CFD simulation of particle segregation in a rotating drum. Part II: Effects of specularity coefficient

Segregation of binary particle mixture in a rotating drum is numerically studied using the Eulerian multiphase computational fluid dynamics (CFD) simulations coupling the solid phase kinetic theory of granular flow model. The corresponding solid kinetic viscosities of the two particulate phases are determined by the previous granular bed surface fitting (BSF) method. The effects of the specularity coefficients used in the simulations on the segregation patterns in the rotating drums are systematically studied by using the specularity coefficient values ranging from 0.15 to 1.0. When using a smaller specularity coefficient value in the simulation, the momentum transferring from the drum wall to the particulate phase is poorer, lowering the kinetic energy of the particulate phase. The lower particulate phase kinetic energy causes slower particle motion in the bed and hence delays the segregation core/band formation. At the same simulation time, the concentration of the smaller particles in the segregation core increases with the increasing of the specularity coefficient value used in the simulation. When the specularity coefficient values larger than 0.4 are used in our simulations, the realistic three-dimensional segregation structures are well predicted. A proper specularity coefficient value should be adopted in Eulerian multiphase CFD simulations of granular flows.     

Frictional behavior of granular gravel–ice mixtures in vertically rotating drum experiments and implications for rock–ice avalanches

Rapid mass movements involving large proportions of ice and snow can travel significantly further downslope than pure rock avalanches and may transform into debris-flows as the ice melts and as water from the stream network or water-saturated debris is incorporated. Currently, ice is thought to have three distinctive effects: 1) reduction of the friction within the moving mass itself, 2) increase of pore pressure as the ice melts and consequent reduction of the shear resistance of the flowing material, and 3) reduction of boundary friction where the failing mass travels on a glacier. However, measurement-based evidence to support these hypotheses is largely missing. In this study, laboratory experiments on the first two mechanisms were carried out in two partially-filled large rotating drums, one in Vienna (Austria) and a second in Berkeley (USA). Varying proportions of cold gravel and gravel-sized ice were mixed and added to the rotating drum running at constant rotational velocity until all ice had melted. Flow behavior was recorded with flow depth, normal force, shear force, pore-water pressure, and temperature sensors. The bulk friction coefficient was found to decrease linearly with increasing ice content by ~ 20% in the early phase of the experiments, before significant portions of the ice transformed into water. For ice contents larger than 40% by volume, the transformation from a dry granular flow to debris-flow-like movement or hyperconcentrated flow was observed when pore-water pressures rose and approached the normal forces along the flow profile. Pore-water pressure from melting ice developed within several minutes after the start of the experiments and, as it increased, progressively reduced the friction coefficient. The results emphasize that the presence of ice in granular moving material can significantly reduce the friction coefficient of both dry and partially-saturated debris. Due to size effects and the absence of other factors reducing friction (e.g. surfaces with low friction and rock comminution), the absolute measured friction coefficients from the laboratory experiments were larger than those found from natural events. However, the relative changes in friction coefficients depending on the ice and water content may also be considered in real-scale hazard assessments of rapid mass movements in high mountain environments.     

DEM simulation and experimental validation for mechanical response of ellipsoidal particles under confined compression

The representation of non-spherical particles in discrete element method (DEM) has not been addressed adequately. Although the multiple sphere method (MSM) is the most popular approach to describe non-spherical particle shape, the validity of the MSM has not been established yet. The purpose of this study is to examine the validity and adequacy of the MSM. A uni-axial confined compression test was designed and set up to study the mechanical behaviour of an ellipsoidal granular assembly under vertical loading and the load transfer to the contacting boundary. Four levels of multi-sphere approximation for an axi-symmetric ellipsoidal particle were employed in DEM simulation to investigate the adequacy of multi-sphere approximation. A comparison on compression characteristics between the numerical and experimental results was made and discussed in this paper. Most of the compared physical properties showed reasonable agreement, indicating that capturing the key linear dimensions of a non-spherical particle may be sufficient to predict reasonable results. A small number of sub-spheres (say, N?≥?5) for representing an axi-symmetric ellipsoidal particle can give plausible results. However, the DEM simulations also produced a certain extent of discrepancy in loading stiffness with experiments. Plausible explanations are provided and require further investigation.     

Simulation of granular packing of particles with different size distributions

The study of granular matter composed of spherical particles is of interest in manufacturing, material, and metallurgy. The viscoelastic and frictional contacts between the particles are the cause of forming the agglomeration. We present a numerical simulation for particles packing with three different kinds of size distributions: monosize, bimodal, and Gaussian, using distinct element method (DEM). The particles are initially put randomly but without any overlap, and then fall down due to the gravity force and collide with neighbor particles. Because of the dissipative factors of viscoelastic collision and frictional force, all the particles finally come together to form an agglomeration. Coordination number, porosity, radial distribution function, and force distribution are calculated for different size distributions. It is demonstrated that particle size distribution does affect the granular packing structure.     

Estimating the segregation of a granular bed subjected to vibration in various modes

We present in this paper a DEM study on the segregation behavior of vibrated binary mixture, by focusing on the influence of vibration modes. The numerical simulation program includes a number of vibration tests on a binary mixture in a cylindrical bed, which are performed under different vibration velocity modes, frequencies and amplitudes. We utilize a novel segregation index, namely, the graphic segregation index (GPSI), to characterize the segregation behavior and trace the segregation evolution for binary mixtures. The numerical simulations reveal that the influence of velocity mode is coupled with that resulting from vibration frequency. The binary mixture tends to segregate at a low frequency, with little influence exerted by the velocity mode, whereas it does not fulfill complete segregation at a relatively high frequency, with the vibration frequency having some limited impact on the segregation behavior. Given an intermediate frequency the segregation behavior of the mixture is a little mixed for various velocity modes. It is also found that increasing vibration amplitude enhances the segregation degree of binary mixture. The operation of percolation mechanism in the broad sense is assumed to be primarily responsible for the occurrence of segregation in this study, and this alleged percolation mechanism, as an overall effect, is a result of three effects: the random gap effect, the size-and-mass dependent acceleration and the intrusion and expulsion effect.     

Numerical analysis of flow pattern transition in a conical silo with ellipsoid particles

Gravity-driven discharge flow in conical silos is ubiquitous in manufacturing processes for numerous industries such as food, pharmaceutical and chemical industries, wherein flow pattern is the key topic to be studied. In this work, discrete element method was used to study discharge flow behaviors in a special conical silo. This work aims to understand the dynamic evolution of discharge flow pattern and establish methods for regional determination of flow pattern transition. The results indicated that both mass flow and funnel flow patterns coexist in the silo at the initial stage of discharge, and there is a definite transition process from mass flow to funnel flow. Furthermore, the flow pattern transition is revealed by the change in discharge flow characteristics. Specifically, the change in force acting on particles leads to the change of particle orientation and particle velocity field, macroscopically resulting in the flow pattern transition. Finally, based on the kinetic stress field and shear rate, the height and radial region of flow pattern transition were determined, respectively. Understanding of the flow pattern transition is useful to the design, scale-up and optimization of silos and similar structural devices.     

The investigation of particle flow mechanisms of bulk materials in dustiness testers

ABSTRACT

The generation of dust occurs in many bulk materials handling applications, including during free-fall, material impact on conveyor transfers, or impact with other materials. Dust has potentially serious consequences to the surrounding environment as well as workers and nearby communities. Companies need to identify and quantify the dust being generated so they can find ways to reduce or eliminate this dust generation. Dustiness testers are one method which can be used to quantify dust generation. This paper investigates the experimental material flow and the subsequent discrete element method (DEM) simulation in the rotating drums of two dustiness testers: the European Standard dustiness tester and the Australian Standard dustiness tester. Preliminary comparisons of the rotating drum designs were undertaken using particle/bulk parameters of polyethylene pellets, a granular “non-dusty” material to investigate the flow behavior, to provide a reference base to compare equivalent simulations and subsequent analysis. A calibrated DEM material model for polyethylene pellets was generated via experimental comparison. Investigations of the rotational speed, volume, and initial loading location of product sample have been performed. The motion of particles in the simulated rotating drums has been compared to visual observation from experimental testing.     

Simulation of granular crystallization of cubic particles in twisting container using discrete element method

Granular compaction is a process in which the volume fraction, or density, of the granular materials increases when an excitation is applied. A recent experiment reported that twisting a large number of cubic particles in a cylindrical container leads to an ordered and dense arrangement. This structure is similar to the crystal lattice formed in solidification process. In this article, this phenomenon is repeated by using discrete element method (DEM) simulation. Two different shaped containers are used and it is found that the rectangular angles between the sidewalls and the bottom,namely wall effect, plays a key role. In addition, gravitation is also a very important parameter in this process. The higher gravitation added, the faster crystallization process is achieved. On the contrary, shear force due to friction between particles may slow down this process.     

Effect of lognormal particle size distributions on particle spreading in additive manufacturing

Additive manufacturing (AM) has attracted much attention worldwide in various applications due to its convenience and flexibility to rapidly fabricate products, which is a key advantage compared to the traditional subtractive manufacturing. This discrete element method (DEM) study focusses on the impact of particle polydispersity during the particle spreading process on parameters that affect the quality of the final product, like packing and bed surface roughness. The particle systems include four lognormal particle size distribution (PSD) widths, which are benchmarked against the monodisperse system with the same mean particle diameter. The results reveal that: (i) the solid volume fraction of the initial packed particle bed in the delivery chamber increases then plateaus as the PSD width increases; (ii) regardless of PSD width, the solid volume fraction of the particle bed increases with spreading layer height before compression, but decreases with layer height after compression; (iii) the bed surface roughness increases with PSD width or layer height both before and after the compression of the spreading layer; (iv) the extent of increase in solid volume fraction during compression is correlated with the extent of decrease in bed surface roughness; and (v) the broader PSDs exhibit larger fluctuations of solid volume fraction of the particle bed and bed surface roughness due to greater variability in the arrangement of particles of different sizes. The results here have important implications on the design and operation of particle-based AM systems.     

Experimental study and discrete element method simulation of Geldart Group A particles in a small-scale fluidized bed

Geldart Group A particles are of great importance in various chemical processes because of advantages such as ease of fluidization, large surface area, and many other unique properties. It is very challenging to model the fluidization behavior of such particles as widely reported in the literature. In this study, a pseudo-2D experimental column with a width of 5 cm, a height of 45 cm, and a depth of 0.32 cm was developed for detailed measurements of fluidized bed hydrodynamics of fine particles to facilitate the validation of computational fluid dynamic (CFD) modeling. The hydrodynamics of sieved FCC particles (Sauter mean diameter of 148 µm and density of 1300 kg/m³) and NETL-32D sorbents (Sauter mean diameter of 100 µm and density of 480 kg/m³) were investigated mainly through the visualization by a high-speed camera. Numerical simulations were then conducted by using NETL’s open source code MFIX-DEM. Both qualitative and quantitative information including bed expansion, bubble characteristics, and solid movement were compared between the numerical simulations and the experimental measurement. The cohesive van der Waals force was incorporated in the MFIX-DEM simulations and its influences on the flow hydrodynamics were studied.     

Mixing assessment of non-cohesive particles in a paddle mixer through experiments and discrete element method (DEM)

In this study the mixing kinetics and flow patterns of non-cohesive, monodisperse, spherical particles in a horizontal paddle blender were investigated using experiments, statistical analysis and discrete element method (DEM). EDEM 2.7 commercial software was used as the DEM solver. The experiment and simulation results were found to be in a good agreement. The calibrated DEM model was then utilized to examine the effects of the impeller rotational speed, vessel fill level and particle loading arrangement on the overall mixing quality quantified by the relative standard deviation (RSD) mixing index. The simulation results revealed as the impeller rotational speed was increased from 10?RPM to 40?RPM, generally a better degree of mixing was reached for all particle loading arrangements and vessel fill levels. As the impeller rotational speed was increased further from 40?RPM to 70?RPM the mixing quality was affected, for a vessel fill level of 60% and irrespective of the particle loading arrangement. Increasing the vessel fill level from 40% to 60% enhanced the mixing performance when impeller rotational speed of 40?RPM and 70?RPM were used. However, the mixing quality was independent of vessel fill level for almost all simulation cases when 10?RPM was applied, regardless of the particle loading arrangement. Furthermore, it was concluded that the particle loading arrangement did not have a considerable effect on the mixing index. ANOVA showed that impeller rotational speed had the strongest influence on the mixing quality, followed by the quadratic effect of impeller rotational speed, and lastly the vessel fill level. The granular temperature data indicated that increasing the impeller rotational speed from 10?RPM to 70?RPM resulted in higher granular temperature values. By evaluating the diffusivity coefficient and Peclet number, it was concluded that the dominant mixing mechanism in the current mixing system was diffusion.     

Influence of boundary condition on the sound velocity in granular assembly: Spiral tube versus cylinder

The properties of elastic wave propagation in granular assemblies have become a subject of immense interest in recent years, however, the influence of different confinements on the sound velocity is seldom investigated. This study provides a method to determine the contact point between spherical, super-ellipsoidal particles and complex boundaries, in order to investigate how the anisotropy induced by particle shape or boundary affects velocity. Taking cylinder and spiral tube confinements as examples, the falling process of spherical and super-ellipsoidal assemblies are simulated to verify the validation by the discrete element method (DEM). The convergence of the kinetic energy during the falling process and the equilibrium state with zero residual kinetic energy guarantees the stability and correctness. On the basis, elastic wave propagation of spherical and super-ellipsoidal systems in spiral tube and cylindrical confinements under different pressures are modelled, and sound velocities are calculated. The effective medium theory (EMT), granular solid hydrodynamics (GSH), and elastic stiffness are used to interpret the relationship between velocity and stress in cylindrical confinement. However, the results in the spiral tube deviate from EMT and GSH, which means the boundary affects velocity significantly. The difference of velocity between spiral tube and cylinder is qualitatively explained from the perspective of anisotropy of contact force distribution in the system. The simulation results show that anisotropy introduced by the curved surface affects the acoustic properties greatly. The method used for spiral boundary is also suitable for other complicated confinements.     

Finite element treatment of soft elastohydrodynamic lubrication problems in the finite deformation regime

Soft elastohydrodynamic lubrication (EHL) problem is studied for a reciprocating elastomeric seal with full account of finite configuration changes. The fluid part is described by the Reynolds equation which is formulated on the deformed boundary of the seal treated as a hyperelastic body. The paper is concerned with the finite element (FE) treatment of this soft EHL problem. Displacement-based FE discretization is applied for the solid part. The Reynolds equation is discretized using the FE method or, alternatively, the discontinuous Galerkin method, both employing higher-order interpolation of pressure. The performance of both methods is assessed by studying convergence and stability of the solution for a benchmark problem of an O-ring seal. It is shown that the solution may exhibit spurious oscillations which occur in severe lubrication conditions. Mesh refinement results in reduction of these oscillations, while increasing the pressure interpolation order or application of the discontinuous Galerkin method does not help significantly.     

Propagation behaviour of microstructural short fatigue cracks in the high-cycle fatigue regime

In the high-cycle fatigue regime, it is assumed that crack initiation mechanisms and short fatigue crack propagation processes govern fatigue life of a component. Moreover, it is now becoming accepted that the conventional fatigue limit does not imply complete reversibility of plastic strain and is connected to crack initiation. However, interaction of the crack tip with microstructural barriers, such as, e.g. grain boundaries or second phases, leads to a decrease and eventually to a stop in the crack propagation. In the present contribution, examples for propagating and non-propagating conditions of short fatigue cracks in the microstructure of a duplex steel are given, quantified by means of automated EBSD. To classify the results within the scope of predicting the service life for HCF- and VHCF-loading conditions, a numerical model based on the boundary element method has been developed, describing crack propagation by means of partially irreversible dislocation glide on crystallographic slip planes in a polycrystalline model microstructure (Voronoi cells). This concept is capable to account for the strong scattering in fatigue life for very small strain amplitudes and to contribute to the concept of tailored microstructures for improved cyclic-loading behaviour.     

DEM simulation of the packing structure and wall load in a 2-dimensional silo

The filling and discharge of a two-dimensional wedged-bottom silo holding circular objects was modelled using DEM technique to examine the influence of method of silo filling on distribution of orientations of unit vectors normal to contact points (contact normals) and normal contact forces. It was found that packing structure determined through method of generation of grain bedding significantly influenced distribution of contact normals. Nearly hexagonal network of contact normals was obtained for central filling of silo while sprinkle filling provided higher anisotropy of contact normals. The significance of frictional conditions and number of particles in system on distribution of contact normals was analysed. Increase in number of grains reduced disturbance from boundaries on behaviour of assembly. Distribution of loads on silo bottom obtained in simulation for different wall roughness was found in qualitative agreement with experimental data.     

A multiscale approach and microstructure design of the elastic composite behavior reinforced with natural particles

The morphology characterization and computational methods favored numerical simulation and design of microstructures. Indeed, the multiscale approaches enable us to determine the elastic properties of materials. In this paper, the objective is to develop a three-dimensional microstructure of biocomposites containing natural particles. The biocomposite is made of polypropylene matrix mixed with natural fillers. The image is obtained using the microscope. We describe a serial sectioning process and finite element simulations to reproduce, visualize and model these microstructures. Statistical methods are introduced to study the representativity of specimen. The statistical representative volume element is introduced to determine the minimum volume which provides the representativeness. This statistical volume is compared with experimental and numerical ones.     

A numerical study of the similarity of fully developed laminar flows in orthogonally rotating rectangular ducts and stationary curved rectangular ducts of arbitrary aspect ratio

 The present study showed that a quantitative analogy of fully developed laminar flow in orthogonally rotating rectangular ducts and stationary curved rectangular ducts of arbitrary aspect ratio could be established. In order to clarify the similarity of the two flows, the dimensionless parameters K _LR=Re/(Ro)^1/2 and the Rossby number, Ro=w _m /Ωd _h , in a rotating straight duct were used as a set corresponding to the Dean number, K _LC=Re/λ^1/2, and curvature ratio, λ=R/d _h , in a stationary curved duct. Under the condition that the value of the Rossby number and the curvature ratio was large enough, the flow field satisfied the `asymptotic invariance property'; there were strong quantitative similarities between the two flows such as in the friction factors, flow patterns, and maximum axial velocity magnitudes for the same values of K _LR and K _LC. Based on these similarities, it is possible to predict the flow characteristics in rotating ducts by considering the flow in stationary curved ducts, and vice versa. Received: 10 September 2001 / Accepted: 13 May 2002