Modelling the motion of cylindrical particles in a nonuniform flow

The models currently used in computational fluid dynamics codes to predict solid fuel combustion rely on a spherical shape assumption. Cylinders and disks represent a much better geometrical approximation to the shape of bio-fuels such as straws and woods chips. A sphere gives an extreme in terms of the volume-to-surface-area ratio, which impacts both motion and reaction of a particle. For a nonspherical particle, an additional lift force becomes important, and generally hydrodynamic forces introduce a torque on the particle as the centre of pressure does not coincide with the centre of mass. Therefore, rotation of a nonspherical particle needs to be considered. This paper derives a model for tracking nonspherical particles in a nonuniform flow field, which is validated by a preliminary experimental study: the calculated results agree well with measurements in both translation and rotation aspects. The model allows to take into account shape details of nonspherical particles so that both the motion and the chemical reaction of particles can be modelled more reasonably. The ultimate goal of such a study is to simulate flow and combustion in biomass-fired furnaces using nonspherical particle tracking model instead of traditional sphere assumption, and thus improve the design of biomass-fired boilers.     

On the Settling Velocity in a Nonstationary Atmosphere

A general drag coefficient has been used in the equation of motion for solid spherical particles. The time constants, stopping times, and settling velocities in a still atmosphere are computed for a wide range of Reynolds numbers. The settling times are compared with the times calculated when a particle is falling in a fluctuating atmosphere. It is found that such particles will get significantly longer settling times owing to an enhancement in the drag coefficient caused by an increase of the relative velocity between the particle and the fluid. Surprisingly, this enhancement is present for a horizontal wind field due to a coupling between particle motion in different directions, but it is also present for a vertical field. The effect is most pronounced in the intermediate Reynolds number region, slightly above the Stokes range, where the increase in settling time can be more than 10% for certain fluctuation frequencies and amplitudes. This indicates that such particles must be carefully treated when they are falling in a nonstationary medium     

Measurement of the Size of Fine Nonspherical Particles with a Light-Scattering Particle Counter

To characterize flow separation and classification processes, particle size distributions must be measured in the airborne state without affecting the state of dispersion or disturbing the flow. Light-scattering devices with an optically defined measuring volume are specially designed for this purpose. However, the light-scattering device must be calibrated using nonideal particles which are present within the multiphase flow, preferably on an equivalent diameter based on settling rate. The cyclone cut size calibration can solve this problem. By means of this aerodynamic calibration technique, it is possible to measure size distributions of nonspherical particles with a light-scattering particle counter in industrially relevant cases.     

CHEMICALLY INDUCED MIGRATION OF PARTICLES ACROSS FLUID STREAMLINES

The velocity of a colloidal particle that moves because of a gradient of concentration of a molecular solute depends on the concentration field at the surface of the particle. Effects of macroscopic convection of the suspending fluid on two such transport phenomena, capillary-driven movement of fluid particles and diffusiophoresis of rigid particles, are considered here. In the case of fluid particles our results also apply to motion caused by a temperature gradient. If the particles are in a laminar flow with the solute gradient directed perpendicular to the direction of flow, as might arise in the boundary layer near a surface to which the particles are being deposited, the local solute concentration field around each particle is disturbed from that of pure diffusion of the solute. Using published results for these concentration disturbances in a simple-shear flow, we determine the effect of the imposed velocity gradient on the speed of the particles in the direction of the solute gradient. For both fluid and rigid particles, the correction due to macroscopic shear is 0(Pe^3/2:) where Pe is the Peclet number based on particle radius and fluid shear rate; this effect opposes the zero-shear particle velocity. A possible consequence of this result is that by increasing the shear rate in a laminar boundary layer in the hope of enhancing the rate of particle adsorption, one may actually be decreasing the rate.     

Conditions for Cloud Settling and Rayleigh-Taylor Instability

Most aerosol motion can be analyzed by individual particle motion or by the motion of the suspending gas. There are, however, two related situations in which an aerosol can exhibit bulk motion: cloud settling and Rayleigh-Taylor instability. In both cases, the aerosol particles move faster as a cloud than they do as individual particles. In the case of cloud settling, the aerosol is usually a spheroidal cloud surrounded by clean air. Rayleigh-Taylor instability occurs when a dense aerosol layer overlies a layer of clean air. This instability is characterized by abrupt breakthrough of the aerosol layer into the clean air layer at multiple points. High-concentration, submicrometer test aerosols were generated in two experimental systems that permitted observation of the transition from particle-dominated motion to cloud, or bulk, dominated motion and measurement of cloud settling velocities and characteristics. In both systems aerosol concentration could be controlled over two orders of magnitude. One system used commercial ventilation smoke tubes to release a dense stream of aerosol into a low velocity wind tunnel. The other used diluted mainstream cigarette smoke from a smoking machine in an aerosol centrifuge. Based on these experiments, theoretical equations for cloud settling predict cloud settling velocity within an order of magnitude. The transition from individual particle motion to observable bulk motion occurs when predicted cloud settling velocity is from 0.01 to 0.05 m/s. Cloud settling appears to be initiated from an aerosol stream or layer by Rayleigh-Taylor instability. The ratio of cloud settling velocity to particle settling velocity does not appear to be a reliable predictor of the transition from particle to bulk motion.     

Charged Particle Trajectory Statistics and Deposition in a Turbulent Channel Flow

The statistical properties of charged particles and their wall deposition in a turbulent channel flow in the presence of an electrostatic field is studied in this paper. For a dilute concentration, the influence of small particles on the fluid motion is neglected. The instantaneous velocity field is generated by a direct numerical simulation of the Navier-Stokes equation via a pseudospectral method. The case in which each particle carries a single unit of charge and the case in which the particles have a saturation charge distribution are analyzed. Ensembles of 8192 particle trajectories are used for evaluating various statistics. Effects of size and electric field intensity on particle trajectory statistics and wall deposition rate are studied. RMS particle velocities and particle concentrations at different distances from the wall are evaluated and discussed. The results for deposition rates are compared with those obtained from empirical equations.     

Mass transfer in centrifugal extractors

This contribution presents the methods of measuring the mass transfer in centrifugal extractors and of determining it during the individual life stages of a fluid element of the dispersed liquid, i.e. drop formation, motion, coalescence and stay in the stationary layer of the dispersed phase. The experimental mass transfer coefficients of the dispersed and continuous phases are compared with well-known theoretical models developed for extraction columns in gravitational field. Due to the fast motion and coalescence of the fluid particles at high centrifugal field intensities, mass transfer in centrifugal extractors takes place during short contact times. Nevertheless, this contribution shows that mass transfer in a centrifugal field can be calculated with selected theoretical models of the gravitational field. The investigations on mass transfer are completed by a classification of the strongly deformed fluid particles in centrifugal field into regimes of circulating and oscillating drops. In addition, data on the performance of centrifugal extractors, undergoing several exchange steps, are given.     

Low-Reynolds-number motion of a heavy sphere between two parallel plane walls

A novel boundary-integral algorithm [Staben, M.E., Zinchenko, A.Z., Davis, R.H., 2003. Motion of a particle between two parallel plane walls in low-Reynolds-number Poiseuille flow. Physics of Fluids 15, 1711-1733; Erratum: Phys. Fluids 16, 4206] is used to obtain O(1)-nonsingular terms that are combined with two-wall lubrication asymptotic terms to give resistance coefficients for near-contact or contact motion of a heavy sphere translating and rotating between two parallel plane walls in a Poiseuille flow. These resistance coefficients are used to describe the sphere's motion for two cases: a heavy sphere driven by a Poiseuille flow in a horizontal channel and a heavy sphere settling due to gravity through a quiescent fluid in an inclined channel. When the heavy sphere contacts a wall in either system, which occurs when the gap between the sphere and the wall becomes equal to the surface roughness of the sphere (or plane), a contact-force model using the two-wall resistance coefficients is employed. For a heavy sphere in a Poiseuille flow, experiments were performed using polystyrene particles with diameters 10%-60% of the channel depth, driven through a glass microchannel using a syringe pump. The measured translational velocities for these particles show good agreement with theoretical results. The predicted translational velocity increases for increasing particle diameter, as the spheres extend further into the Poiseuille flow, except for particles that are so large (diameters of 80%-85% of the channel depth) that the upper wall has a dominant influence on the particle velocity. For a heavy sphere settling in a quiescent fluid in an inclined channel, the transition from the no-slip regime to slipping motion occurs for a larger inclination angle of the channel with respect to the horizontal for an increase in particle diameter, since the larger particles are more slowed by the second wall. Limited experiments were performed for Teflon spheres with diameters 64%-95% of the channel depth settling in a very viscous fluid along the lower wall of an inclined acrylic channel. The measured translational velocities, which are only about 15%-25% of the tangential component of the undisturbed Stokes settling velocity, are in close agreement with theory using physical parameters obtained from similar experiments with a single wall [Galvin, K.P., Zhao, Y., Davis, R.H., 2001. Time-averaged hydrodynamic roughness of a noncolloidal sphere in low Reynolds number motion down an inclined plane. Physics of Fluids 13, 3108-3119].     

Rheology and flow behavior of suspensions of nanosized plate‐like particles in polyester resins at the startup of shear flows; Experimental and modeling

Applications of organoclays to polymer resins are potentially of great technical interest. This research targets preparation and characterization of nanocomposites of organoclays in an unsaturated polyester resin (UP). The nanocomposites with two distinct dispersion levels were compounded in a complex multisteps mixing process at three concentrations and subsequently their microstructures were characterized by XRD. The solution‐state rheological properties of layered silicate/UP were measured in the start‐up of steady state in the simple shear mode and analyzed based on our observations of internal structure of nanoparticles dispersion. Strong shear thinning behavior caused by increasing particle alignment induced by the shear field was observed for the suspensions. Effects of nanoparticles loadings and shearing on transient viscosity of the UP resin were examined. The experimental results show that increasing shear time in nanosuspension preparation steps and hence improvements of nanoplate dispersion in the polyester resin give rise to viscosity of the suspensions. A theoretical analysis of the motion of rigid ellipsoidal particles in a Newtonian fluid based on the thermodynamic approach and Jeffery's analysis of the motion of ellipsoid particles with an interaction term was developed to determine the orientation state of disc‐shape layers and then, the expression for the extra stress tensor was calculated to predict transient viscosity and normal stress differences. It is found that the thin oblate particles have significant orientation preference in the shearing direction. POLYM. COMPOS., 2009. © 2008 Society of Plastics Engineers     

Estimation of Concentration of Particles in Polymerizing Fluid during Centrifugal Casting of Functionally Graded Polymer Composites

The concentration of uniformly distributed particles in a fluid changes with time in the direction of gravitational or centrifugal force to form a concentration gradient. The change in the concentration is an outcome of velocity variation of particles in a fluid. A modified equation for terminal velocity, v _m of particles in polymerizing-fluid under centrifugal force is proposed to estimate the changes in the volume fraction of particles in the graded composites. The proposed equation introduces the effect of cure kinetics of polymer and its effect on particle movement in the model that was based on the modified Stoke’s law, considering the parameters related to particle hindrance, centrifugal force, particle dimensions, viscosity variation etc. The model predictions of concentration changes at the different locations of samples were compared with calcium carbonate filled polysulphide-modified-epoxy graded composites prepared by centrifugal casting.. The effect of particle size, delayed curing rate of matrix were explored. The simulated results are in good agreement with those of experiments.     

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。     

Zur Bewegung feiner Partikeln,die in turbulent strömenden Medien suspendiert sind

Motion of fine grained particles, suspended in turbulent flow . This article considers the motion of particles, suspended in turbulent flow. If the particles are sufficiently small to respond to turbulence, their motion includes stochastic components. Concerning processes like air classification or separation of fine powders the stochastic contribution – characterized by the conception of a particle diffusivity – the particle motion exhibits a detrimental influence. Sharpness of cut and separation efficiency are reduced. The paper aims to present the state of the art in particle diffusion. First, theoretical investigations are reported, attention being focused on the equation of motion of the particle which is the link between the motion of the fluid and the motion of the particle. Then, experimental results are reviewed. The following tendencies can be seen: Particles which response to turbulence of fluid flow show increasing diffusivity with increasing inertia. Field forces like gravity or electrical field forces exhibit a damping effect on diffusivity.     

从统计力学推导流体状态方程(Ⅱ)——非球形多方阱势硬粒子微扰理论

本文从考虑真实分子的形状与势能出发,引进一新的用级数表示的径向分布函数形式,导出了任意形状硬粒子流体的级数状态方程.用此方程描述参考体系,用多方阱势来近似真实分子的势能曲线,采用Barker与Henderson的方法近似高级微扰项,导出了非球形多方阱势硬粒子微扰理论的通用表达式,以作为进一步导出实用状态方程的基础.     

A Model for the Relative Velocity of a Particle in an Impingement Dryer: Application to Heat Transfer

A simplified mathematical model for the relative gas-particle motion in a confined jet impingement dryer is developed. Model predictions based on an unsteady momentum balance are in good agreement with the observed cycling motion of a spherical particle. The model is applied to coriander seeds submerged in a flow field of superheated steam. It is found that relative motion occurs in unsteady turbulent regime, and that steady settling velocity of particles is never achieved. Model results are applied to correlate experimental heat transfer data of an impingement dryer. Experimental Nu numbers compare fairly well with correlations for fluidized 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.     

A Model for the Relative Velocity of a Particle in an Impingement Dryer: Application to Heat Transfer

Abstract

A simplified mathematical model for the relative gas-particle motion in a confined jet impingement dryer is developed. Model predictions based on an unsteady momentum balance are in good agreement with the observed cycling motion of a spherical particle. The model is applied to coriander seeds submerged in a flow field of superheated steam. It is found that relative motion occurs in unsteady turbulent regime, and that steady settling velocity of particles is never achieved. Model results are applied to correlate experimental heat transfer data of an impingement dryer. Experimental Nu numbers compare fairly well with correlations for fluidized 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.     

Motion of a magnetic flow follower in two‐phase flow — application to the study of airlift reactor hydrodynamics

A low‐cost and simple magnetic particle tracer method was adapted to characterize the hydrodynamic behavior of an internal‐ and an external‐loop airlift reactor (ALR). The residence time distribution of three magnetic particles differing in diameter (5.5, 11.0 and 21.2 mm) and with a density very close to that of water was measured in individual reactor sections. The measured data were analyzed and used to determine the velocity of the liquid phase. Validation of the experimental results for liquid velocity was done by means of the data obtained by an independent reference method. Furthermore, analysis of the differences found in the settling velocity of the particle in single‐liquid and gas‐liquid phases was carried out, using a simplified 3D momentum transfer model. The model considering particle‐bubble interaction forces resulting from changes in the liquid velocity field due to bubble motion was able to predict satisfactorily the increase in the particle settling velocity in the homogeneous bubbly regime. The effective drag coefficient in two‐phase flow was found to be directly dependent on particle Reynolds number to the power of ? 2 but independent of gas flow‐rate for all particle diameters studied. Based on the experimental and theoretical investigations, the valid exact formulation of the effective buoyancy force necessary for the calculation of the correct particle settling velocity in two‐phase flow was done. In addition, recommendations concerning the use of flow‐following particles in internal‐loop ALRs for liquid velocity measurements are presented. Copyright © 2006 Society of Chemical Industry     

Stochastic Modeling of a New Spectrometer

A new spectrometer for classifying aerosol particles according to specific masses is being considered (Ehara et al. 1995). The spectrometer consists of concentric cylinders which rotate. The instrument is designed so that an electric field is established between the cylinders. Thus, aerosol particles injected into the spectrometer are subjected to a centrifugal force and an electric force. Depending on the balance between these two forces, as well as Brownian motion, charged particles either pass through the space between the cylinders or stick to either cylinder wall. Particles which pass through are detected. Given the rotation rate, voltage drop and physical dimensions of the device, we calculate the probability of detection in terms of particle density, diameter and charge. This is the transfer function. In this work, the focus is on situations where Brownian motion is significant. To solve for the transfer function, the trajectory of a particle in the spectrometer is modeled with a stochastic differential equation. Laminar flow is assumed. Further, attention is restricted to spherical particles with uniform density. The equation is solved using both numerical and Monte Carlo methods. The agreement between methods is excellent.     

An experimental investigation of the electrophoretic sedimentation of fine particles in waste kerosene

This study concerns the separation, by electrophoretic sedimentation, of fine positively charged oxidized aluminum and iron particles from waste kerosene used in an aluminum foil rolling operation. Settling experiments were carried out in a laboratory-scale cell which allowed the influence of an electric field to be studied simultaneously with gravitational settling. The study spans the clarification and thickening concentration ranges and includes the effects of field strength, settling height and electrical heating on the observed settling rates of several different samples of the particle—kerosene suspension. A number of correlations were found for the experimental results generally based on correlations for gravitational settling modified to take into account the imposition of an electric field.