Investigating mixing in a multi-dimensional rotary mixer: Experiments and simulations

Mixing is an important but poorly understood aspect in petrochemical, food, ceramics, fertilizer and pharmaceutical processing and manufacturing. Segregation and mixing phenomenon occur in most systems of powdered or granular solids and have a significant influence on their behavior. Deliberate mixing of granular solids is an essential operation in the production of industrial powder products usually constituted from different ingredients. The knowledge of particle flow and mixing in a blender is critical to optimize the design and operation. Since performance of the product depends on blend homogeneity, the consequence of variability can be detrimental. A common approach to powder mixing is to use a tumbling blender, which is essentially a hollow vessel horizontally attached to a rotating shaft. This single axis rotary blender is one of the most common batch mixers among in industry, and finds use in myriad of application as dryers, kilns, coaters, mills and granulators. In most of the rotary mixers, the radial convection is faster than axial dispersion transport. This slow dispersive process hinders mixing performance in many blending, drying and coating applications. A double cone mixer is designed and fabricated which rotates around two axes, causing axial mixing competitive to its radial counterpart. Discrete Element Method (DEM) based numerical model is developed to simulate the granular flow within the mixer. Digitally recorded mixing states from experiments are used to fine-tune the numerical model. Discrete pocket samplers are also used in the experiments to quantify the characteristics of mixing. A parametric study of the effect of initial loading, particle size, fill ratio, vessel speeds, on the granular mixing is investigated by experiments and numerical simulation. Incorporation of dual axis rotation enhances axial mixing by 60 to 90% in comparison to single axis rotation. Mixing is achieved faster with front-back initial loading than with side-side loading. Particle size and fill level are found to have no significant effect on mixing characteristics.     

Review and extension of normal force models for the Discrete Element Method

For the simulation of dense granular systems the Discrete Element Method based on a soft-sphere approach is commonly used. In such simulations collisions between particles take a finite time. The equations of motion are applied for each particle and solved numerically. Therefore models for the forces acting between particles in contact need to be specified. In this paper the focus is set on normal contacts. Based on macroscopic and microscopic accessible parameters like coefficient of restitution, collision time, force, displacement and displacement rate a wide range of commonly used force schemes are reviewed. Results obtained from these commonly used models are compared to experimental data on collisions of different metal alloys, ice and marble as reported in literature. Due to obvious limitations extensions are presented. The new extended models based on linear and non-linear models are compared to experimental data and their accuracy and applicability are discussed.     

DEM simulations of the particle flow on a centrifugal fertilizer spreader

Usually, the performance of centrifugal spreaders must be evaluated in large halls by capturing the fertilizer distribution patterns in standardized tests, often carrying a big cost to the manufacturers. In contrast, this paper proposes a first attempt to model a particle flow subjected to a spinning disc using the Discrete Element Method (DEM) starting from the particle outflow of a bin, using flat as well as inclined discs. The model is validated by experiments in two different ways. The first manner is the measurement of the cylindrical mass distribution along the edge of the disc by a device that collects the fertilizer particles in a tray of baskets around the disc. A second method consists of collecting the particles on the ground after their ballistic flight through the air. Both validation methods are relatively cheap and fit into the present statistical or qualitative interpretation of DEM simulations. Additionally, a number of rotational disc speeds is chosen (300-650 rpm) to incorporate velocity dependent effects of the particle flow. It was found that the DEM simulations show a good qualitative and considerable quantitative agreement with the experiments. The deviations between the simulations and experiments are profound at high disc rotational speeds (500-650 rpm) and can be identified as (1) an underestimation of the simulated particle velocities at the edge of the disc and (2) a too low dispersion on the (vertical) simulated particle velocities at the edge of the disc. A parameter study revealed that (1) can be resolved by introducing a velocity dependent friction coefficient, in agreement with literature. The influence of other model parameters such as particle damping and stiffness appears to be small, while the introduction of a rolling friction coefficient to mimic rolling resistance or particle shape does not provide any answer either, and hence reason (2) at this moment must be addressed to unknown external factors such as disc plane vibrations appearing at higher disc speeds.     

Prediction of screw conveyor performance using the Discrete Element Method (DEM)

Screw conveyors are used extensively in agriculture and industry for transporting and/or elevating bulk materials over short to medium distances. They are very effective conveying devices for dry particulate solids, giving good control over the throughput. Despite their apparent simplicity, the mechanics of the transportation action is very complex and designers have tended to rely heavily on empirical performance data. The performance of a screw conveyor is affected by the operating conditions, such as: the rotational speed of the screw; the inclination of the screw conveyor; and the volumetric fill level of the bulk material. In this paper we examine how these operating conditions influence the performance of a screw conveyor by applying the Discrete Element Method (DEM) to simulate a single-pitch screw conveyor with periodic boundary conditions. The DEM modelling gives predictions of screw conveyor performance in terms of variations of: particle speeds, mass flow rate, energy dissipation and power consumption, due to changes in the operating conditions.     

串罐式无钟高炉炉顶炉料运动的离散元分析

建立了串罐式无钟炉顶装料系统全模型,应用离散单元法对炉料从皮带到炉喉运动的全过程进行数值计算,考察了皮带上上下料罐内的粒度偏析,对比了料罐内是否安装石盒对料罐内炉料分布、料罐装料和卸料时炉料运动及布料时料流粒度变化的影响. 结果表明,皮带上小颗粒向料层下部渗透,皮带末端料层下部平均粒度比上部小. 炉料沿上料罐周向、径向和纵向存在粒度偏析;沿下料罐径向和纵向存在粒度偏析,周向上分布较均匀,相对粒度变化的标准差为0.03. 料罐内安装石盒对周向和纵向粒度分布影响较小,石盒附近小颗粒渗透影响径向粒度分布,料面基本水平,料罐卸料呈活塞流;无石盒时料面形成堆尖,料罐卸料呈漏斗流. 布料时料流粒度变化受料罐内料流运动和炉料分布影响,料罐内不安装石盒时料流粒度变化的标准差为7.15,安装石盒时为10.42,料流粒度变化更明显.     

Discrete particle simulations for flow of binary particle mixture in a bubbling fluidized bed with a transport energy weighted averaging scheme

Flow behavior of small and big particles with the same particle density in a bubbling fluidized bed is modeled by a combined approach of discrete particle method and computational fluid dynamics (CFD-DPM). The collision time of a collision pair is computed by a quartic equation in which the effect of acceleration due to the different diameters is considered. A transport energy weighted averaging approach is proposed to determine the local gas velocity at a particle. The fluidization behavior of binary mixture differing in size is experimentally and numerically studied in the gas bubbling fluidized bed. The distributions of mass fraction of small and big particles along the bed height are simulated, and the profiles of the mean particle diameters of binary mixture are determined. The numerical results are in agreement with experimental data. The distributions of granular temperature, stresses, and shear viscosities of small and big particles are compared.     

Effect of size ratio on the behaviour of agglomerates embedded in a bed of particles subjected to shearing: DEM analysis

This paper presents the results of analysis of the deformation and breakage of spherical agglomerates embedded in a bed of particles and subjected to shearing, a situation commonly encountered in powder granulation. The study is based on three dimensional distinct element method (DEM), in which the inter-particle interactions are governed by theories of contact mechanics. An agglomerate was first generated in a bed of particles having the same size as the primary particles forming the agglomerate. Different size ratios (i.e., the ratio of the diameter of agglomerate to the diameter of surrounding particles) in the range 3-10 were then simulated by varying the size and number of surrounding particles. The agglomerates were subjected to shearing (shear rate and strain of about and 0.3, respectively) and their breakage characteristics were analysed. The agglomerate with the size ratio 10 does not break but undergoes some structural deformation by re-arrangements of contacts. However, the agglomerates with ratio about 7 or smaller suffer breakage. For the size ratio equal or smaller than 5, the agglomerate breaks significantly leading to full disintegration. The results of stress analysis of the agglomerates suggest that the resistance to breakage for the agglomerate with size ratio of 10 is due to the nature of stresses exerted on the agglomerate. For large size ratios the stress on the agglomerate is predominantly hydrostatic. The ratio of deviatoric stress over hydrostatic pressure increases as the size ratio of the agglomerate is reduced. The nature of stresses experienced by agglomerates with smaller size ratios is predominantly deviatoric, thus causing shear deformation and breakage. The results are compared with physical experiments and a satisfactory agreement is obtained.     

Analysis of granule breakage in a rotary mixing drum: Experimental study and distinct element analysis

Rotary drums are commonly used in particulate solid industries for mixing, coating and reactions. The process is often accompanied by undesirable breakage of granules. For this reason, a scaled-down version is sometimes used as an attrition testing device. In this work, the attrition of granules inside a rotary drum at 18, 35 and 52 rpm drum rotation speeds for 4000 cycles is studied. The granules used in this study have been produced by extrusion and spheronisation with a size range of 500 to 1000 μm. The rotary drum has an internal diameter of 0.39 m, axial length of 0.3 m and a single baffle. The extent of breakage is quantified by sieving out fine debris which is two sieve sizes smaller than the feed particles. To relate the extent of breakage in the drum to granule characteristics, single granule impact tests have been performed on one type of granule at several velocities. The effects of particle size and impact velocity are analysed and a power-law relationship is fitted between impact velocity and single granule breakage. This information is then used to simulate granule breakage in a rotary drum by Distinct Element Method (DEM). The drum is simulated for 5 rotations at the rotational speeds stated above and the breakage rate is extrapolated to 4000 cycles where it is compared to experimental results obtained. The trends for particle breakage in both experiments (determined by sieving) and extrapolated DEM simulations are in agreement however the orders of magnitudes are different. The comparison shows that the extent of breakage obtained from extrapolated simulations is overestimated at drum speed of 35 and 52 rpm and underestimated at 18 rpm. There is close agreement between experiments and extrapolated DEM simulations for particle breakage at 18 rpm only after 4000. Furthermore, the effect of air drag on the attrition of granules by impact at a drum rotation speed of 52 rpm is investigated, where it is found to significantly reduce the breakage results.     

Modelling of dense gas-particle flow in a circulating fluidized bed by Distinct Cluster Method (DCM)

Computational Fluid Dynamics (CFD) is a powerful tool to study the dense gas-solid flow in a circulating fluidized bed. Most of the existing methods focus on the microscopic properties of individual particle. Therefore, the simulation scale is significantly limited by the huge number of individual particles, and so far the numbers of particles in most of the reported simulations are less than 10⁵. The hydrodynamics behaviour of particle clustering in a dense gas-solid two-phase flow has been verified by several experimental results. The Distinct Cluster Method (DCM) was proposed in this paper by studying the macroscopic particle clustering behaviour, and comprehensive models for cluster motion, collision, break-up, and coalescence have been well developed. We model the dense two-phase flow field as gas-rich lean phase and solid-rich cluster phase. The particle cluster is directly treated as one discrete phase. The gas turbulent flow is calculated by Eulerian approach, and the particle behaviour is studied by Lagrangian approach. Using the proposed method, a three-dimension dense gas-particle two-phase flow field in a circulating fluidized bed with square-cross-section, with particle number up to 7.162 × 10⁷ are able to be numerically studied, on which few results have been reported. Details on instantaneous and time-averaged distributions are obtained. Developing process of non-uniform particle distribution is visualized. These results are in agreements with experimental observations, which justified the feasibility of using the DCM method to model and simulate dense gas-solid flow in a circulating fluidized bed with large number of particle numbers.     

Impact of Contact Scaling and Drag Calculation on the Accuracy of Coarse-Grained Discrete Element Method

The accuracy of coarse-grained discrete element method (CGDEM) relies on appropriate scaling rules for contact and fluid-particle interaction forces. For fluidized bed applications, different scaling rules are used and compared with DEM results. The results indicated that in terms of averaged values as mean particle position and voidage profile, the coupling of computational fluid dynamics and CGDEM leads to accurate results for low scaling factors. Regarding the particle dynamics, the approach leads to an underestimation of RMS values of particle position indicating a loss of particle dynamics in the system due to coarse graining. The impact of cell cluster size on drag force calculation is studied. The use of energy minimization multiscale drag correction is investigated, and a reduced mesh dependency and good accuracy are observed.     

Influence of interface energy of primary particles on the deformation and breakage behaviour of agglomerates sheared in a powder bed

In this paper, the parameters that affect the deformation and breakage of agglomerates embedded in a bed of particles subjected to rapid shearing are identified and analysed. The influences of interface energy between the primary particles and the size ratio (between agglomerates and particles of the bed) on the deformation characteristics of the agglomerate are addressed. The study is based on computer simulations using the distinct element method (DEM). It has recently been shown that for agglomerates having a size ratio greater than about 7, the nature of stresses experienced by the agglomerates when sheared inside a particulate bed is predominantly hydrostatic, hence it is difficult to break them (Hassanpour et al., 2007). However, the role of the interface energy between primary particles coupled with the effect of size ratio on the breakage and deformation characteristics of agglomerates during shearing has not been analysed. This feature is of great interest in the agglomeration process and is hence addressed in the present study. It is found that despite the predominantly hydrostatic nature of stresses responsible for retarding the breakage, agglomerates with size ratio greater than about 7 could undergo macroscopic deformation when the surface energy between the primary particles is decreased below a critical value. Furthermore, a failure map of agglomerates is presented in terms of their size ratio and the value of interface energy of the primary particles.     

Discrete Element Method Simulation of the Effect of Tumbling Time and Particle Size in a 300‐mm Diameter Mill

This paper investigates ore abrasion resistance using a small tumbling mill. Three kilograms of different size fractions of ore are tumbled in a 300‐mm diameter by 300‐mm length mill for varying times. The effect of particle size, milling time and stiffness of particles on abrasion characteristics were studied. As might be expected, the grinding time affects the degree of abrasion of particles. Longer grinding times produce more fragments. The size and stiffness of particles also affect the degree of abrasion. For the same quantity of mass, smaller particles (more in number) show more collisions and, hence, a higher probability of abrasion.     

Numerical Study of Particle Behaviour in Split-Flow Thin-Channel Fractionation Using the Discrete Element Method

Abstract

This study examines the usefulness of the discrete element method (DEM) for studying particle motion in SPLITT fractionation. The method was tested against the conventional SPLITT theory and published experimental data for particle sizes 7, 10, and 15 µm at various run conditions and good agreement was achieved. Illustrative studies presented in this paper show that particle collisions occur at concentrations as low as 0.05%(v/v); and particle trajectory deviates from theory more notably for larger particles, 15 µm diameter and greater. The finding suggests the DEM can be useful in SPLITT calculations for modeling the influence of particle-particle interactions.     

Numerical simulation of local and global mixing/segregation characteristics in a gas–solid fluidized bed

Researches on solids mixing and segregation are of great significance for the operation and design of fluidized bed reactors. In this paper, the local and global mixing and segregation characteristics of binary mixtures were investigated in a gas–solid fluidized bed by computational fluid dynamics-discrete element method (CFD-DEM) coupled approach. A methodology based on solids mixing entropy was developed to quantitatively calculate the mixing degree and time of the bed. The mixing curves of global mixing entropy were acquired, and the distribution maps of local mixing entropy and mixing time were also obtained. By comparing different operating conditions, the effects of superficial gas velocity, particle density ratio and size ratio on mixing/segregation behavior were discussed. Results showed that for the partial mixing state, the fluidized bed can be divided into three parts along the bed height: complete segregation area, transition area and stable mixing area. These areas showed different mixing/segregation processes. Increasing gas velocity promoted the local and global mixing of binary mixtures. The increase in particle density ratio and size ratio enlarged the complete segregation area, reduced the mixing degree and increased the mixing time in the stable mixing area.     

Numerical Investigation on Granular Flow from a Wedge‐Shaped Feed Hopper Using the Discrete Element Method

The discharge process of granular material from a wedge‐shaped feed hopper was numerically simulated using a 3D discrete element method. The effects of particle size, feed pipe, side and rear wedge angle on the discharge performance were investigated in terms of flow pattern, discharge rate, and stability. The results show that with larger particle size the granular flow pattern gradually transforms from mass flow to edge flow where the flow rate decreases and the discharging integrity and stability become worse. The presence of the feed pipe reduces the discharge rate and stability. The increase of the feed pipe diameter will diminish the discharge rate and enhance the discharge stability. Both the side and the rear wedge angle have a certain effect on the discharge performance. The effects of feed pipe, side and rear wedge angle on the discharge stability become more significant with larger particle size.     

Numerical simulation of motion of rigid spherical particles in a rotating tumbler with an inner wavelike surface

The present work is a numerical simulation of motion of rigid spherical particles within a 2-D tumbler with an inner wavelike surface. The rotation of the tumbler is simulated as a traveling sine wave around a circle. The discrete element method (DEM, a hard sphere approach) is used. The particle-wall interactions are taken into account in a changed numerical approach of hard sphere model. The effects of two basic factors of the rotating velocity (phase velocity) and the wave numbers are separately investigated. A simple but useful method for cluster identification is provided and used. The energy-based analysis of particle clusters and the motion pattern study indicate the existence of a pulsed variation in the kinetic energy of the clusters at low wave numbers and a cyclic bulk motion of the clusters at high wave numbers. The necessary conditions for the pulsed variation of motion of particle clusters at low wave number are analyzed and a mode for industrial application, e.g. coal grinding process in power plant, is demonstrated.     

Mixing and segregation in a bidisperse gas–solid fluidised bed: a numerical and experimental study

In many industrial applications of dense gas–solid fluidised beds, mixing and segregation phenomena play a very important role. The extent of mixing and segregation is strongly influenced by the bubble characteristics. Therefore, the extent of mixing and segregation, induced by a single bubble injected in a monodisperse and bidisperse fluidised bed at incipient fluidisation conditions and in freely bubbling fluidised beds has been studied both with well-defined experiments and with a 3D Euler–Lagrangian model. Particle image velocimetry (PIV) was successfully applied to obtain the ensemble averaged particle velocity profile in the vicinity of the bubble in dense gas–solid fluidised systems.

The bubble size of a single injected bubble in a fluidised bed at minimum fluidisation conditions calculated with a 3D discrete particle model (DPM) depended strongly on the selected gas-particle drag model. The widely used Ergun equation combined with the Wen and Yu [Powder Technol. 98 (1998) 38; Chem. Eng. Sci. 47 (1992) 1913] relations overpredicted the bubble size due to an overprediction of the drag force. The DPM with the drag model proposed by Koch and Hill [Annu. Rev. Fluid Mech. 33 (2001) 619], based on Lattice–Boltzmann simulations, gave much better agreement with the experimental findings.

The segregation rates in a bidisperse freely bubbling fluidised bed predicted by the DPM agreed very well with the experimentally measured segregation rates by Goldschmidt [M.J.V. Goldschmidt, Hydrodynamic modelling of fluidised bed spray granulation, PhD thesis, Twente University, 2001].     

Discrete element study of particle circulation in a 3-D spouted bed

A spouted bed is simulated by a discrete element method in a full 3-D cylindrical coordinate system. The vessel is a flat-bottomed cylinder 0.5 m in height and 0.15 m in diameter. In the simulation 300,000 mono-sized spherical glass beads are used. The numerical scheme is based on a second order finite difference method in space and a second order Adams-Bashforth method for time advancement. Gas-particle interaction is modelled to obey the Ergun equation for void fraction less than 0.8, and the Wen-Yu model, for void fraction greater than 0.8. In the present study, particle motion and circulation are investigated. Predicted streamlines of time-averaged particle flow are almost vertical in the upper part of the bed, gradually bending to the spout core in the lower region. Particle velocities along the streamlines are uniform in the upper part of the annulus, becoming non-linear with respect to the distance from the dead zone in the lower part of the annulus. The predicted total passages of particles across the spout-annulus boundary are in good agreement with measurements reported in the literature. Particles are found to feed from annulus to spout along the entire length of the spout. The net mass flux (from annulus to spout) is found to be constant in the upper part of the bed, increasing gradually with the depth in the lower part.     

Flow patterns of solids in a two-dimensional spouted bed with draft plates: PIV measurement and DEM simulations

Particle flow behaviors in a two-dimensional spouted bed (2DSB) with draft plates were studied using both the particle image velocimetry (PIV) and the combined technique of discrete element method and fluid dynamic computation (DEM-CFD) while considering the gas turbulence effect. The bed consisted of a rectangular column, 152 mm wide and 15 mm deep, a conical section with an included 60° angle and two draft plates with a distance of 15 mm. Images of particle flow were recorded by a high speed CCD camera and analyzed using a self-developed PIV algorithm to obtain a time-averaged particle velocity field. Experiments predict that the addition of draft plates not only makes the streamline of particles in the annulus steeper, but the velocity magnitude is made smaller as well. DEM results predict well the longitudinal profile of the particle vertical velocity along the bed centerline, especially during the rapid acceleration stage at the lower part of the spout. Finally, the distributions of drag forces and net forces are introduced in this paper to explain the particle velocity profiles by PIV measurement.