corresponding increase of the non-linear viscosity function with lower n-values.     

Numerical simulations of linear viscoelasticity of monodisperse emulsions of Newtonian drops in a Newtonian fluid from dilute to concentrated regime

The bulk viscoelastic properties of monodisperse emulsions of Newtonian drops in a Newtonian matrix subjected to small amplitude oscillatory shear (SAOS) flow are investigated by means of arbitrary Lagrangian Eulerian finite element method 3D numerical simulations. Volume fractions of the suspended phase from the dilute to the concentrated regime (up to 30 %), and a range of several orders of magnitude of the drops-to-matrix viscosity ratio and of the frequency of the oscillatory flow are examined; the eventual presence of slip between the two fluids is also considered. The computational results are compared with theory, yielding a quantitative agreement with Oldroyd (Proc R Soc Lond A 218:122–132, 1953) predictions in a wide range of values of the considered parameters, even well beyond the dilute regime, and also in the cases with slip.     

Numerical simulation of particle-laden flow in an industrial wastewater sedimentation tank

Meccanica - The wastewater of steel production factories consists of a large amount of very small metal particles. The metal particles in this wastewater enter a large sedimentation tank and are...     

Creeping flow of Newtonian fluids in curved rectangular channels

The object of this paper is to present accurate numerical data concerning the creeping flow in curved annular channels with rectangular cross sections of which the outer wall is rotating with constant angular velocity. Dimensionless expressions for velocity profiles, flow rates and friction factors are obtained analytically for both the “drag” and “pressure” flow contributions. Numerical data were obtained on a digital computer and are presented in tabular and graphical form. The results of the theoretical analysis are also expressed in terms of the flow rate correction factors widely used in calculating the pumping efficiency of screw-pumps, agitators and extruders. This enables to estimate the effect of flight curvature on the pumping capacity.     

Numerical simulation of particle migration in asymmetric bifurcation channel

In this work we provide numerical validation of the particle migration during flow of concentrated suspension in asymmetric T-junction bifurcation channel observed in a recent experiment [1]. The mathematical models developed to explain particle migration phenomenon basically fall into two categories, namely, suspension balance model and diffusive flux model. These models have been successfully applied to explain migration behavior in several two-dimensional flows. However, many processes often involve flow in complex 3D geometries. In this work we have carried out numerical simulation of concentrated suspension flow in 3D bifurcation geometry using the diffusive flux model. The simulation method was validated with available experimental and theoretical results for channel flow. After validation of the method we have applied the simulation technique to study the flow of concentrated suspensions through an asymmetric T-junction bifurcation composed of rectangular channels. It is observed that in the span-wise direction inhomogeneous concentration distribution that develops upstream persists throughout the inlet and downstream channels. Due to the migration of particles near the bifurcation section there is almost equal partitioning of flow in the two downstream branches. The detailed comparison of numerical simulation results is made with the experimental data.     

Calculation of a conductive-laminar thermo-convection regime of a Newtonian fluid in a rectangular cavity with isothermal vertical boundaries

A method of calculating a free-convection flow of a viscous incompressible medium in a rectangular cavity is proposed. The lateral boundaries of the cavity have the same constant temperature, the top and bottomboundaries are thermally insulated, and the half-width to height ratio is much smaller than unity. A decomposition of the flow domain into zones with ascending and descending flows made it possible to formulate and solve analytically a coupled parabolic system of linear equations based on the classic Oberbeck-Boussinesq assumptions.     

Numerical simulation for rotating internal weakly viscoelastic flows in rectangular ducts

The present work develops a numerical method for the solution of rotating internal weakly viscoelastic flows in rectangular ducts for dimensionless parameters such as the Reynolds, Rossby and Weissenberg numbers, taken respectively in the intervals between 171 and 12000, 0.047 and 1/12 and up to 1/10000. It is shown that the usual counter‐rotating double‐vortex configuration of secondary flow breaks down with the increase of the Reynolds number (over the threshold of 171). For higher Reynolds numbers such as 7500 and 12000 the secondary flow diffuses to the interior of the duct where it assumes a fully developed configuration and the transition to the turbulence structure is observed. The Sobolev norms increase almost proportionally to the increase of the Reynolds number, and play an essential role for more complex problems involving transition to turbulence modelling. Copyright © 2002 John Wiley & Sons, Ltd.     

NUMERICAL SIMULATION OF THREE DIMENSIONAL TURBULENT FLOW IN SUDDENLY EXPANDED RECTANGULAR DUCT

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