Bin and Hopper Design

1
Bin and Hopper Design

• Karl Jacob
• The Dow Chemical Company
• Solids Processing Lab
• jacobkv_at_dow.com

2
The Four Big Questions

• What is the appropriate flow mode?
• What is the hopper angle?
• How large is the outlet for reliable flow?
• What type of discharger is required and what is
  the discharge rate?

3
Hopper Flow Modes

• Mass Flow - all the material in the hopper is in
  motion, but not necessarily at the same velocity
• Funnel Flow - centrally moving core, dead or
  non-moving annular region
• Expanded Flow - mass flow cone with funnel flow
  above it

4
Mass Flow
D
Does not imply plug flow with equal velocity
Typically need 0.75 D to 1D to enforce mass flow
Material in motion along the walls
5
Funnel Flow
Active Flow Channel
Dead or non-flowing region
6
Expanded Flow
Funnel Flow upper section
Mass Flow bottom section
7
Problems with Hoppers

• Ratholing/Piping

8
Ratholing/Piping
Stable Annular Region
9
Problems with Hoppers

• Ratholing/Piping
• Funnel Flow

10
Funnel Flow
-Segregation -Inadequate Emptying -Structural
Issues
Coarse
Coarse
Fine
11
Problems with Hoppers

• Ratholing/Piping
• Funnel Flow
• Arching/Doming

12
Arching/Doming
Cohesive Arch preventing material from exiting
hopper
13
Problems with Hoppers

• Ratholing/Piping
• Funnel Flow
• Arching/Doming
• Insufficient Flow

14
Insufficient Flow
- Outlet size too small - Material not
sufficiently permeable to permit dilation in
conical section -gt plop-plop flow
Material under compression in the cylinder section
Material needs to dilate here
15
Problems with Hoppers

• Ratholing/Piping
• Funnel Flow
• Arching/Doming
• Insufficient Flow
• Flushing

16
Flushing

• Uncontrolled flow from a hopper due to powder
  being in an aerated state
• - occurs only in fine powders (rough rule of
  thumb - Geldart group A and smaller)
• - causes --gt improper use of aeration devices,
  collapse of a rathole

17
Problems with Hoppers

• Ratholing/Piping
• Funnel Flow
• Arching/Doming
• Insufficient Flow
• Flushing
• Inadequate Emptying

18
Inadequate emptying
Usually occurs in funnel flow silos where the
cone angle is insufficient to allow self draining
of the bulk solid.
Remaining bulk solid
19
Problems with Hoppers

• Ratholing/Piping
• Funnel Flow
• Arching/Doming
• Insufficient Flow
• Flushing
• Inadequate Emptying
• Mechanical Arching

20
Mechanical Arching

• Akin to a traffic jam at the outlet of bin -
  too many large particle competing for the small
  outlet
• 6 x dp,large is the minimum outlet size to
  prevent mechanical arching, 8-12 x is preferred

21
Problems with Hoppers

• Ratholing/Piping
• Funnel Flow
• Arching/Doming
• Insufficient Flow
• Flushing
• Inadequate Emptying
• Mechanical Arching
• Time Consolidation - Caking

22
Time Consolidation - Caking

• Many powders will tend to cake as a function of
  time, humidity, pressure, temperature
• Particularly a problem for funnel flow silos
  which are infrequently emptied completely

23
Segregation

• Mechanisms
• - Momentum or velocity
• - Fluidization
• - Trajectory
• - Air current
• - Fines

24
What the chances for mass flow?

• Cone Angle Cumulative of
• from horizontal hoppers with mass flow
• 45 0
• 60 25
• 70 50
• 75 70
• data from Ter Borg at Bayer

25
Mass Flow (/-)

• flow is more consistent
• reduces effects of radial segregation
• stress field is more predictable
• full bin capacity is utilized
• first in/first out
• - wall wear is higher (esp. for abrasives)
• - higher stresses on walls
• - more height is required

26
Funnel flow (/-)

• less height required
• - ratholing
• - a problem for segregating solids
• - first in/last out
• - time consolidation effects can be severe
• - silo collapse
• - flooding
• - reduction of effective storage capacity

27
How is a hopper designed?

• Measure
• - powder cohesion/interparticle friction
• - wall friction
• - compressibility/permeability
• Calculate
• - outlet size
• - hopper angle for mass flow
• - discharge rates

28
What about angle of repose?
Pile of bulk solids
?
?
?
29
Angle of Repose

• Angle of repose is not an adequate indicator of
  bin design parameters
• In fact, it (the angle of repose) is only
  useful in the determination of the contour of a
  pile, and its popularity among engineers and
  investigators is due not to its usefulness but to
  the ease with which it is measured. - Andrew W.
  Jenike
• Do not use angle of repose to design the angle on
  a hopper!

30
Bulk Solids Testing

• Wall Friction Testing
• Powder Shear Testing - measures both powder
  internal friction and cohesion
• Compressibility
• Permeability

31
Sources of Cohesion (Binding Mechanisms)

• Solids Bridges
• -Mineral bridges
• -Chemical reaction
• -Partial melting
• -Binder hardening
• -Crystallization
• -Sublimation
• Interlocking forces

• Attraction Forces
• -van der Waals
• -Electrostatics
• -Magnetic
• Interfacial forces
• -Liquid bridges
• -Capillary forces

32
Testing Considerations

• Must consider the following variables
• - time
• - temperature
• - humidity
• - other process conditions

33
Wall Friction Testing
Wall friction test is simply Physics 101 -
difference for bulk solids is that the friction
coefficient, ?, is not constant.
P 101
F ?N
34
Wall Friction Testing
Jenike Shear Tester
35
Wall Friction Testing Results
Wall Yield Locus (WYL), variable wall friction
Wall shear stress, ??
Wall Yield Locus, constant wall friction
?
Normal stress, ?
Powder Technologists usually express ? as the
angle of wall friction, ?
?? arctan ?
36
Jenike Shear Tester
W x A
Bracket
Cover
Ring
S x A
Bulk Solid
Bulk Solid
Shear plane
37
Other Shear Testers

• Peschl shear tester
• Biaxial shear tester
• Uniaxial compaction cell
• Annular (ring) shear testers

38
Ring Shear Testers
Arm connected to load cells, S x A
Bulk solid
Bottom cell rotates slowly
W x A
39
Shear test data analysis
?
C
fc
?1
?
40
Stresses in Hoppers/Silos

• Cylindrical section - Janssen equation
• Conical section - radial stress field
• Stresses Pressures

41
Stresses in a cylinder
Consider the equilibrium of forces on a
differential element, dh, in a straight-sided
silo Pv A vertical pressure acting from above ?
A g dh weight of material in element (Pv dPv)
A support of material from below ? ? D dh
support from solid friction on the wall
Pv A
h
? ? D dh
dh
(Pv dPv) A
? A g dh
D
(Pv dPv) A ? ? D dh Pv A ? A g dh
42
Stresses in a cylinder (contd)
Two key substitutions ? ? Pw (friction
equation) Janssens key assumption Pw K Pv
This is not strictly true but is good enough from
an engineering view. Substituting and
rearranging, A dPv ? A g dh - ?? K Pv ? D
dh Substituting A (?/4) D2 and integrating
between h0, Pv 0 and hH and Pv Pv Pv (? g
D/ 4 ? K) (1 - exp(-4H ?K/D)) This is the Janssen
equation.
43
Stresses in a cylinder (contd)
hydrostatic
Bulk solids
Notice that the asymptotic pressure depends only
on D, not on H, hence this is why silos are tall
and skinny, rather than short and squat.
44
Stresses - Converging Section
Over 40 years ago, the pioneer in bulk solids
flow, Andrew W. Jenike, postulated that the
magnitude of the stress in the converging section
of a hopper was proportional to the distance of
the element from the hopper apex. ? ? ( r,
?) This is the radial stress field assumption.
?
r
45
Silo Stresses - Overall
hydrostatic
Bulk solid
Notice that there is essentially no stress at the
outlet. This is good for discharge devices!
46
Janssen Equation - Example
A large welded steel silo 12 ft in diameter and
60 feet high is to be built. The silo has a
central discharge on a flat bottom. Estimate the
pressure of the wall at the bottom of the silo if
the silo is filled with a) plastic pellets, and
b) water. The plastic pellets have the following
characteristics ? 35 lb/cu ft ? 20º The
Janssen equation is Pv (? g D/ 4 ? K) (1 -
exp(-4H ?K/D)) In this case D 12 ft ? tan ?
tan 20º 0.364 H 60 ft g 32.2 ft/sec2
? 35 lb/cu ft
47
Janssen Equation - Example
K, the Janssen coefficient, is assumed to be 0.4.
It can vary according to the material but it is
not often measured. Substituting we get Pv
21,958 lbm/ft - sec2. If we divide by gc, we get
Pv 681.9 lbf/ft2 or 681.9 psf Remember that Pw
K Pv,, so Pw 272.8 psf. For water, P ? g H
and this results in P 3744 psf, a factor of 14
greater!
48
Types of Bins
Conical
Pyramidal
Watch for in-flowing valleys in these bins!
49
Types of Bins
Chisel
Wedge/Plane Flow
L
B
Lgt3B
50
A thought experiment
51
The Flow Function
52
Determination of Outlet Size
?c,t
?c,i
Flow factor
53
Determination of Outlet Size
B ?c,i H(?)/?
H(?) is a constant which is a function of hopper
angle
54
H(?) Function
3
Circular
H(?)
2
Square
Rectangular outlets (L gt 3B)
1
60
20
50
10
30
40
Cone angle from vertical
55
Example Calculation of a Hopper Geometry for
Mass Flow
An organic solid powder has a bulk density of 22
lb/cu ft. Jenike shear testing has determined
the following characteristics given below. The
hopper to be designed is conical. Wall friction
angle (against SS plate) ? 25º Bulk density
? 22 lb/cu ft Angle of internal friction ?
50º Flow function ?c 0.3 ?1 4.3
Using the design chart for conical hoppers, at ?
25º
?c 17º with 3º safety factor ff 1.27
56
Example Calculation of a Hopper Geometry for
Mass Flow
ff ?/?a or ?a (1/ff) ? Condition for no
arching gt ?a gt ?c (1/ff) ? 0.3 ?1
4.3 (1/1.27) ? 0.3 ?1 4.3 ?1 8.82
?c 8.82/1.27 6.95 B 2.2 x 6.95/22 0.69
ft 8.33 in
57
Material considerations for hopper design

• Amount of moisture in product?
• Is the material typical of what is expected?
• Is it sticky or tacky?
• Is there chemical reaction?
• Does the material sublime?
• Does heat affect the material?

58
Material considerations for hopper design

• Is it a fine powder (lt 200 microns)?
• Is the material abrasive?
• Is the material elastic?
• Does the material deform under pressure?

59
Process Questions

• How much is to be stored? For how long?
• Materials of construction
• Is batch integrity important?
• Is segregation important?
• What type of discharger will be used?
• How much room is there for the hopper?

60
Discharge Rates

• Numerous methods to predict discharge rates from
  silos or hopper
• For coarse particles (gt500 microns)
• Beverloo equation - funnel flow
• Johanson equation - mass flow
• For fine particles - one must consider influence
  of air upon discharge rate

61
Beverloo equation

• W 0.58 ?b g0.5 (B - kdp)2.5
• where W is the discharge rate (kg/sec)
• ?b is the bulk density (kg/m3)
• g is the gravitational constant
• B is the outlet size (m)
• k is a constant (typically 1.4)
• dp is the particle size (m)
• Note Units must be SI

62
Johanson Equation

• Equation is derived from fundamental principles -
  not empirical
• W ?b (?/4) B2 (gB/4 tan ?c)0.5
• where ?c is the angle of hopper from vertical
• This equation applies to circular outlets
• Units can be any dimensionally consistent set
• Note that both Beverloo and Johanson show that W
  ? B2.5!

63
Discharge Rate - Example

• An engineer wants to know how fast a compartment
  on a railcar will fill with polyethylene pellets
  if the hopper is designed with a 6 Sch. 10
  outlet. The car has 4 compartments and can carry
  180000 lbs. The bulk solid is being discharged
  from mass flow silo and has a 65 angle from
  horizontal. Polyethylene has a bulk density of 35
  lb/cu ft.

64
Discharge Rate Example

• One compartment 180000/4 45000 lbs.
• Since silo is mass flow, use Johanson equation.
• 6 Sch. 10 pipe is 6.36 in diameter B
• W (35 lb/ft3)(?/4)(6.36/12)2 (32.2x(6.36/12)/4
  tan 25)0.5
• W 23.35 lb/sec
• Time required is 45000/23.35 1926 secs or 32
  min.
• In practice, this is too long - 8 or 10 would
  be a better choice.

65
The Case of Limiting Flow Rates

• When bulk solids (even those with little
  cohesion) are discharged from a hopper, the
  solids must dilate in the conical section of the
  hopper. This dilation forces air to flow from
  the outlet against the flow of bulk solids and in
  the case of fine materials either slows the flow
  or impedes it altogether.

66
Limiting Flow Rates
Interstitial gas pressure
Bulk density
Vertical stress
Note that gas pressure is less than ambient
pressure
67
Limiting Flow Rates

• The rigorous calculation of limiting flow rates
  requires simultaneous solution of gas pressure
  and solids stresses subject to changing bulk
  density and permeability. Fortunately, in many
  cases the rate will be limited by some type of
  discharge device such as a rotary valve or screw
  feeder.

68
Limiting Flow Rates - Carleton Equation
69
Carleton Equation (contd)

• where
• v0 is the velocity of the bulk solid
• ? is the hopper half angle
• ?s is the absolute particle density
• ?f is the density of the gas
• ?f is the viscosity of the gas

70
Silo Discharging Devices

• Slide valve/Slide gate
• Rotary valve
• Vibrating Bin Bottoms
• Vibrating Grates
• others

71
Rotary Valves
Quite commonly used to discharge materials from
bins.
72
Screw Feeders
Dead Region
Better Solution
73
Discharge Aids

• Air cannons
• Pneumatic Hammers
• Vibrators
• These devices should not be used in place of a
  properly designed hopper!

They can be used to break up the effects of time
consolidation.