Download - CHE572 Chapter 5 Hopper Design.pdf

8/19/2019 CHE572 Chapter 5 Hopper Design.pdf

1/19

67

CHAPTER 5HOPPER DESIGN

5.1 Bulk solid handling

• Measuring the flow properties of bulk solids and howto use this information for the design of storagevessel.

• Definitions:Bin: Any upright container for storing bulk solids.Silo: A tall bin, where H > 1.5DBunker: A shallow bin, where H < 1.5DHopper: A converging sloping wall section attachedto the bottom of a silo.

5.2 Solid flow pattern

• As solid flow from a bin, the boundaries betweenflowing and non-flowing regions define the flow

pattern.• Three types of common pattern:i) Funnel flow / core flowii) Mass flowiii) Expanded flow

5.2.1 Flow obstruction

• Interruption of solid flow in a bin can be caused by 2types of obstructions:i) An arch

• Sometimes called as a bridge• Formed across a flow channel


2/19

68

ii) Bin opening / rathole

• Formed when the flow channel empties,leaving the surrounding stagnant material inplace.

• Important in understanding the forces acting on thewall 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 slidealong the wall during the flow.

• Funnel flow through an entire bin - Rathole, formedwhen stagnant materials gains sufficient strength toremain in place as flow channel empties (refer figure10.1, page 266)

• 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 orarch over the discharged opening.

• The flow channel may not well defined

o particle segregation might occur.o material surrounding the channel may be

unstableo this will cause stop and start flowing, pulsating

or “jelly” flow.o could lead to the damage of material structure.


3/19

69

• As bin emptied; solid continually slough off the topsurface into the channel.

• Storage bin having a funnel flow pattern is mostcommon in industry.o the design do not consider the stagnant materials.o thus, resulting in less discharged capacity.

• Funnel flow is usually the least costly design.

• It has several disadvantages when handling certainmaterials:

i) Flow rate from the discharged opening can beerratic:

• Arches tends to form and break.

• Flow channel becomes unstable.• Upset volumetric feeder installed at the silo

discharged

• Powder density at discharged vary widely dueto varying stresses in flow.

ii) Fine powders :

• Flush/aerated uncontrollably• Sudden collapse of rathole/arch

iii) Caking/degrading of solid:

• Left under consolidating stresses in thestagnant areas.

iv) A stable rathole/ pipe formed

• Stagnant material gain sufficient strength toremain stagnant.


4/19

70

v) Level indicator

• Would not give correct signal on materialslevel.

• Submerged in stagnant area

• Despite all of the above, funnel flow is still adequatefor (advantage) :

i) Non-caking or non-degradableii) Discharge opening adequately sized to prevent

bridging/ratholing.

• However, many mechanical devices could be used topromote 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 wallsi.e all materials is in motion and sliding against thewall of bin and hopper.

Advantages:

i) Erratic flow, channeling and flooding of powders areavoided.

ii) Stagnant regions in the silo are eliminated.

iii) First in, first out flow occurs. Resulting in minimizingcaking, degrading and segregation during process.

iv) Little particle segregation or eliminated


5/19

71

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-powderfriction and the powder-wall friction.

• There is no such thing as mass flow hopper - ahopper that gives mass flow with one powder maygive core flow with another.

Mass Flow

Figure 10.2 pg 266


6/19

72

Funnel / core flow

Figure 10.3 pg 267

Expanded flow:

• Term used to describe flow in a vessel that combinesa core flow converging hopper with a mass flowattached below it.

• The mass flow hopper section ensures a uniform,controlled flow from the outlet. Its upper diameter issized such that no stable pipe can form in the coreflow hopper portion above it.

• Expanded flow is used where a uniform discharged indesired, but where space or cost restrictions rule outa fully mass flow bin.

• This arrangement can be used to modify existingfunnel flow bins to correct flow problems.


7/19

73

• Multiple mass flow hoppers are sometimes mountedunder a large core flow silo.

5.4 The Design Philosophy

Blockage or obstruction to flow = arching.

• From above diagram: powders develop strength under the action of

compacting stresses

Arch of powder withsufficient strength toprevent flow

Powder

Figure 10.5 page 268


8/19

74

the greater the compacting stress, the greaterthe 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 ofconsolidating pressure to support obstruction to flowis 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 thearch.

The hopper flow factor (ff )

• the ff relates the stress developed in a particulatesolid within the compacting stress acting in a

particular hopper.

powder theindeveloped stress

hopper theinstresscompacting ff

D

C

⋅⋅⋅⋅

⋅⋅⋅⋅==

σ

σ

• 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


9/19

75

5.5.1 Unconfined yield stress, σy

• σy = yield stress of the powder in the exposed surfaceof the arch.

• For flow to occur:- stresses developed in the powder forming the

arch are greater than the unconfined yieldstress of the powder in the arch, flow will occur.

- For flow, σD> σy or yC

ff σ

σ >

5.5.2 Powder flow function

• the unconfined yield stress, σY of the solid varies withcompacting stress, σC ;i.e:

( )C y fn σ σ =

• the relationship is determined experimentally

• the relationship is called powder flow function

5.5.3 Critical condition for flow

The limiting condition for flow:

yc

ff σ

σ

=

to reveal conditions under which the flow will occur.


10/19

76

(a) – powder has a yield stress greater than σc / ff ⇒ noflow 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.

5.6 Critical outlet dimension

For a given hopper geometry, the stress developed inthe arch is related to the size of the hopper outlet, B,and the bulk solid, ρs, of the material.

Minimum outlet dimension, B

g

H B

b

crit

ρ

σ θ )(=

σD/ σy

(b)

(c)

Powder flow

function

σc


11/19


12/19

78

5.7 Shear cell test

The Jenike shear cell test allows powder to becompacted to any degree and sheared under

controlled load conditions. At the same time, shearand stress can be measured.

Powders change bulk solid under shear. Under theaction of shear:

- a loosely packed powder would contract (↓ρB)- a very tightly packed powder would expand (↑ρB)- a critically packed powder would not change in

volume.

Figure 10.8 page 272

5 or 6 samples of powder are prepared.

Normal force and shear force are recorded.

The pair of values (normal and shear force) areplotted to give a yield locus.


13/19

79

The end point of yield locus corresponds to criticalcondition. Where initiative of flow is not accompaniedby a change in the bulk density.

Figure 10.9 pg 273

5.8 Mohr`s circle

Represents the possible combination of normaland shear stresses acting on any plane in apowder (or a body) under stress.

The entire process is repeated 2 or 3 times withsamples prepared with different ρB.

In this way, a family of yield loci is generated.

These yield loci characterize the flow properties ofthe unaerated powder.


14/19

80

Figure 10.10 pg 273

Figure 10.12 pg 275


15/19

81

Each point on a yield locus represents that pointon a particular Mohr`s circle for which failure oryield of powders occurs.

A yield locus is tangent to all the Mohr`s circlerepresenting stress system when the powder fail to

flow.

a and b represents stress system under which thepowder would fail.

c - stresses are insufficient to cause flow. d – not relevant since the system cannot support

stress combinations above the yield locus. a and b – interest us in analyzing the flow.

5.9 Determination of σy and σc

Figure 10.13 pg 275

Circle A- represents condition of the free surface ofthe arch.- at the free surface zero shear and zero normal

stress.


16/19

82

- circle A must pass the origin.- gives the value of unconfined yield stress, σy

Circle B- the Mohr`s circle is tangent to the yield

locus at its critical condition of failure.

Major principle stress = compacting stress, σc

5.10 Determination of δ from Shear Cell Test.

δ- effective angle of internal friction of the solid.- tangent of the ratio of shear stress to normal stress.

YL – yield locus For a free-flowing solid, there is only one yield locus

and coincides with the effective yield locus. The relationship between normal stress and shear

stress is known as friction.

Figure 10.14 pg 276


17/19

83

5.11 Kinematic angle of friction between powderand wall, Φw

Also known as the angle of wall friction.

Gives relationship between the normal stress actingbetween powder and wall and the shear stress underconditions.

Wall yield locus is determined by shearing powderagainst a sample of the wall material under variousnormal load.

Figure 10.15 pg 277

Kinematic angle of wall friction is the gradient ofthe wall yield locus:

walltheat stressnormal

walltheat stressshear w

....

....tan =Φ


18/19

84

5.12 Determination of Hopper Flow Factor, ff.

Determination of the hopper flow factor, ff

Eg: δ= 30

o

Φw= 19

o

From the graph; θ = 30.5 (X) allow 3o margin for safety Thus; the semi-included angle of conical hopper

= 27.5o (Y) Thus; the hopper flow factor, ff = 1.8

Figure 10.16 pg 277

Figure 10.17 pg 278


19/19

85

5.13 Summary of design procedure

Shear cell test on powder give a family yield loci.

Mohr`s circle stress analysis gives pairs of values ofσ y and σ c and the value of the effective of internal

friction, δ .

Pairs of values of σ c and σ y give the powder flowfunction.

Shear cell tests on the powder and the material of thehopper wall give the kinematic angle of wall friction,Φw .

Φw and δ are used to obtain hopper flow factor, ff andsemi- included angle of conical hopper wall slope,θ .

Powder flow function and hopper flow factor arecombined to give the stress corresponding to thecritical flow- no flow condition, σ crit .

σ crit , H( θ ) and bulk density, ρB are used to calculate

the minimum diameter of the conical hopper outlet, B .

Download - CHE572 Chapter 5 Hopper Design.pdf

Top Related