A study of the hold-up in rotary drums with discharge end constrictions

This paper describes the results of a detailed investigation of operating conditions on the hold-up of material in a rotating drum. It was found that the hold-up increases linearly with increasing feed rate, decreases linearly with increasing slope of the drum, and behaves in a complex manner with increasing drum speed. The combined effect of some of these operating variables on the hold-up was also studied and interpreted in terms of the type of flow of material in the drum. A semi-empirical model was adopted to predict the hold-up of material in a horizontal rotating cylinder with an end constriction.     

Modeling non-Newtonian slurry convection in a vertical fracture

A model of non-Newtonian slurry convection in a fracture was developed. Based on the simulation [Eskin, D., Miller, M., 2008. A model of non-Newtonian slurry flow in a fracture. Powder Technol. 182, 313-322] and experimental [Tehrani, M.A., 1996. An experimental study of particle migration in pipe flow of viscoelastic fluids. J. Rheology 40, 1057-1077] results on particle migration across a fracture, an accepted modeling system is a three-layer flow consisting of the central core of high particle concentration surrounded by pure fluid layers. The obtained solution describes convection in a small fracture domain where both the mean shear rate and the local particle concentration are known. Numerical study of the developed model shows that the solids settling rate caused by convection is much higher (regularly, by a factor of 10-30) than the particle settling rate, calculated based on an assumption that the particle concentration is uniformly distributed across a fracture. The convection model can be incorporated in one of the known numerical codes for computation of slurry dynamics in a whole fracture. An engineering modification of the convection model allows computing particle slug transport in a fracture.     

Metering of solids by a rotary valve feeder

The construction of a rotary vane-type solid feeder valve is described. It is shown that at low speeds the rate of solids flow through the valve is directly proportional to the rate of revolution. At higher speeds, the rate of increase of solid feed rate falls off until the rate becomes constant when the rate of solid flow through the rectangular orifice is limiting. The rate of flow through the valve is correlated by an equation that links the speed and geometry of the valve to the properties of the solid.     

Scale-up of the axial profile of material hold-up in horizontal rotating cylinders

Scale-up of the axial profile of the hold-up of material flowing through grate-discharge horizontal rotating cylinders is presented. parameters investigated were drum length, rotational speed and material feed rate. Equations useful for engineering design for relating material hold-up in the cylinder to the feed rate, cylinder dimensions and speed of rotation are given.     

Development of an artificial neural network correlation for prediction of hold-up of slurry transport in pipelines

In the literature, very few correlations have been proposed for hold-up prediction in slurry pipelines. However, these correlations fail to predict hold-up over a wide range of conditions. Based on a databank of around 220 measurements collected from the open literature, a correlation for hold-up was derived using artificial neural network (ANN) modeling. The hold-up for slurry was found to be a function of nine parameters such as solids concentration, particle dia, slurry velocity, pressure drop and solid and liquid properties. Statistical analysis showed that the proposed correlation has an average absolute relative error (AARE) of 2.5% and a standard deviation of 3.0%. A comparison with selected correlations in the literature showed that the developed ANN correlation noticeably improved prediction of hold-up over a wide range of operating conditions, physical properties and pipe diameters. This correlation also predicts properly the trend of the effect of the operating and design parameters on hold-up.     

Sliding in inclined slurry pipelines at shutdown

The sliding phenomenon which is reported to impose a restriction upon the slope of slurry pipelines is investigated experimentally. Two different types of behavior which could be called “sliding” were observed. At pipe inclianations greater than 22° to the horizontal, fully settled layers of solid particles would slide with shear occurring at or near the pipe wall. The critical angle of inclination increased as the particle size decreased. When the slurry was not fully settled, a natural convective flow process was observed to move the slurry down a pipe incline. This flow occurred at much lower pipe inclinations. Concentration profiles measured near the bottom of a pipe incline showed little effect of slurry type or concentration, provided the slurry contained a significant amount of slowly settling solids. In this case, pipe slope was the most important variable.     

Author index

High-frequency screen tests of a number of different fine slurries are analyzed to determine the effect of slurry feed rate and weight per cent solids on screen size selectivity values. Results of this analysis indicate that for the screen cloths tested, slurry feed rate has a negligible effect on size selectivity values but that increasing the feed solids concentration causes finer but less efficient particle size separation. The size selectivity data are analyzed to give values for the d₅₀, the sharpness index and apparent bypass parameters of a screen size selectivity equation. Approximate empirical relationships between these parameters and screen aperture size and slurry feed solids concentration are given, and an example of the use of the size selectivity equation in grinding-circuit simulations is presented.     

Mean residence time and hold-up of solids in rotary kilns

The influence of operational variables on the mean residence time (MRT) and hold-up of the solids in rotary kilns has been investigated by many researchers. However, their reports on the influence of the feed rate on MRT, for example, are not consistent with one another. In this study, experiments are conducted on a 400 mm ID pilot kiln with a cylindrical discharge dam. Sand is used as the testing solids. MRT and the hold-up are measured under various feed rates and rotation speeds. Experimental results indicate that MRT increases slightly with the feed rate, and that the gradient is smaller at high rotation speeds. The hold-up shows a near-linear increase with the mass of feed per kiln rotation. The experimental data are then used to test equations provided by different researchers for the prediction of MRT. Comparisons show that, results of the empirical equation from Sullivan, J.D., Maier, C.G., Ralson, O.C. [1927. Passage of solid particles through rotary cylindrical kilns. U.S. Bureau of Mines Technical Paper No. 384.] agree well with measurements for the cases of low kiln loadings, while the numerical model of Saeman, W.C. [1951. Passage of solids through rotary kilns: factors affecting time of passage. Chemical Engineering Progress 47, 508-514.] gives good predictions over the entire range of parameters considered.     

Solid‐liquid mass transfer in a rotary drum

The solid‐liquid mass transfer coefficient for slurries agitated in rotating drums with baffles was measured using the dissolution of β‐naphthol as a tracer in silica sand slurries. The effects of drum rotation rate (0.33 to 15 min^?1), slurry holdup (4.4% to 17%) and solids volume fraction (0 to 0.62) on the solid‐liquid mass transfer were investigated with a slurry particle diameter of 4.6 × 10^?4 m. Mass transfer coefficients were corrected for the effect of particle shrinkage due to dissolution of the tracer. The mass transfer coefficient increased with increasing rotational speed of the drum from 0.005 to 0.045 mm.^5‐1. Two types of slurry motion were observed; well mixed slurry flowing over the baffles and segregation of solids on the baffles. The mass transfer coefficients from the present study, along with literature data, correlated with the Froude number to the 0.36 power, for Froude numbers from 10^?6 to 10^?1.     

Scale-up of particulate hold-up in rotary drums

This paper presents a group of dimensionless parameters which are useful in scaling-up the material hold-up in cylindrical drums of different geometry. These parameters include feed rate, drum rotational speed and discharge opening diameter. It also presents a semi-empirical model which can be used to predict the material hold-up in rotating drums for a wide range of operating and design variables. The values of hold-up predicted with this model are slightly lower than the corresponding experimental values, possibly due to end effects.     

Synthesis of submicron barium carbonate using a high-gravity technique

The purpose of this study was to build a platform for producing fine particles by applying a high-gravity (higee) technique to achieve reactive precipitation. Barium carbonate was chosen as a model compound and was produced in a spinning disk reactor (SDR), which is one type of higee equipment, via a carbonation route and a once-through mode. For size measurement, a suitable dispersion method was developed to obtain reproducible particle size data, using a laser-light analyzer. Several factors that affected the particle size of barium carbonate, including the CO₂ flow rate, the feed rate of Ba(OH)₂ slurry, the rotation speed, and the solid-content of feed slurry, were investigated. A high rotating speed and low feeding rate of slurry yielded small particles. The optimum solid-content of feeding slurry for obtaining small particles was also determined. However, the effect of the CO₂ flow rate on the particle size of the product was not significant.     

Solids mixing and residence time distribution in a horizontal rotary drum reactor

For the design of a rotary drum reactor, knowledge of the mechanism of both heat transfer and the dispersion of the solids is important. In this contribution the movement of solids in a horizontal rotary drum is investigated. Residence time distribution measurements were performed in an industrial scale reactor. Also, in model sections of this reactor, the behaviour of solids was studied visually. In the model sections the rotational speed of the drum, the number and height of the strips on the reactor wall and the angle between strip and wall, as well as the degree of filling, were varied.Model sections 0.60 and 1.40 m in diameter were used: the length of the industrial scale drum was 9.0 m, its diameter 0.60 m.Potato starch, particle size range from 15 to 100 μm, was used as the solid material.It was shown that in a drum provided with strips for rotational speeds above 5 r.p.m. and a degree of filling less than 15%, the transverse mixing was virtually completed within 2 revolutions of the drum. At these speeds and degrees of filling the extent of axial mixing is still very low as was shown by the residence time distribution measurements, the length of a mixing unit being 0.1 m or less.     

A Computational Fluid Dynamics Study of Particle Penetration through an Omni-Directional Aerosol Inlet

Computational fluid dynamics (CFD) was used to study aerosol penetration through the entrance section of a bell-shaped omni-directional ambient aerosol sampling inlet. The entrance section did not include either an insect screen or a large-particle pre-separator. Simulations of the flow field were carried out for wind speeds of 2, 8, and 24 km/h and a fixed exhaust flow rate of 100 L/min; and, particle tracking was performed for 2 to 20 μ m aerodynamic diameter particles. Penetration calculated from CFD simulations was in excellent agreement with experimental results from previous studies with the root mean square relative error between simulation and experimental data being 3.8%. CFD results showed that the most significant regional particle deposition occurred on the upwind side of a curved flow passage between two concentric axisymmetric shells of the inlet housing and that deposition at the leading edges of the shells and within the exhaust tube was far less significant. At a wind speed of 2 km/h, penetration was affected by gravitational settling, e.g., penetration of 20 μ m particles was 71.9% when gravity was included and 80.4% without gravity. At higher wind speeds gravity had little effect. An empirical equation was developed to relate aerosol penetration to a Stokes number, a gravitational settling parameter, and a velocity ratio. Good fits of the correlation curves to experimental data and numerical results were obtained.     

Flow of particulate solids through tumbling mills

The transport behavior of particulate solids flowing through tumbling mills depends strongly on the mill operating conditions. This paper presents the results of a detailed study to delineate the effect of the important operating variables on the hold-up, mean residence time and residence time distribution of particulate solids flowing through ball mills and rod mills. The effects of feed rate, media load, and mill speed on these transport parameters are discussed, emphasizing the fundamental differences between particulate transport in ball mills and rod mills. Under identical dimensionless operating conditions over the range of the investigation, the material hold-up and the Peclet number of the flow regime in the rod mill were always higher than those in the ball mill. Mechanistic interpretations of the observed transport phenomena are presented, and their implications in the context of tumbling mill analysis and design pointed out.     

油剂逆流接触提升管进料段固含率及颗粒速度的径向分布

在一套大型冷模实验装置中,考察了喷嘴射流与催化剂逆向接触的提升管进料段固含率和颗粒速度沿径向的分布及其对操作条件的影响,并与传统提升管进料段结构进行对比. 结果表明,沿轴向由下至上可将该新型结构的进料段分为喷嘴上游过渡区(H=-0.675~-0.375 m)、喷嘴射流控制区(H=-0.375~0.375 m)及喷嘴下游过渡区(H=0.375~0.675 m). 与传统形式相比,新型结构可使进料喷嘴安装截面以上射流影响区的高度明显缩短,喷嘴截面以下影响区域范围增大;油剂初始接触区域内催化剂沿径向的分布更均匀. 根据实验结果,得到新型进料段中射流控制区内典型截面固含率径向分布的经验模型,计算值与实验值吻合较好.     

Effect of solid particles on gas hold-up in bubble columns

The gas hold-up in bubble columns containing fluidised plastic particles as solid phase was measured as a function of superficial gas velocity and solids concentration. The effects of particle size, density, wettability and concentration on gas hold-up and bubble coalescence were studied. It was found that the addition of non-wettable solids to the air/water mixture promotes bubble coalescence and, therefore, reduces the gas hold-up, while the addition of wettable solids suppresses bubble coalescence and increases the gas hold-up.     

The effect of particle shape on pipeline friction for newtonian slurries of fine particles

Experiments have been conducted to assess the effect of particle shape on pipeline friction in turbulent flow, using laboratory pipelines of nominal diameter 50 mm and 150 mm. The experiments were intended to examine the extent to which a fluid model is appropriate for slurries of this type, especially at high solids concentrations. The experiments confirm that fluid friction at low and moderate solids concentrations is proportional to slurry density, with particle shape being of minor importance. At high solids concentrations, additional increases in friction are observed and these depend upon the ratio of the solids concentration to the maximum settled concentration. Although this friction increase is qualitatively similar to that which would result from increased slurry viscosity, the evidence suggests that particle‐wall contact is the mechanism. However, the transition from turbulent to laminar flow indicates that an effective viscosity should be used in calculating critical Reynolds numbers.     

AN RTD STUDY FOR THE FLOW OF LIGNITE PARTICLES THROUGH A PILOT ROTARY DRYER PART I; BARE DRUM CASE

In Part I of the present work a pilot rotating cylindrical drum, without an internal lifting flight system (bare) has been employed for the study of lignite motion through it, at ambient temperature. Tracer pulse stimulus - response experiments have been carried out io deduce residence time distribution ( RTD) data and relate them to the operating conditions ( slope, speed of revolution, etc.). Mean residence time, space-time and solids hold-up have been correlated with the drum operating conditions. Experimental data of mean axial velocity of solids have been compared with theoretical predictions and found to deviate within a ± 15% margin. A size segregation of particles during their motion through the kiln under a variety of operating conditions has been confirmed and quantified. An average maximum divergence of 20% between the residence time of the smallest and that of the largest nominal particle sizes has been assessed.     

Particle suspension hydrodynamics in a tapered gas agitated reactor

Experiments were carried out in a tapered gas agitated solid-liquid-gas (S-L-G) reactor at 4 reactor volumes (up to 4 m³ ) with 4 different slurry densities (up to 40 mass%). Using monodisperse sand particles (260 μm diameter) at a low specific power input (ranging from 50-300 W/m³), minimal suspension was achieved. The spatial solids hold-up distributions were determined using a specially designed sampling probe. In combination with a mathematical model, the measurements show that a decrease in the ratio of the eddy length and the particle diameter (l_e/d_P) takes place at increasing slurry densities. At a solids hold-up of about 0.4, the critical lower limit (l < l_e/d_p < 5). below which no suspension state can exist, is reached.     

耦合流化床提升管内固含率径向分布及沿轴向的发展

针对催化汽油辅助反应器改质降烯烃工艺,结合提升管与流化床的特点,建立了一套提升管与流化床耦合反应器大型冷态实验装置. 在不同操作条件下,采用PV-4A型光纤密度仪测定了提升管内固含率沿径向的分布规律. 结果表明,固含率径向分布整体上呈现中心小、边壁大的环-核结构分布特征;沿轴向向上,各径向位置上的固含率在颗粒加速区逐渐降低,在充分发展区趋于稳定,在颗粒约束返混区又有所升高;各径向位置上的固含率随表观气速增大或颗粒循环强度减小而减小,且均匀性变好;提升管上部流化床内颗粒静床高度只对颗粒约束返混区内固含率径向分布有影响,而对颗粒加速区和充分发展区的固含率径向分布影响较小;当表观气速较低或颗粒循环强度较大时,颗粒约束返混区上部局部固含率最大值出现在无因次半径f=r/R=0.7附近,此时局部无因次固含率es*=es/ 沿轴向在H>5.33 m时不再具有相似性;通过比较径向不均匀指数,得到轴向各区固含率径向分布趋于均匀的程度依次为：充分发展区>颗粒约束返混区>颗粒加速区. 利用实验数据回归出了局部固含率径向分布关联式,其平均相对误差在6%以内.