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。     

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.     

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).     

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.     

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。     

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.     

Numerical simulation on dense phase pneumatic conveying of pulverized coal in horizontal pipe at high pressure

A kinetic–frictional model, which treats the kinetic and frictional stresses in an additive manner, was incorporated into the two fluid model based on the kinetic theory of granular flow to simulate three dimensional flow behaviors of dense phase pneumatic conveying of pulverized coal in horizontal pipe. The kinetic stress was modeled by 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. Frictional–collisional constitutive relations for granular materials, with application to plane shearing. Journal of Fluid Mechanics 176, 67–93] and the modeled frictional shear viscosity model proposed by Syamlal et al. [1993. MFIX documentation and theory guide, DOE/METC94/1004, NTIS/DE94000087. Electronically available from http://www.mfix.org], which was modified to fit experimental data. For the solid concentration and gas phase Reynolds number was high, the gas phase and particle phase were all treated as turbulent flow. The experiment was carried out to validate the prediction results by three kinds of measurement methods. The predicted pressure gradients were in good agreement with experimental data. The predicted solid concentration distribution at cross section agreed well with electrical capacitance tomography (ECT) image, and the effects of superficial velocity on solid concentration distribution were discussed. The formation and motion process of slug flow was demonstrated, which is similar to the visualization photographs by high speed video camera.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

粗糙颗粒动理学及流化床内气固流动的数值模拟

基于气体分子动理学和颗粒动理学理论,考虑颗粒旋转流动对颗粒碰撞能量交换和耗散的影响,建立粗糙颗粒动理学。采用Chapman-Enskog颗粒速度分布函数,提出了颗粒相应力、热通量和颗粒碰撞能量耗散计算模型。采用欧拉-欧拉气固双相流模型,数值模拟鼓泡流化床内气体-颗粒两相流动特性。模拟结果得到了床内颗粒相速度和脉动速度分布,与Yuu等实验结果相吻合。分析不同的切向弹性恢复系数对颗粒相拟总温的变化规律,结果表明在低颗粒浓度时颗粒拟总温随切向弹性恢复系数而增加。     

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.     

Spout Shape Predictions in Spouted Beds

A theoretical study to predict spout‐annulus interface variation with bed level for different column geometries of spouted beds is proposed. A previous mathematical model (Krzywanski et al., 1989), developed for spout shape predictions in two‐dimensional spouted beds, is here proposed to be applied also for cylindrical, conical or cone‐based cylindrical columns. Its predictions depend on the average spout diameter and on the spout expansion angle. While there exists empirical equations available to estimate the first model parameter, the second one requires a rigorous stress analysis of the particles at the entrance of the bed. To avoid this difficulty, this work proposes a simple mathematical strategy to calculate the spout expansion angle. The reliability of this approach was checked by comparison with several experimental results obtained in cone‐based cylindrical (Lim et al., 1974; Wu et al., 1987; He et al., 1998) and rectangular (Zanoelo, 1994) spouted beds.     

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.     

喷动床内气固二相流体动力行为颗粒动理学

应用气固二相双流体模型数值模拟了喷动床内流体动力行为,模型中采用稠密固相动力-摩擦应力模型。模型中同时考虑了动理学理论和摩擦应力理论。应用贴体坐标系使得网格与喷动床的倒锥体边界符合良好。模拟得到的喷动床内颗粒速度和浓度实验数据吻合较好。     

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。