Sand Flow in Hour Glass Geometry
A good appreciation of the differences between liquid and granular flows can be gained from a simulation of a two-dimensional hour-glass geometry in which sand is initialized in the upper half of the glass and allowed to flow into the lower half under the action of gravity. The adjacent snapshot shows the computed flow after 14s. A corresponding animation covers the entire flow history leading to all the sand at rest in the lower half of the glass.
The height of the hour glass is 49.0cm with a 1.0cm diameter opening at the waist. The sand has a uniform grain diameter of 0.045cm and is specified to have an angle of repose of 34°. The total simulation time was 40s, which required 6.5 minutes of CPU time on a single-processor desktop computer.
Several important observations can be made from the snapshot plot. Most significantly, the only sand that is flowing (shown by short vectors) is at the surface of the sand in both the top and bottom sections. Everywhere away from a surface the sand is fully packed and unable to flow. Second, the sand in the bottom section does not flow out across the bottom, as a liquid would, but packs and stops flowing. As the sand piles up there is a flow on the surface of the pile that resembles unsteady avalanches. This flow results in a slow outward spread of the pile at its base. At the termination of flow the angle of the pile in the lower section is close to the specified angle of repose.
For more information about this model, download the Flow Science Report on Granular Media.