Measurement of constant drying rate of wet material placed in a fluidized bed of inert particles under reduced pressure

The objective of this study is to estimate the drying characteristics of a relatively large material immersed in a fluidized bed under reduced pressure by measuring the constant drying rate. The constant drying-rate period in a fluidized bed under reduced pressure is difficult to measure because it is extremely short. To maintain the constant drying-rate period, distilled water is directly supplied to the drying material. Through our experiment, the heat transfer coefficient of the material surface was also determined. The results were compared with data on hot air drying. The constant drying rate is higher for fluidized bed drying than for hot air drying. It suggests that the heat transfer coefficient on the surface of the drying material is much larger for fluidized bed drying than for hot air drying. For fluidized bed drying, the effect of pressure in the drying chamber on the heat transfer coefficient is slight at the same normalized mass velocity of dry air (G/G_mf). The temperature difference between the inside of the drying chamber and the drying material is much smaller for fluidized bed drying than for hot air drying. The constant drying rate increases as the pressure in the drying chamber decreases.     

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.     

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

Experimental work was conducted to investigate the effect of particle size and particle density upon the wall-to-bed heat transfer characteristics in liquid—solid fluidized beds with a 95.6 mm column diameter over a wide range of operating conditions. The radial temperature profile was found to be parabolic, indicating the presence of a considerable bed resistance. The effective radial thermal conductivity and the apparent wall film coefficient were obtained on the basis of a series thermal resistance model. The modified Peclet number of the radial thermal conductivity decreases upon the onset of fluidization, has a minimum at a bed porosity of 0.6 to 0.7 and increases with further increase of bed porosity. The modified Peclet number decreases considerably with decreasing particle size or increasing particle density. The apparent wall heat transfer coefficient can be represented well by a Colburn j-factor correlation over a wide range of data as follows: j′_H = 0.137 Re′^?0.271 A close analogy is found to exist between the modified j-factor for wall heat transfer coefficient and that for wall mass transfer coefficient, in liquid—solid fluidized beds.     

Heat Transfer from Immersed Vertical Cylinders in Gas‐Liquid and Gas‐Liquid‐Solid Fluidized Beds

The heat transfer coefficient, h, was measured using a cylindrical heater vertically immersed in liquid‐solid and gas‐liquid‐solid fluidized beds. The gas used was air and the liquids used were water and 0.7 and 1.5 wt‐% carboxymethylcellulose (CMC) aqueous solutions. The fluidized particles were sieved glass beads with 0.25, 0.5, 1.1, 2.6, and 5.2 mm average diameters. We tried to obtain unified dimensionless correlations for the cylinder surface‐to‐liquid heat transfer coefficients in the liquid‐solid and gas‐liquid‐solid fluidized beds. In the first approach, the heat transfer coefficients were successfully correlated in a unified formula in terms of a modified j_H‐factor and the modified liquid Reynolds number considering the effect of spatial expansion for the fluidized bed within an error of 36.1 %. In the second approach, the heat transfer coefficients were also correlated in a unified formula in terms of the dimensionless quantities, Nu/Pr^1/3, and the specific power group including energy dissipation rate per unit mass of liquid, E^1/3D^4/3/ν_l, within a smaller error of 24.7 %. It is also confirmed that a good analogy exists between the surface‐to‐liquid heat transfer and mass transfer on the immersed cylinder in the liquid‐solid and gas‐liquid‐solid fluidization systems.     

INVESTIGATION ON THE INCIPIENT FLUIDIZATION AND HEAT TRANSFER IN A CENTRIFUGAL FLUIDIZED BED DRYER

Abstract

Based on the continuum theory, a physical model of gas-solid two phase flow in a centrifugal fluidized bed has been proposed. A set of governing equations to describe the fluidization state are obtained and solved numerically after some simplifying. The quantitative experimental study on the characteristics of the incipient fluidization in the centrifugal fluidized bed is performed to examine the proposed model. Gas-solid two phase heat transfer in CFB during a drying process is also conducted. The influences of bed thickness, particle diameter, physical properties of particle, rotating speed of the bed and the gas superficial velocity on heat transfer characteristics are examined. A correlation that can be used to calculate the heat transfer coefficients in the drying process in CFB is obtained.     

Effects of Chaotic Temperature Fluctuations on the Heat Transfer Coefficient in Liquid‐Liquid‐Solid Fluidized Beds

The effect of chaotic temperature fluctuations on the immersed heater‐to‐bed heat transfer coefficient (h) are investigated in a liquid‐liquid‐solid fluidized bed (0.152 m ID × 2.5 m in height). The time series of temperature fluctuations are measured and analyzed by means of the multidimensional phase space portraits and Kolmogorov entropy (K), in order to characterize the chaotic behavior of heat transfer coefficient fluctuations in the bed. The overall heat transfer coefficient is inversely proportional to the Kolmogorov entropy of temperature fluctuations, as well as the fluctuation range of heat transfer coefficient (Δh_i). The Kolmogorov entropy and fluctuation range of the heat transfer coefficient (Δh_i) increase with increasing dispersed phase velocity, but decrease with increasing particle size. However, they attain their minima with variation of the continuous phase velocity as well as the bed porosity, at which point the flow regime of particles in the beds changes. The overall heat transfer coefficient is directly correlated with the Kolmogorov entropy, as well as the fluctuation range of heat transfer coefficient.     

Experimental study and simulation of vibrated fluidized bed drying

The paper addresses numerical simulation for the case of convective drying of seeds (fine-grained materials) in a vibrated fluidized bed, analyzing agreement between the numerical results and the results of corresponding experimental investigation. In the simulation model of unsteady simultaneous one-dimensional heat and mass transfer between gas phase and dried material during drying process it is assumed that the gas-solid interface is at thermodynamic equilibrium, while the drying rate (evaporated moisture flux) of the specific product is calculated by applying the concept of a “drying coefficient”. Mixing of the particles in the case of vibrated fluidized bed is taken into account by means of the diffusion term in the differential equations, using an effective particle diffusion coefficient. Model validation was done on the basis of the experimental data obtained with narrow fraction of poppy seeds characterized by mean equivalent particle diameter (d_S,d = 0.75 mm), re-wetted with required (calculated) amount of water up to the initial moisture content (X₀ = 0.54) for all experiments. Comparison of the drying kinetics, both experimental and numerical, has shown that higher gas (drying agent) temperatures, as well as velocities (flow-rates), induce faster drying. This effect is more pronounced for deeper beds, because of the larger amount of wet material to be dried using the same drying agent capacity. Bed temperature differences along the bed height, being significant inside the packed bed, are almost negligible in the vibrated fluidized bed, for the same drying conditions, due to mixing of particles. Residence time is shorter in the case of a vibrated fluidized bed drying compared to a packed bed drying.     

Systematic study on heat transfer and surface hydrodynamics of a vertical heat tube in a fluidized bed of FCC particles

Bed‐to‐wall heat transfer properties of a vertical heat tube in a fluidized bed of fine fluid catalytic cracking (FCC) particles are measured systematically using a specially designed heat tube. Two important surface hydrodynamic parameters, i.e. the packet fraction (δ_pa) and mean packet residence time (τ_pa) based on the packet renewal theory, are determined by an optical fiber probe and a data processing method. The experimental results successfully reveal the axial and radial profiles of heat‐transfer coefficient, the effects of superficial gas velocity, and static bed height on heat‐transfer coefficient, most of which can be explained successfully by the measured τ_pa, an indicator of packet renewal frequency. τ_pa is found to play a more dominant role than δ_pa on bed‐to‐wall heat transfer. With a fitted correction factor, the modified Mickley and Fairbanks model is able to predict the heat‐transfer coefficients with enough accuracy based on the determined packet parameters. © 2014 American Institute of Chemical Engineers AIChE J, 61: 68–83, 2015     

Experimental Study of the Heat and Mass Transfer During Drying in a Fluidized Bed Dryer

ABSTRACT

Drying curves obtained in a pilot-scale fluidized bed dryer using biological source solids (sawdust, soya and fish meal) were used to estimate the parameters involved in heat and mass transfer phenomenas: heat transfer coefficient and moisture diffusivity coefficient. Parameters involved in mass transfer were estimated from drying models based on diffusional mechanisms and others that in addition consider internal and external resistance to the mass transfer. The estimate ef ective diffusivity coefficient was between 2x10-11 to lx10 (m2/s) for the considered products. Heat transfer coefficient was estimated from drying data points in the constant drying rate period when the external resistance to the mass transfer controls the process.     

Estimation of Coefficients of Fluidized Bed Drying through the PSO and GA Metaheuristic Approaches

This article shows the results of heat and mass transfer coefficients estimation in a fluidized bed drying obtained through two independent metaheuristics, particle swarm optimization (PSO) and genetic algorithms (GAs). Upon estimating parameters, we aimed to minimize errors between the experimental data provided by Vitor (Modeling of Biomass Drying in Fluidized Bed, D.Sc. Thesis, 2003) and those calculated through a three-phase drying differential-algebraic model. The computational results showed that the two metaheuristics chosen were suitable to estimate the drying parameters proposed here. When the two metaheuristics are compared, the PSO shows slightly better results in much shorter computational times. The coefficient of heat transfer estimated here is compared to results obtained from other experiments and proves to be quite adequate.     

低温振动流化床气固传热的实验研究

在低温粉碎工程中,振动流化床常用于固体颗粒的预冷。为了深入认识振动流化床低温下气固传热的特性,本文介绍了不同的振幅,气流速度和料层厚度下低温实验的结果,通过分析实验结果首次得到了振动流化床中低温气固的传热关联式与普通流化床相比,由于引入了振动,振动流化床气固传热换热系数大幅度提高。     

惰性粒子振动流化床中膏状物料干燥

报道了采用带浸没加热管的惰性粒子振动流化床干燥膏状物料的实验研究结果。考察了加料速率、振动条件、进气温度、进气速度、加热管功率等参数对干燥过程的影响,提出采用体积传热系数来评价干燥器传热性能,并得出了计算体积传热系数的准数关联式。结果表明,在流化床中增设振动和浸没加热管装置,能大大强化传热、传质,干燥器热效率达60%,干燥强度超过300 kg·m^-3·h^-1,体积传热系数可达25 kW·m^-3·K^-1,激光粒度分析仪的测定结果表明产品的粒度分布范围较窄,该流化床干燥可以直接得到平均粒径为0.35 μm、比表面积为5.024 m²·g^-1的粉状产品。     

Heat and mass transfer characteristics in a gas-slurry-solid fluidized bed

The gas-slurry-solid fluidized bed is a unique operation where the upward flow of a liquid-solid suspension contacts with the concurrent up-flow of a gas, supporting a bed of coarser particles in a fluidized state. In the present study we measured the gas holdup, the coarse particle holdup, the cylinder-to-slurry heat transfer coefficient, and the cylinder-to-liquid mass transfer coefficient at controlled slurry concentrations. The slurry particles were sieved glass beads of 0.1 mm average diameter and their volumetric fraction was varied at 0, 0.01, 0.05 or 0.1. The slurry and the gas velocities were varied up to about 12 and 15 cm/s, respectively. The coarse particles fluidized were sieved glass beads of average diameters of 3.6 and 5.2 mm. The individual phase-holdup values were measured and served for use in correlating the heat and mass transfer coefficients. The heat and mass transfer coefficients in the slurry flow, gas-slurry transport bed, slurry-solid fluidized bed and gas-slurry-solid fluidized bed operations can be correlated well by dimensionless equations of a unified formula in terms of the Nusselt (Sherwood) number, the Prandtl (Schmidt) number and the specific power group including the energy dissipation rate per unit mass of slurry, with different numerical constants and exponent values, respectively, to the heat and mass transfer coefficients. The presence of an analogy between the heat and mass transfer from the vertically immersed cylinder in these slurry flow, gas-slurry transport bed and gas-slurry-solid fluidized bed systems is suggested.     

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 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 to Immersed and Boundary Surfaces in Fluidized Beds

An experimental study of heat transfer into gas‐fluidized beds has been carried out with heat transfer into discriminated areas of the boundary walls, and into single and multiple elements immersed in the bed. The experiments have been carried out with glass ballotini ranging in size from 100 μm to 1 mm in diameter, on Diakon (Perspex) particles of 325 μm, and on nickel particles of 275 μm and 325 μm covering a range of Archimedes numbers from 100 to 10⁵. Beds of different diameter with distributors of several different types have been examined. The entire experimental results have been compared with literature data on heat transfer to immersed elements. It is shown that the onset of slugging in the fluidized bed has a large effect on heat transfer. Once the effect of slugging has been introduced, it is shown that the results of this investigation and others in the literature within the range of Archimedes numbers from 100 to 10⁹ may be correlated.     

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     

SIMULATION OF THE HEAT AND MOISTURE TRANSFER PROCESS DURING DRYING IN DEEP GRAIN BEDS

ABSTRACT

Grain drying is a simultaneous heat and moisture transfer problem. The modelling of such a problem is of significance in understanding and controlling the drying process. In the present study, a mathematical model for coupled heat and moisture transfer problem is presented. The model consists of four partial differential equations for mass balance, heat balance, heat transfer and drying rate. A simple finite difference method is used to solve the equations. The method shows good flexibility in choosing time and space steps which enable the simulation of long term grain drying/cooling processes. A deep barley bed is used as an example of grain beds in the current simulation. The results are verified against experimental data taken from literature. The analysis of the effects of operating conditions on the temperature and moisture content within the bed is also carried out     

Quantifying lateral solids mixing in a fluidized bed by modeling the thermal tracing method

Thermal tracing is a simple method for studying solids mixing in fluidized beds. However, the measurement of temperatures is influenced by both mixing and heat transfer, which limits its usefulness for inferring mixing quantitatively. In this work, a semiempirical model is developed to quantify lateral solids mixing in fluidized beds. The model couples the tracer mass balance, the enthalpy balance of tracers and bed particles, and the response dynamic of thermometers. A series of tests is pezrformed in a lab‐scale fluidized bed, with particle sizes of 0.28–0.45, 0.45–0.6, 0.6–0.8, and 0.8–1.0 mm, and fluidizing velocity from 0.3 to 2.3 m/s. By evaluating the measured transient temperatures using the model, the lateral dispersion coefficient (D_sr) is determined to be between 0.0002 and 0.0024 m²/s. Its reliability is confirmed by bed collapse experiments. Finally, the values of D_sr is compared with a collection of data in the literature. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Mathematical Modeling of the Fluidized Bed Drying of Cubic Materials

The unsteady‐state simultaneous heat and mass transfer between gas and potato cubes during the drying process in a batch fluidized bed was described by a mathematical model. Mass transfer was considered to occur in three dimensions whereas heat transfer between the gas and dried material was assumed to be lumped. It was found that the model could describe the drying process with acceptable accuracy. The moisture profile inside the material at any cross‐section and at any time can be predicted by the model.