Chemical Engineering October 2020 - 20

Facts At Your Fingertips
Hopper Outlet Geometry and Arching
Department Editor: Scott Jenkins
W
hen transferring stored
bulk-solids materials from
hoppers, bins and silos,
fl ow stoppage can occur because
of bridging or arching at the vessel
outlet. Hopper outlets must be large
enough to prevent cohesive arches
or stable ratholes from developing.
Determining the size and shape of
the hopper outlet is critical to ensuring
that the bulk material fl ows. This
column provides information on the
interplay between bulk material properties
and vessel geometry and how
those relate to outlet size and shape.
Arch and rathole formation
Bulk solids can experience a range of
conditions within a bin, silo or storage
hopper. Consolidation pressures range
from zero at the surface, to relatively
large values at increasing depth within
the container. If a solid gains cohesive
strength because of the pressures applied
to it, an arch or rathole could form.
An arch (also called a bridge or dome)
is a stable obstruction that forms over
the point of narrowest cross-section
of the storage vessel (usually the discharge
outlet). The arch supports the
rest of the bin contents, preventing
discharge (Figure 1, left). A rathole is a
stable pipe or vertical cavity that empties
out over the outlet. Material is left
stranded in stagnant zones that usually
remain in place until an external force is
applied to dislodge them.
Flow functions
Cohesive strength can be measured
as a function of the applied consolidation
pressure. By conducting the
test over a range of consolidation
states, the relationship between consolidation
pressure and the cohesive
strength of the bulk material can be
established, following a procedure
established and described by Jenike
[1]. In a laboratory, a sample of the
material is placed in a direct shear
tester and both compressive and
shear loads are applied to simulate
fl ow conditions in a container. Once
the sample has been consolidated,
its strength is measured by shearing it
to failure. By repeating this procedure
20
Consolidation of solids can form a
stable arch in a mass-fl ow bin
BC = Minimum outlet diameter
BP = Minimum slot width
FIGURE 1. The size of the discharge outlet is a critical element in preventing the formation of an arch in a
mass-flow bin
under different conditions, the resulting
value of strength versus consolidating
pressure (called a fl ow function)
can be developed. The material's
fl ow function is then used to calculate
minimum outlet dimensions.
Once a material's fl ow function has
been determined, the minimum outlet
width or diameter that will prevent
cohesive arching can be calculated
using the hopper's fl ow factor. The
fl ow factor is a function of the powder's
effective angle of internal friction,
the hopper angle and the wall friction
angle. Typical values of the fl ow factor
range between 1.1 and 1.7. For more
on calculating fl ow functions and fl ow
factors, see Refs. 2 and 3.
Mass- versus funnel-fl ow bins
Two types of bin fl ow patterns are possible.
A mass-fl ow bin has a relatively
long, tapered discharge section. In
mass fl ow, all of the material is in motion
during discharge, so no stagnant
regions form. Conversely, a funnel-fl ow
bin has a relatively short converging
section. While storage capacity for a
given height is greater in a funnel-fl ow
bin, this geometry allows material in
the center to move, while material at
the walls is stationary. The resultant
stagnant regions may interrupt fl ow.
Compared with a mass-fl ow bin,
there are several potential advantages
to using a funnel-fl ow bin. The relatively
shallow hopper requires less headroom
for a given storage capacity, and
since there is minimal fl ow along the
walls, the likelihood of abrasion and
particle attrition is minimized. However,
In general, only free-fl owing solid materials
with large (≥1/4 in.) particle sizes
and minimal tendency to degrade (via
oxidation, caking and so on) will fl ow
reliably in funnel-fl ow bins.
Preventing arching
For a mass-fl ow bin with a circular outlet,
the minimum outlet diameter needed
to prevent arching is expressed as
BC (Figure 1, center). Consider a material
whose critical outlet dimension,
BC, is 12 in. If this material is placed in
a mass-fl ow bin with an outlet diameter
of 6 or 8 in., a stable arch will form.
Conversely, if the outlet size is 12 or 14
in., a stable arch cannot form, so the
material will fl ow.
To prevent an arch from forming in a
funnel-fl ow bin, the minimum width of a
slotted outlet must be determined. The
critical rathole diameter, DF, must also
be determined. Ratholing is likely when
the diameter of the fl ow channel (set by
the size of the outlet) is smaller than DF.
Planar versus conical fl ow
The stress needed to deform a given
solid also depends on the form of fl ow
channel. In general, a wedge-shaped
confi guration with an elongated outlet
is a more forgiving geometry that can
handle a wider range of conditions for
a given material without fl ow stoppages.
The minimum outlet width required
to prevent an arch from forming
in a wedge-shaped, mass-fl ow
hopper is expressed as BP (Figure 1,
right). For a given material, this value
is usually about half that of BC. ■
References
1. Jenike, A.W., Storage and fl ow of solids, University of Utah, Engineering
Experiment Station Bulletin, No. 123, November 1964.
2. Carson, J., Pittenger, B. and Marinelli, J., Characterize Bulk Solids
to Ensure Smooth Flow, Chem. Eng., April 2016, pp. 50-59.
3. Mehos, G. and Morgan, D., Hopper Design Principles, Chem.
Eng. January 2016, pp. 58-63.
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