Interfacial stress in non-Newtonian flow through packed bed

This study investigates the pressure drop characteristics, shear stress in packed bed with shear thinning power law type non-Newtonian liquid. A mechanistic model has also been developed to analyze the pressure drop and interfacial stress in packed bed with non-Newtonian liquid by considering the loss of energy due to wettability. The Ergun's and Foscolo's equations were used for comparison with the experimental data. The Ergun equation was modified to account for the effect of flow behavior index of non-Newtonian fluid in the column. The intensity factor of shear stress and the friction factor were analyzed based on energy loss due to wettability effect of liquid on the solid surface.     

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.     

Performance of stress-transport models in the prediction of particle-to-fluid heat transfer in packed beds

Computational fluid dynamics (CFD) as a simulation tool allows obtaining a more complete view of the fluid flow and heat transfer mechanisms in packed bed reactors, through the resolution of 3D Reynolds averaged transport equations, together with a turbulence model when needed. This tool allows obtaining mean velocity and temperature values as well as their fluctuations at any point of the bed. An important problem when a CFD modeling is performed for turbulent flow in a packed bed reactor is to decide which turbulence model is the most accurate for this situation. Turbulence models based on the assumption of a scalar eddy viscosity for computing the turbulence stresses, so-called eddy viscosity models (EVM), seem insufficient in this case due to the big flow complexity. The use of models based on transport equations for the turbulence stresses, so-called second order closure modeling or Reynolds stress modeling (RSM), could be a better option in this case, because these models capture more of the involved physics in this kind of flow.To gain insight into this subject, a comparison between the performance in flow and heat transfer estimation of RSM and EVM turbulence models was conducted in a packed bed by solving the 3D Reynolds averaged momentum and energy equations. Several setups were defined and then computed. Thus, the numerical pressure drop, velocity, and thermal fields within the bed were obtained. In order to judge the capabilities of these turbulence models, the Nusselt number (Nu) was computed from numerical data as well as the pressure drop. Then, they were compared with commonly used correlations for parameter estimations in packed bed reactors. The numerical results obtained show that RSM give similar results as EVM for the cases checked, but with a considerably larger computational effort. This fact suggests that for this application, even though the RSM goes further into the flow physics, this does not lead to a relevant improvement in parameter estimation when compared to the performance of EVM models used.     

Cavity formation and breakup forces in conical spouted beds

A method has been developed to deduce a “breakup” force in a packed bed based on measured pressure drop and internal cavity size hysteresis data in a conical spouted bed. The pressure drop over the vertical jet is estimated by the Eulerian-Eulerian two-fluid model using the commercial Fluent software. The pressure drop over the packed bed is extracted from the measured total pressure drop following a flow rate descending process in the spouted bed, while the “breakup” force is determined from the combination of measured total pressure drop and internal jet height following the flow ascending process, the simulated pressure drop over the gas jet and the pressure drop over the loosely packed upper bed section. Such a proposed method can be applied in the future to develop a generalized expression for the “breakup” force in spouted beds and other packed bed systems where a vertical fluid jet is issued into the packed particles.     

生物膜填料床内含有生化反应的多相传输模型

废气处理生物膜滴滤塔的多孔填料床内是带有气液两相流动、有机污染物扩散、生物膜内生化反应的复杂生化反应体系.在平行平板理论模型基础上,建立了生物膜多孔填料床内含生化反应的多元多相流动及传输特性的多相混合模型,获得了废气处理生物膜滴滤塔净化效率的理论计算方法.模型的理论预测值与生物膜滴滤塔净化低浓度甲苯废气的实验结果基本吻合.     

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.     

Tracer experiments in fixed beds: effects of flow maldistribution on the estimation of transport kinetic parameters

A systematic study of liquid phase axial dispersion was conducted in glass columns (inner diameters, 1 cm and 1.6 cm), packed randomly with granular sand, by varying the fluid flow rate, particle size and bed height. Pulse and step response techniques, with KCl as an inert tracer, were used. The resultant data, covering the Reynolds number range from 1 to 50, are presented as plots of the Peclet number based on particle diameter against Reynolds number.Inert tracer experiments were also carried out in a column (inner diameter, 1.6 cm) packed with activated carbon granules, using different particle sizes, fluid flow rates and bed heights, in order to estimate the effective intraparticle diffusivity. We show that flow maldistribution produces pulse response curves with sharp, narrow peaks which, when compared with theoretical curves, result in small intraparticle diffusivities.We illustrate how the outer-phase transfer function can be obtained from the overall transfer function of the activated carbon bed and we compare it with the transfer function obtained directly using impermeable particles similar to the activated carbon granules.     

Flow Field Simulation and Measurement in Packed Beds Based on 4D-X-Ray Computed Tomography

X-ray computed tomography (XCT) combined with computational fluid dynamics (CFD) simulations have proved to be a powerful and versatile tool to describe fluids flow through packed bed systems. In this contribution, two examples of the application of XCT experiments to track the fluid flow and fluid penetration in packed bed systems are shown. The first one shows how geometrical information extracted from XCT measurements can be coupled to CFD simulations to assess fluid flows reliably. Here the example of a packed bed of three-dimensional (3D) printed cylindrical-shaped particles is considered. Finally, a short case study on the monitoring of the progress of the water penetration front in a packed bed composed of glass spheres using four-dimensional (4D) XCT imaging data is presented.     

Correlating gas–liquid co‐current flow hydrodynamics in packed beds using the F‐function concept

A phenomenological model based on the generalization of the single‐phase Forchheimer equation was recently proposed for predicting pressure drop and phase saturations in gas–liquid co‐current horizontal and downward high‐pressure packed beds. Here, we extend the model to packed‐bubble (co‐current upflow) and trickle‐bed operation using phase saturation power laws similar to Corey relative permeabilities. The power‐law exponents were fitted using a wide pressure gradient and liquid saturation databank in co‐current up/downward packed‐bed flows. It was found that this approach, as well as other in the literature developed for down‐flow reactors apply also to upward flows; the prediction accuracy was comparable for both flow directions to existing literature approaches. Copyright © 2004 Society of Chemical Industry     

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.     

Flow characteristics in packed and fluidized rotating beds

Free particles in a rotating tapered cylindrical container are, as a consequence of the circular motion, forced radially outwards towards the circumference to form a packed annular bed. If the container wall is porous and a fluid is allowed to flow radially inward, the bed material may become fluidized. In the resultant centrifugal fluidized bed, radial accelerations many times one g can be generated, permitting much larger fluid flow rates during fluidization than are possible with a conventional fluidized bed. Entrainment of material can also be greatly reduced in such a geometry.The flow in both packed and fluidized beds in a rotating system is analyzed. Expressions are found for the shape of the bed as well as the distribution of particles in packed beds containing mixtures of materials having different size distributions and densities. Based on these results, equations predicting the pressure drop and radial flow distribution are deduced. The condition and location where initial fluidization of the packed bed occurs are predicted. Similarly, conditions in the fluidized state are analyzed, and it is shown that the tangential velocity distribution in the bed under these conditions is directly proportional to the bed radius.Experiments confirming the validity of the analytic models are conducted over a range of operating conditions for different bed materials.     

THE FLOW OF MICROEMULSIONS THROUGH PACKED BEDS AND CAPILLARY TUBES

The flow behavior of water-in-oil microemulsions through beds packed with glass spheres was studied experimentally. The microemulsions used in this study exhibited a shear thinning viscosity described by a simple power law model. The flow of the microemulsions was accompanied by significant apparent slip effects, quantified by an effective slip velocity. The effective slip velocity increased with increasing surfactant concentration, but it differed in magnitude for the packed bed and the capillary tube flows.

In the absence of apparent slip effects, the capillary-power law (CPL) model predicted the superficial velocities in the packed beds with an average error of less than 6%. This provides a direct verification of the applicability of the capillary-power law model to inelastic shear thinning fluids in the absence of “anomalous” wall effects.     

Optimization and simulation of the Sabatier reaction process in a packed bed

The Sabatier reaction in a testing packed bed was investigated experimentally and theoretically, and was used to convert waste carbon dioxide and hydrogen to provide needed water for closing the life‐support loop on orbit in space. A three‐dimensional model including fluid flow, gas dispersion, heat and mass transfer, and chemical reaction was developed by coupling some semi‐empirical correlated equations in chemical engineering science into computational fluid dynamics theory. Good agreements between the simulating results and experimental data for the effect of some parameters on reaction verified this model, for example, heat exchange between reactor and atmosphere, the material property of reactor, the catalyst deactivated and gas mass flux and so on. By using this model as the designing tools, an optimized packed bed is proposed. Compared with the testing packed bed, the relevant reactor length can be reduced from 220 to 150 mm with the same hydrogen conversion and lower pressure drop. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2879–2892, 2016     

A CFD model for predicting the heat transfer in the industrial scale packed bed

Compared to the traditional lumped-parameter model,computational fluid dynamics (CFD) attracted more attentions due to facilitating more accurate reactor design and optimization methods when analyzing the heat transfer in the industrial packed bed.Here,a model was developed based on the CFD theory,in which the heterogeneous fluid flow was resolved by considering the oscillatory behavior of voidage and the effective fluid viscosity.The energy transports in packed bed were calculated by the convection and diffusion incorporated with gaseous dispersion in fluid and the contacting thermal conductivity of packed particles in solids.The heat transfer coefficient between fluid and wall was evaluated by considering the turbulence due to the packed particles adjacent to the wall.Thus,the heat transfer in packed bed can be predicted without using any adjustable semi-empirical effective thermal conductivity coefficient.The experimental results from the literature were employed to validate this model.     

The flow of non-Newtonian solutions through packed beds

The rheological behavior of aqueous solutions of Separan AP-30®, polymethylcellulose, and polyvinylpyrrolidone was studied experimentally. These solutions exhibit non-Newtonian flow behavior in simple shear, and are characterized by one of several 2, 3, or 4 parameter rheological equations. The equations used included the power law, the Ellis model, Spriggs equation, the Herschel-Bulkley equation, and Meter's model. The power law model fits the data for each of the solutions over a limited range of shear rates, whereas the other models, which include either a lower shear rate limiting Newtonian viscosity, and/or an upper shear rate limiting Newtonian viscosity, or a yield stress, fit the data well over a wide range of shear rates from 0.00675 to 1076 sec^?1. The pressure drop-flow rate data for the same aqueous solutions flowing through packed beds were correlated well by the Ergun equation using the various rheological models applied in this work to evaluate a modified fluid viscosity. In each case it was found that the rheological model which best fit the viscometric data also gave the best packed bed friction factor correlation, and that no one model, such as the powerlaw, or the Ellis model, is the best one to use in all cases for all solutions. For polyvinylpyrrolidone solutions large deviations between experimental values of friction factor and those from the Ergun equation occurred for modified Reynolds numbers greater than one. A pseudo viscoelastic parameter was used to improve the friction factor correlation empirically at high Reynolds numbers.     

Flow through porous media of a shear-thinning liquid with yield stress

Darcy's law for the laminar flow of Newtonian fluids through porous media has been modified to a more general form which will describe the flow through porous media of fluids whose flow behavior can be characterized by the Herschel-Bulkley model. The model covers the flow of homogeneous fluids with a yield value and a power law flow behavior. Experiments in packed beds of sand were carried out with solutions of paraffin wax in two oils and with a crude oil from the Peace River area of Canada. The model fitted the data well. A sensitivity analysis of the fitting parameters showed that the model fit was very sensitive to errors in the flow behavior index, n , of the Herschel-Bulkley model. A comparison of the “n” values calculated from viscometer measurements and from flow measurements agreed well. A more general Reynolds number for flow through porous media, which includes a fluid yield value, was developed. The data were fitted to a Kozeny-Carman type equation using this Reynolds number. The constant in the Kozeny-Carman equation was determined for the two packed beds studied using Newtonian oils. The data could all be represented, within the experimental error, by the relationship f^* = 150/Re^*. Since the mean volume to surface diameter of the packing was determined by the measurement of its permeability to a Newtonian oil, assuming C' = 150, the new definition of the Reynolds number allows the direct use of the Kozeny-Carman equation with Herschel-Bulkley type fluids.     

固定床流体流动特征数值模拟

为了研究固定床边壁效应、固定床床层数的变化以及颗粒的填充倾斜角度等参数对床内流体流动状况的影响,基于Ergun方程建立了轴对称多孔介质数学模型。同时对床内流体流动状况进行了研究:在床高确定的情况下,随着床层数的增加,压强降减少;随着颗粒填充倾斜角度的增加,压强降也减少,速度径向分布不均;在固定床边壁附近,气体速度明显增大。计算结果与实验值的比较表明模型能有效地描述固定床压强降和床内流体流动状况。     

A viscous–inertial model of foam drainage

The common factor that links various current methods of estimating drainage rate through a gas–liquid foam is that all losses of pressure due to flow are assumed to be entirely viscous. However, by drawing analogy with liquid flow through a packed bed, it is apparent that, for foams that are relatively wet or have relatively high Galileo number, there is a significant inertial loss. This is further demonstrated by determining, using computational fluid dynamics, the pressure losses at a constant expansion with fluid flow boundaries. A foam drainage equation that accounts for inertial pressure losses is proposed by adapting the functional form of the Ergun equation for pressure loss due to flow in a packed bed. This is tested against forced drainage data for foam stabilised by SDS with a mono-dispersed bubble size distribution from the literature. It is shown that the model accurately predicts the results with the use of only one adjustable constant, which is, in fact, the number of inertial velocity heads lost due to flow through a slice of foam of one bubble radius in thickness.     

Flow distribution and velocity measurement in a radial flow fixed bed reactor using electrical resistance tomography

Electrical resistance tomography is a relatively simple and inexpensive technique for imaging electrically conducting systems. It has been applied to visualise the flow pattern and distribution inside a radial flow packed bed of novel design for improving reactor performance with lower pressure drop. The density of information yielded by electrical tomography is suitable for validation of Computational fluid dynamics. Sets of tomographic images representing slices through a packed bed have been obtained for a 8-plane × 16-electrode sensor configuration which produces of the order 10³ conductivity measurements in three-dimensions. Pulse injections of high conductivity tracer, both uniformly in the feed and localised, can be imaged as multiple tomographic images or 3D solid-body images, revealing the internal flow pattern. Differentiation of the motion of the tracer peak conductivity within pixels in the sensing planes and between the planes allows the local flow velocities and directions to be determined. This quantifies the flow pattern for uniformity and radial distributive properties.     

小直径比固定床壁效应的CFD分析

引言固定床作为反应器、分离器、换热器等单元设备广泛应用于化工、能源、环境等许多领域。因用途的不同固定床的管径-粒径比(D/d)的范围很宽(1～1000的数量级)。大热负荷的填充床设备,如强放热的化学反应器、核反应堆的冷却壁管列等,常采用较小的管径-粒径比,以利于热量通过