Numerical simulation of gas–solid flow with two fluid model in a spouted-fluid bed

The flow characteristics in a spouted-fluid bed differ from those in spouted or fluidized beds because of the injection of the spouting gas and the introduction of a fluidizing gas. The flow behavior of gas–solid phases was predicted using the Eulerian–Eulerian two-fluid model (TFM) approach with kinetic theory for granular flow to obtain the flow patterns in spouted-fluid beds. The gas flux and gas incident angle have a significant influence on the porosity and particle concentration in gas–solid spouted-fluid beds. The fluidizing gas flux affects the flow behavior of particles in the fountain. In the spouted-fluid bed, the solids volume fraction is low in the spout and high in the annulus. However, the solids volume fraction is reduced near the wall.     

Numerical simulation of gas-solid flow with two fluid model in a spouted-fluid bed

The flow characteristics in a spouted-fluid bed differ from those in spouted or fluidized beds because of the injection of the spouting gas and the introduction of a fluidizing gas. The flow behavior of gas-solid phases was predicted using the Eulerian-Eulerian two-fluid model （TFM） approach with kinetic theory for granular flow to obtain the flow patterns in spouted-fluid beds. The gas flux and gas incident angle have a significant influence on the porosity and particle concentration in gas-solid spouted-fluid beds. The fluidizing gas flux affects the flow behavior of particles in the fountain. In the spouted-fluid bed, the solids volume fraction is low in the spout and high in the annulus. However, the solids volume fraction is reduced near the wall.     

The influence of the drag force due to the interstitial gas on granular flows down a chute

Fully-developed steady flow of granular material down an inclined chute has been a subject of much research interest, but the effect of the interstitial gas has usually been ignored. In this paper, new expressions for the drag force and energy dissipation caused by the interstitial gas (ignoring the turbulent fluctuations of the gas phase) are derived and used to modify the governing equations derived from the kinetic theory approach for granular–gas mixture flows, where particles are relatively massive so that velocity fluctuations are caused by collisions rather than the gas flow. This new model is applied to fully-developed, steady mixture flows down an inclined chute and the results are compared with other simulations. Our results show that the effect of the interstitial gas plays a significant role in modifying the characteristics of fully developed flow. Although the effect of the interstitial gas is less pronounced for large particles than small ones, the flowfields with large particles are still very different from granular flows which do not incorporate any interactions with the interstitial gas.     

变速运动颗粒所受非恒定作用力分析

本文利用典型函数试验法对变速运动颗粒所受非恒定作用力（Ｂａｓｓｅｔ力和附加质量力）进行了深入分析和比较，结果表明：Ｂａｓｓｅｔ力对重质颗粒运动的影响很大，不能忽略；对于轻质颗粒，则以附加质量力的作用为主，Ｂａｓｓｅｔ力可忽略不计．     

Dynamic coupling of fluid and structural mechanics for simulating particle motion and interaction in high speed compressible gas particle laden flow

In this work, structural finite element analyses of particles moving and interacting within high speed compressible flow are directly coupled to computational fluid dynamics and heat transfer analyses to provide more detailed and improved simulations of particle laden flow under these operating conditions. For a given solid material model, stresses and displacements throughout the solid body are determined with the particle–particle contact following an element to element local spring force model and local fluid induced forces directly calculated from the finite volume flow solution. Plasticity and particle deformation common in such a flow regime can be incorporated in a more rigorous manner than typical discrete element models where structural conditions are not directly modeled. Using the developed techniques, simulations of normal collisions between two 1 mm radius particles with initial particle velocities of 50–150 m/s are conducted with different levels of pressure driven gas flow moving normal to the initial particle motion for elastic and elastic–plastic with strain hardening based solid material models. In this manner, the relationships between the collision velocity, the material behavior models, and the fluid flow and the particle motion and deformation can be investigated. The elastic–plastic material behavior results in post collision velocities 16–50% of their pre-collision values while the elastic-based particle collisions nearly regained their initial velocity upon rebound. The elastic–plastic material models produce contact forces less than half of those for elastic collisions, longer contact times, and greater particle deformation. Fluid flow forces affect the particle motion even at high collision speeds regardless of the solid material behavior model. With the elastic models, the collision force varied little with the strength of the gas flow driver. For the elastic–plastic models, the larger particle deformation and the resulting increasingly asymmetric loading lead to growing differences in the collision force magnitudes and directions as the gas flow strength increased. The coupled finite volume flow and finite element structural analyses provide a capability to capture the interdependencies between the interaction of the particles, the particle deformation, the fluid flow and the particle motion.     

Coupling between countercurrent gas and solid flows in a moving granular bed: The role of shear bands at the walls

We extended the standard approach to countercurrent gas–solid flow in vertical vessels by explicitly coupling the gas flow and the rheology of the moving bed of granular solids, modelled as a continuum, pseudo-fluid. The method aims at quantitatively accounting for the presence of shear in the granular material that induces changes in local porosity, affecting the gas flow pattern through the solids. Results are presented for the vertical channel configuration, discussing the gas maldistribution both through global and specific indexes, highlighting the effect of the relevant parameters such as solids and gas flowrate, channel width, and wall friction. Non-uniform gas flow distribution resulting from uneven bed porosity is also discussed in terms of gas residence time distribution (RTD). The theoretical RTD in a vessel of constant porosity and Literature data obtained in actual moving beds are qualitatively compared to our results, supporting the relevance under given circumstances of the coupling between gas and solids flow.     

Investigation of the acceleration of aluminum particles behind a shock wave using instantaneous Laser Doppler Velocimetry

The acceleration of aluminum particles with a 5μm diameter in the flow field behind an incident shock wave was investigated experimentally in a 10-m long and 70 mm inner diameter shock tube. By means of instantaneous Laser Doppler Velocimetry (LDV) the velocity of the particles was observed directly. The light scattered by the moving particles is Doppler shifted and sent to the laser Doppler velocimeter. The velocimeter essentially consists of a phase-stabilized Michelson interferometer used as a sensitive spectrometer. An electro-optical circuit ensures the phase stabilization that results in a voltage signal independent of the scattered light intensity and proportional to the mean velocity of the particles at the measurement point. Because of the very short response time (1μs) of the LDV system used here, the latter gives a continuous real-time signal of the particle acceleration. To avoid particle oxidation the particles were accelerated by a high-speed nitrogen gas flow. From the measured velocity the dimensionless drag coefficient was calculated. The drag coefficient is related to the fluid dynamic force exerted by the gas on the particles. The experimental data were compared to theoretical models from the literature. A significant deviation between the model and the experimental data was observed. This deviation is supposed to be induced by the shock wave, which hits the particles and breaks them into pieces of a smaller diameter. Further experiments will be carried out in the future to check the size distribution of the particles after the shock has gone past them.      

Flow regime diagrams for gas-solid fluidization and upward transport

Flow regime maps are presented for gas-solids fluidized beds and gas-solids upward transport lines. For conventional gas solids fluidization, the flow regimes include the fixed bed, bubbling fluidization, slugging fluidization and turbulent fluidization. For gas solids vertical transport operation, solids flux must be incorporated in the flow regime diagrams. The flow regimes then include dilute-phase transport, fast fluidization or turbulent flow, slug/bubbly flow, bubble-free dense-phase flow and packed bed flow. In practical circulating fluidized beds and transport risers, operation below the fast fluidization regime is commonly impossible due to equipment limitations. Practical flow regime maps are proposed with the flow regimes, including homogeneous dilute-phase flow, core-annular dilute-phase flow (where there are appreciable lateral gradients but small axial gradients) and fast fluidization (where there are both lateral and axial gradients). The boundary between fast fluidization and dilute-phase pneumatic transport is set by the type A choking velocity, at which the uniform suspension collapses and particles start to accumulate in the bottom region of the transport line, while the mechanism of transition from fast fluidization to dense-phase flow depends on the column and particle diameters.     

气固两相流动的湍流脉动扩散数学模型及其应用

本文提出了气固两相流动的湍流扩展数学模型，本模型用k-ε双方程模型求解气相湍流场，并根据气流脉动的频谱、能谱曲线提出了随机富工级数来模拟气相脉动速度，用拉氏方法描述颗粒的运动，故称为脉动频谱随机颗粒轨道模型。本文还给出了本模型在气固多相射流和流化床内应用的实例。     

气固两相流介尺度LBM-DEM模型

LBM-DEM耦合方法通常是指一种颗粒流体系统直接数值模拟算法,即是一种不引入经验曳力模型的计算方法,颗粒尺寸通常比计算网格的长度大一个量级,颗粒的受力通过表面的粘性力与压力积分获得,其优点是能描述每个颗粒周围的详细流场,产生详细的颗粒-流体相互作用的动力学信息,可以探索颗粒流体界面的流动、传递和反应的详细信息及两相相互作用的本构关系,但其缺点是计算量巨大,无法应用于真实流化床过程模拟。本文针对气固流化床中的流体以及固体颗粒间的多相流体力学行为,建立了一种稠密气固两相流的介尺度LBMDEM模型,即LBM-DEM耦合的离散颗粒模型,实现在颗粒尺度上流化床的快速离散模拟。该耦合模型采用格子玻尔兹曼方法(LBM)描述气相的流动和传递行为,离散单元法(DEM)用于描述颗粒相的运动,并利用能量最小多尺度(EMMS)曳力解决气固耦合不成熟问题,以提高其模拟精度。通过经典快速流态化的模拟,验证了介尺度LBM-DEM耦合模型的有效性。模拟结果表明介尺度LBM-DEM模型是一种探索实验室规模气固系统的有力手段。     

Flow computation with lattice gases

Cellular automata offer a simple way to simulate flow in complex geometries. The algorithm computes flow by tracking the paths of individual particles of a simple lattice gas. An advantage of this approach is that many of the traditional problems of conventional numerical techniques in dealing with complex boundaries are avoided. In particular explicit front tracking of moving interfaces in two-phase flow is not necessary. On the other hand, some problems appear that are specific to lattice gas models. In this paper we propose solutions to these problems. Furthermore, we give an overview of the current status of lattice gas algorithms with respect to applications in fluid flow.     

CFD-DEM simulation of spouting of corn-shaped particles

Three dimensionally coupled computational fluid dynamics (CFD) and discrete element method (DEM) were used to investigate the flow of corn-shaped particles in a cylindrical spouted bed with a conical base. The particle motion was modeled by the DEM, and the gas motion by the k-? two-equation turbulent model. A two-way coupling numerical iterative scheme was used to incorporate the effects of gas–particle interactions in terms of momentum exchange. The corn-shaped particles were constructed by a multi-sphere method. Drag force, contact force, Saffman lift force, Magnus lift force, and gravitational force acting on each individual particle were considered in establishing the mathematical modeling. Calculations were carried out in a cylindrical spouted bed with an inside diameter of 200 mm, a height of 700 mm, and a conical base of 60°. Comparison of simulations with experiments showed the availability of the multi-sphere method in simulating spouting action with corn-shaped particles, but it depended strongly on the number and the arrangement of the spherical elements. Gas–solid flow patterns, pressure drop, particle velocity and particle concentration at various spouting gas velocity were discussed. The results showed that particle velocity reaches a maximum at the axis and then decreases gradually along the radial direction in the whole bed. Particle concentration increases along the radial direction in the spout region but decreases in the fountain region, while it is nearly constant in the annulus region. Increasing spouting gas velocity leads to larger pressure drop, remarkably increased speed of particle moving upward or downward, but decreased particle concentration.     

Experimental and numerical investigation of the shock-induced fluidization of a particles bed

An experimental study on unsteady two phase flow is conducted in a vertical shock tube. Shock Mach numbers range from 1.3 to 1.5 in 1 bar. The particles are initially positioned in horizontal beds of various thicknesses. Our research covers a large domain of void fraction from 1 (single particles) to 0.35 (compact beds). The experiments provide shadowgraph images for the recording of particle trajectories (effect of the gas on the particles) and side-wall pressures (action of the particles on the gas). A dense two phase flow model has been elaborated and numerically solved using a finite difference scheme with pseudoviscosity. The simulated shock-induced fluidization of a 2 cm thick bed of 1.5 mm diameter glass particles is compared to the experiment. Received 10 September 1996 / Accepted 4 January 1997     

Analysis of the flow in inhomogeneous particle beds using the spatially averaged two-fluid equations

The drag force term appearing in two-fluid models for fluid–particle flows is commonly closed by expressing it as a function of the local quantities, such as the local particle volume fraction, the local slip velocity between the particle and fluid phases, and the local mean-squared fluctuating velocity of the particles. The adequacy of such closures for inhomogeneous suspensions has been debated in the literature and some researchers have suggested the need for additional terms involving spatial gradients in these quantities. To test this proposition, simulations of flow in inhomogeneous steady beds of particles have been performed using the lattice-Boltzmann method. The particle beds consisted of disordered assemblies with a density profile on a scale much larger than the particle radius. Inhomogeneous beds with a controlled density profile were generated in three different ways, (i) by inhomogeneous stretching of the particle bed in one direction, (ii) by applying an inhomogeneous force to the particle phase during random motion of the particles, and (iii) by taking snapshots of a direct simulation of a traveling wave in a fluidization simulation. The global structure of the three beds was comparable, while assessment of the radial distribution functions showed that the three beds exhibited clearly different microscopic structures.     

Effects of grid size on predictions of bed expansion in bubbling fluidized beds of Geldart B particles: A generalized rule for a grid-independent solution of TFM simulations

Numerical simulations of gas–solid fluidized beds based on the kinetic theory of granular flow exhibit a significant dependence on domain discretization. Bubble formation, bubble size and shape all vary greatly with the discretization, and the use of an inappropriate scale resolution leads to inaccurate predictions of fluidization hydrodynamics. In this study, grid-independent solutions of the two fluid model were examined by comparing the bed expansions obtained from numerical simulations with experimental results and empirical predictions, based on bubbling fluidized beds of Geldart B particles. Grid independence was achieved with a grid resolution equal to 18 times the particle diameter. The simulation results were compared with previously published data for verification purposes. The results of this work should provide a guideline for choosing the appropriate grid size and thereby minimize the time and expense associated with large simulations.     

Insights in hydrodynamics of bubbling fluidized beds at elevated pressure by DEM–CFD approach

A numerical simulation was conducted to study the effect of pressure on bubble dynamics in a gas–solid fluidized bed. The gas flow was modeled using the continuum theory and the solid phase, by the discrete element method (DEM). To validate the simulation results, calculated local pressure fluctuations were compared with corresponding experimental data of 1-mm polyethylene particles. It was shown that the model successfully predicts the hydrodynamic features of the fluidized bed as observed in the experiments. Influence of pressure on bubble rise characteristics such as bubble rise path, bubble stability, average bubbles diameter and bubble velocity through the bed was investigated. The simulation results are in conformity with current hydrodynamic theories and concepts for fluidized beds at high pressures. The results show further that elevated pressure reduces bubble growth, velocity and stability and enhances bubble gyration through the bed, leading to change in bed flow structure.     

An improved model for two-phase flow through beds of coarse particles

A one-dimensional model for two-phase flow in packed particle beds is presented. Compared with earlier models, the improved model takes into account the effect of interfacial drag forces between liquid and gas, which are of considerable influence in beds of coarse particles. The model is based on the momentum equations for separated flow, which are closed by empirical relations for the wall shear stress and the interfacial drag. The model is applied to the situation of a one-component two-phase flow in an internally heated bed of uniform spherical particles. An increased dryout heat flux is predicted if liquid enters the bed through the bottom.     

Heat Transfer and Gas Flow through Feed Stream within Horizontal Pipe

In the feeding process, the feed stream forms a moving packed bed of particle from the feedstock in the feed channel. When the feeding is at emergency interruption especially in the case of flooding and uncontrollable discharge, the hot gases from reactor would infiltrate into the feed stream. The high heat penetration into feed stream would affect the feeder performance. In this paper, transient thermal response of feed stream within horizontal pipe is described mathematically with a gas flow and heat transfer model. Influences of varied factors on the thermal penetration into feed stream are examined for different conditions. The temperature of the packed-bed particles and the gas velocity distribution curves are obtained for the feeding service at interruption and at normal operating conditions. The numerical results show that the thermal penetration to the packed-bed particles by the seepage flow fluid is high only in the position near the gas entrance. The thermal penetration depth tends to increase with the seepage flow velocity and decrease with feeding rate. There is no appreciable thermal penetration in the feed stream when the feeding service is at normal running. The operating conditions and the porosity of solid bed have importance effects on the gas velocity and temperature field in the thermal penetration zone. A test system is set up to determine the transient thermal response experimentally for the packed bed of particles within a horizontal pipe. The model results are found to compare favorably with the experimental data.     

粗糙颗粒动理学及稠密气固两相流动的数值模拟

考虑颗粒碰撞过程中摩擦作用,给出了粗糙颗粒碰撞动力学.引入颗粒相拟总温来表征颗粒平动和转动脉动能量的特征.基于气体分子运动论,建立颗粒碰撞中平动和旋转共同作用的粗糙颗粒动理学,给出了颗粒相压力和黏度等输运参数计算模型.运用基于颗粒动理学的欧拉-欧拉气固两相流模型,数值模拟了流化床内气体颗粒两相流动特性,分析了颗粒旋转流动对颗粒碰撞能量交换和耗散的影响.模拟得到的流化床内径向颗粒浓度和提升管内颗粒轴向速度与他人实验结果相吻合.模拟结果表明随着颗粒浓度的增加,颗粒相压力和能量耗散逐渐增加,而颗粒拟总温先增加后下降.随着颗粒粗糙度系数的增加,床内平均颗粒相拟总温和能量耗散增加,表明颗粒旋转产生的摩擦将导致颗粒旋转脉动能量的改变,影响床内气体-颗粒两相宏观流动特性.