Flow patterns in hoppers
When a silo is discharging material, there are two distinct flow patterns that can occur; core-flow (funnel-flow) and mass-flow as illustrated in fig 1a, b & c.
The core-flow pattern is the default pattern that most vessel operate in (unless mass-flow has been specifically designed for) where by material flows down a preferential flow channel above the outlet and the material around the walls remains static.
If the product is free-flowing and the silo has a tall parallel section the flow channel can expand to the walls in the upper silo as shown in fig 1a.
If the material has a degree of cohesion, the flow channel expansion angle will be very steep, so the flow channel will extend to the top surface of the inventory in the silo.
This core-flow pattern gives a first in last out form of stock rotation, can lead to;
- flushing of aeratable materials, i.e. freshly loaded aerated material passes straight into the flow channel,
- caking (unwanted agglomeration) of time sensitive materials, i.e. static regions around walls can harden over time and take up permanent residence in the silo,
- segregation of materials with a wide size distribution, i.e. if centrally loaded, an angle repose forms in the silo, coarse particles roll to the base of the pile (wall) and the fines are less mobile and collect in the centre of silo. When discharged in core flow fines come out first followed by an increasing proportion of coarse particles.
The alternative and desirable flow pattern for difficult to handle materials is mass-flow (shown in fig 1c) where the hopper has much steeper walls so that material slip occurs at the walls and all the material is in motion when discharge occurs.
This gives a first in first out discharge pattern and all material has a consistent residence time, minimising chances of agglomeration and flooding. While segregating material separate within the silo during loading the uniform draw down causes them to remix on discharge. Mass-flow also gives a gravity discharge rate that is more consistent over time and independent of inventory level.
The key disadvantages of mass-flow are the potential for wear of the walls if product stored is very abrasive (either core-flow or a wear allowance must be made), the higher pressures on the wall during discharge (because all contents is live) particularly at the transition from the parallel to converging sections of the silo, and a greater head room requirement to store a given volume of material due to the steeper hopper.
Fig 1 Silo flow patterns a) core-flow (free flowing material) b) core-flow (cohesive material) and c) mass-flow
Wall Friction Measurement
The determination of whether a material will mass-flow or core-flow requires a measurement of the friction between the hopper wall and the stored powder. This can be done by shearing a cell of consolidated powder over a sample of wall measuring the shear force whilst controlling the normal force.
The shear force is plotted as a function of normal force, the wall yield locus, the angle of which represents the wall friction angle, i.e. the angle at which the wall must be inclined to cause slip of the powder down the wall.
The relationship between mass-flow hopper half angle and the wall friction angle is presented in fig 2a&b and shows that as the wall friction angle reduces the limiting hopper angle for mass-flow becomes shallower. I.e. the higher the friction between the powder and the hopper wall, the steeper the hopper required for mass-flow.
Two extremes of hopper shape are presented a conical hopper and plane or wedge shape hopper. The latter gives mass-flow at larger half angles because material converges in only one direction rather than two for a cone.
When a silo fails to discharge under gravity there are a three primary types of flow obstruction namely mechanical arching, cohesive arching and rat-holing, see fig 3a, b & c respectively.
Mechanical arching is the relatively trivial case where the particles are too big, relative to the size of the outlet, and several particles can mechanically jam over the outlet.
To avoid this the diameter of a circular outlet (or diagonal of a slot outlet) must be approx. 10 times greater than the maximum particle size.
Cohesive arching and rat-holing are where the material gains strength when consolidated due to cohesion as a function of either a fine particle size typically below 100microns (where van-der-Waals forces dominate over gravity forces) or presence of surface liquid where the surface tension binds the particles together.
With cohesive material if the size of the outlet is too small then an obstruction will form, and gravity flow will only occur when outlet diameter/ width is sufficiently wide that the weight of the bulk solid in the arch exceeds the unconfined strength of the material. Cohesive arching is the flow limiting condition in a mass-flow silo, rat-holing is the flow limiting condition in a core-flow silo.
The rat-hole occurs because for the diameter of the core, the hoop stress is insufficient to overcome the strength of the material, so as before the outlet diameter must be increased thus increasing the hoop stress until failure occurs.
For a mass-flow silo, the critical outlet dimension is largely independent of the size of the silo, however for a core-flow silo the critical rat-hole dimension can increase significantly as the vessel gets larger (of diameter and height) and the consolidation stress in the pipe increases.
To size the outlet of a silo to overcome cohesive arching or rat-holing, the cohesive strength of the material is measured and represented as the flow function (fig 4a) which is a blue print for the flowability of given material. The flow function measurement is best illustrated by the concept a sand castle test (see fig 4b).
In the first stage of the “sand castle” test, the bulk solid is compacted uniaxially in a mould (bucket) to a given normal stress. In the second stage of the test, the mould (bucket) is removed to reveal the bulk solid “sand castle”.
An increasing vertical stress is then applied to the unconfined bulk solid (sand castle) and the peak strength at failure recorded. The horizontal axis of the flow function represents the consolidation stress, “the stress applied to compact the sand castle in the bucket”, versus the unconfined failure strength “the strength of the free-standing sand castle” on the vertical axis. Although the means of measurement in practice is by shear testing rather than uniaxial action, the meaning is the same.
For both types of silo time consolidation can be a significant factor. This is where the material strength increases as a function of the time-period of static storage, where particles move closer together increasing the strength.
Thus, if the material is left static in the hopper over a week-end a large outlet size required to get the material to flow on Monday morning. This can be designed for by characterising the strength over the required time-period.
Alternatively, if this time-period is used infrequently discharge aids could be employed from the outlet to the diameter of the time outlet to be used only when reinitiating flow from a long static storage period.
Having got the geometry of the silo correct for reliable gravity flow, it is possible to convert a mass-flow silo back to a core-flow one, through inappropriate feeder interfacing. There are numerous feeder types used to control the discharge rate of products from silo including; screws, belts, chains, vibratory slides, ploughs, rotary valves and for each there is a correct and incorrect way to interface.
A screw and a belt are used below to describe the principal of good interfacing practice. A standard incorrect interface for a screw is a constant pitch and diameter which gives a fixed transport volume.
Thus, screw moves material forward from the first pitch, so the only place material in the silo can enter the screw is from the back of the slot. Thus, a mass-flow silo discharges in a core-flow manner because of poorly design feeder interface geometry.
What is required to support mass-flow is a screw with fixed outer diameter, but an increasing pitch and reducing shaft diameter in the direction of feed. Thus, the volume moved by the screw increases in the direction of feed and material flows along the full length of the slot in mass-flow.
Similar principals apply for a belt, a horizontal interface will draw from the font of the slot only see fig 5a. What is required is an outlet that increases in height at approx. 5° so that slot width has taper to give an increasing width in the direction feed, creating a progressively widening and heightening pile on the belt in the direction of flow to support mass-flow see fig 5b.
Retrofit techniques silo inserts
A common approach that can be used to correct discharge problems with a core-flow silo are static inserts. Surprisingly, an internal obstruction within the silo (usually an inverted cone) if of the correct size and in the right position can dramatically improve the discharge characteristics of a core-flow silo to something approaching mass-flow.
This technique works by changing the shape of the flow channel from a cone to wedge wrapped into an annulus. As shown previously the wedge achieves mass-flow at significantly lower angles and is less sensitive to changes in inventory.
To adequately design a silo for reliable flow you need to know your material. If the material is free-flowing and always remains so and segregation is not a problem than core-flow may be acceptable for your process.
However, if your material is cohesive, time dependent (prone to caking), fluidises readily, or highly segregable, then a mass-flow pattern is probably required. To achieve mass-flow you need to measure the flow properties of your material, the; wall friction, flow function, internal friction, bulk density and time flow function so that the critical outlet size and converging angle can be specified to give reliable flow.
Finally remember that the feeder interface geometry must be correctly designed to support mass-flow.