Hydrodynamic modelling of dense gas-fluidised beds: comparison and validation of 3D discrete particle and continuum models

A critical comparison of a hard-sphere discrete particle model, a two-fluid model with kinetic theory closure equations and experiments performed in a pseudo-two-dimensional gas-fluidised bed is made. Bubble patterns, time-averaged particle distributions and bed expansion dynamics measured with a nonintrusive digital image analysis technique are compared to simulation results obtained at three different fluidisation velocities. For both CFD models, the simulated flow fields and granular temperature profiles are compared. The effects of grid refinement, particle-wall interaction, long-term particle contacts, particle rotation and gas-particle drag are studied. The mechanical energy balance for the suspended particles is introduced, and the energy household for both CFD models is compared. The most critical comparison between experiments and model results is given by analysis of the bed expansion dynamics. Though both models predict the right fluidisation regime and trends in bubble sizes and bed expansion, the predicted bed expansion dynamics differ significantly from the experimental results. Alternative gas-particle drag models result in significantly different bed dynamics, but the gap between model and experimental results cannot be closed. In comparison with the experimental results, the discrete particle model gives superior resemblance. The main difference between both CFD models is caused by the neglect of particle rotation in the kinetic theory closure equations embedded in the two-fluid model. Energy balance analysis demonstrates that over 80% of the total energy is dissipated by sliding friction. Introduction of an effective restitution coefficient that incorporates the additional dissipation due to frictional interactions significantly improves the agreement between both models.     

Extension of the kinetic theory of granular flow to include dense quasi-static stresses

Fluidized bed technology has diverse industrial applications ranging from the gasification of coal in the power industry to chemical reactions for the plastic industry. Due to their complex chaotic non-linear behaviour understanding the hydrodynamic behaviour in fluidized beds is often limited to pressure drop measurements and a mass balance of the system. Computational fluid dynamics has the capability to model multiphase flows and can assist in understanding gas-solid fluidized beds by modeling their hydrodynamics. The multiphase Eulerian-Eulerian gas-solid model, extended and validated here improves on the kinetic theory of granular flow by including a closure term for the quasi-static stress associated with the long term particle contact at high solid concentrations. Similar quasi-static models have been widely applied to slow granular flow such as chute flow, flow down an incline plane and geophysical flow. However combining the kinetic theory of granular flow and the quasi-static stress model for the application of fluidized beds is limited. The objective of the present paper is to compare two quasi-static stress models to the experimental fluidized bed data of Bouillard et al. [4]. A quasi-static granular flow model (QSGF) initially developed by Gray and Stiles [18] is compared to the commonly used Srivastava and Sundaresan [37]. Both models show good agreement with the experimental bubble diameter and averaged porosity profiles. However only the QSGF model shows a distinct asymmetry in the bubble shape which was documented by Bouillard et al. [4].     

Hydrodynamic modelling of binary mixture in a gas bubbling fluidized bed using the kinetic theory of granular flow

A multi-fluid Eularian CFD model with closure relationships according to the kinetic theory of granular flow has been applied to study the motions of particles in the gas bubbling fluidized bed with the binary mixtures. The mutual interactions between the gas and particles and the collisions among particles were taken into account. Simulated results shown that the hydrodynamics of gas bubbling fluidized bed related with the distribution of particle sizes and the amount of energy dissipated in particle-particle interaction. In order to obtain realistic bed dynamics from fundamental hydrodynamic models, it is important to correctly take the effect of particle size distribution and energy dissipation due to non-ideal particle-particle interactions into account.     

Prediction of particle motion in a two-dimensional bubbling fluidized bed using discrete hard-sphere model

The solids motion in a gas-solid fluidized bed was investigated using a discrete hard-sphere model. Detailed collision between particles and a nearest list method are presented. The turbulent viscosity of gas phase was predicted by subgrid scale (SGS) model. The interaction between gas and particles phases was governed by Newton's third law. The distributions of concentration, velocity and granular temperature of particles are obtained. The radial distribution function is calculated from the simulated spatio-temporal particle distribution. The normal and shear stresses of particles are predicted from the simulated instantaneous particle velocity. The pressure and viscosity of particles are obtained from both the kinetic theory of granular flow and the calculated stresses of particles. For elastic particles the individual lateral and vertical particle velocity distribution functions are isotropic and Maxwellian. The observed anisotropy becomes more pronounced with increasing degree of inelasticity of the particles.     

Flow behaviors of a large spout-fluid bed at high pressure and temperature by 3D simulation with kinetic theory of granular flow

Flow behaviors of a large spout-fluid bed (I.D. 1.0 m) at high pressure and temperature were investigated by Eulerian simulation. The gas phase was modeled with k − ε turbulent model and the particle phase was modeled with kinetic theory of granular flow. The development of an internal jet, gas-solid flow patterns, particle concentrations, particle velocities and jet penetration depths at high pressure and temperature at different operating conditions were simulated. The results show that the bed operated at an initial bed height larger than the maximum spoutable bed height resembles the flow patterns of jetting fluidized beds. The radial profiles of particle velocities and concentrations at high temperature and pressure have the similar characteristic shapes to those at ambient pressure and temperature. The particle concentrations and velocities appear to depend on the bed heights when increasing pressure while keeping the gas velocities and temperature constant. The particle velocities in the lower region of the bed increase with increasing pressure, while they tend to decrease in the middle and upper regions of the bed. The particle concentrations have an opposite dependency with increasing pressure. They decrease in the lower region of the bed but increase in the middle and upper regions of the bed. Besides, the jet penetration depths are found to increase with increasing pressure.     

Numerical simulations of gas-solid flow in tapered risers

Hydrodynamic behavior of gas-solid flow in tapered risers was simulated using the two-fluid model based on the kinetic theory of granular flow representing the constitutive relations of the solid phase. Present numerical model was verified by comparing with experimentally measured solid mass fluxes, particle concentrations and velocities in column risers. Computed results showed that the core-annular flow structure existing in the column riser may disappear in the tapered risers. The distributions of particle concentration tend to be more uniform in the tapered riser than that in the column riser under the same operating conditions. The uniform particle distribution can be achieved by changing the inclined angle of the tapered riser under specific operating conditions.     

模拟颗粒流动的离散元方法及其应用

介绍了离散元 (DEM)方法的基本原理、颗粒运动控制方程和颗粒相互作用力的数学模型。综述了DEM在流化床和固定床反应器 ,以及一些单元操作如料仓卸料过程、混合过程等中的最新应用和研究结果 ,表明DEM能够反映过程的本质机理 ,可以利用基本的数据模拟复杂的颗粒流动系统。最后指出了DEM发展中亟待解决的问题     

CFD simulation of the high shear mixing process using kinetic theory of granular flow and frictional stress models

In order to enhance process understanding and to develop predictive process models in high shear granulation, there is an ongoing search for simulation tools and experimental methods to model and measure the velocity and shear fields in the mixer. In this study, the Eulerian-Eulerian approach to model multiphase flows has been used to simulate the mixer flow. Experimental velocity profiles for the solid phase at the wall in the mixer have been obtained using a high speed camera following the experimental procedure as described by Darelius et al. [2007a. Measurement of the velocity field and frictional properties of wet masses in a high shear mixer. Chemical Engineering Science, 62, 2366-2374]. The governing equations for modelling the dense mixer flow have been closed by using closure relations from the kinetic theory of granular flow (KTGF) combined with frictional stress models. The free slip and partial slip boundary conditions for the solid phase velocity at the vessel wall have been utilized. The partial slip model originally developed for dilute flows by Tu and Fletcher [1995. Numerical computation of turbulent gas-solid particle flow in a 90^° bend. A.I.Ch.E. Journal, 41, 2187-2197] has been employed. It was found that the bed height could be well predicted by implementing the partial slip model, whereas the free slip model could not capture the experimentally found bed height satisfactorily. In the simulation, the swirling motion of the rotating torus formed was over-predicted and the tangential wall velocity was under-predicted, probably due to the fact that the frictional stress model needs to be further developed, e.g. to tackle cohesive particles in dense flow. The advantage of using the Eulerian-Eulerian approach compared to discrete element methods is that there is no computational limitation on the number of particles being modelled, and thus manufacturing scale granulators can be modelled as well.     

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.     

Comparison of multifluid and discrete particle modelling in numerical predictions of gas particle flow in circulating fluidised beds

From the perspective of wanting to evaluate the modelling of the particulate phase in multifluid computational fluid dynamics simulations, numerical predictions from a multifluid model is compared with predictions from a discrete particle model. Simulations with both one and three representative particle diameters for the particulate phase are performed. The predicted results are compared with experimental findings obtained with Laser Doppler Anemometry. The numerical predictions from the discrete particle code are found to be in better agreement with the experimental findings, but the multifluid code is by far the most efficient. To evaluate the modelling of collisions in the multifluid model, discrete particle simulations which only take into account of energy loss caused by head-on collisions are compared with discrete particle simulations, which take nonfrontal collisions into account.     

Modelling of dense and complex granular flow in high shear mixer granulator—A CFD approach

In the aspect of granulation process control, the numerical simulations appear to be a cost-effective and flexible tool to investigate the flow structure of granular materials in mixer granulators of various configurations and operating conditions. Computational fluid dynamics (CFD) is used in this study to model the granular flow in a vertical high shear mixer granulator. The simulation is based on the continuum model of dense-gas kinetic theory [Gidaspow, D., Bezburuah, R., Ding, J., 1992. Hydrodynamics of circulating fluidized beds, kinetic theory approach. In: Fluidization, vol. VII, Proceedings of the 7th Engineering Foundation Conference on Fluidization, Brisbane, Australia, pp. 75-82] with consideration of inter-particle friction force at dense condition [Schaeffer, D.G., 1987. Instability in the evolution equations describing incompressible granular flow. Journal of Differential Equations 66 (1), 19-50]. This study aims to verify this numerical method in modelling dense and complex granular flows, where the solids motion obtained from the simulation is validated against the experimental results of positron emission particle tracking (PEPT) technique [Ng, B.H., Kwan, C.C., Ding, Y.L., Ghadiri, M., Fan, X.F., 2007. Solids motion of calcium carbonate particles in a high shear mixer granulator: a comparison between dry and wet conditions. Powder Technology 177 (1), 1-11]. In general, the Eulerian based continuum model captures the main features of solids motion in high shear mixer granulator including the bed height and dominating flow direction (the tangential velocity). However, the continuum based kinetic-frictional model is not capable of capturing the complex vertical swirl pattern. Quantitative comparison shows over-predictions in the tangential velocity and stiff drops of the tangential velocity at the wall region. These results demonstrate the deficiency in transmitting forces in the bed of granular materials which indicate the necessity to improve the constitutive relations of dense granular materials as a continuum.     

CFD simulations of bubbling beds of rough spheres

Hydrodynamics of three-dimensional gas-solid bubbling fluidized beds are numerically analyzed. The particle-particle interactions are simulated from the kinetic theory for flow of dense, slightly inelastic, slightly rough sphere proposed by Lun [1991. Kinetic theory for granular flow of dense, slightly inelastic, slightly rough sphere. Journal of Fluid Mechanics 233, 539-559] to account for rough sphere binary collisions and the frictional stress model proposed by Johnson et al. [1990. Frictional-collisional equations of motion for particulate flows and their application to chutes. Journal of Fluid Mechanics 210, 501-535] to consider the frictional contact forces between particles. The present model is evaluated by measured particle distributions and velocities of Yuu et al. [2001. Numerical simulation of air and particle motions in group-B particle turbulent fluidized bed. Powder Technology 118, 32-44] and experimental bed expansion of Taghipour et al. [2005. Experimental and computational study of gas-solid fluidized bed hydrodynamics. Chemical Engineering Science 60, 6857-6867]. Our computed results indicated that the present model gives better agreement with experimental data than the results from original kinetic theory for frictionless slightly inelastic sphere of Ding and Gidaspow [1990. A bubbling fluidization model using kinetic theory of granular flow. A.I.Ch.E. Journal 36, 523-538] with and without solid friction stress model.     

Numerical simulation of flow behavior of particles and clusters in riser using two granular temperatures

Cluster in CFB riser significantly affects performance of circulating fluidized beds. To model hydrodynamic behavior in CFB risers, three phase flows were assumed in the riser, the gas phase, the dispersed particle phase, and the clusters phase. The gas-solid multi-fluid model is extended to give the macroscopic averaged equations with constitutive equations for both particle phases from kinetic theory of granular flow. The clusters and the dispersed particles have their own fluctuating energy or two individual granular temperatures. Interactions between the cluster and its surrounding dispersed particles were obtained from kinetic theory of granular flow. Drag force for gas to dispersed particles and the clusters are empirically determined. The momentum exchange between dispersed particles and clusters is modeled using the concept of molecular dynamics. Cluster properties are predicted with the cluster-based approach. The distributions of volume fractions and velocities of gas, dispersed particles and clusters are predicted. Computed solid mass fluxes and volume fractions agree with Manyele et al. [S.V. Manyele, J.H. Parssinen, J.X. Zhu, Characterizing particle aggregates in a high-density and high-flux CFB riser, Chemical Engineering Journal, 88 (2002) 151-161.] and Knowlton [T.M. Knowlton, Modelling benchmark exercise. Workshop at the Eighth Engineering Foundation Conference on Fluidization, Tours, France, 1995.] experimental data.     

An extension of the preconditioned advection upstream splitting method for 3D two-phase flow calculations in circulating fluidized beds

For the calculation of gas–solid flow in circulating fluidized beds, a Eulerian–Eulerian approach is taken. An integration scheme based on dual time stepping and a finite volume technique is developed and implemented in 3D. The inviscid part of the equations is treated following an extension of the preconditioned advection upstream splitting method (AUSMP) to two-phase flows. Calculations on an industrial size straight riser are performed. The influence of the inelasticity of particle–particle collisions on the stability of the flow is investigated. Further, the effects of a double abrupt side outlet configuration are shown.     

A model for gas-solid flow in a horizontal duct with a smooth merge of rapid-intermediate-dense flows

Granular flow in the rapid flow regime is dominated by particle-particle collisions and the constitutive relations for the solid stress are obtained from the classic kinetic theory of granular flow. In the dense flow regime, on the other hand, particles interact via enduring contacts and the solid stress can be deduced from soil mechanics theories. In this paper, constitutive equations, recently proposed by Tardos et al. [2003. Slow and intermediate flow of frictional bulk powder in the Couette geometry. Powder Technology 131, 23-39.] has been incorporated in the simulation of gas-solid flow in a horizontal duct. These equations smoothly merge the rapid granular flow solution with the so-called “intermediate” regime (where both kinetic/collisional and frictional contributions might play a role) and reduce to Coulomb yield condition for slow frictional flow (shear rate → 0). The results of this new modelling approach have shown good qualitative agreement with the reported experimental observation on wide range of gas-solid flow conditions. In this study, we also present the definition of boundaries between rapid-intermediate-dense flow regimes based on the dimensionless shear rate (λ), and a modified Reynolds number (Re). We have shown that the intermediate flow regime can be classified at approximately 0.1<λ<1.0 and 100<Re<3000.     

颗粒旋转对鼓泡流化床内气固两相流动特性影响的数值模拟

运用考虑颗粒自旋转流动对颗粒碰撞能量交换和耗散影响的颗粒动理学方法,建立鼓泡流化床气固两相Euler-Euler双流体模型,数值模拟流化床内气体颗粒两相流动特性。分析表明,颗粒平动温度与旋转温度之比是法向和切向颗粒弹性恢复系数和摩擦系数的函数。与不考虑颗粒旋转效应计算结果相比,考虑颗粒旋转效应后床内较容易形成气泡,颗粒自旋转运动将导致床内非均匀结构更明显。并且床层平均空隙率和床层膨胀高度增加,床中心区域颗粒轴向速度提高,床内颗粒平动温度下降。考虑颗粒旋转效应后预测的颗粒轴向速度和颗粒脉动速度与文献实验结果基本吻合。考虑颗粒旋转效应后获得的气泡直径更接近于前人经验关联式。     

Hydrodynamics of binary fluidization in a riser: CFD simulation using two granular temperatures

A new computational fluid-dynamic (CFD) model with a separate granular temperature (2/3 random particle kinetic energy per unit of mass) equation for each phase or particle size was developed using constitutive equations derived earlier by Huilin, Gidaspow and Manger. In agreement with the experiment and model of Mathiesen, Solberg and Hjertager the new model computes the observed core-annular flow regime. It predicts the trends of the observed radial and axial particle diameter distributions. For elastic particles the computed particle velocity distributions are parabolic. They are close to the laminar type approximate analytical solution for flow in a pipe, where the mean velocity equals the inlet flux divided by the particle density and volume fraction. The computed turbulent intensity is lower for large particles than for small particles, as measured. This is in agreement with an approximate analytical solution for the granular temperature in the developed flow region of a riser for elastic particles. Computations show that for sufficiently inelastic particles the granular temperature in the center can be lower than near the wall resembling the measured particle fluctuating velocity distribution.     

Numerical simulation and validation of dilute turbulent gas-particle flow with inelastic collisions and turbulence modulation

This work describes a theoretical and numerical study of turbulent gas-particle flows in the Eulerian framework. The equations describing the flow are derived employing Favre averaging. The closures required for the equations describing the particulate phase are derived from the kinetic theory of granular flow. The kinetic theory proposed originally is extended to incorporate the effects of the continuous fluid on the particulate phase behavior. Models describing the coupling between the continuous phase kinetic energy and particulate phase granular temperature are derived, discussed, and their effect on the flow predictions is shown.The derived models are validated with benchmark experimental results of a fully developed turbulent gas-solid flow in a vertical pipe. The effect of the models describing the influence of turbulence on the particle motion as well as the turbulence modulation due to the presence of particles is analyzed and discussed.     

Modeling of cluster structure-dependent drag with Eulerian approach for circulating fluidized beds

Flow behavior of gas and solids is simulated in combination the gas-solid two-fluid model with a cluster structure-dependent (CSD) drag coefficient model. The dispersed phase is modeled by a Eulerian approach based upon the kinetic theory of granular flow (KTGF) including models for describing the dispersed phase interactions with the continuous phase. The drag forces of gas-solid phases are predicted from the local structure parameters of the dense and dilute phases based on the minimization of the energy consumed by heterogeneous drag. The cluster structure-dependent (CSD) drag coefficients are incorporated into the two-fluid model to simulate flow behavior of gas and particles in a riser. Simulation results indicate that the dynamic formation and dissolution of clusters can be captured with the cluster structure-dependent drag coefficient model. Simulated solid velocity and concentration of particles profiles are in reasonable agreement with experimental results.