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Experimental analysis of the resistance of packed beds based on the morphology of cylinder
Abstract
Accurate prediction of the resistance of packed beds with cylindrical particles is critical for industrial applications. In this work, a series of experiments were performed to explore the effect of the morphology of cylinder on the pressure drop of airflow through packed beds. We used machined stainless-steel cylindrical particles with diameters of 3, 4, and 6 mm and an aspect ratio H/D = 1–10 to conduct the resistance experiment. The novelty was to propose an Ergun constant of porosity to modify the Ergun equation on the condition of cylindrical particles, which improved the accuracy of resistance prediction of packed beds. The sphericity, porosity, and Ergun constant of the cylindrical particles were found only relating to H/D. The obtained data were substituted into the existing resistance-prediction models and proposed model respectively to compare the predicted errors of resistance, and the highest goodness of fit was obtained by our model.
... Packed bed heat storage is a popular subject for research, both in terms of interaction with other energy storage systems and basic research into the effect of parameters on TES (Thermal Energy Storage) performance. Zhang et al. [11] investigated a packed bed with cylindrical elements on a small scale. The elements were made of stainless steel, which precludes their use on a large scale due to the potential cost. ...
... The effectiveness of prediction using the Ergun equation has been proven repeatedly through experimental and numerical studies [11,[23][24][25]. The concept of determining the pressure drop of a fluid based on Euler's number was presented by Feng et al. [26], and its effectiveness was demonstrated on the basis of experimental data developed for this purpose. ...
This article is a broad literature review of materials used and defined as potential for heat storage processes. Both single-phase and phase-change materials were considered. An important part of this paper is the definition of the toxicity of heat storage materials and other factors that disqualify their use depending on the application. Based on the literature analysis, a methodology was developed for selecting the optimal heat storage material depending on the typical parameters of the process and the method of heat transfer and storage. Based on the presented results, a solution was proposed for three temperature ranges: 100 °C (low-temperature storage), 300 °C (medium-temperature storage) and 500 °C (high-temperature storage). For all defined temperature levels, it is possible to adapt solid, liquid or phase-change materials for heat storage. However, it is essential to consider the characteristics of the specific system and to assess the advantages and disadvantages of the accumulation material used. Rock materials are characterised by similar thermophysical parameters and relatively low prices compared with their universality, while liquid energy storage allows for greater flexibility in power generation while maintaining the operational parameters of the heat source.
... In the present work additional series of validation tests is conducted in Section 5 using experimental data cases from Table 2 Fig. 4. Void fractions ranges obtained for beds of equilateral FC in previous works [41,55,[111][112][113][114][115][116] and in the present study. The information about ∕ ratio is in brackets. ...
Cylindrical particles are widely employed in chemical engineering when a high surface area is necessary for process intensification. However, reliable information about the orientation of non-spherical particles in random packed beds is very scarce. Moreover, a potential effect of the orientation of cylindrical particles on fluid flow has not been examined yet in a real packing geometry. In this work, a new experimental approach has been applied to perform systematic studies of global and local orientation of cylindrical particles in random packed beds. Five different column-to-particle diameter Dc/Dp ratios were examined, ranging from 4 to 15.1. Orientation distribution was measured in the entire bed, with the bottom region excluded and in the core zone. Next, the experimental cases were reconstructed numerically with different packing densities. Finally, the effect of different orientation distributions of cylindrical particles, including full cylinders (FC) and Raschig rings (RR), on pressure drop (for identical bulk void fraction) in a selected packed bed configuration was examined numerically through computational fluid dynamics simulations. Reproducibility of particles’ orientation distributions was found to be dependent on the number of particles per layer. A substantial effect of the column wall and its bottom on particles orientation was observed. The effect of orientation of FC on pressure drop was found to be moderate, however, in the case of RR, the maximum difference in pressure drop among investigated orientation distributions was as high as 400%.
... As the AR of cylinders increased, the difference between the three equivalent diameters increased. Zhang et al. (2020) conducted packing experiments of cylinders with ARs of 1 and 2 and proposed that when D/d vs ≥ 10, the wall effect could be ignored. However, as AR increased, d vs would be significantly larger than d sd . ...
Particle packing is widely applied in organic pollutant adsorption, catalytic reaction, biomass combustion, nuclear cooling, and other scenarios. Due to the complexity of the shape, the studies on the void fraction of the cylindrical particles are not as thorough as the spherical particles. This study investigated the influence of the filling rate, material properties and sphericity on the void fraction of cylinders through experiments and simulation. DEM (discrete element method) was validated by the internal structures of the packing obtained by CT (computed tomography). Based on the logarithmic correlation between the void fraction and filling rate, an ingenious framework for predicting the void fraction of cylindrical particles was presented with two intermediate coefficients. By correlating the coefficients with the material property and sphericity, a novel void-fraction prediction model was established with R-squared of 0.996. The mechanism of void fraction under random loose packing for cylinders was eventually found in this study.
... Zaki [10] investigated the effect of the structure of a flat-bottomed cylindrical silo on the mass flow rate and flow velocity distribution for different outlet shapes with the help of DEM-based open-source software. Zhang [11] analysed the flow pattern transition affected by the structural parameters of a silo for storing grain material. Liu [12] studied the effect of curved geometry hoppers with different contraction rates on the particle discharge flow with the help of the DEM method. ...
Good particle flow patterns and uniform particle velocity distributions enhance the performance of heat transfer and smooth flow processes in vertical sinter cooling beds (VSCBs). The effect of three typical geometries, conical, curved and rectangular, on the performance of flow profiles and segregation in a VSCB is investigated comparatively and quantitatively based on the discrete element method (DEM). The evolution of flow profiles and particle segregation directly influence the evenly distributed sinter layers and the efficiency of heat exchange in VSCBs. In this research, a 3D packed bed model is established for the three geometry types to quantitatively and qualitatively investigate the influence of structural parameters on the evolution of flow patterns and segregation. The comparison of the effect of the three geometry types on the particle flow process showed that the curved geometry types greatly improve the performance of the flow pattern and size segregation. The height of the mass flow pattern for the curved geometry varies with the structural parameters by 1.5-fold that of the flow pattern for the other two geometry types. The curved geometry dramatically reduces the magnitude of the segregation index (SI) near the sidewall, while this magnitude fluctuates near 1.0 in the central flow passage of the VSCB.
Firebrand piles are known to ignite combustible infrastructure resulting in significant damage; however, the parameters that impact the heat transfer from firebrand piles to a combustible surface are not well understood. Heat transfer from a firebrand pile is directly related to the local firebrand temperatures which can vary significantly due to changes in the burning behavior. A two-phase flow analytical model was developed that includes time varying firebrand diameter, reradiation effects between firebrands, gas temperature and species evolution, and pile porosity effects. The analytical model was used to quantify the temperature of cylindrical firebrands and explore the effects of changing firebrand diameter, firebrand aspect ratio (pile porosity), gas velocity, and local oxygen mass fraction. All of these parameters were found to impact firebrand temperatures. Firebrand pile porosity has a significant impact on the velocity within the pile, with a decrease in pile porosity resulting in lower velocities and lower firebrand temperatures. The modeling results were used to explain the trends in heat transfer measured for firebrand piles on a horizontal plate.
In this work, porous electrospun microfibers (PEMFs) were prepared using a polyimide/polyvinylpyrrolidone/polyethylene glycol (PI/PVP/PEG) solution mixture with coaxial ultrasonic water vapor spraying. After removing PVP and PEG by ultrasonic water washing, the PEMFs were successfully demonstrated as adsorbents for solid phase extraction (SPE). Most non-porous electrospun nanofibers are hundreds of nanometers in diameter, with a specific surface area of dozens of square meters per gram. In contrast, the diameter of the as-prepared PEMFs was tuned between 3–8 μm, the specific surface area was 76 m² g⁻¹ and the pore size was ca 25 nm. Therefore, the flow resistance of the PEMF-SPE cartridges was similar to those of conventional commercial SPE cartridges, and much lower than those of SPE cartridges packed with electrospun nanofibers. Using the PEMF-SPE cartridges with ultra-performance liquid chromatography-fluorescence detector (UPLC-FLD), five fluoroquinolones (FQs) in tap water, egg and milk samples were extracted and quantified successfully. After optimizing the extraction conditions, FQs in water samples were extracted and eluted with high recoveries of 84.8–114.8%. The inter-batch and intra-batch relative standard deviation (RSD) values for the FQs were in the range of 1.9–9.5% (n=3), and the limits of detection were between 0.0024–0.014 μg L⁻¹. The method was linear in the concentration range of 0.005–10 μg L⁻¹. The reliability of the developed method was validated by analyzing tap water, egg and milk samples, and the recovery values were found to be in the range of 74.8–116.6% under the optimized conditions.
The pressure drop in the wick significantly affects the heat pipe heat transfer rates. This study experimentally investigated the pressure drop in wicks with spherical and irregularly shaped particles with comparisons with existing correlations to evaluate their applicability for predicting the pressure drops in wicks. Ten types of copper particles with various shapes and sizes were used to fabricate wicks using loose sintering. The particles included four spherical and six irregular particles with particle sizes from 25 μm to 150 μm. The results showed that the 75 μm spherical particles had the lowest pressure drop and that the pressure drop of the irregular particle wicks decreased with increasing porosity. The Morcom correlation most accurately predicted the pressure drops in the spherical particle wicks with a mean average error (MAE) of 20.11%. For the irregular particle wicks, the Meyer and Smith correlation gave the best predictions for small particle sizes while The Morcom correlation gave the best predictions with larger particles.
A simple geometry model for tortuosity of flow path in porous media is proposed based on the assumption that some particles in a porous medium are unrestrictedly overlapped and the others are not. The proposed model is expressed as a function of porosity and there is no empirical constant in this model. The model predictions are compared with those from available correlations obtained numerically and experimentally, both of which are in agreement with each other. The present model can also give the tortuosity with a good approximation near the percolation threshold. The validity of the present tortuosity model is thus verified.
A new model for resistance of flow through granular porous media is developed based on the average hydraulic radius model
and the contracting–expanding channel model. This model is expressed as a function of tortuosity, porosity, ratio of pore
diameter to throat diameter, diameter of particles, and fluid properties. The two empirical constants, 150 and 1.75, in the
Ergun equation are replaced by two expressions, which are explicitly related to the pore geometry. Every parameter in the
proposed model has clear physical meaning. The proposed model is shown to be more fundamental and reasonable than the Ergum
equation. The model predictions are in good agreement with the existing experimental data.
The knowledge of the pressure drop across a packed bed of irregular shaped wood particles is of great importance for achieving optimal control and maximum efficiency in many applications, such as wood drying, pyrolysis, gasification and combustion. In this work the effect of porosity, average particle size and main particle orientation on the pressure drop in a packed bed is investigated. To this end, particle size distributions and porosities are determined experimentally. Based on the experimental results obtained in this study, the form coefficient C and the permeability K of the Forcheimer equation are calculated for different packed beds. The Ergun equation requires an average equivalent particle diameter that is derived from the measured particle size distribution. This equivalent diameter and the corresponding bed porosity are used in the well known Ergun equation in order to derive adapted shape factors A and B. Since a change in bed porosity and particle size, caused by the degradation of the wood particles and gravity, can be expected in a reacting packed bed, a set of shape factors for use with the Ergun equation is determined that are independent of porosity and particle diameter and fit the experimental data very well.
Rodlike particles have been usually found in industrial applications, such as the straw and needle catalyst in energy and chemical engineering. Compared to spherical particles, rodlike particles exhibit different behaviour in the packing structure due to their rotational movement. In this work, we have experimentally explored the packing structure and its friction factor for fluid flow. The porosity of packing structure generated by two packing methods is measured for four kinds of rodlike particles. The experimental results show that the porosity of bed of rodlike particles in the poured packing is not a monotonic function of the aspect ratio of particles. This is due to the competition between the “self-fitting” effect and excluded effect. The porosity of bed of rodlike particles is more sensitive to the packing method than that of spherical particles. To describe the pressure drop of fluid flow through the packing structure, the Ergun equation is further modified by introducing the modified Reynolds number and Galileo number. By combing the experimental data for packed bed generated by the fluidised packing method, and other experimental work in current literature, a new empirical equation is proposed to predict the friction factor of the packing structure of rodlike particles, in which the effects of the particle orientation and particle shape are both considered by the equivalent sphericity. These experimental results would be of interest from applied standpoints as well as revealing fundamental effects of the aspect ratio of rodlike particles on the packing structure.
Volatile organic compounds (VOCs) have been recognized as one of the major environment hazards in air that seriously harm both the environment and human health. Adsorptive removal and catalytic oxidation are two potential technologies for the effective removal of VOCs. The development of efficient adsorbents and catalysts for VOCs with varied nature are critical. In this review, the types of typical VOCs and their properties are summarized. Research progresses on the development of adsorbents and catalysts for different types of typical VOCs removal are overviewed and compared in parallel. Possible adsorption/catalytic oxidation mechanisms are introduced. The barriers, i.e. competitive adsorption of water vapor in adsorptive removal of VOCs, CO byproduct, water vapor and coking suppressions in catalytic oxidation of VOCs are summarized. The perspectives on the potential future directions of the adsorptive removal and catalytic oxidation of VOCs are given.
Adequate equivalent diameters for non-spherical particles in predicting the pressure drop of fluid flow through particle beds were pursued. A series of experiments to measure the pressure drop of single-phase air flow through particle beds were performed using three kinds of spherical particles (2, 3.5 and 5 mm diameter) and four kinds of cylindrical particles. The experimental data were utilized for evaluating previous models and for proposing a new model, a modified Wu et al. (2008) model with an alternative Ergun constant for the viscous energy loss term.
The proposed model agreed well with the pressure drop of single-phase flow through spherical particle beds within 10% in average. The experimental data for cylindrical particle beds also agreed well with the proposed model within 16% in average by applying the equivalent diameter proposed by Li and Ma (2011) as a characteristic size of non-spherical particles.
Understanding separation behavior in an adsorption bed is crucial for well-designed adsorption processes. Since adsorption phenomena depend on temperature, thermal parameters, such as the internal heat transfer (hi), isosteric heat of adsorption (Qst) and axial thermal conductivity of the bed (Kw), can affect the adsorption dynamics and performance of the bed. In this study, the effects of these thermal parameters on the adsorption dynamics and breakthrough curves were analyzed with the experimental results using integrated gasification combined cycle gas from the carbon capture process (IGCC gas; H2 : CO : N2 : CO2 : Ar = 88 : 3 : 6 : 2 : 1 mol%) as a purification gas and blast furnace gas (BFG; H2 : CO : N2 : CO2 = 20 : 0.1 : 44.5 : 35.4 mol%) as a bulk separation gas. The results were then compared with the isothermal and adiabatic results. Considering the variation of the internal heat transfer coefficient and isosteric heat of adsorption along with the propagation of gas in the bed, the temperature profiles inside the bed could be predicted better than in the case using constant values. The axial thermal conductivity of the bed significantly affected the temperature profiles as the temperature excursion was sharp. In the prediction of breakthrough curves, these variable thermal parameters could be replaced by suitable constant values estimated from experimental and theoretical approaches when well-fitted isotherm parameters were applied considering the partial pressure of each component in the feed.
The knowledge on pressure drop over the packed layers of sintered ore particles (SOPs) is deemed essential to have a deep understanding on the flow and heat transfer in emerging vertically arranged sinter coolers for waste heat recovery. In this work, the wall effects on pressure drop over a packed bed of SOPs were studied experimentally. Experiments for SOPs with bed-to-diameter ratio ranging from 7 to 35 and glass beads with the ratio between 6 and 22 were performed. The results revealed that the voidage effect tends to be pronounced for relatively low ratio values, while the friction effect becomes more significant for relatively high ratio values when it is lower than 40. Comparing to the confining walls, the particle characteristics were shown to have a dominant effect on the flow regime in the voids of the SOP-filled beds, whereas an opposite comparison was observed for the smooth glass beads as a reference. The correlations for the wall corrected friction factor proposed in the literature (Exp. Heat Transfer 12 (1999) 309), with varying coefficients, fit well to predict the pressure drop through packed beds for both glass beads and SOPs with considering the wall effects. Improved correlations were also proposed for spherical particles, SOPs and their blends with fairly good predictive accuracy.
The paper presents theoretical analysis of adsorptive drying of gaseous mixtures, containing water vapor and volatile organic compound (VOC), in a cyclic thermal swing adsorption (TSA) system. The system consists of two fixed bed adsorption columns each containing three layers of different adsorbents. The first two layers consist of silica gel and zeolite 13X, as adsorbents of water vapor. The third layer consists of activated carbon, as an adsorbent of the organic component (benzene). A non-equilibrium, non-isothermal, and non-adiabatic mathematical model is developed in order to simulate the performance of a TSA gas drying unit employing the layered bed. The results of the computer simulation show that the layered bed, containing silica gel and zeolite 13X, reveals a longer water vapor breakthrough time compared with those for single bed with silica gel and zeolite 13X, and that desorption behavior of the layered bed is significantly enhanced compared with single bed. The quantity of adsorbed benzene on silica gel and zeolite 13X is considerably smaller than that on activated carbon. The validation of the modeling results showed fairly good agreement between experimental and theoretical data for both the zeolite 13X and layered bed containing silica gel and zeolite 13X.
Packed beds have been used or proposed for many different applications, including thermal storage in buildings and in solar thermal power plants. In order to size the blowers and predict the operating and capital cost, the packed bed pressure drop must be known. The Ergun equation, commonly used for predicting packed bed pressure drop, over-predicts the pressure drop through randomly packed or structured beds of smooth spheres at Ergun Reynolds numbers in excess of approximate to 700, and previous work has found it to under-predict the pressure drop through beds of rock by a factor as high as 5. Present measurements of the pressure drop for air flow through beds of rough spheres, smooth cylinders, cubes and crushed rock are significantly higher than those for smooth spheres, and all differ from the Ergun equation. Particle shape, arrangement (including packing method) and surface roughness are shown to influence the pressure drop. Recent correlations for non-spherical particles are shown to differ significantly from present measurements. Different pressure drop measurements obtained for irregularly shaped rock packed into the test section in two different directions relative to the flow direction show that random packing is not necessarily isotropic. In order to predict the pressure drop over a packed bed of irregular particles such as crushed rock with any degree of accuracy, an empirical equation must be obtained from a sample of the particles for a given packing arrangement.
Many of the current research works performed in the SARNET-2 WP5 deal with the study of the coolability of debris beds in case of severe nuclear power plant accidents. One of the difficulties for modeling and transposition of experimental results to the real scale and geometry of a debris bed in a reactor is the difficulty to perform experiments with debris beds that are representative for reactor situations. Therefore, many experimental programs have been performed using beds made of multi-diameter spheres or non-spherical particles to study the physical phenomena involved in debris bed coolability and to evaluate an effective diameter. This paper first establishes the ranges of porosity and particle size distribution that might be expected for in-core debris beds and ex-vessel debris beds. Then, the results of pressure drop and dry-out heat flux (DHF) measurements obtained in various experimental setups, POMECO, DEBRIS, COOLOCE/STYX and CALIDE/PRELUDE, are presented. The issues of particle size distribution and non-sphericity are also investigated. It is shown that the experimental data obtained in “simple” debris beds are relevant to describe the behavior of more complex beds. Indeed, for several configurations, it is possible to define an “effective” diameter suitable for evaluating (with the porosity) some model parameters as well as correlations for the pressure drop across the bed, the steam flow rate during quenching and the DHF.
The packing of rodlike particles with a micro size widely exists in various engineering applications, such as the process of separation and catalytic reaction. In this work, a mathematical analysis of the rod packing has been carried out by employing the discrete element method (DEM). The emphasis is focused on the influence of material properties of the rodlike particles on the characteristics of the packing structure, which is quantified in terms of the packing porosity, coordination number and intersection angle. The results show that the porosity increases with the friction coefficient and surface energy while decreasing with the restitution coefficient. The coordination number and intersection angle vary in line with the porosity correspondingly and the correlation between the macrostructural and microstructural properties of the packing structure is established. The variations of the rod packing due to the friction coefficient and surface energy are much more pronounced than that of the restitution coefficient and stiffness. It also shows that the changes of the packing structure can be strongly related to the contact force. Those findings would be of interest from applied standpoints as well as showing fundamental effects of material properties on the rod packing.
The effect of particle shape on the flow of purely viscous type non-Newtonian fluids through beds of non-spherical particles has been investigated experimentally. Extensive pressure drop measurements are reported for scores of Newtonian and non-Newtonian fluids through beds of three different types of packing materials (two sizes of Raschig rings and one size of gravel chips). It is established that the widely used Ergun equation provides a satisfactory representation of data for non-Newtonian fluids also if a volume equivalent diameter and a sphericity factor are used to account for non-spherical shape of particles. The experimental results reported herein encompass the following ranges of conditions: 0.0016<Re<400; 0.49<n<1.0, and 0.472<ϵ<0.704.
The study focuses on the characterization of randomly packed monodispersed rigid fibers. We show that porosity can vary over a wide range of values, depending on the size of the fibers. A systematic study was carried out for fiber aspect ratios r (length-to-diameter) ranging between 4 and 70. Analysis and discussion of these results are presented in this paper. It is shown that the porosity law is dependent only on the fiber aspect ratio. This result was analyzed using the concept of excluded volume developed by Onsager in 1948 for systems at a molecular scale. In this work, we propose a simple law linking porosity to the aspect ratio of the fibers on the basis of experimental results and on the expression of excluded volume: ε=1−11π2r+6+2r.
We examine the effect of various contributory factors, such as structural properties, on the pressure drop of fluids through packed beds so that appropriate correlations with wide practical applicability can be established
In the present study verification is carried out of mathematical criteria that define the boundary between two hydrodynamic regimes: the gas continuous flow (GCF) regime and the pulsing flow (PF) regime. Attention is focused on the criterion derived using the model of K. Grosser, R.G. Carbonell and S. Sundaresan, AIChE J., 34 (1988) 1850–1860, and the parametric sensitivity of this criterion is analysed. Next, based on the measured values of the gas pressure drop in a reactor the verification of some selected parameters is carried out by fitting the theoretical and experimental boundary lines separating the GCF and PF regimes. Experimental results are also presented concerning the determination of parameters characterising the pulsing flow through the bed, namely the frequency of pulsations and the pulse structure. These parameters were determined for the system nitrogen–water, and also for liquids differing from water in their physicochemical properties.
Les variations de la fraction volumique de particules de syme´trie sphe´rique ou axiale, dans des empilements au hasard, sonte´tudie´es en fonction du rapport, l/d, longueura`diame`tre des particules. Deux types d'arrangements, dits laˆches ou denses, peuventeˆtre de´finis. Ils correspondent respectivement au minimum et au maximum de la fraction volumique. Il est montre´dans les deux cas que quand le rapport l/d est suffisamment grand (fibres), l'inverse de la fraction volumique varie line´airement avec ce rapport, mais que, par contre, elle tend vers des valeurs constantes quand le rapport tend vers ze´ro. Enfin, unee´quivalence, effectue´e entre les empilements au hasard de fibres et de sphe`res, permet de conside´rer, dans ces conditions, les fibres comme des sphe`res virtuelles, dont le diame`tre est une fonction simple de leurs parame`tres morphologiques.AbstractThe variation of the volumic fraction of particles of spherical or axial symmetry, in random stackings, is examined as a function of the ratio of the length (l) to the diameter (d) of the particles. Two types of ordering, loose or dense, can be defined. They correspond respectively to the minimum and maximum value of the volumic fraction. In both cases, when the ratio l/d is large enough (fibres), the inverse of the volumic fraction varies linearly with this ratio, but, conversely, it tends towards a constant value when the ratio tends towards zero. Finally, an equivalence, established between random stackings of fibres and spheres allows, under these conditions, the fibres to be considered as virtual spheres the diameter of which is a simple function of their morphological characteristics.
A very simple model is presented for the effect of the container wall on the pressure drop in a fluid flowing through a bed of spheres. It is based on the application of the Ergun equation to the bulk region of the bed, unaffected by the wall. Pressure loss predictions are found to correspond well to the opposing trends reported in the literature for the viscous- and inertial-flow regimes.
Studies on pressure-drop characteristics of beds of equilateral and non-equilateral solid cylinders of aspect ratios ranging from 0.5 to 2.0 have been carried out. These studies have exposed the shortcomings of the commonly used Ergun type correlations for predicting the pressure drop in packed systems. An empirical correlation to predict pressure drop in beds of cylindrical particles has been developed. In addition, derivatives of cylinders, such as hollow cylinders, have been examined, and comparisons have been made with particles, such as spheres.
An experimental study was conducted to determine the pressure drop characteristics of cylindrical packed beds through which turbulent pipe flow was passing. This study was planned to clarify the applicability of the well-known Ergun correlation proposed for beds composed with spherical particles on beds with non-spherical particles. The experimental packed beds were constructed by using two different irregular-shaped and one spherical-shaped packing materials for understanding the effects of particle shape or sphericity, particle size, bed porosity, and bed length to diameter ratio on the pressure drop. The beds were constructed by using zeolite, chickpea and glass bead materials to cover the particle sphericity range of 0.55 ≤ Φ ≤ 1.00. Systematic experiments and the data analysis procedure showed that the well-known Ergun correlation can be applied to all of the experimental beds composed with non-spherical and/or spherical particles with a maximum deviation of ±20%. This deviation can, however, be decreased to a negligible level of ±4% if some simple modifications, including the use of particle Reynolds number, Rep, a new form of particle friction factor, f*p, and some adopted empirical constants in the well-known Ergun correlation, are used.
Packed bed unit operations are required for many commercial chemical processes. The ability to a priori predict void fraction and pressure drop in a packed bed would significantly improve reactor design as well as allow for optimization around catalyst performance, catalyst design, and the resulting process pressure drop. Traditionally, the packed bed reactor designs are based on a homogeneous model with averaged empirical correlations. These correlations are often inapplicable for low tube-to-particle diameter ratios (D/d < 4) in which tube wall and local phenomena dominate. In this work, the discrete element method (DEM) and computational fluid dynamics (CFD) are coupled to model a fixed bed reactor with low tube-to-particle diameter ratios (D/d < 4). DEM is used to generate a realistic random packing structure for the packed bed with spherical or cylindrical particles, which is then imported into the CFD preprocessor (Gambit) to generate the mesh for the CFD simulation. Two types of experiments were conducted: the laboratory-scale experiments with up to 150 particles to allow simulation of entire packed beds in CFD, including random packing and structured packing, and the plant-scale experiments conducted with up to 1500 randomly packed particles. The concept of a “porosity correction factor” was introduced to compensate for the effect of porosity deviation between actual packing and the CFD model, which can be accumulated during DEM simulation, and particle shrinkage for purposes of grid generation in the CFD model. The predicted pressure drops match well with the experimental measurements with errors less than the desired limit (10%) for industrial design of packed bed reactors. The pressure drops calculated by the empirical correlations confirmed the inconsistency and unreliability of the empirical correlations for the packed beds with low tube-to-particle diameter ratios (D/d < 4) as well as the advantage of the DEM/CFD approach.
This paper introduces some of the basic principles of the combined packing of rods and spheres and illustrates how the ratio of sphere to fiber diameter affects void volume, which is resin demand. It also points out how minimum packing parameters change with respect to fiber length to diameter ratio and how choosing size combinations can optimize benefits from packing. It is believed that these concepts can be applied to other aspects of the reinforced plastics business.
Es werden Gleichungen zur Berechnung des Druckverlustes einphasig durchströmter Kugel- und Zylinderschüttungen angegeben. Die Gleichungen sind aus fremden und eigenen Messungen an Schüttungen abgeleitet, bei denen das Verhältnis von Rohrbzw. Säulendurchmesser D zu Füllkörperdurchmesser d in weiten Grenzen variiert wurde (1,7 < D/d < 91 für Kugeln; 2, 1 < D/d < 40 für Zylinder). Die Einflüsse der Schüttungsberandungen auf den Druckverlust werden berücksichtigt.
Some structural properties of packed bed systems on both the local and overall scales which are available in the literature and of interest in chemical engineering applications are discussed. Regular and random packings of uniformly sized spheres are initially analyzed as a basis for the later examination of the more general case of random packed beds containing particles of various sizes and shapes, with or without restraining surfaces.On discute, sur une échelle locale et globale, certaines propriétés structurales deg systèmes à base de lits garnis qu'on mentionne dans des écrits et qui sont intéressantes à cause de leurs applications en génie chimique. On analyse d'abord des garnitures régulières et irrégulières de sphères aux dimensions uniformes, et ce comme base d'un examen ultérieur du cas des lits qui sont garnis irrégulièrement, continnent des particules de dimensions et formes diverses et possèdent des surfaces restreintes on non.
An experimental investigation of the packing of some ternary mixtures of nonspherical particles has been conducted. The double extrapolation method is used to determine the packing density of a particle mixture in infinite space. The application of experimental design to particulate mixture problems is demonstrated. The results indicate that the similarity between the packing systems of spherical and nonspherical particles can be readily depicted in terms of specific volume variation.
Liquid holdups and pressure drops for gas and liquid concurrent flow in packed beds were measured experimentally. To calculate the Ergun type constants, pressure drops were also measured for single- (gas)-phase flow through the same packings. These measurements reveal that the Ergun type inertial constant depends on the particle shape. The beds were packed with porous and nonporous spheres, cylinders, extrudates, and Raschig rings. The experimental data were analyzed using the concept of relative permeabilities. The liquid-phase relative permeability correlated well with the reduced liquid saturation in a unique power-law form for all particles independent of their shape. The gas-phase relative permeability as a function of the gas-phase saturation followed the same law, but the exponent depends on the particle shape and gas-phase Reynolds number. Predicted and experimental values for liquid holdups for all particle shapes agreed well with mean relative deviations less than 10%. Predictions of pressure drops for spherical particles, cylinders, and extrudates are at least as accurate as other less rigorous correlations (mean relative errors between 25 and 40%). Pressure drop predictions for Raschig rings are poorer (mean relative deviations of 90%), reflecting in part the variations in pressure drops from experiment to experiment with these particles.
: The aim of this work is to study the porosity of three-dimensional and two-dimensional packing of stiff cylindrical fibres
according to their aspect ratio. First, we have carried out an experimental study of the porosity for 3D and 2D packing. In
this last case, the elementary representative surfaces have been determined. Then, an attempt of interpretation of the porosity
variations for 2D stacks has been realized on the basis of the excluded volume theory and a variation law has been proposed.
To conclude, we have studied the relevance of a simplified packing model based on a single geometry of the defects.
An experimental study is conducted to determine the characteristics of frictional pressure drops of fluid flow in porous beds
packed with non-spherical particles. The objective is to examine the applicability of the Ergun equation to flow resistance
assessment for packed beds with non-spherical particles. The experiments are carried out on the POMECOFL facility at KTH.
Hollow spheres and cylinders are used to pack the beds. Either water or air is chosen as the working fluid. The experimental
data show that the Ergun equation is applicable to all the test beds if the effective particle diameter used in the equation
is chosen as the equivalent diameter of the particles, which is the product of Sauter mean diameter and shape factor of the
particles in each bed.
KeywordsPorous media–Non-spherical particles–Frictional pressure drop–Equivalent diameter
Experimental and theoretical studies were performed on adsorption of benzene from nitrogen gas stream and thermal regeneration by hot nitrogen purge, in fixed beds charged with activated carbon. System temperature and effluent concentration data were collected during adsorption-regeneration runs. A mathematical model was developed to simulate temperature and concentration data of adsorption and regeneration. The model developed was based on non-equilibrium, non-isothermal and non-adiabatic conditions. Three heat transfer resistances were considered in interfaces of gas–solid, gas–wall, and wall–atmosphere. A linear driving force mass transfer model with a variable lumped-resistances coefficient was found to provide an acceptable fit to the experimental data. Experimental and modelling results were used to study the effects of adiabatic and non-adiabatic operations, contact time, gas velocity, regeneration temperature and initial bed loading on the regeneration efficiency. Besides, the specific energy requirement and purge gas consumption were evaluated to discuss the process efficiency.
Pressure drop, bubble size, gas hold-up and convective heat transfer have been studied both experimentally and theoretically at constant wall heat flux for single and two-phase flow through unconsolidated porous media. Single-phase pressure drop and heat transfer coefficients have been measured over a wide range of particle size, heat flux and liquid flow rate. The conservation equations and the Kozeny-Carman equation are used to describe single-phase flow pressure drop and convective heat transfer through the porous media. The measured pressure drops have been used to evaluate the validity of the predictive expressions available in the literature. Mathematical models are developed for the prediction of temperature profiles and single-phase heat transfer coefficients, which predict the experimental data with good accuracy. A large number of new experimental data are presented on two-phase pressure drop, bubble size, gas hold-up and heat transfer coefficients for co-current upward gas/liquid flow through beds of different particle sizes under constant wall heat flux. The experimental data suggest the existence of two distinct regimes, i.e. homogeneous and heterogeneous flow. The experimental data on two-phase pressure drop and gas hold-up have also been compared with the prediction of published correlations. Finally, mathematical models are presented for the prediction of pressure drop, bubble size, gas hold-up and heat transfer which predict the experimental data with good accuracy.
Single-phase pressure drop was studied in a region of flow rates that is of particular interest to trickle bed reactors . Bed packings were made of uniformly sized spherical and non-spherical particles (cylinders, rings, trilobes, and quadralobes). Particles were packed by means of two methods: random close or dense packing (RCP) and random loose packing (RLP) obtaining bed porosities in the range of 0.37–0.52. It is shown that wall effects on pressure drop are negligible as long as the column-to-particle diameter ratio is above 10. Furthermore, the capillary model approach such as the Ergun equation is proven to be a sufficient approximation for typical values of bed porosities encountered in packed bed reactors. However, it is demonstrated that the original Ergun equation is only able to accurately predict the pressure drop of single-phase flow over spherical particles, whereas it systematically under predicts the pressure drop of single-phase flow over non-spherical particles. Special features of differently shaped non-spherical particles have been taken into account through phenomenological and empirical analyses in order to correct/upgrade the original Ergun equation. With the proposed upgraded Ergun equation one is able to predict single-phase pressure drop in a packed bed of arbitrary shaped particles to within ±10% on average. This approach has been shown to be far superior to any other available at this time.
An experimental study has been carried out under both loose and dense random packing conditions to quantify the dependence of the packing characteristics such as porosity and packing size on particle shape. It is shown that the porosity of mono-sized particles is strongly dependent on both particle shape and packing method, and for a given packing method, the porosity-shape relation can be approximately by the proper use of the packing results of cylinders and disks. The results indicate that the equivalent packing diameter of a particle is only affected by particle shape and not sensitive to the method of evaluation including factors such as the packing method and the mixing composition. Based on the measurements, correlations have been formulated for predictive purposes. The formulated porosity-shape and packing size-shape relations are demonstrated to be useful in particle characterization and in porosity prediction of non-spherical particle mixtures.
Flow through porous media-the Ergun equation revisited
- Macdonald
Dispersion, pressure drop, and chemical reaction in packed beds of cylindrical particles
- England