柱状颗粒沉降过程的CFD-DEM联合仿真和实验研究

针对柱状催化剂颗粒相对于球形颗粒的不同运动特性,选择不同长度直径为2 mm的5种柱状颗粒,采用CFD-DEM数值模拟仿真,研究柱状颗粒在管状容器中沉降的运动行为,并建立柱状颗粒沉降试验台,采用高速摄像拍摄的方法进行实验研究。结果表明,在不同位置释放相同直径和长度的柱状颗粒时,靠近壁面释放的颗粒会在沉降过程中向中心漂移,且比中心释放的颗粒沉降更慢,时间更长;改变柱状颗粒与水平面的夹角,在圆管中心释放颗粒,最终颗粒都会旋转至水平状态,与水平面夹角越大,底部所受阻力越大,转动持续时间随之增加;推导柱状颗粒沉降斯托克斯方程,并通过实验数据对方程中的阻力系数进行修正,将修正后的阻力系数导入用户自定义函数(UDF)计算颗粒沉降末速度,相对误差从原来使用球形颗粒阻力系数的50%下降到17%以内,模拟较为可靠。     

Lateral migration of spherical particles in porous flow channels: application to membrane filtration

Lateral migration of spherical rigid neutrally buoyant particles moving in a laminar flow field in a porous channel is induced by an inertial lift force (tubular-pinch effect) and by a permeation drag force due to convection into the porous walls. The analysis of Cox and Brenner [7], for the particle motion in a nonporous duct is extended to include the effect of the wall porosity. Criteria are established under which the inertial and permeation drag force in the lateral direction can be vectorially added. Particle trajectories and concentrations profiles are calculated for a plane Poiseuille flow with one porous wall. For particles with radius of 1 μm, inertial and permeation drag forces are of comparable size under flow conditions often met in ultra- and hyperfiltration of dilute suspensions. For smaller particles the permeation drag force dominates.     

Motion of a sphere parallel to plane walls in a Poiseuille flow. Application to field-flow fractionation and hydrodynamic chromatography

The motion of a solid spherical particle entrained in a Poiseuille flow between parallel plane walls has various applications to separation methods, like field-flow fractionation and hydrodynamic chromatography. Various handy formulae are presented here to describe the particle motion, with these applications in mind. Based on the assumption of a low Reynolds number, the multipole expansion method coupled to a Cartesian representation is applied to provide accurate results for various friction factors in the motion of a solid spherical particle embedded in a viscous fluid between parallel planes. Accurate results for the velocity of a freely moving solid spherical particle are then obtained. These data are fitted so as to obtain handy formulae, providing e.g. the velocity of the freely moving sphere with a 1% error. For cases where the interaction with a single wall is sufficient, simpler fitting formulae are proposed, based on earlier results using the bispherical coordinates method. It appears that the formulae considering only the interaction with a nearest wall are applicable for a surprisingly wide range of particle positions and channel widths. As an example of application, it is shown how in hydrodynamic chromatography earlier models ignoring the particle-wall hydrodynamic interactions fail to predict the proper choice of channel width for a selective separation. The presented formulae may also be used for modeling the transport of macromolecular or colloidal objects in microfluidic systems.     

THE MEASUREMENT OF THE FLOW AROUND A SPHERE SETTLING IN A RECTANGULAR BOX USING 3-DIMENSIONAL PARTICLE IMAGE VELOCIMETRY

A novel three-dimensional particle image velocimetry technique is used to measure the planar three-dimensional flow field about the centreline of a sphere sedimenting in a rectangular shaped box. Measurements are made in the center of the container and also one diameter from a plane wall. Results are presented for a sphere falling in both a constant viscosity elastic (Boger) fluid and a shear-thinning elastic liquid. In the center of the box, the flow field is essentially two-dimensional as expected. Near the wall, there is substantial out-of-plane motion in the shear-thinning solution due to the presence of the wall. Surprisingly, there is little out-of-plane motion for a sphere sedimenting near the wall in the Boger fluid. There are significant qualitative differences in the flow field for the sphere sedimenting in the shear-thinning and constant viscosity elastic liquids. The results are compared with previously published work for a sphere settling in a non-Newtonian fluid and also with results obtained in an identical geometry for a Newtonian fluid. Reasons for the differences in the velocity maps are discussed. The drag coefficient for each geometry and fluid is calculated.     

THE MEASUREMENT OF THE FLOW AROUND A SPHERE SETTLING IN A RECTANGULAR BOX USING 3-DIMENSIONAL PARTICLE IMAGE VELOCIMETRY

A novel three-dimensional particle image velocimetry technique is used to measure the planar three-dimensional flow field about the centreline of a sphere sedimenting in a rectangular shaped box. Measurements are made in the center of the container and also one diameter from a plane wall. Results are presented for a sphere falling in both a constant viscosity elastic (Boger) fluid and a shear-thinning elastic liquid. In the center of the box, the flow field is essentially two-dimensional as expected. Near the wall, there is substantial out-of-plane motion in the shear-thinning solution due to the presence of the wall. Surprisingly, there is little out-of-plane motion for a sphere sedimenting near the wall in the Boger fluid. There are significant qualitative differences in the flow field for the sphere sedimenting in the shear-thinning and constant viscosity elastic liquids. The results are compared with previously published work for a sphere settling in a non-Newtonian fluid and also with results obtained in an identical geometry for a Newtonian fluid. Reasons for the differences in the velocity maps are discussed. The drag coefficient for each geometry and fluid is calculated.     

Turbulence structure for plane Poiseuille–Couette flow and implications for drag reduction over surfaces with slip

Direct numerical simulations were used to simulate plane channel and plane Poiseuille–Couette flows. For Poiseuille–Couette flow, the walls of the channel were moving with a specified velocity. This is equivalent to forcing a slip velocity at the wall of the channel, and such flow behaviour can be viewed as the effect due to an ultra‐hydrophobic wall. It was found that the location of the zero Reynolds stress value shifted towards the wall moving in the streamwise direction. The near‐wall eddies were found to be longer and weaker than for the plane‐Poiseuille channel flow. It appears that such an eddy structure can lead to turbulence drag reduction.     

SHEAR AND INTERFACIAL INSTABILITIES OF OIL-WATER FLOW IN AN INCLINED CHANNEL

A study of the linear stability of a laminar flow of an oil-water system in an inclined channel is presented. A novel shear-mode of instability, which is necessarily decaying in plane Poiseuille flow, is found to be the primary instability in certain situations. When the channel is sufficiently inclined, the long-wave mode can become unstable, regardless of the total volumetric flow rate of the fluids The consequences to oil transport are discussed.     

Interaction of two touching spheres in a viscous fluid

The nature and effects of contacts between suspended particles were studied through a process in which a heavy sphere falls past a light sphere in a viscous fluid at low Reynolds number. Teflon and nylon spheres were used for the heavy and light spheres, respectively, with natural surface roughness and with the nylon sphere artificially roughened. Because of the existence of microscopic roughness on the sphere surfaces, the particles are able to make physical contact, breaking the symmetry of the trajectory predicted by hydrodynamic theory for smooth spheres. The experimental results are compared with numerical results calculated according to the theory of Davis (Phys. Fluids A 4 (1992) 2607), with a particular focus on the rotational velocities of the spheres. The numerical results from the roll/slip model provide the best fit of the experimental data. Instead of locking together like a rigid body and rotating together, two spheres initially roll without slipping and then roll with slipping after the maximum friction force is reached.     

Effective particle diameters for simulating fluidization of non‐spherical particles: CFD‐DEM models vs. MRI measurements

Computational fluid dynamics—discrete element method (CFD‐DEM) simulations were conducted and compared with magnetic resonance imaging (MRI) measurements (Boyce, Rice, and Ozel et al., Phys Rev Fluids. 2016;1(7):074201) of gas and particle motion in a three‐dimensional cylindrical bubbling fluidized bed. Experimental particles had a kidney‐bean‐like shape, while particles were simulated as being spherical; to account for non‐sphericity, “effective” diameters were introduced to calculate drag and void fraction, such that the void fraction at minimum fluidization (ε_mf) and the minimum fluidization velocity (U_mf) in the simulations matched experimental values. With the use of effective diameters, similar bubbling patterns were seen in experiments and simulations, and the simulation predictions matched measurements of average gas and particle velocity in bubbling and emulsion regions low in the bed. Simulations which did not employ effective diameters were found to produce vastly different bubbling patterns when different drag laws were used. Both MRI results and CFD‐DEM simulations agreed with classic analytical theory for gas flow and bubble motion in bubbling fluidized beds. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2555–2568, 2017     

A Numerical Simulation of the Boycott Effect

The lattice Boltzmann method has been used to simulate the velocity field induced and the motion of an ensemble of particles during the sedimentation process in inclined tubes. The simulations show the trajectories and flow behavior of individual particles and particle-particle and particle-wall interactions as well as the formation of particle clusters. The global convection motion that was experimentally observed during such processes and tends to enhance the sedimentation process is also reproduced numerically. In addition we have found that smaller intermittent vortices, formed from the wakes of groups of settling particles, also play an important role in the sedimentation process and the final distribution of particles.     

A Numerical Simulation of the Boycott Effect

The lattice Boltzmann method has been used to simulate the velocity field induced and the motion of an ensemble of particles during the sedimentation process in inclined tubes. The simulations show the trajectories and flow behavior of individual particles and particle-particle and particle-wall interactions as well as the formation of particle clusters. The global convection motion that was experimentally observed during such processes and tends to enhance the sedimentation process is also reproduced numerically. In addition we have found that smaller intermittent vortices, formed from the wakes of groups of settling particles, also play an important role in the sedimentation process and the final distribution of particles.     

Simulations of scalar dispersion in fluidized solid–liquid suspensions

Direct, particle‐resolved simulations of solid–liquid fluidization with the aim of quantifying dispersion have been performed. In addition to simulating the multiphase flow dynamics (that is dealt with by a lattice‐Boltzmann method coupled to an event‐driven hard‐sphere algorithm), a transport equation of a passive scalar in the liquid phase has been solved by means of a finite‐volume approach. The spreading of the scalar—as a consequence of the motion of the fluidized, monosized spherical particles that agitate the liquid—is quantified through dispersion coefficients. Particle self‐diffusivities have also been determined. Solids volume fractions were in the range 0.2–0.5, whereas single‐sphere settling Reynolds numbers varied between approximately 3 and 20. The dispersion processes are highly anisotropic with lateral spreading much slower (by one order of magnitude) than vertical spreading. Scalar dispersion coefficients are of the same order of magnitude as particle self‐diffusivities. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1880–1890, 2014     

Respiratory Deposition of Fibers in the Non-Inertial Regime—Development and Application of a Semi-Analytical Model

A semi-analytical model describing the motion of fibrous particles ranging from nano- to micro scale was developed, and some important differences in respiratory tract transport and deposition between fibrous particles of various sizes and shapes were elucidated. The aim of this work was to gain information regarding health risks associated with inhalation exposure to small fibers such as carbon nanotubes. The model, however, is general in the sense that it can be applied to arbitrary flows and geometries at small fiber Stokes and Reynolds numbers. Deposition due to gravitational settling, Brownian motion and interception was considered, and results were presented for steady, laminar, fully developed parabolic flow in straight airways. Regarding particle size, our model shows that decrease in particle size leads to reduced efficiency of sedimentation but increased intensity of Brownian diffusion, as expected. We studied the effects due to particle shape alone by varying the aspect ratios and diameters of the microfibers simultaneously, such that the effect of particle mass does not come into play. Our model suggests that deposition both due to gravitational settling and Brownian diffusion decreases with increased fiber aspect ratio. Regarding the combined effect of fiber size and shape, our results suggest that for particles with elongated shape the probability of reaching the vulnerable gas-exchange region in the deep lung is highest for particles with diameters in the size range 10–100 nm and lengths of several micrometers. Note that the popular multi-walled carbon nanotubes fall into this size-range.     

Inclined Wall Effects on the Low Reynolds Number Motion of a Chiral Filament

The trajectories of a single rigid particle settling under gravity in a quiescent fluid are studied in this article. The particle is sufficiently small and its motion relative to the surrounding fluid satisfies the conditions for local Stokes flow. Thus force and torque on the particle are linearly related to the local flow conditions. The resistance tensors relating the force and torque on the particle to its translational and angular velocities are found in terms of distributions of singularities along the centerlines of the particle itself and an image particle on the opposite side of the inclined wall. The solution of the no-wall problem can be found, for slender filaments, by the formulation of the flow field in terms of a singularity distribution of stokeslets along the filament according to the integral equation found by Johnson (1977, 1980). This equation can be solved by a direct matrix inversion technique. On the other hand, the velocity field solution to the near-wall problem requires both the stokeslet distribution and a set of singularities distributed along the centerline of a mirror image of the filament behind the inclined wall. The time variations of the orientation angles and the center of mass location of a particle have been determined by using a fourth-order Runge-Kutta scheme.     

表面活性剂虫状胶束流体中颗粒沉降负尾迹模拟

颗粒在剪切稀释黏弹性表面活性剂形成的蠕虫状胶束流体中沉降时会产生负尾迹，负尾迹的形成对该种复杂流体与固体颗粒之间的相互作用具有重要影响。基于Giesekus本构方程，采用POLYFLOW软件模拟了黏弹性表面活性剂(Viscoelastic Surfactant, VES)蠕虫状胶束流体中单颗粒的沉降过程，分析了流体松弛时间和迁移因子对颗粒周围速度场及应力场的影响，重点研究了颗粒尾部速度负尾迹的产生原因及其对颗粒曳力的影响。结果表明，Giesekus本构方程能够描述VES流体的非线性剪切变稀行为和弹性导致的拉伸变形。流体弹性导致颗粒尾部产生较大的拉伸变形，剪切稀化和流体弹性的共同作用使颗粒尾部产生拉伸变形，导致负尾迹出现。表征流体弹性的De(黛博拉数)越大，流体拉伸黏度的Tr(特劳顿数)越小，负尾迹越长。负尾迹的出现使VES流体中颗粒所受曳力减小，沉降速度开始增加。模拟结果为此种流体的进一步应用提供了一定的研究基础。     

Boundary effects on thermophoresis of aerosol cylinders

An analytical study is presented for the thermophoretic motion of a circular cylindrical particle in a gaseous medium with a transversely imposed temperature gradient near a large plane wall parallel to its axis in the quasisteady limit of negligible Peclet and Reynolds numbers. The Knudsen number is assumed to be small so that the fluid flow is described by a continuum model with a temperature jump, a thermal slip, and a frictional slip at the particle surface. The presence of the confining wall causes two basic effects on the particle velocity: first, the local temperature gradient on the particle surface is altered by the wall, thereby speeding up or slowing down the particle; secondly, the wall enhance the viscous retardation of the moving particle. Through the use of cylindrical bipolar coordinates, the transport equations governing this problem are solved and the wall effects on the thermophoresis of the aerosol cylinder are computed for various cases. The presence of the plane wall can reduce or enhance the particle velocity, depending upon the relative thermal conductivity and surface properties of the particle, the relative particle-wall separation distance, and the direction of the applied temperature gradient. The direction of the thermophoretic motion of a cylindrical particle near a plane wall is different from that of the prescribed thermal gradient, except when it is oriented parallel or perpendicular to the wall. The effects of the plane wall on the thermophoresis of a cylinder are found to be much more significant than those for a sphere at the same separation.     

A NUMERICAL SOLUTION OF THE FLOW AROUND A SPHERE IN A CIRCULAR CYLINDER

A numerical solution of the Navier-Stokes equations is presented for Poiseuille flow around an axially placed, fixed sphere in a circular cylinder. Streamlines and isovorticity lines are calculated from the governing equations for the strearnfunction and the vorticity. Isobars are calculated from a Poisson equation, derived from the Navier-Stokes equations. The pressure and vorticity distribution on the surface of the sphere, the additional pressure drop and the drag coefficients are presented. Solutions are obtained for Reynolds numbers up to 150 (based on cylinder diameter and mean velocity). The wall effects are examined by comparison with results of previous investigations for an unbounded flow around a sphere.     

A NUMERICAL SOLUTION OF THE FLOW AROUND A SPHERE IN A CIRCULAR CYLINDER

A numerical solution of the Navier-Stokes equations is presented for Poiseuille flow around an axially placed, fixed sphere in a circular cylinder. Streamlines and isovorticity lines are calculated from the governing equations for the strearnfunction and the vorticity. Isobars are calculated from a Poisson equation, derived from the Navier-Stokes equations. The pressure and vorticity distribution on the surface of the sphere, the additional pressure drop and the drag coefficients are presented. Solutions are obtained for Reynolds numbers up to 150 (based on cylinder diameter and mean velocity). The wall effects are examined by comparison with results of previous investigations for an unbounded flow around a sphere.