Batch top-spray fluid bed coating: Scale-up insight using dynamic heat- and mass-transfer modelling

A mathematical model was developed for batch top-spray fluid bed coating processes based on Ronsse et al. [2007a, b. Combined population balance and thermodynamic modelling of the batch top-spray fluidised bed coating process. Part I—model development and validation. Journal of Food Engineering 78, 296-307; Combined population balance and thermodynamic modelling of the batch top-spray fluidised bed coating process. Part II—model and process analysis. Journal of Food Engineering 78, 308-322]. The model is based on one-dimensional discretisation of the fluid bed into a number of well-mixed control volumes. In each control volume, dynamic heat and mass balances were set up allowing the simulation of the contents of water vapour, water on core particles and deposited coating mass as well as fluidisation gas, particle and chamber wall temperature. The model was used to test different scale-up principles by comparing simulation results with experimental temperature and humidity data obtained from inorganic salt coating of placebo cores in three pilot fluid bed scales being a 0.5 kg small-scale (GEA Aeromatic-Fielder Strea-1), 4 kg medium-scale (GEA Niro MP-1) and 24 kg large-scale (GEA MP-2/3). Results show good agreement between simulated and experimental outlet fluidisation air temperature and humidity as well as bed temperature. Simulations reveal that vertical temperature and humidity gradients increase significantly with increasing scale and that in fluid beds as the simulated 900 kg (RICA-TEC Anhydro) production-scale, the gradients become too large to use the simple combined drying force/relative droplet size scale-up approach without also increasing the inlet fluidisation air temperature significantly. Instead, scale-up in terms of combinations of the viscous Stokes theory with simulated particle liquid layer profiles (obtained with the model) is suggested. In this way, the given fluid bed scale may be optimised in terms of low agglomeration tendency for a given process intensity across scale.     

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.     

固定床内错流传热——II.床层对壁给热系数的经验关联式

采用3种导热性能不同的固体颗粒为填充物,以空气为介质,在床层被加热的情况下,研究了固定床中内置圆管的错流传热.采用最小二乘法对实验数据进行拟合,得到以床层对壁的平均给热系数、气体的导热系数和床层中被加热圆管的管径计算的Nusselt准数经验关联式:Nuf=31(lb0/ls)1.4(Db/Dp)0.2Rep0.33Pr0.62,Rep=10~180,Db/Dp=28~116,lb0/ls=0.5~0.2.Reynolds数以固体颗粒的等外表面积当量直径进行计算.结果表明,在错流传热过程中,表征气体流动特性的参数Rep仍是错流传热的重要影响因素,Nusselt准数除与床层的结构参数Db和颗粒的当量直径Dp有关外,还与颗粒的导热系数ls和床层的导热系数lbo密切相关.     

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.     

Effect of annular fins on heat transfer of a horizontal immersed tube in bubbling fluidized beds

Experiments were conducted in a bubbling air-fluidized bed to investigate the effect of annular fins of constant thickness on heat transfer. Steady state time averaged local heat transfer coefficient measurements were made by the local thermal simulation technique in a cold bubbling fluidized bed (90 mm ID, 260 mm tall) with horizontally immersed tube initially with no fin and then with three fixed annular fins of constant thickness. Silica sand of mean particle diameter 307 μm and 200 μm were used as the bed materials. The superficial velocity of air was from minimum fluidization conditions, u_mf, to approximately 3 × u_mf. The results indicate that, although the heat transfer coefficient falls with the use of fins, the total heat transfer rises as a result of the greater surface area. Increasing the particle diameter reduces the heat transfer coefficient not only for unfinned horizontal tube but also for annular finned horizontal tube at the same conditions of fluidized bed. Based on the experimental data, correlations are proposed for predicting heat transfer coefficient from fluidized bed to horizontally immersed tubes with and without fins.     

Heat transfer of gas-solid two-phase mixtures flowing through a packed bed

This paper reports an experimental study on both transient and steady-state heat transfer behavior of a gas-solid two-phase mixture flowing through a packed bed under constant wall temperature conditions. A logarithmic mean temperature difference (LMTD) method is used to process the temperature data to obtain the overall heat transfer coefficient. The influences of particle loading and gas flow Reynolds number are investigated. The results show that the introduction of suspended particles greatly enhances heat transfer between the flowing gas-solid two-phase mixture and the packed bed, and the enhancement increases approximately linearly with increasing particle loading. The heat transfer coefficient data are processed to give the Nusselt number, which is found to correlate well to the Reynolds number, the Archimedes number and the suspended particle loading ratio. A comparison of the data of this work with the published data reveals large discrepancy. Possible reasons for the discrepancy are discussed.     

Kinetic theory based computation of PSRI riser: Part II—Computation of mass transfer coefficient with chemical reaction

The design of circulating fluidized bed systems requires the knowledge of mass transfer coefficients or Sherwood numbers. A literature review shows that these parameters in fluidized beds differ up to seven orders of magnitude.To understand the phenomena, a kinetic theory based computation was used to simulate the PSRI challenge problem I data for flow of FCC particles in a riser, with an addition of an ozone decomposition reaction. The mass transfer coefficients and the Sherwood numbers were computed using the concept of additive resistances. The Sherwood number is of the order of 4 × 10⁻³ and the mass transfer coefficient is of the order of 2 × 10⁻³ m/s, in agreement with the measured data for fluidization of small particles and the estimated values from the particle cluster diameter in part one of this paper. The Sherwood number is high near the inlet section, then decreases to a constant value with the height of the riser. The Sherwood number also varies slightly with the reaction rate constant. The conventionally computed Sherwood number measures the radial distribution of concentration caused by the fluidized bed hydrodynamics, not the diffusional resistance between the bulk and the particle surface concentration. Hence, the extremely low literature Sherwood numbers for fluidization of fine particles do not necessarily imply very poor mass transfer.     

Modeling and Numerical Analysis of an Atypical Convective Coal Drying Process

This work presents modeling and numerical simulation of batch convective coal drying in a deep packed bed after a high-pressure steam treatment (a part of the Fleissner coal drying process). The process is atypical, because ambient air is used to dry and cool hot particles, while usually, e.g., in the deep packed bed drying of biomaterials, hot air is contacting cold particles. Product-specific data (intraparticle mass transfer, gas-solids moisture equilibrium) for coal (here lignite) are taken over from literature. Available data on coal drying in packed beds of medium height are used for model validation. Then, the model is applied to the considered industrial process. The design point of the process is critically reviewed, and alternatives are developed by systematically simulating the influence of inlet air conditions (temperature, humidity, flow-rate) and coal particle size. This type of analysis is necessary for efficiently scheduling plant dryers, since coal particle size may change, and air inlet temperature and humidity are changing with the ambient conditions.     

Simultaneous heat and mass transfer in spouted beds

The results of a fluid-particle heat and mass transfer study in air spouted beds of silica gel and activated coal particles, using a 9 cm I.D. column with a 30° and 90° conical base, are reported. The effects of gas velocity, particle size, bed depth and cone angle on the heat and mass transfer coefficients are discussed. Equations correlating heat and mass transfer coefficients have been established. The ratio (jn)_s/(j_D)₈ has been found to be dependent on the Reynolds number and the system of spouting.     

Total and gas convective heat transfer from a vertical tube to a mixed particle gas—solid fluidized bed

Experimental data were obtained for the average gas convective and total heat transfer coefficients for a vertical tube immersed in an air-fluidized bed of narrowly as well as widely distributed particle size mixtures. The gas convective heat transfer coefficient was determined by measuring the rate of mass loss from a vertical naphthalene tube 0.0262 m in diameter and 0.1012 m in length and using a heat and mass transfer analogy. These data were obtained at a bed temperature of about 330 K and superficial velocity of 0.1 to 1.1 m/s. The total heat transfer coefficients were measured under identical conditions using an electrically heated vertical tube. The total heat transfer coefficient decreased with an increase in particle diameter from 0.237 to 1.35 mm. The addition of fines was found to increase the total heat transfer coefficient. The gas convective heat transfer coefficient increased with increase in particle size and fluidizing velocity. The dependence of the gas convective heat transfer coefficient on gas velocity was more pronounced for large particles. The addition of fines resulted in decrease in gas convective coefficient. The relative contribution of the gas convective component of heat transfer coefficient was found to increase with increase in particle diameter. Its dependency on fluidizing velocity was found to be more complex. The experimental data were compared with the existing heat transfer models and correlations.     

锯齿翅片的传热与阻力性能试验

在风洞试验台上对16种不同结构参数的板翅换热器中使用锯齿翅片进行了传热和流动阻力性能试验,分析比较了翅片间距和翅片长度对其表面对流传热系数和空气阻力性能的影响。同时通过对16种翅片的244个试验数据点进行多元回归和F显著性检验,获得了j因子和f因子的经验关联式。在Re=500～7500范围内,经验关联式的最大误差范围为±10%,绝对平均偏差分别为4.2%和5.3%。     

Particle-to-fluid heat transfer coefficients in miniporous media

The heat transfer between the solid particles and the fluid in a miniporous media was studied experimentally and numerically. The experimental test section was a sintered bronze porous media with an average particle diameter of 0.2 mm. Particle-to-fluid heat transfer coefficients in the miniporous media were determined experimentally using a transient single-blow technique. A lumped capacitance method (method 1) was used to calculate the particle-to-fluid heat transfer coefficients from the experimental data. The particle-to-fluid heat transfer coefficients were also calculated from a one-dimensional numerical analysis of the experimental data (method 2) which has been used by many researchers. The experimental results for h_sf using the two methods agreed very well. Therefore, method 1 is also deemed acceptable and much simpler than method 2. Three-dimensional numerical simulations using the CFD code FLUENT was also used to predict the particle-to-fluid heat transfer coefficients and to provide details of the fluid flow inside the miniporous media.     

Surface-to-bed heat transfer in fluidised beds of fine particles

This work reports experimental results on the heat transfer between a fluidised bed of fine particles and a submerged surface. Experiments have been carried out using different bed materials (polymers, ballotini, corundum, carborundum and quartz sand) with Archimedes number between 2 and 50. Dry air at ambient pressure and temperature has been used as fluidising gas. Three different exchange surfaces, namely a sphere and two cylinders with different base diameter and same height, have been used.Experimental results show that the heat transfer coefficient increases with particle Archimedes number and is almost independent from particle thermal conductivity for K_p/K_g > 30. Finally, the comparison of heat transfer coefficient for the different surfaces shows that the effect of the surface geometry may account for a 30% variation in the heat transfer coefficient, with higher differences occurring for coarser particles.     

Heat transfer and flow behaviour of aqueous suspensions of titanate nanotubes (nanofluids)

Titanate nanotubes of an aspect ratio of ~ 10 are synthesized, characterised and dispersed in water to form stable nanofluids containing 0.5, 1.0 and 2.5 wt.% of the nanotubes. Experiments are then carried out to investigate the effective thermal conductivity, rheological behaviour and forced convective heat transfer of the nanofluids. The results show a small thermal conductivity enhancement of ~ 3% at 25 °C and ~ 5% at 40 °C for the 2.5 wt.% nanofluid. The nanofluids are found to be non-Newtonian with obvious shear thinning behaviour with the shear viscosity decreasing with increasing shear rate at low shear rates. The shear viscosity approaches constant at a shear rate higher than ~ 100-1000 s^− 1 depending nanoparticle concentration. The high shear viscosity is found to be much higher than that predicted by the conventional viscosity models for dilute suspensions. Despite the small thermal conduction enhancement, an excellent enhancement is observed on the convective heat transfer coefficient, which is much higher than that of the thermal conductivity enhancement. In comparison with nanofluids containing spherical titania nanoparticles under similar conditions, the enhancement of both thermal conductivity and convective heat transfer coefficient of the titanate nanotube nanofluids is considerably higher indicating the important role of particle shape in the heat transfer enhancement. Possible mechanisms are also proposed for the observed enhancement of the convective heat transfer coefficient.     

LIQUID-SOLID MASS TRANSFER IN A THREE PHASE DRAFT TUBE FLUIDIZED BED REACTOR

Liquid-solid mass transfer coefficients in a three phase draft tube fluidized bed reactor have been measured using spherical ion exchange particles. The particle diameters ranged from 655 to 1119μm and solids volume fractions of approximately 5 and 10% were employed in water at 28°C. The experimental data can be successfully correlated using a Reynolds number derived using Kolmogoroffs theory of isotropic turbulence, although it is doubtful whether isotropic turbulence actually prevails in the fluidized bed over the range of conditions employed. Comparison with correlations determined for bubble columns and gas-liquid fluidized beds is performed. A model which considers the draft tube reactor as comprising two distinct fluid mechanical regions is developed to explain the apparently lower values of mass transfer coefficients obtained in a draft tube as opposed to conventional fluidized bed reactor.     

低熔点熔盐圆管内强迫对流换热

熔融盐具有使用温度高、热稳定性和传热性能好等优点,被认为是太阳能热发电系统中最有前途的传热、蓄热介质之一。通过搭建槽式太阳能熔盐集热传热实验台,进行了低熔点熔盐管内受迫对流换热实验,获得了不同熔盐流速下套管式熔盐-水传热单元的总传热系数;通过最小二乘法获得了低熔点熔盐管内充分发展紊流段对流换热Nusselt数随Reynolds数的变化曲线和实验关联式,并与经典关联式进行了对比,结果表明,实验数据和Dittus-Boelter方程、Colburn方程、Seider-Tate方程以及Gnielinski方程最大偏差分别为+23%、+13%、-10%和-20%,实验数据和经典公式符合较好。     

Properties of ceramic foam catalyst supports: mass and heat transfer

Mass and heat transport properties have been determined for 30 PPI -Al₂O₃ ceramic foam containing 6 wt.% γ-Al₂O₃ washcoat. The foam was loaded with 5 wt.% platinum and the rate of carbon monoxide oxidation measured for a 0.3 cm cylindrical segment of the foam operating with mass transfer controlling at 550 °C. This gave a mass transfer factor versus Reynolds number correlation that was equivalent to a packed bed of particles.

A correlation for the radial heat transfer coefficient in a bed of ceramic foam was determined by measuring outlet temperatures achieved when air at varying flow rates and inlet temperatures was passed through a bed of foam pellets. Correlation parameters of a 1D model were fitted from 700 to 1000 °C using a Simplex optimization routine. Radial heat transfer coefficients were two to five times higher than those predicted from packed bed correlations.     

A simple energy balance to determine heat transfer coefficients from low temperature measurements in a fluidised bed

A bench-scale fluidised bed (105 × 200 mm) was set-up for studying bed-to-gas and wall-to-bed heat transfer. Low temperature (17-200 °C) experiments were conducted at steady state avoiding excessive instrumentation and time. Compressed dry air at ambient temperature entered the bed through a distributor of a 200-mesh brass sieve and fluidised the single charge of alumina particles with a mean diameter of approximately 250 μm. The superficial gas velocity ranged from 0.085 to 0.412 m s^− 1. A simple model was developed based on steady state energy balances, i.e. equating the electrical power input separately to the rate of heat transfer from the heater walls to the bed and from the bed to the gas. The bed-to-gas heat transfer coefficient was calculated from the model equations. Inserting this value into the relevant heat transfer equations then extracted the wall-to-bed and bed-to-gas heat transfer coefficients. The agreement between the experimental and predicted values of temperatures validated the model. The latter may be successfully used to design fluidised beds for e.g. drying or combustion.     

松木屑颗粒热解过程中的热/质传递规律

为探索在固定床反应器中有机固废颗粒热解过程中的热量、质量传递机理,本研究从颗粒尺度上对有机固废松木屑颗粒热解过程建模分析,模型中考虑了焦油的二次裂解反应及挥发分在颗粒孔隙中的质量、动量传递过程,并采用达西定律模拟了挥发分在颗粒孔隙内的流动现象,对颗粒热解过程的吸热反应以及挥发分逸出时的对流换热对颗粒温度的影响进行考察。基于两步反应动力学模型,探讨了不同颗粒尺寸、热解温度对有机固废松木屑颗粒热解过程的影响。结果表明,热解吸热反应和挥发分的对流换热阻碍了热量向颗粒中心的传递,延长了颗粒达到均温的时间;松木屑颗粒热解时,颗粒内会存在明显的温度梯度,在颗粒表面主要受化学反应动力学限制,在颗粒内部则主要受热量传递过程限制。此外,热解温度越低,粒径越大,颗粒内部的传热阻力越大。松木屑颗粒完全热解所需时间会随着颗粒粒径的增大而增加,但当颗粒粒径在10mm以上时,随着颗粒粒径的增大,颗粒完全热解所需时间的增量要大于10mm以下颗粒。     

Liquid–liquid mixing using micro-fluidised beds

This study experimentally investigates the application of a solid–liquid micro-fluidised bed as a micro-mixing device. The experiments were performed in a borosilicate capillary tube with an internal diameter of 1.2 mm (i.e. near the upper-limit dimension of a micro-fluidic system) using borosilicate particles with a mean diameter of 98 μm. Refractive index matching technique using sodium iodide solution was employed to achieve a transparent fluidised bed. Mixing performance of the micro-fluidised bed in terms of mixing time was investigated using a dye dilution technique. Experiments were carried out in the creeping flow regime at Reynolds numbers ranging between 0.27 and 0.72. It was demonstrated that the micro-fluidised bed mixing time sharply decreases as the Reynolds number increases. That is because at relatively high Reynolds numbers, the particle oscillation is stronger creating larger disturbances in the flow. The energy dissipation rate in micro fluidised bed was estimated to be four orders of magnitude less than other passive micro mixers which operate in the turbulent regime. It was also demonstrated that the ratio of mixing time and the energy dissipation rate for fluidised bed micro-mixer was comparable to K-M, Tangential IMTEK, and interdigital micro-mixers. However, the fluidised bed micro-mixer was found to operate at much lower Reynolds numbers compared to other passive mixers, with a mixing time of the order of few seconds.