二维喷动床CFD-DEM模拟中曳力模型的影响

CFD-DEM已经广泛应用到喷动床的研究中,其模拟的准确性与用于处理颗粒-流体相互作用的曳力模型密切相关。为了探究不同曳力模型对喷动床CFD-DEM模拟结果的影响,基于非结构化网格的喷动床仿真,使用7个曳力模型分别对锥底喷动床内气固两相运动进行了数值模拟。综合床层压降、喷动高度和颗粒速度特性三个方面,Wen-Yu模型和Gibilaro模型预测的气固两相运动最剧烈,其次是Di Felice模型、Syamlal-O’Brien模型、Gidaspow模型和Huilin-Gidaspow模型,BVK模型预测的气固两相运动最平缓。由于模拟的气固两相体系属于密相体系,Huilin-Gidaspow模型的光滑过渡函数没有产生效果,所以Gidaspow模型和Huilin-Gidaspow模型在各个方面的预测结果基本一致。     

LBM-DEM四向耦合喷动床内介尺度模拟与分析

研究喷动床内颗粒的流动特性对于喷动床的设计和优化具有重要意义。基于气固两相流流动的LBM-DEM四向耦合模型,对单孔射流喷动床中颗粒的流动进行数值模拟。其中,气相采用修正的格子玻尔兹曼方法,颗粒相采用离散单元法,流固之间受力的双向耦合基于牛顿第三定律,颗粒与颗粒及颗粒与壁面的受力双向耦合采用软球模型。模拟得到了流化过程、颗粒与气体的速度分布、床层膨胀高度变化以及床宽对流化过程的影响。结果表明,喷动床内存在强烈的内循环,床宽增加导致颗粒运动能力减弱,射流速度增加使颗粒运动更加剧烈,床层膨胀高度增加。     

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.     

Application of CFD-DEM to the study of solid exchange in a dual-leg fluidized bed

The CFD-DEM model was developed to simulate solid exchange behavior between two half beds in a bench-scale two-dimensional dual-leg fluidized bed （DL-FB）. Power spectrum density （PSD） analysis was applied to obtain the dominant frequency （F） of the simulated differential particle number （APLR） between the two half beds. Effects of fluidization velocity （u） and bed material inventory （H） on the solid exchange behavior were studied using the CFD-DEM model. Not only snapshots of the simulated particle flow patterns using the OpenGL code but also the dominant frequency of APLR was similar to the experimental results. The simulation results show that higher fluidization velocity assists the exchange of more particles between the two half beds, but the dispersion of clusters on the bed surface into single particles decreases the cluster exchange frequency. A greater bed material inventory results in more intense cluster exchange. The cluster exchange frequency decreases with an increase of the bed material inventory.     

An extended unresolved CFD-DEM coupling method for simulation of fluid and non-spherical particles

This study develops an extended unresolved CFD-DEM coupling method for simulation of the fluid–solid flow with non-spherical particles. The limitation of fluid grid size is discussed, by simulating the settling of a cylinder in a Newtonian fluid based on the resolved and unresolved CFD-DEM coupling method. Then, the calculation of porosity and the fluid–particle relative velocity based on the particle shape enlargement method for simulation of non-spherical particles is proposed. The availability of the particle shape enlargement method for the simulation of non-spherical particles with different sphericity is discussed in this work, by comparing it with the results from the equivalent diameter enlargement method. The limitation of the equivalent diameter enlargement method for non-spherical particles is revealed from the simulation results. Several typical cases are employed to elaborate and verify the extended unresolved CFD-DEM method based on particle shape enlargement method, by presenting a good consistency with the experimental results. It proves that the extended unresolved CFD-DEM method is suitable for different CFD grid size ratios, and consolidates that it is a universal calculation method for CFD-DEM coupling simulation.     

Mixing and segregation of solid particles in a conical spouted bed: Effect of particle size and density

In this work, the mixing and segregation of binary mixtures of particles with different sizes and densities in a pseudo-2D spouted bed were studied experimentally. A binary mixture of solid particles including sand, gypsum, and polyurethane was used. To determine the particles mass fraction, and their mixing and segregation in the bed, an image-processing technique was developed and used. Important hydrodynamic parameters, such as the axial and radial segregation profiles of the solid particles, were measured. The effects of air velocity, particle size, and particle mass fraction were also evaluated. The flow regime in the spouted bed and the time required for reaching the equilibrium state of the solid particles were discussed. The results showed that the segregation of solid particles and the time to equilibrium both decreased when the air velocity increased to much larger than the minimum spouting velocity. The axial segregation increased with the diameter ratio of the particles. Upon completion of the test, coarse particles were concentrated mainly in the spout region, while fine particles were aggregated in the annulus region. Examination of the flow pattern in the spouted bed showed that the particles near the wall had longer flow paths, while those near the spout region had shorter flow paths.     

CFD-DEM investigation into flow characteristics in mixed pulsed fluidized bed under electrostatic effects

Static electricity has an important effect on gas–solid fluidized bed reactor fluidization performance. In the process of fluidization, electrostatic interaction between particles will obviously accelerate particle agglomerate formation, which consequently reduces the fluidization performance. Pulsed gas flow injection is an efficient method to enhance particle mixing, thereby weakening the occurrence of particle agglomerate. In this study, the two-dimensional hybrid pulsed fluidized bed is established. The flow characteristics are studied by using the coupled CFD-DEM numerical simulation model considering electrostatic effects. Influences of different pulsed frequencies and gas flow ratios on fluidized bed fluidization performance are investigated to obtain the optimal pulsed gas flow condition. Results show that in the presence of static electricity, the bubble generation position is lower, which is conducive to the particle flow. Pulsed gas flow can increase the particle velocity and improve the diffusion ability. The bubble generation time is different at different frequencies, and the frequency of 2.5 Hz has the most obvious effect on the flow characteristics. Different gas flow ratios have significant impacts on the particle movement amplitude. When the pulse gas flow accounts for a large ratio, the particle agglomerate tends to be larger. Therefore, in order to improve the fluidization effect, the ratio of pulsed gas flow to stable gas flow should be appropriately reduced to 0.5 or less.     

Minimum spouting velocity of flat-base spouted fluid bed

Experiments were performed on spout characteristics of a cylindrical spout-fluidized bed (I.D. = 10 cm) with different static heights and two materials (Al₂O₃ and high density polyethylene). Results of minimum spouting velocity obtained in this study were compared with reported correlations for both spouted and spout-fluidized beds. Considerable discrepancies were found between the values obtained using different model equations as well as with respect to experimental results. Based on the Mathur–Gishler correlation, a new correlation is proposed for calculating the minimum spouting velocity that introduces the ratio U/U_mf. It was found that the minimum spouting velocity decreases with increasing fluidizing gas velocity (U/U_mf). The pressure drop at the point of minimum spouting velocity is also correlated using this dimensionless group and is presented in this work. This investigation demonstrates that the use of correlations reported in the literature that focus primarily on conical bottom spouted beds are not applicable to flat-bottom spouted and spout-fluidized beds.     

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.     

Sand attrition in conical spouted beds

A study was carried out on the attrition in conical spouted beds using two sands with different properties for several bed heights and gas flow rates. Furthermore, the influence of a draft tube was studied at ambient and high temperatures. The main objective was to acquire knowledge on the attrition of sand beds for biomass pyrolysis in a pilot plant provided with a conical spouted bed reactor. A first-order kinetic equation is proposed for sand attrition in a conical spouted bed at room temperature. The predicted attrition rate constant depends exponentially on excess air velocity over that for minimum spouting. Both the draft tube and temperature increase contribute to reduction of attrition.     

Evaluation of coarse-grained CFD-DEM models with the validation of PEPT measurements

Computational Fluid Dynamics coupled with Discrete Element Method (CFD-DEM) is a commonly used numerical method to model gas-solid flow in fluidised beds and other multiphase systems. A significant limitation of CFD-DEM is the feasibility of the realistic simulation of large numbers of particles. Coarse-graining (CG) approaches, through which groups of multiple individual particles are represented by single, larger particles, can substantially reduce the total number of particles while maintaining similar system dynamics. As these three CG models have not previously been compared, there remains some debate, however, about the best practice in the application of CG in CFD-DEM simulations. In this paper, we evaluate the performance of three typical CG methods based on simulations of a bubbling fluidised bed. This is achieved through the use of a numerical validation framework, which makes full use of the high-resolution 3D positron emission particle tracking (PEPT) measurements to rigorously validate the outputs of CFD-DEM simulations conducted using various different coarse-graining models, and various different degrees of coarse-graining. The particle flow behaviours in terms of the particle occupancy field, velocity field, circulation time, and bubble size and velocity, are comprehensively analysed. It is shown that the CG simulation starts to fail when the size ratio between the bed chamber and the particles decreases to approximately 20. It is also observed, somewhat surprisingly, that the specific CG approach applied to interparticle contact parameters does not have a substantial effect on the simulation results for the bubbling bed simulations across a wide range of CG factors.     

A note on a boundary condition for spouted beds

The boundary condition, zero solids pressure at the top of a particle bed of maximum spoutable height, Hm, is shown to eliminate any resort to empiricism in the derivation of the fluid velocity in the annulus of a spouted bed for which both viscous and inertial effects are taken into account. The same boundary condition fails when applied to a spouted bed for which the bed height H 〈 Hm, especially when H 〈 0.8Hm.     

基于五阶WENO格式的燃气在药床中流动过程二维两相流研究

为研究内弹道初始阶段中心点火管燃气在膛内药床中的流动特性和传播规律,设计了可视化点传火实验平台,并进行了膛内假药床的点传火实验。基于加权本质无震荡(weighted essentially non-oscillatory, WENO)格式,构造了膛内轴对称二维内弹道两相流模型,对膛内燃气在假药床中的流动过程进行数值模拟。计算结果与可视化实验结果符合较好,全局压力平均误差为5.35%。表明数值计算准确地描述了燃气流动特性,完整地呈现了点火管燃气在假药床中的发展过程。在点火初始阶段,膛内压力径向效应明显,气相沿径向传播较快,药床药粒基本不会发生运动;随着燃气逐渐在膛内传播,膛内压力呈现径向一致、轴向梯度分布的特征,在压力梯度作用下,气相轴向速度开始占据主导,径向速度在膛底和中部区域减小为零,而固相速度随气相速度变化而变化;气相在到达弹底前,由于固相颗粒的壅塞,会提前出现速度反向波动现象。     

Hydrodynamic behaviour of Cellets™ (Ph.Eur./USP) in a spouted bed using image processing method

The hydrodynamic behaviour of the spouted bed in the pharmaceutical industries has been found to be less addressed. The present paper has focused on the hydrodynamic characteristics of a spouted bed where the Cellets™ (Ph.Eur./USP) is adopted as the bed material. Experiments are carried out with three different static bed heights (H₀) of shallow depth (2D_i ≤ H₀ < 3D_i) using two different particle sizes. The spouted bed employed with D_i/D₀ of 5 has given the experimental information on external spouting (U_es) by mapping the pressure drop, and fountain height (H_f) against the superficial gas velocity (U_g) is represented with the image contours, which show the intrinsic behaviour. All the 1000 μm and 700 μm particles have been found to exhibit symmetric and asymmetric spouting. With increasing U_g, the fully suspended particles are limited to a certain height in the freeboard region due to the gas-solid cross-flow, which implies the clusters have identified with the image processing method.     

Particle convective heat transfer near the wall in a supercritical water fluidized bed by single particle model coupled with CFD-DEM

Supercritical water fluidized bed (SCWFB) is a promising reactor to gasify biomass or coal. Its optimization design is closely related to wall-to-bed heat transfer, where particle convective heat transfer plays an important role. This paper evaluates the particle convective heat transfer coefficient (h_pc) at the wall in SCWFB using the single particle model. The critical parameters in the single particle model which is difficult to get experimentally are obtained by the computational fluid dynamics-discrete element method (CFD-DEM). The contact statistics related to particle-to-wall heat transfer, such as contact number and contact distance, are also presented. The results show that particle residence time (τ), as the key parameter to evaluate h_pc, is found to decrease with rising velocity, while increase with larger thermal boundary layer thickness. τ follows a gamma function initially adopted in the gas–solid fluidized bed, making it possible to evaluate h_pc in SCWFB by a simplified single particle model. The theoretical predicted h_pc tends to increase with rising thermal gradient thickness at a lower velocity (1.5 U_mf), while first decreases and then increases at higher velocity (1.75 and 2 U_mf). h_pc occupies 30%–57% of the overall wall-to-bed heat transfer coefficient for a particle diameter of 0.25 mm. The results are helpful to predict the overall wall-to-bed heat transfer coefficient in SCWFB combined with a reasonable fluid convective heat transfer model from a theoretical perspective.     

Influence of cycle time distribution on coating uniformity of particles in a spray fluidized bed by using CFD-DEM simulations

Cycle Time Distribution (CTD) plays a critical role for determining uniformity of particle coating in spray fluidized beds. However, the CTD is influenced by both geometrical structure and operating conditions of fluidized bed. In this study, a spray fluidized bed of coating process is simulated by a comprehensive Computational Fluid Dynamics-Discrete Element Model (CFD-DEM). To achieve different behaviors of CTD, some modifications are designed on a pseudo-2D internally circulating fluidized bed, which traditionally composes of a high-velocity upward bed and low-velocity downward bed. These modifications include making the air distributor slope and/or laying a baffle in the downward bed. First, the CTD and evolution of particle size distribution under different bed structures are compared. The CTD directly influences the coating uniformity. By making the particles flowing along a parallel direction in the downward bed through the geometrical modifications, the CTD becomes narrower and the coating uniformity is significantly improved. Second, under the optimized bed structure, the influence of operating conditions on the coating uniformity is studied. Properly increasing the fluidization gas velocity and the fluidization gas temperature and reducing the liquid spray rate can improve the coating uniformity.     

Experimental study and modeling of particle drying in a continuously-operated horizontal fluidized bed

Multistage fluidized beds are frequently used for product drying in industry. One advantage of these fluidized beds is that they can achieve a high throughput, when operated continuously. In this study, γ-Al₂O₃ particles were dried in a pilot-scale horizontal fluidized bed, without considering any comminution effects. For each experiment, the particle moisture content distribution and residence time distribution were determined. To take into account particle back mixing in our experiments, a one-dimensional population balance model that considers particle residence time was introduced into a fluidized bed-drying model. Experimental particle residence time distributions were reproduced using a tank-in-series model. Subsequently, the moisture content distribution was implemented, as a second dimension to the population balance in this model. These two-dimensional simulations were able to describe the experimental data, especially the spread in the residual particle moisture distribution, much more accurately than one-dimensional simulations. Using this novel two-dimensional model, the effects of different operating parameters (process gas temperature, solid feed rate, superficial air velocity) on the particle moisture content distribution were systematically studied.     

Particle shape effect on hydrodynamics and heat transfer in spouted bed: A CFD–DEM study

Spouted bed has drawn much attention due to its good heat and mass transfer efficiency in many chemical units. Investigating the flow patterns and heat and mass transfer inside a spouted bed can help optimize the spouting process. Therefore, in this study, the effects of particle shape on the hydrodynamics and heat transfer in a spouted bed are investigated. This is done by using a validated computational fluid dynamics–discrete element method (CFD–DEM) model, considering volume–equivalent spheres and oblate and prolate spheroids. The results are analysed in detail in terms of the flow pattern, microstructure, and heat transfer characteristics. The numerical results show that the prolate spheroids (Ar = 2.4) form the largest bubble from the beginning of the spouting process and rise the highest because the fluid drag forces can overcome the interlocking and particle–particle frictional forces. Compared with spherical particles, ellipsoidal spheroids have better mobility because of the stronger rotational kinetic energy resulting from the rough surfaces and nonuniform torques. In addition, the oblate spheroid system exhibits better heat transfer performance benefiting from the larger surface area, while prolate spheroids have poor heat transfer efficiency because of their orientation distribution. These findings can serve as a reference for optimizing the design and operation of complex spouted beds.     

Influences of the fluidizing and spouting pulsation on particle motion in spout-fluid beds

Effects of variable airflow on particle motion in spout-fluid beds are studied. Computational fluid dynamics using Navier–Stokes equations for the gas phase coupled with the discrete element method using Newton’s laws for the solid phase have been employed. Results indicate that increasing the fluidizing velocity diminishes dead zones and increases both the total height of the bed and the traversed distance by particles in the steady spout-fluid bed. In pulsed airflows, two configurations are investigated, namely, the spouted pulsed-fluidized bed with pulsed flow of the fluidizing velocity, and the pulsed-spouted fluidized bed with pulsed flow of the spouting velocity. The positive effect of pulsation on particle motion is shown and the effects of parameters, such as amplitude and frequency, on the dynamics of the bed are investigated in each configuration. An increase of up to 19% in traversed distance is found for the range studied, which suggests flow pulsation as a promising technique for increasing particle mixing in spout-fluid beds.     

填充床中气体渗流与化学波耦合问题的研究

研究等温和显著气固反应条件下填充床内反应气体浓度(物质)波推进与混合气体渗流的相互作用,指出化学反应对流动的影响包括两个方面,反应过程中混合气体质量的变化和密度的变化。混合气体流动将反过来影响反应进程。分析表明,按耦合模型和非耦合模型得到的速度场完全不同;按耦合模型,反应气体的浓度(物质)波阵面的推进对混合气体的流场有显著影响,因此按耦合模型计算的混合气体流场强烈地依赖于时间;忽略化学反应引起的混合气体密度变化的耦合模型,将导致一个质量消失的汇(或质量生成的源),因此将引起混合气体渗流速度的明显变化,并可能导致物理上不合理的结果;按耦合模型和非耦合模型计算的浓度场也有很大差别;当反应气体与惰性气体摩尔质量相差较大时,不能忽略反应过程中混合气体密度的变化;研究表明对于显著气固反应不能忽略化学反应与气体渗流的相互作用。