Norbert L. Ackermann

Constitutive equations for a simple shear flow of a disk shaped granular mixture

Abstract Constitutive equations are derived for a granular flow of disk shaped solids in a 2-dimensional, simple shear field. Binary collisions are assumed to be the major mechanism for momentum transfer. Stresses are computed as the average rate of momentum transfer across a surface due to the interparticle collisions. Stresses are formulated explicitly in terms of the shearing rate, concentration of solids, and the physical properties of the solid constituent. The anisotropic collision distribution on the circumference of the disks due to the mean flow gradient is explicitly quantified. The frictional impact during collisions is treated in sufficient detail so that the singularity which existed in previous constitutive equations [1, 2] is removed. This detailed analysis of collision geometry and its effect upon frictional dissipation includes important considerations that have not been included in the numerical simulation models of Campbell and Brennen [3] where particles, after impact, are considered to not have any relative tangential velocity. This assumption by Campbell and Brennen will most likely be the technique by which frictional effects will be commonly handled in the future. Hence the present study will provide an important reference for assessing the effects of using simplifying assumptions when determining frictional effects during particle collisions. The constitutive relationships developed in this investigation are compared to data obtained from computer simulated experiments [3]. The result of the 2-dimensional analysis has practical applications in the study of ice flows on a river surface as reported in [4] and in the conveyance of bulk solids in chutes. Except for geometric complications, the procedure developed in the analysis can be extended to 3-dimensional flows of spherical particles.

Experimental studies of sediment enrichment of arctic ice covers due to wave action and frazil entrainment

Two processes are investigated that are believed to contribute to the sediment enrichment of ice covers in coastal arctic waters. One process results from wave action which pumps sediment rich underlying water into the surface cover. The other enriching mechanism is produced by rising frazil that entrains suspended sediment which subsequently becomes incorporated in the surface ice layer. In both processes the sediment enrichment of the ice cover is found to depend upon the sediment size and concentration in the underlying water column. In the wave dependent process the rate of sediment enrichment is influenced by the period, amplitude, and duration of the wave action as well as the size of the ice particles and motion of the cover. Frazil rising through sediment laden water was found to entrain particles of sand far more effectively than silt. Sand laden frazil floe would often become so loaded with sediment that the floe would eventually settle to the floor of the water column.

Physical Experiments and Numerical Simulation of Two Dimensional Chute Flow

Synopsis Numerical simulations and physical experiments were used to study the two dimensional flow of disks in a chute. For a chute with a fixed geometry, inclination, and material properties the physical experiments and their computer simulations produced a series of steady, uniform flows over a range of bulk solids concentrations from approximately C=0.1 to C=0.7. These results were in contrast to findings obtained from the numerical integration of the governing equations that described the corresponding boundary value problem. General agreement was observed between computer simulated values of velocity and solids concentration and those dtermined from physical experiments.

Energy diffusion in a granular flow of disk shaped solids

Abstract The kinetic energy of a granular flow consists in part of the energy associated with the random velocity fluctuations v′ of the individual solid particles. When the magnitude of v′varies throughout the flow field a transfer of kinetic energy ρv 2 2 occurs that must be considered when evaluating the energy balance relationship. In the present investigation this energy transfer or diffusion is quantified for the flow of a granular continuum consisting of disk-shaped solids. The theoretical development involves a detailed analysis of the binary collision mechanics which results from the interaction between adjacent disks within the granular mixture. The energy diffusion term developed in this investigation, in conjunction with the stress and energy dissipation functions previously reported by Shen and Ackermann [1], provide all of the constitutive relationships that are necessary to describe the two-dimensional uniform flow of a granular mixture of disk-shaped solids.

Rapid Shear Flow of Densely Packed Granular Solids

Abstract Present theories cannot yet accurately describe the rapid shear flow of granular solids. Most theoretical formulations of the equations of motion contain undetermined functions or coefficients. Those equations that are fully deterministic predict stresses that differ from experimentally determined results by one or more orders of magnitude. Previous investigations that have provided a quantifiable description of the stress state have adopted a binary collision model to describe the momentum exchange within the granular flow. A preliminary analysis which incorporates the kinematic constraints of the flow process, indicates that a lateral mass transfer occurs that has a significant effect upon the momentum exchange between colliding solids. These effects have not been previously reported. By incorporating the effects of this lateral mass transfer into the analytical procedure proposed by Shen and Ackermann (1982), theoretically predicted stresses are found which agree well with experimentally determined values.

Microstructure in rapid gravity channel flow

Abstract Numerical simulations were conducted for two-dimensional disks in an inclined channel. These flows produced slugs or regions along the channel characterized by the occurrence of densely packed groups of flowing disks. These groups of particles or slugs were in a continual state of change as they enlarged or shrunk in length. The nonuniformity of the flow or occurrence of slugs increased as the disks were made more inelastic. The length of these slugs and the frequency of their occurrence were studied in terms of their dependence upon the length of channel between the periodic boundaries in the flow simulation, slope of the channel and the material properties of the disks.

Microstrueture in Rapid Gravity Channel Flow

Numerical simulations were conducted for two-dimensional disks in an inclined channel. These flows produced slugs or regions along the channel characterized by the occurrence of densely packed groups of flowing disks. These groups of particles or slugs were in a continual state of change as they enlarged or shrunk in length. The nonuniformity of the flow or occurrence of slugs increased as the disks were made more inelastic. The length of these slugs and the frequency of their occurrence was studied in terms of their dependence upon the length of channel between the periodic boundaries in the flow simulation, slope of the channel and the material properties of the disks.