Numerical Simulations of the Effect of Conical Dimension on the Hydrodynamic Behaviour in Spouted Beds

The flow behaviours of gas‐solids were predicted by means of a hydrodynamic model of dense gas‐solid flow in spouted beds. Constitutive equations describing the particulate solids pressure and viscosity were implemented into a hydrodynamic simulation computer program. The effect of operating conditions (inclined angle and gas spouting velocity) on particle velocity and concentration in the spout, annulus and fountain regions were numerical studied. Both vertical and horizontal particle velocities increased with increasing spouting gas velocity. The diameter of the spout increases with decreasing the inclination angle. As the inclination angle is set greater than 60°, the spout cross‐section starts becoming bottlenecked, limiting the upwards flow of solids.     

二维导流管喷动床离散颗粒动力学模拟

采用离散单元法(DEM)-计算流体力学(CFD)双向耦合数值方法对二维导流管喷动床进行了模拟,颗粒的运动通过DEM模型描述,而气体的运动用Navier-Stokes方程进行求解,气体和固体颗粒之间的相互作用通过曳力形式传递。文中将DEM和边界元方法(BEM)结合起来解决颗粒在具有复杂边界设备内的运动。通过采用BEM+DEM-CFD相结合的方法进行模拟计算,得到了喷动床的最小喷动速度,研究了不同表观气速下床内的流型,得到了二维导流管喷动床的床层压降与表观气速的关系,统计分析了喷射区、环隙区内颗粒的运动速度和相应的空隙率,全面地描述了二维导流管喷动床内的气固流动特征。     

Discrete element study of particle circulation in a 3-D spouted bed

A spouted bed is simulated by a discrete element method in a full 3-D cylindrical coordinate system. The vessel is a flat-bottomed cylinder 0.5 m in height and 0.15 m in diameter. In the simulation 300,000 mono-sized spherical glass beads are used. The numerical scheme is based on a second order finite difference method in space and a second order Adams-Bashforth method for time advancement. Gas-particle interaction is modelled to obey the Ergun equation for void fraction less than 0.8, and the Wen-Yu model, for void fraction greater than 0.8. In the present study, particle motion and circulation are investigated. Predicted streamlines of time-averaged particle flow are almost vertical in the upper part of the bed, gradually bending to the spout core in the lower region. Particle velocities along the streamlines are uniform in the upper part of the annulus, becoming non-linear with respect to the distance from the dead zone in the lower part of the annulus. The predicted total passages of particles across the spout-annulus boundary are in good agreement with measurements reported in the literature. Particles are found to feed from annulus to spout along the entire length of the spout. The net mass flux (from annulus to spout) is found to be constant in the upper part of the bed, increasing gradually with the depth in the lower part.     

Discrete element simulation of a flat-bottomed spouted bed in the 3-D cylindrical coordinate system

A spouted bed is simulated in three dimensions by a discrete element method (DEM) in a cylindrical coordinate system. The numerical scheme is based on a second order finite difference method in space and a second order Adams-Bashforth method for time advancement. Gas-particle interaction is assumed to obey the Ergun equation (for void fraction less than 0.8) and its corrected model by Wen and Yu (for void fraction greater than 0.8). The spouted bed vessel is a flat-bottomed cylinder in height and in diameter. The gas inlet diameter is . Three hundred thousand monosized spheres of diameter are used in the simulation. The typical characteristics of spouted beds, such as spout, annulus and fountain, are reproduced. Particle velocity profiles show good agreement with experimental results and self-similarity of the radial distribution of axial particle velocities is reported. Gas flow patterns are also studied and the effect a vortex ring fixed at the bottom of the vessel is investigated. The simulation is validated through comparisons with results reported in the literature.     

Coupling of smoothed particle hydrodynamics and finite volume method for two-dimensional spouted beds

A coupled method with smoothed particle hydrodynamics (SPH) and finite volume method (FVM) is proposed in this work for the simulation of the particle dynamics in two-dimensional spouted beds. Based on the pseudo-fluid model, SPH is used for discrete phase to trace the movement of each individual particle and FVM for continue phase to compute the turbulent fluid. Two phases are coupled through effects of drag force, gas pressure and volume fraction of each phase. A two-dimensional tapered-based spouted bed is chosen as a case study to demonstrate the performance of the SPH–FVM coupled algorithm. The simulation results show a good agreement with the experimental data and other simulation results by the two-fluid model and discrete element method in the literature. The spouted shape, time-averaged particle velocities and particle vertical velocities in the spout are analyzed and the distribution of gas flow field and turbulent kinetic energy are then discussed. It indicates that the present method is more suitable to study the fluidization within the spouted beds.     

喷动床内气固两相流体动力行为的数值模拟

引　言喷动床被广泛应用于不同工业领域中 ,如石油裂解反应 -再生器、煤和农业废弃物气化和燃烧 ,喷动床还被应用于粮食和药品的干燥等[1] .因此 ,喷动床设计应满足不同应用的要求 .喷动床内气相反应物的反应时间和停留时间依赖于床体几何结构和运行参数 .尽管已有许多的实验对喷动床内气固两相流动进行了研究 ,得到了喷射区、环形区和喷泉区内的气固两相流动流体动力特性 ,然而由于喷动床内气固两相流动的复杂性 ,人们对床体几何结构和运行参数对喷动床动力学的影响至今并不清楚 .因此 ,床体几何结构和运行参数等对喷动床动力学的影响成为…     

Numerical simulation of two-dimensional spouted bed with draft plates by discrete element method

A discrete element method (DEM)-computational fluid dynamics (CFD) two-way coupling method was employed to simulate the hydrodynamics in a two-dimensional spouted bed with draft plates. The motion of particles was modeled by the DEM and the gas flow was modeled by the Navier-Stokes equation. The interactions between gas and particles were considered using a two-way coupling method. The motion of particles in the spouted bed with complex geometry was solved by combining DEM and boundary element method (BEM). The minimal spouted velocity was obtained by the BEM-DEM-CFD simulation and the variation of the flow pattern in the bed with different superficial gas velocity was studied. The relationship between the pressure drop of the spouted bed and the superficial gas velocity was achieved from the simulations. The radial profile of the averaged vertical velocities of particles and the profile of the averaged void fraction in the spout and the annulus were statistically analyzed. The flow characteristics of the gas-solid system in the two-dimensional spouted bed were clearly described by the simulation results.     

Study of Flow Characteristics of Ultrafine CaCO3 Powders in a Spouted Bed

The flow behavior of gas and ultrafine powder in a spouted bed was numerically investigated by using a two‐fluid model coupled with a population balance equation (PBE). The aggregation process is controlled by the PBE, which is solved by the direct quadrature method of moments. The agglomerate diameter is calculated according to the change in particle number. The solid pressure and viscosity were modified for agglomerates on the basis of the kinetic theory of granular flow. Distributions of diameter, solids volume fraction, and velocity are obtained by the new model. The influence of cohesive intensity and gas velocity on the diameter distribution were analyzed. The spout diameter, a vital parameter for the design of spouted beds, was calculated and a calculation formula is proposed.     

Cold flow experimental study and computer simulations of a compact spouted bed reactor

Spouted beds are a very interesting class of gas–solid contactors that possess excellent heat transfer and mixing characteristics, while they are particularly suited to process coarse particles. Proper design of such beds requires the prediction of various hydrodynamic characteristics, such as the minimum spouting velocity and maximum spoutable height. Contrary to their typical initial applications, spouted beds have been finding recently more frequent use on the one hand at endothermic processes and on the other hand using much finer particle sizes. In the current work, the hydrodynamic characteristics of a laboratory scale spouted bed of 0.05 m diameter have been investigated via cold flow studies using olivine particles of 3.55–5.00 × 10⁻⁴ m size. Hydrodynamic parameters have been measured at this compact geometry and fine particle size and were compared with common literature correlations. An empirical correlation was derived to predict the fountain height for the studied fine particle spouted bed. Computer simulations have been further used to investigate the heat transfer characteristics of the bed under endothermic reactive conditions, using methane reforming as a case study. Given sufficient external heat supply, a spouted bed operating at a well-mixed regime can efficiently drive even highly endothermic reactions.     

Numerical simulation of two-dimensional spouted bed with draft plates by discrete element method

A discrete element method (DEM)-computational fluid dynamics (CFD) two-way coupling method was employed to simulate the hydrodynamics in a two-dimensional spouted bed with draft plates. The motion of particles was modeled by the DEM and the gas flow was modeled by the Navier-Stokes equation. The interactions between gas and particles were considered using a twoway coupling method. The motion of particles in the spouted bed with complex geometry was solved by combining DEM and boundary element method (BEM). The minimal spouted velocity was obtained by the BEMDEM-CFD simulation and the variation of the flow pattern in the bed with different superficial gas velocity was studied. The relationship between the pressure drop of the spouted bed and the superficial gas velocity was achieved from the simulations. The radial profile of the averaged vertical velocities of particles and the profile of the averaged void fraction in the spout and the annulus were statistically analyzed. The flow characteristics of the gas-solid system in the two-dimensional spouted bed were clearly described by the simulation results. __________ Translated from Chemical Engineering (China), 2007, 35(6): 24–28 [译自: 化学工程]     

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.     

Influence of solid-phase wall boundary condition on CFD simulation of spouted beds

The influence of solid-phase wall boundary condition in terms of specularity coefficient and particle–wall restitution coefficient on the flow behavior of spouted beds was investigated using two-fluid model approach in the computational fluid dynamics software FLUENT 6.3. Parametric studies of specularity coefficient and particle–wall restitution coefficient were performed to evaluate their effects on the flow hydrodynamics in terms of fountain height, spout diameter, pressure drop, local voidage and particles velocity. The numerical predictions were compared with available experimental data in the literatures to obtain the suitable values of specularity coefficient and particle–wall restitution coefficient for spouted beds. The simulated results show that the solid-phase wall boundary condition plays an important role in CFD modeling of spouted beds. The specularity coefficient has a pronounced effect on the spouting behavior and a small specularity coefficient (0.05) can give good predictions, while the particle–wall restitution coefficient is not critical for the holistic flow characteristics.     

Hydrodynamic modeling of a circulating fluidized bed

Hydrodynamics plays a crucial role in defining the performance of circulating fluidized beds (CFB). The numerical simulation of CFBs is very important in the prediction of its flow behavior. From this point of view, in the present study a dynamic two dimensional model is developed considering the hydrodynamic behavior of CFB. In the modeling, the CFB riser is analyzed in two regions: The bottom zone in turbulent fluidization regime is modeled in detail as two-phase flow which is subdivided into a solid-free bubble phase and a solid-laden emulsion phase. In the upper zone core-annulus solids flow structure is established. Simulation model takes into account the axial and radial distribution of voidage, velocity and pressure drop for gas and solid phase, and solids volume fraction and particle size distribution for solid phase. The model results are compared with and validated against atmospheric cold bed CFB units' experimental data given in the literature for axial and radial distribution of void fraction, solids volume fraction and particle velocity, total pressure drop along the bed height and radial solids flux. Ranges of experimental data used in comparisons are as follows: bed diameter from 0.05-0.418 m, bed height from 5-18 m, mean particle diameter from 67-520 μm, particle density from 1398 to 2620 kg/m³, mass fluxes from 21.3 to 300 kg/m²s and gas superficial velocities from 2.52-9.1 m/s.As a result of sensitivity analysis, the variation in mean particle diameter and superficial velocity, does affect the pressure especially in the core region and it does not affect considerably the pressure in the annulus region. Radial pressure profile is getting flatter in the core region as the mean particle diameter increases. Similar results can be obtained for lower superficial velocities. It has also been found that the contribution to the total pressure drop by gas and solids friction components is negligibly small when compared to the acceleration and solids hydrodynamic head components. At the bottom of the riser, in the core region the acceleration component of the pressure drop in total pressure drop changes from 0.65% to 0.28% from the riser center to the core-annulus interface, respectively; within the annulus region the acceleration component in total pressure drop changes from 0.22% to 0.11% radially from the core-annulus interface to the riser wall. On the other hand, the acceleration component weakens as it moves upwards in the riser decreasing to 1% in both regions at the top of the riser which is an important indicator of the fact that hydrodynamic head of solids is the most important factor in the total pressure drop.     

Computer simulations of gas-solid flow in spouted beds using kinetic-frictional stress model of granular flow

A gas-solid two-fluid flow model is presented. The kinetic-frictional constitutive model for dense assemblies of solids is incorporated in the simulations of spouted beds. This model treats the kinetic and frictional stresses of particles additively. The kinetic stress is modeled using the kinetic theory of granular flow, while the friction stress is from the combination of the normal frictional stress model proposed by Johnson et al. (J. Fluid Mech. 210 (1990) 501) and the modified frictional shear viscosity model proposed by Syamlal et al. (MFIX documentation. US Department of Energy, Federal Energy Technology Center, Morgantown, 1993). The body-fitted coordination is used to make the computational grids best fit the shape of conical contour of the base in the spouted beds. The effects of inclined angle of conical base on the distributions of particle velocities and concentrations in the spout, annulus and fountain zones were numerical studied. Calculated particle velocities and concentrations in spouted beds were in agreement with experimental data obtained by He et al. (Can. J. Chem. Eng. 72 (1994a) 229; (1994b) 561) and San Jose et al. (Chem. Eng. Sci. 53 (1998) 3561).     

Effects of Draft Tubes on Particle Velocity Profiles in Spouted Beds

The vertical particle velocity profiles in a full‐column cylindrical conical spouted bed, with or without a draft tube, are measured using a fibre optic probe system. The profiles have different characteristics for a draft tube spouted bed (DTSB) than for a conventional spouted bed (CSB). The spout of a CSB consists of a central flow where particle velocities fit exponential distributions, and a boundary layer where particle velocities are nearly uniform. The spout of a DTSB has no boundary layer and its radial particle velocity profiles are approximately linear. The particle velocities in the spout of a DTSB increase when superficial gas velocity increases, draft tube diameter decreases, or when entrainment height decreases. A kinematic model has been used to simulate the granular flow in the annulus of a CSB and DTSB, and they are compared with the experiments. The particle velocities in the annulus of a DTSB are much lower than that of a CSB. Their radial profiles are also different with a CSB. The dependence of particle velocities in the annulus of a DTSB on superficial gas velocity, draft tube diameter, and entrainment height are also discussed. One concludes that the draft tube diameter and entrainment height are two key factors for the solid circulation rate of a DTSB.     

Computational fluid dynamics (CFD) modeling of spouted bed: Influence of frictional stress, maximum packing limit and coefficient of restitution of particles

Following the previous article [Du, W., Bao, X., Xu, J., Wei, W., 2006. Computational fluid dynamics (CFD) modeling of spouted bed: assessment of drag coefficient correlations. Chemical Engineering Science 61 (5), 1401-1420], this contribution describes the influences of the frictional stress, maximum packing limit and coefficient of restitution of particles on CFD simulation of spouted beds. Using the two-fluid method embedded in the commercial CFD simulation package Fluent 6.1, the spouting hydrodynamics of a cylindrical-conical spouted bed was simulated and verified with the experimental data of He et al. [He, Y.L., Lim, C.J., Grace, J.R., Zhu, J.X., Qin, S.Z., 1994a. Measurements of voidage profiles in spouted beds. Canadian Journal of Chemical Engineering 72 (4), 229-234; He, Y.L., Qin, S.Z., Lim, C.J., Grace, J.R., 1994b. Particle velocity profiles and solid flow patterns in spouted beds. Canadian Journal of Chemical Engineering 72(8), 561-568]. The results showed that, for coarse particles, the frictional stress is important only for the annulus computation and has no obvious effects on the hydrodynamics of the solids flow in the spout region. The specification of the maximum packing limit could significantly affect the properties of the pseudo-fluid phase of the particles by changing the radial distribution function. The strong dependence of the pseudo-fluid properties of the particle phase, such as pressure, bulk viscosity and shear viscosity, on the granular temperature accounts for the influence of the coefficient of restitution of particles on CFD modeling. The solids volume fraction at loose packing state is suitable for spouted bed simulations, and a pretest of the coefficient of restitution of particles must be conducted when no experimental datum is available.     

Numerical Simulation of a Spouted Bed Using Computational Fluid Dynamics (CFD)

In this article, computational fluid dynamics (CFD) technology is used to model a spouted bed(SB). The multifluid Eulerian-Eulerian approach based on kinetic theory of granular flows and Gidaspow's drag model for the interaction between gas and particles are applied in the modeling. The effects of the SB properties—that is, cone angle, particle size, cylinder diameter, and static bed height of particles—on its dynamics performance are investigated. The simulated results—that is, flow pattern of particles, fountain height, voidage, and particle velocity of the spout zone—are presented. It is shown that periodic fluctuation of spouting appears in an SB with conical angle of 30° and inlet velocity at 16.6 m/s. When the SB cylinder diameter becomes 0.52 m, periodic fluctuation appears, too. The stable spouting of the SB with a 90° cone angle could be obtained at an inlet air velocity of 24.3 m/s. The fountain height of particles decreased with an increase in particle size and the static bed height of particles. It is kept at about 0.19 m when different SB cylinder diameters in the range of 0.36 to 0.48 m are used. In the spouting region, the voidage decreased with static particle height in bed, but the particle velocity increased. For a certain particle size, the voidage decreased with an increase in particle height, but the velocity of the particles increased. It was also found that the cylinder diameter did not affect the volume fraction of particles except for the cylinder diameter 0.52 m and the change in particle velocity was minimal in the spout zone. With the different static bed height of particles used, the voidage and particle velocity did not change much at the same level of spout zone.     

Influence of Longitudinal Vortex Generator Configuration on the Hydrodynamics in a Novel Spouted Bed

The gas‐solid flow in a cylindrical spouted bed with a pair of spherical longitudinal vortex generators (LVGs) was numerically investigated by a two‐fluid model with kinetic theory for granular flow. Simulations and analyses were conducted on five types of spouted beds: a conventional spouted bed without disturbance units as well as spouted beds with a pair of LVGs in which the radius of spheres installed on the LVGs had four different dimensions. Results of the computational fluid dynamics demonstrate that the fountain height decreases with larger radius, and the influence range of the longitudinal vortex increases with the greater radius, both for the gas phase and particle phase. The turbulent kinetic energy of the gas phase along the radial and axial directions in the spouted bed was also promoted significantly by the longitudinal vortex and increased with larger radius, which is due to the higher LVG volume.     

Influence of void fraction calculation on fidelity of CFD‐DEM simulation of gas‐solid bubbling fluidized beds

The correct calculation of cell void fraction is pivotal in accurate simulation of two‐phase flows using a computational fluid dynamics‐discrete element method (CFD‐DEM) approach. Two classical approaches for void fraction calculations (i.e., particle centroid method or PCM and analytical approach) were examined, and the accuracy of these methodologies in predicting the particle‐fluid flow characteristics of bubbling fluidized beds was investigated. It was found that there is a critical cell size (3.82 particle diameters) beyond which the PCM can achieve the same numerical stability and prediction accuracy as those of the analytical approach. There is also a critical cell size (1/19.3 domain size) below which meso‐scale flow structures are resolved. Moreover, a lower limit of cell size (1.63 particle diameters) was identified to satisfy the assumptions of CFD‐DEM governing equations. A reference map for selecting the ideal computational cell size and the suitable approach for void fraction calculation was subsequently developed. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2000–2018, 2014     

Hydrodynamics of pulsed spouted beds: Effects of pulsation waveform,amplitude, and frequency

The effect of flow pulsations is studied via a discrete element model on hydrodynamics of spouted bed, which is being used in many important industries like drying processes. Decreased horizontal air percolation and preserving upward momentum, increased particle circulation, increased particle traverse distance, and better homogeneity are resulted from flow pulsations in spouted beds. Among the waveforms studied, square and triangular waveforms differ most and least from steady spouting, respectively. The predictions indicate that the pulsed spouted bed has the potential to enhance both gas and particle motion, hence being useful in drying and other operations.