Fluid dynamic simulation in a chemical looping combustion with two interconnected fluidized beds

Flow behavior of gas and particles is simulated in a 2-D chemical-looping combustion (CLC) process with two interconnected fluidized beds. A Eulerian continuum two-fluid model is applied for both the gas phase and the solid phase. Gas turbulence is modeled by using a k-ε turbulent model. 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. Instantaneous and local velocity, concentration of particles and granular temperature are obtained. Predicted time-averaged particle concentrations and velocities reflect the classical core-annular flow structure in the air reactor. Flow behavior of bubbles is predicted in the fuel reactor and pot-seal. Computed leakage qualitatively agrees with experimental data in the fuel reactor and pot-seal.     

摩擦-动力应力模型研究喷动床内气固两相流动过程

考虑颗粒滑动的半持续性接触应力和颗粒碰撞瞬时接触应力对颗粒相应力的贡献,建立了喷动床内气体颗粒两相流动计算模型。采用颗粒动理学和Johnson 等的摩擦应力模型,数值模拟喷动床颗粒流动过程,获得了喷动床喷射区、环隙区和喷泉区内颗粒流动特性。模拟计算与He等的实验结果进行了对比。同时分析了摩擦应力模型对颗粒相黏度变化的影响,表明中速颗粒流的颗粒相摩擦应力模型将直接影响喷动床气体颗粒两相流动的预测。     

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.     

水平管加压密相煤粉气力输送数值模拟

针对加压密相气力输送,对现有的颗粒静摩擦力模型进行适当修正,并将其与颗粒动理学理论相结合,建立了可以描述加压密相气力输送的气固湍流流动状况的多相流模型。该模型充分考虑了颗粒间碰撞和摩擦力作用,以及气相和颗粒团湍流脉动之间的相互作用。采用该模型对水平管内加压密相气力输送进行了三维数值模拟研究,模拟得到了气相和固相的速度、浓度和湍流强度分布,以及压降梯度的变化规律,再现了颗粒沉积层的形成和运动的动态过程。并进行了加压密相煤粉气力输送试验研究,预测的压降梯度与试验测量结果相符合。     

补充风对水平管高压密相气力输送影响的模拟研究

针对水平管高压密相气力输送数理模型的缺陷与不足,引入Savage径向分布函数修正的颗粒动理学理论、基于Berzi摩擦压应力模型构建的摩擦应力模型以及修正的三段式曳力模型,在欧拉-欧拉方法的基础上建立了一个能同时兼顾水平管高压密相气力输送中稀相流、过渡流以及密相流输送特性的三维非稳态数理模型。并采用该数理模型考察了补充风对水平管高压密相气力输送的影响,模拟结果精准地预测了水平管压降及其随补充风的变化规律,而且其预测的水平管固相体积浓度分布与ECT图也是相吻合的,从而验证了数理模型的可靠性。模拟结果表明：随着补充风的增加,气固两相速度和湍动能以及颗粒拟温度增大,固相体积浓度减小。     

大涡模拟方法模拟鼓泡床内气固两相流动

采用大涡模拟（LES）方法模拟气相湍流,颗粒动理学方法考虑颗粒相碰撞产生的动量和能量传递和耗散,采用颗粒相大涡模拟方法（LESp）模拟颗粒脉动导致的能量耗散,同时考虑介观尺度对颗粒相压力的影响,建立了气体-颗粒LES-θ-LESp双流体模型,研究鼓泡流化床内气固两相流动的特性。数值模拟与文献实测颗粒速度和实测颗粒浓度结果具有相同的变化趋势。     

Simulations of flow behavior of gas and particles in a spouted bed using a second-order moment method-frictional stresses model

Flow behavior of gas and particles is simulated in the spouted beds using an 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 interaction of particle collisions is modeled by means of a second-order moment method, while the frictional 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. The distributions of concentration, velocity, second-order moments and granular temperature of particles are obtained in the spouted bed. Calculated particle velocities, concentrations and spout diameter in a spouted bed are in agreement with experimental data obtained by He et al., 1994a, He et al., 1994b. Simulated results indicate that the second-order moment component in the axial direction is higher that the second-order moment component in the lateral direction in both the spout and the fountain. In the annulus, the values of second-order moments are very small. The simulated mean value of the ratio of the normal second-order moment in the axial direction to the normal second-order moment in the lateral direction is in the range of 2.5–3.2 in the spout and the annulus. The bubblelike normal Reynolds stresses per unit bulk density is predicted from the simulated velocity of particles. The predicted bubblelike Reynolds stresses are very low in spouted bed. The values of the normal second-order moments are on the average three magnitudes in order larger than that of the bubblelike Reynolds stresses per unit bulk density in a spouted bed.     

Numerical predictions of flow behavior and cluster size of particles in riser with particle rotation model and cluster-based approach

Flow behavior of particles in a circulating fluidized bed (CFB) riser is numerically simulated using a two-fluid model incorporating with the kinetic theory for particle rotation and friction stress models. The particle rotations resulting from slightly friction particle-particle collisions was considered by introducing an effective coefficient of restitution based on the kinetic theory for granular flow derived by Jenkins and Zhang [2002. Kinetic theory for identical, frictional, nearly elastic spheres. Physics of Fluids 14, 1228-1235]. The normal friction stress model proposed by Johnson et al. [1990. Frictional-collisional equations of motion for particles flows and their application to chutes. Journal of Fluid Mechanics 210, 501-535] and a modified frictional shear viscosity model proposed by Syamlal et al. [1993. MFIX Documentation and Theory Guide, DOE/METC94/1004, NTIS/DE94000087] were used as the particle frictional stress model. The drag force between gas and particle phases was modified with cluster-based approach (CBA). The flow behavior of particles and the cluster size in a riser of Wei et al. [1998. Profiles of particle velocity and solids fraction in a high-density riser. Powder Technology 100, 183-189] and Issangya et al. [2000. Further measurements of flow dynamics in a high-density circulating fluidized bed riser. Powder Technology 111, 104-113] experiments are predicted. Effects of the rotation and friction stress models on the computed results are analyzed. It is concluded that particle rotations reduce the cluster size and alter the particle flows and distributions through more particle fluctuation energy dissipations. Effects of frictional stress on flow behavior and cluster size are not significant because the particle phase in the CFB riser is not dense enough to take into account for the particle-particle contact interactions.     

Hydrodynamic simulations of gas–solid spouted bed with a draft tube

Flow behavior of particles in a two-dimensional spouted bed with a draft tube is studied using a continuous kinetic-friction stresses model. The kinetic stress of particles is predicted from kinetic theory of granular flow, while the friction stress is computed from a model proposed by Johnson et al. (1990). A stitching function is used to smooth from the rapid shearing viscous regime to the slow shearing plastic regime. The distributions of concentration and velocities of particles are predicted in the spouted bed with a draft tube. Simulated results compare with the vertical velocity of particles (Zhao et al., 2008) measured and in the spout bed with draft plates and solid circulation rate (Ishikura et al., 2003) measured in the spouted bed with a draft tube. The impact of the friction stress of particles on the spout, annulus, fountain and entrancement regions is analyzed in gas–solid spouted bed with a draft tube. Numerical results show that the gas flow rate through the annulus increases with the increase of the entrainment zone. The solids circulation rate decreases with the decrease of inlet gas velocity and the height of the entrainment zone. The effect of spouting gas velocity on distributions of concentration, velocity and particle circulation is discussed.     

循环流化床多组分颗粒气固两相流动模型和数值模拟

基于稠密气体分子运动论和颗粒动力学,考虑多组分颗粒中颗粒组分与颗粒组分、颗粒组分内颗粒之间的相互作用以及气体与颗粒之间的相互作用,提出多组分颗粒非等温颗粒气固两相流动模型.以颗粒压力、径向分布函数、黏度、颗粒碰撞耗散等耦合各颗粒组分间和颗粒间的相间作用.采用大涡模拟方法模拟气相湍流流动.提出了多组分颗粒的径向分布函数计算方法.对循环流化床上升管中双组分颗粒气固两相流动特性进行了数值模拟,模拟结果揭示了上升管中双组分颗粒气固两相流动的环-核流动结构,得到了平均颗粒粒径的轴向和径向分布规律,计算结果与文献中实验结果相吻合.     

喷动床内气固二相流动行为的计算模拟

采用双流体模型结合颗粒动理学理论对喷动床内气固二相流体流动行为进行了计算模拟研究。模型中运用颗粒动理学理论描述颗粒相应力封闭流体控制方程,使用Gidaspow曳力模型描述气固相间作用。喷动床内颗粒在浓相区的体积分数很大,采用Schaeffer′s模型描述颗粒间的摩擦应力。模拟计算结果表明,喷动床内分喷射区、喷泉区、环隙区3个区域,在射流入口处形成一个瓶颈。模拟计算得到的颗粒速度和空隙度分布与实验数据进行比较,计算结果与实验结果吻合较好。     

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.     

Flow of gas and particles in a bubbling fluidized bed with a filtered two-fluid model

Numerical simulations of gas-particles flow in a bubble fluidized bed with two large eddy simulations of gas and solid phases are presented. For gas phase and solid phase, the sub-grid scale model for the viscosity is based on the Smagorinsky form. The sub-grid model for the particle pressure proposed by Igci et al. (2008) is modified by replacing the minimum fluidization velocity. The collisional interaction of particles is considered by the kinetic theory of granular flow. Flow behavior of gas and particles is performed by means of these two sub-grid scale models. The subgrid closure for the particle phase viscosity and pressure led to a qualitative change in the simulation results. Predictions are compared with experimental data measured by Yuu et al. (2000) and Taghipour et al. (2005) in the bubbling fluidized beds. The distributions of concentration and velocity of particles are predicted in the bubbling fluidized bed. The predicted filtered particle phase pressure increases and the filtered particle phase viscosity decreases with the increase of particle concentration. The qualitative importance of the model constant c_s of particles is demonstrated.     

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).     

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.     

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.     

A critical comparison of frictional stress models applied to the simulation of bubbling fluidized beds

The behaviour of a gas-solid flow in a bubbling fluidized bed operated near the minimum fluidization condition is strongly influenced by the frictional stresses between the particles, these being highly concentrated and their motion dominated by enduring contact among them and with the walls.The effect of the introduction of frictional stresses in a Eulerian-Eulerian two fluid model based on the kinetic theory of the granular flow is evaluated. The models of Johnson and Jackson [1987. Frictional-collisional constitutive relations for granular materials, with application to plane shearing. Journal of Fluid Mechanics 176, 67-93], Syamlal et al. [1993. Mfix documentation: volume I, theory guide. Technical Report DOE/METC-9411004, NTIS/DE9400087, National Technical Information Service, Springfield, VA], and Srivastava and Sundaresan [2003. Analysis of a frictional-kinetic model for gas-particle flow. Powder Technology 129, 72-85] are compared with the kinetic theory of the granular flow and with experimental data both in a bubbling fluidized bed with a central jet and in a bubbling fluidized bed with a porous distributor. The predicted evolution of the bubble diameter along the height of the fluidized beds is examined, the shapes of the bubbles predicted by the models are compared and the evolution in time of the bubbles is shown. In the case of the bed with a central jet, the bubble detachment time is also calculated. The results show that the introduction of a frictional stress model improves the prediction of the bubbles diameter in a bubbling fluidized bed with a central jet and positively affects the bubbles diameter distribution in a uniformly fed bubbling fluidized bed. The high sensitivity of the model to the value of the particulate phase fraction at which frictional stresses start to be accounted for is pointed out through a sensitivity analysis performed on the Srivastava and Sundaresan [2003. Analysis of a frictional-kinetic model for gas-particle flow. Powder Technology 129, 72-85] model.     

Simulation of particles and gas flow behavior in a riser using a filtered two-fluid model

Flow behavior of gas and particles is predicted by a filtered two-fluid model by taking into the effect of particle clustering on the interphase momentum-transfer account. The filtered gas–solid two-fluid model is proposed on the basis of the kinetic theory of granular flow. The subgrid closures for the solid pressure and drag coefficient (Andrews et al., 2005) and the solid viscosity (Riber et al., 2009) are used in the filtered two-fluid model. The model predicts the heterogeneous particle flow structure, and the distributions of gas and particle velocities and turbulent intensities. Simulated solids concentration and mass fluxes are in agreement with experimental data. Predicted effective solid phase viscosity and pressure increase with the increase of model constant c_g and c_s. At the low concentration of particles, simulations indicate that the anisotropy is obvious in the riser. Simulations show the subgrid closures for viscosity of gas phase and solid phase led to a qualitative change in the simulation results.     

CFD study of hydrodynamics behavior of a vibrating fluidized bed using kinetic-frictional stress model of granular flow

The hydrodynamics of a vertically vibrating fluidized bed was studied using an Eulerian-Eulerian two-fluid model (TFM) incorporating the kinetic theory of granular flow and including the frictional stress effects. Influences of frictional stresses, vibration amplitudes and frequency on behavior of the particles were studied. In the case with vertical vibration, the numerical results showed three regions of solid concentration along the bed height: a low particle concentration region near the bottom of the bed, a high concentration region in the middle of the bed, and a transition region at top of the bed. The accuracy of results was found to be closely related to the inclusion of the frictional stresses. Ability of the two-fluid model for predicting the hydrodynamics of vibrating fluidized beds was discussed and confirmed.