U. Tüzün

Discrete element simulation of granular flow in 2D and 3D hoppers: Dependence of discharge rate and wall stress on particle interactions

Abstract Discrete element Newtonian dynamics simulations have been carried out of filling and discharge under gravity of non-cohesive discs (in two dimensions) and spheres (in three dimensions) from model hoppers. The current model improves that developed previously by us (Langston et al. , 1994) in several respects. We introduce a continuous and gradual hopper filling method, a more realistic normal-tangential interaction between the particles, particle size polydispersity, and the model is extended from two to three dimensions (3D). The hopper discharge rate has been computed as a function of material head height, outlet size and the hopper half-angle. The model results are, in general, in very good agreement with established literature empirical predictions. The hopper wall stresses have been compared in the static state after filling and in the dynamic state during discharge. Generally there is encouraging agreement with predictions from the continuum differential slice force balance method, with significant improvements over our previous work. We have also observed, for the first time in a discrete element simulation of hoppers, the appearance of rupture zones within the material and associated wall stress peaks where the rupture zones intersect with the hopper wall. We consider that the current model is more successful than the previous one because the particle interactions include a much greater level of frictional “engagement” at low loads, with less variation at high loads.

Modelling and measuring of cohesion in wet granular materials

Using a Cohesive Discrete Element Method (CDEM), three-dimensional simulations have been performed to investigate the internal tensile stress and the tensile strength and shear strength of fine, cohesive granular materials. Interparticle cohesion is taken into account by modelling liquid bridges in pendular state. The influence of surface roughness is considered by a minimum separation distance of the particles with respect to liquid bridges. Agglomerates of mono-sized spheres have been formed to measure the stress caused by liquid bridges. A good general agreement with Rumpfs equation is demonstrable, and divergences may be explained by the existence of stretched bridges. Spheres and more complex particle shapes have been used for shear and tensile test simulations. Applying negative loads, the yield loci in the tensile range could be measured successfully. A comparison with experimental ring shear tests on glass beads demonstrates a good agreement.

Continuous potential discrete particle simulations of stress and velocity fields in hoppers: transition from fluid to granular flow

A number of numerical hopper discharge experiments were conducted using a novel simulation technique in which the individual circular disc particles are allowed to fill a two-dimensional hopper under gravity and are subsequently discharged through a central slot orifice. The novel aspect of the present technique is the incorporation of a continuous otential interaction for frictional granular flows which ensures the stability of contact mechanical force algorithms over much larger time steps than were hitherto possible. This is achieved by allowing softer interactions which vary on the same scale as the nominal particle size rather than the micro-contact scale used in the majority of previous literature. The resulting technique allows the filling and discharge events to be simulated over a sufficiently long time scale. The continuous potential confers on the particles an “excluded volume” which prevents excessive overlap. In addition, the effects of frictional forces are introduced via a tangential displacement vs force model similar to that developed by Mindlin for contacts of perfectly elastic spheres, but scaled to the normal potential interaction. Transition from fluid-like to granular flow is simulated by increasing the friction coefficient from zero. During both the filling and discharge stages of the simulation, the radial and tangential components of particle velocities are damped by a force proprotional to the relative particle velocities. The effects of material head in the hopper, the outlet size and the hopper half-angle were investigated to predict material discharge rates as well as the wall stress profiles during both filing and discharge. The effects of the ratio of the interparticle and wall friction coefficients on the prevailing flow and stress fields wree also investigated in both “mass-flow” and “funnel-flow” hoppers. Encouraging agreement was found between the simulation and experimental flow behaviour.

Discrete element simulation of internal stress and flow fields in funnel flow hoppers

Abstract Newtonian dynamics simulations have been carried out for the filling and discharge of funnel flow hoppers under both plane-strain (2D) and axially-symmetric (3D) conditions using assemblies of the order of 10 4 particles. The present work follows directly from our previous discrete element simulations which were used to predict discharge rates and hopper wall stresses. In this paper, we concentrate on the prediction of the internal and wall distributions of the normal and tangential components of the bulk stresses, distributions of particle velocities and interstitial voidage in both static and flowing (dynamic) conditions. In order to illustrate the effects on the bulk phenomena of different particle interaction laws, simulations have been carried out contrasting (i) Hertz-type (elastic) interaction which simulates well nearly rigid particles at high normal loads with (ii) a soft continuous interaction which allows for significant frictional engagement between particles at very small normal loads similar to the conditions known to prevail near the hopper outlet during discharge. A non-intrusive local averaging technique was developed to compute bulk stresses from the values of local interparticle contact stresses which allowed us to monitor the changes in the orientation of the major principal normal stress as well as the magnitude of the shear stress in different hopper sections. Distributions of contact tangential displacement vectors have been computed to compare the frequency of rupture zones (i.e. high shear regions) in both plane-strain and axial-symmetric flows. Corresponding maps of particle velocity vectors have also been generated to provide information about slow and fast moving regions of the flow fields and the extent of bulk dilation accompanying flow. The internal flow patterns and distributions of high shear regions are shown to be affected significantly by the nature of the particle interaction law chosen with softer interactions giving rise to more well-developed rupture zones in both plane-strain and axial-symmetry. In some contrast, the internal distribution of the bulk normal stress is affected very little by the choice of the particle normal force interaction law.

Stratification in poured granular heaps

The stratification of poured granular mixtures into layers according to particle size has long been identified as an important mechanism by which such materials segregate,. The implications of this effect for the process industries have also been discussed,. Makse et al. suggestthat stratification takes place only when there is a marked difference in the shape of large and small grains; specifically, when the angle of repose of the coarse phase is much greater than that of the fines. Our experiments show that stratification can occur in the absence of such heterogeneity of particle shapes within the mixture.

Three-dimensional particle shape descriptors for computer simulation of non-spherical particulate assemblies

Recent advances, accelerated by the application of computer technology, allow numerical characterization of particle shape in two dimensions. However, characterization of three-dimensional (3D) particle shapes is still largely an unresolved problem. Here, 3D pseudo-shape descriptors are proposed for characterising the particle shapes. The microscopic characteristics are recorded using a computer-based image analysis system to assess particle shape. The particle shapes are based on the complete coverage by a set of images of the particle projections in three mutually perpendicular directions. The circularity of particle projections in each plane was measured in turn and found to be suitable for particle shape estimation. Analogues of the resulting 3D pseudo-shapes are constructed for the purposes of computer simulation of non-spherical particulate assemblies. Preliminary results of the simulation work are illustrated.

Distinct element simulation of interstitial air effects in axially symmetric granular flows in hoppers

Two-phase flow of interstitial air in a moving packed bed of granular solids is modelled using a distinct element (DE) technique which considers the Newtonian dynamics of particle motion passing through a radial flow field of air in a mass flow hopper. The air flow is assumed to be incompressible and the mass flux of air at any height within the hopper is assumed to be constant. These assumptions allow the simulation of air-retarded and air-assisted flows in mass flow hoppers without the need for an extensive development of the momentum balance calculations on an Eulerian fixed gird. The particle-particle and particle-hopper wall interactions are modelled using a Hertizian interaction law and a contact friction algorithm of the Mindlin analytic form (Langston et al., 1995, Chem. Engng Sci.50, 967). Predictions of discharge rates in both air-retarded and air-assisted flows are compared with the continuum mechanics calculations based on the steady-state flow assumption. The DE simulation results indicate certain transient and oscillatory features of the flow fields which have not hitherto been demonstrated by the continuum theories. Furthermore, it is shown that air-assisted flow leads to increased wall stresses which reduce the bulk solids discharge rate for discharge through small orifices.

Microstructural simulation and imaging of granular flows in two- and three-dimensional hoppers

Abstract Distinct element simulations of granular flows in two- and three-dimensional hoppers are compared with imaging data from conventional photography and gamma-ray tomography where information of the order of the particle size can be extracted. A novel feature of these comparisons is that both particle and vessel dimensions are matched exactly between the experiments and the computer simulations, thereby leaving little scope for speculation regarding śscale effects’ which are often used to justify scepticism over the validity of simulation predictions. Another novel feature of the work is that quantitative comparisons are provided during the entire period of filling and discharge events rather than selecting an arbitrary ‘snapshot’ in time, as is often the case in such simulation studies. Microstructural inspection of two-dimensional photographs of systems with large disc particles provides quantitative information which shows good agreement with simulation in terms of packing height, static and flowing voidage, stagnant/flow boundaries in funnel flow and heap/repose angles. Three-dimensional solids fraction data from packed beds of 7 mm diameter maple peas obtained by transmission gamma-ray tomography show encouraging agreement with simulation. An important result of these investigations is the degree of correlation between the flowing voidage and flow velocity of particles which are individually both affected by variations in particle size and shape but are mutually compensating in their effects on the simulated and measured discharge rates. In general, the simulations produce a less dilated assembly moving at smaller velocities.

A single-particle friction cell for measuring contact frictional properties of granular materials

Abstract A novel shear cell has been developed which allows for simultaneous measurements of the contact stresses and surface displacements during the sliding motion of a single particle against either another particle or a substrate representing a wall surface. Internal and wall friction behaviour of particles down to 500 μm in size were quantified by inducing relative displacements of contact surfaces over a range of 30 μm in steps of 0.1 μm, while measuring the resulting normal and shear forces at the contact to an accuracy of 0.01 N. Experiments were performed to determine the normal and tangential compliance of the test materials during the micro-slip of contact surfaces, leading to the gross sliding limit of friction. The results are compared with predictions based on the Theory of Elastic Contacts. Significant non-elastic behaviour is found to result during tangential loading of the contact region at high normal loads even when the normal load compliance is perfectly elastic. This result is believed to have important implications in the flow simulations of granular materials based on contact mechanics. Further tests were performed to quantify the normal load dependence of the internal and wall friction coefficients measured at the gross sliding limit. These measurements are interpreted using the Adhesion Model of Friction.

Examining nanoparticle assemblies using high spatial resolution x-ray microtomography

An experimental system has been designed to examine the assembly of nanoparticles in a variety of process engineering applications. These applications include the harvesting from solutions of nanoparticles into green parts, and the subsequent sintering into finished components. The system is based on an x-ray microtomography with a spatial resolution down to 5μm. The theoretical limitations in x-ray imaging are considered to allow experimental optimization. A standard nondestructive evaluation type apparatus with a small focal-spot x-ray tube, high-resolution complementary metal oxide semiconductor flat-panel pixellated detector, and a mechanical rotational stage is used to image the static systems. Dynamic sintering processes are imaged using the same x-ray source and detector but a custom rotational stage which is contained in an environmental chamber where the temperature, atmospheric pressure, and compaction force can be controlled. Three-dimensional tomographic data sets are presented here for sample...