Fluid mechanics of circulating fluidized beds

A fluid mechanical model of segregated vertical gas-solids flow has been developed. Mass and force balances were set up with the aid of this model and, finally, a dimensionless state and pressure drop diagram was calculated. In this diagram, the pressure gradient caused by the solids transport is plotted in dimensionaless form versus the superficial gas velocity in the form of a particle Froude number. Parameter is the ratio of the solids volumetric flow rate at minimum fluidization to the gas volumetric flow rate. The state and pressure drop diagram is valid for a given gas-solids system, i.e. for a given Archimedes number and given minimum fluidization porosity. The fluid mechanical behaviour of different types of circulating fluidized beds can be explained with the aid of the state and pressure drop diagram for segregated vertical gas-solids flow. As an example, the operating behaviour of circulating fluidized bed with a syphon in the solids downcomer is discussed. Measurements of the circulating solids mass flow rates are compared with calculation results.     

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.     

Axial pressure profile in circulating fluidized beds

Design and operation of a circulating fluidized bed requires the knowledge of fluid mechanics. According to heat and mass transfer as well as chemical reactions, the effect of the set superficial gas velocity on the axial pressure profile is of particular interest. The axial pressure profile was measured for a variety of solids, as a function of the superficial gas velocity, in a cylindrical circulating fluidized bed with an inner diameter of 0.19 m and an overall height of 11.5 m. Depending on the solids content and superficial gas velocity, two or one sections can be observed in the plant where the pressure gradient is constant. A pressure profile with one pressure gradient exists only at high gas velocities, so long as the acceleration pressure drop immediately above the gas distributor is negligible. Comparison of measured pressure drops in circulating fluidized beds with those measured in vertical pneumatic conveying led to a state diagram for vertical gas-solid flows. The operation behaviour of different types of circulating fluidized bed plants can be explained with the aid of this diagram.     

流化床中气固均匀分布的失稳现象

流化床因其均匀且剧烈的气固相互作用保证了其优异的流动和传递性能,因而广泛应用于化学工业中。因此,构建定量计算气固均匀分布的失稳临界点既是重要的学术问题又具有工程意义。本文分别使用气相和固体颗粒相的质量分数表示气固分布状态;引入颗粒床层压力载荷（Φ _T）描述分布器输入的规则负熵和固体颗粒床层自身混沌熵产生之间相互作用;由于密相颗粒床层远离平衡态且具有强非线性耗散项,因此需基于普利高津最小超量熵增原理给出气固密相流在并联系统均布状态的失稳临界点（Φ _Tc）：分布器和固体颗粒床层总熵增在气固均布和气固非均布情况下相等;由于并联系统的对称性,可将N单元路径并联系统气固均布稳定性分析简化为判断单元路径压降二阶导数正负;在此基础上讨论了操作参数、固体颗粒性质和分布器结构参数对气固密相床层均布稳定性的影响。此外,通过气体示踪和压力脉动频谱分析在直径为300mm冷模实验验证了颗粒床层压力载荷（Φ _T）对密相气固均布稳定性的影响;同时应用该方法论计算了工业流化床反应器临界床层高度、临界表观气速以及分布器临界阻力系数,指导了操作工况的调整和分布器结构设计,对比分析了改造前后的反应情况。     

Numerical investigation of gas-solid heat transfer in rotating fluidized beds in a static geometry

Gas-solid heat transfer in rotating fluidized beds in a static geometry is theoretically and numerically investigated. Computational fluid dynamics (CFD) simulations of the particle bed temperature response to a step change in the fluidization gas temperature are presented to illustrate the gas-solid heat transfer characteristics. A comparison with conventional fluidized beds is made. Rotating fluidized beds in a static geometry can operate at centrifugal forces multiple times gravity, allowing increased gas-solid slip velocities and resulting gas-solid heat transfer coefficients. The high ratio of the cylindrically shaped particle bed “width” to “height” allows a further increase of the specific fluidization gas flow rates. The higher specific fluidization gas flow rates and increased gas-solid slip velocities drastically increase the rate of gas-solid heat transfer in rotating fluidized beds in a static geometry. Furthermore, both the centrifugal force and the counteracting radial gas-solid drag force being influenced by the fluidization gas flow rate in a similar way, rotating fluidized beds in a static geometry offer extreme flexibility with respect to the fluidization gas flow rate and the related cooling or heating. Finally, the uniformity of the particle bed temperature is improved by the tangential fluidization and resulting rotational motion of the particle bed.     

Heat transfer to immersed surfaces in gas-fluidized beds of large particles and powder characterization

A particle classification scheme is proposed for fluidized beds by considering simultaneously the hydrodynamic and thermal properties. The powder characterization is obtained by considering Archimedes number together with Reynolds number at minimum fluidization. The powders are classified in three groups and the validity of the scheme is demonstrated by considering heat transfer data from fluidized beds of sands (d_p = 0.794 and 1.225 mm) and fire clay (3.0 mm) at ambient temperature and pressure in conjunction with heat transfer correlations and models developed for ‘large-particles’.     

Effect of air distributor on the fluidization characteristics in conical gas fluidized beds

The effect of an air distributor on the fluidization characteristics of 1 mm glass beads has been determined in a conical gas fluidized bed (0.1 m-inlet diameter and 0.6 m in height) with an apex angle of 20‡. To determine the effect of distributor geometry, five different perforated distributors were employed (the opening fraction of 0.009–0.037, different hole size, and number). The differential bed pressure drop increases with increasing gas velocity, and it goes from zero to a maximum value with increasing or decreasing gas velocity. From the differential bed pressure drop profiles with the distributors having different opening fractions, demarcation velocities of the minimum and maximum velocities of the partial fluidization, full fluidization, partial defluidization and the full defluidization are determined. Also, bubble frequencies in the conical gas fluidized beds were measured by an optical probe. In the conical bed, the gas velocity at which the maximum bed pressure drop attained increases with increasing the opening fraction of distributors.     

Experimental methods in chemical engineering: Reactors—fluidized beds

Industry relies on fluidized beds to synthesize chemicals (acrylonitrile, maleic anhydride, titanium dioxide, vinyl chloride), combust coal, dry powders, and treat waste. Fluidized bed folklore declares that they are hard to scale‐up and the gas phase is backmixed. Commercial failures that disregard standard design criteria around powder management, gas/solids injection, and mixing reinforce this belief. However, engineers select fluidized beds for processes that are impractical with conventional technologies to achieve economies of scale for highly exothermic, endothermic, or explosive reactions, for catalysts that deactivate in seconds (or minutes), and for chemistry that requires multiple dosing cycles. Failures are more frequent for these challenging applications. For this reason, researchers study reaction kinetics in fixed beds despite internal mass transfer limitations and axial and radial temperature and concentration gradients. Fluidized bed hydrodynamics vary with powder properties (particle diameter, size distribution, density, sphericity), operating conditions (gas density, viscosity, temperature, pressure), reactor geometry (diameter, height, mass, grid geometry). The minimum fluidization velocity (U_mf) is a property that identifies the transition from the fixed bed regime to the fluidized bed regime and equals the gas velocity at which the upward drag force equals the weight of the powder. At the experimental scale, fluidized beds operate isothermally, solids are completely backmixed, and the gas phase is close to plug flow (). Here, we describe the relationship between powder properties and fluidization quality, list experimental techniques, describe recent applications, and gas phase hydrodynamics and uncertainties.     

Hydrodynamic characteristics of activated carbon in air- and water-fluidized beds

The hydrodynamic characteristics of small hydrophobic activated carbon particles were determined in air flowing through both fixed and fluidized bed layers and water flowing through an inverse fluidized bed. Based on experimental data the Ergun-equation was corrected. A new relationship is proposed to predict the pressure drop in a fixed bed with gas flowing by using the minimum fluidizing velocity (u _mf ) and particle terminal velocity (u _t ). Apparent density of oven-dried activated carbon increases with filling the internal pores by water. After the bed density reaches the density of water, the system switches from an inverse fluidized layer into the classical fluidized state. Finally, it has been demonstrated that the Reynolds number (Re _mf ) at u _mf associated with the original Archimedes number (Ar) for gas-solid fluidized system and the modified Ar numbers characterizing the inverse fluidized beds lie on identical curves.     

气-固微型流化床压降特性及最小流化速度的实验研究

在内径3~20 mm的4个气?固微型流化床中,分别考察了A类和B类两种类型颗粒的流化特性,同时研究了床几何结构、操作条件、物相性质等各因素对其最小流化速度的影响。结果表明,气?固微型流化床中的床层压降特性与颗粒类型密切相关,不同的流动状态下两种类型颗粒的流动特性存在显著地差异。在固定床阶段,与B类颗粒相比,A类颗粒与壁面间的相互作用更强,导致实验压降值偏离计算值更大;在流化床阶段,较大颗粒粒径和密度的B类颗粒在床层内表现出了更高的气泡聚并和破裂程度,加剧了颗粒间的碰撞,增加了能量损失,从而形成了较高的实验压降。气?固微型流化床的最小流化速度除了与操作条件和物相性质有关外,床内径与静态床层高度对其也会产生显著影响。随着床径减小及静态床高增加,最小流化速度逐渐增加。综合考察各影响的因素,提出了适用于实验考察范围内预测微型流化床最小流化速度的经验关联式。     

On the heat transfer mechanism in three phase fluidized beds

A two resistance model is proposed for the heat transfer between a coaxially mounted heater and a three phase fluidized bed. Effects of gas and liquid velocity and particle size on individual heat transfer resistances in the heater and in the fluidized bulk zones have been determined. The optimum bed porosity at which the maximum heat transfer coefficient occurred coincided with the bed porosity at which the boundary layer thickness around the heater attained a minimum value. The fluidized bed resistance attained its minimum value when the maximum heat transfer coefficient is achieved in two and three phase fluidized beds. The heat transfer in the zone adjacent to the healer is found to be the rate controlling step since the contribution of fluidized bed resistance was found to be less than 10% of the heater zone resistance in two and three phase fluidized beds. The heat transfer resistances in liquid and three-phase fluidized beds have been represented by a modified Stanton and Peclet numbers based on the heat transfer resistances in the heater zone and in the fluidized bulk zone in series.     

Heat transfer between gas fluidized beds of solid particles and the surfaces of immersed heat exchanger elements,part I

After some general remarks about fluidization, and a section on the hydrodynamic behaviour of fluidized beds, the mechanisms of heat transfer between the surfaces of heat exchanger elements and gas—solid fluidized beds are discussed in detail. A theoretical model, presented some years ago, is slightly modified and further developed to improve its applicability within a wide range of variables. The model makes use of some of the basic concepts of molecular kinetic theory as applied to solid particles in a fluidized bed. A complete derivation as well as all the parameters required to apply the model equations are given.     

离心流化床初始流化状态的研究(Ⅰ)基本理论

通过简化求解离心流化床连续介质模型基本控制方程,获得了初始流化速度、压力、空隙率、空隙气速、床层膨胀和床层压降的计算方程式。理论预报的临界流化速度和床层压降与实验结果吻合得很好。揭示了离心流化床随流速增大由表面逐层初始流化;流化后各半径处流化程度不同。理论分析还表明气体压缩性的影响随着床体转速的增大而增大。     

气固脉冲流化床流体力学特性的研究

在φ７０ｍｍ的流化床内，采用聚氯乙烯、玻璃珠和不规则天然刚玉等Ｂ类、Ｄ类颗粒，测定了０￣５．０Ｈｚ脉冲频率下气固流化床的基本流体力学特性，探讨了影响床层流化特性的一些主要因素，并根据实验数据对脉冲流化床的临界流化速度和临界流化压降的无因次准数式进行了关联。     

Convective solids transport in large diameter gas fluidized beds

It is demonstrated that the convective solids transport occurring in large diameter gas fluidized beds can be predicted quantitatively on the basis of measured properties of the bubble phase. Based on the fundamental findings of Rowe and co-workers [5], who have shown the solids mixing in gas fluidized beds for particle diameters greater than 100 μm to be caused solely by the action of rising bubbles, an equation has been derive from extensive measurements of the bubble development in a 1 m diam. fluidized bed of quartz sand which relates the convective solids mass flow due to solids transport in the bubble wakes to easily determinable parameters. The predictions of this relationship are found to bein good agreement with direct measurements of the convective solids transport carried out by Schmalfeld [21] on a pilot scale in a semicylindrical bed of 0.8 m diam.     

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

Wall-to-bed heat transfer in gas—liquid—solid fluidized beds with a cocurrent upflow was analyzed on the basis of a series thermal resistance model. The effective radial thermal conductivity and the apparent wall heat transfer coefficient were determined over a wide range of experimental conditions. The behavior of the effective thermal conductivity strongly depends on the flow mode for the three-phase fluidized bed, directly indicating the trend of the radial liquid mixing. The modified Peclet number for the radial thermal diffusivity takes on a minimum with respect to the liquid velocity in a manner similar to that in a liquid—solid fluidized bed, but the value of the modified Peclet number decreases significantly with gas velocity. The apparent wall heat transfer coefficient can be correlated well with a Colburn type equation which at zero gas velocity reduces to the same equation as that proposed for liquid—solid fluidization, as follows: j′_H = 0.137 Re′_l.g^?0.271     

Heat transfer in aggregative and particulate liquid-fluidized beds

Wall-to-bed heat transfer in liquid fluidized beds, particulately and aggregatively fluidized, was studied. Glass particles fluidized with water gave particulate fluidization and lead particles with water gave aggregative fluidization. Local heat transfer coefficients and bed temperature profiles were measured. Heat transfer coefficients were found to be strongly dependent on particle size and porosity and increased with increasing particle size, but were independent of the height of the heater surface from the grid. Any variations in local bed properties, such as porosity do not affect wall-to-bed heat transfer. The heat transfer coefficients show a characteristic, maximum at porosities near 0.7 for both systems. Bed temperature profiles deviate considerably from open-pipe values.A two-resistance model for the heat transfer resistance agrees well with the data. Bed resistance is modeled by a radial eddy diffusivity, which indicates the mixing effectiveness in the core of the bed. Glass beds (particulate) show a maximum mixing effectiveness at porosities near 0.7 and the mixing effectiveness increases with particle diameter. Lead beds (aggregative) show two maxima in mixing effectiveness, the first between porosities of 0.5 and 0.6, and the second between porosities of 0.7 and 0.8. Mixing is greatest at an intermediate particle size in the case of lead beds. In both systems the fraction of the total resistance in the bed core increases as porosity decreases towards packed bed conditions.     

Solids flow between interconnected shallow fluidized beds

Many industrial processes utilising two or more fluidized beds are connected such that one bed flows through an opening into the other. By operating regions of the two beds at different superficial gas velocities, a bulk density difference can be created between them to effect a solids transfer through a submerged opening. The resultant flow of solids between fluidized beds of sand (194 μm and 224 μm) is modelled on the basis of a liquid analogy and force-momentum balances. The correct functional dependency of the solids flow rate is predicted for a range of gas velocities; experimental results are 70–90% of the predicted values. The prediction of the solids flow rate for changes in the size of the openings between the beds is less satisfactory, possibly because of the return flow of solids which is associated with the forward flow.