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.     

Computational study of heat transfer in a bubbling fluidized bed with a horizontal tube

A combined approach of discrete particle simulation and computational fluid dynamics is used to study the heat transfer in a fluidized bed with a horizontal tube. The approach is first validated through the good agreement between the predicted distribution and magnitude of local heat transfer coefficient with those measured. Then, the effects of inlet fluid superficial velocity, tube temperature and main particle properties such as particle thermal conductivity and Young's modulus are investigated and explained mechanistically. The relative importance of various heat transfer mechanisms is analyzed. The convection is found to be an important heat transfer mode for all the studied conditions. A large convective heat flux corresponds to a large local porosity around the tube, and a large conductive heat flux corresponds to a large number of particle contacts with the tube. The heat transfer is enhanced by the increase of particle thermal conductivity while it is little affected by Young's modulus. Radiative heat transfer becomes increasingly important as the tube temperature is increased. The results are useful for temperature control and structural design of fluidized beds. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

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。     

Characteristics of a Pressurized Gas‐Solid Magnetically Fluidized Bed

The hydrodynamic, heat and mass transfer characteristics of a pressurized co‐current gas‐solid magnetically fluidized bed (MFB) were systematically investigated considering major influence factors, such as magnetic field strength, superficial gas velocity, and operating pressure. It was shown that this pressurized gas‐solid MFB has the advantages of a wider operation range of the superficial gas velocity under bubble‐free particulate fluidization, a larger bed voidage with smaller pressure drop across the bed, and larger heat transfer efficiency, compared with a conventional fluidized bed. Moreover, the minimum bubbling velocity, gas‐solid mass, and heat transfer coefficients were correlated at high accuracy within the investigated range of operating conditions.     

EVALUATION OF CONDUCTIVE HEAT TRANSFER MECHANISMS BETWEEN AN IMMERSED SURFACE AND THE ADJACENT LAYER OF PARTICLES IN BUBBLING FLUIDIZED BEDS

The evaluation of the heat transfer coefficient h_wp between a heat exchanging surface immersed in a gas fluidized bed and the adjacent layer of dense phase particles is analyzed in this contribution. Gas convective and radiant effects are not included in the present analysis.

The inclusion of h_wp, or an equivalent formation, in mechanistic models describing heat transfer has been necessary because the sudden voidage variation close to the immersed wall restrains significantly the heat transfer rate. However, there is not at present a widely accepted expression to evaluate h_wp.

A precise formulation for h_wp accounting for transient conduction inside spherical particles, the Smoluchowski effect, the concentration of particles in the adjacent layer (N_p) and an effective separation gap (l₀) is developed here.

Although N_p can be estimated, in principle, from experimental evidence in packed beds, and it is reasonably expected that l₀ = 0, the analysis of experimental heat transfer rates in moving beds, packed beds, and bubbling fluidized beds indicate that values of h_wp are, in general, smaller than expected from these assumptions. Appropriate values of l₀ and N_p are then stimated by fitting the experimental data.

The probable effect of surface asperities is also discussed by analyzing a simplified geometrical model. It is concluded that the parameter l₀ can be also effective to account for particle roughness, independently of thermal properties.     

Thermal Blending Time Associated With a Charge of Hot Particles Added to a Fluidized Bed of Uniform Temperature

The process of heat transfer between particles in a fluidized bed is important for many industrial fluidized bed processes. The problem associated with studying this phenomenon is the confounding effect of particle mixing on heat transfer. The work described here was undertaken to describe the process in which heat is added to a fluid bed process by adding a hot charge of particles to a colder fluidized bed. The rate of heat transfer in this instance can have a significant impact on performance of the fluid bed process, depending upon its application. Both the method of analysis and the results of the work are applicable to other fluidized bed processes, particularly those associated with the thermal upgrading of heavy oil. The method of data analysis, based on binomial statistics, allowed useful data to be extracted from a complex system without the need for a large number of experiments. The analysis also allowed for some assessment of the relative importance of mixing and heat transfer, which has not been possible with other approaches. The results of the experiments were further explored using a bubbling bed model that incorporated both heat transfer and solids mixing. This allowed for the formation of a conceptual model, validated by the experimentation, that explains the relative functions of the two transfer processes in the dispersion of heat from a hot charge of particles to the bulk of a fluidized bed.     

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.     

HEAT TRANSFER CHARACTERISTICS OF THREE PHASE FLUIDIZED BEDS

Heat transfer characteristics of two (liquid-gas, liquid-solid) and three (liquid-gas-solid) phase fluidized beds have been studied in a 15.2 cm-ID column fitted with an axially mounted cylindrical healer. Effects of gas velocity (0-12 cm/s). liquid velocity (0-16cm/s), particle size (1.7-8.0 mm) and liquid viscosity (0.001-0.039 Pa s) on heat transfer coefficient were determined. The heat transfer coefficient increased with fluid velocities and particle size and it decreased with liquid viscosity in two and three phase fluidized beds. The bed porosity at which the maximum heat transfer occurred decreased with particle size but increased with liquid viscosity. The coefficient were correlated in terms of experimental variables. Modified Nusselt number from the present and previous studies has been correlated with modified Prandtl and Reynolds numbers.     

柱形流化床传热特性的数值模拟

对Shedid等搭建的圆柱体流化床采用欧拉?欧拉法进行三维数值模拟,考察了颗粒球形度、表观进气速度和床料初始堆积高度对流化床内垂直加热壁面与流动床料之间对流传热特性的影响,采用有效导热系数分别计算气相和固相的对流传热系数。结果表明,随表观进气速度增大,流化床内颗粒物料湍流运动加剧,加热壁面平均温度和流体平均温度下降,壁面流体间传热平均温度差减小,壁面流体间对流传热系数增大;随初始床料高度增加,流化床内颗粒与加热壁面的接触面积增大,导致固相平均对流传热系数增大。     

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 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.     

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.     

Convective Heat and Mass Transfer Modeling in Gas‐Fluidized Beds

This review examines selected mechanistic and empirical models reported in the literature to predict convective heat and mass transfer coefficients in gas‐fluidized beds. The role of hydrodynamics in heat and mass transfer is briefly outlined before embarking on the modeling approaches. Both bed to wall and interphase heat transfer, are considered. In bed to wall heat transfer, the main focus of the review is the modeling of particle convective components, based on surface renewal. The concepts of transient and local heat transfer models are also discussed briefly. In the case of mass transfer, only interphase transfer is considered. Emphasis is placed on models based on combustion where mass transfer is seen to occur from a few active particles contained in a fluidized bed of inert particles.     

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 in gas fluidized beds. Part 2: Dependence of heat transfer on gas velocity

Part 1 of this report investigated the effects of system properties on heat transfer between heating or cooling surfaces and bubbling fluidized beds. This investigation produced six correlations, which define the respective maximum heat transfer. The present contribution shows that the heat transfer depends on superficial gas velocity, with the relationship expressed in terms of a dimensionless excess gas velocity which defines the ratio of effective thermal conductivity by particle mixing to that of the fluidizing agent. Simple procedures for a reliable prediction of heat transfer in bubbling fluidized beds are presented.     

Comparison of fibre optical measurements and discrete element simulations for the study of granulation in a spout fluidized bed

Spout fluidized beds are frequently used for the production of granules or particles through granulation. The products find application in a large variety of applications, for example detergents, fertilizers, pharmaceuticals and food. Spout fluidized beds have a number of advantageous properties, such as a high mobility of the particles, which prevents undesired agglomeration and yields excellent heat transfer properties.A discrete element model is used describing the dynamics of the continuous gas phase and the discrete droplets and particles. For each element momentum balances are solved. The momentum transfer among each of the three phases is described in detail at the level of individual elements.The results from the discrete element model simulations are compared with local measurements of time time-averaged particle volume fractions as well as particle velocities by using a novel fibre optical probe in a fluidized bed of 400 mm I.D. Simulations and experiments were carried out for three different cases using Geldart B type aluminium oxide particles: a freely bubbling fluidized bed; a spout fluidized bed without the presence of droplets and a spout fluidized bed with the presence of droplets. It is found that the experimental and numerical results agree in a qualitative manner.It is demonstrated how the discrete element model can be used to obtain information about the interaction of the discrete phases, i.e. the growth zone in a spout fluidized bed. Additional analysis of the numerical results indicates that liquid breakthrough does not take place for the studied test case.     

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.     

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.