Analysis of granular flow in a cone
This page contains a preliminary analysis of some DEM simulations in a cone carried out at Sandia labs. The geometry consists of a cone with angle 30° to the vertical, connected to an exit pipe of diameter 10d. Approximately 1,500,000 particles were used, filling the cone up to an approximate height of z=150d. A case with wall friction, and a case without wall friction were considered.
Click on the images below to see movies of the simulations for wall friction (left) and no wall friction (right).
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Density profile movie
The movie below shows evolution of the local packing fraction in the simulation, using the Voronoi cell code from the pebble bed simulations. The packing fraction appears to decrease smoothly as the particles approach the orifice, which is different to the reactor simulations, where a sharp crossover in density can be seen in the funnel-like region.
Velocity profiles
The two graphs below show velocity profiles in the vertical component as a function of the radial distance from the z-axis φ (where φ² = x² + y²).
Rescaled velocity profiles
In the graph below, the radial distance has been scaled by the width of the cone R(z), and the velocity has been scaled by the area of the cone at height z, A(z) = π R(z)². Using this scaling, the curves collapse to a high level of accuracy.
The radial velocity component was also considered. It was plotted at a function of the angle from the vertical, for several different distances from the apex of the cone r (where r² = x² + y² + z²). Rescaling by the spherical cross sectional area As(r) = 2π (1 - cos 30°) r² also causes the profiles to collapse.
How radial is the flow?
The above movie shows the same simulation data as above, but this time with the particles colored accoring to their angle from the vertical. During the movie, the positions of these boundaries stay almost perfectly in place, although some particle diffusion can be seen. The flow profile appears to be radial to a surprising degree of accuracy.
As further confirmation, the graph below shows the rescaled θ component of velocity. Apart from ordering effects near the wall, we see that vθAs(r) is almost always less than 0.1 d³/τ, which is much smaller than the values of 30 d³/τ to 50 d³/τ which are observed in the radial direction.
