The effect of elliptical pores on mercury porosimetry results

Heat transfer coefficients were measured between gas-fluidized beds and spherical calorimetric probes of different sizes and to a water-cooled horizontal tube. The bed materials used were alumina and sand of narrow size ranges. Operating temperatures extended up to 980 °C and some estimate of the magnitude of the radiant heat transfer component was obtained by comparing the results for surfaces of oxidized copper (high emissivity) and polished fine gold (low emissivity). Tests with small spherical calorimetric probes immersed in beds of large mean particle diameter showed that there is an effect of relative heat capacity leading to enhanced bed-to-surface heat transfer coefficients if the heat capacity of the ‘heat transfer surface’ is less than an order of magnitude greater than that of the bed particles. Relative bed/surface temperature affects the heat transfer coefficient in two ways: through the temperature influence on gas thermal conductivity affecting the particle convective component of the coefficient, and through the rate of cooling of material directly adjacent to the transfer surface affecting the radiant component of heat transfer. Bed-to-tube coefficients are lower than those to a small calorimetric probe because of the sustained low temperature of a coolant tube and the obstruction that it presents to the circulation of the fluidized solids. The predictive capabilities of the published correlations are poor over the range of operating temperatures tested.     

Heat transfer in a swirling fluidized bed with geldart type-D particles

A relatively new variant in fluidized bed technology, designated as the swirling fluidized bed (SFB), was investigated for its heat transfer characteristics when operating with Geldart type D particles. Unlike conventional fluidized beds, the SFB imparts secondary swirling motion to the bed to enhance lateral mixing. Despite its excellent hydrodynamics, its heat transfer characteristics have not been reported in the published literature. Hence, two different sizes of spherical PVC particles (2.61 mm and 3.65 mm) with the presence of a center body in the bed have been studied at different velocities of the fluidizing gas. The wall-to-bed heat transfer coefficients were measured by affixing a thin constantan foil heater on the bed wall. Thermocouples located at different heights on the foil show a decrease in the wall heat transfer coefficient with bed height. It was seen that only a discrete particle model which accounts for the conduction between the particle and the heat transfer surface and the gas-convective augmentation can adequately represent the mechanism of heat transfer in the swirling fluidized bed.     

Spheroidization of Titanium Carbide Powders by Induction Thermal Plasma Processing

Highly spherical particles of titanium carbide (TiC) have been produced by in-flight heat processing of irregularly shaped TiC powders in an aerosol reactor under argon-hydrogen and argon-helium induction thermal plasma. The spherical powders obtained by the plasma treatment consist of unagglomerated and uniform particles with mean diameters between 25 and 28.5 μm, which is smaller than the original TiC particle mean diameters (29.5 μm) because of partial evaporation of the particles during the plasma treatment. The spheroidization ratio of the treated TiC powders increases with the increase of hydrogen flow rate in plasma gases and the reduction of powder feeding carrier gas flow rate. Under certain processing conditions, the TiC powders have been completely spheroidized. The morphology and structure of individual spherical particles were examined and their formation mechanism was discussed based on calculation of heat transfer kinetics of the particles in the thermal plasma.     

Numerical study of mixing and thermal conduction of granular particles in rotating tumblers

A discrete element method (DEM) study is conducted to investigate the mixing and heat‐transfer characteristics of steel spherical particles under various rotation speeds and flow regimes of a rotating tumbler. The mixing degree, weighted temperature, temperature discrepancy at the mixing interface, temperature radial distribution, and information entropy are used to analyze the effect of mixing structure and evolution duration on the heat‐transfer characteristics. The results under the same revolution and the same evolution time are compared to show the effects of evolution time and mixing structure on thermal conduction. After a detailed analysis, the joint contribution of mixing degree and duration to granular heat transfer is explained, and the different approaches in static thermal conduction and dynamic mixing are shown. Moreover, a new method is proposed using the mean increase rate of temperature information entropy to determine the most effective operating condition for thermal conduction in granular particles. © 2013 American Institute of Chemical Engineers AIChE J, 59: 1906–1918, 2013     

Wärmestrahlung in dispersen Feststoffsystemen

Heat radiation in packed solids . The term packed solids embraces fixed beds and all other, sometimes less rigidly fixed, arrangements of solids particles of any shape in a gaseous environment. Cell and quasihomogeneous models have been developed for determining heat radiation in such systems and their predictions compared with one another and especially with available experimental data. Since fixed beds of spherical particles have been considered most frequently so far, they receive the greatest attention in this article. Topics such as radiation components in insulation systems, in chemical fixed bed reactors, in porous particles, and the effect of radiation on the wall heat transfer coefficient are mentioned only briefly.     

Heat transfer and flow pattern in vertical liquid-solids flow

Wall-to-bed heat transfer in hydraulic transport of spherical glass particles of diameter 1.20, 1.94 and 2.98 mm and in single-phase flow regime was studied. Experiments were performed by transporting the spherical glass particles with water in a 25.4 mm I.D. copper tube equipped with a steam jacket.In the runs without particles, the tube Reynolds number varied between 2280 and 21,300, while in hydraulic transport runs, the tube Reynolds number varied between 3300 and 20,150. The loading ratio (G_p/G_f) was between 0.07 and 0.328, and the fluid superficial velocity was between 0.29·U_t and 2.86·U_t, where U_t represents the single particle terminal velocity. For these ratios, the voidage ranged from 0.715 to 0.895.The data for the heat transfer factor (j_H) in single-phase flow are correlated using a general form j_H=f(Re). The data for wall-to-bed heat transfer in the hydraulic transport of particles show that an analogy between heat and momentum transfer exists. The data were correlated by treating the flowing fluid-particle suspension as a pseudofluid, by introducing a modified suspension-wall friction coefficient (f_w) and a modified Reynolds number (Re_m).     

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.     

Particle-resolved simulation of packed beds by non-body conforming locally refined orthogonal hexahedral mesh

The traditional fixed-bed reactor design is usually not suitable for the low tube-to-particle diameter ratios (N=D/d < 8) where the local phenomena of channeling near the wall and backflow in the bed are dominant. The recent "solid particle" meshing method is too complicated for mesh generation, especially for non-spherical particles in large random packed beds, which seriously hinders its development. In this work, a novel high-fidelity mesh model is proposed for simulation of fixed bed reactors by combining the immersed boundary and adaptive meshing methods. This method is suitable for different shapes of particles, which ingeniously avoids handling the complex "contact point" problem. Several packed beds with two different shapes of particles are investigated with this model, and the local flow in the bed is simulated without geometrical simplification. The predicted pressure drop across the fixed bed and heat transfer of the single particle are in good agreement with the corresponding empirical relations. Compared with spherical particles, the packed bed packing with pentaphyllous particles has lower pressure drop and better heat/mass transfer performance, and it shows that this method can be used for the screening of particle shapes in a fixed bed.     

Gas-to-particle heat transfer in vertical pneumatic conveying of granular materials

The results of the investigation of interphase heat transfer from gas (air) to spherical particles of different diameter in vertical pneumatic conveyin valid over a wide range of volumetric concentrations of the solid and of particle Reynolds numbers. Possible reasons for discrepancies between this rel (compared in the common range of variables studied) were analysed.     

Utilization of a Radial Temperature Model for Heat Conduction within Spherical Particles to Model Granular Assemblies

A heat transfer (DEM) model for application in the particle based discrete element simulation method is presented. It utilizes an analytical solution of the heat diffusion equation for a solid spherical particle to obtain temporal and radial solutions of the temperature distributions within the particles. This radial temperature model avoids the shortcomings of the usual assumption of spatially uniform temperature profiles in particles. The concept is designed to minimize computing power and memory requirement in order to allow the computation of granular assemblies consisting of a large number of particles. Results obtained for a particle subject to transient convective boundary conditions are compared with a Crank‐Nicholson implicit scheme as numerical reference solution. A first implementation of the radial temperature model in a discrete element code reveals the additional computational cost as negligible compared to the demands of contact identification and force calculation.     

Model for devolatilization of coal particles in fluidized beds

A model for the devolatilization of coal in a non-combusting fluidized bed is proposed. Previous studies have either considered devolatilization as a non-rate process or assumed the devolatilization coal particle as isothermal. The assumption of an isothermal particle requires the heat transfer Biot number ?0.02. In view of the larger Biot numbers predicted using existing fluidized bed gas-solid heat exchange correlations and reported values for thermophysical properties, the present model considers the devolatilizing particle to be, in general, non-isothermal. The temperature profiles are computed from the analytical solution of the one-dimensional spherical coordinate unsteady heat transport equation with a convective boundary condition. The temperatures are then used in the non-isothermal coal decomposition kinetic expression proposed by Anthony et al., integrated over the particle to obtain the fractional volume average devolatilization at any given time. Parametric studies show a chemical kinetics controlled regime for small particles, a heat transfer controlled regime for larger particles and a mixed regime for intermediate particle sizes. The extent of the mixed regime depends on the type of coal as well as the operating conditions. The model results are also compared with the fluidized CH₄ and CO evolution data reported in the literature for various particle sizes and different temperatures.     

Countercurrent plug flow mass exchange with internal particle diffusion

The model for countercurrent steady state mass transfer between uniform dispersed phase particles and a continuous phase, both assumed to move in plug flow, with diffusion resistance inside the particles, and film resistance around the particles, is solved analytically for three particle geometries: infinite plates, infinite cylinders and spheres. In the solution, the direct relation between the local continuous phase concentration, and the average dispersed phase concentration is accounted for in the boundary condition. Concentration profiles in the mass exchanger are derived from the analytical solution, as well as asymptotic Sherwood numbers. The analytical solution requires the determination of roots of the characteristic equations, which is cumbersome for spherical particles. Correlations are provided for the asymptotic Sherwood numbers for easy computation. The model can easily be used for the analogous direct heat exchange problem.     

FCC提升管反应器中颗粒聚团对裂化反应的影响

在对气固流动体系颗粒聚团实验现象分析的基础上,以减压馏分油裂化反应为例,对反应器中最常见的球形和椭球形聚团上的流动、传热和反应过程进行了模拟计算,得到了聚团内外油气和催化剂颗粒的速度分布、温度分布、浓度分布以及反应速率分布。研究结果表明,催化剂颗粒聚团的存在阻碍了油气与催化剂颗粒的充分接触,进而造成系统内速度和温度的不均匀分布,影响了裂化反应的发生,使得有颗粒聚团时的一次反应速率明显低于无聚团时的反应速率,颗粒聚团显著影响了油气在颗粒上的反应时间,最终导致气体和焦炭产率升高,对裂化反应产品收率分布十分不利。     

A Model for the Relative Velocity of a Particle in an Impingement Dryer: Application to Heat Transfer

A simplified mathematical model for the relative gas-particle motion in a confined jet impingement dryer is developed. Model predictions based on an unsteady momentum balance are in good agreement with the observed cycling motion of a spherical particle. The model is applied to coriander seeds submerged in a flow field of superheated steam. It is found that relative motion occurs in unsteady turbulent regime, and that steady settling velocity of particles is never achieved. Model results are applied to correlate experimental heat transfer data of an impingement dryer. Experimental Nu numbers compare fairly well with correlations for fluidized systems.     

On shape factors for irregular particles-I. The steady-state problem. Diffusion and reaction

The problem of heat or matter transfer for a bed of spherical particles has been fully solved by Amundson. In this paper we consider the modifications which must be made in steady-state solution when the bed may consist of irregularly shaped particles. Considering the case of diffusion limitation of a first-order reaction, it is shown that the results for all shapes will lie close together if the characteristic dimension of the particle is taken to be v_p/s_x, the ratio of its volume to its external surface area.     

加入惰性固体粒子的二元物系的流动沸腾传热特性

引　言流动沸腾传热广泛存在于石油、化工、轻工、动力及能源等各个领域 ,但三相流动沸腾传热的研究极少 .李修伦等[1]在流动沸腾系统中加入惰性固体粒子 ,进行了汽 -液 -固三相流沸腾传热的初步研究 .李修伦、闻建平[2 ,3]进一步将三相流和沸腾换热相结合 ,较好地解决了沸腾传热强化和防垢、除垢问题 .李修伦、张利斌等[4 ]又采用循环流化床技术 ,结合粒子在沸腾系统中的强化特性 ,开发了汽 -液 -固三相循环流化床蒸发器 ,它具有良好的强化传热和防、除垢性能 .上述研究均属于单组分三相流动沸腾传热 ,而关于二元物系三相流动沸腾传热的研…     

惰性粒子对水沸腾传热强化的实验研究

通过加入不同种类和体积分率的惰性粒子,在垂直管中进行了水的流动沸腾传热实验,研究了三相流沸腾传热特性。实验中预先对水加热,采用了沸点进料。实验发现,传热膜系数随热通量、液体流量的增加及粒子体积分率的增大而增加。对于不同粒子,这种变化趋势比较一致,但不同粒子对沸腾传热的强化效果不同。实验结果表明:由于固体粒子的存在,强化了沸腾传热,三相流沸腾传热系数是相同条件下汽液二相流沸腾传热系数的1.3—1.7倍。     

A THEORETICAL STUDY OF THE LIMITING HEAT TRANSFER COEFFICIENT IN FLUIDIZED BEDS

A new model is presented to describe the heat transfer process occurring in fluidized beds under the limiting condition of very short contact times between the heat transfer surface and the emulsion phase. Unlike other work in this area the proposed model assumes that the particles are in constant motion close to the surface throughout the heat transfer process. The effect of the non-continuum gas film assumption (the Smoluchowski effect) when particles are very close to the surface is found to be of secondary importance when compared with the movement of particles close to the surface. Expressions for both the instantaneous and time averaged heat transfer coefficients for individual and a spatial distribution of parlicles are presented.     

A Model for the Relative Velocity of a Particle in an Impingement Dryer: Application to Heat Transfer

Abstract

A simplified mathematical model for the relative gas-particle motion in a confined jet impingement dryer is developed. Model predictions based on an unsteady momentum balance are in good agreement with the observed cycling motion of a spherical particle. The model is applied to coriander seeds submerged in a flow field of superheated steam. It is found that relative motion occurs in unsteady turbulent regime, and that steady settling velocity of particles is never achieved. Model results are applied to correlate experimental heat transfer data of an impingement dryer. Experimental Nu numbers compare fairly well with correlations for fluidized systems.