Discrete particle simulation of particulate systems: A review of major applications and findings

▪ Abstract Granular materials segregate. Small differences in either size or density lead to flow-induced segregation, a complex phenomenon without parallel in fluids. Modeling of mixing and segregation processes requires the confluence of several tools, including continuum and discrete descriptions (particle dynamics, Monte Carlo simulations, cellular automata computations) and, often, considerable geometrical insight. None of these viewpoints, however, is wholly satisfactory by itself. Moreover, continuum and discrete descriptions of granular flows are regime dependent, and this fact may require adopting different subviewpoints. This review organizes a body of knowledge that forms—albeit imperfectly—the beginnings of an expandable continuum framework for the description of mixing and segregation of granular materials. We focus primarily on noncohesive particles, possibly differing in size, density, shape, etc. We present segregation mechanisms and models for size and density segregation and introduce ch...

Mixing and Segregation of Granular Materials

The transverse motion of solids in rotating cylinders—forms of motion and transition behavior

Slumping and rolling beds have been studied extensively in a continuous pilot kiln and batch rotary cylinders. Solids investigated include nickel oxide pellets, limestone, sand, and gravel. The effect of variables such as rotational speed, bed depth, cylinder diameter, particle size, and particle shape on bed motion has been determined. For a given material, the different modes of bed motion can be delineated conveniently on a Bed Behavior Diagram which is a plot of bed depthvs rotational speed. The scaling of bed behavior with respect to particle size and cylinder diameter requires similarity of Froude number modified by(D/d
 p)1/2, and pct fill. Measurements of key variables characterizing slumping and rolling beds have also been made.

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Experimental study of transverse bed motion in rotary kilns

Magnetic Resonance Imaging (MRI) was used to measure granular-flow in a partially filled, steadily rotating, long, horizontal cylinder. This non-invasive technique can yield statistically averaged two-dimensional concentrations and velocity profiles anywhere in the flow of suitable granular materials. First, rigid body motion of a cylinder fill with granular material was studied to confirm the validity of this method. Then, the density variation of the flowing layer where particles collide and dilate, and the depth of the flowing layer and the flow velocity profile were obtained as a function of the cylinder rotation rate.

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Non-invasive measurements of granular flows by magnetic resonance imaging

Mathematical models have been developed to predict the conditions giving rise to the different forms of transverse bed motion in a rotary cylinder: slumping, rolling, slipping, cascading, cataracting, and centrifuging. Model predictions of the boundaries between these modes of bed motion compare well with previously reported measurements, and can be represented conveniently on a Bed Behavior Diagram which is a plot of pct fill against Froude number (or bed depthvs rotational speed). The location of the boundaries is shown to depend on material variables which characterize frictional conditions in the bed. For the slumping/rolling boundary these are primarily the shear angle and the limiting wedge angle which defines the solids involved in a slump. For the slipping/slumping and slipping/rolling boundaries the governing material variables are the bed/wall friction angle and the upper angle of repose and dynamic angle of repose, respectively. Similarly, the location of the other boundaries related to cascading and cataracting is determined by the dynamic angle of repose. Complete Bed Behavior Diagrams have been calculated for solids having different particle size and particle shape rotated in cylinders having different diameters.

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The modeling of transverse solids motion in rotary kilns

A model of rotary kiln heat transfer, which accounts for the interaction of all the transport paths and processes, is presented in a three-part series. In this second paper, the development of a unified model for heat transfer at a kiln cross-section is described. Heat transfer within the kiln refractory wall was solved using a finite-difference approximation for one-dimensional transient conduction. A ray tracing technique was applied to derive coefficients for radiative heat transfer in the kiln freeboard, and the finite-difference model was extended into the contacting bed ma-terial in order to calculate the exchange between the covered wall and the bed. The cross-section model is shown to simulate the measured thermal performance of the pilot kiln for several feed materials: fine and coarse sand, limestone, and pctroleum coke. The interaction among the heat-transfer processes at cross-sections of the pilot kiln was examined, and explanations were made for both the observed close coupling of the bed and inside wall temperatures and the high rates of heat input to the bed occurring near the kiln entrance and in the presence of an endothermic bed reaction. Conclusions regarding the likely effects of kiln internal devices on heat transfer to the bed and the importance of preheaters are reached from the model predictions for a 4 m I.D. prototype kiln.

A heat-transfer model for the rotary kiln: Part II. Development of the cross-section model

A model for rotary kiln heat transfer, which accounts for the interaction of all the transport paths and processes, is presented in a three-part series. In this first paper, the pilot kiln facility is described, and the significant results from the heat-transfer trials are identified. Limestone, Ottawa sand, and pctroleum coke were heated using a range of firing rates, while other operating variables were held nearly constant. Measurements were made to obtain the net rates of heat transfer for the bed material, freeboard gas, refractory wall, and, unique to the study, the radial heat flux at the inside refractory surface as a function of circumferential position. High rates of net heat input to the bed material, occurring very near the feed end, were found to decline quickly with distance, and for an inert bed, leveled out at a value well below the rate of loss through the kiln wall. The onset of an endothermic bed reaction resulted in sharp increases in both the temperature cycling at the inside refractory surface and the net heat input to the bed, but no corresponding jump in the kiln wall heat loss. The temperatures of the bed material and inside refractory surface always were coupled closely, even in the presence of bed reaction. Regenerative heat transfer from the covered wall to the contacting bed material was not a major component of the net input to the bed, and for the inert bed, negative regeneration was en-countered beyond the kiln midpoint.

A heat-transfer model for the rotary kiln: Part I. pilot kiln trials

An experimental study has been conducted to elucidate the mechanism of radial segregation in the bed of a rotary kiln and to determine the size and composition of the segregated core Bed-behavior diagrams were obtained, and slumping and rolling characteristics were measured, for two sand mixtures and one limestone mixture containing fines The fines resulted in significant changes in bed behavior, but no effects were observed on either static or dynamic angle of repose, shear angle, slumping frequency, or active-layer thickness Therefore it was concluded that the fines do not segregate according to the differential flow of particles down the surface of the bed Instead percolation, in which the fines pass through the voids in the coarser solids, appears to be the operative mechanism The size of the segregated core was measured by sampling the bed of solids Predictions of core width based on geometric considerations and a core composition having the minimum void fraction agreed reasonably well with measurements A second region of segregation was found adjacent to the wall The two zones of segregation can influence deleteriously kiln performance Solids in the central core are not exposed to the hot freeboard gases and therefore may only partially react The zone of fines at the kiln wall can reduce wall/bed friction to the extent that the bed slips against the wall

A. P. Watkinson

Papers

Experimental study of transverse bed motion in rotary kilns

The modeling of transverse solids motion in rotary kilns

A heat-transfer model for the rotary kiln: Part II. Development of the cross-section model

A heat-transfer model for the rotary kiln: Part I. pilot kiln trials

An Experimental Study of Segregation in Rotary Kilns