Problems in Particulate Flow, Part A -- Flow Regimes, by Lyn Bates
Fig. 6 - Bin profile due to repose flow during filling
The angle of repose of this surface reflects the maximum sustainable stable slope inclination of the 'poured' loose material. Any bulk material that behaves in a fluid condition when it is very dilated will flush out to a level surface, as in Fig. 7, and display hydrostatic conditions until settled.
Fig. 7 - Unsettled dilated fill (high air content) will NOT exhibit mass flow
Repose flow taking place on the surface of the material during emptying is usually at a different inclination to the slope formed during filling. With free-flowing granular products this drained angle of repose is slightly steeper than the poured repose angle. This reflects particle interference in the convergence of the flow route focussing to the outlet channel, compared with their separation on the diverging flow surface of a growing conical pile. The effect is magnified nearest to the focal point of the convergence or divergence. The difference in repose flow inclination thus decreases progressively with distance from the focus, to become similar at large radii.
Consistent angles of repose are only formed by free-flowing materials. Cohesive products may form a particular repose angle on filling, according to how the pile is formed, but are capable of sustaining 'cliffs' or 'overhangs' during discharge, depending upon how firmly the material has consolidated. Angles of repose should be quoted only for materials that form consistent inclinations of slope during the formation of a pile. Its only value for design purposes is for calculating the volume of the pile or of the unusable storage space above the pile (the ullage).
With a bulk material that attains strength when settled, the manner in which the surface collapses can vary widely. In some cases the material is strong enough to support a vertical surface. The central core of flow then empties to leave a hole through the bulk, as a stable pipe or rathole form of flow stoppage. The surface layer may develop circumferential cracks near the centre core and move down in a drained cone manner, but with an irregular 'stepped' surface profile if the material can only sustain a certain height of 'cliff' for a given concave radius. The compacting loads acting on the upper layers of bulk during storage varies with the head of material, hence the repose or rathole characteristics may change as the contents of a deep storage container are discharged.
The profile of the surface is not of design interest for flow, but it is relevant for designing hopper content indicators when level detectors are positioned on the side walls of the container. For a given level of material against the wall, variations of the surface profile -- ranging from a deposited cone to a drained cone -- may represent large differences in capacity (Fig. 8).
Fig. 8 - Inconsistent level indication from sensors at the wall
in the presence of poured or drained cones, cliffs, and ratholes
The shape and length of the filling slope also has a major bearing on any segregation taking place during the filling process. Various mechanisms are active in an inclined surface stream of flow to favour the deposition of fines and the continuation of motion for coarse fractions. The usual result is that fines collect around the centre of a pile while lumps congregate around the periphery, against the container walls. The ultimate consequences then depend heavily upon the pattern by which the stored contents discharge.