CONVECTIVE DRYING OF THIN AND DEEP BEDS OF GRAIN

The object of this paper is the experimental and theoretical investigation of heat and mass transfer during drying of packed beds of grain. A deep bed of grain was regarded as a series of thin beds. Analytical expressions for the thin bed drying rate were obtained by defining the air parameters at the grain surface in the falling rate period of drying and using the results of drying experiments. The paper also contains a simulation model for drying deep beds of grain, consisting of four partial differential equations based on energy and mass balances in a bed element. The system of equations was solved using finite difference techniques and a digital computer. A comparison between numerical solutions and experimental results is illustrated.     

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     

CFD方法在固定床反应器传热研究中的应用

固定床反应器是一种常见的化学和生化反应器,由于内部结构十分复杂,固定床内的局部流动和传热过程研究一直是一个颇具挑战性的问题。有效参数法是长期以来固定床传热研究的常用方法,但是由于对固定床内温度场缺乏准确的了解,目前为止许多基于有效参数法的传热模型的普适性仍然存在问题。计算流体力学（CFD）的数值模拟方法是近年来应用于固定床流动和传热研究的一种新的研究方法,它通过数值方法求解流动和传递的微分方程组而获得流场和温度场。CFD数值模拟方法能够提供精确的局部流动和传递信息如速度分布、压力分布、温度分布、组分浓度分布等。本文综述和分析了CFD方法在固定床反应器的流动和传热研究领域的最新进展,讨论了CFD方法在该领域的应用前景。     

Effect of Non‐Newtonian Characteristics on Convective Liquid‐Solid Heat Transfer in Packed and Fluidised Beds of Spherical Particles

In this work, the field (continuity, momentum and thermal energy) equations togetherwith a cell model have been solved numerically to elucidate the influence of non‐Newtonian (Power law rheology) liquid characteristics on liquid‐solid heat transfer in packed and fluidised beds of spherical particles. The results presented herein relate to wide ranges of conditions of bed voidage, power‐law index and Peclet number but are limited to low Reynolds number (≤1) flow conditions. Within the range of conditions, the effect of power‐law index is found to be small and this is also consistent with the available experimental results on liquid‐solid mass transfer in these systems.     

Ablation and thermal degradation behaviour of a composite based on resol type phenolic resin: Process modeling and experimental

During atmospheric re-entry, ballistic or space vehicle is subjected to severe aerodynamic heating and its successful return through the Earth's atmosphere depends largely on the provision that is made for reducing aerodynamic heat transfer to its structure. For this purpose ablative heat shield is normally used which undergoes physical, chemical, and mostly endothermal transformations. These transformations produce new liquid or gas phases which are subsequently injected into the environment.Mass and energy balance equations have been solved in order to model the ablation and thermal degradation behaviour of an ablative composite. A method to determine and calculate some of the parameters in the ablative equation is proposed from the simultaneous thermal gravity and differential scanning calorimetry analysis techniques.The objective of this work is to model ablating, charring and thermal degradation behaviour of a heat shield resol-type phenolic resin/asbestos cloth composite in oxyacetylene flame test. This requires solving serious heat transfer equations with moving boundaries. Explicit forward finite difference method (FDM) is used for heat transfer calculation. Moving boundaries are fixed by the Landau transformation. The ablation equation has been solved numerically.Temperature distribution through the composite thickness, temperature of moving surface, and the rate of moving boundary changes are evaluated. The results are in a good agreement with the experimental data obtained from oxyacetylene flame tests. The model can successfully be used for both material selection and thickness calculation in the design of thermal protection shields.     

Study of Flow Characteristics of Ultrafine CaCO3 Powders in a Spouted Bed

The flow behavior of gas and ultrafine powder in a spouted bed was numerically investigated by using a two‐fluid model coupled with a population balance equation (PBE). The aggregation process is controlled by the PBE, which is solved by the direct quadrature method of moments. The agglomerate diameter is calculated according to the change in particle number. The solid pressure and viscosity were modified for agglomerates on the basis of the kinetic theory of granular flow. Distributions of diameter, solids volume fraction, and velocity are obtained by the new model. The influence of cohesive intensity and gas velocity on the diameter distribution were analyzed. The spout diameter, a vital parameter for the design of spouted beds, was calculated and a calculation formula is proposed.     

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.     

A theoretical investigation of enhancement of mass transfer from a packed bed using acoustic oscillations

This paper describes a theoretical investigation of the possibility of improving the performance of packed bed dryers using acoustic oscillations. It was motivated by the increasing interest in the use of acoustic oscillations to improve the performance of energy‐intensive, industrial processes. Sound propagation in a packed bed was modelled as propagation through a porous medium. The effect of acoustic oscillations on the drying rate was then investigated by numerically integrating the heat and mass transfer equations. The model used quasi‐steady correlations for heat and mass transfer. The results show that threshold values for void fractions and sound pressure levels exist, above which significant increase in drying rate can be obtained. The increase in mass transfer decreases with effective particle diameter.     

Convective heat transfer for power law fluids in packed and fluidised beds of spheres

The forced convection heat transfer characteristics for an incompressible and steady flow of power law liquids in fixed and extended beds of spherical particles has been studied numerically. The sphere-sphere hydrodynamic interactions have been accounted for by using a simple cell model. Within the framework of such a cell model, the momentum and energy equations have been solved using a finite difference method to obtain the velocity and temperature fields. Extensive numerical estimates of the local and average Nusselt numbers as functions of the physical, rheological and kinematic variables have been presented and discussed for the two commonly employed thermal boundary conditions. In broad terms, the Nusselt number for power law fluids (both shear-thinning and shear-thickening conditions) normalized with respect to the corresponding value for a Newtonian fluid shows weak additional dependence on the power law flow behaviour index. The shear-thinning behaviour is seen to promote heat transfer and as expected the shear-thickening behaviour impedes heat transfer in fixed and fluidised beds. All in all, the present results encompass wide ranges of conditions as follows: Reynolds number: 1-500; Peclet number: 1-500; bed voidage: 0.4-0.8 and the flow behaviour index: 0.5-1.8 thereby covering extremely shear-thinning and shear-thickening types of fluid behaviours. The paper is concluded by presenting detailed comparisons with the limited analytical and/or experimental results available for liquid-solid mass transfer in such systems.     

Transient heat transfer in a fixed bed of slab-shaped and spherical particles with intraparticle conduction

The mathematical equations for heat transfer between a flowing fluid and both slab-shaped and spherical particles with intraparticle conduction in a fixed bed, are numerically solved using the method of lines. The solution for spherical particles was used to confirm previous results for zero and non-zero Biot numbers. Conditions are identified under which heat transfer to beds of slabs should not be approximated by available solutions for spheres.     

Batch and continuous spouted bed drying of cereal grains: The thermal equilibrium model

A complete set of equations with no adjustable parameters are written for numerically predicting the variation of grain temperature and moisture content with time for batch drying of well mixed deep beds of three cereal grains, as well as the exit grain and air moisture contents and temperatures for continuous drying. Unlike previous studies, the surface moisture content of the grains is not assumed constant. Agreement with both batch and continuous spouted bed drying data from the literature is good, in the continuous case especially when the assumed exit age distribution of the isothermal bed solids is specific to spouting.     

Flow in the annulus of a bed of fine particles spouted with water

The flow in the annulus of a water spouted bed of glass particles (275 to 774 μm) was studied experimentally in a cylindrical half-column 50.8 mm in diameter. An axisymmetric model, which assumes Darcy flow in the annulus and uses the experimental spout pressure distribution, predicts the flow and pressure fields in the annulus. The substantial differences between this flowfield and that for coarse particle beds that are observed are caused by differences in the normalized interfacial pressure profile. The model predicts that both the fluid velocity and the normalized fluid velocity at the top of the annulus decrease as the particle size and bed height are reduced. Particles are observed to enter the spout primarily near the spout inlet in agreement with predictions of the axial spout voidage distribution. The residence time distribution of the fluid in the annulus is relatively broad and the measured residence times are about 25% higher than those calculated.     

Viscoelastic flow in packed beds or porous media

An analysis of viscoelastic flow in packed beds or porous media is presented based on a capillary hybrid model of the flow which incorporates a viscous mode and an elongational mode. The development includes modelling of the elongational mode of the flow to obtain the elongational flow contribution to the potential drop for a viscoelastic fluid. A general expression describing viscoelastic flow in porous media is developed which utilizes the viscous response determined by the fluid model equation and an elongational flow response characterized by an elongational viscosity difference for the fluid. The expression applies to all three traditional bed models employing the tortuosity and Kozeny constant. The relationship yielded extensions of Darcy's law applicable to viscoelastic flow in porous media and an expression representing the flow of a viscoelastic fluid in a packed bed or porous core of length L. The relationship of the friction factors and respective Reynolds numbers is also presented.     

The onset of double-diffusive convection in a stably stratified fluid layer heated from below

The time of the onset of double-diffusive convection in time-dependent, nonlinear temperature fields is investigated theoretically. The initially quiescent horizontal fluid layer with a uniform solute gradient experiences ramp heating from below, but its stable solute concentration is to reduce thermal effects which invoke convective motion. The related stability analysis is conducted on the basis of the propagation theory. Under the linear stability theory the thermal penetration depth is used as a length scaling factor and the linearized perturbation equations of similarity transform are solved numerically. The resulting correlations of the critical time to mark the onset of regular cells are derived as a function of the thermal Rayleigh and the solute Rayleigh numbers. The predicted stability criteria are apparently consistent with existing experimental results for aqueous solution of sodium chloride.     

Hydrodynamic Model for Horizontal Two‐phase Flow Through Porous Media

A unidirectional, two‐fluid model based on the volume‐average mass and momentum balance equations was developed for the prediction of two‐phase pressure drop and external liquid hold‐up in horizontally positioned packed beds experiencing stratified, annular and dispersed bubble flow regimes. The so‐called slit model drag force closures were used for the stratified and annular flow regimes. In the case of dispersed bubble flow regime, the liquid‐solid interaction force was formulated on the basis of the Kozeny‐Carman equation by taking into account the presence of bubbles in reducing the available volume for the flowing liquid. The gas‐liquid interaction force was evaluated by using the respective solutions of drag coefficient for an isolated bubble in viscous and turbulent flows. The proposed drag force expressions for the different flow patterns occurring in the bed associated with the two‐fluid model resulted in a predictive method requiring no adjustable parameter to describe the hydrodynamics for horizontal two‐phase flow in packed beds.     

Solvent extraction of vegetable oils: Numerical and experimental study

A process for the extraction of vegetable oils from soybean seeds with a solvent was developed experimentally. The extraction was carried out in a continuous, fixed-bed extractor. A non-dimensional transient model was applied to simulate the mass transfer process which occurs during the extraction in a packed bed column. The governing dimensionless differential equations were numerically solved using the method of finite volumes. The numerical results were compared with data obtained from the experimental extraction, presenting good agreement. The values obtained numerically for the total oil mass extracted in the fluid phase presented a maximum error of 20%, when compared to the experimental data. The greatest discrepancy was observed at the end of the extraction. This maximum error can be considered small due to the use of a simple numerical model.     

CONVECTIVE DRYING OF THIN AND DEEP BEDS OF GRAIN

The object of this paper is the experimental and theoretical investigation of heat and mass transfer during drying of packed beds of grain. A deep bed of grain was regarded as a series of thin beds. Analytical expressions for the thin bed drying rate were obtained by defining the air parameters at the grain surface in the falling rate period of drying and using the results of drying experiments. The paper also contains a simulation model for drying deep beds of grain, consisting of four partial differential equations based on energy and mass balances in a bed element. The system of equations was solved using finite difference techniques and a digital computer. A comparison between numerical solutions and experimental results is illustrated.     

DSMC-LES方法研究循环流化床内颗粒团聚物的流动特性

采用直接模拟Monte Carlo方法法DSMC）模拟颗粒间的碰撞,采用考虑颗粒脉动流动对气相湍流流动影响的大涡模拟（LES）研究气相湍流.单颗粒运动满足牛顿第二定律,颗粒相和气相相间作用的双向耦合由牛顿第三定律确定.数值模拟垂直管内气固两相上升流动,对管内气相速度和颗粒相速度、浓度以及聚团流动进行分析.研究平均单个颗粒团聚物的存在时间、颗粒团聚物的时间份额和颗粒团聚物的生成频率分布特性,模拟结果与文献的实验结果基本吻合.     

Simulation of Turbulent Flow in a Packed Bed

Numerous models for simulating the flow and transport in packed beds have been proposed in the literature with few reported applications. In this paper, several turbulence models for porous media are applied to the gas flow through a randomly packed bed and are examined by means of a parametric study against some published experimental data. These models predict widely different turbulent eddy viscosity. The analysis also indicates that deficiencies exist in the formulation of some model equations and selection of a suitable turbulence model is important. With this realization, residence time distribution and velocity distribution are then simulated by considering a radial profile of porosity and turbulence induced dispersion, and the results are in good agreement with the available experimental data.