Radial porosity in packed beds of spheres

A functional approach has been developed to investigate the radial porosity of mono-sized spheres in cylinders. Analytical and semi-analytical equations have been developed to calculate the local radial porosity and the radial porosity distribution, respectively, within a cylindrical packing structure. The analytical equations are based upon fundamental principles and are simple, straightforward and provide highly accurate results for the radial porosity with minimal computational prerequisites. The analytical equations have been developed for the fixed packing of identical spheres in cylindrical containers with D/d ≥ 2.0. The predicted results for the local radial porosity and the radial porosity distributions are benchmarked with an existing analytical equation and available experimental data, respectively, for mono-sized spheres in cylindrical containers.     

The Effect of Particle Size Distribution on Pressure Drop through Packed Beds of Cooked Wood Chips

The pressure drop of process liquors through columns of wood chips determines the operability, efficiency and control of both batch and continuous pulp digesters and the quality of the pulp produced from them. Pressure drop was measured through columns of industrial white spruce chips (produced with a chipping head‐rig) as a function of the chip size distribution and the extent of delignification. Flow resistance depended on the porosity of the chip bed which was affected by the kappa number of the chips (which affected their flexibility) and chip size distribution, the compaction forces applied to the column, and the liquid superficial velocity. The chip beds were compressible and inelastic. Previous work from the literature using the Ergun equation to characterize pressure losses through chip beds is examined and compared with results of this work.     

Numerically packing spheres in cylinders

A novel approach has been developed to numerically pack spheres in cylinders. The packing algorithm uses a simple sequential technique that is based on a dimensionless packing parameter. The dimensionless packing parameter includes both axial and radial variables in order to determine a sphere's sequential placement within a cylindrical packing structure. The numerical simulation has been applied to the loose packing of identical spheres in cylindrical containers with D/d ≥ 2.0. The predicted results for the mean porosity and the radial porosity distributions are validated against the available experimental data for spheres in cylindrical containers. The simulated results are highly accurate and the simple packing algorithm requires minimal computational prerequisites.     

Packed bed structure: Evaluation of radial particle distribution

A model describing the radial distribution of monosized spheres in randomly packed beds up to distances of about two particle diameters from the vessel wall is presented here. The model is based on the existence of a highly ordered layer of particles adjacent to the wall followed by a more diffuse, but still identifiable, second layer. Expressions generated from simple geometrical concepts (intersection between a cylindrical surface and a sphere) straightforwardly allow calculating the radial voidage profile given the radial distribution of particle centers and vice versa. These expressions are employed to fit the model to measures of voidage profiles within a wide range of aspect ratios, a = (R_T/R_P). The model can be used to accurately predict radial voidage profiles, but it is stressed that the identification of particle distribution constitutes more valuable information than an empirical expression for describing voidage variations.     

Firing of coal and biomass and their mixtures in 50 kW and 12 MW circulating fluidized beds - Phenomenon study and comparison of scales

The combustion dynamics of coal, wood chips and their mixture is investigated. Load change capability and the effect of the individual control variables, for example the mixture ratio of different fuels, on pilot-scale CFB boiler dynamics were also studied.Disturbances in fuel feeding cause fluctuations in the flue gas concentrations. Changes in the heating value are possible due to varying moisture content of the fuel. Both these disturbances affect the instantaneous firing rate in a boiler. Also the characteristics of the fuels have to be taken into consideration when designing boiler control systems. When co-firing two fuels with clearly distinct combustion characteristics, direct assumptions based on each fuel’s characteristics cannot be made about combustion behaviour of their mixture.Combustion experiments with coal and wood chips and their co-firing were carried out in a pilot-scale CFB reactor (VTT) and a large-scale CFB boiler (Chalmers). A comparison of the combustion in the two different size reactors, provides information about scaling. The combustion responses due to changes in the fuel feeding of the two circulating fluidized beds are analyzed by a dynamic model.     

不同圆球复合无序堆积床内流动传热数值分析

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

Radial porosity distribution in cylindrical beds packed with spheres

Experimental determinations of radial porosity for cylindrical beds packed with spheres are reported. The data indicate that, for a wide range of bed and sphere sizes, porosity varies significantly and regularly near the container wall. For uniformly sized spheres, the oscillations in porosity can be detected up to a distance of about 5 particle diameters from the wall. For mixtures of spheres of two sizes, regular oscillations are detected only up to 2 or 3 diameters from the wall and for three sizes the effect of the wall is observed only within a distance of 1 particle diameter.     

Elucidation of mean voidage in packed beds

Mean voidage is a global structural property of packed beds and its accurate prediction is therefore of great significance in any plug-flow type model. A general correlation has been developed which enables this parameter to be evaluated. The work reported here deals with mono-size non-porous spherical packing, but also tackles related issues such as size distribution and the way in which they influence the mean voidage. In addition, an attempt has been made to discuss the merits of alternative packing arrangements.     

Power generation using coir-pith and wood derived producer gas in diesel engines

Partial combustion of biomass in the gasifier generates producer gas that can be used for heating purposes and as supplementary or sole fuel in internal combustion engines. In this study, the potential of coir-pith and wood chips as the feedstock for gasifier is analyzed. The performance of the gasifier–engine system is analyzed by running the engine for various producer gas–air flow ratios and at different load conditions. The system is experimentally optimized with respect to maximum diesel savings and lower emissions in the dual fuel mode operation while using coir-pith and wood chips separately. The performance and emission characteristics of the dual fuel engine are compared with that of diesel engine at different load conditions. Specific energy consumption in the dual fuel mode of operation is found to be in the higher side at all load conditions. The brake thermal efficiency of the engine while using wood chips in the dual mode operation is higher than that of coir-pith. The CO emission is higher in the case of dual fuel mode of operation as compared to that of diesel mode. In the dual fuel mode of operation, the higher diesel savings is achieved while using wood chips as compared to that of coir-pith. The comparison of the performance and emission characteristics of the dual fuel engine with diesel engine is also described.     

Relationship between packing structure and porosity in fixed beds of equilateral cylindrical particles

Fixed beds of cylindrical particles are important in chemical engineering applications, but their packing structures are not as well understood or as well characterized as sphere packings. In this work, X-ray microtomography is used to obtain 3D images of 1.8 mm diameter equilateral cylinders in a 23 mm cylindrical container over a range of bulk porosities. A novel algorithm is used to computationally reconstruct the packings, resulting in data sets that give the location and orientation of each cylinder in the imaged packings. Extensive analysis has been performed, including bulk and local porosities, radial distribution functions, and parameters describing local and global ordering. The major factors affecting packing structure are the overall packing density and the proximity to the wall. At the highest overall packing densities, near-wall porosity becomes nearly equal to interior porosity, and significant global ordering occurs near the wall. For a vertical container, global ordering is characterized by the alignment of the particles with an orthogonal coordinate system that has one axis coincident with r (as defined by the container) and the other two axes in the z-θ plane, but rotated 45^° with the horizontal. The observed structures are relevant in the context of flow maldistribution and heat transfer in fixed beds.     

Experimental investigation of pressure drop in packed beds of irregular shaped wood particles

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.     

Effect of particle granularity on smoldering fire in wood chips made from wood waste: An experimental study

Fires in wood waste storages cause financial losses, are difficult to extinguish, and emit large amounts of fire effluents. The mechanisms related to fires in wood chip piles are not well elucidated. To find suitable preventive measures for handling such fires in wood waste, a better understanding of the physical properties of wood waste is needed. The present study investigates how granularity affects mechanisms of smoldering fire and transition to flaming in wood chip piles. Eighteen experiments with samples inside a top-ventilated, vertical cylinder were conducted. Heating from underneath the cylinder induced auto-ignition and smoldering fire, and temperatures and mass loss of the sample were measured. The results showed that granularity significantly affects the smoldering fire dynamics. Material containing larger wood chips (length 4-100 mm) demonstrated more irregular temperature development, higher temperatures, faster combustion, and higher mass losses than material of smaller wood chips (length <4 mm). The larger wood chips also underwent transition to flaming fires. Flaming fires were not observed for small wood chips, which instead demonstrated prolonged and steady smoldering propagation. The differences are assumed to be partly due to the different bulk densities of the samples of large and small wood chips affecting the ventilation conditions. Increased knowledge about these combustion processes and transition to flaming is vital to develop risk-reducing measures when storing wood chips made from wood waste in piles.     

Predicting the effective thermal conductivity of polydispersed beds of softwood bark and softwood char

In this paper, the effective thermal conductivity (ETC) of softwood bark and softwood char particle beds which are highly polydispersed has been studied theoretically and experimentally. Use of the linear packing theory and unit cell model of heat conduction enabled to express ETC of polydisperded beds as a function of particle size distribution. Each of the softwood bark and softwood char samples were sieved into seven fractions. The initial porosity and binary packing size ratio of the particles have been characterized as a function of mean sieve size. ETC of polydispersed beds of bark and char has been predicted as a function of particle size distribution. Model predictions were in good agreement with the experimental measurements. The proposed approach can be used to predict the ETC of any size distribution of softwood bark and softwood char beds without measuring the in situ bed porosity.     

Angular porosity distributions in fixed packed beds of low diameter aspect ratio

The angular porosity distribution for fixed packed beds of monosized spheres in cylindrical containers with low diameter aspect ratios (1 ≤ D/d ≤ 2) is determined from the spheres' center coordinates. By dividing the packed bed into a large number of identical wedge-shaped segments, the angular porosity distribution is established from the local angular porosity and the angular positions within the cylindrical container. A correlation which accurately predicts the local angular porosity is determined from the angular porosity distributions. The correlation is a function of D/d and the angular position in the cylindrical container.     

Fragmentation of wood char in a laboratory scale fluidized bed combustor

Casuarina equisetifolia, a hard wood, and a popular energy crop in many tropical countries, was investigated experimentally for its char fragmentation in a laboratory scale atmospheric bubbling fluidized bed combustor. The effect of fuel shape and size on wood char fragmentation was studied. Wood particles of spherical, cylindrical (aspect ratio of 1), and cubical shapes of different sizes ranging from 10 to 25 mm were used in the experiments. Fragmentation of wood char was quantified in terms of various parameters, such as Number of Fragments (NF), Percentage of Fragmentation Events, Frequency of Fragmentation, Timing interval of Fragmentation, Size distribution of char and Fragmentation Index (FI). Also, qualitative observations on the evolution of char in terms of deformation, cracks and surface texture are discussed. It was observed that Casuarinaequisetifolia wood of sizes greater than 15 mm, of all shapes undergoes primary fragmentation during the devolatilization phase. Furthermore, chars fragment at the early stages (1st or 2nd quarter) of the char combustion phase, underscoring the significance of the phenomenon in fluidized bed combustion. For all the shapes of wood considered, there appears to be a cut-off size of the initial wood, below which its char certainly undergoes fragmentation. It was observed that the average char particle size at any instance during its combustion falls in a narrow range of 3.7–6.9 mm, 3–6.6 mm and 3–9.5 mm for spherical, cylindrical and cubical wood particles, respectively. Wood of initially cylindrical shape undergoes extensive fragmentation when compared with spherical and cubical shapes.     

填充床中空隙率分布的研究综述

综述了充床中空隙率径向分布的几种主要测量技术和数学模型,概括了空隙率分布的一般规律,为试验研究和工程设计工作提供重要依据。     

烯烃催化裂解反应器局部颗粒堆积结构的颗粒解析模拟

烯烃催化裂解固定床工艺中的反应过程对压力敏感,深入研究催化剂堆积颗粒结构中的流动及压力分布对优化固定床结构及操作参数有重要意义。颗粒解析模拟方法广泛用于固定床内堆积结构的模拟,可以准确描述堆积结构中的流体力学行为,但对于复杂堆积结构网格生成困难。采用基于多孔介质模型的浸入边界法(PMM-IBM)结合网格自适应,实现了对固定床堆积结构的颗粒解析模拟,既解决了网格划分困难的问题,又节省了计算资源。采用网格自适应技术后,与均匀网格相比,堆积结构的网格总数减少大约80%。通过与贴体网格法的单颗粒表面受力分析对比,确定了此浸入边界法的关键模拟参数。随后模拟预测了三种床层与颗粒直径比值条件下堆积结构的空隙率及其内部的压力及流动分布。研究表明,堆积结构空隙中的局部轴向速度的最大值可以达到入口速度的10倍以上,轴向平均速度的径向分布与轴向平均空隙率分布一致,均成震荡衰减趋势。除此之外,预测的床层压降与Reichelt经验关联式结果较为吻合。在此基础上,耦合单颗粒内扩散和烯烃裂解的主反应,预测了反应物随孔径和孔隙率的变化,为进一步考虑外流场的变化奠定了方法基础。     

A 3-zone model for protein adsorption kinetics in expanded beds

The adsorption behavior of expanded beds is more complex than that of fixed beds, since the adsorbent particle size, local bed voidage and liquid axial dispersion will vary axially with expanded height. Models applicable to fixed beds maybe not adequately describe the hydrodynamic and adsorption behavior in expanded beds. In this paper, a 3-zone model is developed, in which the model equations are written for the bottom zone, middle zone, and top zone of the column, respectively, and the model parameters, such as the adsorbent particle diameter, bed voidage and liquid axial dispersion coefficient, are zonal values. In-bed breakthrough curves are predicted by the 3-zone model, and tested against literature data for lysozyme adsorption on Streamline SP in an expanded bed.Model parametric sensitivity is analyzed. The effects of film mass transfer resistance, liquid axial dispersion and adsorbent axial dispersion on the breakthrough curves are weaker than that of protein intraparticle diffusion resistance for stable expanded beds. Adsorbent particle size axial distribution and bed voidage axial variation significantly affect in-bed breakthrough curves, therefore, model parameters should not be assigned uniform values over the whole column; instead the model should account for the adsorbent particle size axial distribution and bed voidage axial variation.     

On the relationship between porosity and interparticle forces

This paper presents an attempt to quantify the relationship between porosity and interparticle forces for mono-sized spheres. Two systems are considered: the packing of wet coarse spheres where the dominant interparticle force is the capillary force, and the packing of dry fine spheres where the dominant force is the van der Waals force. The interrelationships between porosity, capillary force and liquid content are first discussed based on the well-established theories and experimental observations. The resultant relationship between porosity and capillary force is then applied to the packing of fine particles to quantify the van der Waals force in a packing. A generalised relationship between porosity and interparticle forces results as an extension of this analysis. The usefulness of this relationship is finally demonstrated in depicting the fundamentals governing the relationship between porosity and particle size.