bin and hopper design lecture
TRANSCRIPT
![Page 1: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/1.jpg)
3/17/00 KVJ 1
Bin and Hopper Design
Karl Jacob
The Dow Chemical Company
Solids Processing Lab
![Page 2: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/2.jpg)
3/17/00 KVJ 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?
![Page 3: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/3.jpg)
3/17/00 KVJ 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
![Page 4: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/4.jpg)
3/17/00 KVJ 4
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
![Page 5: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/5.jpg)
3/17/00 KVJ 5
Funnel Flow
“Dead” or non-flowing region
Act
ive
Flo
w
Cha
nnel
![Page 6: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/6.jpg)
3/17/00 KVJ 6
Expanded Flow
Funnel Flow upper section
Mass Flow bottom section
![Page 7: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/7.jpg)
3/17/00 KVJ 7
Problems with Hoppers
Ratholing/Piping
![Page 8: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/8.jpg)
3/17/00 KVJ 8
Ratholing/Piping
Stable Annular Region
Vo
id
![Page 9: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/9.jpg)
3/17/00 KVJ 9
Problems with Hoppers
Ratholing/Piping Funnel Flow
![Page 10: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/10.jpg)
3/17/00 KVJ 10
Funnel Flow-Segregation
-Inadequate Emptying
-Structural Issues
Coa
rse
Coa
rse
Fin
e
![Page 11: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/11.jpg)
3/17/00 KVJ 11
Problems with Hoppers
Ratholing/Piping Funnel Flow Arching/Doming
![Page 12: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/12.jpg)
3/17/00 KVJ 12
Arching/Doming
Cohesive Arch preventing material from exiting hopper
![Page 13: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/13.jpg)
3/17/00 KVJ 13
Problems with Hoppers
Ratholing/Piping Funnel Flow Arching/Doming Insufficient Flow
![Page 14: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/14.jpg)
3/17/00 KVJ 14
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
![Page 15: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/15.jpg)
3/17/00 KVJ 15
Problems with Hoppers
Ratholing/Piping Funnel Flow Arching/Doming Insufficient Flow Flushing
![Page 16: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/16.jpg)
3/17/00 KVJ 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 --> improper use of aeration devices, collapse of a rathole
![Page 17: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/17.jpg)
3/17/00 KVJ 17
Problems with Hoppers
Ratholing/Piping Funnel Flow Arching/Doming Insufficient Flow Flushing Inadequate Emptying
![Page 18: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/18.jpg)
3/17/00 KVJ 18
Inadequate emptyingUsually occurs in funnel flow silos where the cone angle is insufficient to allow self draining of the bulk solid.
Remaining bulk solid
![Page 19: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/19.jpg)
3/17/00 KVJ 19
Problems with Hoppers
Ratholing/Piping Funnel Flow Arching/Doming Insufficient Flow Flushing Inadequate Emptying Mechanical Arching
![Page 20: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/20.jpg)
3/17/00 KVJ 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
![Page 21: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/21.jpg)
3/17/00 KVJ 21
Problems with Hoppers
Ratholing/Piping Funnel Flow Arching/Doming Insufficient Flow Flushing Inadequate Emptying Mechanical Arching Time Consolidation - Caking
![Page 22: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/22.jpg)
3/17/00 KVJ 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
![Page 23: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/23.jpg)
3/17/00 KVJ 23
Segregation
Mechanisms
- Momentum or velocity
- Fluidization
- Trajectory
- Air current
- Fines
![Page 24: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/24.jpg)
3/17/00 KVJ 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
![Page 25: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/25.jpg)
3/17/00 KVJ 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
![Page 26: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/26.jpg)
3/17/00 KVJ 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
![Page 27: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/27.jpg)
3/17/00 KVJ 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
![Page 28: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/28.jpg)
3/17/00 KVJ 28
What about angle of repose?
Pile of bulk solids
![Page 29: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/29.jpg)
3/17/00 KVJ 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!
![Page 30: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/30.jpg)
3/17/00 KVJ 30
Bulk Solids Testing
Wall Friction Testing Powder Shear Testing - measures both
powder internal friction and cohesion Compressibility Permeability
![Page 31: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/31.jpg)
3/17/00 KVJ 31
Sources of Cohesion (Binding Mechanisms)
Solids Bridges
-Mineral bridges
-Chemical reaction
-Partial melting
-Binder hardening
-Crystallization
-Sublimation Interlocking forces
Attraction Forces
-van der Waal’s
-Electrostatics
-Magnetic Interfacial forces
-Liquid bridges
-Capillary forces
![Page 32: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/32.jpg)
3/17/00 KVJ 32
Testing Considerations
Must consider the following variables
- time
- temperature
- humidity
- other process conditions
![Page 33: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/33.jpg)
3/17/00 KVJ 33
Wall Friction TestingWall friction test is simply Physics 101 - difference for bulk solids is that the friction coefficient, , is not constant.
P 101
N
FF = N
![Page 34: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/34.jpg)
3/17/00 KVJ 34
Wall Friction Testing
Jenike Shear Tester
Wall Test Sample
Ring
CoverW x A
S x A
Bracket
Bulk Solid
![Page 35: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/35.jpg)
3/17/00 KVJ 35
Wall Friction Testing Results
Wall Yield Locus, constant wall friction
’
Normal stress,
Wa
ll sh
ear
str
ess
,
Wall Yield Locus (WYL), variable wall friction
Powder Technologists usually express as the “angle of wall friction”, ’
’ = arctan
![Page 36: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/36.jpg)
3/17/00 KVJ 36
Jenike Shear Tester
Ring
CoverW x A
S x A
Bracket
Bulk SolidBulk Solid
Shear plane
![Page 37: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/37.jpg)
3/17/00 KVJ 37
Other Shear Testers
Peschl shear tester Biaxial shear tester Uniaxial compaction cell Annular (ring) shear testers
![Page 38: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/38.jpg)
3/17/00 KVJ 38
Ring Shear Testers
W x ABottom cell rotates slowly
Arm connected to load cells, S x A
Bulk solid
![Page 39: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/39.jpg)
3/17/00 KVJ 39
Shear test data analysis
C fc 1
![Page 40: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/40.jpg)
3/17/00 KVJ 40
Stresses in Hoppers/Silos
Cylindrical section - Janssen equation Conical section - radial stress field
Stresses = Pressures
![Page 41: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/41.jpg)
3/17/00 KVJ 41
Stresses in a cylinder
h
dh
Pv A
D
(Pv + dPv) A
A g dh
D d
hConsider 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 + dPv) A + D dh = Pv A + A g dh
![Page 42: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/42.jpg)
3/17/00 KVJ 42
Stresses in a cylinder (cont’d)Two key substitutions
= Pw (friction equation)
Janssen’s 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 h=0, Pv = 0 and h=H and Pv = Pv
Pv = ( g D/ 4 K) (1 - exp(-4H K/D))
This is the Janssen equation.
![Page 43: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/43.jpg)
3/17/00 KVJ 43
Stresses in a cylinder (cont’d)
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.
![Page 44: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/44.jpg)
3/17/00 KVJ 44
Stresses - Converging Section
r
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.
![Page 45: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/45.jpg)
3/17/00 KVJ 45
Silo Stresses - Overall
hydrostatic
Bulk solidNotice that there is essentially no stress at the outlet. This is good for discharge devices!
![Page 46: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/46.jpg)
3/17/00 KVJ 46
Janssen Equation - ExampleA 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
![Page 47: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/47.jpg)
3/17/00 KVJ 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!
![Page 48: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/48.jpg)
3/17/00 KVJ 48
Types of BinsConical Pyramidal
Watch for in-flowing valleys in these bins!
![Page 49: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/49.jpg)
3/17/00 KVJ 49
Types of BinsWedge/Plane Flow
B
L
L>3B
Chisel
![Page 50: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/50.jpg)
3/17/00 KVJ 50
A thought experiment
1c
![Page 51: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/51.jpg)
3/17/00 KVJ 51
The Flow Function
1
c
Flow function
Time flow function
![Page 52: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/52.jpg)
3/17/00 KVJ 52
Determination of Outlet Size
1
c
Flow function
Time flow function
Flow factor
c,i
c,t
![Page 53: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/53.jpg)
3/17/00 KVJ 53
Determination of Outlet Size
B = c,i H()/
H() is a constant which is a function of hopper angle
![Page 54: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/54.jpg)
3/17/00 KVJ 54
H() Function
Cone angle from vertical10 20 30 40 50 60
1
2
3
H(
)
Rectangular outlets (L > 3B)
Square
Circular
![Page 55: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/55.jpg)
3/17/00 KVJ 55
Example: Calculation of a Hopper Geometry for Mass FlowAn 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
![Page 56: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/56.jpg)
3/17/00 KVJ 56
Example: Calculation of a Hopper Geometry for Mass Flow
ff = /a or a = (1/ff)
Condition for no arching => a > 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
![Page 57: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/57.jpg)
3/17/00 KVJ 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?
![Page 58: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/58.jpg)
3/17/00 KVJ 58
Material considerations for hopper design
Is it a fine powder (< 200 microns)? Is the material abrasive? Is the material elastic? Does the material deform under
pressure?
![Page 59: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/59.jpg)
3/17/00 KVJ 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?
![Page 60: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/60.jpg)
3/17/00 KVJ 60
Discharge Rates
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
![Page 61: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/61.jpg)
3/17/00 KVJ 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
![Page 62: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/62.jpg)
3/17/00 KVJ 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!
![Page 63: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/63.jpg)
3/17/00 KVJ 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.
![Page 64: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/64.jpg)
3/17/00 KVJ 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.
![Page 65: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/65.jpg)
3/17/00 KVJ 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.
![Page 66: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/66.jpg)
3/17/00 KVJ 66
Limiting Flow Rates
Vertical stress
Bulk
density
Interstitial gas pressure
Note that gas pressure is less than ambient pressure
![Page 67: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/67.jpg)
3/17/00 KVJ 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.
![Page 68: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/68.jpg)
3/17/00 KVJ 68
Limiting Flow Rates - Carleton Equation
gd
v
B
v
ps
ff 3/5
3/40
3/23/120
15sin4
![Page 69: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/69.jpg)
3/17/00 KVJ 69
Carleton Equation (cont’d)
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
![Page 70: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/70.jpg)
3/17/00 KVJ 70
Silo Discharging Devices
Slide valve/Slide gate Rotary valve Vibrating Bin Bottoms Vibrating Grates others
![Page 71: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/71.jpg)
3/17/00 KVJ 71
Rotary Valves
Quite commonly used to discharge materials from bins.
![Page 72: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/72.jpg)
3/17/00 KVJ 72
Screw FeedersDead Region
Better Solution
![Page 73: Bin and Hopper Design Lecture](https://reader030.vdocuments.us/reader030/viewer/2022013107/546f15efb4af9f6f098b4738/html5/thumbnails/73.jpg)
3/17/00 KVJ 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.