Flow characteristics in packed and fluidized rotating beds

Free particles in a rotating tapered cylindrical container are, as a consequence of the circular motion, forced radially outwards towards the circumference to form a packed annular bed. If the container wall is porous and a fluid is allowed to flow radially inward, the bed material may become fluidized. In the resultant centrifugal fluidized bed, radial accelerations many times one g can be generated, permitting much larger fluid flow rates during fluidization than are possible with a conventional fluidized bed. Entrainment of material can also be greatly reduced in such a geometry.The flow in both packed and fluidized beds in a rotating system is analyzed. Expressions are found for the shape of the bed as well as the distribution of particles in packed beds containing mixtures of materials having different size distributions and densities. Based on these results, equations predicting the pressure drop and radial flow distribution are deduced. The condition and location where initial fluidization of the packed bed occurs are predicted. Similarly, conditions in the fluidized state are analyzed, and it is shown that the tangential velocity distribution in the bed under these conditions is directly proportional to the bed radius.Experiments confirming the validity of the analytic models are conducted over a range of operating conditions for different bed materials.     

On the influence of particle shape and process conditions in the pressure drop and hydrodynamics in a wall-effect fixed bed

A low tube-to-particle diameter ratio (d_t/d_e,p) fixed bed, packed with spherical and nonspherical catalyst supports, was used to investigate pressure drop at varying temperature (298–673?K) and inlet pressure (245–294?kPa). The d_t/d_e,p ranged from 3 to 6, namely, a large wall-effect fixed bed, with an average void fraction between 0.38 and 0.61. These conditions pertain to multitubular fixed-bed reactors used for exothermic reactions. The pressure drop was notably influenced by the particle size and morphology as well as temperature. The use of particles with d_t/d_e,p?0.55) appeared suitable for pressure drop control. The fluid velocity profiles were calculated by applying the Navier–Stokes–Darcy–Forchheimer equation computing the respective permeability parameters with refitted state-of-the-art pressure drop correlations. The fluid flow exhibited different velocity zones across the fixed bed, the highest velocity zone being located near the reactor wall. The axial velocity component was influenced by the catalyst morphology, as well as temperature and inlet pressure.     

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。     

固定床流体流动特征数值模拟

为了研究固定床边壁效应、固定床床层数的变化以及颗粒的填充倾斜角度等参数对床内流体流动状况的影响,基于Ergun方程建立了轴对称多孔介质数学模型。同时对床内流体流动状况进行了研究:在床高确定的情况下,随着床层数的增加,压强降减少;随着颗粒填充倾斜角度的增加,压强降也减少,速度径向分布不均;在固定床边壁附近,气体速度明显增大。计算结果与实验值的比较表明模型能有效地描述固定床压强降和床内流体流动状况。     

Thermal and flow effects during adsorption in conventional,diluted and annular packed beds

Previous investigations have shown a complex combination of thermal and flow effects during adsorption in highly loaded, narrow packed beds. Respective conditions were realized by packing relatively large zeolite particles in a narrow tube (which causes wall channelling) and adsorbing water vapour from air on the particles (which is highly exothermic). The present work extends the investigation to novel column configurations with purposely altered conditions of heat generation and flow—namely to diluted beds, annular beds and beds consisting of coated particles. Experimental results obtained by near infrared tomography are compared with the results of breakthrough experiments in conventional columns and with numerical calculations. The latter are conducted with a non-isothermal, two-dimensional model that not only considers the increase of porosity and flow velocity near the tube wall, but also expresses the effective transport coefficients as functions of the radial coordinate. The model provides reasonable accuracy under conditions for which the usual plug-flow assumption is questionable.     

Characterisation of flow and heat transfer patterns in low aspect ratio packed beds by a 3D network-of-voids model

Using an illustrative sphere packing assembly, it is demonstrated that flow structure and wall heat transfer patterns in low aspect ratio fixed bed reactors are more realistically modelled by properly accounting for the discrete void fraction variations. A 3D network-of-voids (NoV) model has been devised to characterise and examine the discrete flow and heat transfer phenomena in a low aspect ratio packed bed with d_t/d_p = 1.93. The model as formulated is deliberately designed to be not too complicated so as not to place severe demands on computational resources. Hence, the model can potentially easily be applied to simulate the typically large sets of tubes (often comprising more than 10,000) in the case of industrial multi-tubular reactors, where every tube is different due to the random insertion of the packing particles. Because of its simplicity, the model offers an opportunity of coupling the individual catalyst pellet level transport with the complex interstitial flows at the reactor scale. Illustrative studies of this NoV model on a random packed bed of spheres predict large variations of discrete in-void angular velocities and consequently wall heat transfer coefficients within a single tube. The wide variations of wall heat transfer coefficients imply that the different angular sections of the tube will transfer heat at radically different rates resulting in potentially large temperature differences in different segments of the tube. This may possibly result in local temperature runaway and/or hot spot development leading to several potentially unanticipated consequences for safety and integrity of the tube and hence the reactor. The NoV model predictions of the overall pressure drop behaviour are shown to be consistent with the quantitative and qualitative features of correlations available in the literature.     

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.     

Modelling of gas interstitial velocity radial distribution over cross-section of a tube packed with granular catalyst bed; effects of granule shape and of lateral gas mixing

The previously presented [Zió?kowska, I., Zió?kowski, D., 1993. Modelling of gas interstitial velocity radial distribution over a cross-section of a tube packed with granular catalyst bed. Chemical Engineering Science 48, 3283-3292] mathematical model of gas flow field within a tube packed with a bed of spherical elements has been modernised. The modernisation consists in more rigorous treating of the radial gas dispersion within the bed voids in the fluid dynamic equations and in involving the formulae correlating the flow resistance in beds packed with various non-spherical elements (Raschig rings, cylinders) with their characteristics. The model solution relates the gas interstitial and superficial radial distributions with an empirical parameter—the local effective viscosity or corresponding Reynolds number, dependent on the geometric, aerodynamic and physical properties of the system which are usually known. The effective viscosity is associated with the kinetic energy dissipation due to the interface friction, the shear stresses in molecular and turbulent motion and the radial dispersion in the gas stream. Its knowledge makes possible the evaluation of the radial profiles of the gas interstitial velocity, as well as the dispersion coefficient, or corresponding Péclet number and the drag coefficient for individual element within the bed. The effective viscosity has been determined experimentally for beds of Raschig rings and cylinders by the method presented previously [Zió?kowska, I., Zió?kowski, D., 2001. Experimental analysis of isothermal gas flow field in tubes packed with spheres. Chemical Engineering and Processing 40, 221-233] and the results have been correlated with the system characteristics. Then the correlations have been used, according to the model, in evaluation of the radial distributions of the gas interstitial velocity, the radial dispersion coefficient and the drag coefficient for individual element within the bed.     

SUSPENSION MODEL FOR BLOOD FLOW THROUGH ARTERIAL CATHETERIZATION

This article is concerned with the analysis of a dusty model for the axi-symmetric flow of blood through coaxial tubes such that the outer tube with an axially nonsymmetreic but radially symmetric mild stenosis and the inner tube have a balloon (assumed that is axi-symmetric in nature). The mild stenosis approximation is used to solve the problem. To estimate the effect of the stenosis shape, a suitable geometry has been considered such that the axial shape of the stenosis can be changed easily just by varying a parameter (referred to as the shape parameter). The model is also employed to study the effect of the volume fraction density of the particles C, the maximum height attained by the balloon δ₂, the radius of the inner tube, which keeps the balloon in position κ, and the axial displacement of the balloon x _d . Flow parameters such as velocity, the resistance to flow (the resistance impedance), the wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis (stenosis throat) have been computed numerically for different shape parameters n, C, δ₂, κ, and x _d . It is shown that the resistance to flow decreases with increasing values of the parameter determining the stenosis shape n and the axial displacement of the balloon x _d , while the resistance to flow increases with the volume fraction density of the particles C, the radius of the inner tube, which keeps the balloon in position κ, and the maximum height attained by the balloon δ₂. The magnitudes of the resistance to flow are higher in the case of a dusty fluid model than in the case of a Newtonian fluid model. The wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis possess a character similar to the resistance to flow with respect to C, δ₂, κ, and x _d . Finally, the effect of the volume fraction density of the particles C, δ₂, and x _d on the velocity profile are discussed.     

小管径-粒径比颗粒无序堆积通道内壁面效应数值研究

采用DEM-CFD方法对小管径-粒径比颗粒无序堆积通道内壁面效应进行了数值研究。针对D/d_p=5.0圆球无序堆积通道构建了光滑壁面和波节壁面两种通道壁面结构,分析了不同壁面结构堆积通道内孔隙率分布、流动和温度场分布及其流动换热性能。结果表明：小管径-粒径比光滑壁面颗粒无序堆积通道内壁面效应显著,壁面附近平均流速明显高于堆积中心区域,而平均温度要低于堆积中心区域,壁面附近0.5d_p区域内通过的流体质量流量比例为46%;波节壁面结构抑制了通道壁面附近漏流,可小幅提高堆积通道的换热能力,但堆积通道内的流动阻力也随之增大,其综合换热性能较光滑壁面堆积通道有所下降。     

Wall-to-particle heat transfer in steam reformer tubes: CFD comparison of catalyst particles

Computational fluid dynamics (CFD) was used to simulate non-reacting heat transfer in a steam reforming packed reactor tube of tube-to-particle diameter ratio (N) equal to 4, with cylindrical multi-hole catalyst particles. These simulations extend those of our previous study [Nijemeisland, M., Dixon, A.G., Stitt, E.H., 2004. Catalyst design by CFD for heat transfer and reaction in steam reforming. Chemical Engineering Science 59, 5185-5191] to provide accurate tube wall temperatures, runs at constant pressure drop in addition to those at constant mass flow rate and simulations of particles with different sizes of holes. At constant pressure drop, particles with higher void fractions allowed higher mass flow rates, resulting in tube wall temperatures and radial temperature profiles in order: solid cylinders>one-hole particles>multi-hole particles. Little difference was seen between three-hole and four-hole particles. The particles with multiple holes gave a substantial reduction in tube wall temperature, with only a small decrease in core tube heat transfer. The effect of hole size was small, for the cases investigated in this study.     

Bubble behavior in corrugated‐wall bubbling fluidized beds—Experiments and CFD simulations

A new concept to harness bubble dynamics in bubbling fluidization of Geldart D particles was proposed. Various geometrical declinations of a cold‐prototype corrugated‐wall bubbling fluidized bed were compared at different flow rates (U_g) to conventional flat‐wall fluidized bed using high‐speed digital image analysis. Hydrodynamic studies were carried out to appraise the effect of triangular‐shaped wall corrugation on incipient fluidization, bubble coalescence (size and frequency), bubble rise velocity, and pressure drop. Bubble size and rise velocity in corrugated‐wall beds were appreciably lower, at given U_g/U_mb, than in flat‐wall beds with equal flow cross‐sectional areas and initial bed heights. The decrease (increase) in size (frequency) of bubbles during their rise was sustained by their periodic breakups while protruding through the necks between corrugated plates. Euler‐Euler transient full three‐dimensional computational fluid dynamic simulations helped shape an understanding of the impact of corrugation geometry on lowering the minimum bubbling fluidization and improving gas distribution. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Experimental and numerical investigation of structure and hydrodynamics in packed beds of spherical particles

In chemical industry, flows often occur in nontransparent equipment, for example in steel pipelines and vessels. Magnetic resonance imaging is a suitable approach to visualize the flow, which cannot be performed with classical optical techniques, and obtain quantitative data in such cases. It is therefore a unique tool to noninvasively study whole‐field porosity and velocity distributions in opaque single‐phase porous media flow. In this article, experimental results obtained with this technique, applied to the study of structure and hydrodynamics in packed beds of spherical particles, are shown and compared with detailed computational fluid dynamics simulations performed with an in‐house numerical code based on an immersed boundary method‐direct numerical simulation approach. Pressure drop and the radial profiles of porosity and axial velocity of the fluid for three packed beds of spheres with different sizes were evaluated, both experimentally and numerically, in order to compare the two approaches. © 2018 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 64: 1896–1907, 2018     

Hydrodynamics and droplet size distribution of liquid–liquid flow in a packed bed reactor with orifice plates

A packed bed reactor with orifice plates (PBR@OP) was designed by adding orifice plates periodically in packed beds. Hydrodynamics and droplet size distribution in PBR@OP were experimentally investigated using fatty acid methyl esters (FAME)/water as the model liquid–liquid system. In PBR@OP, the flow pattern was close to plug flow. Droplets with Sauter mean diameter (d₃₂) of 150–550 μm were generated. The pressure drop of orifice, flow velocity and plate spacing were key parameters to control the droplet size. The reactor performance was evaluated by analyzing a FAME epoxidation process. At the same d₃₂ and residence time, the length and total pressure drop of PBR@OP were about 1/3 and 1/4 of those of PBR without orifice plates, respectively. Furthermore, a semi-empirical correlation describing the d₃₂ change in PBR@OP was developed, revealing a relative mean deviation of 8.64%. PBR@OP presents a cost-effective option for the intensification of liquid–liquid medium rate reactions.     

Fluidization Characteristics in Micro‐Fluidized Beds of Various Inner Diameters

The fluidization characteristics of quartz sand and fluid catalytic crack (FCC) catalyst particles in six micro‐fluidized beds with inner diameters of 4.3, 5.5, 10.5, 15.5, 20.5, and 25.5 mm were investigated. The effects of bed diameter (D_t), static bed height (H_s), particles and gas properties on the pressure drop and minimum fluidization velocity (u_mf) were examined. The results show that the theoretical pressure drops of micro‐fluidized beds deviated from the experimental values under different particles and gas properties. The possible reason is due to an increase in bed voidage under smaller bed diameters. The equations for conventional fluidized beds did not fit for micro‐fluidized beds. u_mf increased with decreasing D_t. When the ratio of H_s to D_t ranged from 1:1 to 3:1, u_mf was characterized by a linear equation with H_s, while the slope of the equation u_mf versus H_s decreased with increasing D_t. In this paper, D_t/d_p and H_s/d_p were defined as dimensionless variables and a new equation was developed to predict u_mf in micro‐fluidized beds under the present experimental conditions.     

A study of particle shape and size effects on hydrodynamic parameters of trickle beds

Uniform-spherical and cylindrical-extrudate particles are employed to study air-water downflow in a packed bed of 14 cm i.d. The effect of particle shape, neglected in the literature so far, is shown to be very significant. A packed bed of extrudates displays significantly greater global dynamic liquid holdup h_d and pressure drop, as well as a trickling-to-pulsing transition boundary at higher gas flow rates, compared to beds of spheres of comparable size. Moreover, packed extrudates exhibit a significant increase of holdup, h_d, in the axial flow direction, a trend reported for the first time as there are no similar data available in the literature; on the contrary beds of spherical particles are characterized by practically constant h_d in the axial direction. Although an explanation for this h_d axial variation is not obvious, one might attribute it to the anisotropy and non-uniformity of interstitial voids of packed cylindrical particles. For beds of uniform spheres, in the diameter range examined (3-6 mm), the effect of size on both dynamic holdup and pressure drop, although quite pronounced, is not as significant as the effect of particle shape. An extensive survey of literature data, obtained with similar spherical particles, suggests that small bed diameters have an appreciable influence on trickling-to-pulsing transition boundary. Comparisons are reported with literature methods for predicting the measured parameters; discrepancies between data and predictions may be partly due to the inadequacy of a single “equivalent” diameter to represent both shape and size of non-spherical particles; predictive methods performing best are also identified.     

Axial Dispersion and Wall Effects in Narrow Fixed Bed Reactors: A Comparative Study Based on RTD and NMR Measurements

Axial dispersion and wall effects in narrow fixed beds with aspect ratios < 10 were investigated, both by classical methods and by NMR imaging. The residence time distribution (RTD) in the center and at the wall was measured, system water/NaCl‐solution as tracer, and subsequently compared with radial velocity profiles based on NMR imaging. The influence of the aspect ratio and Re_p on dispersion and on the degree of non‐uniformity of the velocity profile was studied. The NMR results are consistent with the RTD and also with literature data of numerical simulations. For low aspect ratios, dispersion/wall effects have a strong influence on the reactor behavior, above all, in cases where a low effluent concentration is essential, as proven by breakthrough experiments with the reaction of H₂S with ZnO.     

Near-wall porosity characteristics of fixed beds packed with wood chips

Packed beds of fuel wood chips are commonly found in thermal conversion processes such as combustion or gasification. Wood chips in particular are mostly used as fuel for small-scale domestic heating boilers but also for commercial-scale combustion units. The characterization of spatial voidage distribution inside the wood chip beds is of great importance for flow and reactor modelling. This study focuses on the radial porosity variations of cylindrical beds of three different types of commercially available wood chips including chips classified as G30 size class. The conventional technique of consolidating packed beds with a resin was chosen as the experimental procedure. The radial voidage distribution in different cylindrical beds is determined by image analysis of sections of the solidified packings. Additionally, a packing of monosized spheres was investigated in order to assess the selected procedure in comparison with widely available literature data for spheres. The results are discussed and summarized in a mathematical expression correlating the radial voidage distribution depending on average wood chip size, packing core porosity and dimensionless distance from the tube wall.     

基于离散相模型的旋转填充床内的流场分析

利用CFD软件Fluent初步模拟了旋转填充床(Rotating Packed Bed,RPB)内的流体流动.计算中气相采用RNGk-ε湍流模型,液相采用拉格朗日离散相模型(DPM).通过一定简化后建立了旋转填充床二维模型,考察了液体颗粒在填充床内的速度分布,以及转速对液体颗粒速度的影响.结果显示液滴速度随转速的增加而增加,转速对液滴径向速度的影响不大.此外还针对转速、气体进口速度对干床压降的影响做了一定的研究,发现压降随转速的增加而增加,但其影响没有气体进口速度对压降的影响明显.填料的内缘处存在剧烈的端效应,模拟结果表明,端效应区的湍动强度明显大于其他区域.     

Modelling of the behaviour of gas-solid two-phase mixtures flowing through packed beds

This work is concerned about gas-solid two-phase mixtures flowing upwards through packed beds. An Eulerian-based two-fluid model coupled with a newly proposed porosity distribution model is used to simulate the flow behaviour. The results are compared with recently published experimental results in terms of both hydrodynamics and solids motion. It is found that the use of the newly proposed porosity model not only gives better agreement with experimental porosity data, but also provides a much better prediction of the pressure drop than other porosity models could do. The results also show that the model predicts very well the dynamic hold-up of suspended particles, and captures the main features of the radial distributions of the suspended solids concentration and the axial solids velocity. A discrepancy occurs, however, at the wall region where the predicted axial solids velocity peak is sharper and higher than the measurements. The work also leads to a new relationship for the pressure drop of dilute gas-solid two-phase mixtures flowing through packed beds, which agrees very well with experiments.