Heat transfer in a fluidized bed. Part I. The effect of thermal driving force on the heat transfer coefficient

The influence of the thermal driving force on the coefficient for heat exchange between a fluidized bed (diam. 30 cm) and part of a submerged vertical cylinder (diam. 7 cm) is described. In the experiments both negative and positive driving forces have been applied (the heat flow being considered positive if directed towards the bed).

Beds of glass beads, quartz sand and silica-alumina catalyst powders have been used to cover a range of particle size and density. For powders exhibiting dense phase expansion, heat transfer coefficients are found which are significantly affected by the driving force. At driving forces of about − 70°C heat transfer coefficients in a 40 μm catalyst bed were only half of those at driving forces approaching zero.

The behaviour of a transparent ‘two-dimensional’ fluidized bed showed that this might be the result of a reduction of solids mobility in the vicinity of the relatively cold surface. In an attempt to explain this reduction three mechanisms were considered; of these the decrease of the dense phase expansion due to a temperature gradient proved to be the most important one.

Powders not exhibiting dense phase expansion show heat transfer coefficients which are only slightly affected by the driving force, the differences resulting entirely from changes in physical properties with temperature.     

A phenomenological model for heat transfer in freeboard of fluidized beds

A phenomenological model was developed to predict heat transfer to tubes located in the freeboard region of gas fluidized beds. The model is concerned with the conductive/convective mechanism of heat transfer. For high temperature applications, an additional contribution by thermal radiation would need to be incorporated. The model considers that the tube surface experiences alternating contact with a dense emulsion phase and a lean void phase. Contributions by dense and lean phases are represented by transient conduction and convection mechanisms, respectively. Particletube contact information was obtained experimentally for a wide range of operating conditions at room temperature and pressure. Predictions of the model were compared with measured heat transfer coefficients. Over a 20-fold range in magnitudes of heat transfer coefficients, the model successfully predicted the measured values with an average deviation of 44 percent.     

Surface-to-suspension heat transfer model in lean gas–solid freeboard flow

Heat transfer in dense fluidized beds have been extensively studied. However, there is not much detailed information about the mechanism of surface-to-suspension heat transfer in the freeboard region. In the present work, a newly designed heating plate was used to measure the plate-surface-to-particle-suspension heat transfer coefficients in the freeboard.The experimental unit consisted of a 30 cm i.d. fluidized bed reactor packed with fluidized catalytic particles of mean particle size 90 μm. Three types of plate orientations were used to test directional effects of surface on heat transfer rate. Height of the freeboard was 171 cm, and the superficial gas velocity was varied from 0.28 to 0.64 m/s. Local solids concentrations in the freeboard were also obtained by a nozzle-type sampling probe. Data on axial distribution of solids concentration were used to find out the solids kinematics in the freeboard region. Finally, a surface-to-suspension heat transfer model was developed to elucidate the surface to particle heat transfer mechanism in this lean phase system.The model is based on the transient gas-convective heating of single particles when sliding over the heating plate and the assumption of instantaneous attachment–detachment equilibrium between particles and the plate surface.     

Particle‐scale simulation of the flow and heat transfer behaviors in fluidized bed with immersed tube

A kind of new modified computational fluid dynamics‐discrete element method (CFD‐DEM) method was founded by combining CFD based on unstructured mesh and DEM. The turbulent dense gas–solid two phase flow and the heat transfer in the equipment with complex geometry can be simulated by the programs based on the new method when the k‐ε turbulence model and the multiway coupling heat transfer model among particles, walls and gas were employed. The new CFD‐DEM coupling method that combining k‐ε turbulence model and heat transfer model, was employed to simulate the flow and the heat transfer behaviors in the fluidized bed with an immersed tube. The microscale mechanism of heat transfer in the fluidized bed was explored by the simulation results and the critical factors that influence the heat transfer between the tube and the bed were discussed. The profiles of average solids fraction and heat transfer coefficient between gas‐tube and particle‐tube around the tube were obtained and the influences of fluidization parameters such as gas velocity and particle diameter on the transfer coefficient were explored by simulations. The computational results agree well with the experiment, which shows that the new CFD‐DEM method is feasible and accurate for the simulation of complex gas–solid flow with heat transfer. And this will improve the farther simulation study of the gas–solid two phase flow with chemical reactions in the fluidized bed. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Heat transfer between an isolated bubble and the dense phase in a fluidized bed

Heat transfer between the bubble and dense phases of a bubbling fluidized bed plays a very important role in the system performance, especially for applications involving solids drying and gas‐phase combustion. However, very few experimental data are available on this subject in the literature. An experimental and modelling investigation on the heat transfer behaviour of isolated bubbles injected into an incipiently fluidized bed is reported in this paper. A new single‐thermocouple technique was developed to measure the heat transfer coefficient. The effects of bed particle type and size, and bubble size on the heat transfer coefficient were examined. The heat transfer coefficient was found to exhibit a maximum as the bubble size increased in the bubble size range investigated. The bed particle size had a comparatively small effect on the heat transfer coefficient. A simple mathematical model was developed which provides good agreement with experimental data.     

竖直管气固鼓泡流化床传热机理的CPFD模拟

针对细颗粒气固鼓泡流化床中床料与竖直传热管壁面间的传热行为,在前期实验的基础上,采用计算颗粒流体力学(CPFD)方法从颗粒在传热壁面更新的角度,深入分析了传热特性与壁面气固流动行为之间的关联性。结果表明,模拟得到的传热管壁面颗粒更新通量和基于颗粒团更新模型的颗粒团平均停留时间均能很好解释实验测得的传热系数变化规律,这证实颗粒团更新是影响传热过程的控制性因素。模拟还发现随加热管从床层中心向边壁的移动,加热管周向方向上颗粒更新通量和传热系数的不均匀性都呈增大趋势。随着表观气速的增大,气泡行为导致床层颗粒内循环流率增大,这是导致颗粒团在加热管壁面上的更新频率增大以及床层与壁面间传热系数增大的根源。     

Modeling of radiative heat transfer between high-temperature fluidized beds and immersed walls

This paper presents a theoretical model for predicting the radiative heat transfer rate between high-temperature fluidized bed and immersed walls, which can be used upon the base of emulsion packet model of heat transfer in bubbling fluidized bed. The model adopted radiative flux computation method to calculate radiative heat transfer between fluidized disperse phase contacting to the wall and immersed walls, in which the absorption and back-scattering coefficients was obtained from the reflectivity and the absorptivity of a layer of disperse media of a single particle thickness. In such a model, many factors, such as particle size, particle emissivity, bed void fraction, fluidized bed and wall temperatures, and so on, are included theoretically to calculate radiative heat transfer between immersed walls and fluidized beds. As a result, the model results provide a reasonable explanation of the experimental observation of that radiative heat transfer rate in fluidized beds increases with the increases of the superficial fluidizing velocity. In addition, the modeling prediction for the trend of radiative heat transfer rate between the fluidized bed and its immersed surface on the variation of wall temperature conforms to the classical experimental trend.     

Heat transfer mechanisms in gas fluidized beds. Part 1: Maximum heat transfer coefficients

This contribution presents the prediction of maximum heat transfer coefficients in bubbling fluidized beds, which takes into account thermal and fluid-dynamic properties of particulate material and fluidizing agent. The analysis suggests that heat transfer between heating or cooling surfaces and bubbling fluidized beds consists mainly in a particular manifestation of convective heat transfer. Another feature is an appropriate modelling of the particle convective component leading to a two-phase Prandtl number.     

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.     

A Practical Method to Estimate the Bed Height of a Fluidized Bed of Fine Particles

Knowledge of both dense bed expansion and freeboard solids inventory are required for the determination of bed height in fluidized beds of fine particles, e.g., Fluidized Catalytic Cracking (FCC) catalysts. A more accurate estimation of the solids inventory in the freeboard is achieved based on a modified model for the freeboard particle concentration profile. Using the experimentally determined dense bed expansion and the modified freeboard model, a more practical method with improved accuracy is provided to determine the bed height both in laboratory and industrial fluidized beds of FCC particles. The bed height in a fluidized bed can exhibit different trends as the superficial gas velocity increases, depending on the different characteristics of the dense bed expansion and solids entrainment in the freeboard. The factors that influence the bed height are discussed, showing the complexity of bed height and demonstrating that it is not realistic to determine the bed height by a generalized model that can accurately predict the dense bed expansion and freeboard solids inventory simultaneously. Moreover, a method to determine the bed height, based on axial pressure fluctuation profiles, is proposed in this study for laboratory fluidized beds, which provides improved accuracy compared to observation alone or determining the turning points in the axial pressure profiles, especially in high‐velocity fluidized beds.     

Heat transfer efficiency in a fliuidized bed

The equilibrium stage concept used in staged contacting operations was adopted as a measure of heat transfer efficiency for a fluidized bed. A simple model was developed which postulates that solids flow through the bed can be by perfect mixing, plug flow and short-circuiting. Efficiencies were determined experimentally in a 150 mm diameter fluidized bed with air as the fluidizing medium and sand as the solid. Heat transfer efficiencies greater than 100% were obtained indicating that small diameter, low aspect ratio fluidized beds do not behave as perfect mixers. The results indicate that heat transfer measurements can be used to develop information on solids flow behavior.     

Heat transfer to the ceiling of the riser of a circulating fluidized bed

Very little information on the heat transfer to the ceiling of a circulating fluidized bed (CFB) boiler is available in the published literature though it constitutes a significant part of the furnace heat absorption. So, to explore this less-known heat transfer process a series of experiments were conducted at four different superficial gas velocities and three external solids circulation rates in a CFB pilot plant with a riser having a height of 5 m and a cross section of . The experimental results suggest that both solids circulation rates and superficial gas velocities had a significant influence on the local heat transfer to the ceiling close to the riser exit to the gas solids separator. However, on the ceiling, opposite of the exit, solids circulation rates and superficial gas velocities had only a minor influence on the local heat transfer coefficients.     

Eulerian–Eulerian simulation of heat transfer between a gas–solid fluidized bed and an immersed tube-bank with horizontal tubes

A two dimensional Eulerian–Eulerian simulation of tube-to-bed heat transfer is carried out for a cold gas fluidized bed with immersed horizontal tubes. The horizontal tubes are modelled as obstacles with square cross section in the numerical model. Simulations are performed for two gas velocities exceeding the minimum fluidisation velocity by 0.2 and 0.6 m/s and two operating pressures of 0.1 and 1.6 MPa. Local instantaneous and time averaged heat transfer coefficients are monitored at four different positions around the tube and compared against experimental data reported in literature. The effect of constitutive equations for the solid phase thermal conductivity on heat transfer is investigated and a fundamental approach to modelling the solid phase thermal conductivity is implemented in the present work. Significant improvements in the agreement between the predicted and measured local instantaneous heat transfer coefficients are observed in the present study as compared to the previous works in which the local instantaneous heat transfer coefficients were overpredicted. The local time averaged heat transfer coefficients are within 20% of the measured values at the atmospheric pressure. In contrast, underprediction of the time averaged heat transfer coefficient is observed at the higher pressure.     

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.     

The clustered dense phase model for group A fluidization: I. Dense phase hydrodynamics

A new hydrodynamic model is proposed to represent the gas flow in the dense phase of fluidized Group A powders. The model views that the particles form clusters under the influence of inter-particle forces, giving rise to the formation of a heterogeneous void structure consisting of clusters of particles and interstitial cavities. The model contains two parameters, one representing the intrinsic void structure of the clusters and the other representing their size.The model predictions have been tested against reported experimental dense phase hydrodynamic data of Group A powders, both in bubble-free beds and in freely bubbling beds. The results show 2-3 particle clusters in bubble-free beds, but considerably larger clusters, containing 100 particles or so, in the dense phase of freely bubbling beds. The model also provides predictions for bubble through-flow, bubble splitting from below, dense-phase solids circulation, and interstitial gas bypassing in freely bubbling beds.     

流化床内自由移动石墨球表面的传热系数

密相区内自由移动的煤颗粒表面传热系数是循环流化床锅炉设计和运行的重要参数。利用石墨球模拟煤颗粒,在小型流化床实验台上对由粒度较小的石英砂颗粒组成的密相区内自由移动的石墨球表面传热系数进行了测量。测量结果显示,随着流化风速的增加,石墨球表面传热系数首先升高,当流化风速达到某一临界值时,继续增大流化风速,传热系数将保持不变,从传热的角度证明了流化床内煤颗粒基本停留在乳化相内。在多数情况下,石墨球表面传热系数随床料粒度的增大而减小。而在较低流化风速的情况下,随着床料粒度的增大,石墨球表面传热系数呈先下降后升高的趋势。当流化风速和床料粒径保持不变时,石墨球表面传热系数随着石墨球直径的增大而减小,且下降的趋势随石墨球直径的增大而减弱。而随着床层高度的增加,石墨球表面传热系数将会略有 升高。     

Heat transfer in a horizontal rotary drum reactor

The heating of carbohydrates (particle size 15 – 100 μm) has been studied in an industrial scale horizontal drum reactor. The drum was 9.0 m long and had a diameter of 0.6 m. Strips were mounted on the inside wall and the drum was heated externally by steam. Solid movement in the drum was observed in a transparent experimental segment of the drum. From these experiments it became clear that the heat transfer between wall and solids may be described by the penetration model. In separate experiments the product of the effective thermal conductivity of the bulk material and its heat capacity has been determined. The theoretical heat transfer coefficients agree quite well with the experimental values verified by heat transfer measurements in the large-scale drum.The heat transfer coefficients between wall and gas phase and between bulk solid and gas phase have also been measured. The magnitude of the heat transfer coefficient between wall and gas phase indicates a natural convection mechanism.     

Numerical analysis of heat transfer mechanisms to pneumatically conveyed dense phase flow

Mass and energy balances are required in power generation, chemical, pharmaceutical, food and commodity transfer processes in order to achieve efficient utilization of energy and raw materials. There is a need for accurate, reliable, on-line, continuous and non-invasive measurement of solids' mass flow rate in many industrial processes mentioned above. Thermal flowmeters, in theory, provide a true indication of the mass flow of solids in pneumatic conveying pipelines.A complicated heat transfer between a pipe wall and a gas-solid flow in a conveying pipeline inevitably takes place in a thermal solids' mass flow measurement process. A study of heat transfer mechanisms to pneumatically conveyed gas-solid dense phase flow as a means to mass flow rate measurement has been conducted experimentally and numerically to evaluate the heat transfer coefficient between the hot wall and the gas-solid dense phase flow. The prediction of the heat transfer coefficient is compared with the experimental findings. It was found that the heat transfer coefficient between the pipe wall and the gas-solid dense flow is a function of solids loading ratio. Increasing the gas stream velocity significantly augments the heat transfer between the hot wall and the gas-solid dense phase flow.     

Modelling of fluidized bed reactors—VI(b): The nonisothermal bed with stochastic bubbles

Two stochastic nonisothermal fluidized bed reactor models are developed to investigate the significance of the fluctuating nature of fluidized beds on reactor performance. Fluctuating bubble size distributions within the bed are simulated by stochastic mass and heat transfer coefficients. Results of hybrid computer simulations indicate that randomness can enhance or inhibit reactor performance depending on the operating parameters of the nonisothermal model. Bubble and dense phase concentration statistics are fairly similar to those of corresponding isothermal models because dense phase temperatures are relatively insensitive to transfer coefficient fluctuations due to the high dense phase beat capacity. However, the corresponding stochastic isothermal models predict decreases in conversion with increasing variance in the transfer coefficients for all operating conditions. Results indicate that a deterministic system with two stable steady states may have fewer stable random stationary solutions. The existence of the stationary states is dependent on fluctuation frequency and variance of the transfer coefficients.     

在加热阶段滚塑模具内表面传热系数的两种研究方法

提出了获得电加热滚塑模具内表面传热系数的两种研究方法，这两种方法适用于模内粉料开始熔融前的加热阶段。第一种方法是首先在4种情形下测量该滚塑模具的外表面温度和模内温度，然后根据能量守恒原理建立一个传热模型，并通过该模型将这些实测的温度值转换为在这4种情形下模具的内表面传热系数。第二种方法是将实际的滚塑模具等效地简化为一个二维圆筒，将模内空气当成主相流体，粉料当成第二相流体，通过FLUENT软件的多相流模块中的Mixture模型进行仿真计算以得到模具内表面的传热系数。结果表明，这两种方法所得的结果在其中的3种情形下都吻合得很好。随着模内粉料的体积百分比的增加，模具的内表面传热系数先是快速增大，然后增大的速率变慢，在达到最大值61.2 W/（m²·K）后开始减小。当粉料的体积百分比不在58 %~74 %的范围内，由第二种方法仿真所得的模具内表面传热系数的相对误差不超过10 %。