3/17/00kvj1 bin and hopper design karl jacob the dow chemical company solids processing lab...
TRANSCRIPT
3/17/00 KVJ 1
Bin and Hopper Design
Karl Jacob
The Dow Chemical Company
Solids Processing Lab
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?
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
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
3/17/00 KVJ 5
Funnel Flow
“Dead” or non-flowing region
Act
ive
Flo
w
Cha
nnel
3/17/00 KVJ 6
Expanded Flow
Funnel Flow upper section
Mass Flow bottom section
3/17/00 KVJ 7
Problems with Hoppers
Ratholing/Piping
3/17/00 KVJ 8
Ratholing/Piping
Stable Annular Region
Vo
id
3/17/00 KVJ 9
Problems with Hoppers
Ratholing/Piping Funnel Flow
3/17/00 KVJ 10
Funnel Flow-Segregation
-Inadequate Emptying
-Structural Issues
Coa
rse
Coa
rse
Fin
e
3/17/00 KVJ 11
Problems with Hoppers
Ratholing/Piping Funnel Flow Arching/Doming
3/17/00 KVJ 12
Arching/Doming
Cohesive Arch preventing material from exiting hopper
3/17/00 KVJ 13
Problems with Hoppers
Ratholing/Piping Funnel Flow Arching/Doming Insufficient Flow
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
3/17/00 KVJ 15
Problems with Hoppers
Ratholing/Piping Funnel Flow Arching/Doming Insufficient Flow Flushing
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
3/17/00 KVJ 17
Problems with Hoppers
Ratholing/Piping Funnel Flow Arching/Doming Insufficient Flow Flushing Inadequate Emptying
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
3/17/00 KVJ 19
Problems with Hoppers
Ratholing/Piping Funnel Flow Arching/Doming Insufficient Flow Flushing Inadequate Emptying Mechanical Arching
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
3/17/00 KVJ 21
Problems with Hoppers
Ratholing/Piping Funnel Flow Arching/Doming Insufficient Flow Flushing Inadequate Emptying Mechanical Arching Time Consolidation - Caking
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
3/17/00 KVJ 23
Segregation
Mechanisms
- Momentum or velocity
- Fluidization
- Trajectory
- Air current
- Fines
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
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
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
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
3/17/00 KVJ 28
What about angle of repose?
Pile of bulk solids
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!
3/17/00 KVJ 30
Bulk Solids Testing
Wall Friction Testing Powder Shear Testing - measures both
powder internal friction and cohesion Compressibility Permeability
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
3/17/00 KVJ 32
Testing Considerations
Must consider the following variables
- time
- temperature
- humidity
- other process conditions
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
3/17/00 KVJ 34
Wall Friction Testing
Jenike Shear Tester
Wall Test Sample
Ring
CoverW x A
S x A
Bracket
Bulk Solid
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
3/17/00 KVJ 36
Jenike Shear Tester
Ring
CoverW x A
S x A
Bracket
Bulk SolidBulk Solid
Shear plane
3/17/00 KVJ 37
Other Shear Testers
Peschl shear tester Biaxial shear tester Uniaxial compaction cell Annular (ring) shear testers
3/17/00 KVJ 38
Ring Shear Testers
W x ABottom cell rotates slowly
Arm connected to load cells, S x A
Bulk solid
3/17/00 KVJ 39
Shear test data analysis
C fc 1
3/17/00 KVJ 40
Stresses in Hoppers/Silos
Cylindrical section - Janssen equation Conical section - radial stress field
Stresses = Pressures
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
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.
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.
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.
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!
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
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!
3/17/00 KVJ 48
Types of BinsConical Pyramidal
Watch for in-flowing valleys in these bins!
3/17/00 KVJ 49
Types of BinsWedge/Plane Flow
B
L
L>3B
Chisel
3/17/00 KVJ 50
A thought experiment
1c
3/17/00 KVJ 51
The Flow Function
1
c
Flow function
Time flow function
3/17/00 KVJ 52
Determination of Outlet Size
1
c
Flow function
Time flow function
Flow factor
c,i
c,t
3/17/00 KVJ 53
Determination of Outlet Size
B = c,i H()/
H() is a constant which is a function of hopper angle
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
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
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
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?
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?
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?
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
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
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!
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.
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.
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.
3/17/00 KVJ 66
Limiting Flow Rates
Vertical stress
Bulk
density
Interstitial gas pressure
Note that gas pressure is less than ambient pressure
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.
3/17/00 KVJ 68
Limiting Flow Rates - Carleton Equation
gd
v
B
v
ps
ff 3/5
3/40
3/23/120
15sin4
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
3/17/00 KVJ 70
Silo Discharging Devices
Slide valve/Slide gate Rotary valve Vibrating Bin Bottoms Vibrating Grates others
3/17/00 KVJ 71
Rotary Valves
Quite commonly used to discharge materials from bins.
3/17/00 KVJ 72
Screw FeedersDead Region
Better Solution
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.