Episode 44 : Flow Behavior of Granular Materials and PowdersPart III Law of hydrodynamics do not apply to the flow of solid granular materials through orifices: Pressure is not distributed equally in all directions due to the development of arches and to frictional forces between the granules. The rate of flow is not proportional to the head, except at heads smaller than the container diameter. No provision is made in hydrodynamics for size and shape of particles, which greatly influence the flow rate. SAJJAD KHUDHUR ABBAS Ceo , Founder & Head of SHacademy Chemical Engineering , Al-Muthanna University, Iraq Oil & Gas Safety and Health Professional – OSHACADEMY Trainer of Trainers (TOT) - Canadian Center of Human Development

1. SAJJAD KHUDHUR ABBAS
Ceo , Founder & Head of SHacademy
Chemical Engineering , Al-Muthanna University, Iraq
Oil & Gas Safety and Health Professional – OSHACADEMY
Trainer of Trainers (TOT) - Canadian Center of Human
Development
Episode 44 : Flow Behavior of
Granular Materials and Powders
Part III

2. Bin and Hopper Design

3. Figure 1: a. pressure in a silo filled with a fluid (imaginary); b. vertical stress
after filling the silo with a bulk solid; c. vertical stress after the discharge of
some bulk solid

4. Gravity flow through orifices
• Law of hydrodynamics do not apply to the flow of solid granular
materials through orifices:
• Pressure is not distributed equally in all directions due to the development of
arches and to frictional forces between the granules.
• The rate of flow is not proportional to the head, except at heads smaller than
the container diameter.
• No provision is made in hydrodynamics for size and shape of particles, which
greatly influence the flow rate.

5. Particle history

6. 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

7. Mass Flow
Typically need 0.75 D to 1D to
enforce mass flow
D
Material in motion
along the walls
Does not imply plug
flow with equal velocity
all the material in
the hopper is in
motion at
discharge, but
not necessarily at
the same velocity

8. Funnel Flow
“Dead” or non-
flowing region or
stagnant zone
ActiveFlow
Channel
If a hopper wall is too
flat and/or too rough,
funnel flow will
appear.
(centrally moving
core, dead or non-
moving annular
region)

10. Expanded Flow
Funnel Flow
upper section
Mass Flow
bottom
section
mass flow cone with
funnel flow above it

11. Problems with Hoppers
• Ratholing/Piping and Funnel Flow
• Arching/Doming
• Insufficient Flow
• Irregular flow
• Inadequate Emptying
• Time Consolidation - Caking

12. Ratholing/Piping
Stable
Annular
Region
Void
• Occurs in case of funnel flow.
• The reason for this is the strength
(unconfined yield strength) of the bulk
solid.
• If the bulk solid consolidates
increasingly with increasing period of
storage at rest, the risk of ratholing
increases.

13. Funnel Flow
-Segregation
-Inadequate Emptying
-Structural Issues
Coarse
Coarse
Fine

14. Segregation
• In case of centric filling, the larger particles
accumulate close to the silo walls, while the smaller
particles collect in the centre.
• In case of funnel flow, the finer particles, which are
placed close to the centre, are discharged first while
the coarser particles are discharged at the end. If
such a silo is used, for example, as a buffer for a
packing machine, this behaviour will yield to
different particle size distributions in each packing.
• In case of a mass flow, the bulk solid will segregate at
filling in the same manner, but it will become
"remixed" when flowing downwards in the hopper.
Therewith, at mass flow the segregation effect
described above is reduced significantly.

15. Arching/Doming
Cohesive Arch
preventing material from
exiting hopper
• If a stable arch is formed above the outlet
so that the flow of the bulk solid is stopped,
then this situation is called arching.
• In case of fine grained, cohesive bulk
solid, the reason of arching is the strength
(unconfined yield strength) of the bulk solid
which is caused by the adhesion forces
acting between the particles.
• In case of coarse grained bulk solid,
arching is caused by blocking of single
particles.
• Arching can be prevented by sufficiently
large outlets.

16. Insufficient Flow
- Outlet size too small
- Material not sufficiently
permeable to permit dilation in
conical section -> “plop-plop”
flow
Material needs
to dilate here
Material under
compression in
the cylinder
section

17. Irregular flow
• Irregular flow occurs if arches and ratholes are formed and collapse
alternately. Thereby fine grained bulk solids can become fluidized
when falling downwards to the outlet opening, so that they flow out
of the silo like a fluid.
• This behaviour is called flooding. Flooding can cause a lot of dust, a
continuous discharge becomes impossible.

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. 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

20. 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

21. 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

22. 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

23. How is a hopper designed?
• Measure
- powder cohesion/interparticle friction
- wall friction
- compressibility/permeability
• Calculate
- outlet size
- hopper angle for mass flow
- discharge rates

24. Types of Bins
Conical Pyramidal
Watch for in-
flowing valleys
in these bins!

25. Types of Bins
Wedge/Plane Flow
B
L
L>3B
Chisel

26. Design diagram for mass flow (wedge-shaped
hopper)
φw
(angle of wall friction)
θ (slope of hopper wall)
δ = effective angle
of internal friction
θ
δ

27. Design diagram for mass flow (conical
hopper)
φw
(angle of wall friction)
θ (slope of hopper wall)
δ = effective angle
of internal friction
θ δ

28. Stress conditions in the hopper (emptying)
σ′1 = bearing stress, σ1 = major principal stress σc = unconfined yield strength
σc > σ′1 :
arching is stable, no flow
σc < σ′1 : flow

29. Flow function and time flow function

30. Hopper forms

31. Summary
• The design of silos in order to obtain reliable flow is possible on the
basis of measured material properties and calculation methods.
Because badly designed silos can yield operational problems and a
decrease of the product quality, the geometry of silos should be
determined always on the basis of the material properties. The
expenses for testing and silo design are small compared to the costs
of loss of production, quality problems and retrofits.

32. Critical dimensions of hopper openings
• To determine critical dimension, failure conditions must be
established for two basic obstructions; arching (no flow) and piping
(flow may be reduced or limited).
• Consider that the strongest possible arch may form, the critical
opening dimension (B) becomes:
• B ≥ σc/w (for slot opening)
• B ≥ 2σc/w (for circular opening)
Where w = bulk density

33. θ
σ′1
T = thickness
B = opening dimension

34. Flow factor (ff) depends upon:
• δ (effective angle of internal friction)
• φw (angle of wall friction)
• θ (slope of hopper wall)

35. φw
θ
Mass flow
funnel
flow
ff

36. Example
• Calculate the critical width B for arching of the slot opening of a
wedge shaped, mild steel hopper with θ = 30°C

37. • For mild steel hopper
with wall friction angle
= 35°, the maximaum
effective angle of
friction (δ) = 55°
55

38. ff =
1.25

39. ff =
1.25
No
intersection
of ff and this
FF, there is
no arching
problem

40. • From σ1 = 65 lb/ft2
, σc = 50 lb/ft2
, w = 90 lb/ft3
and δ =
55°, therefore B ≥ 50/90 ≥ 0.6 ft or critical slot with for
arching is about 7 inches.
ff =
1.25
There is an
intersection
of ff and this
FF, there is
arching
problem
σc = 50
σ1 = 65

41. Determination of Outlet Size
B = σc,i H(θ)/W
H(θ) is a constant which is a function of hopper angle
Bulk density = W

42. H(θ) Function
Cone angle from vertical
10 20 30 40 50 60
1
2
3
H(θ)
Rectangular outlets (L > 3B)
Square
Circular

43. 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) = ϕw = 25º
Bulk density = W = 22 lb/cu ft
Angle of internal friction = δ = 50º
Flow function σc = 0.3 σ1 + 4.3
Using the design chart for conical hoppers, at ϕw = 25º
θc = 17º with 3º safety factor
& ff = 1.27

44. Example: Calculation of a Hopper Geometry for Mass
Flow
ff = σ/σa or σa = (1/ff) σ
Condition for no arching => σa > σc
(1/ff) σ = 0.3 σ1 + 4.3 (1/1.27) σ = 0.3 σ1 + 4.3
σ1 = 8.82 σc = 8.82/1.27 = 6.95
B = 2.2 x 6.95/22 = 0.69 ft = 8.33 in

45. Discharge Rates (Q)
• Numerous methods to predict discharge rates from silos or hopper
• For coarse particles (>500 microns)
Beverloo equation - funnel flow
Johanson equation - mass flow
• For fine particles - one must consider influence of air upon discharge
rate

46. Beverloo equation
• Q = 0.58 ρb g0.5
(B - kdp)2.5
where Q is the discharge rate (kg/sec)
ρb 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

47. Johanson Equation
• Equation is derived from fundamental principles - not
empirical
• Q = ρb (π/4) B2
(gB/4 tan θc)0.5
where θc 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 Q α B2.5
!

48. Silo Discharging Devices
• Slide valve/Slide gate
• Rotary valve
• Vibrating Bin Bottoms
• Vibrating Grates
• others

49. Rotary Valves
Quite commonly used to discharge
materials from bins.

50. Screw Feeders
Dead Region
Better Solution

51. 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.

52. Flow rate equations
• From Ewalt and Buelow (1963), measuring flow of shell corn from
straight-sided wooden bins equipped with test orifices:
• Horizontal openings, circular orifice (8.4% MC db)
• Q = 0.1196 B3.1
• Horizontal openings, rectangular orifice (12.1% MC db)
• Q = 0.153 W1.62
L1.4
• Vertical openings, circular orifice (12.7% MC db)
• Q = 0.0351 B3.3
• Vertical openings, rectangular orifice (12.4% MC db)
• Q = 0.0573 W1.75
L1.5

53. • Q = KWn
• K and n are two constants which can be found either by substituting
experimental data from two sets of tests and solving the two equations
simultaneously or by determination them directly from the slope and y-
intercepts of the straight line plot of Q versus one of the dimensions on log-
log graph paper.
• Q = f(φi, φr, d/D, D, bulk density and etc.)
• There is no single parameter satisfactory relationship for estimating
Q.

54. • Most important parameter is the opening diameter (greatly affect on
flow rate)
• Q ∝ D3
Log Q
Log D
Slope ~ 2.8-3.2

55. Thanks for Watching
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