STUDY ON THE INTERACTION OF SEDIMENTING CYLINDRICAL PARTICLES IN STILL FLUID

The sedimentations of two cylindrical particles in three different initial relative po- sitions are numerically simulated using the lattice Boltzmann method.The movement characteristics and particle interactions during their sedimentation are presented and discussed in detail.The results show that,(i)if the two particles are released parallel but separated horizontally,they push away each other,rotate inwards and separate horizontally as they fall;(ii)if the two particles are released par- allel but separated vertically,the sedimentation behavior can be classified into three stages:trailing, tumbling and separating;(iii)if the two particles are released perpendicular but separated vertically, the sedimentation behavior can be characterized as:trailing and rotating,touching and sliding.In order to validate our simulation,experiments were also conducted and the results agree well with the numerical ones.

Some considerations on the rheology of dense frictional cylindrical particles

Discrete element method simulations of granular shear flows of frictional cylindrical particles are performed. From the simulations, solid-phase pressure, shear stress, and bulk friction coefficient μ can be measured, allowing the investigation of the effects of particle properties on the macroscopic flow behaviors. Thus, the inertial number I based rheological models, which were frequently used for the spherical particles in the previous work, are examined for the applicability to cylindrical particles in the present study. It is found that the particle aspect ratio, interparticle friction coefficient, and particle size polydispersity all affect the bulk friction coefficient-inertial number correlation and the solid volume fraction-inertial number correlation, and their effects vary in different flow regimes, which exhibit different mechanical behaviors.

DISPERSION OF CYLINDRICAL PARTICLES IN TURBULENT FLOWS

With consideration of the Stokes drag and virtual mass force, the equationsfor mean and fluctuating velocities in rotation and translation were given for rigid cylindricalparticles moving in a turbulent flow. Then the rotational and translational dispersion coefficientsof particle were derived. The relationships between the dispersion, coefficients and flow lengthscale as well as particle characteristic parameters were analyzed. The resulting dispersioncoefficients were proved to decrease as the particle length increases. The conclusions are helpfulfor the further research on the motion of cylindrical particles in turbulent flows.

Void fraction for random loose packing of the cylindrical particles considering filling rate,material and shape

Particle packing is widely applied in organic pollutant adsorption,catalytic reaction.biomass combustion,nuclear cooling,and other scenarios.Due to the complexity of the shape,the studies on the void fraction of the cylindrical particles are not as thorough as the spherical particles.This study investigated the influence of the flling rate,material properties and sphericity on the void fraction of cylinders through experiments and simulation.DEM(discrete element method)was validated by the internal structures of the packing obtained by CT(computed tomography).Based on the logarithmic correlation between the void fraction and flling rate,an ingenious framework for predicting the void fraction of cylindrical particles was presented with two intermediate coefficients.By correlating the coefficients with the material property and sphericity,a novel void-fraction prediction model was established with R-squared of 0.996.The mechanism of void fraction under random loose packing for cylinders was eventually found in this study.

Numerical simulation of the sedimentation of cylindrical pollutant particles in fluid

The sedimentation of cylindrical pollutant particles which fall through a fluid is investigated. Differing from previous research work, particle oscillation and effect of particle on the fluid are considered, and the torque exerted on a particle when viscous fluid flow around a particle is got through experiment and included in the numerical simulation. The computational results showed that the sedimentation velocities of particle increase slowly with the increase of particle aspect ratio . For disk like particle, when the motion direction of particle is parallel to axis of particle, particle falls more slowly than the case of perpendicular to axis of particle; while for rod like particle, it is inverse. For sedimentation of a crowd of high frequency oscillating cylindrical particles with arbitrary initial orientation, both vertical velocity and horizontal velocity oscillate dramatically, the degree of oscillation of the former is stronger than the later. A crowd of particles fall more quickly than an isolated particle. Particles tend to strongly align in the direction of gravity. The computational results agreed well with the experimental ones and helpful for controlling of pollutant particles.

Physical study on the vibrated packing densification of mono-sized cylindrical particles

Systematic physical experiments examining the packing densification of mono-sized cylindrical parti- cles subject to 3D mechanical vibration were carried out. The influence of vibration conditions such as vibration time, frequency, amplitude, vibration strength, container size, and the aspect ratio and spheric- ity of the particle on the packing density were analyzed and discussed. For each initial packing density with a certain aspect ratio, operating parameters were optimized to achieve much denser packing. The results indicate that the packing density initially increases with vibration time and then remains con- stant. The effects of vibration frequency and amplitude on the packing densification have similar trends, i.e. the packing density first increases with the vibration frequency or amplitude to a high value and then decreases; too large or small frequency or amplitude does not enhance densification. Increasing the container size can reduce container wall effects and help achieve a high packing density. Varying the particle aspect ratio and sphericity can lead to different dense random packing structures. Overall, based on results of the examined systems, the highest random packing density obtained in an infinite sized container can reach 0.73, which agrees well with corresponding numerical and analytical results in the literature.

Sedimentation of short cylindrical pollutants with mechanical contacts

Lattice Boltzmann method and elastic particle collision model were used to investigate the sedimentation of short cylindrical pollutant particles with mechanical contacts for varying bulk number density ε and terminal Reynolds number ReT. The corresponding experiments were performed as a comparison. The clusters of pollutant particles with an inverted “T” structure were observed, the pollutant particles for high ε and large ReT scattered wider than that for low ε and small ReT. The sedimentation velocities increased suddenly at the initial stage, then decreased drastically, after that swayed around and approached to a steady value. The time to steady state did not depend on ε and ReT. The effect of particle interactions was to hinder the average sedimentation velocity, and hindrance was directly proportional to ε. The orientation distributions of pollutant particles depended on ReT and ε, especially on the former. Both the standard deviations of vertical and horizontal velocity, the former was larger than the latter, were nearly independent on ε and ReT.

NUMERICAL SIMULATION OF ORIENTATION DISTRIBUTION FUNCTION OF CYLINDRICAL PARTICLE SUSPENSIONS

The orientation distribution function of cylindrical particle suspensions was deduced and numerically simulated, and an application was taken in a wedge-shaped flow field. The relationship between the orientation distribution function and particle orientation angles was obtained. The results show that comparing with the most probable angle distribution which comes to being in short time, the distribution of the steady state doesn't vary much. in range; the main difference is the anti-clockwise rotation in the right and upper field, that is, particles rotate more at the points where the velocity gradients are larger. The most probable orientations are close to the direction of local streamlines. In the direction of streamlines, with poleradius decreasing, the most probable angles increase, but the angles between their orientations and the local streamlines decrease.

RESEARCH ON THE FLOW STABILITY IN A CYLINDRICAL PARTICLE TWO-PHASE BOUNDARY LAYER

Based on the momentum and constitutive equations, the modified Orr_Sommerfeld equation describing the flow stability in a cylindrical particle two_phase flow was derived.For a cylindrical particle two_phase boundary layer, the neutral stability curves and critical Reynolds number were given with numerical simulation. The results show that the cylindrical particles have a suppression effect on the flow instability, the larger the particle volume fraction and the particle aspect_ratio are, the more obvious the suppression effect is.

Solution of the Poisson-Boltzmann Equation for a Cylindrical Particle with a Limited Length: Functional Theoretical Approach

With the help of the method of separation of variables and the Debye-Hüchel approximation, the Poisson-Boltzmann equation that describes the distribution of the potential in the electrical double layer of a cylindrical particle with a limited length has been firstly solved under a very low potential condition. Then with the help of the functional analysis theory this equation has been further analytically solved under general potential conditions and consequently, the corresponding surface charge densities have been obtained. Both the potential and the surface charge densities cointide with those results obtained from the Debye-Hüchel approximation when the very low potential of zeψ〈〈kT is introduced.

Orientational Distribution of Fibres in Sheared Fibre Suspensions

Motion of fibres in sheared fibre suspensions is simulated numerically by using the lattice Boltzmann method. The orientational distributions of the fibres are presented for different Reynolds numbers, Stokes numbers, shear rate and fibre aspect ratio. Some computational results are compared with the experimental data of pipe flow, and the qualitative agreement is achieved. The results show that the orientational distributions are greatly affected by the Reynolds numbers, while relatively insensitive to the fibre aspect ratio. The Stokes number and shear rate have obvious influence on the orientation distribution.

Distribution of Orientations in Fibre Suspension Flowing in a Turbulent Boundary Layer

The equation of probability distribution function for mean fibre orientation in a turbulent boundary layer is derived, in which the correlation terms of the fluctuating velocity, fluctuating angular velocity with the fluctuating probability distribution function are related to the gradient of mean probability distribution function and the dispersion coefficients in order to make the equation be solvable. The finite-difference method is used to solve the equation numerically. The results show that the fibres tend to align with the streamline, which is in agreement qualitatively with the experimental result given by visualization. The fibre aspect-ratio has a significant effect on the orientation distribution of fibres, while the effect of the distance from the wall is negligible.

RESEARCH ON THE CYLINDRICAL PARTICULATE FLOWS

The study of cylindrical particulate flows has wide industrial applicability and hence received much attention. The purpose of the present paper is to provide a review on the motion of cylindrical particles in shear layer, converging channel and jet flows, the dynamic of cylindrical particles sedimentation in a Newtonian fluid, the characterization of turbulent cylindrical particulate flows, the property of interaction between the particles, the structural feature and rheology of suspensions, the analysis of hydrodynamic instability of cylindrical particle suspensions. Finally, the concluding remarks are given.

Study on Electric Double Layer of a Cylindrical Particle with Functional Theoretical Approach

A new method, i.e. the iterative method in functional theory, was introduced to solve analytically the nonlinear Poisson-Boltzmann （PB） equation under general potential ψ condition for the electric double layer of a charged cylindrical colloid particle in a symmetrical electrolyte solution. The iterative solutions of ψ are expressed as functions of the distance from the axis of the particle with solution parameters： the concentration of ions c, the aggregation number of ions in a unit length m, the dielectric constant e, the system temperature T and so on. The relative errors show that generally only the first and the second iterative solutions can give accuracy higher than 97%. From the second iterative solution the radius and the surface potential of a cylinder have been defined and the corresponding values have been estimated with the solution parameters, Furthermore, the charge density, the activity coefficient of ions and the osmotic coefficient of solvent were also discussed,