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.     

反应器结构对多段气化炉内颗粒分布的影响

针对多段气化炉(上部快速床、下部鼓泡床),采用MP-PIC(Multi-Phase Particle In Cell)方法模拟了多粒径煤粉颗粒的三维全循环流化过程,考察了鼓泡床与快速床床径比及鼓泡床和快速床之间的过渡段高度对气化炉内流动特性的影响。结果表明,基本工况下,大颗粒主要存在于下部鼓泡床中,细颗粒主要存在于上部快速床内,但细颗粒会通过旋风分离器和回料管再次进入鼓泡床参与循环。进入旋风分离器的大部分为半径622 ?m以下的小颗粒,无1216 ?m以上的大颗粒。旋风分离器对小颗粒的分离效率为99.75%,分离效率良好。增大床径比(即减小快速床直径),快速床中气速增大,整个气化床更快达到稳定状态,被夹带到快速床中的颗粒增多,所夹带的颗粒粒径增大。过渡段高度存在一个适当值(炉高0.6~1.0 m),升高或降低过渡段高度,快速床中颗粒浓度均增大,颗粒通量均升高,旋风分离效率降低。     

鼓泡流化床内高灰煤气化过程的颗粒尺度特性研究

基于多相流体质点网格方法(MP-PIC)对高灰煤在三维鼓泡流化床气化过程进行了数值模拟研究。在欧拉-拉格朗日框架下将气相和固相分别视作连续介质和离散相处理。首先,将模拟得到的出口处气体组分结果与实验数据进行对比,实验数据与模拟结果具有良好的一致性。其次,研究了煤颗粒在气化炉内的温度、传热系数、速度和停留时间,从颗粒尺度揭示了鼓泡流化床气化炉内的颗粒分布特性和气固流动特征。结果表明:在气化炉入口附近煤颗粒与床层温差最大,传热系数最大;由于流化床内强非线性的气固流动,床中煤温度和传热系数的空间分布不均匀;煤颗粒和床料的瞬时速度具有稳定的波动幅度,其中垂直方向速度波动最明显,且煤颗粒的瞬时速度比床料的瞬时速度略大;由于颗粒间的剧烈碰撞,延长了煤颗粒停留时间。此外,对鼓泡流化床中煤气化过程颗粒尺度的研究,有助于深入了解固体颗粒的流动行为以及气固相相互作用特性,对鼓泡流化床反应器的设计优化具有重要意义。     

Simulation and experiment of segregating/mixing of rice husk–sand mixture in a bubbling fluidized bed

The fluidization behavior of rice husk–sand mixture in the gas bubbling fluidized bed is experimentally and theoretically studied. The relevancy of the pressure drop profile of rice husk–sand mixture to the definition of its minimum fluidization velocity is discussed, and the minimum fluidization velocity of rice husk–sand binary mixture is determined. The distributions of mass fraction of rice husk particles along the bed height are measured, and the profiles of the mean particle diameter of mixture are determined. A multi-fluid gas–solid flow model is presented where equations are derived from the kinetic theory of granular flow. Separate transport equations are constructed for each of the particle classes, allowing for the interaction between particle classes, as well as the momentum and energy are exchanged between the respective classes and the carrier gas. The distributions of the mass fraction of rice husk particles and the mean particle diameter of binary mixture are predicted. The numerical results are analyzed, and compared with experimental data.     

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].     

DEM-LES of coal combustion in a bubbling fluidized bed. Part I: gas-particle turbulent flow structure

The gas and particle motions in a bubbling fluidized bed both with and without chemical reactions are numerically simulated. The solid phase is modelled as Discrete Element Method (DEM) and the gas phase is modelled as 2-D Navier-Stokes equations for 2-phase flow with fluid turbulence calculated by large Eddy simulation (LES), in which the effect of particles on subgrid scale gas flow is taken into account. The gas/particle flow structure, the mean velocities and turbulent intensities can be predicted as a function of several operating parameters (particle size, bed temperature, and inlet gas velocity). The lower the inlet gas velocity, the higher the ratio of particle collision. The distributions of the particle anisotropic velocity show that the particles have no local equilibrium, and the distribution of gas kinetic energy corresponds to the distribution of gas-particle coupling moment in the fluidized bed. An intensive particle turbulent region exists near the wall, and the gas Reynolds stress is always much higher than the particle stress. The presence of the large reactive particles in the fluidized bed may affect significantly the gas and particle velocities and turbulent intensities. The effects of the bed temperature and inlet gas velocity on the gas particle flow structure, velocity, and turbulent intensity are also studied.     

不等粒径流化床的软球模拟

基于颗粒轨道模型,提出了粒径分别服从均匀分布与正态分布的软球方法,其中流体运动用Navier-Stokes方程描述,颗粒运动服从牛顿第二定理.模拟了不等粒径流化床中的气泡和节涌现象,并分别研究了表观气速、颗粒刚度系数、粒径分布不同时,固相颗粒的速度分布规律.其研究结果表明：分布板结构和表观气速对气泡行为有一定影响,随表观气速的增加,气泡形成、上升、破裂的速度加快;并且刚度系数越大,颗粒轴向速度随时间衰减越快;宽粒径分布的颗粒轴向速度大于窄粒径分布的颗粒轴向速度.     

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.     

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.     

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.     

气固流化床内鼓泡行为的离散颗粒数值模拟

采用离散颗粒数值模型探讨了气固流化床内多个气泡的运动规律. 数值计算考虑了颗粒与气体的相互作用以及颗粒间的相互作用,颗粒与气体的相互作用采用Gidaspow阻力修正公式,颗粒间的相互作用则采用硬球碰撞模式描述. 给出了一种在二维非结构网格下精确计算颗粒体积分数及两相全隐耦合求解颗粒速度的方法,同时,在硬球模型中对颗粒碰撞事件采用散列表的处理方法,大大提高了计算效率. 数值计算结果表明,由于多个气泡的相互作用而导致气泡的横向运动显著,气泡运动轨迹与气泡形状依赖于流化床内静压力的分布,气泡总是选择压力小、压差梯度大的路径上升,这一现象与气液分离流中气泡的运动规律类似.     

Numerical simulation of gas-particle flow with a second-order moment method in bubbling fluidized beds

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 beds. Predictions are compared with experimental data measured by Jung et al. (2005) in a bubbling fluidized bed and Patil et al. (2005) experiments in a bubbling fluidized bed with a jet. The simulated second-order moment in the vertical direction is on average 1.5-2.3 times larger than that in the lateral direction in the bubbling fluidized bed (Jung et al., 2005). For a bubbling fluidized bed with a jet, the ratio of normal second-order moment in the vertical direction to in the lateral direction is in the range of 0.5-2.5 (Patil et al., 2005). The bubblelike Reynolds normal stresses per unit bulk density used by Gidaspow et al. (2002) are computed from the simulated hydrodynamic velocities. The simulated bubblelike Reynolds normal stresses in the vertical direction is on average 4.5-6.0 times larger than that in the lateral direction in the bubbling fluidized bed (Jung et al., 2005). The predictions are in agreement with experimental second-order moments measured by Jung et al. (2005) and porosity measured by Patil et al. (2005).     

管式布风装置对流化床焚烧炉内流化特性的影响

数值模拟了管式布风装置对流化床内气体和颗粒流动特性的影响,获得了床内气体和颗粒瞬时和时均速度及颗粒体积份额分布. 计算结果表明,床内颗粒宏观流动呈现床中心区域为上升流动、壁面区域为下降流动的内循环流动. 分析了风管小孔风速和颗粒直径对床内流化的影响. 计算结果表明,保证床内颗粒和气体良好流化和混合特性的最佳布风管相对距离应在1.5~1.75之间.     

Numerical simulation of flow behavior of agglomerates in gas–cohesive particles fluidized beds using agglomerates-based approach

Flow behavior of gas and agglomerates is numerically investigated in fluidized beds using a transient two-fluid model. It is assumed that the particles move as agglomerates rather than single particles in the gas–cohesive particles fluidized beds. The present model is coupled a modified kinetic theory model proposed by Arastoopour (2001) with an agglomerate-based approach (ABA). The interaction between gas and agglomerates is considered. The agglomerates properties are estimated from the ABA. Predictions are compared with experimental data measured by Jiradilok (2005) in a bubbling fluidized bed and Li and Tong (2004) in a circulating fluidized bed. The distributions of velocity, concentration and diameter of agglomerates, and pressure drop are numerically obtained. The influences of the contact bonding energy on the distributions of velocity and concentration of agglomerates are analyzed.     

基于EMMS介尺度模型的双分散鼓泡流化床的模拟

双分散气固鼓泡流化床中颗粒通常具有不同粒径或密度,导致产生颗粒偏析等现象,影响传递和反应行为。颗粒分离和混合与气泡运动密不可分,其中相间曳力起关键作用。最近Ahmad等提出了一种基于气泡结构的双分散介尺度曳力模型,能成功预测双分散鼓泡流化床的床层膨胀系数。本研究耦合该曳力模型与连续介质方法,模拟了两种不同的双分散鼓泡流化床,通过分析不同流化状态下的气泡运动、颗粒浓度比的轴向分布等参数,进一步检验模型的适用性。研究表明,当双分散颗粒处于完全流化状态时,耦合双分散介尺度曳力模型可合理预测不同颗粒的分离现象;而其处于过渡流化状态时,新曳力模型和传统模型均无法获得合理结果,此时调节固固曳力可改进模拟结果。     

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。     

Geldart-B类颗粒在气固流化床中的床层膨胀与流型转变

采用理论推导和经验公式相结合方法,建立了Geldart-B类颗粒在流化床中流化过程的床层膨胀比(R)的通式,并在全取值范围内构建了床层膨胀比的收敛迭代公式。采用不同颗粒的流化实验数据对上述通式(模型)进行了验证,结果表明该模型很好地预测了床层膨胀比。进一步讨论了床层膨胀比与鼓泡流化流型变化之间的关系,给出了临界膨胀比的取值规律。有关床层膨胀比的研究结果一定程度上可有效改善流化床的监控,优化操作条件选取。     

Effective particle diameters for simulating fluidization of non‐spherical particles: CFD‐DEM models vs. MRI measurements

Computational fluid dynamics—discrete element method (CFD‐DEM) simulations were conducted and compared with magnetic resonance imaging (MRI) measurements (Boyce, Rice, and Ozel et al., Phys Rev Fluids. 2016;1(7):074201) of gas and particle motion in a three‐dimensional cylindrical bubbling fluidized bed. Experimental particles had a kidney‐bean‐like shape, while particles were simulated as being spherical; to account for non‐sphericity, “effective” diameters were introduced to calculate drag and void fraction, such that the void fraction at minimum fluidization (ε_mf) and the minimum fluidization velocity (U_mf) in the simulations matched experimental values. With the use of effective diameters, similar bubbling patterns were seen in experiments and simulations, and the simulation predictions matched measurements of average gas and particle velocity in bubbling and emulsion regions low in the bed. Simulations which did not employ effective diameters were found to produce vastly different bubbling patterns when different drag laws were used. Both MRI results and CFD‐DEM simulations agreed with classic analytical theory for gas flow and bubble motion in bubbling fluidized beds. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2555–2568, 2017     

Numerical simulation of particle motion in vibrated fluidized beds

Flow behavior of particles is simulated in a two-dimensional vibrated bubbling fluidized bed. The motion of particles is simulated by discrete element method (DEM). The distributions of velocity and concentration of particles are analyzed at the different amplitudes and frequencies of vibration. In the case with vertical vibration, the bed consists of three different regimes along bed height: a low particle concentration regime with a vibration gap near the bottom, a high concentration regime in the middle of the bed and a transition regime at the bed surface. The gas pressure losses are reduced with the vibration. The phase delay time between the time at the maximum pressure loss and the time at the maximum displacement of vibrated distributor in one cycle decreases with the increase of amplitudes. The contacting interaction between the vibrated distributor and particles increases as the distributor moves up, and trends to zero as the distributor moves down with the increase of frequency of vibration. The vibrating energy is transferred by collisions between the vibrated distributor and particles at the period of acceleration of the distributor.     

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。