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     

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     

Segregation of granular particles by mass,radius, and density in a horizontal rotating drum

The impact of particle properties on segregation and mixing of bidisperse granular beds in a rotating horizontal drum have been studied by discrete element method (DEM) simulations. Bidispersities in radius, density, and mass have pronounced influences on the stationary mixing pattern, although they hardly affect the granules' flow regime. At 50% fill level, all beds mix well for a Froude number of ～0.56, corresponding to a flow regime intermediate to cascading and cataracting, while segregation occurs both at lower (rolling and cascading regime) and higher (cataracting/centrifuging regime) Froude numbers. These observations are explained qualitatively by noticing that the angular drum velocity dictates the flow regime, which in turn determines the effectiveness and direction of four competing (de)mixing mechanisms: random collisions, buoyancy, percolation, and inertia. A further dozen particle properties have been varied, including the friction coefficients and elastic modulus, but these proved inconsequential to the steady‐state degree of mixing. © 2013 American Institute of Chemical Engineers AIChE J, 60: 50–59, 2014     

Numerical Simulation and Analysis of Particle Mixing and Conduction in Wavy Drums

A thermal discrete element method (DEM) is used to simulate particle mixing and heat conduction inside wavy drums to explore the effects of wavy walls. Sinusoidal configurations with different waves on the walls are simulated. The Lacey mixing index is applied to analyze the mixing characteristics. The driven forces from the wavy wall, either positive/negative or effective driven forces, are analyzed to explain the mechanisms of mixing enhancement in the wavy drum. A new control parameter is proposed to explain the mechanism of mixing enhancement. It is found that a locally oscillating effect exists in wavy drums, which is imparted on the bulk rotating motions of particles and enhances the characteristics of particle mixing and heat conduction significantly. Except over large wave numbers and rotating speeds when the flow regime is deteriorated for mixing, the wavy drum is generally beneficial for mixing augmentation as well as conduction enhancement.     

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.     

颗粒物料在半封闭式回转鼓内的混合特性

采用DEM离散单元法,对不同转速与倾角下半封闭式回转鼓内颗粒物料的混合过程进行了模拟。通过“颗粒接触数”定义的分离指数S,分析了不同转速和倾角对回转鼓内颗粒物料径向与轴向混合特性的影响。结果表明：转速与倾角对回转鼓内颗粒物料径向与轴向混合特性有显著的影响;倾角不变,转速分别为15r/min、30r/min、45r/min时,颗粒物料的径向与轴向混合速度随转速的增加而增加,当转速超过30r/min后,增加转速对径向与轴向混合速度的影响越来越小;转速不变,倾角分别为0°、17°、34°时,增大倾角能有效的增加轴向混合速度,但对径向混合速度没有促进作用,当倾角超过17°后,轴向混合速度的增幅随着倾角的增加而逐渐变小,而径向混合速度随着倾角的增大而减小,但增加转速可以减小径向混合速度下降幅度。     

Simulation of the granular flow of cylindrical particles in the rotating drum

This study aims at unveiling the effect of particle shape on granular flow behavior. Discrete element method is used to simulate cylindrical particles with different aspect ratios in the rotating drum operating in the rolling regime. The results demonstrate that the cylindrical particles exhibit similar general flow patterns as the spherical particles. As the aspect ratio of the cylindrical particles increases, the active‐passive interfaces become steeper, and the number fraction, solid residence time, and collision force in the active region decreases. The mechanism underlying the difference is the preferential orientation, with particles of greater aspect ratios increasingly orientating their longitudinal axes perpendicular to the drum length. Also, particle alignment in the active region is more uniform than that in the passive region. The results obtained in this work provide new insights regarding the impact of particle shape on granular flow in the rotating drum. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3835–3848, 2018     

A soft-sensor approach to flow regime detection for milling processes

Due to the many industrial applications of rotating drums, a wide range of operating conditions, including different particle flow regimes, are used. Knowledge of the flow regimes inside a drum is beneficial for process optimisation and control. This paper shows how the unique insights provided by a discrete element method (DEM) model of a rotating drum can be used to create soft-sensor models that detect flow regime. Impacts between particles and the drum wall are simulated, from which the feature variables are extracted. A soft-sensor model which links these feature variables to flow regime is constructed using the multivariate statistical technique of Fisher discriminant analysis (FDA). This model is able to successfully classify new testing data, which are not used in soft-sensor model training, as belonging to rolling, cascading and cataracting flow regimes.     

滚筒端面对颗粒物料轴向混合过程影响的离散模拟

基于离散单元法模拟了仅颜色存在差异的两组分颗粒物料在轴径比0.3的窄滚筒中的轴向混合过程,滚筒的左侧端面固定,右侧端面可随侧壁旋转。结果表明,不同物料装载量和滚筒转速下,在达到完全混合状态前,黄红颗粒物料初始轴向界面处可能出现3种不同的径向结构：黄?红结构、红?黄?红结构和红?黄结构。红?黄?红结构和红?黄结构工况下,固定端面一侧还可出现更复杂的多层三明治结构。径向结构源自滚筒端面效应导致的颗粒轴向对流,颗粒轴向速度在切向截面上的分布决定了径向结构的类型。     

Simulation of a continuous granular mixer: Effect of operating conditions on flow and mixing

Continuous particulate blending has received much attention in the recent decade as it provides a more economical and efficient alternative over batch blending for large scale manufacturing. The influence of operating conditions in continuous blenders is not well understood quantitatively, even though qualitative parallels can be drawn with batch blending for similar geometries. This work investigates the influence of fill level and impeller rotation rate (Froude number) in a horizontal bladed continuous blender using the discrete element method (DEM). Particle flow within the blender was found to be strongly dependent on the Froude number and fill level, with distinct fluidized and quasi-static regimes at smaller fills. The axial flow rates showed significant variation with Froude number and fill, and also showed considerable variation over the course of a shaft revolution. Favourable mixing was obtained at smaller impeller rotation rates for larger fills, but at larger impeller rotation rates for smaller fills.     

Continuous versus discrete modelling of heat transfer to agitated beds

Heating of free-flowing particles by contact with the wall of a rotary drum without inserts has been simulated in two dimensions by means of the thermal version of the Discrete Element Method (DEM). The results are in qualitative agreement with existing experimental data and with the classical penetration model (PM) for the following limiting cases: heat transfer controlled by a contact resistance at the wall of the drum; heat transfer to agitated beds with significant bed-side resistance; heat transfer to the stagnant bed. The latter can be used to establish an equivalence (calibration) between the discrete (DEM) and the continuous (PM) modelling approach. Thermal mixing times can be derived from asymptotic overall heat transfer coefficients obtained via thermal DEM for agitated beds. They are found to be significantly smaller than purely mechanical mixing times. For the investigated conditions, they are also much smaller than previous recommendations based on the PM. The ability of thermal DEM to provide information not accessible to the penetration model, like temperature distributions, is discussed. It is pointed out that a decrease of the high computational cost of the method is necessary in order to enhance its applicability.     

Using the discrete element method to predict collision-scale behavior: A sensitivity analysis

Discrete element method (DEM) simulations have recently been used to investigate collision-scale measurements such as collision frequency and impact velocity distributions. These simulations are typically validated against particle velocity fields using experimental techniques such as particle image velocimetry or positron emission particle tracking. An important question that has not been addressed is whether validation of a macroscopic velocity field or solid fraction field also implies a validation of collision-scale measurements such as collision frequency. In this study, DEM measurements of solid fraction, shear rate, collision frequency, and impact velocity are made in a small region just beneath the free surface in a rotating drum. The effects of periodic drum length, particle stiffness, coefficient of restitution, and particle size are investigated. The solid fraction and shear rate do not vary with particle stiffness or coefficient of restitution over the range of values studied. However, the collision rate increases with increasing particle stiffness and coefficient of restitution. In addition, the average collision speed decreases as particles become stiffer or less elastic. The shear rate varies with particle size, but the average collision velocity remains constant. These findings indicate that validation against particle velocity and solid fraction fields does not necessarily imply validation of collision frequency and impact velocity. Indeed, the velocity and solid fraction fields were found to be relatively insensitive to a range of DEM contact stiffnesses and coefficients of restitution while the collision distributions were sensitive.     

Advances in micro-mechanical modeling using a bonded-particle model and periodic homogenization within discrete element framework applied to heterogeneous ceramics

The Discrete Element Method (DEM) can account for microcracks initiations and propagations within the microstructure and their impact on the macroscopic properties of ceramics. Combing the DEM with the Periodic Homogenization (PH) allows working with a limited number of elements, thus facilitating the multiscale transition of the elastic properties of ceramics: from the microscale (inclusion/pores scale) to the macroscopic elastic behavior of such continuum media. However, the PH approach for a continuum media is currently less developed in DEM than the FEM. Hence, this study aims to consolidate a DEM framework, using a bonded-particle model and PH to improve the prediction of the elastic properties (Cij tensor) of ceramics. Here, a face-centered cubic unit cell is combining? with periodic boundary conditions to build a 3D representative volume element in DEM to model the macroscopic elastic properties of model materials and is validated by experimental data, analytical and FEM approaches.     

Simulation of dry powder inhalers: Combining micro‐scale,meso‐scale and macro‐scale modeling

The flow of carrier particles, coated with active drug particles, is studied in a prototype dry powder inhaler. A novel, multiscale approach consisting of a discrete element model (DEM) to describe the particles coupled with a dynamic large eddy simulation (LES) model to describe the dynamic nature of the flow is applied. The model consists of three different scales: the micro‐scale, the meso‐scale, and the macro‐scale. At the micro‐scale, the interactions of the small active drug particles with larger carrier particles, with the wall, with the air flow, and with each other is thoroughly studied using discrete element modeling and detailed computational fluid dynamics (CFD), i.e., resolving the flow structures around the particles. This has led to the development of coarse‐grained models, describing the interaction of the small active drug particles at the larger scales. At the meso‐scale the larger carrier particles, and all of their interactions are modeled individually using DEM and CFD‐LES. Collisions are modeled using a visco‐elastic model to describe the local deformation at each point of particle‐particle contact in conjunction with a model to account for cohesion. At the macro‐scale, simulations of a complete prototype inhaler are carried out. By combining the relevant information of each of the scales, simulations of the inhalation of one dose from a prototype inhaler using a patient relevant air flow profile show that fines leave the inhaler faster than the carrier particles. The results also show that collisions are not important for particle‐particle momentum exchange initially but become more important as the particles accelerate. It is shown that for the studied prototype inhaler the total release efficiency of the fine particles is between 10 and 30%, depending on the Hamaker constant, using typical settings for the properties of both particles. The results are also used to study regions of recirculation, where carrier particles can become trapped, and regions where fines adhere to the wall of the device. © 2016 American Institute of Chemical Engineers AIChE J, 63: 501–516, 2017     

Study of cold powder compaction by using the discrete element method

The discrete element method (DEM), based on a soft-sphere approach, is commonly used to simulate powder compaction. With these simulations a new macroscopic constitutive relation can be formulated. It is able to de-scribe accurately the constitutive material of powders during the cold compaction process. However, the force-law used in the classical DEM formulation does not reproduce correctly the stress evolution during the high density compaction of powder. To overcome this limitation at a relative density of about 0.85, the high density model is used. This contact model can reproduce incompressibility effects in granular media by implementing the local solid fraction into the DEM software, using Voronoi cells. The first DEM simulations using the open-source YADE software show a fairly good agreement with the multi-particle finite element simulations and experimental results.     

A square‐force cohesion model and its extraction from bulk measurements

Accurate modeling of interparticle forces in DEM is critical to predicting the rheology of cohesive particles. Rigorous cohesion models usually include parameters associated with particle surface roughness. However, both roughness measurement and its distillation into appropriate model parameters remain challenging. We propose a square‐force cohesion model, where cohesive force remains constant until a cutoff separation, above which cohesion vanishes. We demonstrate the square‐force model is a valid surrogate of more rigorous models. Specifically, when two parameters of square‐force model are chosen to match the two key quantities governing dense and dilute flows, namely maximum cohesive force and critical cohesive energy, respectively, DEM results using square‐force and more rigorous models show good agreement. For practical application of the square‐force model to lightly cohesive systems, a method is established to extract its parameters via defluidization, enabling determination of particle–particle cohesion from simpler bulk measurements than complicated and expensive scans on individual grains. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2329–2339, 2018     

Continuous blending of cohesive granular material

Results are presented from discrete element method (DEM) computer simulations of cohesive particles in a periodic slice of a continuous blender. The influence of inter-particle cohesion at various impeller speeds and fill levels is reported. Although increasing cohesion does not significantly change axial flow rates, mixing rates in the transverse plane and axial direction are affected. Mixing is generally enhanced for slightly cohesive materials, but decreases for larger cohesion, similar to trends observed in tumbling batch mixers. Changes in fill level are also shown to affect axial transport rates and mixing. These results suggest that the controllable operating parameters, such as feed rate and impeller speed, may be adjusted for cohesive powder formulations to obtain optimal mixing performance.     

Influence of random pore defects on failure mode and mechanical properties of SiC ceramics under uniaxial compression using discrete element method

To investigate the relationship between micro-defects in ceramic materials and macro mechanical properties and behaviours, a computational model of SiC ceramics with randomly oriented elliptical pores was established using the discrete element method (DEM). The effects of pore defect content and its aspect ratio on the failure mode, stress-strain curve and mechanical properties of specimen were investigated under uniaxial compression. The effective Young's modulus which was obtained from DEM simulations was compared with the predictions of Mori-Tanaka scheme (MTS) and Self-Consistent scheme (SCS) at various pore defect densities. The results showed that the compressive strength and crack initiation stress decrease nonlinearly as the pore defect content increases. Furthermore, the smaller the aspect ratio of the elliptical pore defects was, the more obvious the weakening trend was. As the pore defect content increases, the failure mode of the specimen changed from brittle fracture to tensile-shear mixing and then to axial splitting. The stress-strain curves showed a certain “softening” period during the loading process. The effective Young's modulus obtained from the DEM simulations coincides with the approximations of MTS and SCS at low pore densities. However, when the pore defect density became larger, the DEM simulation results were slightly lower than the theoretical results of the Mori-Tanaka scheme, which only considers the weak interaction between defects.     

滚筒端面对颗粒物料轴向流动特性影响的离散模拟研究

针对碎渣工艺中仅一个端面可随侧壁转动的短滚筒体系，采用离散单元法模拟研究了滚筒轴径比和转动速度对颗粒物料轴向流动特性的影响。模拟结果表明，系统内形成了显著的轴向对流结构：物料层顶部处颗粒物料会朝向滚筒固定端面一侧运动，而物料层趾部区域颗粒则朝向滚筒转动端面一侧运动。低转速条件下，沿物料自由表面由顶部到趾部，颗粒轴向速度呈非对称分布，顶部区域颗粒轴向速度绝对值显著小于趾部区域颗粒轴向速度绝对值；两部分区域颗粒轴向速度绝对值分别在y/R=±0.725处达到极大值，且轴向速度为0的位置并不出现在切向的中间位置。改变滚筒的轴长对这种非对称分布的影响近似可忽略，但是增大滚筒转速会增大颗粒轴向运动速度并逐步减弱这种非对称性。改变滚筒转速，对物料顶部区域颗粒的轴向流动的影响要大于对趾部区域颗粒轴向流动的影响。当滚筒轴径比达到1.2后，滚筒转动端面对物料轴向流动的影响区域不会随滚筒转速的增大而呈现显著变化。这些结果为实际滚筒碎渣工艺的结构优化提供了理论指导。     

Formulation of a physically motivated specific breakage rate parameter for ball milling via the discrete element method

A physically based specific breakage rate parameter of the population balance model for batch dry‐milling is formulated, which explicitly accounts for the impact energy distribution calculated by the discrete element method (DEM). Preliminary DEM simulations of particle impact tests were first performed, which concluded that dissipation energy should be used in contrast to collision energy to accurately define the impact energy distribution. Subsequently, DEM simulations of the motion of spheres representing silica glass beads in a ball mill were performed to determine the specific breakage rate parameter, which was in good agreement with those found experimentally. An analysis of the impact energy distribution, which was only possible within context of the physically motivated specific breakage rate parameter, emphasized the importance of accounting for a threshold impact energy. Without proper assessment of the impact energy distribution, DEM simulations may lead to an erroneous evaluation of milling experiments. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2404–2415, 2014