Determination of non-spherical particle terminal velocity using particulate expansion data

A new method is proposed for the determination of the terminal velocity of non-spherical particles and compared with experimental data. The method is based on particulate expansion data of fluidized bed and variational model for calculating fluid–particle interphase drag coefficient. Other methods require knowledge of the particle shape, a parameter that is not easy to obtain for real materials. We use pressure drops data in packed bed for indirect determination of particle shape factor which depends on the reliability of coefficients in the Ergun equation. Our data, however, show that these coefficients are system-specific. The proposed method for the determination of non-spherical particle settling velocity in liquid as well as extrapolation to system gas-particles gives results which are in good agreement with experimental data. The method is restricted to particles which can be fluidized particulately by liquid.     

Comparison of numerical simulations and experiments in conical gas-solid spouted bed

Flowbehavior of gas and particles in conical spouted beds is experimentally studied and simulated using the twofluid gas-solid model with the kinetic theory of granular flow. The bed pressure drop and fountain height are measured in a conical spouted bed of 100mmI.D. at different gas velocities. The simulation results are compared with measurements of bed pressure drop and fountain height. The comparison shows that the drag coefficient model used in cylindrical beds under-predicted bed pressure drop and fountain height in conical spouted beds due to the partial weight of particles supported by the inclined side walls. It is found that the numerical results using the drag coefficient model proposed based on the conical spouted bed in this study are in good agreement with experimental data. The present study provides a useful basis for further works on the CFD simulation of conical spouted bed.     

Cluster-based drag coefficient model for simulating gas-solid flow in a fast-fluidized bed

Drag coefficient is of essential importance for simulation of heterogeneous gas-solid flows in fast-fluidized beds, which is greatly affected by their clustering nature. In this paper, a cluster-based drag coefficient model is developed using a hydrodynamic equivalent cluster diameter for calculating Reynolds number of the particle phase. Numerical simulation is carried out in a gas-solid fast-fluidized bed with an Eulerian-Lagrangian approach and the gaseous turbulent flow is simulated using large eddy simulation (LES). A Lagrange approach is used to predict the properties of particle phase from the equation of motion. The collisions between particles are taken into account by means of direct simulation Monte Carlo (DSMC) method. Compared with the drag coefficient model proposed by Wen and Yu, results predicted by the cluster-based drag coefficient model are in good agreement with experimental results, indicating that the cluster-based drag coefficient model is suitable to describe various statuses in fast-fluidized beds.     

气体的温度和压力及颗粒形状对固定床压降的影响

本文在Ａ－Ｓ方程的基础上推导出气体流经固定床时的压降表达式。     

Flow of a gas-solid two-phase mixture through a packed bed

This paper is concerned with an upward co-current flow of a gas-solid two-phase mixture through a packed bed, a system employed in a number of industrial processes. Experimental work was carried out by using glass balls for packed bed, and both glass beads and FCC as suspended particles. The effects of solids loading and gas velocity on the pressure drop as well as the static and dynamic solid hold-ups within packed bed were examined. Experimental results showed different behaviour of the FCC from glass beads. At a given gas velocity, pressure drop increased approximately linearly with solids loading with a slope for FCC much higher than that for glass beads. The static hold-up of glass beads was much lower than corresponding dynamic hold-up at a given gas velocity, and it did not seem to change much with solids loading under the conditions of this work. At a given gas velocity, the static hold-up of FCC, however, was found to be comparable with the corresponding dynamic hold-up. An analysis was conducted on the pressure drop using a modified version of the Ergun equation by taking into account the effects of suspended particles on the viscosity and density, as well as the gravitational force. It was found that the modified Ergun equation agreed well with the experimental results of both this work and those reported in the literature. Effort was also made to develop relationships for the dynamic hold-up and the interaction coefficient between the suspended and the packed particles, the so-called solid-phase friction factor in the literature. The dynamic hold-up was found to increase with an increase in the product of velocity ratio of the solid to gas phases and the square root of the diameter ratio of the suspended to packed particles, whereas the interaction coefficient increased in general with increasing Froude number but with significant scattering.     

Numerical simulation of horizontal jet penetration in a three-dimensional fluidized bed

The introduction of reactant gas as a jet into a fluidized bed chemical reactor is often encountered in various industrial applications. Understanding the hydrodynamics of the gas and solid flow resulting from the gas jet can have considerable significance in improving the reactor design and process optimization. In this work, a three-dimensional numerical simulation of a single horizontal gas jet into a cylindrical gas-solid fluidized bed of laboratory scale is conducted. A scaled drag model is proposed and implemented into the simulation of a fluidized bed of FCC particles. The gas and particles flow in the fluidized bed is investigated by analyzing the transient simulation results. The jet penetration lengths of different jet velocities have been obtained and compared with published experimental data as well as with predictions of empirical correlations. The predictions by several empirical correlations are discussed. A good agreement between the numerical simulation and experimental results has been achieved.     

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.     

Pressure-drop predictions in a fixed-bed coal gasifier

In the Sasol Synfuels plant in Secunda, Sasol-Lurgi fixed-bed dry-bottom gasifiers are used for the conversion of low-grade bituminous coals to synthesis gas (syngas). The gasifiers are fed with lump coal having a particle size in the range from 5 to 100 mm. Operating experience shows that the average particle size and particle-size distribution (PSD) of feed coal, char and ash influence the pressure drop across the bed and the gas-flow distribution within the bed. These hydrodynamic phenomena are responsible for stable gasifier operation and for the quality and production rate of the syngas. The counter-current operation produces four characteristic zones in the gasifier, namely, drying, de-volatilization, reduction and combustion. The physical properties of the solids (i.e. average particle size, PSD, sphericity and density) are different in each of these zones. Similarly, the chemical composition of the syngas, its properties (temperature, density and viscosity) and superficial velocity vary along the height of the bed. The most popular equation used to estimate the pressure drop in packed beds is that proposed by Ergun. The Ergun equation gives good predictions for non-reacting, isothermal packed beds made of uniformly sized, spherical or nearly spherical particles. In the case of fixed-bed gasifiers, predictions by the Ergun equation based on the average or inlet values of bed and gas flow parameters are unsatisfactory because the bed structure and gas flow vary significantly in the different reaction zones. In this study, the Ergun equation is applied to each reaction zone separately. The total pressure drop across the bed is then calculated as the sum of pressure drops in all zones. It is shown that the total pressure drop obtained this way agrees better with the measured result.     

粗颗粒在锥型床中的流化特性

通过Ｇｅｌｄａｒｔ－Ｄ类粗颗粒在三种锥形床中的实验表明：随着入口的表观气速的增加,在床中依次出现固定床流区,部分流化区和喷动流区。在固定床区内,压降和表观气速关系可以通过Ｅｒｇｕｎ公式求得：在部分流化床区内;实验和理论计算均表明了由于颗粒所受到的曳力档的轴向高度增加而减小,造成床层轴向上部未流化的颗粒对下部硫化颗粒膨和压制作用,在喷动流化区内,给出了预测锥形床的初始喷动气速和喷动压降的经验公式。     

快速流态化气固两相间的动量交换

本文根据一维定常态流动模型,对快速流化床内气固两相间的相互作用及其机理进行了研究.结果表明,在快速流态化条件下,颗粒总是趋于聚集,以减小气固两相间的相互作用力,从而使曳力系数c_D小于单颗粒标准曳力系数c_(DS)(c_D/c_(DS)<1.0).c_D/c_(DS)不仅与(?)有关,而且受气固流动状况以及颗粒物性、床层直径等因素的影响.通过对大量数据的分析,得到预测曳力系数的经验关联式(平均相对偏差小于5%)c_D/c_(DS)=1.685(?)~(0.253)(Re_r/Re_t)~(-1.213)(d_p/D)~(0.105)     

Mathematical modeling of gas dehydration using adsorption process

In this study, a mathematical model was developed to simulate an adsorption process for dehydration of a gas stream. In deriving the model, the following assumptions were made. Variation of the gas velocity along the bed length was accounted for and the bed pressure drop was calculated by the Ergun equation. Mass and heat transfer outside the solid particles were assumed to be convective and those inside the particle were assumed to be diffusive. The dual site Langmuir isotherm was employed in predicting adsorption equilibrium and the Peng–Robinson equation was used as the PVT relation. The resulting mathematical model was solved by the finite volume method and the results were verified against experimental data reported by Mohamadinejad et al. [2000. Separation Science and Technology 35,1] and Gorbach et al. [2004. Adsorption 10,1]. Good agreement was observed between the predictions of the model and the experimental data. The developed model was used to perform parametric study. Our results suggest that the break-through time decreases linearly with the square of particles diameter. It also decreases linearly with the inverse of particles tortuosity. A similar trend appears to exist for variations of the bed percent saturation. The bed pressure drop increases linearly with the inversed diameter of particles.     

Flow through packed bed reactors: 1. Single-phase flow

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.     

涓流床反应器中流区过渡的气相渗透率表征

由于Ergun方程可适用于气液间无相互作用的两相流动压降计算,并且由气相单相和气液两相并流下的气相压降比值可计算气相相对渗透率,因此,Ergun方程可用于涓流床中不同流区过渡和气液相互作用程度的表征。为检验这一方法的有效性,实验测定了空气-水体系在内径140mm有机玻璃塔中不同粒径玻璃珠(1.9、3.6、5.2、9.3mm)组成的床层压降和持液量。由于采用了压力传感器和电容层析成像仪,因此可测定脉冲流状态下的瞬态数据。通过压降的实验值与理论值比较,发现Ergun方程的适用范围有限,在没有进入脉冲流前先已失效,说明此时气液间作用已经相当显著。鉴于此,改用气液两相压降实验值代替理论值进行了气体渗透率的计算,发现不同气液流速和颗粒直径下出现脉冲流时的气体渗透率均低于0.08。     

Apparent drag reduction phenomenon in the defluidized packed dense bed of the multisolid pneumatic transport bed

Experiments were performed to study the pressure drop behavior in the packed bed of dense particles in the multisolid pneumatic transport bed (MPTB). The packed bed under extensive analysis is established by fluidizing and then defluidizing the dense particle bed by increasing and then decreasing the air flow rate at a constant fine particle flow rate. The pressure drop in a packed bed established in this manner initially decreases significantly and then increases as the fine particle flow rate increases at a given air flow rate. This behavior signifies the apparent drag reduction phenomenon in the defluidized packed bed. The classical pressure drop equation by Ergun[1] was modified to account for this phenomenon.     

Mathematical model for gas flow through a packed bed in the presence of sources and sinks

Flow within a packed bed is normally calculated by attempting to simultaneously satisfy the continuity and Ergun equations. However, the presence of gas sources/sinks within the bed escalates the complexity of the problem, particularly when the flow is two-dimensional and a solution to the full Ergun equation is required. In quest of an efficient and dependable algorithm for the calculation of gas flow, a critical review of existing solution methods was undertaken and a new method, ‘FLOW’, is now proposed. The technique retains the viscous and inertial pressure gradient terms of the Ergun equation, and both are treated as linear functions of the flow. Solutions are approached iteratively; using finite difference techniques, the continuity and linearized Ergun equations are solved for the pressure field; a new flow field is then calculated from which is derived an adjustment to the inertial resistance term of the Ergun equation. The sequence is repeated until satisfactory convergence is obtained. Relatively few iterations are normally required and, for the case of negligible inertial pressure drop, one calculation cycle is sufficient. A comparison of results obtained using the ‘FLOW’, modified ‘SIMPLE’ and vorticity procedures is presented. The proposed method allow flexibility in the specification of boundary conditions and can be applied to compressible or incompressible flow, as well as for the case of nonisothermal beds.     

CFD modeling and validation of the turbulent fluidized bed of FCC particles

An experimental and computational study is presented on the hydrodynamic characteristics of FCC particles in a turbulent fluidized bed. Based on the Eulerian/Eulerian model, a computational fluid dynamics (CFD) model incorporating a modified gas‐solid drag model has been presented, and the model parameters are examined by using a commercial CFD software package (FLUENT 6.2.16). Relative to other drag models, the modified one gives a reasonable hydrodynamic prediction in comparison with experimental data. The hydrodynamics show more sensitive to the coefficient of restitution than to the flow models and kinetics theories. Experimental and numerical results indicate that there exist two different coexisting regions in the turbulent fluidized bed: a bottom dense, bubbling region and a dilute, dispersed flow region. At low‐gas velocity, solid‐volume fractions show high near the wall region, and low in the center of the bed. Increasing gas velocity aggravates the turbulent disorder in the turbulent fluidized bed, resulting in an irregularity of the radial particle concentration profile. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Heat transfer simulation in a raining packed bed exchanger

A model is presented that predicts the thermal performance of a raining packed bed heat exchanger (RPBE) from hydrodynamic data. The main feature of this gas-solids countercurrent heat exchanger is the presence of a packed zone which greatly enhances energy transfer between the two phases by slowing down the falling particles. The model based on the Ergun equation for evaluating an effective solids hold-up in the packed zone correctly predicts the fact that the efficiency passes by a maximum as the hot gas velocity increases. Experimental results obtained with sand particles of 205 μm mean dia. in a column filled with Pa11–15 rings agree reasonably well with the predicted ones.     

Study of gas cavity size hysteresis in a packed bed using DEM

When a high velocity gas jet is introduced into a packed bed a cavity is formed. The size of the cavity shows hysteresis on increasing and decreasing gas flow rates. This hysteresis leads to different cavity sizes at same gas flow rate depending on the bed history. The size of cavity affects the gas flow profiles in the packed bed. In this study the cavity size hysteresis phenomenon has been modeled using discrete element method along with turbulent gas flow. A reasonable agreement has been found between computed and experimental results on cavity size hysteresis. The effect of various parameters, such as nozzle height from the bed bottom and packing height, on the cavity size hysteresis has been studied. It is found that inter-particle interaction forces along with gas drag and bed porosity play an important role in describing the cavity size hysteresis. The injection of gas flow allows the particles to go to an unconstrained state than they were previously in, and their ability to remain in that state, even under decreased gas drag force, leads to the phenomenon of cavity size hysteresis.     

循环流化床中颗粒聚团特性的模拟

考虑到循环流化床中分散颗粒和颗粒聚团同时存在的多尺度结构,确定了密相和稀相加速度与计算网格局部参数之间的关系,建立了多尺度曳力消耗能量最小的稳定性条件,基于双变量极值理论,构建了考虑颗粒团聚效应的多尺度气固相间曳力模型。结合双流体模型,对循环流化床内气固流动特性以及颗粒聚团特性进行了模拟研究。通过与实验值比较,考虑颗粒聚团影响的计算模型可以更好地贴近实验结果,颗粒聚团直径随颗粒浓度增大呈现先增大后减小的分布趋势,气体和颗粒的加速度在模拟中与重力加速度同处一个数量级,求解过程中不能被忽略。