Vacuum contact drying of free flowing mechanically agitated particulate materialVakuum-kontakttrocknung von rieselfähigem,mechanisch durchmischtem Granulat

The drying rate of packed and mechanically agitated beds heated by immersed surfaces is controlled by the contact heat transfer resistance at the surface followed by the heat penetration resistance of the wet bulk. Both resistances can be predicted from model equations with sufficient accuracy. The contact resistance and the bulk penetration resistance for packed beds follow from physical properties, while the prediction of the bulk penetration resistance for mechanically agitated beds requires the introduction of an empirical parameter, the so-called mixing number, in order to describe the random particle motion. The mixing number was found to lie between 2 and 25, depending on the dryer type as well as on the Froude number. It is identical for dry and for wet beds.     

Wärmeübertragung zwischen einer Wand und dispersen Gas/Feststoff-Systemen

Heat transfer from a rigid wall to gas-solid particulate systems. Considerable progress made in the last twenty years now permits a better understanding of heat transfer between a rigid wall and gas/solid particulate systems. The following paper reviews this progress. The heat transfer from a rigid wall to fixed, agitated, and fluidized beds as well as to fixed beds with fluid flow is discussed, and an example of indirect cooling of high-capacity computers is given. In modelling, the concept of a contact and a penetration resistance in series is applied. The physical significance and the calculation of these resistances are discussed.     

Heat transfer to packed and stirred beds from the surface of immersed bodiesWärmeübergang zwischen ruhenden und mechanisch durchmischten schüttgütern und darin eingebetteten heizflächen

The heat transfer between packed and stirred beds and immersed surfaces is controlled by the contact resistance at the surface followed by the heat penetration resistance of the bulk. Both resistances can be predicted from model equations with sufficient accuracy. The contact resistance and the bulk penetration resistance for packed beds follow from physical properties, while the prediction of the bulk penetration resistance for stirred beds requires the introduction of an empirical parameter, the so-called mixing number in order to describe the random particle motion. The mixing number was found to lie between 2 and 25, depending on the design of the stirrer.     

Transverse mixing and heat transfer in horizontal rotary drum reactors

The transverse mixing of quartz sand (mean particle sizes 157, 323, 794 and 1038 μm) and sodium carbonate (soda) (mean particle size 137 μm) has been investigated in a laboratory rotary drum reactor of 300 mm length and 310 mm diam. Solid movement in the drum was observed by means of colored tracers and successive exposures as well as by means of hot tracers and recording the local temperature in the bulk of particles. Three different types of the particles and bulk behaviour could be observed for stickly particles. The time constant of the mixing was estimated as a function of the rotational speed of the drum. The “cooling-down” curves of the bulk of particles were measured in a laboratory oven of 250 mm diam. and 600 mm length. The temperature variation as a function of the time can be described by the Newtonian cooling law, from which the heat transfer coefficient at the wall α_w was estimated.The absolute value of α_w's and their dependence on the contact time and particle diameter cannot be calculated by the heat penetration model, which disregards the film resistance at the bulk/wall contact. By taking into account this resistance a good quality of fitting can be achieved.     

Mixing and Heat Transfer of Granular Materials in an Externally Heated Rotary Kiln

A heat transfer model based on the discrete element software EDEM and the secondary development tool C++ is developed to simulate the mixing and heat transfer process of particles under different parameters. This model is validated by comparison with experimental data and proved reasonable. It aims to study the heat transfer law of flowing particles in an externally heated rotary kiln and reveal the correlation between mixing and heat transfer from the mechanism. The results show that the combination of the total contact area between adherent particles and the drum wall, the mean temperature difference between adherent particles and the drum wall, the total contact area between particles, and the mean temperature difference between particles affect the heat transfer process. Changes in the temperature differences caused by the mixing rate dominate the heat transfer at different speeds or filling rates.     

Heat transfer in a horizontal rotary drum reactor

The heating of carbohydrates (particle size 15 – 100 μm) has been studied in an industrial scale horizontal drum reactor. The drum was 9.0 m long and had a diameter of 0.6 m. Strips were mounted on the inside wall and the drum was heated externally by steam. Solid movement in the drum was observed in a transparent experimental segment of the drum. From these experiments it became clear that the heat transfer between wall and solids may be described by the penetration model. In separate experiments the product of the effective thermal conductivity of the bulk material and its heat capacity has been determined. The theoretical heat transfer coefficients agree quite well with the experimental values verified by heat transfer measurements in the large-scale drum.The heat transfer coefficients between wall and gas phase and between bulk solid and gas phase have also been measured. The magnitude of the heat transfer coefficient between wall and gas phase indicates a natural convection mechanism.     

Convective Drying of Agitated Silica Gel and Beech Wood Particle Beds—Experiments and Transient DEM-CFD Simulations

With coupled discrete element (DEM)–computational fluid dynamics (CFD) simulations, drying processes can be simultaneously described on the system scale while resolving detailed subprocesses on the particle scale. In this contribution, DEM-CFD simulations are used to analyze the transient heat and mass transfer in mechanically agitated particle beds during drying. Results are compared to convective batch-drying experiments with silica gel and beech wood spheres and mixing effects are studied in detail. A good agreement with the measurements of both single-particle and particle bed drying is achieved by resolving heat and moisture transport three-dimensionally inside each particle.     

Mixing of particles in rotary drums: A comparison of discrete element simulations with experimental results and penetration models for thermal processes

The transverse mixing of free flowing particles in horizontal rotating drums without inlets has been simulated by means of the Discrete Element Method (DEM) in two dimensions. In the simulations the drum diameter has been varied from 0.2 to 0.57 m, and the rotational frequency of the drum from 9.1 to 19.1 rpm, for drum loadings of 20% or 30%, and average particle diameters of 2.5 and 3.4 mm. The choice of operating parameters allows for comparison with experimental data from literature. Though simple models for inter-particle interactions have been implemented, the overall agreement is good. The results are presented and discussed in terms of mixing times and mixing numbers that means numbers of revolutions necessary for uniform mixing of the solids. In this way, comparison with penetration models, as typically applied to modelling of thermal processes, is possible. The limitations of such continuum models are pointed out, along with the potential of DEM to replace them, in the long term.     

Numerical Simulation and Analysis of Particle Mixing and Conduction in Wavy Drums

A thermal discrete element method (DEM) is used to simulate particle mixing and heat conduction inside wavy drums to explore the effects of wavy walls. Sinusoidal configurations with different waves on the walls are simulated. The Lacey mixing index is applied to analyze the mixing characteristics. The driven forces from the wavy wall, either positive/negative or effective driven forces, are analyzed to explain the mechanisms of mixing enhancement in the wavy drum. A new control parameter is proposed to explain the mechanism of mixing enhancement. It is found that a locally oscillating effect exists in wavy drums, which is imparted on the bulk rotating motions of particles and enhances the characteristics of particle mixing and heat conduction significantly. Except over large wave numbers and rotating speeds when the flow regime is deteriorated for mixing, the wavy drum is generally beneficial for mixing augmentation as well as conduction enhancement.     

Wall to fluid heat transfer in liquid fluidised beds: Part 2

Wall to fluid heat transfer coefficients and radial temperature profiles have been obtained for beds of hydrodynamically similar spheres fluidized with water in a 2.058 inch pipe at a constant heat flux. From packed bed to open pipe conditions, heat transport occurs mainly by turbulent mixing, although conduction through the particles and possibly particle convection have some effect at low porosities. This result contradicts a previously published prediction based on model calculations using erroneous temperature profiles⁽²⁴⁾. The model predicts a minor role for particle convection when appropriate temperature profiles are used. A series model based on the observed shift of thermal resistance from the wall region to the bulk of the bed with decreasing porosity is used to correlate heat transfer coefficients. The shift in resistance largely accounts for the maximum in heat transfer coefficient plots.     

Particle-fluid heat transfer and dispersion in fluidised beds

The dynamic response of a gas fluidised bed has been measured for a range of particle sizes of lead glass ballotini and a range of particle Reynolds numbers. A dispersion model has been formulated that includes the effects of gas and particle mixing, fluid-to-particle heat transfer and intraparticle thermal conductivity, and the dynamic thermal response in theory has been found by solving the partial differential equations in the Laplace transform domain. The coefficient of thermal dispersion, the particle-to-fluid heat transfer coefficient and the intraparticle thermal conductivity have been found for the experimental response by non-linear regression. The coefficient of axial dispersion was found to be large and the particle to fluid heat transfer coefficients agreed with an established correlation for fixed and fluidised beds. The intraparticle thermal conductivity agreed with literature values for lead glass, the estimates showed no trend with flowrate, and the standard deviation of the estimate was three times smaller than the deviation found from similar experiments in fixed beds.     

不同圆球复合无序堆积床内流动传热数值分析

圆球堆积床内孔隙分布影响其内部流场及温度场分布, 且小管径-球径比堆积床由于壁面限制, 内部孔隙率变化剧烈, 其内部流动和传热不均匀现象明显。针对D/d_p为3的圆球无序堆积床构建了3种非等直径圆球复合堆积结构:径向分层复合堆积、轴向分层复合堆积以及随机复合堆积结构, 并采用DEM-CFD方法建模计算, 从径向及整体角度分析比较不同复合堆积床内流动换热特性及其流场和温度场分布的均匀性。结果表明:孔隙率及孔隙大小分布共同影响堆积床内流场和温度场分布;相对于单一等直径圆球堆积, 采用复合堆积结构能使堆积床内部孔隙率分布更均匀, 其内部流场和温度场分布也更为均匀;对于D/d_p为3的堆积通道, 径向分层堆积结构对于提高整体流动换热性能及改善内部流动换热均匀性都有显著效果。     

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     

PARTIUE FLOW AND CONTACf HEAT TRANSFER CHARACTERISTICS OF STIRRED GRANULAR BEDS

This paper presents a new contact heat transfer model for estimation of wallto- bed heat transfer rates based exclusively on information on particle flow and mixing within a stirred granular bed. The effects of solids flow ability, bed height, blade rotational speed, size of the annular wall-to-blade clearance, vessel diameter and aeration of the bed on the overall solids mixing patterns, particle renewal rates and contact heat transfer in vessels agitated with flat paddles are presented and discussed. The model is shown to yield satisfactory agreement With expenrnental data.     

Modeling of Contact Dryers

Contact drying of stagnant or agitated beds can be reliably described by the penetration model under vacuum or inert conditions. However, the penetration model has disadvantages in the consideration of granular mechanics and statistics due its continuous nature. The fact that such disadvantages can be avoided by discrete approaches is illustrated by application of the discrete element method to the problem of heating of particles in a rotary drum. Important limiting cases are treated, along with conditions for equivalence between continuous and discrete model. Time constants and scaling aspects are addressed and opportunities of combined product and process engineering are pointed out.     

Identification of the Limiting Mechanism in Contact Drying of Agitated Sewage Sludge

In spite of a great number of industrial applications, the thermal design of contact dryers for sewage sludge remains empirical. To improve the understanding of drying mechanisms, the penetration theory developed by Schlünder and coworkers for mono- and multidispersed packing is used to represent the experimental results from a laboratory-scale dryer. For granular packing, the only adjustment parameter of the model is the mixing number, which characterizes the dryer and its stirrer. For pasty-like materials, the pasty phase is assumed to be a saturated particulate phase. As the calculation of the effective properties calculation is cumbersome for a multi-granular packing, the particulate phase is considered as a monodispersed packing, whose dimension is unknown. To identify the two adjustment parameters, the mixing number was quantified from experiments performed on activated alumina balls, for which physical and thermal characteristics are known, and then the characteristic dimension of the sludge was determined by adjustment of experimental drying kinetics measured in a batch agitated dryer. According to this model, drying is exclusively controlled by the contact resistance between the wall and the biggest particles contained in the dewatered sludge. The model permits to find most of the tendencies experimentally observed for different operating conditions.     

小管径-粒径比颗粒无序堆积通道内壁面效应数值研究

采用DEM-CFD方法对小管径-粒径比颗粒无序堆积通道内壁面效应进行了数值研究。针对D/d_p=5.0圆球无序堆积通道构建了光滑壁面和波节壁面两种通道壁面结构,分析了不同壁面结构堆积通道内孔隙率分布、流动和温度场分布及其流动换热性能。结果表明：小管径-粒径比光滑壁面颗粒无序堆积通道内壁面效应显著,壁面附近平均流速明显高于堆积中心区域,而平均温度要低于堆积中心区域,壁面附近0.5d_p区域内通过的流体质量流量比例为46%;波节壁面结构抑制了通道壁面附近漏流,可小幅提高堆积通道的换热能力,但堆积通道内的流动阻力也随之增大,其综合换热性能较光滑壁面堆积通道有所下降。     

HEAT TRANSFER BETWEEN PACKED,AGITATED AND FLUIDIZED BEDS AND SUBMERGED SURFACES

Heat transfer between packed, agitated and fluidized beds and submerged surfaces is treated by a common theoretical concept. The thermal properties appearing in this concept may be predicted a priori. The remaining problem is how to describe the particle motion. It is shown that the penetration model, which is well known from gas liquid systems, also applies to gas-solid systems. The results of the theoretical approach are compared with numerous experimental data obtained from literature.     

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.     

Thermal dispersion and wall heat transfer in packed beds

A new analysis showing the effect of axial and radial thermal dispersion and wall thermal resistance upon heat transfer to fixed beds of solids is presented. By application of this theory and non-linear regression, coefficients of axial and radial dispersion and wall heat transfer coefficients are calculated from experimental measurements of radial temperature profiles in fixed beds heated at the wall.The experiments have been performed for beds packed with glass and with metallic particles within the particle Reynolds number range from 1 to 400.The calculated coefficients are compared with experimental values reported by other workers. Some differences are attributed to the neglect of axial dispersion in the work of others, but other differences are significant in that, for example, thermal characteristics of fixed beds of metallic particles differ from those of non-metallic particles.