考虑颗粒旋转的颗粒动力学模拟提升管气固两相流动特性

流化床内颗粒旋转会影响颗粒相的流动特性,目前在流化床数值模拟中普遍采用的颗粒动力学模型却没有考虑颗粒的旋转效应。今运用基于颗粒动力学理论的欧拉-欧拉气固多相流模型,考虑颗粒旋转流动对颗粒碰撞能量交换和耗散的影响,提出了考虑颗粒旋转效应的颗粒动力学模型以及颗粒相守恒方程,数值模拟提升管内气体颗粒两相流动特性。计算结果表明提升管内中心区域为低浓度-高速的颗粒上升流动、壁面区域为高浓度-低速的颗粒下降流动。分析了颗粒粗糙度系数对颗粒相能量耗散、颗粒平动温度和黏度的影响。随着颗粒粗糙度系数的增加,颗粒碰撞能量耗散先逐渐增加后减小。颗粒平动温度和黏度的变化趋势是相反的,表明颗粒旋转产生摩擦将导致颗粒旋转脉动能量的改变,影响提升管内气体-颗粒两相宏观流动特性。     

快速流化床一维轴向稳态流动模型

本文对稳态操作的快速流化床气固两相流动进行了分析,表明颗粒在床内的加速运动对床层各项参数有显著影响。考虑了颗粒加速作用以及由于颗粒聚集使气固两相相互作用力减小的事实后,可采用一维轴向稳态流动模型获得截面平均颗粒速度、空隙率以及曳力系数等参数及其轴向分布规律。模型预测与实验直接测定结果吻合很好。     

DSMC-LES方法数值模拟鼓泡流化床内气泡和颗粒流动行为

基于稠密气体分子动力学和气固两相流体动力学,建立流化床稠密气固两相离散颗粒运动-碰撞解耦模型,采用直接模拟蒙特卡罗方法(DSMC)模拟颗粒间的碰撞,采用考虑颗粒脉动流动对气相湍流流动影响的大涡模拟(LES)研究气相湍流,单颗粒运动满足牛顿第二定律,颗粒相和气相相间作用的双向耦合由牛顿第三定律确定.数值模拟流化床中颗粒流动以及气泡的生成、长大和破碎过程,获得颗粒轴向和径向速度的概率密度分布,及颗粒浓度分布.计算结果表明床内气泡的形成造成床内颗粒的循环,使得流化床内颗粒具有不同的轴向和径向脉动速度,颗粒分速度分布近似服从高斯分布.颗粒温度随颗粒浓度增加,达到最大值后,随颗粒浓度增大而下降.流化床颗粒浓度脉动主要是低频部分,高频分量较低,表明在流化床内颗粒浓度脉动频率低,能量高,颗粒浓度脉动主频率为0.4～1.0Hz,其值与Pain et al.获得的颗粒浓度脉动主频率基本吻合.     

流化床密相区颗粒扩散系数的CFD数值预测

应用离散颗粒模型直观获得颗粒运动情况,并从单个颗粒和气泡作用的角度分析颗粒运动和混合,证实气泡在床层中上升、在床层表面爆破以及气泡上升引起的乳化相下沉运动对颗粒混合起关键作用。应用基于颗粒动理学的双流体模型系统地对床宽分别为0.2、0.4、0.8 m的二维流化床在鼓泡区和湍动区的气固两相流动行为进行数值模拟。受离散颗粒模型启发,在双流体模型计算结果基础上,引入理想示踪粒子技术计算床内平均颗粒扩散系数。计算结果表明,颗粒横向扩散系数(D_x)总体上随流化风速增大而增大,但受床体尺寸影响较大;颗粒轴向扩散系数随流化风速增大而增大,受床体尺寸影响较弱。文献报道的密相区颗粒横向扩散系数分布在10^-4～10^-1 m²·s^-1数量级。本文提出的计算方法在数量级上与文献实验结果吻合,表明在大尺寸流化床且高流化风速下,颗粒横向扩散系数远大于小尺寸鼓泡流化床,为不同研究者实验结果的分歧提供了理论依据,也为预测大型流化床内颗粒扩散速率提供了放大策略。     

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。     

加压二维鼓泡床气固流动特性的数值模拟

采用欧拉双流体模型模拟了加压下二维鼓泡床内的气固流动特性,结果表明:在相同的表观气速下,加压使气泡体积分数增大,气泡相与乳化相间的分解越发明显,气固两相流动、混合剧烈;同时,床层中上部颗粒轴向速度的径向分布不均匀性增强:中心区颗粒速度增加,近壁区下降;随着操作压力变大,流化床膨胀高度增大,相应地,整体气含率增大,床层下部的颗粒浓度减小,而上部颗粒浓度增加,固含率在轴向上的分布更均匀;床层压力波动主要由两种成分构成:低频率高幅值和低幅值高频率成分.压力脉动强度随床高的增加呈现先增大后迅速减小的趋势;此外,加压下床层压力脉动强度变大,即床压波动更加剧烈;而且加压下颗粒拟温度增大,即颗粒速度脉动增强.     

倒置液固流化床内液固两相流动特性的数值模拟

基于欧拉-欧拉双流体模型,数值模拟倒置液固流化床内液固两相流动行为.数值模拟预测了床内颗粒的速度、浓度分布以及空隙率的变化.研究结果表明颗粒在床内分布呈现非均匀分布,床内形成局部高空隙率的流体团;随着床层高度增加,颗粒轴向速度增大:数值模拟床内空隙率与Renganthan等的实验结果相吻合.     

提升管内气固两相双组分颗粒流动的离散颗粒硬球模型的模拟

基于离散颗粒(DPM)硬球模型,数值模拟提升管内双组分颗粒气固两相湍流流动行为。应用Vreman的亚格子尺度（SGS）模型模拟气体湍流,建立考虑不同颗粒加速度效应的两颗粒碰撞最小时间计算模型。数值模拟预测了大颗粒和小颗粒的速度和浓度分布。研究结果表明小颗粒具有高的轴向速度和脉动速度,而大颗粒具有低的轴向速度和脉动速度。在床中心区域,小颗粒轴向速度分布出现3个峰值,对于大颗粒轴向速度仅出现两个峰值。在壁面区域大颗粒和小颗粒速度均出现两个峰值。沿床径向方向呈现床中心颗粒浓度低、壁面区域颗粒浓度高的环核流动结果。随着表观气速的增大,颗粒浓度沿径向和床高分布趋于均匀。在床中心区域模拟计算轴向颗粒速度、颗粒浓度和RMS速度与文献实验结果相吻合。在提升管内气体湍流对小颗粒流动具有一定的影响,颗粒间碰撞作用对颗粒相流动的影响大于气相湍流的影响。     

气固流化床中流动结构调控的研究进展

由于气固流化床内部气相与颗粒相的流动使得两相的传热传质效率变高，所以在工业中可以影响工业产品的收率，这使得床层中的气体与颗粒的流动备受学者们的关注。充分了解床层中气固两相的行为进而提高气固两相之间的接触，对气固流化床的更广泛应用、工业产能的提高、资源的更有效利用等方面具有重要的意义。介绍目前气固流化床内流动结构的研究进展，总结了气泡与颗粒一定的运动规律。此外，对研究颗粒流动的方法进行了讨论，并对它们的应用前景进行了展望。     

流动方向对循环流化床中颗粒混合行为的影响

对循环流化床提升管及下行床两种不同气固流动方式对颗粒混合行为的影响进行了较为深入的对比分析，发现在影响循环流化床颗粒混合的众多因素（如操作条件、床层直径、颗粒性质及床层内构件等）中，气固流动方向是影响颗粒轴向混合的最主要因素．当气固流动为顺重力场时（下行床），颗粒的轴向混合很小，流型接近平推流；当气固流动为逆重力场的提升管时，轴向颗粒混合将成倍增大，颗粒流动远离平推流流动．分析表明，下行床中颗粒混合仅为单一的弥散颗粒扩散，而提升管中则存在着两种颗粒混合机制：弥散颗粒扩散及颗粒团扩散．弥散颗粒的扩散基本以平推流的形式通过循环流化床，提升管中大量的颗粒轴向返混归因于颗粒团的严重返混并由此形成了提升管中颗粒停留时间的双峰分布．     

Hydrodynamic modeling of particle rotation for segregation in bubbling gas-fluidized beds

A multi-fluid Eulerian model has been improved by incorporating particle rotation using kinetic theory for rapid granular flow of slightly frictional spheres. A simplified model was implemented without changing the current kinetic theory framework by introducing an effective coefficient of restitution to account for additional energy dissipation due to frictional collisions. Simulations without and with particle rotation were performed to study the bubble dynamics and bed expansion in a monodispersed bubbling gas-fluidized bed and the segregation phenomena in a bidispersed bubbling gas-fluidized bed. Results were compared between simulations without and with particle rotation and with corresponding experimental results. It was found that the multi-fluid model with particle rotation better captures the bubble dynamics and time-averaged bed behavior. The model predictions of segregation percentages agreed with experimental data in the fluidization regime where kinetic theory is valid to describe segregation and mixing.     

Numerical simulation of bubble and particles motions in a bubbling fluidized bed using direct simulation Monte-Carlo method

Flow behavior of bubbles and particles in a bubbling fluidized bed were numerically computed using Euler-Lagrange approach. Particle collision was simulated by means of the direct simulation Monte-Carlo (DSMC) method and hard-sphere model. The computed velocities and fluctuations of particles were in agreement with experimental data of Yuu et al. [S. Yuu, H. Nishikawa, T. Umekage, Numerical simulation of air and particle motions in group-B particle turbulent fluidized bed, Powder Technol. 118 (2001) 32-44]. The distributions of velocity, concentration, granular temperature and collision frequency of particles in a bubbling fluidized bed were analyzed. The wavelet multi-resolution analysis was used to investigate flow behavior of bubbles and particles. The bubble frequency of random-like bubble fluctuation was determined from the wavelet multi-resolution analysis over a time-frequency plane.     

Hydrodynamics of gas-solid flow around immersed tubes in bubbling fluidized beds

A numerical study was conducted based on the gas-solid two-fluid model using the body-fitted coordinate system to analyze the behavior of particles and bubbles flow in bubbling fluidized beds without and with immersed tubes. The kinetic theory of granular flow was implemented in the model. The images of simulated instantaneous particle concentration and velocity gave the process of the formation, coalescence and eruption of bubbles. The effects of the tube pitch and superficial gas velocity on the fluidization in a bubbling fluidized bed were investigated. Calculated bubble frequencies without and with immersed tubes were in agreement with previous experimental and simulation findings. The wavelet multi-resolution analysis was used to analyze the simulated data of instantaneous particle concentration. From the random-like particle concentration fluctuations, the fluctuating components due to particle flow and bubble motion can be extracted based on the wavelet multi-resolution analysis over a time-frequency plane.     

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.     

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.     

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.     

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.     

A second-order moment method of dense gas-solid flow for bubbling fluidization

A gas-solid two-fluid model with the second-order moment method is presented to close the set of equations applied to fluidization. With the kinetic theory of granular flow, transport equations for the velocity moments are derived for the particle phase. Closure equations for the third-order moments of velocity and for the fluid-particle velocity correlation are presented. The former is based on a modified model with the contribution of the increase of the binary collision probability, and the latter uses an algebraic model proposed by Koch and Sangani [1999. Particle pressure and marginal stability limits for a homogeneous monodisperse gas-fluidized bed: kinetic theory and numerical simulations. Journal of Fluid Mechanics 400, 229-263]. Boundary conditions for the set of equations describing flow of particles proposed by Strumendo and Canu [2002. Method of moments for the dilute granular flow of inelastic spheres. Physical Review E 66, 041304/1-041304/20] are modified with the consideration of the momentum exchange by collisions between the wall and particles. Flow behavior of gas and particles is performed by means of gas-solid two-fluid model with the second-order moment model of particles in the bubbling fluidized bed. The distributions of velocity and moments of particles are predicted in the bubbling fluidized bed. Predictions are compared with experimental data measured by Muller et al. [2008. Granular temperature: comparison of magnetic resonance measurements with discrete element model simulations. Powder Technology 184, 241-253] and Yuu et al. [2000. Numerical simulation of air and particle motions in bubbling fluidized bed of small particles. Powder Technology 110, 158-168]. in the bubbling fluidized beds. The simulated second-order moment in the vertical direction is 1.1-2.5 [Muller, C.R., Holland, D.J., Sedeman, A.J., Scott, S.A., Dennis, J.S., Gladden, L.F., 2008. Granular temperature: comparison of magnetic resonance measurements with discrete element model simulations. Powder Technology 184, 241-253] and 1.1-4.0 [Yuu, S., Umekage, T., Johno, Y., 2000. Numerical simulation of air and particle motions in bubbling fluidized bed of small particles. Powder Technology 110, 158-168] times larger than that in the lateral direction because of higher velocity fluctuations for particles in the bubble fluidized bed. The bubblelike Reynolds normal stresses per unit bulk density used by Gidaspow et al. [2004. Hydrodynamics of fluidization using kinetic theory: an emerging paradigm 2002 Flour-Daniel lecture. Powder Technology 148, 123-141.] are computed from the simulated hydrodynamic velocities. The predictions are in agreement with experimental second-order moments measured by Muller et al. [2008. Granular temperature: comparison of magnetic resonance measurements with discrete element model simulations. Powder Technology 184, 241-253] and fluctuating velocity of particles measured by Yuu et al. [2000. Numerical simulation of air and particle motions in bubbling fluidized bed of small particles. Powder Technology 110, 158-168].