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.     

Experimental and Numerical Study of Grinding Media Flow in a Ball Mill

An experimental and numerical study on the grinding media dynamics inside a baffled ball mill under different solid‐flow regimes, namely, cascading, cataracting, and centrifuging, is described. The Eulerian approach was used for all simulations and the boundary condition at the drum wall was investigated by means of the specularity coefficient parameter. This effort is an important approach in representing the particle‐wall interaction in a ball mill. The restitution coefficient of the balls was experimentally measured using a video camera, and its influence was evaluated by comparing the numerical and experimental outcome of flow patterns. The simulations results proved that the specularity and restitution coefficients effects at the drum wall were more evident at high rotational speeds.     

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     

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     

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.     

CFD simulation of gas–solid flow in a spouted bed with a non-porous draft tube

A multi-fluid Eulerian–Eulerian approach incorporating the kinetic theory of granular flow was used to simulate a spouted bed containing non-porous draft tube. Drag function and coefficient of restitution were investigated. Solid and gas velocity vector, gas flow rate in annulus and spout regions and longitudinal pressure distribution were evaluated. In addition, the effects of the entrainment height and the draft tube diameter were studied. Simulation indicates the formation of three regions namely, annulus, spout and fountain; similar to a conventional spouted bed. Current model predicts acceptable results in both spout and annulus regions. Simulation results indicate that the model can be employed for both mono-size and multi-size particles reasonably. This paper provides useful basis for further works on understanding gas–solid flow mechanism in spouted beds containing a non-porous draft tube.     

Discrete element method simulation of three-dimensional conical-base spouted beds

A discrete element method (DEM) simulation of three-dimensional conical-base spouted beds is presented. The overall height and diameter of the vessel are 0.5 and 0.15 m, respectively, and the nozzle diameter is 0.02 m. The inclined angle of the conical section varies from 0 to 60 degrees. The gas flow is described by the continuity and Navier-Stokes equations and solved by a finite difference method of second order accuracy in space and time. For gas-particle interaction, the Ergun equation (for void fraction smaller than 0.8) and the Wen-Yu model (for void fraction of 0.8 and above) are employed. A new method for treatment of the boundary condition for 3-D gas flow along the cone surface is proposed. This boundary condition satisfies both the continuity and momentum-balance requirements for the gas phase. Usefulness of the present simulation for studying gas flow pattern and particle motion in conical-base spouted beds is demonstrated. The effects of the inclined angle and draft tube on gas and particle flow in spouted beds are discussed.     

Scale-up relationships of spouted beds by solid stress analyses

This article describes a new set of scale-up parameters of spouted beds derived from solid stress analyses. Compared with the first set of scale-up parameters of spouted beds proposed by He et al. [He Y. L., Lim C. J., Grace J. R., Scale-up studies of spouted beds, Chemical Engineering Science, 52 (2), 329-339, 1997], this set introduced a new parameter, the coefficient of restitution of particles, that accounts for the effects of particle-particle collisions in the spout region of a spouted bed. To verify the present set of scale-up parameters, a series of experiments were designed and conducted in two spouted beds of 80 mm and 120 mm in diameter, respectively, operated in the different testing cases consisting of different combinations of the involved scale-up parameters. The results showed that the more closely the scale-up parameters of the spouted beds tested were matched, the higher hydrodynamic similarity could be achieved. The comparisons of the hydrodynamic properties such as fountain height, spout diameter and bed voidage measured in the different testing cases revealed that the coefficient of restitution of particles could significantly impact the particle-particle interactions and thus its effects should be taken into account in scaling-up spouted beds.     

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     

HEAT TRANSFER IN SPOUTED BEDS

Experiments were carried out in order to analyse the wall-to-bed and fluid-to-particle heat transfer coefficients in spouted Beds. wall-to-bed heat transfer coefficients were determined in cylindrical-conical and conical spouted beds for various gas flow rates, particle sizes and bed heights for spouted beds with and without draft tubes.

A new definition for wall-to-bed transfer coefficient was proposed baaed on experimental observations.

The heat tranefer area was also studied to ensure that a physically significant fluid-to-particle heat transfer coefficient was achieved.     

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…     

Analysis of conical spouted bed fluid dynamics using carton mixtures

The pyrolysis has risen as an important alternative technology for generating value from waste. Among the modern solid wastes, the post-consumer carton packaging highlights due to the high value-added of the primary products obtained from pyrolysis. In an attempt to use conical spouted beds (CSBs) as a pyrolysis reactor for processing cartons, this present research aims at analyzing experimentally the air–carton mixtures flow dynamics in CSBs and stating comparisons with characteristic fluid dynamics obtained by using CFD technique. The flow behavior of air–carton disk is experimentally investigated by analyzing data of bed pressure drop, air velocity and fountain height. For the carton disk and polyethylene mixtures up to 50% cartons (in mass), and carton disks and sand mixtures comprising 5 and 10% cartons (in mass), the analysis of the experimental data shows that the stable spouted regimes are achieved. Furthermore, the simulated results demonstrate that the Eulerian approach using the Syamlal drag model is able to predict qualitatively the flow behavior in conical spouted beds comprising non-spherical particle mixtures.     

Simulation of the Hydrodynamics and Drying in a Spouted Bed Dryer

Gas-particle flow behavior in a spouted bed of spherical particles was simulated using the Eulerian-Eulerian two-fluid modeling approach, incorporating a kinetic-frictional constitutive model for dense assemblies of the particulate solid. The interaction between gas and particles was modeled using the Gidaspow drag model and the predicted hydrodynamics is compared with published experimental data. To investigate drying characteristics of particulate solids in axisymmetric spouted beds, a heat and mass transfer model was developed and incorporated into the commercial computational fluid dynamics (CFD) code FLUENT 6.2. The kinetics of drying was described using the classical and diffusional models for surface drying and internal moisture drying, respectively. The overall flow patterns within the spouted bed were predicted well by the model; i.e., a stable spout region, a fountain region, and an annular downcomer region were obtained. Calculated particle velocities and concentrations in the axisymmetric spouted bed were in reasonable agreement with the experimental data of He et al. (Can. J. Chem. Eng. 1994a, 72:229; 1994b, 72:561). Such predictions can provide important information on the flow field, temperature, and species distributions inside the spouted bed for process design and scale-up.     

A bubbling fluidization model using kinetic theory of rough spheres

Collisional motion of inelastic rough spheres is analyzed on the basis of the kinetic theory for flow of dense, slightly inelastic, slightly rough sphere with the consideration of gas–solid interactions. The fluctuation kinetic energy of particles is introduced to characterize the random motion of particles as a measure of the translational and rotational velocities fluctuations. The kinetic energy transport equation is proposed with the consideration of the redistribution of particle kinetic energy between the rotational and translational modes and kinetic energy dissipation by collisions. The solid pressure and viscosity are obtained in terms of the particle roughness and restitution coefficient. The partition of the random‐motion kinetic energy of inelastic rough particles between rotational and translational modes is shown to be strongly affected by the particle restitution coefficient and roughness. Hydrodynamics of gas–solid bubbling fluidized beds are numerically simulated on the basis of the kinetic theory for flow of rough spheres. Computed profiles of particles are in agreement with the experimental measurements in a bubbling fluidized bed. The effect of roughness on the distribution of energy dissipation, kinetic energy, and viscosity of particles is analyzed. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Effect of Operating Parameters on Gas‐Solid Hydrodynamics and Heat Transfer in a Spouted Bed

Through a combined computational fluid dynamics and discrete element method approach, the effect of the operating parameters on the hydrodynamics and heat‐transfer properties of gas‐solid two‐phase flows in a spouted bed are extensively investigated. Considering the high velocity in the fountain region, gas turbulence is resolved by employing the large‐eddy simulation. The rolling friction model is adopted for more precise predictions of solid behavior near the wall. Subsequently, the gas‐solid flow patterns, gas‐solid velocities, and temperature evolution are investigated. Moreover, different operating conditions and geometry configurations are evaluated with respect to heat‐transfer performance. The results provide a fundamental understanding of heat‐transfer mechanisms in spouted beds.     

Numerical simulations of flow behavior of gas and particles in spouted beds using frictional-kinetic stresses model

Flow behavior of gas and particles is simulated in the spouted beds using a Eulerian-Eulerian two-fluid model on the basis of kinetic theory of granular flow. The kinetic-frictional constitutive model for dense assemblies of solids is incorporated. 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 and Jackson (1987) and the frictional shear viscosity model proposed by Schaeffer (1987) to account for strain rate fluctuations and slow relaxation of the assembly to the yield surface. An inverse tangent function is used to provide a smooth transitioning from the plastic and viscous regimes. The distributions of concentration, velocity and granular temperature of particles are obtained in the spouted bed. Calculated particle velocities and concentrations in spouted beds are in agreement with the experimental data obtained by He et al. (1994a, b). Simulated results indicate that flow behavior of particles is affected by the concentration of the transition point in spouted beds.     

A Study of Particle Rebounding Characteristics of a Gas–Particle Flow over a Curved Wall Surface

The particle rebounding characteristics of a gas–particle flow over a cylindrical body is investigated. With the aid of both computational and experimental approaches, the mean particle flow patterns, comprising both incident and rebound particles resulting from the impact of particles on a curved wall surface, are examined. In the experimental investigation, a two-dimensional Laser Doppler Anemometry (LDA) technique is used in the immediate vicinity of the body surface to measure the instantaneous incident and rebound particle velocities. The Reynolds-Averaging Navier-Stokes equations are solved for the continuum gas phase, and the results are used in conjunction with a Lagrangian trajectory model to predict the particle-rebound behavior in the immediate vicinity of the cylindrical wall. The computational observations, also confirmed through experiments, reveal a particle rebound zone where the mean particle flow pattern is significantly modified due to the contribution of the rebound particles during the process of particle–wall impact interaction. This particle rebound zone is found to be a function of mainly the Stokes number (particle inertia), and to a lesser extent on the fluid Reynolds number (gas flow condition), except for high gas flow velocities and restitution coefficients (particle-wall impact characteristics). Analysis of the effect of the above-mentioned parameters on the rebounding particle flow characteristics and their interrelationship has provided a better understanding of the behavior of particle flow impinging on a solid wall body. The beneficial contributions of the experimental and computational approaches in their ability to better quantify the particle–wall impact interaction phenomena present additional foundational investigations that could be further undertaken to better comprehend the particle behavior in curved wall surfaces. Such invaluable information has direct applications to industrial devices such as commercial heat exchangers and inertial impactors.     

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.