Wall mass transfer in liquid-fluidized beds

Ionic mass transfer coefficients between the wall and a liquid fluidized bed of 0.043 inch lead glass spheres have been measured using the diffusion controlled reduction of ferricyanide ion at a nickel cathode. The coefficients obtained are correlated in terms of the dimensionless j factor and are compared with dissolution mass transfer results by this author and with a recent liquid fluidized bed heat transfer study⁽¹⁾ with these same particles. It is concluded that in the dissolution study either mechanical erosion or roughness effects or both were present. No analogy was found to exist between overall heat and mass transfer in a liquid fluidized bed in which there is a large difference between the Schmidt and Prandtl numbers because the dominant resistance is different for the two cases.     

Mass transfer in liquid-fluidized beds at low reynolds numbers

The mass transfer data measured in the liquid fluidized beds of ion exchange resins in the Reynolds number range 0.22–6.4 are presented. A comparison was made between the experimental results and the values predicted by the recent theory of Nelson and Galloway and by the modified theory proposed by Rowe. The observed change of exponent on Reynolds number is predicted by the theory of Nelson and Galloway, but this theory fails to predict the correct dependance of Sherwood number of voidage. The modified theory proposed by Rowe predicts successfully the mass transfer coefficients at very low Reynolds number and in addition it predicts also approximately the Reynolds number region in which the change of exponent on Reynolds number is observed, but it fails to predict the correct dependance of Sherwood number on voidage in this region.     

Mass transfer in liquid-fluidized and spouted beds of ion exchange resin at low Reynolds number

Rates of mass transfer from the liquid phase to small ion exchange resin particles (0.78 mm in mean diameter) in fluidized and spouted beds were studied experimentally. Dilute aqueous solution of sodium hydroxide was fed into the beds of strong cation exchange resin and the exit concentration of the solution was determined by conductivity measurement. In spouted beds, the initial conversion and K_l increased with bed height, but decreased with fluid flowrate. The model, applying material balance of the reactant and axisymmetric flow of fluid in the annulus of a spouted bed, predictions of the initial conversion in spouted beds are satisfactory. In fluidized beds, the obtained mass transfer coefficients were correlated and compared with other works.     

Heat transfer and diffusion in fixed beds

On the basis of a set of fairly accurate frequency response measurements, various models for the dynamics of heat propagation in a fixed bed of lead balls have been examined.It has been shown that the calculated average heat transfer coefficient in the particles in the bed, depends very strongly on the type of mathematical model used. Hence, the heat loss from the bed to the surroundings, but even much more the axial dispersion in the fluid phase, have dramatic effects on the calculated heat transfer coefficient, when these physical factors are included in the mathematical model. Their significances are estimated from simple criteria developed in this paper. In general, mathematical models should be used with care when process parameters are predicted from the experiments results.As far as the frequency response characteristics are concerned, it is extremely difficult to distinguish one model from another. The residual of model fitting to the experimental frequency response remains almost the same. Therefore, systematic deviations from constancy in the evaluated process parameters have been used as a criterion for the selection of the models.     

Heat transfer in three-phase fluidized beds

Heat transfer coefficients h have been measured in two-phase (water—air, water—glass beads) and three-phase (water—air—glass beads) fluidized beds. Experiments were performed over a wide range of liquid and gas flowrates in a 0.24 m diam. column fitted with an axially mounted cylindrical heater. Four solids were employed ranging in size from 0.5 to 5 mm.Typical maximum values of h in the three-phase, liquid—gas, liquid—solid and liquid beds were approximately 4800, 4300, 3800 and 1300 W/m²K respectively. In the three-phase beds h generally increased with liquid and gas velocity and with particle size. Correlations are presented to calculate h in the different beds.     

Heat transfer in flowing packed beds

Heat transfer coefficients were determined between a small exposed heat transfer surface and a flowing bed of particles. The experiments were carried out with a range of particles of different properties and of mean size between 160 and 2370 μm, using Air, Freon, Helium and Argon as the “stagnant” gas medium. Particle residence times at the transfer surface ranged between 1 and 10 sec. The results fitted closely the predictions of a modified version of the “Mickley” packet model with the inclusion of an additional resistance to heat transfer at the transfer surface.     

Heat transfer mechanisms in gas fluidized beds. Part 3: Heat transfer in circulating fluidized beds

Part 1 of this contribution reported on the effects of system properties on heat transfer between heating or cooling surfaces and bubbling fluidized beds. This investigation produced four correlations which define the respective maximum heat transfer. Part 2 of this study suggests that the heat transfer between exchanger surfaces and bubbling fluidized beds depends on superficial gas velocity, expressed as dimensionless excess gas velocity. The present paper shows that heat transfer coefficients in circulating fluidized beds can be predicted by evaluation of a state diagram, which combines three dimensionless groups: Nusselt number, Archimedes number and a dimensionless pressure gradient. A comparison of coal combustion experiments with own cold model measurements indicates that the radiative component of heat transfer coefficients is only evident at very low dimensionless pressure gradients.     

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.     

Heat transfer in small diameter packed beds

The heat transfer results of Agnew and Potter are re-analyzed using additional data obtained from mass transfer experiments carried out with geometrically identical beds. A two-phase heat conduction model of the packed bed is employed to relate this additional data to the heat transfer situation.The results indicate that radial transfer by fluid dispersion is identical in the two transfer situations and this agreement is interpreted as a confirmation of the validity of the theoretical basis of the analysis.     

Heat transfer to submerged surfaces in coarse-grained pressurized fluidized beds and fixed beds

This contribution reports on the theory underlying a uniform representation of heat transfer to submerged surfaces in fixed bed reactors and of gas convective part of heat transfer in fluidized beds with coarse-grained bulk solids and/or at elevated pressure. Based on an analysis of the pressure drop behaviour of fixed bed percolation at different gas pressures and with different bulk solids, a new dimensionless pressure drop parameter was developed. Fixed bed heat transfer data are very well correlated by this new dimensionless number. As soon as fluid throughput is in excess of minimum fluidization velocity, the pressure drop parameter transforms into the well-known Archimedes number. These two dimensionless numbers are connected by the condition of equilibrium for pressure drop and mass of practices in a fluidized bed. This equilibrium is fulfilled as soon as fluidization commences. Up to now, the Archimedes number has been generally accepted as the significant parameter, determining the gas convective part of heat transfer in fluidized beds; however, without any physical interpretation of this parameter. Introduction of the pressure drop number, which is consistent with the Archimedes number, reduces the heat transfer behaviour to pressure drop characteristics. The usefulness of this concept is proven by the comparison of experimental results and prediction.     

Fluid velocity profiles near the wall of liquid-fluidized beds

A direct, non-disturbing flash photolysis dye technique has been used to measure liquid velocities in 2.465-in. beds of 0.1248, 0.233 and 0.368-in. diameter lucite spheres at porosities of 0.8 and 0.9. Aggregative fluidization, including layering, was observed in all beds, and increased in magnitude with the larger spheres. Distinct velocity maxima were found from 0.5 to 2 particle diameters from the wall and distinct minima at from 0.6 to 1.2 particle diameters for the more particulately fluidized beds. Variations in velocity greater than the mean were observed. Conservatively estimated wall shear stresses were 2 to 5 times times larger than in the open pipe.     

Heat transfer in fluidized beds: design methods

Large-scale fluidized beds for commercial processes commonly require heat transfer surfaces. Design then demands that heat transfer coefficients be specified. Empirical correlations are unable to cover the wide range of variables and conditions encountered. Mechanistic models are more reliable, but must be chosen carefully. For bubbling beds, the packet model approach gives reasonable predictions for the convective component of transfer, but further work is required to provide reliable estimates of two required time constants, dependent on the hydrodynamics. For industrial-scale circulating beds, a mechanistic model that incorporates the key factors influencing heat transfer, assumes fully developed transfer, and utilizes results from large-scale units is recommended.     

Heat transfer in packed beds—a reevaluation

Data for heat transfer from packed beds are reexamined in the light of new insights. Much of the data includes a length effect, resulting from a higher$\text{Bid}{}_{\mathrm{p}}\text{?}\text{R}\text{(1-?}$)=0.27.     

Heat transfer between particle beds and submerged surfaces

Theoretical modelling of heat transfer to particle beds comprises two sequential steps: transfer from the heating surface to contacting particles followed by transfer to the interior of the bed. Two different limiting case can be formulated for the second step: unmixed and homogeneously mixed bed. In the case, heat is transferred gradually via a repeated sequence of heat transfer in the gap between adjacent particles and conduction in the particulate material. In the second case, heat is transferred to the interior of the bed by mixing of particles which have previously attained the temperature of the heating surface. On the other hand, the mixing motion maintains a homogeneous lower temperature throughout the bed. Theory predicts a significant and easily measurable difference in the behaviour of heat transfer coefficients for the two regimes at long contact times t: unmixed beds ∝ $$ \sqrt t $$ and homogeneously mixed beds ∝ 1/t. For short times t, both regimes show the same behaviour, namely of t. From a theoretical standpoint, it makes sense to differentiate further between the behaviour patterns of unmixed beds: at long times t, instantaneous heat transfer coefficients are independent of heat transfer form the heating surface to adjacent particles. Comparison with experimental result from literature shows that the derived models, which are consistent, are suitable for describing the heat transfer from submerged surfaces to unmixed and mixed beds of particles.     

Heat transfer to liquid fluidized beds in annuli

Heat transfer coefficients to a liquid/solid fluidized bed in an annulus have been measured. Water and Bayer liquor have been used as liquids, while glass spheres and two types of steel cylinders have been used as solid particles. The possible operating parameters, heat flux, flow velocity and bulk temperature, have been varied over a wide range. The measurements with water are compared with the predictions of 13 correlations from the literature. The formation of sodium aluminium silicate on the heat transfer surface was studied for the fluidized bed section and for plain annular flow.     

液固流化床内固含率时空分布特性的CFD模拟

采用Brandani等考虑拟平衡状态下颗粒与流体相互作用的双流体模型,通过在商业软件CFX4.4平台上增加用户自定义子程序模拟了高0.5 m、宽0.1 m的二维液固流化床内固含率的时空分布特性。为了保证数值模拟精度、节省计算机运行时间,首先确定了适宜的网格尺度、时间步长和收敛判据。随后,考察了液固两相物性和操作条件对流化床内固含率时空分布特性的影响,模拟结果表明：增大颗粒粒径或密度会使颗粒向下加速运动,导致床层高度下降而垂直方向上任一水平面的平均固含率呈现增大的趋势;减小液体黏度或密度则会使颗粒向下加速运动,导致床层固含率增大;突然增大液速会使颗粒向上加速运动,导致床层固含率减小;升高温度的实质是使液体的黏度和密度均呈现下降的趋势,结果使颗粒向下加速运动,床层固含率增大。上述模拟结果与颗粒受力的理论分析相一致。