Numerical simulation of cohesive particle motion in vibrated fluidized bed

The effect of vibration on the cohesive particle motion in the bed was examined by using discrete element method(DEM). The bed of dried fine particles was treated as the objective of calculation. The van der Waals force was used as the cohesive force because the van der Waals force was considered to be the main cohesive force in this case. Since the actual calculation time was too long, the fine cohesive particle was difficult to be treated. So a relatively large particle (1.0 mm in diameter) was used in calculation and the van der Waals force was assumed that the ratio of gravity force to van der Waals force of particle used in this calculation was equal to that of a fine particle (6.0 μm in diameter), to express the effect of van der Waals force significantly. The calculation results were compared with that case of cohesionless particle.In the case with vibration, the cohesive particle motion in the bed is observed, though no fluidization state appears in the case without vibration, and there is no bubble in the bed even the fluidization state. In the case of cohesive particle, the collision energy between particle and wall caused by vibration gap propagates from the bottom to top of bed, and the particle moves vigorously at the top of bed in the case with vibration. As the vibration gap increases, the effect of vibration on the cohesive particle motion becomes larger, i.e., the low vibration frequency at the same vibration strength or the large vibration strength at the same vibration frequency promotes the fluidization of the bed.     

Modelling of pharmaceutical tablet swelling and dissolution using discrete element method

This work presents a novel use of the Discrete Element Method (DEM) combined with inter-particle mass transfer in order to simulate polymer swelling and dissolution. Each particle can absorb water and swell, pushing on its neighbours and causing an overall expansion. Once the disentanglement threshold is reached, the polymer dissolves and the particle reduces in size. This paper applies DEM to simulate the radial swelling and dissolution of cylindrical tablets. The method was validated against exact numerical solution of the same system to assess the accuracy of the DEM simulations for different DEM particle sizes. Parametric studies were done to assess the impact of physical parameters – namely the concentration-dependent diffusion coefficient of water through the polymer, the dissolution rate constant of the polymer and the disentanglement threshold of the polymer – on the radial expansion of the tablet. It was found that different settings of the concentration-dependent water diffusion coefficient function could produce similar radial expansion curves but with different internal concentration profiles. Increasing the dissolution rate constant or decreasing the disentanglement threshold of the polymer caused a reduction in the maximum radius of tablet. Lastly, ATR-FTIR spectroscopic imaging was used to obtain chemical images of a pure hydroxy-propyl methylcellulose (HPMC) tablet swelling and dissolving. The model was optimised to match both the HPMC tablet radius and the concentration profiles over time.     

Effects of blade rake angle and gap on particle mixing in a cylindrical mixer

Performance optimization of a mixer is an issue of great significance in many industrial technologies dealing with particulate materials. By means of Discrete Element Method (DEM), this work examines how the mixing performance of a cylindrical mixer is affected by the two design parameters: blade rake angle and blade gap at the vessel bottom, extending our previous work on particulate mixing. The flow and mixing performance are quantified using the following: velocity fields in vertical cylindrical sections, Lacey’s mixing index, inter-particle forces in vertical cylindrical sections through the particle bed and the applied torque on the blade. Simulation results show that the mixing rate is the fastest for a blade of 90° rake angle, but inter-particle forces are large. Conversely, the inter-particle forces are small for a blade of 135° rake angle, but the mixing rate is slow. The simulation results also indicate that the force applied on particles, velocity field and mixing are interrelated in that order.     

Particle dynamics simulations of a piston-based particle damper

A piston-based particle damper geometry is proposed and investigated using experiments and particle dynamics simulations. In particle damping, energy is dissipated through the inelastic collisions and friction between granular particles. Due to their temperature-independent performance, particle dampers are promising alternatives for use in extreme temperature conditions. Using the appropriate inter-particle force models, the simulations agree well with the experimental results. Using simulations, many parameters are investigated in this work for their effects on the damping performance, including material properties, particle size, device geometry, and excitation level. These results provide new understanding of particle damping and may help in the design of next generation particle dampers.     

Mixing of particles in rotary drums: A comparison of discrete element simulations with experimental results and penetration models for thermal processes

The transverse mixing of free flowing particles in horizontal rotating drums without inlets has been simulated by means of the Discrete Element Method (DEM) in two dimensions. In the simulations the drum diameter has been varied from 0.2 to 0.57 m, and the rotational frequency of the drum from 9.1 to 19.1 rpm, for drum loadings of 20% or 30%, and average particle diameters of 2.5 and 3.4 mm. The choice of operating parameters allows for comparison with experimental data from literature. Though simple models for inter-particle interactions have been implemented, the overall agreement is good. The results are presented and discussed in terms of mixing times and mixing numbers that means numbers of revolutions necessary for uniform mixing of the solids. In this way, comparison with penetration models, as typically applied to modelling of thermal processes, is possible. The limitations of such continuum models are pointed out, along with the potential of DEM to replace them, in the long term.     

On the optimal numerical time integration for DEM using Hertzian force models

The numerical accuracy of a selection of different time integration techniques used to solve particle motion is investigated using a normal collision employing the non-linear Hertzian contact force. The findings are compared against the linear force model where it has been found that the expected order of accuracy of higher-order integration schemes is not realised (Tuley et al., 2010). The proposed mechanism for this limitation has been cited as the errors in integration which occur across the force profile discontinuity. By investigating the characteristics of both the non-linear elastic and the non-linear damped Hertzian contact models, it has been found that higher orders of accuracy are recoverable and depends on the degree of the governing non-linear equation. The numerical errors of the linear and non-linear force models are however markedly different in character.     

Study of cluster formation in dense two-phase flow using a multi-lattice deterministic model

To simulate cluster formation in dense two-phase flow, a multi-lattice deterministic trajectory (MLDT) model is developed. The actual inter-particle collision and particle motion are treated by a Lagrangian trajectory model with three sets of lattices to reduce computation time. Initially, the MLDT model is used to simulate dense gas-particle flow in a vertical channel for validation with available simulated and experimental data. Using the MLDT model, effects of particle properties and flow parameters on cluster formation are studied. It is shown that cluster formation is enhanced by the reduction of particle restitution coefficient and increase of original particle volume fraction.     

Particle‐resolved direct numerical simulation of gas–solid dynamics in experimental fluidized beds

Particle‐resolved direct numerical simulations (PR‐DNS) of a simplified experimental shallow fluidized bed and a laboratory bubbling fluidized bed are performed by using immersed boundary method coupled with a soft‐sphere model. Detailed information on gas flow and individual particles’ motion are obtained and analyzed to study the gas–solid dynamics. For the shallow bed, the successful predictions of particle coherent oscillation and bed expansion and contraction indicate all scales of motion in the flow are well captured by the PD‐DNS. For the bubbling bed, the PR‐DNS predicted time averaged particle velocities show a better agreement with experimental measurements than those of the computational fluid dynamics coupled with discrete element models (CFD‐DEM), which further validates the predictive capability of the developed PR‐DNS. Analysis of the PR‐DNS drag force shows that the prevailing CFD‐DEM drag correlations underestimate the particle drag force in fluidized beds. The particle mobility effect on drag correlation needs further investigation. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1917–1932, 2016     

Discrete element method simulation of three-dimensional conical-base spouted beds

A discrete element method (DEM) simulation of three-dimensional conical-base spouted beds is presented. The overall height and diameter of the vessel are 0.5 and 0.15 m, respectively, and the nozzle diameter is 0.02 m. The inclined angle of the conical section varies from 0 to 60 degrees. The gas flow is described by the continuity and Navier-Stokes equations and solved by a finite difference method of second order accuracy in space and time. For gas-particle interaction, the Ergun equation (for void fraction smaller than 0.8) and the Wen-Yu model (for void fraction of 0.8 and above) are employed. A new method for treatment of the boundary condition for 3-D gas flow along the cone surface is proposed. This boundary condition satisfies both the continuity and momentum-balance requirements for the gas phase. Usefulness of the present simulation for studying gas flow pattern and particle motion in conical-base spouted beds is demonstrated. The effects of the inclined angle and draft tube on gas and particle flow in spouted beds are discussed.     

Effect of particle size on flow and mixing in a bladed granular mixer

A number of studies have modeled flow and mixing of granular materials using the discrete element method (DEM). In an attempt to reduce computational costs, many of these DEM studies model particles larger than the actual particle size without investigating the implications of this assumption. Using DEM, the influence of the modeled particle size on flow and mixing in a bladed granular mixer is studied. The predicted flow microdynamics, including mixing rates, are strongly dependent on the particle diameter. The effect of particle size on macroscopic advective flow also is significant, particularly for dilute flow regions. These results suggest that the influence of particle size needs to be taken into consideration when using larger particles in DEM mixing simulations. To guide scale‐up efforts, particle‐size‐based scaling relationships for several key flow measurements are presented. © 2014 American Institute of Chemical Engineers AIChE J, 61: 46–57, 2015     

Numerical modeling of particle fluidization behavior in a rotating fluidized bed

In this study, numerical modeling of particle fluidization behaviors in a rotating fluidized bed (RFB) was conducted. The proposed numerical model was based on a DEM (Discrete Element Method)-CFD (Computational Fluid Dynamics) coupling model. Fluid motion was calculated two-dimensionally by solving the local averaged basic equations. Particle motion was calculated two-dimensionally by the DEM. Calculation of fluid motion by the CFD and particle motion by the DEM were simultaneously conducted in the present model. Geldart group B particles (diameter and particle density were 0.5 mm and 918 kg/m³, respectively) were used for both calculation and experiment. First of all, visualization of particle fluidization behaviors in a RFB was conducted. The calculated particle fluidization behaviors by our proposed numerical model, such as the formation, growth and eruption of bubble and particle circulation, showed good agreement with the actual fluidization behaviors, which were observed by a high-speed video camera. The estimated results of the minimum fluidization velocity (U_mf) and the bed pressure drop at fluidization condition (ΔP_f) by our proposed model and other available analytical models in literatures were also compared with the experimental results. It was found that our proposed model based on the DEM-CFD coupling model could predict the U_mf and ΔP_f with a high accuracy because our model precisely considered the local downward gravitational effect, while the other analytical models overpredicted the ΔP_f due to ignoring the gravitational effect.     

Selection of an appropriate time integration scheme for the discrete element method (DEM)

With increasing computer power simulation methods addressing discrete problems in a broad range of scientific fields become more and more available. The discrete element method is one of these discontinuous approaches used for modeling granular assemblies. Within this method the dynamics of a system of particles is modeled by tracking the motion of individual particles and their interaction with their adjacencies over time. For the interaction of particles, force models need to be specified. The resulting equations of motion are of coupled ordinary differential configuration, which are usually solved by explicit numerical schemes. In large-scale systems like avalanches, planetary rings, hoppers or chemical reactors vast numbers of particles need to be addressed. Therefore, integration schemes need to be accurate on the one hand, but also numerically efficient on the other hand. This numerical efficiency is characterized by the method's demand for memory and CPU-time. In this paper a number of mostly explicit numerical integration schemes are reviewed and applied to the benchmark problem of a particle impacting a fixed wall as investigated experimentally by Gorham and Kharaz [Gorham, D. A., & Kharaz, A. H. (2000). The measurement of particle rebound characteristics. Powder Technology, 112(3), 193–202]. The accurate modeling which includes the correct integration of the equations of motion is essential. In discrete simulation methods the accuracy of properties on the single particle level directly influence the global properties of the granular assembly like velocity distributions, porosities or flow rates, whereas their correct knowledge is often of key interest in engineering applications. The impact experiment is modeled with simple force displacement approaches which allow an analytical solution of the problem. Aspects discussed are the dependency of the step size on the accuracy of certain collision properties and the related computing time. The effect of a fixed time step is analyzed. Guidelines for the efficient selection of an integration scheme considering the additional computational cost by contact detection and force calculation are presented.     

DEM simulation of particle mixing in flat-bottom spout-fluid bed

The particle mixing mechanism affects the rate of the process and the achievable homogeneity. This paper presents a numerical study of the particle motion and mixing in flat-bottom spout-fluid bed. In the numerical model, the particle motion is modeled by discrete element method (DEM) and the gas motion is modeled by κ–? two-equation turbulent model. Validation with experiments is first carried out by comparing solid flow pattern and bed pressure drop at various gas velocities. Then, particle velocities, obtained from DEM simulations, are presented to reveal the mixing mechanisms. On the basic, the dependence of mixing index on the time and the effect of gas velocity on mixing and dead zone (stagnant solid) are discussed, respectively. The results indicate that the spouting gas is the driving force for the formation of particle circulation roll, resulting in the mixing. The convective mixing caused by the motion of circulation roll, shear mixing induced by the relative move of circulation rolls and diffusive mixing generated by random walk of particle among circulation rolls are three different mixing mechanisms in spout-fluid bed. The increase of spouting gas velocity promotes the convective and shear mixing. While increasing the fluidizing gas velocity improves significantly the convective mixing and but weakens the shear mixing. Both of them yield a reduction in the dead zone.     

Combination of the direct-forcing fictitious domain method and the sharp interface method for the three-dimensional dielectrophoresis of particles

In this paper, we combine the direct-forcing fictitious domain (DF/FD) method and the sharp interface method (SI) to resolve the problem of particle dielectrophoresis in three dimensions. The flow field is solved with the DF/FD method. The electric field governed by a Laplace equation with a jump coefficient across the particle surface is solved with the sharp interface (SI) method, and the dielectrophoretic force on particles is then calculated with the Maxwell stress tensor (MST) method. The main feature of our method is that both hydrodynamic and dielectrophoretic forces on particles are calculated with the interface-resolved methods instead of the point-particle model. The accuracy of the SI/MST method for the dielectrophoretic force without the consideration of the flow is validated via two problems: the electrostatic force on the particle in a non-uniform electric field, and the electrostatic force between two particles. The capability of the proposed DF/FD-SI/MST method is demonstrated with two numerical examples: the aggregation of particles due to the conventional dielectrophoretic force, and the motion of particles due to both conventional and traveling wave dielectrophoretic forces.     

A CFD-DEM study of the cluster behavior in riser and downer reactors

This paper presents a numerical study of the particle cluster behavior in a riser/downer reactor by means of combined computational fluid dynamics (CFD) and discrete element method (DEM), in which the motion of discrete particles is obtained by solving Newton's equations of motion and the flow of continuum gas by the Navier-Stokes equations. It is shown that the existence of particle clusters, unique to the solid flow behavior in such a reactor, can be predicted from this first principle approach. The results demonstrate that there are two types of clusters in a riser and downer: one is in the near wall region where the velocities of particles are low; the other is in the center region where the velocities of particles are high. While the extent of particle aggregation appears to be similar, the duration time for the first type in a downer is shorter than in a riser. Furthermore, it is demonstrated that the formation of clusters is affected by a range of variables related to operational conditions, particle properties, and bed properties and geometry. The increase of solid volume fraction, sliding and rolling friction between particles or between particles and wall, or damping coefficient can enhance the formation of clusters. The use of multi-sized particles can also promote the formation of clusters. But the increase of gas velocity or use of a wider bed can suppress the formation of clusters. The van der Waals force may enhance the formation of clusters when solid concentration is high but suppress the formation of clusters near the wall region when solid concentration is low.     

Comparison of DEM results and Lagrangian experimental data for the flow and mixing of granules in a rotating drum

This work assesses the accuracy of the discrete element method (DEM) for the simulation of solids mixing using non‐intrusive Lagrangian radioactive particle tracking data, and explains why it may provide physically sound results even when non‐real particle properties are used. The simulation results concern the size segregation of polydisperse granules in a rotating drum operated in rolling mode. Given that the DEM is sensitive to simulation parameters, the granule properties were measured experimentally or extracted from the literature. Several flow phenomena are investigated numerically and experimentally, including the particle residence time, the radial segregation, and the radial variation of the axial dispersion coefficient. An analysis of the DEM model is then presented, with an emphasis on the Young's modulus and friction coefficients. Finally, dimensionless motion equations and corresponding dimensionless numbers are derived to investigate the effect of simulation parameters on particle dynamics. © 2013 American Institute of Chemical Engineers AIChE J, 60: 60–75, 2014     

基于LBM-DEM的鼓泡床内气泡-颗粒动力学数值模拟

将修正后的格子Boltzmann方法（LBM）与离散单元法（DEM）相结合,建立LBM-DEM四向耦合模型对单口射流鼓泡床中气泡运动进行模拟。其中,流体相采用格子Boltzmann方法中经典的D2Q9模型,颗粒相求解采用离散单元软球模型,颗粒曳力求解采用Gidaspow模型,流固耦合基于牛顿第三定律。应用Fortran语言编程对上述模型进行求解,模拟得到了鼓泡床内气泡演化过程,并与相关实验进行对比,有效验证了当前模型的准确性。同时,分析了床层内颗粒速度、颗粒体积分数以及能量分布。结果表明：颗粒时均速度分布不仅能体现颗粒运动强弱,也可以反映气泡运动过程;床内空隙率与颗粒体积分数分布在预测床层膨胀高度上具有高度的一致性;初始堆积效应使得床内颗粒势能始终大于颗粒动能;随颗粒密度增加,势能增大,动能逐渐减小。     

Air-suspension coating in the food industry: Part II — micro-level process approach

A review of air-suspension particle coating concluded that, in order to speed product and process development, a phenomenological approach is necessary to develop generic guidelines for the selection of coating materials and process variables. This paper identifies 10 fundamental phenomena (micro-level processes) that occur during an air-suspension particle coating process: particle motion, atomisation, droplet-particle collision, droplet impact and adherence, droplet impact and spreading, infiltration, drying, film formation, layering and inter-particle agglomeration. Their relevance to the coating objectives is discussed and from these four are identified as key micro-level processes: drying, droplet impact and spreading, and stickiness which encompasses the two key micro-level processes of droplet impact and adherence and inter-particle agglomeration. It is believed that significant advances in particle coating research can be made through examination of these key micro-level processes.     

The influence of DEM simulation parameters on the particle behaviour in a V-mixer

Results are described of simulations based on the discrete element method (DEM) using a code developed by Tsuji, Kawaguchi, and Tanaka (Discrete particles simulation of 2-dimensional fluidized bed. Powder Technology 77 (1993) 79-87). The mechanical interactions between particles and also between particles and the walls in granular flows are modelled by linear springs, dash-pots and friction sliders. The simulation parameters are the restitution coefficient, normal stiffness, friction coefficient between particles and between particles and the walls, and two ratios which relate the normal and tangential stiffness and damping coefficients. Their influence on particle motion in a V-mixer has been evaluated and compared with radioactive tracer measurements of particle motion. A number of quantitative methods for comparing DEM and experimental data were developed. Given the simplified nature of the modelled interactions, the agreement between the predicted and measured data is remarkably close for restitution coefficient values of 0.7 and 0.9, internal friction coefficient values of 0.3 and 0.6 and wall friction coefficient values of 0 and 0.3. The internal and wall friction coefficients are important in determining the initiation of particle movement, while the value of the restitution coefficient has a larger influence on particles in a dynamic state. The simulation of the fully elastic case (coefficient of restitution =1.0) with zero internal and wall friction, gives results that are very different from the experiment data.     

垂直管道中塞状流的模拟

运用简化的硬球模型模拟垂直管道中的塞状流. 固相行为通过跟踪离散颗粒的运动轨迹处理,气相运动由局部平均的Navier–Stokes方程处理,气固两相间的耦合作用服从牛顿第三定律. 每个颗粒的运动过程被分解为颗粒间相互碰撞的过程及流体对其悬浮的过程. 该模型定性地模拟了垂直管道中的塞状流,即在细而长的管道中,颗粒形成沿管道运动的塞状物,且塞状物的运动速度独立于塞状物的长度,但随着气体速度的增加而增加.