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     

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。     

AIR-SOLIDS DRAG IN CASCADING ROTARY DRYERS

This paper describes the results of theoretical and experimental studies on the effect of air flow on particle transport through cascading rotary dryers. Two possible models are formulated. In the first, the drag coefficient between the air and the solids is calculated on the assumption that the particles can be regarded as isolated spheres. This approach has been employed widely in the literature to estimate particle residence times in rotary dryers. The results yielded coefficients which were 1-2 orders of magntiude greater than those measured experimentally; this demonstrates the inadequacy of this approach. In the second model, the curtains are treated as flat. two-sided plates and the drag coefficient calculated accordingly. The predictions of this model are in much closer accord with the     

AIR-SOLIDS DRAG IN CASCADING ROTARY DRYERS

ABSTRACT

This paper describes the results of theoretical and experimental studies on the effect of air flow on particle transport through cascading rotary dryers. Two possible models are formulated. In the first, the drag coefficient between the air and the solids is calculated on the assumption that the particles can be regarded as isolated spheres. This approach has been employed widely in the literature to estimate particle residence times in rotary dryers. The results yielded coefficients which were 1–2 orders of magntiude greater than those measured experimentally; this demonstrates the inadequacy of this approach. In the second model, the curtains are treated as flat. two-sided plates and the drag coefficient calculated accordingly. The predictions of this model are in much closer accord with the     

颗粒团绕流曳力系数的LBM计算

采用格子Boltzmann方法(Lattice Boltzmann method, LBM) 中的LBGK(Lattice Bhatnagar- Gross-Krook)模型和二阶精度的曲线边界条件处理方法对二维颗粒团绕流现象进行了数值模拟,并同时使用动量交换法计算了两种颗粒团构型中不同颗粒的曳力系数。结果表明：颗粒团曳力系数与颗粒聚团的构型有着密切联系,颗粒聚团的形成将导致颗粒团曳力系数大幅度减小。除颗粒团构型因素外,颗粒间距和流动Reynolds数也是导致颗粒团曳力系数发生改变的主要因素。当颗粒聚团存在时,颗粒团中不同颗粒的受力有较大差异,若忽略颗粒聚团效应,则颗粒团曳力系数的计算必然将产生偏差。     

The Effects of Bluntness and Orientation on Two-Dimensional Samplers in Calm Air

This article uses numerical simulation to investigate the effect of sampler bluntness, particle size, and sampler orientation on aspiration efficiency in calm air. The procedure is to first numerically solve the velocity field around the sampler in calm air and then to trace the particle trajectories and calculate the the aspiration efficiency. Two samplers are studied: a two-dimensional parallel plate and a two-dimensional blunt cylinder. The variation of aspiration efficiency with particle size shows two minima between two asymptotic values. When the samplers are facing upward, the asymptotic values are 1 for very small particles and the ratio of particle settling velocity to suction velocity for very large particles. At other orientations, the horizontal-facing and the downward-facing, the asymptotic value for large particles is 0. The sampler bluntness has an important effect in the region of particle size where there is competition between the particle inertia and the fluid drag force (i.e., 5 μm < d > 100 μm in our case). A blunt sampler always has higher aspiration efficiency than does a sharp-edged sampler in this region of particle sizes. For very small particles and very large particles, the aspiration efficiencies approach asymptotic values and the sampler bluntness has little effect. The results also show that the sampler orientation affects the predicted aspiration efficiency     

用改进的单元胞模型数值模拟液体穿过球形颗粒群的流动

The cell model developed since 1950s is a useful tool for exploring the behavior of particle assemblages,but it demands further careful development of the outer cell boundary conditions so that interaction in a particle swarm is better repressented.In this paper,the cell model and its development were reviewed,and the modifications of outer cell boundary conditions were suggested.Athe cell outer boundary,the restriction of uniform liquid flow was removed in our simulation conducted in the reference frame fixed with the particle.Zero shear stress condition was used to evaluate the outer boundary value of the stream function.Boundary vorticity was allowed to evolve to values compatible to existing stream function at the free shear outer boundary.The fore-aft symmetry of vorticity distribution at the outer boundary is thought critical to ensure the continuity of inflow and outflow between touching neighbor cells,and is also tested in the modified cell model.Numerical simulation in terms of stream function and vorticity based on the modified cell models was carried out to shed light on the interaction between liquid and particles.Lower predicted drag coefficient by the modified cell models was interpreted with the feature of flow structure.The drag coefficient from the simulation was also compared with correlations of drag coefficient reported in literature.It is found that the modified cell model with the uniformity of external flow relaxed and the fore-aft symmetry of boundary vorticity enforced was the most satisfactory of the overall performance of prediction.     

Determination of non-spherical particle terminal velocity using particulate expansion data

A new method is proposed for the determination of the terminal velocity of non-spherical particles and compared with experimental data. The method is based on particulate expansion data of fluidized bed and variational model for calculating fluid–particle interphase drag coefficient. Other methods require knowledge of the particle shape, a parameter that is not easy to obtain for real materials. We use pressure drops data in packed bed for indirect determination of particle shape factor which depends on the reliability of coefficients in the Ergun equation. Our data, however, show that these coefficients are system-specific. The proposed method for the determination of non-spherical particle settling velocity in liquid as well as extrapolation to system gas-particles gives results which are in good agreement with experimental data. The method is restricted to particles which can be fluidized particulately by liquid.     

Particle Collection Efficiency for Nylon Mesh Screens

Nylon mesh screens, unlike metal screens, are attractive as a collection substrate for nanoparticles because they can be digested or ashed prior to chemical analysis. A theoretical single-fiber efficiency expression developed for wire-mesh screens was evaluated for estimating the collection efficiency of 11–300 nm particles for nylon mesh screens. Pressure drop across the screens, the effect of particle morphology (spherical and highly fractal-like) on collection efficiency, and single-fiber efficiency were evaluated experimentally for three pore sizes (60, 100, and 180 μm) at three flow rates (2.5, 4, and 6 Lpm). The pressure drop across the screens was found to increase linearly with superficial velocity. The collection efficiency of the screens was found to vary by less than 4% regardless of particle morphology. Single-fiber efficiency calculated from experimental data was in good agreement with that estimated from theory for particles between 40 and 150 nm but deviated from theory for particles outside this size range. New coefficients for the single-fiber efficiency model were identified that minimized the sum of square error (SSE) between the values estimated with the model and those determined experimentally. Compared to the original theory, the SSE calculated using the modified theory was at least one order of magnitude lower for all screens and flow rates with the exception of the 60-μm pore screens at 2.5 Lpm, where the decrease was threefold.

Copyright 2012 American Association for Aerosol Research     

基于格子Boltzmann方法的单颗粒绕流数值模拟

采用格子Boltzmann方法（LBM）研究了单颗粒绕流流动过程。通过使用LBM中的LBGK（lattice Bhatnagar-Gross-Krook）模型和二阶精度的曲线边界条件处理方法,实现了对单颗粒绕流问题的定常及非定常流动过程中涡结构的模拟。采用动量交换法分别计算了Reynolds数在0.1～200范围内27个不同Reynolds数时的曳力系数,并将计算结果拟合得到基于LBM数值模拟的曳力曲线。计算结果表明,LBM在气固两相流的模拟计算中具有精确、可靠的优点,使用LBM模拟计算曳力曲线的方法经济、易行,并且可以克服由传统实验方法获得曳力曲线的局限性。     

Single-Fiber Interception Efficiency for Elliptical Fibers

Synthetic fibers with non-circular cross-sections are used in air filters. These fibers may offer performance advantages over traditional fibers with circular cross sections because they have more surface per unit volume of fiber upon which particles can collect. Starting with a solution for the velocity field around fibers with elliptical cross-sections, expressions for predicting the single-fiber efficiency for particle collection by the interception mechanism were developed for elliptical fibers. The interception efficiency predictions depend on filter solidity, fiber properties such as size, aspect ratio, and orientation of the cross section relative to the incoming flow, and particle diameter. The expressions demonstrate that single fiber interception efficiency for elliptical fibers generally increases with increasing particle diameter, increasing solidity, increasing aspect ratio, and as the major axis of the ellipse becomes more perpendicular to the incoming air flow.     

大长径比细长颗粒的沉降实验和曳力系数的关联

引　言对球状颗粒的研究已取得丰硕的成果[1] ,但对其他形状颗粒的研究则较少 ,特别是细长颗粒 .形状的特殊性使细长颗粒的曳力系数与球状颗粒明显不同 ,仅有的文献[2～ 4] 将研究重点放在静止液体中颗粒沉降时的取向和终端沉降速度 ,且一般采用球形度表示曳力系数 ,颗粒长径比     

Numerical study of cluster formation in a gas–particle circulating fluidized bed

Simulations with two-way coupling are performed for two-dimensional gas–solid flow in a circulating fluidized bed with a total solids concentration of 3% in the riser. The motion of particles is treated by a Lagrangian approach, and particles are assumed to interact through binary, instantaneous, non-frontal, and inelastic collisions with friction. The model for the interstitial gas phase is based on the Navier–Stokes equations for two-phase flow with fluid turbulence calculated by using LES. Several porosity functions exist in the literature relating the drag force for a particle in a cloud to the drag force on an isolated particle. We have studied the influences of this porosity function, observing large differences in the local flow structure. The fluctuating gas–solid motion has been investigated showing a strong anisotropic flow behaviour, which is similar to experimental findings. The instabilities in these flows are strongly linked to the non-linear drag function due to the group effect of particles in a cloud. The collision parameters have been found to have an important influence on the cluster structures.     

Calculation of the Velocity of Free Settling of Solid Particles in a Newtonian Liquid

A cubic equation for the velocity of free settling of solid particles in a Newtonian liquid is derived on the basis of a simple approximate expression for the drag coefficient of spherical particles as a function of the Reynolds number using the concept of the effective diameter of a particle of arbitrary shape, which characterizes the surface, volume, and midsection of the particle. The exact and approximate solutions are compared, and some experimental data are analyzed.     

Single-Fiber Diffusion Efficiency for Elliptical Fibers

Fibers with elliptical cross-sections have higher surface to volume ratios than those with circular cross-sections and may therefore lead to increased filter collection efficiency. Single-fiber theory and velocity flow fields developed for elliptical fibers can be used to predict collection efficiency by diffusion for elliptical fibers. Utilizing the convective diffusion equation in elliptical coordinates, single-fiber diffusion efficiency was calculated for 4,312 combinations of cross-section aspect ratio, filter solidity, orientation of the cross-section to the air flow, and Peclet number. An empirical expression was developed from the results of these model runs to predict single-fiber diffusion efficiency for any combination of conditions. The equation indicates that diffusion efficiency is most strongly influenced by the Peclet number because decreases in particle size and increases in air velocity affect diffusion substantially. Increases in aspect ratio and solidity also increase the diffusion efficiency by making more fiber surface available for collection. Although the angle of orientation has the least effect of any of the factors, elliptical fibers with the major axis of the cross-section parallel to the incoming flow may have performance advantages over circular fibers if the angle of orientation can be controlled during filter production. This is because some elliptical fibers with the major axis parallel to the incoming flow have both higher single-fiber diffusion efficiency and less drag than circular fibers.     

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.     

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     

Particle Orientation During Tape Casting in the Fabrication of Grain-Oriented Bismuth Titanate

Slurries containing platelike Bi₄Ti₃O₁₂ particles have been tape cast to prepare green sheets with aligned particles. The slurries contain well-dispersed particles and show nearly Newtonian flow behavior. The effect of slurry composition and casting conditions on the particle orientation has been examined. The particle orientation in the green sheet is determined mainly by powder content; other parameters, such as binder content, casting speed, and blade opening, have little effect. The interaction between particles is a main cause for particle alingnment. The slurry with a large powder content is favorable for preparing dense grain-oriented ceramics.     

Numerical study of cluster and particle rebound effects in a circulating fluidised bed

Gas-particle flows in a vertical two-dimensional configuration appropriate for circulating fluidised bed applications were investigated numerically. In the computational study presented herein the motion of particles was calculated based on a Lagrangian approach and particles were assumed to interact through binary, instantaneous, non-frontal, inelastic collisions including friction. The model for the interstitial gas phase is based on the Navier-Stokes equations for two-phase flows. The numerical study of cluster structures has been validated with experimental results from literature in a previous investigation. Numerical experiments were performed in order to study the effects of different cluster and particle rebound characteristics on the gas-particle flow behaviour.Firstly, we investigated the hard sphere collision model and its effect on gas-particle flow behaviour. The coefficient of restitution in an impact depends not only on the material properties of the colliding objects, but also on their relative impact velocity. We compared the effect of a variable restitution coefficient, dependent on the relative impact velocity, with the classical approach, which supposes the coefficient of restitution to be constant and independent of the relative impact velocity.Secondly, we studied the effects of different cluster properties on the gas-particle flow behaviour. Opposing clustering effects have been observed for different particle concentrations: within a range of low concentrations, groups of particles fall faster than individual particles due to cluster formation, and within a well-defined higher concentration range, return flow predominates and hindered settling characterises the suspension. We propose herein a drag law, which takes into account both opposing effects and have compared the resulting flow behaviour with that predicted by a classical drag law, which takes into account only the hindered settling effect.     

Wall effects on the velocities of a single sphere settling in a stagnant and counter-current fluid and rising in a co-current fluid

Experimental results were obtained on the steady settling of spheres in quiescent media in a range of cylindrical tubes to ascertain the wall effects over a relatively wide range of Reynolds number values. For practical considerations, the retardation effect is important when the ratio of the particle diameter to the tube diameter (λ) is higher than about 0.05. A new empirical correlation is presented which covers a Reynolds number range Re = 53-15,100 and a particle to tube diameter ratio λ < 0.88. The absolute mean deviation between the experimental data and the presented correlation was 1.9%. The well-known correlations of Newton, Munroe and Di Felice agree with the presented data reasonably well. For steady settling of spheres in a counter-current water flow, the slip velocity remains practically the same as in quiescent media. However, for rising spheres in a co-current water flow, the slip velocity decreases with increasing co-current water velocity, i.e., the wall factor decreases with increasing co-current water velocity. Consequently, the drag coefficient for rising particles in co-current water flow increases with increasing water velocity.