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.     

Study of wall boundary condition in numerical simulations of bubbling fluidized beds

The influence of the solid-phase wall boundary condition was investigated in Eulerian-Eulerian numerical simulations of a bubbling fluidized bed. Parametric studies of the particle-wall restitution coefficient and specularity coefficient were performed to evaluate their impact on the predicted flow hydrodynamics in terms of bed expansion, local voidage, and solid velocity. Both two- and three-dimensional simulations were conducted and compared with available experimental data on solid velocity and bubble properties. It is found that the wall effect plays an important role in CFD models. Such factors as the voidage at the bubble boundary, averaging method, and minimum bubble size also influence the mean bubble diameter.     

Revisiting Johnson and Jackson boundary conditions for granular flows

In this article, we revisit Johnson and Jackson boundary conditions for granular flows. The oblique collision between a particle and a flat wall is analyzed by adopting the classic rigid‐body theory and a more realistic semianalytical model. Based on the kinetic granular theory, the input parameter for the partial‐slip boundary conditions, specularity coefficient, which is not measurable in experiments, is then interpreted as a function of the particle‐wall restitution coefficient, the frictional coefficient, and the normalized slip velocity at the wall. An analytical expression for the specularity coefficient is suggested for a flat, frictional surface with a low frictional coefficient. The procedure for determining the specularity coefficient for a more general problem is outlined, and a working approximation is provided. Published 2011 American Institute of Chemical Engineers, 2012     

Evaluation of wall boundary condition parameters for gas–solids fluidized bed simulations

Wall boundary conditions for the solids phase have significant effects on numerical predictions of various gas–solids fluidized beds. Several models for the granular flow wall boundary condition are available in the open literature for numerical modeling of gas–solids flow. A model for specularity coefficient used in Johnson and Jackson boundary conditions by Li and Benyahia (Li and Benyahia, AIChE J. 2012;58:2058–2068) is implemented in the open‐source CFD code‐MFIX. The variable specularity coefficient model provides a physical way to calculate the specularity coefficient needed by the partial‐slip boundary conditions for the solids phase. Through a series of two‐dimensional numerical simulations of bubbling fluidized bed and circulating fluidized bed riser, the model predicts qualitatively consistent trends to the previous studies. Furthermore, a quantitative comparison is conducted between numerical results of variable and constant specularity coefficients to investigate the effect of spatial and temporal variations in specularity coefficient. Published 2013 American Institute of Chemical Engineers AIChE J, 59: 3624–3632, 2013     

Numerical Simulation of Tube Erosion in a Bubbling Fluidized Bed with a Dense Tube Bundle

Tube erosion in a bubbling fluidized bed is numerically studied using the Eulerian‐Eulerian method coupled with a monolayer kinetic energy dissipation model. The hydrodynamical simulations are performed under conditions with three different superficial gas velocities. The time‐averaged bubble frequency and bubble rise velocity are calculated to characterize the bed hydrodynamics. The erosion rates of two target tubes are simulated and the influence of the bubble behaviors on erosion rates is evaluated. Compared with the experimental data in the literature, the bubble behaviors are well captured by the simulations. Good agreement between the calculated and measured erosion rates is also obtained for the two target tubes. The bubble behaviors around the tubes have direct impact on the tube erosion. Only small discrepancies in the calculated erosion rates are found when using different particle‐wall restitution coefficients and specularity coefficients.     

颗粒相壁面条件对提升管内气固流动模拟的影响

引言提升管是非均匀结构显著的气固两相流动体系,其流动特性主要表现为轴向空隙率的"S"形分布、径向的"环-核"结构以及团聚物的生成和破碎等。近年来,国内外学者致力于数值计算方法的研究增多,其中双流体模型的应用最为广泛;颗     

粗糙颗粒碰撞参数对鼓泡流化床内气固流动模拟的影响

结合粗糙颗粒动力学理论和双流体方法,数值模拟了碰撞参数对鼓泡流化床内稠密气固两相流动特性的影响. 结果表明,增大摩擦系数或减小法向弹性恢复系数会使床内颗粒分布更为不均,并增强床层膨胀及压力降脉动. 合理选取摩擦系数模拟得到时均气固流场分布,与实验吻合,罂粟籽颗粒的摩擦系数取0.3~0.6较合适. 法向弹性恢复系数改变不影响时均气固流场分布的基本形态,其取值敏感性不如摩擦系数;切向弹性恢复系数对鼓泡流化床动态特性及时均气固流场的影响相对较弱.     

基于DEM模拟气固鼓泡床中颗粒碰撞参数对流场间歇性的影响

采用计算流体力学和离散元(CFD-DEM)方法研究鼓泡床内的气固流动状态, 考察了颗粒弹性系数和恢复系数对流场间歇性的影响, 并利用小波变化分析方法分析了颗粒弹性系数和恢复系数对流场相干结构的影响。研究结果表明:颗粒弹性系数和恢复系数对颗粒速度脉动能、床层平均高度、平坦因子以及流场间歇性有一定影响。随着颗粒弹性系数取值的变大, 高频区能量和平坦因子先降低后增加, 床层高度先增加后降低, 流场间歇性先减弱后增强;颗粒恢复系数取值越大, 高频区能量和平坦因子越低, 床层高度越大, 流场间歇性越弱。     

Using the discrete element method to predict collision-scale behavior: A sensitivity analysis

Discrete element method (DEM) simulations have recently been used to investigate collision-scale measurements such as collision frequency and impact velocity distributions. These simulations are typically validated against particle velocity fields using experimental techniques such as particle image velocimetry or positron emission particle tracking. An important question that has not been addressed is whether validation of a macroscopic velocity field or solid fraction field also implies a validation of collision-scale measurements such as collision frequency. In this study, DEM measurements of solid fraction, shear rate, collision frequency, and impact velocity are made in a small region just beneath the free surface in a rotating drum. The effects of periodic drum length, particle stiffness, coefficient of restitution, and particle size are investigated. The solid fraction and shear rate do not vary with particle stiffness or coefficient of restitution over the range of values studied. However, the collision rate increases with increasing particle stiffness and coefficient of restitution. In addition, the average collision speed decreases as particles become stiffer or less elastic. The shear rate varies with particle size, but the average collision velocity remains constant. These findings indicate that validation against particle velocity and solid fraction fields does not necessarily imply validation of collision frequency and impact velocity. Indeed, the velocity and solid fraction fields were found to be relatively insensitive to a range of DEM contact stiffnesses and coefficients of restitution while the collision distributions were sensitive.     

不同曳力模型及颗粒碰撞恢复系数对短接触旋流反应器内气固流场的影响

为考察曳力模型和颗粒碰撞恢复系数对短接触旋流反应器内流动特性的影响,基于双流体模型, 结合颗粒动力学理论,对反应器内气固两相流场进行模拟研究。分别采用Gidaspow、Wen & Yu和Syamlal-O’Brien 3种曳力模型, 考察颗粒速度特性以及固含率径向分布。对比分析不同曳力模型的计算结果表明,Syamlal-O’Brien模型计算结果与实验结果误差较大,Wen & Yu模型在反应器边壁附近区域的计算结果误差较大,Gidaspow模型计算结果与实验结果最为吻合。此外,颗粒碰撞恢复系数较小时,所得计算值小于实验测量值,当恢复系数为0.95时颗粒扩散效果最好,计算结果与实验数据吻合度最高。     

Numerical investigation of gas mixing in gas‐solid fluidized beds

Gas mixing in a tall narrow fluidized bed operated in the slugging fluidization regime is simulated with the aid of computational fluid dynamics. In the first part, a parametric study is conducted to investigate the influence of various parameters on the gas mixing. Among the parameters studied, the specularity coefficient for the partial‐slip solid‐phase wall boundary condition had the most significant effect on gas mixing. It was found that the solid‐phase wall boundary condition needs to be specified with great care when gas mixing is modeled, with free slip, partial slip and no‐slip wall boundary conditions giving substantial differences in the extent of gas back mixing. Axial and radial tracer concentration profiles for different operating conditions are generally in good agreement with experimental data from the literature. Detailed analyses of tracer back mixing are carried out in the second part. Two parameters, the tracer backflow fraction and overall gas backflow fraction, in addition to axial profiles of cross‐sectional averaged tracer concentrations, are evaluated for different flow conditions. Qualitative trends are consistent with reported experimental findings. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

Granular flow in a rotating drum with gaps in the side wall

This paper presents a numerical investigation of the motion of bi-sized particles in a short rotating drum by using Discrete Element Method (DEM). The side wall of the drum has equally spaced gaps whose width is just between the two particle diameters. One end wall of the drum is fixed while the other rotates with the side wall. Small particles are fed into the drum continuously at the center region in the axial direction. The effect of rotating speed on the volumetric holdup and residence time of small particle is investigated. A critical rotating speed is found, below which the decrease of rotating speed will increase the volumetric holdup and the residence time of the small particles sharply. A jump in the axial distribution of the outflow rate of the small particles is observed at the region adjacent to the fixed end wall. The flow pattern inside the drum is analyzed. In the region between the fixed end wall and the feeding point, all small particles, on average, move towards the fixed end wall. While in the region between the rotating end wall and the feeding point, the small particles curve away the rotating end wall in the upper part of the charge and return to this wall in the lower part. The particle temperature distributions at different rotating speeds are explored to understand the flow behavior observed in these simulations.     

Practical validation of the two-fluid model applied to dense gas-solid flows in fluidized beds

This paper discusses the simulation of bubbling gas-solid flows by using the Eulerian two-fluid approach. Predictions of particle motion, bed expansion, bubble size and bubble velocity in bubbling beds containing Geldart B particles are compared with experimental results and correlations found in the literature. In addition, gas mixing in a bed of Geldart A particles is investigated.An in-house code has been developed based on the finite-volume method and the time-splitting approach using a staggered grid arrangement. The velocities in both phases are obtained by solving the 2D Reynolds-averaged Navier/Stokes equations using a partial elimination algorithm (PEA) and a coupled solver. The k-ε turbulence model is used to describe the turbulent quantities in the continuous phase.In general, the model predictions are in good agreement with experimental data found in the literature. Most important observations are: the level of the restitution coefficient was found to be crucial in order to obtain successful results from 2D axisymmetric simulations of a system containing Geldart B particles. Bubble size and bubble rise velocities are not as sensitive to the restitution coefficient. The turbulence model is of outmost importance concerning gas mixing in a fluidized bed of Geldart A particles.From these numerical analyzes an optimized granular flow two-fluid model can be designed for the purpose of simulating reactive systems in fluidized bed reactors.     

Evaluation of Hydrodynamic Closures for Bubbly Regime CFD Simulations in Developing Pipe Flow

The effect of interfacial forces and relevant closures, particularly the lift and wall lubrication forces, on the predictions of Eulerian‐Eulerian computational fluid dynamics simulations of bubbly flows was studied. The test case under study was a developing turbulent bubbly pipe flow, simulated by using OpenFOAM. The results show that the geometric approach to consider the wall effect leads to better agreement than a standard relation assuming asymmetric drainage around the bubble near the wall. Furthermore, the results verify the need for employing negative lift coefficients in cases with large bubbles. A sensitivity analysis on the lift coefficient highlighted the importance of investigating spatially developing flows to draw general conclusions on the applicability of closure relations.     

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     

Numerical study of cluster and particle rebound effects in a circulating fluidised bed

Gas-particle flows in a vertical two-dimensional configuration appropriate for circulating fluidised bed applications were investigated numerically. In the computational study presented herein the motion of particles was calculated based on a Lagrangian approach and particles were assumed to interact through binary, instantaneous, non-frontal, inelastic collisions including friction. The model for the interstitial gas phase is based on the Navier-Stokes equations for two-phase flows. The numerical study of cluster structures has been validated with experimental results from literature in a previous investigation. Numerical experiments were performed in order to study the effects of different cluster and particle rebound characteristics on the gas-particle flow behaviour.Firstly, we investigated the hard sphere collision model and its effect on gas-particle flow behaviour. The coefficient of restitution in an impact depends not only on the material properties of the colliding objects, but also on their relative impact velocity. We compared the effect of a variable restitution coefficient, dependent on the relative impact velocity, with the classical approach, which supposes the coefficient of restitution to be constant and independent of the relative impact velocity.Secondly, we studied the effects of different cluster properties on the gas-particle flow behaviour. Opposing clustering effects have been observed for different particle concentrations: within a range of low concentrations, groups of particles fall faster than individual particles due to cluster formation, and within a well-defined higher concentration range, return flow predominates and hindered settling characterises the suspension. We propose herein a drag law, which takes into account both opposing effects and have compared the resulting flow behaviour with that predicted by a classical drag law, which takes into account only the hindered settling effect.     

Simulations of dense granular gases without gravity with impact-velocity-dependent restitution coefficient

We report two-dimensional simulations of strongly vibrated granular materials without gravity. The coefficient of restitution depends on the impact velocity between particles by taking into account both the viscoelastic and plastic deformations of particles, occurring at low and high velocities respectively. Use of this model of restitution coefficient leads to new unexpected behaviors. When the number of particles N is large, a loose cluster appears near the fixed wall, opposite the vibrating wall. The pressure exerted on the walls becomes independent of N, and linear in the vibration velocity V, quite as the granular temperature. The collision frequency at the vibrating wall becomes independent of both N and V, whereas at the fixed wall, it is linear in both N and V. These behaviors arise because the velocity-dependent restitution coefficient introduces a new time scale related to the collision velocity near the cross over from viscoelastic to plastic deformation.     

Numerical simulation of three‐dimensional fiber orientation in injection molding including fountain flow effect

It is essential to predict the nature of flow field inside mold and flow‐induced variation of fiber orientation for effective design of short fiber reinforced plastic parts. In this investigation, numerical simulations of flow field and three‐dimensional fiber orientation were carried out in special consideration of fountain flow effect. Fiber orientation distribution was described using the second‐order orientation tensor. Fiber interaction was modeled using the interaction coefficient C_I. Three closure approximations, hybrid, modified hybrid, and closure equation for C_I=0, were selected for determination of the fiber orientation. The fiber orientation routine was incorporated into a previously developed program of injection mold filling (CAMPmold), which was based on the fixed‐grid finite element/finite difference method assuming the Hele‐Shaw flow. For consideration of the fountain flow effect, simplified deformation behavior of fountain flow was employed to obtain the initial condition for fiber orientation in the flow front region. Comparisons with experimental results available in the literature were made for film‐gated strip and centergated disk cavities. It was found that the orientation components near the wall were were accurately predicted by considering the fountain flow effect. Test simulations were also carried out for the filling analysis of a practical part, and it was shown that the currently developed numerical algorithm can be effectively used for the prediction of fiber orientation distribution in complex parts.     

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.