颗粒毛细效应影响因素的离散元分析

颗粒毛细效应是指将一根细管插入填充有颗粒物质的容器中并对管施加竖直振动时颗粒在管内上升并最终达到一个稳定的高度的现象, 该现象为颗粒物料的逆重力输运提供了一种潜在的技术途径. 为探究颗粒毛细效应的影响因素, 采用离散元方法, 模拟再现了颗粒毛细效应过程,展示了不同管径下颗粒竖直方向速度演变特性, 考察了不同容器宽度和振动条件下颗粒最终毛细上升高度随管径的演变规律. 结果表明, 在容器宽度与粒径比为40、管振幅与粒径比为14.33、管振动频率为12 Hz情况下, 管径与粒径比$D/d = 3.33$时, 管内颗粒堵塞严重, 使得颗粒上升缓慢,并造成颗粒柱中断; $D/d = 8.33$时, 起初毛细上升高度增加迅速, 随后毛细上升高度的增大逐渐减缓, 管内颗粒在管径方向几乎不存在速度梯度; $D/d =15$时, 随着颗粒毛细上升高度的增大, 管内颗粒柱分离为速度截然不同的两层, 上层颗粒在管径方向几乎不存在速度梯度, 而下层颗粒存在明显的速度梯度.研究还发现, 在毛细效应能够发生的管径范围内, 存在一个对应于颗粒最终毛细上升高度最大值的临界管径, 当管径小于临界管径时, 颗粒最终毛细上升高度随管径的增大而增大, 当管径大于临界管径时, 颗粒最终毛细上升高度随管径的增大而趋于减小; 增大容器宽度,临界管径有所增大; 增大振幅、适当提高频率能够有效促进临界管径的增大.      

Theoretical investigation on submicron particle penetration through circular tubes inside a porous medium

The analytical infinite series solution of submicron particle transport in a circular tube bounded by a porous wall, such as a pinhole, is determined under the slip velocity boundary condition, and the solution is verified by using the experimental data in the previous studies for the specific cases. The results show that particle penetration rate increases with the increase of the porous parameter, the axial pressure drop, and the pinhole radius, whereas it decreases with increasing the pinhole length. The penetration rate of nano-particles are more sensitive to the variation of these parameters. However, the differences between the penetrations of particles ranging from 0.3 μm to 1 μm are not evident because the diffusion becomes weak gradually in this size range. In addition, a further comparison is performed between the analytical solution and the existing studies, and approximate expressions are presented for accurate calculation of particle penetration rate through pinholes appearing in porous materials including filter devices and masks.     

Efficient approaches of determining the motion of a spherical particle in a swirling fluid flow using weighted residual methods

The motion of a spherical particle released in a swirling fluid flow is studied employing the least-squares method and method of moments. The governing equations are obtained and solved employing the two methods. The accuracy of the results is examined against the results of a fourth-order Runge–Kutta numerical method. The effects of various parameters, namely the initial radius, initial radial velocity, initial angular velocity, and drag-to-inertia ratio, on the non-dimensional velocity profiles and particle position distribution are considered. The results show that the radial velocity increases over time while the angular velocity decreases, and that an increase in the initial radial velocity increases the particle radial distance and angular velocity but decreases the radial velocity profile.     

Wave propagation in an elastic tube: a numerical study

In this paper, a fluid–wall interaction model, called the elastic tube model, is introduced to investigate wave propagation in an elastic tube and the effects of different parameters. The unsteady flow was assumed to be laminar, Newtonian and incompressible, and the vessel wall to be linear-elastic, isotropic and incompressible. A fluid–wall interaction scheme is constructed using a finite element method. The results demonstrate that the elastic tube plays an important role in wave propagation. It is shown that there is a time delay between the velocity waveforms at two different locations and that the peak velocity increases while the low velocity decreases in the elastic tube model, contrary to the rigid tube model where velocity waveforms overlap each other. Compared with the elastic tube model, the increase of the wall thickness makes wave propagation faster and the time delay cannot be observed clearly, however, the velocity amplitude is reduced slightly due to the decrease of the internal radius. The fluid–wall interaction model simulates wave propagation successfully and can be extended to study other mechanical properties considering complicated geometrical and material factors.     

Symmetry of a periodic array of particles and a viscous fluid flow in the stokes approximation

A suspension in which rigid spherical particles of the same radius form a periodic array is considered. A general solution of the Stokes equations periodic with respect to this array is obtained. With reference to a fluid flow through a fixed array and a shear flow with frozen-in particles it is shown that taking the array structure and the symmetry of the conditions on the particle surface into account leads to a considerable simplification of the problem and makes it possible to determine the velocity and pressure distributions over the fluid.     

竖直振动管中颗粒毛细效应的离散元模拟

将一根细管插入填充有颗粒的静止容器中并对管施加竖直振动,颗粒将在管内发生上升运动,并最终稳定在一定高度,这一现象与液体毛细效应类似,被称为颗粒毛细效应.为探究颗粒毛细效应过程中伴随的颗粒尺度动力学行为及机理,基于离散元方法建立颗粒运动模型,对颗粒毛细效应动力学过程和特性开展数值模拟研究.模拟再现了文献中实验得到的颗粒毛细效应全过程,给出了管内颗粒柱高度随时间的演变规律,结果表明,受到颗粒系统参数的影响,本模拟条件下颗粒毛细效应过程呈现单周期上升、倍周期上升和倍周期稳定三个阶段,在倍周期上升阶段颗粒柱上升速度逐渐减小,平缓过渡到稳定阶段.在此基础上,分析了管内颗粒速度场和填充率分布随时间的演变特性,揭示了颗粒毛细效应过程中由容器传输到管内的颗粒的占比分布.研究发现,管内不同高度位置颗粒的运动并不同步,随着管的振动,管内出现速度波,速度波的传播引起管内颗粒出现膨胀和压缩交替的情况,从而管内颗粒填充率随时间发生周期性波动;在上升阶段,越接近管壁由容器传输到管内的颗粒占比越大,在稳定阶段,管内上层颗粒的对流引起容器传输到管内的颗粒占比发生反转.      

Particle motion and turbulence in dense two-phase flows

Measurements of particle mean and r.m.s. velocity were obtained by laser-Doppler anemometry in a descending solid-liquid turbulent flow in a vertical pipe with volumetric concentrations of suspended spherical particles of 270 μm mean diameter in the range 0.1–14%. Similar measurements were obtained in the flow downstream of an axisymmetric baffle of 50% area blockage placed in the pipe with volumetric concentrations of 310 μm particles up to 8% and of 665 μm particles up to 2%. In order to enable measurements in high particle concentrations without blockage of the laser beams the refractive index of the particles was matched to that of the carrier fluid.

The results show that the particle mean velocity profiles become more uniform and the particle r.m.s. velocity decreases with increasing concentration in both flow cases. The particle mean velocity in the pipe flow also decreases with concentration and the relative velocity, the difference between the particle velocity and the fluid velocity in single-phase flow, decreases with increasing Reynolds number. The length of the recirculation region downstream of the baffle was shorter than in single-phase flow by 11 and 24% for particle concentrations of 4 and 8%, respectively. The particle mean velocities were hardly affected by size for concentrations up fo 2%, but the r.m.s. velocities were lower with the larger particles.     

Particle deposition due to thermal force in a tube

Particle deposition in a tube with laminar flow is investigated. An analytical procedure is developed for predicting the particle deposition efficiency by incorporating the velocity of thermophoresis in the equation of conservation of particles. Effects of important parameters, such as temperature difference between the inlet gas and the tube wall, particle size and the Lewis number, on the particle precipitation efficiency are examined. Also considered in this work is the assumption of constant temperature gradient as a limiting case. It is found that particle precipitation efficiency predicted by using constant temperature gradient is much optimistic.     

DEM simulation of particle percolation in a packed bed

The phenomenon of spontaneous particle percolation under gravity is investigated by means of the discrete element method. Percolation behaviors such as percolation velocity,residence time distribution and radial dispersion are examined under various conditions. It is shown that the vertical velocity of a percolating particle moving down through a packing of larger particles decreases with increasing the restitution coefficient between particles and diameter ratio of the percolating to packing particles. With the increase of the restitution coefficient,the residence time and radial dispersion of the percolating particles increase. The packing height affects the residence time and radial dispersion. But,the effect can be eliminated in the analysis of the residence time and radial dispersion when they are normalized by the average residence time and the product of the packing height and packing particle diameter,respectively.In addition,the percolation velocity is shown to be related to the vertical acceleration of the percolating particle when an extra constant vertical force is applied. Increasing the feeding rate of percolating particles decreases the dispersion coefficient.     

DEM simulation of particle percolation in a packed bed

The phenomenon of spontaneous particle percolation under gravity is investigated by means of the discrete element method. Percolation behaviors such as percolation velocity, residence time distribution and radial dispersion are examined under various conditions. It is shown that the vertical velocity of a percolating particle moving down through a packing of larger particles decreases with increasing the restitution coefficient between particles and diameter ratio of the percolating to packing particles. With the increase of the restitution coefficient, the residence time and radial dispersion of the percolating particles increase. The packing height affects the residence time and radial dispersion. But, the effect can be eliminated in the analysis of the residence time and radial dispersion when they are normalized by the average residence time and the product of the packing height and packing particle diameter, respectively. In addition, the percolation velocity is shown to be related to the vertical acceleration of the percolating particle when an extra constant vertical force is applied. Increasing the feeding rate of percolating particles decreases the dispersion coefficient.     

Modelling the flow of power law fluids in a packed bed using a volume-averaged equation of motion

The development of a theoretical model for the prediction of velocity and pressure drop for the flow of a viscous power law fluid through a bed packed with uniform spherical particles is presented. The model is developed by volume averaging the equation of motion. A porous microstructure model based on a cell model is used. Numerical solution of the resulting equation is effected using a penalty Galerkin finite element method. Experimental pressure drop values for dilute solutions of carboxymethylcellulose flowing in narrow tubes packed with uniformly sized spherical particles are compared to theoretical predictions over a range of operating conditions. Overall agreement between experimental and theoretical values is within 15%. The extra pressure drop due to the presence of the wall is incorporated directly into the model through the application of the no-slip boundary condition at the container wall. The extra pressure drop reaches a maximum of about 10% of the bed pressure drop without wall effect. The wall effect increases as the ratio of tube diameter to particle diameter decreases, as the Reynolds number decreases and as the power law index increases.     

Shear wave velocity in sand considering the effects of frequency based on particle contact theory

Since the shear waves involved in in-situ and laboratory measurement methods vary significantly in terms of the frequency range, it is necessary to consider the effects of frequency on the shear wave velocity. In this study, sand particles are assumed to be spherical solid particles with an equal radius and identical material properties, and sand skeletons are regarded as granular aggregations generated through the random packing of sand particles. It is also assumed that the sand particles only undergo elastic deformation during shear wave propagation. Based on a spherical particle model, a formula is obtained for calculating the shear wave velocity in sand, with the shear wave frequency as an extra influencing parameter. The quantitative calculations demonstrate that the shear wave velocity decreases with an increase of sand porosity, and accelerates with increases of vertical effective stress and elastic modulus of the sand particles. It is also indicated that both the particle density and Poisson’s ratio of the sand particles have negligible effects on the shear wave propagation. The frequency dispersion characteristics of shear wave propagating in sand are also discussed. Moreover, the critical frequency is defined and its analytical expression is derived. The calculation results obtained using the proposed equations agree well with the in-situ measurement results and bender element test data.     

Direct numerical simulation of particle-laden plane turbulent wall jet and the influence of Stokes number

The distribution and motion of inertial particles in plane turbulent wall jet are investigated using direct numerical simulation, under the assumption of one-way coupling. To our knowledge, this appears to be the first direct numerical simulation of a particle-laden plane turbulent wall jet. It is shown that, in outer part of the wall jet, the behaviour of particles closely resembles that of a free plane jet. Due to the streamwise decay of particle Stokes number, the particle streaks formed in the near wall region of the wall jet are characterized by their intensity variation, which differs significantly from those in the channel flow. The streamwise growth of the particle velocity half-width is approximately equal to that of the fluid velocity half-width and the maximum velocity of particles decays slower than that of fluid due to inertia. The outer scaling can collapse the mean particle velocity in both the inner and outer region for heavier particles. In the buffer region, the particle–fluid velocity difference can be negative or positive depending on the Stokes number since there are two competing effects, namely the memory effect and turbophoresis. In the viscous region, the larger particles are on average faster than fluid and the velocity difference is found to be self-similar depending on outer Stokes number. The near-wall distribution of velocity difference is significantly correlated with the presence of high-momentum particles which are entrained by vortical structures generated in the outer region of the wall jet. These results are useful for environmental and engineering applications.     

固体颗粒对半球扰动尾迹影响的实验研究

采用粒子图像测速技术(particle image velocimetry, PIV)研究固体颗粒对放置在平板层流边界层中半球粗糙元尾迹的影响. 实验采集了清水和加入粒径为140 $\mu$m, 220 $\mu$m, 350$\mu$m聚苯乙烯固体颗粒4种工况下二维速度场信息, 基于半球半径的雷诺数为994 ($Re_R=RU/\upsilon$), 固体颗粒的体积浓度为$3.0\times10^{-5}$. 对比清水和两相工况下的平均速度剖面、湍流强度等宏观统计量, 分析固体颗粒对半球尾迹流动宏观特性的影响. 分别利用沿流向不同位置的流向脉动速度的二维空间相关系数和法向脉动速度的功率谱密度函数分析颗粒对尾迹结构演化过程及尾迹结构脱落频率的影响. 结果发现: 与清水相比, 回流区随颗粒粒径增大而逐渐增大; 颗粒使湍流强度增大, 回流区的存在导致在半球后流向位置$2R$前后区域湍流强度呈现不同变化趋势; 颗粒使尾迹结构的流向尺度减小并且随着颗粒粒径的增大先减小后增大; 在尾迹结构运动过程中颗粒的存在促进了尾迹结构的周期性加速和减速运动, 促进作用随着颗粒粒径的增大先增强后减弱; 颗粒的存在促进了尾迹结构的脱落, 脱落频率随颗粒粒径的增大先增大后减小.      

Direct numerical simulation of particle behaviour in the wall region of turbulent flows in horizontal channels

The motion of small particles in the wall region of turbulent channel flows has been investigated using direct numerical simulation. It is assumed that the particle concentration is low enough to allow the use of one-way coupling in the calculations, i.e. the fluid moves the particles but there is no feedback from the particles on the fluid motion. The velocity of the fluid is calculated by using a pseudospectral, direct solution of the Navier-Stokes equations. The calculations indicate that particles tend to segregate into the low-speed regions of the fluid motion near the wall. The segregation tendency depends on the time constant of the particle made non-dimensional with the wall shear velocity and kinematic viscosity. For very small and very large time constants, the particles are distributed more uniformly. For intermediate time constants (of the order 3), the segregation into the low-speed fluid regions is the highest. The finding that segregation occurs for a range of particle time constants is supported by experimental results. The findings regarding the more uniform distributions, however, still remain to be verified against experimental data which is not yet available. For horizontal channel flows, it is also found that particles are resuspended by ejections (of portions of the low-speed streaks) from the wall and are, therefore, primarily associated with low-speed fluid. The smaller particles are flung further upwards and, as they fall back towards the wall, they tend to be accelerated close to the fluid velocity. The larger particles have greater inertia and, consequently, accelerate to lower velocities giving higher relative velocities. This velocity difference, as a function of wall-normal distance, follows the same trend as in experiments but is always somewhat smaller in the calculations. This appears to be due to the Reynolds number for the numerical simulation being smaller than that in the experiment. It is concluded that the average particle velocity depends not only on the wall variables for scaling, but also on outer variables associated with the mean fluid velocity and fluid depth in the channel. This is because fluid depth in combination with the wall shear velocity determines how much time a particle, of a given size and density, spends in the outer flow and, hence, how close it gets to the local fluid velocity.     

Motion of a sphere down an inclined plane in a viscous flow

The motion of a rigid particle near a wall in a fluid flow is an important element of particle transport by fluids. The aim of this study was to carry out an experimental and theoretical investigation of the gravity-induced motion of a rigid sphere in a viscous fluid in the presence of a transverse flow. The experimental study of this configuration is a way of understanding the specific features of the hydrodynamically constrained particle motion. It is established that the transverse motion of the fluid substantially increases the particle settling velocity, which grows with increase in the transverse flow velocity. This effect is most pronounced for small angles of inclination of the plane. The difference in the particle settling velocities in the presence and absence of the transverse flow could reach a factor of two.     

Purely tangential flow of a PTT-viscoelastic fluid within a concentric annulus

An analytical solution is presented for the steady state, purely tangential flow of a viscoelastic fluid obeying the Phan-Thien–Tanner (PTT) constitutive equation in a concentric annulus with relative rotation of the inner and outer cylinders. The influence on the velocity distribution within the annulus and on fRe of the Weissenberg number, aspect ratio and an elongational parameter are investigated. The results show that the differences between the radial location of the minimum velocity and of the critical angular velocity compared with their Newtonian counterparts increase as the fluid elasticity increases. The results also show that fRe decreases with increasing Weissenberg number, radius ratio and the elongational parameter in the case of inner-cylinder rotation. In contrast, fRe increases with increasing radius ratio when the outer cylinder is rotating while the inner cylinder is at rest.     

A boundary element simulation of the unsteady motion of a sphere in a cylindrical tube containing a viscoelastic fluid

A boundary element method is used to simulate the unsteady motion of a sphere falling under gravity along the centreline of a cylindrical tube containing a viscoelastic fluid. The fluid is modelled by the upper-convected Maxwell constitutive equation. Results show that the viscoelasticity of the liquid leads to a damped oscillation in sphere velocity about its terminal value. The maximum sphere velocity, which occurs in the first overshoot, is approximately proportional to the square root of the Weissenberg number when the ratio of the sphere radius to the tube radius is sufficiently small. Particular attention is also paid to the wall effects. It is shown that a closer wall reduces the oscillatory amplitude of the sphere velocity but increases its frequency. The results suggest that the falling-ball technique, which is now widely used for viscosity measurement, might also be used for the determination of a relaxation time for a viscoelastic fluid.     

Apparent wall slip velocity measurements in free surface flow of concentrated suspensions

In this work we have experimentally measured the apparent wall slip velocity in open channel flow of neutrally buoyant suspension of non-colloidal particles. The free surface velocity profile was measured using the tool of particle imaging velocimetry (PIV) for two different channels made of plane and rough walls. The rough walled channel prevents wall slip, whereas the plane wall showed significant wall slip due to formation of slip layer. By comparing the velocity profiles from these two cases we were able to determine the apparent wall slip velocity. This method allows characterization of wall slip in suspension of large sized particles which cannot be performed in conventional rheometers. Experiments were carried out for concentrated suspensions of various particle volume concentrations and for two different sizes of particles. It was observed that wall slip velocity increases with particle size and concentration but decreases with increase in the viscosity of suspending fluid. The apparent wall slip velocity coefficients are in qualitative agreement with the earlier measurements. The effect of wall slip on free surface corrugation was also studied by analyzing the power spectral density (PSD) of the refracted light from the free surface. Our results indicate that free surface corrugation is a bulk flow response and it does not arise from boundary problem such as development of slip layer.     

Creeping-flow rotation of a slip spheroid about its axis of revolution

The problem of rotation of a rigid spheroidal particle about its axis of revolution in a viscous fluid is studied analytically and numerically in the steady limit of negligible Reynolds number. The fluid is allowed to slip at the surface of the particle. The general solution for the fluid velocity in prolate and oblate spheroidal coordinates can be expressed in an infinite-series form of separation of variables. The slip boundary condition on the surface of the rotating particle is applied to this general solution to determine the unknown coefficients of the leading orders, which can be numerical results obtained from a boundary collocation method or explicit formulas derived analytically. The torque exerted on the spheroidal particle by the fluid is evaluated for various values of the slip parameter and aspect ratio of the particle. The agreement between our hydrodynamic torque results and the available analytical solutions in the limiting cases is good. It is found that the torque exerted on the rotating spheroid normalized by that on a sphere with radius equal to the equatorial radius of the spheroid increases monotonically with an increase in the axial-to-radial aspect ratio for a no-slip or finite-slip spheroid and vanishes for a perfectly slip spheroid. For a spheroid with a specified aspect ratio, the torque is a monotonically decreasing function of the slip capability of the particle.