Radial porosity distribution in cylindrical beds packed with spheres

Experimental determinations of radial porosity for cylindrical beds packed with spheres are reported. The data indicate that, for a wide range of bed and sphere sizes, porosity varies significantly and regularly near the container wall. For uniformly sized spheres, the oscillations in porosity can be detected up to a distance of about 5 particle diameters from the wall. For mixtures of spheres of two sizes, regular oscillations are detected only up to 2 or 3 diameters from the wall and for three sizes the effect of the wall is observed only within a distance of 1 particle diameter.     

Voidage profiles in packed beds of spheres

Voidage profiles in randomly packed beds of uniformly sized spheres are analysed by dividing the bed into a number of concentric layers of equal thickness, and by expressing the void fraction in a layer in terms of the contributions to the solid volume by spheres with centres lying in appropriate neighbouring layers. The number of spheres in a layer is expressed as a fraction of the total number in the bed. Sets of number fractions in layers up to a distance of about 4–5 particle diameters from the wall are estimated for different aspect ratios using several sets of reported void fraction data obtained by a variety of experimental methods. The number of fractions in the layer next to the one at 0.5 particle diameter from the wall and at 1.5 particle diameters completely characterize the voidage variations up to a distance of about 2 particle diameters from the wall. In this region the confining effect of the wall gives rise to these two non-random layers of the spheres. The two number fractions are correlated exponentially with the aspect ratio. Beyond this region, the structure of the packing becomes more and more random. A procedure is suggested for predicting the void fractions at distances between 2 and 4 particle diameters.     

不同圆球复合无序堆积床内流动传热数值分析

圆球堆积床内孔隙分布影响其内部流场及温度场分布, 且小管径-球径比堆积床由于壁面限制, 内部孔隙率变化剧烈, 其内部流动和传热不均匀现象明显。针对D/d_p为3的圆球无序堆积床构建了3种非等直径圆球复合堆积结构:径向分层复合堆积、轴向分层复合堆积以及随机复合堆积结构, 并采用DEM-CFD方法建模计算, 从径向及整体角度分析比较不同复合堆积床内流动换热特性及其流场和温度场分布的均匀性。结果表明:孔隙率及孔隙大小分布共同影响堆积床内流场和温度场分布;相对于单一等直径圆球堆积, 采用复合堆积结构能使堆积床内部孔隙率分布更均匀, 其内部流场和温度场分布也更为均匀;对于D/d_p为3的堆积通道, 径向分层堆积结构对于提高整体流动换热性能及改善内部流动换热均匀性都有显著效果。     

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].     

Effect of particle characteristics on particle pickup velocity

Particle entrainment is investigated by measuring the velocity required to pick up particles from rest, also known as pickup velocity. Pickup velocity is a function of individual particle characteristics and interparticle forces. Although 5-200 μm particles are investigated, the work presented here focuses on the pickup of particles in a pile in the size range of 5-35 μm. These smaller particle sizes are more typical for pharmaceutical and biomedical applications, such as dry powder inhalers (DPIs). Pickup velocities varied from 3.9 to 16.9 m/s for the range of particle sizes investigated.There is a strong correlation between particle size and the dominating forces that determine the magnitude of the pickup velocity. Preliminary data investigating pickup velocity as a function of particle size indicate the existence of a minimum pickup velocity. For larger particle sizes, the mass of the particle demands a greater fluid velocity for entrainment, and for smaller particle sizes, greater fluid velocities are required to overcome particle-particle interactions. Pickup velocity remains relatively constant at very small particle diameters, specifically, less than 10 μm for glass spheres and 20 μm for nonspherical alumina powder. This can be attributed to the negligible changes in London-van der Waals forces due to a hypothesized decrease in interparticle spacing. At intermediate particle diameters, electrostatic forces are dominant.     

Gas-liquid mass transfer in three-phase fluidized beds with viscous pseudoplastic liquids

Liquid phase volumetric mass transfer coefficients for oxygen were determined in three-phase fluidized beds of 8 mm glass spheres fluidized by a cocurrent flow of air and pseudoplastic polysaccharide solutions (carboxymethyl cellulose, xanthan). A semi-theoretical relation for the effective shear rate was suggested. The mass transfer coefficients could be correlated, together with literature data for particle diameters of 3 mm and 5 mm in other liquids, using the terminal velocity as the particle-specific property.     

流化床中动态行为硬球模拟与软球模拟的比较

用硬球方法和软球方法分别模拟了不等粒径流化床中的动态行为;比较了颗粒平均速度、运动轨迹的差异;研究了恢复系数对流化床中动态行为、颗粒平均速度的影响.研究结果表明：对流化床中动态行为进行模拟的数值结果强烈地依赖于恢复系数,恢复系数较小时,硬球方法可以模拟出鼓泡现象,恢复系数较大时,软球方法可以模拟出鼓泡现象;并且恢复系数越大时,硬球方法中颗粒平均速度随时间的变化越大,而软球方法中颗粒平均速度随时间的变化越小;尽管硬球方法比软球方法更加准确地考虑了颗粒碰撞,但由于硬球方法和软球方法处理颗粒碰撞方式的不同,以及颗粒碰撞时间步长选取原则的差异,使得硬球模拟需要的计算时间远大于软球模拟需要的计算时间.     

An experimental study of the effect of dump packing on wall to fluidized bed heat transfer

The improvements in the performance of gas-fluidized beds to be gained from the introduction of baffles or packing pieces have been discussed in the literature. These include higher conversions in chemical reactions⁽¹⁾, reduction of freeboard necessitated by fluctuations in bed height⁽²⁾ and the possibility of operating with larger length to diameter ratios⁽³⁾. In the case of wall-to-bed heat transfer, however, a preliminary investigation⁽⁴⁾ into the effect of fixed packing in a 4-in. column indicated that the rate of heat transfer was in most cases adversely affected by the presence of packing because of the restriction of particle movement within the bed. This was certainly true in the case of packings of closed structure such as solid spheres, although the data suggested⁽⁴⁾ that heat transfer in beds containing screen mesh packings of open structure may exceed that in unpacked beds in some cases. The work described herein is a quite comprehensive experimental investigation of the effect of many types of dump packings on the rate of wall-to-bed heat transfer. Several commercially available packings as well as cylindrical screen packings produced in this laboratory were employed. A 12-in. diameter bed was used so that the work would give an indication of the effects occurring in larger-scale equipment.     

Periodic pressure fluctuations in fluidized beds

In shallow gas fluidized beds harmonic oscillations of the pressure around its equilibrium value can be observed. Three aspects of these vibrations have been analysed: the frequency, the critical bed height and the damping. The frequency decreases with the inverse of the square root of the bed height for values below the critical height.For bed heights larger than the critical height the fluctuations cease to be harmonic, the bed breaks up and voids are formed leading to the formation of bubbles or slugs. The critical bed height can be calculated from the frequency and the wave velocity. The maximum value of the critical bed height is a few hundred particle diameters, thus most beds will fluidize heterogeneously. Damping of the oscillations is governed by the ratio of the fluid- to solids-density; the lower this values the higher the damping. The damping is liquid fluidized beds is such that oscillations are prevented.     

气-固微型流化床压降特性及最小流化速度的实验研究

在内径3～20 mm的4个气-固微型流化床中,分别考察了A类和B类两种类型颗粒的流化特性,同时研究了床几何结构、操作条件、物相性质等各因素对其最小流化速度的影响.结果 表明,气-固微型流化床中的床层压降特性与颗粒类型密切相关,不同的流动状态下两种类型颗粒的流动特性存在显著地差异.在固定床阶段,与B类颗粒相比,A类颗粒与...     

A CORRELLATION FOR CYLINDER-TO-BED HEAT TRANSFER IN AERATED VIBRATED BEDS OF SMALL PARTICLES

ABSTRACT

Beds of alumina particles (d_p= 27 μm and 100 μm) were vibrated in the vertical direction at frequencies frdm 0–25 Hz and half-amplitudes from 0–4 mm. Air flow rate through a single-hole or multiple-holes bottom plate varied from 0 to 2 times the minimum fluidizing velocity. The contact heat transfer coefficients at resonance are much higher than those in packed beds and in vibrated fluidized beds (up to 1.2 times). The high heat transfer rates are due to enhanced particle mobility which reaches a maximum at the resonant point. A simple semi-empirical correlation is developed for contact heat transfer which is based on particle mobility. Heat transfer coefficients are correlated with frequency using amplitude, bed height and particle size as adjustable parameters. The correlation is found explain the observed trends in the data reasonably well over the range of parameters studied.     

A CORRELLATION FOR CYLINDER-TO-BED HEAT TRANSFER IN AERATED VIBRATED BEDS OF SMALL PARTICLES

Beds of alumina particles (d_p= 27 μm and 100 μm) were vibrated in the vertical direction at frequencies frdm 0-25 Hz and half-amplitudes from 0-4 mm. Air flow rate through a single-hole or multiple-holes bottom plate varied from 0 to 2 times the minimum fluidizing velocity. The contact heat transfer coefficients at resonance are much higher than those in packed beds and in vibrated fluidized beds (up to 1.2 times). The high heat transfer rates are due to enhanced particle mobility which reaches a maximum at the resonant point. A simple semi-empirical correlation is developed for contact heat transfer which is based on particle mobility. Heat transfer coefficients are correlated with frequency using amplitude, bed height and particle size as adjustable parameters. The correlation is found explain the observed trends in the data reasonably well over the range of parameters studied.     

Jet cup attrition testing

Jet cup attrition testing is a common method for evaluating particle attrition in fixed fluidized beds and circulating fluidized beds. An attrition index, calculated from jet cup data, is used to compare with one or more reference materials. However, this method is far from perfect despite its popularity. Results obtained at Particulate Solid Research, Inc. (PSRI) in different-sized jet cups and a 29-cm (11.5-in.) diameter fluidized bed test unit did not provide the same ranking of catalyst with respect to particle attrition. To obtain a better understanding of attrition in a jet cup, both computational fluid dynamics (CFD) and cold flow studies were performed with a 2.5-cm (1-in.) diameter Davison-type jet cup and PSRI's cylindrical 7.6-cm (3-in.) diameter jet cup. Results showed that a significant amount of material in the Davison and PSRI jet cup remained stagnant. Based on these results and additional CFD modeling, PSRI designed a new jet cup, where most of the material was hydrodynamically active. The new jet cup showed a 25% increase in attrition compared to PSRI's cylindrical jet cup under similar conditions and run times. Results were also compared to cyclone attrition data for several materials at PSRI. The new jet cup provided data that correlated with attrition results from the 29-cm (11.5-in.) diameter fluidized bed unit.     

The role of contact stresses and wall friction on fluidization

Fluidization and defluidization experiments, where we increased the gas superficial velocity in small increments and then decreased it, were performed in tubes of different diameters to probe the role of wall friction on pressure drop and bed height. Such experiments, covering the regimes of packed bed, stable bed expansion and bubbling bed, were carried out for several different particles. The compressive yield strength of the particle assemblies at various volume fractions was determined by measuring the height of fully defluidized beds at various mass loading levels. The systematic effect of the tube diameter on pressure drop and bed height hysteresis could be rationalized in terms of a one-dimensional model that accounted for the effect of wall friction and path-dependent contact stresses in the particle phase. Bubbling seemed to set in when the yield stress in the particle assembly could be overcome by the inherent fluctuations. Our experiments, which focused primarily on gas velocities below the minimum bubbling conditions, did not reveal any dramatic change across the Geldart A-B boundary. This is consistent with the original observation by Geldart (Powder Technol. 7 (1973) 285). The distinct difference between beds of group A and B particles in the gently bubbling regime reported by Cody et al. (Powder Technol. 87 (1996) 211) is thus likely to be due to changes in the dynamics of the bubbles, as we observed no striking difference between these beds at gas velocities below minimum bubbling conditions.     

Particle velocity and circulation rate in liquid spouted beds

In this work, the particle velocity and circulation rate in water spouted beds of small glass particles are experimentally studied. The pathline, velocity and residence time of particles 0.53 to 1.40 mm in diameters were measured in the annulus of half-cylindrical columns 40, 60 and 90 mm in diameters. The particle velocity in the annulus and circulation rate increase practically linearly with fluid flowrate. As the column diameter was increased, the average particle velocity in the annulus was decreased, but the particle circulation rate was increased.     

提升管内气固两相双组分颗粒流动的离散颗粒硬球模型的模拟

基于离散颗粒(DPM)硬球模型,数值模拟提升管内双组分颗粒气固两相湍流流动行为。应用Vreman的亚格子尺度（SGS）模型模拟气体湍流,建立考虑不同颗粒加速度效应的两颗粒碰撞最小时间计算模型。数值模拟预测了大颗粒和小颗粒的速度和浓度分布。研究结果表明小颗粒具有高的轴向速度和脉动速度,而大颗粒具有低的轴向速度和脉动速度。在床中心区域,小颗粒轴向速度分布出现3个峰值,对于大颗粒轴向速度仅出现两个峰值。在壁面区域大颗粒和小颗粒速度均出现两个峰值。沿床径向方向呈现床中心颗粒浓度低、壁面区域颗粒浓度高的环核流动结果。随着表观气速的增大,颗粒浓度沿径向和床高分布趋于均匀。在床中心区域模拟计算轴向颗粒速度、颗粒浓度和RMS速度与文献实验结果相吻合。在提升管内气体湍流对小颗粒流动具有一定的影响,颗粒间碰撞作用对颗粒相流动的影响大于气相湍流的影响。     

Packed bed structure: Evaluation of radial particle distribution

A model describing the radial distribution of monosized spheres in randomly packed beds up to distances of about two particle diameters from the vessel wall is presented here. The model is based on the existence of a highly ordered layer of particles adjacent to the wall followed by a more diffuse, but still identifiable, second layer. Expressions generated from simple geometrical concepts (intersection between a cylindrical surface and a sphere) straightforwardly allow calculating the radial voidage profile given the radial distribution of particle centers and vice versa. These expressions are employed to fit the model to measures of voidage profiles within a wide range of aspect ratios, a = (R_T/R_P). The model can be used to accurately predict radial voidage profiles, but it is stressed that the identification of particle distribution constitutes more valuable information than an empirical expression for describing voidage variations.     

Loading,draining and hold-up in periodically operated trickle-bed reactors

Periodic interruption of liquid flow in co-current trickle beds appears to be an attractive mode of operation. For modelling these intermittent-flow reactors, loading and draining times must be known. Experiments were undertaken using beds of activated carbon with water and air as the fluid phases. Loading time was taken as the time to water breakthrough. The gas flow was continuous while the time between the end of drainage and the start of filling was varied to simulate different periods. Drainage experiments followed the liquid flow leaving the bed as a function time. Liquid hold-ups were determined after the filling and draining measurements. Variables considered were particle size, gas and liquid velocity. Loading closely follows the plug flow model; drainage shows tailing but does not follow literature models. Static and dynamic hold-ups at zero gas flow agree with literature correlations for the larger particle size used. A gas velocity effect on both static and dynamic hold-up was observed.     

Bubble dynamics in bubbling fluidized beds of ellipsoidal particles

This article presents a CFD-DEM study on the effect of particle shape on bubble dynamics in bubbling fluidized beds. The particles used are ellipsoids, covering from disk-type to cylinder-type. The phenomena such as bubble coalescence and splitting are successfully generated, and the results are compared with literature, showing a good agreement. The results demonstrate that the bubble forming/rising regions and patterns are influenced significantly by particle shape. Ellipsoidal particles have asymmetrical bubble patterns with two or more circulation vortices while the bubbles for spherical particles form at the bed centerline and rise through the center of the bed. Hence, the vertical mass flux at the bed centerline for spheres is always positive, and ellipsoids have negative or positive vertical mass fluxes. The solid mixing estimated based on the dispersion coefficient revealed poor mixing for ellipsoids. Spherical particles have a larger bubble size and higher bubble rising velocity than ellipsoids.     

Flow structure of the solids in gas-solid fluidized beds

Existence of clusters in dense fluidized beds was investigated by analyzing the time-position data of a tracer obtained in several radioactive particle tracking experiments. It was found that in the case of sand particles, more gas passes through the bed as bubbles with increasing the superficial gas velocity and in the case of FCC powder, flow of the gas through the bed as bubbles does not increase in the turbulent fluidization regime. Cluster diameters were estimated from their velocities and found that descending clusters are generally larger than ascending ones and the size of both increases with increasing the superficial gas velocity. Bubble velocities evaluated in this work are in good agreement with the correlations in the bubbling regime of the fluidization available in the literature.