Heat transfer and axial dispersion in packed beds

The thermal frequency response of beds packed with glass and metallic particles has been measured in the range of Reynolds numbers from 0·05 to 330. Values of the coefficients of axial dispersion of heat, intraparticle thermal conductivity and fluid-particle heat transfer coefficients have been found by non-linear regression. The experimental frequency response at Reynolds numbers less than one was found to be dominated by thermal dispersion and as the range of small Reynolds numbers was approached the values of particle Nusselt group became constant. The experimental values are compared with the results of other workers. The substantial differences at low Reynolds numbers are due to the inclusion of thermal dispersion in this investigation while others have omitted this effect.     

Transient heating and cooling of cocurrent three-phase fluidized beds

The thermal transient behaviour of three-phase fluidized beds have been investigated for a liquid viscosity ranging from 35 to 75 mPa · s. For the operating conditions used in this study, a 6 mm glass particle bed was found to have a thermal response similar to that of a fixed bed. The transient responses, which were not significantly affected by gas sparging, were, however, faster for heating than for cooling. This result has been analyzed from a model assuming liquid plug flow through stationary particles using combined free and forced convection correlations for heat transfer around the particles. Different correlations are then proposed to predict the contribution of natural convection to the liquid-to-particle heat transfer in heating and cooling modes. The effect of gas sparging was found to strongly affect The 2.0 mm particle bed responses but only moderately the 3.9 mm bed responses. These responses were analyzed using axial dispersion models for the liquid and solid phases. For the 3.9 mm particle bed, the axial dispersion coefficient of the solids, E_ZS, was found to be of the same order of magnitude as that of the liquid coefficient, E_ZL. However, the value of E_zs for the 2 mm particle bed was found to be five times that of E_ZL.     

Gas mixing in the cocurrent downflow circulating fluidised bed

An experimental study on the gas dispersion behaviour of a cocurrent downflow gas-solids suspension in a 140 mm i.d. circulating fluidised bed (CDCFB) using the steady-state tracer method is presented. The influence of gas velocity, solids circulating rate and particle density on radial gas dispersion has been examined. Gas dispersion can well be described by an eddy diffusion mechanism and a proposed two dimensional dispersed plug-flow model can fit the experimental data very well. Correlations of the radial diffusion coefficient were obtained. It is found that the axial diffusion coefficient obtained in the CDCFB is much lower than that in conventional circulating fluidised beds.     

Particle scale study of heat transfer in packed and bubbling fluidized beds

The approach of combined discrete particle simulation (DPS) and computational fluid dynamics (CFD), which has been increasingly applied to the modeling of particle‐fluid flow, is extended to study particle‐particle and particle‐fluid heat transfer in packed and bubbling fluidized beds at an individual particle scale. The development of this model is described first, involving three heat transfer mechanisms: fluid‐particle convection, particle‐particle conduction and particle radiation. The model is then validated by comparing the predicted results with those measured in the literature in terms of bed effective thermal conductivity and individual particle heat transfer characteristics. The contribution of each of the three heat transfer mechanisms is quantified and analyzed. The results confirm that under certain conditions, individual particle heat transfer coefficient (HTC) can be constant in a fluidized bed, independent of gas superficial velocities. However, the relationship between HTC and gas superficial velocity varies with flow conditions and material properties such as thermal conductivities. The effectiveness and possible limitation of the hot sphere approach recently used in the experimental studies of heat transfer in fluidized beds are discussed. The results show that the proposed model offers an effective method to elucidate the mechanisms governing the heat transfer in packed and bubbling fluidized beds at a particle scale. The need for further development in this area is also discussed. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Surface-to-bed heat transfer in fluidised beds of fine particles

This work reports experimental results on the heat transfer between a fluidised bed of fine particles and a submerged surface. Experiments have been carried out using different bed materials (polymers, ballotini, corundum, carborundum and quartz sand) with Archimedes number between 2 and 50. Dry air at ambient pressure and temperature has been used as fluidising gas. Three different exchange surfaces, namely a sphere and two cylinders with different base diameter and same height, have been used.Experimental results show that the heat transfer coefficient increases with particle Archimedes number and is almost independent from particle thermal conductivity for K_p/K_g > 30. Finally, the comparison of heat transfer coefficient for the different surfaces shows that the effect of the surface geometry may account for a 30% variation in the heat transfer coefficient, with higher differences occurring for coarser particles.     

Thermal dispersion and wall heat transfer in packed beds

A new analysis showing the effect of axial and radial thermal dispersion and wall thermal resistance upon heat transfer to fixed beds of solids is presented. By application of this theory and non-linear regression, coefficients of axial and radial dispersion and wall heat transfer coefficients are calculated from experimental measurements of radial temperature profiles in fixed beds heated at the wall.The experiments have been performed for beds packed with glass and with metallic particles within the particle Reynolds number range from 1 to 400.The calculated coefficients are compared with experimental values reported by other workers. Some differences are attributed to the neglect of axial dispersion in the work of others, but other differences are significant in that, for example, thermal characteristics of fixed beds of metallic particles differ from those of non-metallic particles.     

流体流过填充床层冷却之传热系数

填充床层之传热系数包括二重阻力,即床层内部的传热阻力和床层与管壁界面间薄膜的传热阻力。本文以空气和水为传热介质,使其流过填充床层冷却,改变操作条件和床层构造,考察了Pr准数,床层高度、填充物的导热系数和形状对於传热系数的影响。由於高速固定床接触反应器和填充热交换器逐渐在工业上取得了应用,高线速下的传热数据需要迫切,因此试验的范围采用了较大的Re准数。 玻璃或磁质等低导热系数球状填充物的传热系数可归纳成: 试验范围: D_p/D_t=0.08～0.5; L/D_t=10～30; Re=250～6500; Pr=0.722～4.8 铜、铁等高导热系数球状填充物的传热系数可归纳成: 试验范围; D_p/D_t=0.1～0.5;　Re=300～10,000; 　 L/D_t=10～30 在此范围内所有试验皆经过二次以上的重复试验,误差一般不大於5%。 以圆柱体为填充物的传热系数,仅须将修正Re准数中的几何量D_p,改成与圆球具有相同的几何表面面积的球径D_p即可。 以上二式说明流体的物理性质即Pr准数对传热系数的影响不很显著,床层高度对传热系数的影响:低导热系数填充物的传热系数随L/D_t比率之减小而逐渐增大,L/D_t>30,影响甚微,L/D_t=20,误差约7%,L/D_t=10,误差可达15%;高导热系数填充物的传热系数随L/D_t的增大略有增大的趋势,但影响     

A new computational method for studying heat transfer in fluid bed reactors

Effective thermal conductivity (ETC) is an important parameter describing the thermal behaviour of packed beds with a stagnant or dynamic fluid, and has been extensively examined in the past decades. Recently, an approach of coupled discrete particle simulation (DPS) and computational fluid dynamics (CFD) has been extended to predict the ETC, allowing the elucidation of the underlying heat transfer mechanisms at a particle scale. However, because of the sensitivity of heat transfer to particle–particle contact, a large Young's modulus and small time step have to be employed in the DPS to generate accurate results, resulting in a high computational cost. This paper proposed a method to overcome this problem. It is done by introducing a correction coefficient in the calculation of the particle–particle contact radius between colliding particles. The treatment is first implemented in our recent DPS-CFD modeling of the heat transfer in gas fluidization, and is validated by comparing the predicted ETC with literature data. The effects of model parameters, particle size, and bed average temperature on ETC are also analyzed.     

固定床内错流传热——II.床层对壁给热系数的经验关联式

采用3种导热性能不同的固体颗粒为填充物,以空气为介质,在床层被加热的情况下,研究了固定床中内置圆管的错流传热.采用最小二乘法对实验数据进行拟合,得到以床层对壁的平均给热系数、气体的导热系数和床层中被加热圆管的管径计算的Nusselt准数经验关联式:Nuf=31(lb0/ls)1.4(Db/Dp)0.2Rep0.33Pr0.62,Rep=10~180,Db/Dp=28~116,lb0/ls=0.5~0.2.Reynolds数以固体颗粒的等外表面积当量直径进行计算.结果表明,在错流传热过程中,表征气体流动特性的参数Rep仍是错流传热的重要影响因素,Nusselt准数除与床层的结构参数Db和颗粒的当量直径Dp有关外,还与颗粒的导热系数ls和床层的导热系数lbo密切相关.     

Wall-to-bed heat transfer in liquid—solid and gas—liquid—solid fluidized beds part I: Liquid—solid fluidized beds

Experimental work was conducted to investigate the effect of particle size and particle density upon the wall-to-bed heat transfer characteristics in liquid—solid fluidized beds with a 95.6 mm column diameter over a wide range of operating conditions. The radial temperature profile was found to be parabolic, indicating the presence of a considerable bed resistance. The effective radial thermal conductivity and the apparent wall film coefficient were obtained on the basis of a series thermal resistance model. The modified Peclet number of the radial thermal conductivity decreases upon the onset of fluidization, has a minimum at a bed porosity of 0.6 to 0.7 and increases with further increase of bed porosity. The modified Peclet number decreases considerably with decreasing particle size or increasing particle density. The apparent wall heat transfer coefficient can be represented well by a Colburn j-factor correlation over a wide range of data as follows: j′_H = 0.137 Re′^?0.271 A close analogy is found to exist between the modified j-factor for wall heat transfer coefficient and that for wall mass transfer coefficient, in liquid—solid fluidized beds.     

Investigation into gas-solid heat transfer in a cryogenic vibrated fluidised bed

Experiments were carried out in a cryogenic vibrated fluidised bed to investigate the heat transfer between gas and rubber particles obtained from discarded tyres. The effects of parameters such as bed layer thickness and gas flow rate on the gas-solid heat transfer were investigated, and a heat transfer correlation obtained by regressing the experimental data. Theoretical analysis based on radial thermal conductivity indicated that higher heat transfer efficiency could be obtained by the use of a fluidised bed rather than a fixed bed or a moving bed, especially for rubber particles having low thermal conductivity under cryogenic conditions. A numerical modelling was developed, based on assumptions of the movement of the particles and the vibrating bed plate, using a unique method of regarding particles as the source term in the energy equation. Computational results from the modelling showed good agreement with the experimental data.     

Dynamic behaviour and stability of non-porous catalyst particles

The stability and dynamic behaviour of a model of an exothermic chemical reaction occurring on a non-porous catalyst particle are studied. The model accounts for the effects of external film heat and mass transfer resistances and intraparticle heat conduction.An orthogonal collocation technique is shown to be superior to the more conventional finite difference methods in obtaining solutions of the system equations.It is found that the thermal conductivity as well as the heat capacity of the particle can have a profound effect on stability and dynamic behaviour. Two simpler models which neglect the effects of thermal conductivity and accumulation of reactants are shown to give very limited insight into the dynamic behaviour of the system.     

基于颗粒尺度的离散颗粒传热模型

颗粒间传热在诸多工业过程中有着十分重要的作用。详细考虑颗粒间传热机理,对颗粒间各传热途径建模,包括颗粒内部导热、颗粒粗糙表面传热、颗粒表面气膜及接触颗粒间隙气膜传热,并与离散颗粒模型(DEM)耦合,建立颗粒尺度下离散颗粒传热模型。以固定床为对象,考察颗粒粒径、颗粒比热容、颗粒热导率及压缩负载对固定床有效传热系数的影响,并将本文计算值和文献的实验值及模型预测值对比,结果表明,该模型可定量预测固定床有效传热系数。本文建立的离散颗粒传热模型为合理预测颗粒体系内的传热提供了一种有效方法。     

Modelling of batch fluidised bed drying of pharmaceutical granules

This paper presents a mathematical model based on a three-phase theory, which is used to describe the mass and heat transfer between the gas and solids phases in a batch fluidised bed dryer. In the model, it is assumed that the dilute phase (i.e., bubble) is plug flow while the interstitial gas and the solid particles are considered as being perfectly mixed. The thermal conductivity of wet particles is modelled using a serial and parallel circuit. The moisture diffusion in wet particles was simulated using a numerical finite volume method. Applying a simplified lumped model to a single solid particle, the heat and mass transfer between the interstitial gas and solid phase is taken into account during the whole drying process as three drying rate periods: warming-up, constant rate and falling-rate. The effects of the process parameters, such as particle size, gas velocity, inlet gas temperature and relative humidity, on the moisture content of solids in the bed have been studied by numerical computation using this model. The results are in good agreement with experimental data of heat and mass transfer in fluidised bed dryers. The model will be employed for online simulation of a fluidised bed dryer and for online control.     

Study on mass transfer of ethyl acetate in polymer adsorbent by experimental and theoretical breakthrough curves

A new polymeric adsorbent with highly hypercrosslinked structure was developed for the removal of VOCs from polluted air. The purpose of this work is to obtain the intraparticle mass transfer coefficient of the adsorbent particles. Adsorption experiments for obtaining breakthrough curves were carried out with a fixed bed system. A dynamic mathematical model for the fixed bed adsorption system was developed. By model fitting, the overall mass transfer coefficient was determined when the deviation error was minimum. Then, the intraparticle mass transfer coefficient of the adsorbent was determined when the external mass transfer resistance was eliminated at higher velocities. Furthermore, a linear relationship of the intraparticle mass transfer coefficient and equilibrium coefficient at lower inlet gas concentrations range was correlated. Moreover, an equation for predicting external mass transfer coefficient at low Reynolds number range at room temperature was obtained.     

A 3-zone model for protein adsorption kinetics in expanded beds

The adsorption behavior of expanded beds is more complex than that of fixed beds, since the adsorbent particle size, local bed voidage and liquid axial dispersion will vary axially with expanded height. Models applicable to fixed beds maybe not adequately describe the hydrodynamic and adsorption behavior in expanded beds. In this paper, a 3-zone model is developed, in which the model equations are written for the bottom zone, middle zone, and top zone of the column, respectively, and the model parameters, such as the adsorbent particle diameter, bed voidage and liquid axial dispersion coefficient, are zonal values. In-bed breakthrough curves are predicted by the 3-zone model, and tested against literature data for lysozyme adsorption on Streamline SP in an expanded bed.Model parametric sensitivity is analyzed. The effects of film mass transfer resistance, liquid axial dispersion and adsorbent axial dispersion on the breakthrough curves are weaker than that of protein intraparticle diffusion resistance for stable expanded beds. Adsorbent particle size axial distribution and bed voidage axial variation significantly affect in-bed breakthrough curves, therefore, model parameters should not be assigned uniform values over the whole column; instead the model should account for the adsorbent particle size axial distribution and bed voidage axial variation.     

Wall-to-bed heat transfer coefficient in gas—liquid—solid fluidized beds

Wall to bed heat transfer has been studied in three-phase fluidized beds with a cocurrent up-flow of water and air. Six sizes of glass beads, two sizes of activated carbon beads and one size of alumina beads, varying in average diameter from 0.61 to 6.9 mm and in density from 1330 to 3550 kg/m³, were fluidized in a 95.6 mm diameter brass column heated by a steam jacket. Complementary heat transfer experiments have been performed also for a gas–liquid cocurrent column and liquid–solid fluidized beds. The wall-to-bed coefficient for heat transfer in the gas–liquid–solid fluidized bed is evaluated on the basis of the axial dispersion model concept. The ratio of the wall-to-bed heat transfer coefficient in the gas–liquid–solid fluidized bed to that in the liquid–solid fluidized bed operated at the same liquid flow rate is correlated in terms of the ratio of the velocity of gas to that of liquid and the properties of solid particles. A correlation equation for estimating the wall-to-bed heat transfer coefficient in the liquid–solid fluidized bed is also developed.     

Reduction of hematite with hydrogen in fixed and fluidised beds

Reduction of hematite with hydrogen has been carried out in fixed and fluidised beds at identical gas flow rates. Influence of gas velocity and particle size has been ascertained. The performances of the two types of bed for the reduction of hematite with hydrogen have been compared. The observed difference in performance is considered to be primarily due to the solids movement characteristics of systems studied. This is also influenced by the bubbling phenomena occurring in fluidised systems.     

WALL AND PARTICLE-SHAPE EFFECTS ON HEAT TRANSFER IN PACKED BEDS

The effective radial thermal conductivity and apparent heat transfer coefficient for a packed bed were experimentally determined for beds of spheres, full cylinders and hollow cylinders, for flow rates giving particle Reynolds numbers in the range 100-1000, and for tube to particle diameter ratios of 5-12. Over these ranges the radial Peclet number Pe_r showed significant dependence on solid conductivity, gas flow rate and particle shape, while the wall Biot number Bi showed significant dependence on tube to particle diameter ratio, gas flow rate and particle shape. These dependencies were predicted well by equations incorporating the effects of these variables into individual gas and solid phase parameters, which were then combined to give the effective or lumped parameters     

The effect of bed materials on the solid/bubble motion in a fluidised bed

Gas fluidisation provides good mixing and contact of the gas and particle phases as well as good heat transfer. These attractive features are achieved by the high degree of bubble-induced particle circulation within the bed. Bubble and particle motion vary with bed materials and operating conditions, as investigated in the present study, by the use of the non-intrusive positron emission particle tracking (PEPT) technique. The selected materials were spherical polyethylene and glass particles.The data obtained by the PEPT technique are used to determine the particle velocities and circulation pattern. Bubble rise velocities and associated sizes can be inferred from the particle velocity data, since particles travel upwards mostly in the bubble wake. The results indicate that the flow structure and gas/solid motion within the fluidised beds were significantly different, even at the same value of the excess gas velocity, U-U_mf. The solid circulation pattern within the beds differ: if for glass beads, a typical UCDW-pattern existed (upwards in the centre of the bed, downwards near the wall), the pattern in the polyethylene bed is more complex combining a small zone of UWDC movement near the distributor and a typical UCDW-pattern higher up the bed. Transformed data demonstrate that at the same value of excess gas velocity, U-U_mf, the air bubbles in the polyethylene fluidised bed were smaller and rose more slowly than in the fluidised bed of glass beads, thus yielding a longer bubble residence time and improved gas/solid contact. For polyethylene beads, the size and rise velocity of air bubbles did not increase monotonically with vertical position in the bed as would be predicted by known empirical correlations, which however provide a fair fit for the glass beads data. Bubble sizes and solid circulation patterns are important parameters in the design of a fluidised bed reactor, and vary with the bed material used.