RADIAL DISPERSION AND BUBBLE CHARACTERISTICS IN THREE-PHASE FLUIDIZED BEDS

The effects of gas and liquid velocities, liquid viscosity and particle size on the radial dispersion coefficient of liquid phase (D_r) and the bubble properties in three-phase fluidized beds have been determined. A new flow regime map based on the drift flux theory in three-phase fluidized beds has been proposed.

In three-phase fluidized beds, D, increases with increasing gas velocity in the bubble coalescing and in the slug flow regimes, but it decreases in the bubble disintegrating regime. The coefficient exhibits a maximum value in the bed of small particles with increasing liquid velocity at lower gas velocities. However, it increases with increasing liquid velocity at higher gas velocities. In two and three-phase fluidized beds of larger particles (6,8 mm), D_r exhibits a maximum value with an increase in liquid viscosity at lower gas velocities, but it increases at higher gas velocities. The mean bubble chord length and its rising velocity increase with increasing gas velocity and liquid viscosity. However, the bubble chord length decreases with an increase in liquid velocity and it exhibits a maximum value with increasing particle size in the bed. The radial dispersion coefficients in the bubble coalescing and disintegrating regimes of three-phase fluidized beds in terms of the Peclet number in the present and previous studies have been well represented by the correlations based on the concept of isotropic turbulence theory.     

Residence time distribution in a liquid flowing cocurrently with a gas through a packed bed

Measurement of response curves to an imperfect pulse signal were carried out in a liquid flowing cocurrently with a gas at two positions in a packed bed. Three types of ceramic packing were investigated, viz. spheres, solid cylinders and Raschig rings, all of nominal size 6 mm. The liquids used were water and a corn sugar solution of viscosity 9.13 mPa·s. The curves were analyzed by means of two models: the axially dispersed plug flow model and the Markov chain model; the latter was solved for this purpose. Empirical correlations for the model parameters were obtained.     

床形结构对气固流化床流化质量和气体返混特性的影响

用实验方法比较了一个二维床和一个大型三维床内FCC颗粒流化床在鼓泡域和湍动域内的流化质量和气体返混特性。实验结果表明,床形对A类颗粒气固流化床具有非常大的影响。二维床和三维床的流动和气固混合行为既具有相似性,如床膨胀随气速的变化趋势;也具有很大的差异性,既包括三维床流化质量差、轴向气体扩散系数大等量上的不同,又包括压力脉动、轴向气体扩散系数的变化趋势以及湾流模式等质上的不同。总之,在本研究中,二维床体现的是一种具有强烈壁效应的小型流化床的特征,而三维床则体现的是静床高度具有很大影响的大型流化床的特征。     

GAS MIXING IN SLUGGING AND TURBULENT FLUIDIZED BEDS

The gas phase mixing in a fluidized bed of glass beads (d_p = 0.362 mm) in the slugging and turbulent flow regimes has been studied in a 0.1 m-ID × 3.0 m high Plexiglas column.

The gas dispersion in the downstream of the bed has been described by a diffusion process with the axial and radial dispersion coefficients. The radial dispersion coefficient of the gas phase is nearly constant with the variation of gas velocity in the slugging flow regime, but it increases with an increase in gas velocity in the turbulent flow regime.

Appreciable backmixing of the gas phase is pronounced in the slugging flow regime whereas the lower gas backmixing is produced in the turbulent flow regime. The gas backmixing coefficient increases with an increase in gas velocity in the slugging flow regime, but it decreases slightly with an increase in gas velocity in the turbulent flow regime.

The radial mixing and backmixing coefficients of the gas in terms of Peclet numbers have been correlated with the relevant dimensionless parameters (U_g/U_mf, p_s/p_g, d_p/D_t).

The gas flow pattern in the bed has been well represented by a simplified model based on the two gas phases in the dilute and dense phases which are percolating through the bed in plug flow. The present model can predict the gas exchange coefficient between the phases, the fractions of the dilute phase, the interstitial gas in the dense phase, and the interstitial gas velocity in the bed.     

Simulation of Turbulent Flow in a Packed Bed

Numerous models for simulating the flow and transport in packed beds have been proposed in the literature with few reported applications. In this paper, several turbulence models for porous media are applied to the gas flow through a randomly packed bed and are examined by means of a parametric study against some published experimental data. These models predict widely different turbulent eddy viscosity. The analysis also indicates that deficiencies exist in the formulation of some model equations and selection of a suitable turbulence model is important. With this realization, residence time distribution and velocity distribution are then simulated by considering a radial profile of porosity and turbulence induced dispersion, and the results are in good agreement with the available experimental data.     

Analysis of flow in rotating packed beds via CFD simulations—Dry pressure drop and gas flow maldistribution

Three-dimensional unsteady-state turbulent rotating single-phase flows were simulated in rotating packed beds (RPB) and were validated using overall dry pressure drop measurements for three RPB designs [Liu, H.-S., Lin, C.-C., Wu, S.-C., Hsu, H.-W., 1996. Characteristics of a rotating packed bed. Industrial and Engineering Chemistry Research 35, 3590-3596; Sandilya, P., Rao, D.P., Sharma, A., Biswas, G., 2001b. Gas-phase mass transfer in a centrifugal contactor. Industrial and Engineering Chemistry Research 40, 384-392; Zheng, C., Guo, K., Feng, Y.D., Yung, C., 2000. Pressure drop of centripetal gas flow through rotating bed. Industrial and Engineering Chemistry Research 39, 829-834]. Analysis of the radial and tangential velocities highlighted the impact of gas feed entrance effects on the peripheral gas maldistribution in the rotating packing module. Recommendations were formulated for an optimum design with the aim to reduce gas flow maldistribution in RPBs. Breakdown of the overall pressure drop in its modular components for the housing, the rotating packing module, the free inner rotational zone, and the gas disengagement showed that the dissipation in the rotating packing could be a minor contributor to the overall pressure drop which may be undesirable in terms of RPB mass transfer and reaction efficiencies. Analysis of the simulated pressure drops allowed development of CFD-based Ergun-type semi-empirical relationships in which the gas-slip and radial acceleration effects, the laminar and inertial drag effects, and the centrifugal effect were aggregated additively to recompose the pressure drops in the rotating packing module.     

Dispersion of tracer gas supplied at the distributor of freely bubbling fluidised beds

The dispersion of tracer gas, continuously injected beneath an isolated area of the distributor plate, has been determined from time averaged concentration measurements in freely bubbling three dimensional air fluidised beds. The concentration profiles at different levels and for a series of flow rates have been plotted dimensionlessly showing them to be substantially alike in shape, this plot has been well fitted with a simple expression [1]. The tracer dispersion at points within the bed has been successfully predicted using a single phase model, depending mainly on the radial dispersion coefficient. The radial dispersion coefficient has been found to be roughly constant at all levels in the bed (except near the bottom where it is high), but increases rapidly, from a value near molecular diffusion, with an increase in the excess gas flow (U — U_m.f.). Within the experimental range considered, it appears that the Peclet number is inversely proportional to the average bubble diameter.     

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     

曳力模型对模拟鼓泡塔气含率的影响

引言 鼓泡塔由于其良好的传热、传质特性而被广泛用于化工、生物制药、冶金等领域.近年来,计算流体力学(CFD)越来越多地被应用于研究鼓泡塔内部复杂的流体力学状态.然而,如何合理地描述气液相间作用及湍流模型是CFD模拟能够准确复现鼓泡塔内复杂流动状态的关键和难点.     

填充床层热之传导——床层之温度分布

作者用低导热系数(包括玻璃、磁)的球体、圆柱体、环柱体与高导热系数(包括铜、铁的球体,圆柱体为填充物,以空气为传热介质,使其在管径为81毫米之填充床层内冷却,改变流体流量,床层高度及填充物大小,通过试验测出在不同的条件下床层的径向温度分布,并应用积分法、直流电模拟计算法及图解法求得床层的有效导热系数及管壁薄膜传热系数.在试验范围:低导热系数填充物D_P/D_t自0.074—0.254;高导热系数填充物D_p/D_t自0.12—0.2,L/D_t自5—15,Re汇数自130—1400,即直线速度自0.5—1.6公尺/分,若以床层进出口平均温度之数学平均值为定性温度,则床层之有效导热系数及管壁薄膜传热系数可分别归纳于下式:低导热系数填充物:K_e=0.182(D_t/D_p)~(0.45)Re~(0.75),h_w=65e~(-4)(D_p/D_t)(K/D_t)((D_t/L))~(0.2)Re~(0.4)高导热系数填充物:K_e=0.3k(D_t/D_p)~(0.6)Re~(0.72),h_w=5.1(K/D_t)(D_t/D_p)~(0.8)(D_t/L)~(0.1)Re~(0.46)填充物形状对K_e及h_w的影响,仅需将D_p用 D’_p代替,同时把K_e式中之常数0182及03各改为0.22及0.38即可.直流电模拟计算法系利用电压表示温度,电阻表示传热阻力,电流表示热的流动,是简单的模拟计算机的一种,它在近代工程上的应用日渐广泛,有了传热数据应用它来求床层的温度分布异常方便.     

Oscillatory flow and axial dispersion in packed beds of spheres

The effect of oscillations in the bulk flow on the axial dispersion coefficient in packed beds of spherical particles has been studied using the imperfect pulse tracer method with two probes located within the bed. Three bed sizes with diameters in the range 25-47.3 mm have been used with oscillation frequencies and amplitudes in the range 0-2.4 Hz and 0-3.5 mm, respectively. In the absence of oscillations, the axial dispersion coefficient increases linearly with interstitial velocity. For a given bulk velocity and oscillation frequency, the axial dispersion coefficient-amplitude relationship shows a minimum. Over the ranges of conditions studied, the best reduction (up to 50%) in the axial dispersion coefficient from the non-oscillation base case occurred at the highest frequency studied and when the wall effect was the greatest, i.e. when the column-to-particle size was the smallest. The axial dispersion coefficient was fitted to a mathematical model, which takes into account the diameters of both the column and the packing, the fluid velocity, and the oscillation intensity (frequency and amplitude). The model was adapted from those developed by Göebel et al. (1986) and Mak et al. (1991) so as to need no a priori assumptions about the relationship between oscillation parameters and the axial dispersion coefficient. The model provides near-perfect fits to the experimental data for the higher frequencies studied.     

气固并流下行床气体扩散行为的研究

采用氢气稳态示踪方法在内径140mm的气固并流下行循环流化床中对气体扩散行为进行了实验研究.实验结果表明:下行床中气体扩散行为可用二维拟均相模型进行描述,其气体的径向扩散系数与气速、固体循环量及颗粒密度的关系可用下列准数关联式表示Pe_r=4.35×10_(-3)Re~(0.95)ε~(-73.4) 1>ε>0.99而下行床中气体轴向扩散系数要比提升管中小1个数量级以上.     

Computational fluid dynamics (CFD) modeling of spouted bed: Influence of frictional stress, maximum packing limit and coefficient of restitution of particles

Following the previous article [Du, W., Bao, X., Xu, J., Wei, W., 2006. Computational fluid dynamics (CFD) modeling of spouted bed: assessment of drag coefficient correlations. Chemical Engineering Science 61 (5), 1401-1420], this contribution describes the influences of the frictional stress, maximum packing limit and coefficient of restitution of particles on CFD simulation of spouted beds. Using the two-fluid method embedded in the commercial CFD simulation package Fluent 6.1, the spouting hydrodynamics of a cylindrical-conical spouted bed was simulated and verified with the experimental data of He et al. [He, Y.L., Lim, C.J., Grace, J.R., Zhu, J.X., Qin, S.Z., 1994a. Measurements of voidage profiles in spouted beds. Canadian Journal of Chemical Engineering 72 (4), 229-234; He, Y.L., Qin, S.Z., Lim, C.J., Grace, J.R., 1994b. Particle velocity profiles and solid flow patterns in spouted beds. Canadian Journal of Chemical Engineering 72(8), 561-568]. The results showed that, for coarse particles, the frictional stress is important only for the annulus computation and has no obvious effects on the hydrodynamics of the solids flow in the spout region. The specification of the maximum packing limit could significantly affect the properties of the pseudo-fluid phase of the particles by changing the radial distribution function. The strong dependence of the pseudo-fluid properties of the particle phase, such as pressure, bulk viscosity and shear viscosity, on the granular temperature accounts for the influence of the coefficient of restitution of particles on CFD modeling. The solids volume fraction at loose packing state is suitable for spouted bed simulations, and a pretest of the coefficient of restitution of particles must be conducted when no experimental datum is available.     

气-液-固三相循环流化床中的液相轴向扩散

The effects of liquid viscosities, solid circulating rates, liquid and gas velocities and phase holdups on the axial dispersion coefficient, Dax, were investigated in a gas-liquid-solid circulating fluidized bed (GLSCFB).Liquid viscosity promotes the axial liquid backmixing when solid particles and gas bubbles are present. Increases in gas velocities and solid circulating rates lead to higher Dax. The effects of liquid velocity on Dax are associated with liquid viscosity. Compared with conventional expanded beds, the GLSCFBs hold less axial liquid dispersion,approaching ideal plug-flow reactors.     

Studies in the vaporization of mercury in irrigated packed beds

Mass transfer coefficients have been measured for the vaporization of mercury flowing countercurrent to air in irrigated packed beds of spheres and Raschig rings. The measured coefficients increased with gas and liquid flow rates, and were correlated in terms of gas Reynolds number and liquid rate. The mass transfer data for liquid metal irrigation were lower than published data for wetting aqueous systems, due to the non-wetting nature of liquid metals. The lower mass transfer coefficients are believed to be attributed to a lower interfacial area for the non-wetting flow of liquid metals, although direct experimental proof was not obtained. The present results are in agreement with data for zinc absorption in molten lead in packed bed (Warner, 1959) when correlated in terms of the relative velocity and total liquid holdup. The results suggest that for liquid metal irrigated beds, the total hold-up is effective in gas phase transfer processes.     

Natural convection mass transfer behaviour of vertical and horizontal cylinders embedded in an inert fixed bed of Raschig rings

Natural convection mass transfer at vertical and horizontal cylinders embedded in a fixed bed of Raschig rings was studied by an electrochemical technique which involves measuring the limiting current of copper deposition from acidified CuSO₄ solution. Variables studied were Raschig ring diameter, physical properties of the solution and cylinder height in case of vertical cylinders or cylinder diameter in case of horizontal cylinders. Under the present conditions where high porosity beds were used, a slight decrease in the rate of mass transfer was observed in the case of vertical cylinders whereas no rate decrease was observed in the case of horizontal cylinders in the bed. Implication of the present results for the design of fixed bed reactors operating at low feed rates and containing a vertical or horizontal array of tubes for heat exchange with the bed was noted.     

Phase holdup and liquid dispersion in gas-liquid-solid circulating fluidized beds

Axial and radial profiles of gas and solids holdups have been studied in agas-liquid-solid circulating fluidized bed at 140mm i.d..Experimental results indicate that the axialand radial profiles of gas and solids holdups are more uniform than those in a conventionalfluidized bed.Axial and radial liquid dispersion coefficients in the gas-liquid-solid circulating fluidizedbed are investigated for the first time.It is found that axial and radial liquid dispersioncoefficients increases with increaes in gas velocity and solids holdup.The liquid velocity has littleinfluence on the axial liquid dispersion coefficient,but would adversely affect the redial liquiddispersion coefficient.It can be concluded that the gas-liquid-solid circulating fluidized bed hasadvantages such as better interphase contact and lower liquid dispersion along the axial directionover the expanded bed.     

Radial liquid distribution in cocurrent two-phase downflow in packed beds

Radial liquid distribution was measured experimentally for cocurrent, two-phase downflow in packed beds. The effects of bed length, water and air flow rates, and type of packing were determined. The experimental data were obtained in the gas-continuous, transition and pulsing trickling-flow regimes. For all finite air rates, the liquid velocity profiles were approximately flat with the maximum average velocity occurring at the center of the packed column. Increasing the air rate increased the center liquid velocity. The gas rate effect was more pronounced in shorter beds. At higher gas rates the liquid rate had less effect on the radial liquid distribution than at lower gas rates. Operation at higher liquid rates resulted in a flatter radial liquid veilocity profile. It was observed that the bed of pellets operated at high liquid rate and low gas rate was unstable. Increasing the bed height increased the stability of the system and a better liquid distribution was obtained. The effects of water flow rate, bed length, and packing type on the shape of the liquid velocity profiles were minor.     

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.     

Computation of gas and solid dispersion coefficients in turbulent risers and bubbling beds

A literature review shows that dispersion coefficients in fluidized beds differ by more than five orders of magnitude. To understand the phenomena, two types of hydrodynamics models that compute turbulent and bubbling behavior were used to estimate radial and axial gas and solid dispersion coefficients. The autocorrelation technique was used to compute the dispersion coefficients from the respective computed turbulent gas and particle velocities.The computations show that the gas and the solid dispersion coefficients are close to each other in agreement with measurements. The simulations show that the radial dispersion coefficients in the riser are two to three orders of magnitude lower than the axial dispersion coefficients, but less than an order of magnitude lower for the bubbling bed at atmospheric pressure. The dispersion coefficients for the bubbling bed at 25 atm are much higher than at atmospheric pressure due to the high bed expansion with smaller bubbles.The computed dispersion coefficients are in reasonable agreement with the experimental measurements reported over the last half century.