Particle size and boundary effects in rapid granular shear flows: An experimental and numerical study.

摘要

The measured shear stress of glass spheres in an annular shear cell experiment is reported. In order to explore the particle size effect, the experiments are run using four different particle diameters, d = 2, 3, 4, and 5mm. It is found that the shear stress follows the Bagnold scaling with respect to the apparent shear rate, but deviates from the Bagnold scaling with respect to particle size. For high solids concentration the results deviate qualitatively from the kinetic theory for bounded granular shear flows, where the non-dimensional shear stress measured with larger particles exceeds that measured for smaller particles by as much as one order of magnitude. The effect of the boundary geometry is explored by using three different boundary types; type 1 employs aluminum radial half-cylinders, type 2 employs aluminum hemispheres arranged in a polar hexagonal closed packed configuration, and type 3 employs sandpaper. It is shown that the geometry of the boundary has an insignificant effect on dilute flows of small particles. For denser flows and/or larger particles the difference is evident. The shear to normal stress ratio is found to depend on the particle diameter, solids concentration, and in some cases on the shearing rate. The effect of boundary type on the stress ratio is only noticeable in dilute flows involving small particles. DEM simulations of the experiments are used to obtain velocity and solids concentrations profiles. It is shown that the extent of shearing within the flow depends on the global solids concentration, particle size, and boundary type. These results imply that in granular materials-structure interaction, the structure's properties are just as important as the properties of the granular material. Their interaction may also depend on the relative size between the structure and the grain size. The dimensional similarity of granular flows is explored by employing two geometrically similar annular shear cells with High Density Polyethylene (HDPE) spheres as the granular material. A dimensional analysis of the flow reveals that the non-dimensional shear stress depends on the parameter E/ rhosgamma2d 2, i.e. (Mach number)-2, and a parameter g /gamma2d, i.e. (Froude number)-2, where E is the particle Young's modulus, rhos is the particle density, gamma is the shearing rate, and g is the acceleration of gravity. It is found that the flow in the experiments is in the elastic-inertial regime and the effect of gravitational forces is significant, particularly for the large shear cell. A simple scaling of the annular shear cell is not possible since there is at least one non-dimensional parameter E/rhosgd that cannot be kept constant in both shear cells.