Cross-sectional and axial flow characteristics of dry granular material in rotating drums

Cross-sectional and axial flow behaviors of dry granular material in rotating drums are closely related to the dynamic characteristics and velocity distributions between the surface layer and bed material. In this study, both 2D and 3D dry granular flow patterns in horizontal rotating drums are experimentally investigated with flow imaging analysis. A dimensionless flow parameter combining the effects of Froude number, relative particle size and volume filling is proposed in this study, which controls the flow characteristics in a rational drum such as dynamic angle of repose, thickness of the flowing layer, relative free surface velocity, and the shear rates in the flowing layer. The dimensionless granular temperature exhibits linear distribution in the flowing layer, being maximum at the free surface and being negligible at the interface in the rolling regime. The measured shear rate of the plug flow departs from drum angular velocity under the wall slip conditions when the drum surface is smooth. Due to the existence of axial convection and lateral surface profile, the mass flux in the flowing layer is always less than that of the plug flow in the 3D granular flows based on sidewall particle images. One the other hand, the mass flux in the flowing layer is always equal or greater than that of the plug flow in the 2D granular flows. 2D granular flows exhibit higher angles of repose and surface velocities than those of the 3D granular flows at the same volume fillings.     

A simulation of Cr depletion in austenitic stainless steel with cellular automaton

A cellular automaton modeling was developed to investigate the growth kinetics of Cr-rich carbides’ precipitation and the three dimensional distribution of Cr concentration. The effects of solution treatment conditions and sensitization temperatures on Cr depletion were studied in detail. The results indicated that the amount of precipitate increased as sensitization temperature increased, decreasing along with the solution treatment temperature. Furthermore, the changing tendency of the precipitate’s amount was in accordance with that of the degree of sensitization (DOS) obtained from the samples treated at the corresponding conditions.     

Microstructural modelling of dynamic recrystallisation using an extended cellular automaton approach

Dynamic recrystallisation (DRX) governs the plastic flow behaviour and the final microstructure of many crystalline materials during thermomechanical processing. Understanding the recrystallisation process is the key to linking dislocation activities at the mesoscopic scale to mechanical properties at the macroscopic scale. A modelling methodology coupling fundamental metallurgical principles with the cellular automaton (CA) technique is here derived to simulate the dynamic recrystallisation process. Experimental findings of a titanium alloy are considered for comparison with theory. The model takes into account practical experimental parameters and predicts the nucleation and the growth kinetics of dynamically recrystallised grains. Hence it can simulate different stages of microstructural evolution during thermomechanical processing. The effects of hot working temperature and strain rate on microstructure were studied, and the results compared with experimental findings.     

Coexisting static and flowing regions in a centrifuging granular heap

We report an unexpectedly rich variety of new flow patterns on a granular heap that is centrifuged so as to simulate a reduction in gravity. These surface patterns exhibit coexisting static and flowing regions that depend strongly on centrifugal stress, but surprisingly not on mass flow rate. A discrete cellular automata model reproduces some of the patterning features and indicates that subsurface jamming may precipitate the formation of localized frozen patterns on the surface. This model provides insights into the mechanics of granular flows under controlled stress environment and jammed-to-flowing transitions in granular media.     

Testing steady and transient velocity scalings in a silo

Gravity-driven discharge experiments were performed in a perspex 3D flat bottomed silo which was filled with a granular material, and had a variable discharge orifice size. The granular material used was amaranth seed with an average diameter of 1?mm. Particle Image Velocimetry (PIV) analysis was performed on a high-speed video recording of the discharge, and used to quantify the velocity field within the silo both at steady state and during the development of flow. We verified not only that the steady-state velocity of the granules in the silo scales with the flow rate, but, additionally, the transition to a steady-state regime is also rate-controlled by the volumetric discharge. We present evidence that, away from the discharge orifice, the flow behaves identically, regardless of the orifice diameter, in a scaled time. We discuss these results with reference to the physics and mathematical modelling of granular flows.     

Discrete-particle simulations of cohesive granular flow using a square-well potential

In the present study, rapid granular flows with attractive inter-particle forces are investigated. In particular, cohesive forces are incorporated into hard-sphere (molecular dynamics) simulations via a square-well potential. The square-well potential treats cohesive forces as both binary and instantaneous. For simple shear flows, an investigation of the input parameter space indicates that two distinct flow regimes are present. For relatively large cohesive forces, the formation of a large, single agglomerate is observed. For moderate cohesive forces, the sheared system is composed of mostly 2-particle, dynamic agglomerates that are fairly evenly distributed throughout the domain. Furthermore, the results for this latter regime indicate that cohesion attenuates the magnitude of the stress components at higher solids fractions (in the collisional regime) as compared to the non-cohesive case. At lower solids fractions (kinetic regime), however the presence of cohesive forces has little impact on the observed stress.The authors would like to thank the U.S. Department of Education GAANN Program in Microparticle and Nanoparticle Technology (Grant No. P2004980454) and the U.S. Department of Energy National Energy Technology Laboratory (via subcontract from Ames National Laboratory) for funding support. The Ames Laboratory is operated for the Department of Energy by Iowa State University under Contract No. W-7405-ENG82.     

Mixing experiments in 3D-printed silos; the role of wall friction and flow correcting inserts

The mixing of particles during silo discharge is of high industrial significance, yet quantitative studies of this process in literature are few. Here we present experimental measurement of particle mixing in 3D-printed silos during complete discharge, accounting for hopper half angle, the wall condition, and the addition of flow correcting inserts. Mono-sized mustard seed are dyed one of two colours (yellow or blue) to enable them to be distinguished during a step-change experiment. The silo is partially filled with yellow particles, followed by an equal mass of blue, then discharged onto a rotating table apparatus which automatically collects particle samples for proportion analysis. The experiments are repeated for six hopper half angles, and for three different wall conditions of different smoothness. Finally, three flow correcting inserts are added to a silo to quantify their influence. It is found that, while the wall condition has a large influence on the mixing and the size of the stagnant “pocket” region (the non-flowing region in a funnel-flow silo), the addition of flow correcting inserts has the greatest effect in reducing mixing and pocket region size. Our method of completely discharging the silo has the advantage that the pocket region mass can be easily quantified, in contrast to classical continuous flow residence-time experiments.     

A note on the velocity of granular flow down a bumpy inclined plane

The velocity distribution of granular flow down a bumpy inclined plane is theoretically studied. The characteristic length scale of local transient cluster plays an important role in determining the flow rheology. After discussing the factors influencing the cluster size, we reproduce all observed velocity distributions successfully.This research was supported by the National Key Basic Research and Development Foundation of the Ministry of Science and Technology of China No. G2000048702.     

The flow rate of granular materials through an orifice

The flow rate of grains through large orifices is known to be dependent on its diameter to a 5/2 power law. This relationship has been checked for big outlet sizes, whereas an empirical fitting parameter is needed to reproduce the behavior for small openings. In this work, we provide experimental data and numerical simulations covering a wide span of outlet sizes, both in three- and two-dimensions. This allows us to show that the laws that are usually employed are satisfactory only if a small range of openings is considered. We propose a new law for the mass flow rate of grains that correctly reproduces the data for all the orifice sizes, including the behaviors for very large and very small outlet sizes.     

Cellular automata model of gravity-driven granular flows

A cellular automata model is used to simulate a variety of granular chute flows. The model is tested against several case studies: flow down a chute, flow past an obstacle, chute flow in which complex, counter-rotating vortices result in streamwise surface stripes and flow near a boundary. The model successfully reproduces experimental observations in all of these cases. These results lead us to propose that simple, rule-based, models such as this can improve our detailed understanding of dynamics and flow within an opaque granular bed.     

DEM study of monodisperse granular flow in a pipe

Flow of granular material through a pipe has several industrial applications but maintaining a uniform mass flux is quite challenging. In this work, monodisperse granular flow (non-turbulent and non-dense phase particle transport) through a vertical pipe was simulated using discrete element method (DEM). Effects of different geometric and granular parameters on mass flux of cohesive and non-cohesive solids were analyzed and evaluated. Several important parameters and their effects on mass flux were studied like: L/D ratio, pipe diameter to particle diameter ratio (D/D_p), Poisson ratio, and pipe inclination angle. Furthermore, effects of moisture content and Bond number on mass flux were also investigated. These parameters influenced mass flux except Poisson ratio which showed no significant improvement in mass flux upon increasing the value of this ratio.     

Simulations for dynamics of granular mixtures in a rotating drum

We present a simple model and carry out simulations to investigate the dynamics of mixtures of granular material within a rotating drum. On the basis of the commonly held belief (supported by considerable experimental evidence) that segregation is due to motion of particles on the active layer, the bulk playing little or no role, we introduce a 2d lattice gas model which takes into account the rotational frequency, frictional forces, and the gravitational field, and represents segregation tendencies via activated effective grain-grain interactions. Our results include the onset of segregation perpendicular to the drum axis, the appearance and subsequent coarsening of bands and peculiarities of the effects of periodic modulation of the drum. Observed effects such as the segregation of rougher (smoother) particles into the bellies (necks) of the modulation are reproduced by our simulation. Received: 30 March 2000     

Steady-state granular flow in a 3D cylindrical hopper with flat bottom: macroscopic analysis

The information of a hopper flow at a particle scale, obtained from discrete particle simulation, is used to investigate the macroscopic dynamic behaviour of granular flow in a cylindrical hopper with flat bottom by means of an averaging technique. The macroscopic properties including velocity, mass density, stress and couple stress are quantified under the cylindrical coordinate framework, and an effort is made to link these variables to the microscopic variables considered. The velocity and density distributions are first illustrated to match qualitatively the experimental and numerical results, confirming the validity of the proposed averaging method. Four components of stress, T_zz, T_rr, T_rz and T_zr, and two dominant components of couple stress, M_{r θ} and M_{z θ}, are then investigated in detail. It is shown that large vertical normal stress is mainly observed in the region close to the bottom corner, large radial normal stress is observed within the particle bed as well as the bottom corner, and large shear stresses in the region adjacent to the vertical wall. The four stresses are relatively small in a region close to the orifice. Their magnitudes are mainly contributed by the interaction forces between particles and between particles and walls. However, the transport of particles also plays a significant role at the orifice, especially, in the vertical normal stress. The couple stress can be ignored except for the regions close to the vertical and bottom walls, where the most dominant components are M_{r θ} adjacent to the vertical wall and M_{z θ} close to the bottom wall. The magnitudes of these macroscopic variables depend on the geometric and physical parameters of the hopper and particles such as the orifice size and wall roughness of the hopper, and the friction and damping coefficients between particles although their spatial distributions are similar.     

Dual imaging modality of granular flow based on ECT sensors

In this study, a previously developed dual modality imaging system is applied to image the flow of granular matter with different electrical properties in cylindrical vessels. The imaging system is based on both capacitance and power measurements acquired by an electrical capacitance tomography (ECT) sensor located around the vessel. The measurement data are then used to reconstruct cross-sectional images of both permittivity and conductivity distributions. A neural network multi-criterion optimization reconstruction technique (NN-MOIRT) is used for the inverse (reconstruction) problem. The contribution of this technology to the field of granular matters is explored through review of research articles that can be a direct application of this development. We discuss the capabilities of this dual-modality acquisition system using synthetic data for granular matter with different electrical properties.     

Stratification of granular matter in a rotating drum: cellular automaton modelling

We propose a generalisation of the cellular automaton model introduced recently by Lai, Jia and Chan [Phys. Rev. Lett. 79, 4994 (1997)] for simulating friction induced segregation in a rotating drum. Our model implements the spherical geometry of the drum explicitly. Therefore it can be used to investigate geometrical properties of the segregation phenomenon in contrast to the original version of the model. Our model reproduces the spontaneous stratification observed recently in experiments for more than half filled drums, as well as the transition to non-stratified segregation for higher rotation speeds. It predicts that stratification can also occur, if the drum is less than half filled.     

The dynamics of granular flow in an hourglass

We present experimental investigations of flow in an hourglass with a slowly narrowing elongated stem. The primary concern is the interaction between grains and air. For large grains the flow is steady. For smaller grains we find a relaxation oscillation (ticking) due to the counterflow of air, as previously reported by Wu et al. [Phys. Rev. Lett. 71, 1363 (1993)]. In addition, we find that the air/grain interface in the stem is either stationary or propagating depending on the average grain diameter. In particular, a propagating interface results in power-law relaxation, as opposed to exponential relaxation for a stationary interface. We present a simple model to explain this effect. We also investigate the long-time properties of the relaxation flow and find, contrary to expectations, that the relaxation time scale is remarkably constant. Finally, we subject the system to transverse vibrations of maximum acceleration Γ. Contrary to results for non-ticking flows, the average flow rate increases with Γ. Also, the relaxation period becomes shorter, probably due to the larger effective permeability induced by the vibrations. Received: 11 February 2000     

Capturing the dynamics of a two orifice silo with the μ(I) model and extensions

Granular material in a silo with two openings can display a ‘flow rate dip’, where a non-monotonic relationship between flow rate and orifice separation occurs. In this paper we study continuum modelling of the silo with two openings. We find that the $\mu \left(I\right)$ rheology can capture the flow rate dip if physically relevant friction parameters are used. We also extend the model by accounting for wall friction, dilatancy, and non-local effects. We find that accounting for the wall friction using a Hele-Shaw model better replicates the qualitative characteristics of the flow rate dip seen in experimental data, while dilatancy and non-local effects have very little effect on the qualitative characteristics of the mass flow rate dip. However, we find that all three of these factors have a significant impact on the mass flow rate, indicating that a continuum model which accurately predicts flow rate will need to account for these effects.     

Velocity depth profile of granular matter in a horizontal rotating drum

Using MRI velocimetry, we verify that the velocity depth profile of the flowing layer near the axial center of a half-filled 3D drum has the form V _m[1 − (r/r ₀)²]-Ω r, where r is the depth measured from the cylinder center, except very close to the free surface where it lies below the quadratic form. We confirm that this deviation is due in part to particles reaching the surface with large components of their velocity in the azimuthal direction. We used a 3D cylinder with a radial “paddle” placed at approximately the dynamic angle of repose, covering the top third of the flow, so as to null any azimuthal velocity. It was found that the deviation from the quadratic form was reduced by the presence of the paddle when the comparison is made at the same solid body rotation rate, at the same free surface velocity, and with the paddle placed at different positions, so long as it makes good contact with the surface. Thus, we conclude that a quadratic velocity depth profile may be a fundamental property of granular shear flows in this geometry, when the sole effect of the cylinder rotation is to transport the particles from the end of the flow to the beginning without imparting velocity perpendicular to the flow.     

Localized instability of a granular layer submitted to an ascending liquid flow

Using a very simple experimental setup, we study the response of a thin layer of immersed granular material to an ascending liquid-flow; a pressure difference Δ P is imposed between the two horizontal free surfaces of a thin layer of glass beads, such that the liquid tends to flow upwards, and the resulting flow-rate v is measured. As generally observed in fluidized beds, the layer destabilizes when the pressure force exactly compensates the weight of the grains. At the free surface, one then observes the formation of a localized fountain of granular material the characteristic size of which is found to be proportional to the grain size and, surprizingly, independent of both the flow-rate and the thickness of the granular layer. Simple theoretical arguments account for the main experimental features.