Modeling of the pressure drop and flow field in a rotating fluidized bed

Rotating fluidized beds (RFB) have found applications as dust filters, dryers, particle coaters, and granulators, and recently as catalytic reactors for the clean up of diesel exhaust. However, successful design and operation of an RFB requires an in-depth understanding of the fundamentals of the fluid dynamics involved. In this study, mechanistic models have been developed to account for the pressure drop relationship with respect to rotating speed, flow rate, properties of the granular particles, and fluidization conditions in the RFB. The models show that the total pressure drop across the bed is quadratically dependent on the rotating speed as well as the flow rate. These quadratic relationships have also been validated experimentally. The pressure drop relationship has further been validated through a full flow field numerical simulation of flow through a rotating bed with a slotted cylindrical distributor but without granular particles in the bed. Using our analytical model together with experimental results from three different types of distributors, a slotted cylinder with a thin metal screen, a perforated cylinder with a thin metal screen, and a sintered metal cylinder, three semi-empirical quadratic equations are obtained to predict the pressure drop across these distributors. A comparison of the distributor pressure drop with that across the fluidized bed (granules only) shows that the pressure drop across the distributor is appreciable and cannot be neglected in RFB applications. The higher the rotating speed, the more significant the pressure drop across the distributor.     

Effect of pressure drop on performance of hollow-fiber membrane module for gas permeation

The pressure drop mainly due to viscous friction inside hollow fibers is taken into consideration by nondimensionalization and numerical simulation of governing equations. For pure gas, the permeation pressure and velocity of actual situations with a viscous fluid deviate significantly from those of the corresponding inviscid or no-pressure-drop cases. The apparent permeability estimated from the relation of permeate flow rate and pressure difference is considerably underestimated in actual situations, and more severely for the region of small pressure difference and large module length. Numerical simulation shows that the estimated permeability behaves as if it were an increasing function of pressure difference for a constant permeability and roughly a constant for a dual-sorption-type permeability, respectively. For binary-mixture permeation the cut ratio and purity of permeate stream are mainly governed by two dimensionless parameters standing for pressure drop and permeability, respectively. The cut ratio and corresponding product composition are predictable without the rigorous simulation of the governing equations.     

测定压敏胶乳液表面张力的简易珠滴重量法

介绍了一种利用常用的酸式滴定管、移液管和电子天平测定乳液表面张力的简易方法。首先通过测定已知表面张力液体的珠滴质量 ,由σ =D×M计算出D值 ,然后测定压敏胶乳液的珠滴质量 ,并利用同样的公式计算出乳液的表面张力。我们利用此方法测定了 5种压敏胶乳液的表面张力。结果表明 ,这种测定乳液表面张力方法操作简便 ,实用性强 ,结果准确可靠。     

An analysis of pressure drop fluctuation in a circulating fluidized bed

The characteristics of pressure drop fluctuation in a 5.0 cm I.D.×250cm high circulating fluidized bed with fine polymer particles of PE and PVC were investigated. The measurements of time series of the pressure drop were carried out along the three different axial locations. To determine the effects of coarse particles and relative humidity of air on the flow behavior of polymer powders-air suspension in the riser, we employed deterministic chaos analysis of the Hurst exponent, correlation dimension and phase space trajectories as well as classical methods such as standard deviation, probability density function of pressure drop fluctuation. From a statistical and chaos analysis of pressure fluctuations, the upper dilute region was found to be much more homogenous flow compared to that in the bottom dense region at the same operating conditions. It was also found that the addition of coarse particles and higher humidity of air reduced the pressure fluctuations, thus enhancing flow stability in the riser. The analysis of pressure fluctuations by statistical and chaos theory gave qualitative and the quantitative information of flow behavior in the circulating fluidized bed.     

Modeling the pressure drop of wet gas in horizontal pipe

A model for gas-liquid annular and stratified flow through a horizontal pipe is investigated,using the two-phase hydrokinetics theory.Taking into consideration the flow factors including the void fraction,the friction between the two phases and the entrainment in the gas core,the one-dimensional momentum equation for gas has been solved.The differential pressure of the wet gas between the two tapings in the straight pipe has been modeled in the pressure range of 0.1-0.8 MPa.In addition a more objective iteration approach to determine the local void fraction is proposed.Compared with the experimental data,more than 83％ deviation of the test data distributed evenly within the band of ± 10％.Since the model is less dependent on the specific empirical apparatus and data,it forms the foundation for further establishing a flow measurement model of wet gas which will produce fewer biases in results when it is extrapolated.     

The effect of reliable prediction of final pressure during pressure equalization steps on the performance of PSA cycles

The present work aims at modeling the performance of isothermal PSA cycles for the production of H₂ from refinery fuel gas by introducing a more reliable calculation of the final pressure during the pressure equalization steps. The latter calculation is performed based on the law of conservation of mass in a system comprehending the depressurizing and pressurizing beds in contact. Single adsorbent (zeolite 5A) dual and six-bed PSA processes have been considered. The PSA cycle performance is compared with a conventional model considering an arithmetic mean for the final pressure during the pressure equalization steps (old model). It is shown that the new model predicts lower values for product purity and recovery when compared with the old model. The error in the estimation of the product recovery is larger than the corresponding value for product purity and may exceed 9%. It is shown that the error in the calculation of purity and recovery strongly depends on the number of beds. The error in the calculation of product recovery increases approximately two-fold increasing the number of beds from 2 to 6. Therefore, the present study shows that implementation of a more robust method for the evaluation of final pressure during the equalization steps is imperative for the development of new models of industrial PSA processes, especially for the number of beds exceeding 2.     

The effect of particle shape on the pressure drop across the dust cake

In order to observe the effect of particle shape of poly-dispersed dusts on filter performance, the pressure drop across the dust cakes of fly ashes from a conventional power plant (PC), fluidized bed combustion (FBC), and paint incinerator (FI) was measured over a metal filter element in the accurate conditions. A fluidized bed column was used to prepare the dust feed stream of uniform particle distribution. The fine particles of FI ash have a tendency to be agglomerated at low transport velocity. The aggregates were broken at high velocity of more than 21 cm/sec. FBC ash composed of jagged type particles and containing high concentration of unburned-carbon showed higher pressure drop than that of PC ash composed mostly of spherical particles. FI ash composed of aggregates of very fine carbon particles presented the highest pressure drop among the fly ashes tested. The shape factors of PC, FBC, and FI ash were estimated as 0.91, 0.76, and 0.65, respectively, by the Ergun equation. The results implied that the irregular particle tends to form a higher pressure drop and to be more compressible than spherical one. This paper is dedicated to Professor Wha Young Lee on the occasion of his retirement from Seoul National University.     

Analysis of a piston PSA process for air separation

The piston driven PSA process offers the potential for achieving productivity improvement by rapid piston action. In the present work, experiments were performed on a laboratory scale piston driven PSA test rig with provisions to vary all the important operating variables, namely, phase angle configuration, stroke length, cycling speed duration and angles of feed introduction and product withdrawal. Air separation on 13X zeolite was chosen as the model experimental system. Experiments with adsorbent particles of two different sizes confirmed that mass transfer resistance is important and may significantly affect the separation performance. A mathematical model was developed to simulate the process. The numerical solution was verified by simulating limiting conditions that had analytical solutions. Some basic model assumptions related to piston motion were verified by comparing with experiments conducted at well-defined limiting conditions like empty column and total recycle. Flow resistance in the connecting tubes seemed to explain the observed difference in both phase and amplitude of the pressure profiles measured at the two ends of the column. The model predictions were generally in good agreement with the experimental observations. The model was used to perform a parametric study in the operating regions that were not covered in the experiments. General inferences are made regarding the operating configurations that are expected to improve system performance.     

Prediction of pressure drop in a modified gas-liquid downflow bubble column

A model for pressure drop in the ejector induced downflow bubble column based on mechanical energy balance within the framework of dynamic interaction of the phases has been formulated. The model includes the effect of bubble formation and form drag at interface on the pressure drop. It provides a functional form of equation for correlating pressure drop. The theoretical model proposed in the present study appears to predict the pressure drop satisfactorily for gas-liquid dispersed flow in the concurrent gas-liquid downflow bubble column.     

OPTO22控制系统在变压吸附提氢装置中的运用

主要介绍了变压吸附生产工艺特点和监控仪表改造安装工作,包括仪表选型、安装施工设计、项目实施及运行效果。     

液-液水力旋流器压力场分布规律分析

利用Fluent软件,选用雷诺应力模型对液-液水力旋流器的压力场分布规律进行研究。通过数值模拟得出了压力场的分布规律:从旋流器的顶部沿轴向向下压力逐渐降低;随着半径的减小,压力也逐渐降低,在中心部位的内旋流区压力损失较大,溢流口处压力降至最低,此处的压力降也最大;入口处的压力损失占总压力损失的40%左右,这部分能量损失对分离不起作用;随着流量的增加底流压力降呈指数形式增加。     

Optimal operation of the pressure swing adsorption (PSA) process for CO<Subscript>2</Subscript> recovery

The operation of PSA (Pressure Swing Adsorption) processes is a highly nonlinear and challenging problem. We propose a systematic procedure to achieve the optimal operation of a PSA process. The model of the PSA process for CO₂ separation and recovery is developed first and optimization is performed to identify optimal operating conditions based on the model. The effectiveness of the model developed is demonstrated by numerical simulations and experiments using CO₂ and N₂ gases and zeolite 13X. Breakthrough curves and temperature changes in the bed are computed from the model and the results are compared with those of experiments. The effects of the adsorption time and reflux ratio on the product purity and the recovery are identified through numerical simulations. The optimization problem is formulated based on nonlinear equations obtained from simulations. The optimal operating conditions identified are applied to experiments. The results show higher recovery of CO₂ under optimal operating conditions.     

Effects of cross-flow velocity, capillary pressure and oil viscosity on oil-in-water drop formation from a capillary

The formation of oil drops from a single capillary with a diameter of 200 μm into a cross-flowing continuous water phase has been studied experimentally with the particle image velocimetry (PIV) technique and numerically with the computational fluid dynamics (CFD) software Fluent. The drop formation time and the volume of the detached drop were used as validation parameters and the results from the two methods corresponded well, with a difference of less than 5% for the drop formation time and 10% for the drop volume. The cross-flow velocity has a major impact on drop size, which decreases as the cross-flow increases. An increase in cross-flow, oil viscosity and capillary pressure displace the position of necking and drop detachment away from the capillary opening, which will have a decreasing effect on the final size of the drop.     

褶型纤维过滤介质压力损失的多尺寸模拟

统筹考虑纤维结构特性、纤维排布及纤维层数等因素,基于MATLAB编写控制程序,建立褶型纤维过滤介质微观尺寸模型,并计算过滤介质固体体积分数?,采用数值模拟方法获取微观尺寸下过滤风速v与压力损失Δp之间的数学关联式,进而获取介质的粘性阻力系数C1。在此基础上,建立褶型纤维过滤介质宏观尺寸模型,基于微观尺寸模拟得到的?及C1,采用数值模拟的方法得到宏观尺寸下迎面风速u与Δp之间的数学关联式,并将数学关联式与多个经验公式进行对比。结果表明,褶型纤维过滤介质内纤维排列方式及介质厚度对Δp有影响,但对C1等性质参数影响不大;微观尺寸研究得到的参数可以为宏观尺寸研究提供指导,微观结构与宏观结构性质参数可以沿用。本研究结果对拓展纤维过滤介质的研究方法及优化其结构具有重要理论及实际意义。     

Analysis of the boundary conditions for the simulation of the pressure equalization step in PSA cycles

In this work, the physical validity of Danckwerts boundary conditions (original and modified) for simulating the connection of two beds in the pressure equalization step of a PSA cycle with a dynamic model including axial dispersion is analyzed. A model of this kind has been employed to simulate the separation of a carbon dioxide/methane mixture with silicalite as the adsorbent using a Skarstrom PSA cycle including a pressure equalization step before the pressurization step of each bed. It is demonstrated that both kinds of boundary conditions can lead to unrealistic results (either mass and heat flux are not conserved or molar fraction and temperature are not continuous in both beds) if the contribution of dispersion to axial mass flow is important, which occurs for long equalization times. To overcome these problems, the continuity of both dependent variables and fluxes as boundary conditions is proposed, which lead to the expected results for very long equalization times (the flux of each component is conserved and flat and continuous spatial profiles of all the dependent variables are obtained in both beds). These boundary conditions, unlike the ones proposed in the literature, can be the same regardless of the direction of flow. The impact of the different kind of boundary conditions on the performance results of the selected PSA process at the cyclic steady state is also analyzed.     

A general correlation for pressure drop in a Kenics static mixer

A new pressure drop correlation in a Kenics static mixer has been developed. Pressure drop data were generated from computational fluid dynamics (CFD) calculations, avoiding the experimental limitations in obtaining comprehensive data enough for developing a reliable pressure drop correlation. Dimensional analysis reveals that the pressure drop characteristic of the Kenics static mixer can be described by three dimensionless groups, i.e., the friction factor, Reynolds number (Re), and aspect ratio of a mixing element (AR). A systematic graphical analysis led to a single master curve governing the pressure drop behavior of the Kenics static mixer, which had never been achieved before. We derived a pressure drop correlation fitting well with the obtained master curve in a general form into which the AR effect on the pressure drop is directly incorporated. Unlike the already existing correlations available in the literature, the correlation proposed in this study can cover the whole range of Re from laminar to turbulence. The reliability of the proposed correlation was validated by the comparison with various pressure drop data reported in the literature.     

Studies on frictional pressure drop of gas-non-Newtonian two-phase flow in a cocurrent downflow bubble column

An exclusive study has been done on experimental investigation of the two-phase frictional pressure drop with air-non-Newtonian liquid (CMC solutions) system in cocurrent downflow bubble column. The effects of gas and liquid flowrate on two-phase frictional pressure drop have been illustrated. An attempt has been made to fit the experimental two-phase frictional pressure drop data by modified Lockhart and Martinelli correlation and Aoki correlation. In another approach, friction factor method was adopted to correlate the experimental results in terms of dimensionless groups of the operating and system variables and the predicted values were found to be in good agreement with the experimental result. The experiments were performed in the bubbly flow regime because of its stability and uniformity.     

Effect of a severe form of initial gas maldistribution on pressure drop of a structured packing bed

The results of an experimental study devoted to establishing the relation between a severe form of initial gas distribution, as created by a chordal blockage set-up used in a recent FRI study, and the hydraulics of a structured packing bed are presented. Both dry and wet bed experiments were conducted with air/water system under ambient conditions, using a 1.4 m i.d. Plexiglas column in conjunction with Montz-pak B1-250 packing bed of the approximately same length, employing liquid loads corresponding to that from the FRI study. From dry and wet experiments it appeared that chordal blanking of 30% of cross-sectional area at gas inlet can influence the pressure drop significantly, particularly that in the lower part of the bed.     

Determination of shear viscosity and shear rate from pressure drop and flow rate relationship in a rectangular channel

In this study, we present a unique approach to calculate the shear viscosity and shear rate with the pressure drop and flow rate data from a channel having a rectangular cross-section with a height-to-width ratio (H/W) of close to one. The derived equation was verified with experimental data from rectangular dies whose height-to-width ratio (H/W) ranges from 0.1 to 1. It was confirmed that the proposed approach is reliable for the calculation of the shear viscosity and shear rate from the flow data in a rectangular channel.