hopper design.pdf

5.0 HOPPER DESIGN 5.1 Bulk solid handling  Measuring the flow properties of bulk solids and how to use this information for the design of storage vessel.  Definitions: Bin: Any upright container for storing bulk solids. Silo: A tall bin, where H > 1.5D Bunker: A shallow bin, where H < 1.5D Hopper: A converging sloping wall section attached to the bottom of a silo.

5.2 Solid flow pattern  As solid flow from a bin, the boundaries between flowing and non-flowing regions define the flow pattern.  Three types of common pattern: i) Funnel flow / core flow ii) Mass flow iii) Expanded flow

5.2.1 Flow obstruction  Interruption of solid flow in a bin can be caused by 2 types of obstructions: i) An arch  Sometimes called as a bridge  Formed across a flow channel ii)

Bin opening / rathole  Formed when the flow channel empties, leaving the surrounding stagnant material in place.

 Important in understanding the forces acting on the wall of the bin and to the material.

5.3 Types of flow pattern 5.3.1 Funnel flow / core flow:  Occurs in bin with flat bottom or hopper having slopes too shallow or too rough to allow solid to slide along the wall during the flow.  Funnel flow through an entire bin - Rathole, formed when stagnant materials gains sufficient strength to remain in place as flow channel empties  Material near to the bin wall becomes stagnant.  First in, last out or do not come out at all.  Rathole / pipe could form.

 In severe cases, the material can form a bridge or arch over the discharged opening.  The flow channel may not well defined -particle segregation might occur. -material surrounding the channel may be unstable -this will cause stop and start flowing, pulsating or “jelly” flow. -could lead to the damage of material structure.  As bin emptied; solid continually slough off the top surface into the channel.

 Storage bin having a funnel flow pattern is most common in industry.  the design do not consider the stagnant materials.  thus, resulting in less discharged capacity.  Funnel flow is usually the least costly design.  It has several disadvantages handling certain materials:

when

i)

Flow rate from the discharged opening can be erratic:  Arches tends to form and break.  Flow channel becomes unstable.  Upset volumetric feeder installed at the silo discharged  Powder density at discharged vary widely due to varying stresses in flow.

ii)

Fine powders :  Flush/aerated uncontrollably  Sudden collapse of rathole/arch

i)

Caking/degrading of solid:  Left under consolidating stresses in the stagnant areas.

ii)

A stable rathole/ pipe formed  Stagnant material gain sufficient strength to remain stagnant.

iii) Level indicator  Would not give correct signal on materials level.  Submerged in stagnant area

 Despite all of the above, funnel flow is still adequate for (advantage) : i) Non-caking or non-degradable ii) Discharge opening adequately sized to prevent bridging/ratholing.  However, many mechanical devices could be used to promote flow.

5.3.2 Mass flow:  Occurs in bin having steep and smooth hoppers.  Material discharges are fully active.  Flow channel coincides with the bin and hopper walls i.e all materials is in motion and sliding against the wall of bin and hopper.

Advantages: i)

Erratic flow, channeling and flooding of powders are avoided.

ii)

Stagnant regions eliminated.

in

the

silo

are

iii) First in, first out flow occurs. Resulting in minimizing caking, degrading and segregation during process. iv) Little particle segregation or eliminated v) Uniform flow at the hopper outlet  flow is easily controlled  pressures are well predictable.

Disadvantages: i)

Friction between moving solids and the silo.  resulting in erosion of the wall  could give rise to contamination of the solids by the material of the hopper wall.  Serious erosion of the wall material.

ii)

For conical hoppers, the slope angle required to ensure mass flow depends on the powder-powder friction and the powder-wall friction.

 There is no such thing as mass flow hopper- a hopper that gives mass flow with one powder may give core flow with another.

Expanded flow:  Term used to describe flow in a vessel that combines a core flow converging hopper with a mass flow attached below it.  The mass flow hopper section ensures a uniform, controlled flow from the outlet. Its upper diameter is sized such that no stable pipe can form in the core flow hopper portion above it.

 Expanded flow is used where a uniform discharged in desired, but where space or cost restrictions rule out a fully mass flow bin.  This arrangement can be used to modify existing funnel flow bins to correct flow problems.  Multiple mass flow hoppers are sometimes mounted under a large core flow silo.

5.4 The Design Philosophy Powder

Arch of powder with sufficient strength to prevent flow

 Blockage or obstruction to flow = arching.

 

powders develop strength under the action of compacting stresses the greater the compacting stress, the greater the strength developed

(Free-flowing solids such as coarse sand will never develop compacting stress)

5.5 Flow- no flow criterion Flow to occur:  strength developed by the solids under the action of consolidating pressure to support obstruction to flow is less than gravity flow of the solids. An arch occurs:  when the strength developed by the solid greater than the stresses acting within the surface of the arch. The hopper flow factor (ff)  the ff relates the stress developed in a particulate solid within the compacting stress acting in a particular hopper.

 C compacting  stress  in  the  hopper ff   D stress  developed  in  the  powder  high value of ff means low flowability.  High σC means greater compaction.  Low σD means more chance of an arch forming. The hopper depends on:  The nature of the solid  The nature of the wall material  The slope of the hopper wall

5.5.2

Powder flow function

 the unconfined yield stress, σY of the solid varies with compacting stress, σC ;i.e:

 y  fn C   the relationship experimentally

is

determined

 the relationship is called powder flow function

Yield locus and family of yield loci

Determination of y and c

y

c

3

Critical condition for flow

The limiting condition for flow:

c ff

y

- to reveal conditions under which the flow will occur.

(a) – powder has a yield stress greater than σc/ff  no flow occurs. (b) – if actual stress developed < σcrit :  no flow. If actual stress developed > σcrit :  flow occurs. (c) – the powder has a yield stress less than σc/ff  flow occurs.

- For flow, σD> σy or

C ff

y

Determination of d and fw

Critical outlet dimension  For a given hopper geometry, the stress developed in the arch is related to the size of the hopper outlet, B, and the bulk solid, ρs, of the material.  Minimum outlet dimension, B B

H ( ) crit

b g

where H(θ) – factor determined by the slope of the wall. g – acceleration due to gravity.  For conical hoppers:

H ( )  2.0 

 60

Critical Outlet Dimension

Hopper flow factor values for conical channels, d=50o