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     

Wall-to-bed heat transfer in three-phase fluidized beds of low density particles

Bed-to-wall heat transfer was measured in three-phase fluidized beds under conditions typical of biochemical process applications. The thermal resistance of the fluidized bed, which was significant in the absence of gas, became negligible when gas was introduced. Decreasing the particle density at constant gas and liquid velocity increased the bed-to-wall heat transfer coefficient. Previously published heat transfer correlations were used and gave poor predictions of our data. A new correlation was developed which predicted very well all the heat transfer coefficient results in this paper.     

Prediction of optimum operating conditions of liquid fluidized bed systems

An important advantage of fluidized beds applied in various chemical and physical operations is the high rate of heat transfer between the bed and the heat transfer surfaces. However, the design of these systems for optimum conditions remains uncertain and essentially empirical. In this study a model for bed voidage and a model for heat transfer are presented which can be used to predict the maximum attainable heat transfer coefficient and the corresponding bed voidage of liquid fluidized bed systems with good accuracy.     

Radiative heat transfer in circulating fluidized bed furnaces

Three methods of estimating the effective emissivity of a gas-particle suspension are compared and the radiative heat transfer coefficient of an isothermal suspension is defined. Heat flux measurements obtained from circulating fluidized bed combustors are examined. Radiation from a particle suspension with core temperature dominates the radiative heat transfer in the upper part of the furnace, where the particle density is low and no substantial particle boundary layers are formed. Over the lower parts of the heat transfer surfaces, where significant thermal and particle boundary layers are present, the radiative heat flux is dominated by emission from the relatively low temperature particle layer in the vicinity of the heat receiving surface.     

流化床浸没换热管传热研究进展

论述了前人对流化床与浸没换热管间传热规律的理解和认识,介绍了常用的传热模型及其实用条件,总结了近年来在实验研究等方面所取得的进展。     

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.     

循环流化床换热器中液固二相流的数值模拟

在循环流化床换热器的流体中加入固体粒子,可以对边界层有扰动作用,加快换热器中的传质与传热.对流化床换热器中的液固二相进行数值模拟,分别讨论了固体粒子对液体动量方程、k-ε方程及能量方程的影响,在单液相方程的基础上进行修正,建立了相应的液固二相流控制方程,确定了物理模型及边界条件.利用FLUENT进行数值计算,分别讨论了...     

The measurement of instantaneous local heat transfer coefficients in a circulating fluidized bed

Instantaneous and time-averaged local bed-to-wall heat transfer coefficients were measured in a 9.3 m tall, 152 mm ID cold model circulating fluidized bed riser at three different heights for 171 μm Ottawa sand at a superficial gas velocity of 7 m/s, and for solids circulation fluxes up to about 70 kg/m².s. All data were obtained with an instantaneous heat transfer probe consisting of a thin platinum film deposited on a 1 cm² piece of glass protected by a thin plastic film. Instantaneous heat transfer coefficients in the riser showed sudden and dramatic peaks caused by strands or sheets of particles sweeping past the probe. Consistent with previous work, time-averaged coefficients varied nearly linearly with suspension density. The heat transfer coefficient decreased from the bottom to the middle of the column, and then increased near the top due to an increase in suspension density for the exit geometry employed.     

Comparison of heat transfer models in DEM-CFD simulations of fluidized beds with an immersed probe

The basic mechanisms governing the process of surface-to-bed heat transfer in fluidized beds and their relative importance have not been fully characterized yet, mainly owing to the lack of reliable data at the particle scale. Numerical simulations based on the discrete element method may prove successful in predicting the evolution of the fluid and particles' temperature fields. In the present work, microscopic models of the fluid-particle, particle-particle, fluid-surface and particle-surface heat transfer have been implemented in a DEM-CFD hydrodynamic code. Details are discussed on the methodology adopted to include immersed objects in the computational domain. Thus, three approaches to represent particle-particle heat transfer are analysed and compared against experimental values, taken from the literature, of the heat transfer coefficient between a hot fluidized bed and a spherical probe. Unfortunately, some parameters appearing in the formulations are difficult to determine, so reasonable estimates are calculated and used in the simulations. Under conditions similar to the experiments, simulation predictions of the heat transfer coefficient range from 43 to 340 W/(m² K) depending on the model used, while the experimental values are located around 160 W/(m² K). The variability of these numerical results confirms their sensitivity to the particle-particle mechanism considered. Finally, it is shown that using the model that produces results in agreement with experiments the heat flows due to the particle convective and the fluid convective transfer are of comparable importance.     

水平液固循环流化床换热器传热性能评价

对管内插入Kenics静态混合器的水平液固循环流化床换热器进行实验研究,实验考察了静态混合器扭率、静态混合器安装方式、液体流速、颗粒体积分数对传热性能和流阻性能的影响,并运用综合强化传热性能评价指标（PEC）对其进行分析。实验发现,传热性能和阻力系数均随扭率增加而减小。当雷诺数在10000~45000之间时,扭率为1.5、2、2.5、3.5的Kenics静态混合器的PEC指标均大于1,说明了水平流化床换热器插入Kenics静态混合器能够改善传热。在雷诺数达到25000左右、Kenics静态混合器扭率为2.5、颗粒体积分数为4%时,水平流化床换热器的PEC指标最高达到1.18。当两个扭率均为2.5的Kenics静态混合器安装间距为200mm时,水平流化床换热器的PEC指标最高。     

振动流化床与浸没水平管平均传热特性理论分析与实验研究

在二维流化床(240mm×80mm)中,以平均粒径dp为1.83mm的玻璃珠为物料,研究了振动流化床与浸没水平管间传热规律;考察了流化数、振动频率、床高、水平管管径等因素对平均传热系数的影响。采用自制探头对浸没加热管束和振动流化床层间平均传热系数进行实验测定,利用颗粒团模型,建立了振动流化床层与浸没水平管间平均传热模型,并对平均传热系数的理论预测值与实验测定值进行了比较。结果表明:计算值与实验值吻合较好,误差在±15%范围内。在较高流化数、低振动频率时,实验值处于理论值上方;随着振动频率、管径增大,平均传热系数实验值逐渐趋于理论预测值甚至低于理论预测值。结果可为带浸没水平管的振动流化床设计和研究提供参考。     

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 between very shallow fluidized beds and an immersed horizontal tube

A new correlation is proposed for the heat transfer coefficient between an immersed horizontal tube and very shallow fluidized beds (static bed heights of 10-40 mm). The correlation is based upon experimental data obtained in this work for a horizontal tube with an outside diameter of 13.1 mm, immersed in beds of spherical alumina particles with mean particle sizes of 335-1261 microns. The maximum bed pressure drop was 92.5 mm water. The effects of tube elevation, static bed height and distributor design were investigated. Nine different distributors were used, with maximum pressure drops ranging from 3 to 800 mm water and open areas from 2.2 to 36%. A comparison between the proposed correlation and data reported in the literature showed an agreement of approximately ±10%.     

Heat transfer within dynamically structured bubbling fluidized beds subject to vibration: A two-fluid modeling study

Bubbling fluidized beds are often used to achieve a uniform particle temperature distribution in industrial processes involving gas and particles. However, the chaotic bubble dynamics pose significant challenges in scale-up. Recent work (Guo et al., 2021, PNAS 118, e2108647118) has shown that using vibration can structure the bubbling pattern to a highly predictable manner with the characteristic bubble properties independent of system width, opening opportunities to address key issues associated with conventional bubbling fluidized beds. Herein, using two-fluid modeling simulations, we studied heat transfer characteristics within the dynamically structured bubbling fluidized bed and compared to unstructured bubbling fluidized beds and packed beds. Simulations show that the structured bubbling fluidized bed can achieve the most uniform particle temperature distribution because it can achieve the best particle mixing while maintaining a global heat transfer coefficient similar to that of a freely bubbling fluidized bed.     

垂直管内三相流化床沸腾传热特性

研究了三相流化床沸腾传热的特性和影响传热系数的诸因素。在传热过程中，由于固体粒子的存在，强化了传热。以玻璃球粒子为固相的三相流化床沸腾传热系数，是相同条件下汽液两相流沸腾传热的二倍。以铜粒子为固相的三相流化床沸腾传热系数，是相同条件下汽液两相流沸腾传热系数的３倍。     

Modeling of grid region heat transfer in a shallow gas-solid fluidized bed

Heat transfer coefficients between the bed and an immersed horizontal tube in the grid-region of a shallow gas-solid fluidized bed were experimentally and theoretically studied. Experiments were carried out in two fluidized bed columns with inside diameters of 88 and 137 mm, respectively. The fluidized particles tested were sand, limestone and glass beads. Experimental parameters also included particle size, superficial gas velocity, tube diameter, tube location and distributor design. A mechanistic model considering the contributions of jet phase, emulsion phase and dead phase was derived for estimating the grid-region heat transfer coefficients. Most of the model predictions were found to be within 25% of the experimentally observed data.     

Voidage profiles in magnetically fluidized beds

Voidage profiles in a fluidized bed of iron particles (230 μm) were investigated under the influence of an external uniform axial magnetic field. Passing a direct current through five solenoids generated uniform magnetic field. The five solenoids were arranged elaborately to get larger uniform magnetic space than that generated by Helmholtz electromagnet coils. A sensitive optical measuring system, based on detection of light reflected by particles, was used to measure local voidage in both dense and dilute phases.

Local voidage was measured as a function of superficial fluidizing air velocity, magnetic field intensity and the position in the bed. At a given magnetic field intensity and at the same position in the bed, the voidage was constant for a low air velocity range (in a fixed bed). The local voidage changed irregularly with increasing air velocity for an intermediate air velocity range (in a magnetically stabilized fluidized bed, MSFB). The local voidage changed linearly with increasing air velocity for a slightly high air velocity range (in a magnetized bubbling fluidized bed, MBFB). A general correlation was developed to predict the local solids fraction at the arbitrary position in the bed: (1−)=(1−)_c+[(1−)_w−(1−)_c](r/R)^B where (1−), (1−)_c and (1−)_w represent the local solids fraction at arbitrary position in the bed, at the bed center and on the bed wall; and B, (1−)_c and (1−)_w are the function of air velocity, distance from the distributor and magnetic field intensity.     

振动流化床浸没水平管传热特性研究

为了深入研究振动流化床浸没水平管的传热特性,分别以沙子和玉米细颗粒作为实验物料,用水平探头测定了振动流化床中这2种床层颗粒与浸没水平管间的传热系数,分析了操作气速、振动频率、空气进口温度等因素对传热过程的影响。结果表明:在低气速下,振动是影响振动流化床中传热的主要因素,振动的引入可以明显改善流化作用,可以在低气速下得到较好的传热效果,同时达到节能的效果。通过分析实验结果,建立了振动流化床的传热关联式,模型计算值与实测值能较好吻合。研究结果可为干燥膏状物料时确定适宜的操作参数提供参考。     

A study of local liquid/solid mass transfer in packed beds under trickling and induced pulsing flow

Induced pulsing flow (by cyclic liquid feeding) in packed beds, operated in the trickling flow regime, is studied as a method of overall improvement of catalytic reactor operation. In this paper results are reported of experiments aimed at determining local and global liquid/solid mass transfer rates, mainly for the so-called fast mode of ON-OFF periodic liquid feeding, with frequencies of order 0.1 Hz. Such mass transfer data for the fast mode of induced pulsing are not available in the literature. Uniform 6 mm glass spheres and alumina cylindrical extrudates, of 1.5 mm diameter and a narrow distribution of lengths, are employed in the tests. For completeness, results are also reported for single-phase (liquid) and trickling flow through the same packed beds. A well-known electrochemical technique is employed to measure instantaneous local mass transfer coefficients by means of quite a few probes distributed throughout the bed. The hydrodynamic characteristics under the above conditions, reported in companion papers, are helpful in interpreting the new mass transfer data.There is a wide spread of the time-averaged local mass transfer rates, in all cases tested, apparently due to packing and flow non-uniformities. This spread is much smaller in the case of packed uniform spheres. In general, the benefits of cyclic liquid feeding are more evident in the packed bed of spheres than in that of cylindrical extrudates; for instance, with increasing mean liquid rate, induced pulsing tends to reduce the spread of local mass transfer coefficients, which suggests that more uniform fluids distribution is promoted. The imposed liquid pulses are reflected in the observed periodic variation of local mass transfer coefficients; the latter appear to decay along the bed in the same manner as the liquid pulses. Other trends of local mass transfer rates are identified and discussed in relation to measured variation of liquid holdup, under the same conditions. For packed spheres, the measured global mass transfer rates are in fair agreement with literature correlations obtained for the trickling flow regime, unlike the case of packed extrudates where significant deviation is observed.