Evaluation of cross-stream sample cutters using three-dimensional discrete element modelling

The quality of samples taken by cross-stream sample cutters has been investigated using three-dimensional DEM models. The sample configurations investigated here are full-size high-flow-rate configurations typical of mineral and bulk materials applications. Detailed quantitative information on overall extraction ratios, size specific extraction ratios, missed and extra sample components can be made by comparing a reference sample to the actual sample. A key advantage of using this modelling approach over physical experimentation is that the reference sample can be measured on precisely the same portion of the stream of material as the actual sample, thereby allowing the elimination of a significant fraction of the variability and allowing statistically significant results to be obtained using many fewer replicates. Quantitative analysis of results broadly supports the commonly used rule that the cutter aperture should be at least three times the nominal topsize of the material being sampled, but does not support the commonly used rule requiring increase in cutter aperture if the cutter speed exceeds 0.6 m/s. It also provides some insights into linkages between the nature of the flows through this sampling equipment and the nature of the samples obtained.     

Sampling of cohesive bulk materials by falling stream cutters

DEM has proved to be a useful method for analysing sample bias for falling stream cutters. It provides detailed information on bias and size-dependant extraction ratios based on closely matched reference and actual samples taken from the same simulations. It has allowed the identification of operational and design parameters which influence sample cutter performance and bias. To date, only cohesionless bulk materials have been considered. Wet bulk materials typically become sticky and this strongly influences their flow behaviour and particularly the mobility of fine particles and the overall flowability of the material. The inclusion of cohesion in DEM simulation of flow from a head pulley shows that the falling stream breaks up into large fragments that move as rigid bodies. The size of these fragments depends on the degree of cohesion. The effect of cohesion on sampler performance is explored. No statistically significant bias was observed with increasing cohesion level even though the extraction ratio was observed to decline. The effect of cohesion for different aperture sizes of the cutter was also investigated. As the cutter becomes narrower the extraction ratio declines sharply. However, even for a cutter of aperture twice the particle top size (which would be highly biased for a cohesionless material) no bias was detectable. For cohesive materials the extraction ratio no longer correlates with sample bias. Cohesion improves sample cutter performance by restricting the ability of different size fractions to move independently in the congested flow region that forms at the cutter opening.     

Analysis of Vezin sampler performance

Vezin samplers are used to take a small fraction of a stream of material which is intended to be representative of all the material. Discrete Element Modelling (DEM) is used to investigate the effects of design, operating and material property factors on the extraction ratio and sample properties and to understand the mechanisms that can lead to sample bias when using a Vezin. This modelling suggests that this type of sampler performs very well giving a very good extraction ratio and negligible sample bias over a wide range of conditions.     

Numerical simulation of breakage of two-dimensional polygon-shaped particles using discrete element method

Using DEM (Discrete Element Method), a model is presented to simulate the breakage of two-dimensional polygon-shaped particles. In this model each uniform (uncracked) particle is replaced with smaller inter-connected sub-particles which are bonded with each other. If the bond between these sub-particles breaks, breakage will happen. With the help of this model, it is possible to study the influence of particle breakage on macro and micro mechanical parameters. In this simulation, the evolution of microstructure in granular assemblies can be seen by tracing of coordination number during the shear process. Also variation of contact normal, normal force and tangential force anisotropy can be tracked. To do so, two series of biaxial test simulations (breakage is enabled and disabled) are conducted on assemblies of two-dimensional polygon-shaped particles and the results are compared. The results are presented in terms of macro and micro mechanical behavior for different confining pressures.     

Validation and experimental calibration of 3D discrete element models for the simulation of the discharge flow in silos

The aim of the present work was to develop 3D discrete element models capable of simulating the observed flow of glass beads (simple glass spheres) and maize grains (represented as a combination of spheres) during their discharge from a small model silo. A preliminary model for each material was constructed based on values for variables measured in the laboratory or taken from the literature. The ability of the models to predict the flow of these materials was then tested by comparing their results with observed discharge flows. Three variables were recorded for this: the mean bulk density at the end of the filling phase, the discharge rate and the flow pattern. The comparison of the results for the last of these variables required the discharge process be filmed using a high speed camera in order to more easily recognise the details of the flow. The preliminary model for the glass beads made very reasonable predictions, but that for the maize grains required calibration. This involved modifying the values of the friction properties of the material until a model capable of making acceptable predictions was obtained. The results obtained highlighted the influence of friction properties on the characteristics of the discharge flow. Finally, some of the numerical results provided by the models were analysed in order to describe the flow characteristics and the behaviour of the discharge rate in more detail.     

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.     

Speed-up of computing time for numerical analysis of particle charging process by using discrete element method

The objective of this paper is to improve the computing time for numerical analysis of particle charging process by using discrete element method. The rule for ignoring the calculations of contact forces and updating trajectories of unmoved particles were discussed. When the relative displacement of a particle within certain calculation steps became less than 0.1% of particle radius, this particle was determined to be unmoved and the calculations of this particle were ignored. The computing time was improved significantly when this new method was used, and its calculation speed was more than two times faster than that of original. It was found that this speed-up method is more useful for the cases that the particle becomes unmoved in short time or the height of charged bed is large. The simulation of charging process in an industrial-scale surge hopper was studied by using new method, the calculation speed became 2.88 times faster than that of original, and the quite similar particle size segregation between original and new methods was given. This new method for speed-up of the charging process in DEM is very useful, and the charging processes of the industrial scale storages can be simulated by using this method.     

Predicting discharge dynamics of wet cohesive particles from a rectangular hopper using the discrete element method (DEM)

Accurate prediction of the discharge rate from hoppers is important in many industrial processes involving the handling of granular materials. The present work investigates the parameters affecting the discharge rate of a wet cohesive system from a quasi-3-D, rectangular hopper using the discrete element method (DEM). The cohesion between the particles is described by a pendular liquid bridge force model and the strength of the cohesive bond is characterized by a Bond number. The Beverloo correlation is applied to cohesive systems by modifying the Beverloo constant as a function of Bond number. The predictions obtained from this modified correlation fit the simulation data reasonably well. In addition, the effect of hopper angle in cohesive systems is shown to follow a trend similar to cohesionless systems, where the discharge rate is insensitive to changes in hopper angle except below a critical angle (with respect to the vertical) where the discharge rate increases rapidly. This critical angle of flow decreases with increasing cohesion.     

A study on tangential force laws applicable to the discrete element method (DEM) for materials with viscoelastic or plastic behavior

The discrete element method is a widely used particle orientated simulation approach for modeling granular systems. It is based on tracking each particle's movement and its interactions with the surroundings over time. The motion of a particle is given by a system of coupled ordinary differential equations which are solved numerically. Therefore, models for the forces acting between particles in contact need to be specified. In the past, detailed investigations dealing with the accuracy of tangential force-displacement models have been very limited, with sparse experimental data considered and the frequent restriction of including only fully elastic materials. In large scale discrete element simulations, on the other hand, viscoelastic or plastic material behavior is often assumed for normal contacts and combined with arbitrary tangential models. To address this situation a number of tangential force-displacement models are reviewed including linear models by Cundall and Strack [1979. A discrete numerical model for granular assemblies, Geotechnique 29, 47-65], Di Maio and Di Renzo [2004. Analytical solution for the problem of frictional-elastic collisions of spherical particles using the linear model. Chemical Engineering Science 59(16), 3461-3475], Brendel and Dippel [1998. Lasting contacts in molecular dynamics simulations. In: Herrmann, H.J., Hovi, J.-P., Luding, S. (Eds.), Physics of Dry Granular Media, Dordrecht. Kluwer Academic Publishers, pp. 313], Walton and Braun [1986. Viscosity, granular temperature and stress calculations for shearing assemblies of inelastic, frictional disks. Journal of Rheology 30, 949] and simple non-linear models by Brilliantov et al. [1996. Model for collisions in granular gases. Physical Review E 53(5), 5382-5392], Tsuji et al. [1992. Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe. Powder Technology 71, 239-250] and Di Renzo and Di Maio [2005. An improved integral non-linear model for the contact of particles in distinct element simulations. Chemical Engineering Science 60(5), 1303-1312]. Whereas for fully elastic materials the parameters of the tangential force-displacement models can be derived directly from mechanical properties a scaling approach is proposed for the estimation of the parameters in the non-elastic case. The effect of different normal force-displacement models is analyzed. For all model combinations macroscopic final collision properties are derived and compared to experimental results by Foerster et al. [1994. Measurements of the collision properties of small spheres. Physics of Fluids 6(3), 1108-1115], Lorenz et al. [1997. Measurements of impact properties of small, nearly spherical particles. Experimental Mechanics 37(3), 292-298], Gorham and Kharaz [2000. The measurement of particle rebound characteristics. Powder Technology 112(3), 193-202] and Dong and Moys [2003. Measurement of impact behaviour between balls and walls in grinding mills. Minerals Engineering 16(6), 543-550; 2006. Experimental study of oblique impacts with initial spin. Powder Technology 161(1), 22-31].     

Comparison of the multi-sphere and polyhedral approach to simulate non-spherical particles within the discrete element method: Influence on temporal force evolution for multiple contacts

In this paper a multi-sphere as well as a polyhedral approach is investigated as method of shape-approximation within the discrete element method. The two approaches are compared against each other using an ellipsoidal particle impacting on a flat wall as a reference scenario. In general it is shown that there is a non-negligible effect of shape approximation on the temporal force evolution in normal and tangential direction. The occurrence of multiple contacts between the particles when approximated by a multi-sphere or a polyhedral approach is detected as a main source of differences between the exact solution and the solution of the approximated particles. A method to account for these effects is provided in order to increase the accuracy when complex particle shapes are used. Moreover the effect of shape-approximation accuracy on the accuracy of the results is investigated. For both approximation procedures higher accuracy levels in terms of particle shape representation do not automatically lead to more accurate results for normal and tangential forces in the investigated collision scenarios. It will be shown that the effects of a more accurate ellipsoid-surface approximation and higher numbers of contact points influence the quality of the results in opposite directions.