Effective drag on spheres immersed in a fluidized bed at minimum fluidization—Influence of bulk solids properties

The aims of this work are to elucidate the effects that bulk solids properties have on the effective drag experienced by large spheres immersed in an emulsion of group-B solids under minimum fluidization conditions and to analyze the ways in which the different suspensions react towards different applied shear rates. To investigate this, magnetic particle tracking was applied to resolve the trajectory of falling-sphere measurements in which the size, density, and sphericity of the bulk solids were varied as well as the size and density of the spherical tracers. The resulting experimental scope included both rising and sinking tracers as well as full segregation and in-bed stagnation of the tracers. The set-up provided highly resolved tracer trajectories, from which the drag experienced by the sphere can be calculated. For sinking tracers, the results showed that an increase in bulk solids size, angularity, and density reduced the terminal velocity of the sphere. This effect correlated well with the bed expansion and Hausner ratio, indicating that a reduced void space among the bulk solids is the main reason for the increase in motion resistance. At lower shear rates, namely, during the de-acceleration towards the stagnant state, beds of larger, more angular, or denser bulk solids yield lower levels of shear stress. The angle of repose of the bulk solids correlated with the rate at which the emulsion thins with increasing shear rate. For rising tracers, shear stress did not show any significant dependency on the properties of the bulk solids.     

浆态床内固含率轴向分布的数值模拟

采用DBS曳力模型计算气液相间作用,分别采用Gidaspow曳力模型、经Brucato修正的Gidaspow曳力模型和Schiller?Naumann曳力模型计算液固相间作用,忽略气固间的直接作用,对比了浆态床内不同颗粒粒径体系轴向固含率的模拟和实验结果. 结果表明,不同液固相间曳力模型对气含率的预测影响不大;在颗粒粒径较大(140 ?m)的体系中,较低表观气速下气液DBS与液固Schiller?Naumann曳力模型组合模拟的固含率随床高度增加而减小,与实验结果吻合,而其它曳力模型组合的模拟结果较差,轴向分布较均匀;在颗粒粒径较小(35 ?m)的体系中,几种曳力模型组合的模拟结果均与实验结果吻合较好,轴向分布较均匀.     

Rotary cylinders: Transverse bed motion prediction by rheological analysis

A method for predicting the transverse motion of a granular bed in a rotary cylinder is proposed, based on a non-Newtonian rheological model of the pseudo-plastic type, i.e. with a flow behaviour index (n) between 0 and 1. For a good simulation of bed motion, the model must be able to adequately reproduce the bed velocity profile in both the upper (downward flowing) and the lower (upward moving) zones. It is shown that to do so there is the need to adjust not only the consistency index K but even more importantly the flow behaviour index, n. The mass and momentum conservation equations are solved by the CFD code FLUENT. The model is applied to the simulation of the motion of an alumina bed and the computed results compared with experimental data.     

宽Re范围内气泡和液滴曳力系数的关联模型

流粒(气泡或液滴)的曳力系数CD和上升/终端速度因有助于准确预测反应器内相含率分布、液相速度分布、流粒停留时间和传质速率而具有重要意义.但现有用于估算流粒CD的关联式大多分段且只在低雷诺数Re区间内有效,并难以同时准确预测不同实验体系和操作条件下的实验结果.针对这些不足,基于实验测量和理论分析,本工作提出了一个能够在整...     

Theoretical Drying Model of Single Droplets Containing Insoluble or Dissolved Solids

A literature survey of published single-droplet drying models has exposed their various shortcomings. An advanced theoretical model of drying of single droplets, containing either insoluble or dissolved solids, has been developed and numerically solved. The validation of the developed model has been accomplished by comparison of the predicted temperature and mass histories with published experimental data for slurries of silica and skim milk solution under different conditions. The results of simulations showed a good agreement between the calculated curves and experimental points in all case studies.     

Drag models coupled with CFD–PBM method for simulation in bubble columns

In this study, three-dimensional numerical simulation of gas–liquid flow in bubble columns was realized by using the computation fluid dynamics (CFD)–population balance model (PBM). The new drag model improves the stability-constrained multi-fluid (SCMF-C) model because of the consideration of the wake accelerating and the hindering effects for calculating the drag correction factor. The gas holdup, axial liquid velocity, and bubble size distribution (BSD) predicted by four drag models at 0.02 and 0.1 m/s were compared. The results revealed that the proposed drag model can provide excellent predictions for both bubbly and heterogeneous flows. Because the wake accelerating and the hindering effects were considered, reliable predictions were achieved for the gas holdup, and the problem of uniform gas holdup distribution was mitigated. Therefore, the SCMF-C model can be extended for nonuniform BSD. The gas holdup and liquid velocity increased, and the nonuniformity of radial results became pronounced at 0.1 m/s. The profiles of four drag models were similar at a low height, whereas the difference between the simulations of the four models became obvious with the variation of heights. The results of the four models were accurate, and the BSD was wide at 0.1 m/s. Subsequently, the feasibility of the four drag models was evaluated at 0.2 and 0.4 m/s. The results of the comparison revealed that the proposed drag model exhibited excellent feasibility at higher gas velocities and was powerful for the simulation of bubble columns.     

AN ANALYTICAL MODEL ON VAPOR EXPLOSION OF A HIGH TEMPERATURE MOLTEN METAL DROP IN WATER INDUCED BY A PRESSURE PULSE

An analytical model for small-scale single drop fuel coolant interaction based on fragmentation caused by the Taylor instability and transient heat transfer during collapse and bounce period is developed. According to our previous analysis, pressure in the vapor film blanketing hot surface increases transiently more than 10 MPa, when thickness of the vapor film decreases less than 10 μm. The transient high pressure makes vapor-liquid interface bounce and causes the Taylor instabilities at both sides of the vapor-liquid interfaces by the large acceleration. As the growth time of the interface instability is enough short compared with the bouncing time, the instabilities result to fragmentation and mixing of both liquids. In the proposed model, the fragmentation time and fragmented particle size were estimated from the growth rate and the wave length of the instability. The analytical model composed of a set of time dependent differential equations was numerically calculated by the Runge-Kutta-Gill method. The numerical results were compared with the experimental ones done in Sandia Laboratory.     

Segregation in a stirred fluidized bed

A bed of particulate solids supported by an upward current of gas can be stirred at moderate power input per unit volume using thin horizontal rods mounted on a vertical shaft. The bed is fluidized, but bubbles are suppressed below a critical value of the fluidizing velocity. Stirring increases bed bulk density and reduces the minimum fluidizing velocity. Segregation in a stirred fluidized bed is enhanced with both flotsam and jetsam tracer particles, but the rate of segregation is reduced with flotsam tracers. The stirred fluidized bed may be useful as a device for dry separation of solids.     

颗粒特性对撞击分离器性能影响的实验与数值研究

颗粒-壁面撞击行为和气固相间作用对撞击分离器的性能具有重要影响。基于玻璃珠及煤粉的单颗粒撞击实验数据建立平均撞击恢复系数模型,采用非球形颗粒曳力模型对平板式撞击分离器的分离性能和气固流动开展数值研究。结果表明,采用基于实验的平均恢复系数模型以及考虑颗粒形状的曳力模型,能够准确地预测撞击式分离器的总分离效率和分级分离效率。颗粒分离过程中,Stokes数较大的颗粒对颗粒-壁面撞击模型比较敏感,Stokes数较小的颗粒对气固曳力模型比较敏感。     

Rotary cylinders: Solid transport prediction by dimensional and rheological analysis

A semi-experimental model for predicting the axial transport of the granular bed in a rotating cylinder is proposed. It is based on dimensional analysis and on the determination of an apparent viscosity characterizing the flow behaviour of the bed. Unknown constants in the model are determined either by analysis or by tuning with experimental data. An example of such tuning is shown to work well. The model is capable of giving, as a function of filling angle and friction angle, the axial velocity that varies along the cylinder axis. This is important for the control of the process taking place inside the cylinder.     

Solids distribution in slurry flow in a linear manifold with a horizontal approach

An experimental study was conducted to examine solids distribution in branches of a linear manifold having a horizontal approach. The manifold was designed to maintain approximately a constant slurry velocity upstream of each branch. Solids concentration in the branches was measured for various manifold orientations (upwards, side and downwards) and upstream conditions. Semi-empirical correlations for the three orientations were developed to predict a branch concentration ratio. This ratio was dependent upon the branch flow ratio, the particle inertia parameter and the vertical solids concentration profile upstream of the branch. The agreement between the experimental and the predicted branch concentration ratio was fairly good.     

Simulation study of the effect of wall roughness on the dynamics of granular flows in rotating semicylindrical chutes

A discrete element model (DEM) is used to investigate the behavior of spherical particles flowing down a semicylindrical rotating chute. The DEM simulations are validated by comparing with particle tracking velocimetry results of spherical glass particles flowing through a smooth semicylindrical chute at different rotation rates of the chute. The DEM model predictions agree well with experimental results of surface velocity and particle bed height evolution. The validated DEM model is used to investigate the influence of chute roughness on the flow behavior of monodisperse granular particles in rotating chutes. To emulate different base roughnesses, a rough base is constructed out of a square close packing of fixed spherical particles with a diameter equal to, smaller, or larger than the flowing particles. Finally, the DEM model is used to study segregation in a binary density mixture for different degrees of roughness of the chute. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2117–2135, 2015     

Shape dependence of resistance force exerted on an obstacle placed in a gravity‐driven granular silo flow

Resistance force exerted on an obstacle in a gravity‐driven slow granular silo flow is studied by experiments and numerical simulations. In a two‐dimensional granular silo, an obstacle is placed just above the exit. Then, steady discharge flow is made and its flow rate can be controlled by the width of exit and the position of obstacle. During the discharge of particles, flow rate and resistance force exerting on the obstacle are measured. Using the obtained data, a dimensionless number characterizing the force balance in granular flow is defined by the relation between the discharge flow rate and resistance‐force decreasing rate. The dimensionless number is independent of flow rate. Rather, we find the weak shape dependence of the dimensionless number. This tendency is a unique feature for the resistance force in granular silo flow. It characterizes the effective flow width interacting with the obstacle in granular silo flow. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3849–3856, 2018     

Solids mixing kinetics and segregation in a vibrostabilized fluid bed

The vibration-induced reduction in internal mobility of a fluidized bed, which was reported in a recent paper (Beeckmans and MacWilliam, 1986), has been confirmed using a larger bed. It has now been found that above a particular fluidization velocity internal mobility is not affected by vibrations. Distributor grid geometry was found to have a small effect on the fluidizing gas velocity at which bubbles are first observed at the surface of the bed, but it had an insignificant effect on solids mixing rates. The extent of segregation at steady state was reduced by vibrations with both flotsam and jetsam tracer particles.     

Expansion behaviour of confined fluidized beds of fine particles

The expansion behaviour of fluidized beds of fine particles confined within packings of coarse spheres has been studied experimentally. An expansion law of the Richardson-Zaki type has been demonstrated to be valid in a wide range of voidages for fine particles belonging to A as well as to B group of Geldart's classification. Parameters of the proposed correlation have been evaluated and their dependence on fines properties discussed.