CONSIDERATIONS TOWARDS AN EFFECTIVE BIN DESIGN CHET SPARKS ADAORA JOHNSON MATTHEW MILANOWSKI ANAS AL RABBAT MICHAEL MCCLURG 1
Transcript
Slide 1
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Slide 2
2 Understand the Problems of Bulk Solid Flow Perform
Calculations Related to Bin Design Create Matlab Programs That Aid
In Calculations Understand the Components of Effective Bin Design
http://www.fil.ion.ucl.ac.uk/spm/software/spm8/
http://eng.tel-tek.no/Powder-Technology/Silo-design-and-powder-mechanics/Silo-design-based-on-powder-mechanics-overview
http://bulksolidsflow.com.au/
Slide 3
Storage capacity: Always keep in mind the amount of material
that you are going to store because that will effect how many bins
you will need to design. The location of the bin will also effect
the design. Discharge Frequency & rate: How much time will the
solid remain without contact? Around what range will the
instantaneous discharge rate be? Does the rate depend on weight or
on the volume? What is the required feed accuracy? KEY POINTS TO
CONSIDER WHEN DESIGNING BINS
http://research.che.tamu.edu/groups/Seminario/numerical-topics/Bin%20Design.pdf
http://jenike.com/files/2012/10/BlueSiloCollapsing-41.jpg
Slide 4
Temperature and Pressure: Will the material be at a low or high
temperature than its surroundings? Is the material being fed into a
positive or negative pressure environment? Fabrication Materials:
Is the solid abrasive or corrosive? Will there be need for
corrosion-resistant alloys? Are ultrahigh-molecular-weight plastic
liners tolerable? Is the application subject to any regulatory
compliance requirements? Safety and environmental considerations:
Are there any safety environmental issues like material explosive
ability or maximum dust composer limits? Bulk solid uniformity:
What is the required material uniformity ( eg: size, shape,
moisture content) How will particle segregation affect production
and the final product?
http://research.che.tamu.edu/groups/Seminario/numerical-topics/Bin%20Design.pdf
KEY POINTS TO CONSIDER WHEN DESIGNING BINS
http://www.proagro.com.ua/eng/research/grain/4064511.html
Slide 5
UNDERSTAND BULK-SOLIDS FLOW PROBLEMS Arching or Bridging: This
is when a no-flow condition occurs in which a material forms a
stable bridge/dome across the outlet of a bin. Ratholing: Another
no-flow condition in which material forms a stable open channel
within the bin resulting in erratic flow to the downstream process.
Flooding or flushing: a condition in which an aerated bulk solid
behaves like a fluid and flows uncontrollably through an outlet or
feeder. Flowrate limitation: Insufficient flowrate, typically
caused by counter-flowing air slowing the gravity discharge of fine
powder. Particle segregation: segregation may prevent a chemical
reaction, cause out of spec product, or require costly rework.
Capacity: As low as only 10-20% of the bins rated storage capacity.
http://research.che.tamu.edu/groups/Seminario/numerical-topics/Bin%20Design.pdf
Void Arching Ratholing
Slide 6
MEASURE THE FLOW PROPERTIES OF THE BULK SOLID The purpose of
measuring the flow properties is mainly in order to control how the
fluid would behave in a bin. The table shows the most important
bulk-solid handling properties. Variables that affect solid
parameters: Moisture content Particle size, shape, and hardness
Pressure Temperature Storage time at rest Wall surface Chemical
additives
http://research.che.tamu.edu/groups/Seminario/numerical-topics/Bin%20Design.pdf
Slide 7
CALCULATE THE APPROXIMATE SIZE OF THE BIN The above equation is
used to find the height of the cylinder section needed to store the
desired capacity. This design process is iterative. H: Height m:
the mass in Kg. A: the cross-sectional area of the cylinder. avg :
Average bulk density in (kg/m^3) Due to the volume lost at the top
of the cylinder which is due to the bulk solids angle of repose and
along with the volume of material in the hopper section, a
reasonable sufficient estimate for the height can be found by
keeping the height of the bin between one and four times the
diameter or width since values out of that range are most often
uneconomical.
http://research.che.tamu.edu/groups/Seminario/numerical-topics/Bin%20Design.pdf
Slide 8
TYPE OF FLOW PATTERNS- FUNNEL FLOW Funnel Flow Discharge Bulk
solids flow much differently than liquids in tanks. A liquid would
flow in a first-in/first-out sequence, but many bins have flows in
a funnel-flow pattern. Funnel-flow is defined as when some of the
material flows in the center of the hopper while the rest remains
stationary along the walls. Funnel- flow is the most economical
choice if the bulk solid is nondegradable, coarse, free-flowing,
and if the segregation during discharge is not an issue.
http://research.che.tamu.edu/groups/Seminario/numerical-topics/Bin%20Design.pdf
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Slide 9
Many problems can occur when there is funnel-flow. Some
problems include ratholes, arches, caking, equipment failure, etc
Mass-flow occurs when all the material moves when any is
discharged. Mass-flow bins work well with powders, cohesive
materials, materials that degrade with time, and whenever sifting
segregation must be minimized. TYPE OF FLOW PATTERNS- MASS FLOW
Mass Flow Discharge
http://research.che.tamu.edu/groups/Seminario/numerical-topics/Bin%20Design.pdf
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Slide 10
The converging hopper section must be steep enough, the wall
surface friction low enough, and the outlet large enough to allow a
flow without stagnant regions. This will also help prevent arching.
In order to determine the wall friction angle, various wall
surfaces are powder tested. These tests are conducted using a
direct shear tester along the lines of ASTM D-6128. DESIGNING FOR
MASS FLOW http://research.che.tamu.edu/groups/Seminario/numerical-
topics/Bin%20Design.pdf http://www.dietmar-schulze.com/storage.html
Sand will require a steep hopper angle in order to achieve mass
flow because it is a highly frictional bulk solid. Smooth catalyst
beds will achieve mass flow at a relatively shallow hopper angle
because it is a low-friction bulk solid. 10
Slide 11
To prevent arching you must measure the cohesive strength of
the material you want to transport. DESIGNING FOR MASS FLOW
http://research.che.tamu.edu/groups/Seminario/numerical-topics/Bin%20Design.pdf
http://www.dietmar-schulze.com/storage.html First the flow function
of the material, the is measured in a laboratory test according to
ASTM D-6128 with a direct shear tester. Just like in the wall
friction test, consolidating forces are applied to a material. In
the test cell, the force required to shear the material is
measured. Minimum outlet sizes needed to avoid arching can be
calculated once the flow function is determined. 11
Slide 12
This equation can be used to approximate the maximum discharge
rate from a converging hopper. This can only be used if the bulk
material is coarse and free- flowing. In order for a material to be
considered coarse, the particles must have a diameter of at least 3
mm (1/8 in). An example of this scenario is on the next slide. In
the above equation, the variables are defined as: M: mass flow rate
(kg/s) : bulk density (kg/m 3 ) A: outlet area (m 2 ) g:
acceleration (m/s 2 ) B: outlet size (m) : mass-flow hopper angle
measured from vertical (deg.) m: outlet parameter dependent on type
of hopper For conical: m = 1 for a circular outlet For
wedge-shaped: m = 0 for a slot-shaped outlet
http://research.che.tamu.edu/groups/Seminario/numerical-topics/Bin%20Design.pdf
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Slide 13
TYPES OF BULK SOLIDS This equation only works for coarse and
free-flowing material because it neglects the materials resistance
to airflow. For example, the equation would not correctly estimate
the flow rate for a fine powder. The fine powder would have
particles with diameters much less than 3 mm and would be greatly
affected by airflow. Thus, the equation would give an answer that
is much greater than the true value for the mass flow rate. Mass
flowing bulk solids
http://upload.wikimedia.org/wikipedia/commons/9/98/Rhodium_powder_pressed_melted.jpg
Does not follow mass flow equations
http://research.che.tamu.edu/groups/Seminario/numerical-topics/Bin%20Design.pdf
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Slide 14
function [ M ] = DischargeRate( rho,A,g,B,theta,m ) %
DischargeRate: Approximates the maximum discharge rate from a
converging % hopper. % For this function to be accurate, one must
assume that the bulk material % is both coarse and free-flowing,
such as plastic pellets. % Input: % rho = bulk density (kg/m^3) % A
= outlet area (m^3) % g = acceleration (m/s^2) % B = outlet size
(m) % theta = mass flow hopper angle measured from vertical (deg.)
% m = 1 for a circular outlet and m = 0 for a slot shaped outlet %
Output: % M = mass flowrate (kg/s)
M=rho*A*sqrt((B*g)/(2*(1+m)*tan(theta*pi/180))); end FUNCTION THAT
CALCULATES MASS FLOW RATE 14
Slide 15
>> DischargeRate(10,1,9.81,1,60,1) ans = 11.8994 >>
DischargeRate(10,1,9.81,1,60,0) ans = 16.8283 RESULTS The first
answer is for a circular outlet. The second answer is for a
slot-shaped outlet with the same parameters.
http://www.inti.gob.ar/cirsoc/pdf/silos/SolidsNotes10HopperDesign.pdf
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FLOW RATE VS HOPPER ANGLE 16
Slide 17
% Creates a graph that shows the comparison of circular and
slot- shaped % outlets. The mass flow rates are plotted versus the
mass flow hopper % angle measured from vertical. % rho = bulk
density (kg/m^3) rho=10; % A = outlet area (m^3) A=1; % B = outlet
size (m) B=1; % g = acceleration (m/s^2) g=9.81; % The values for
theta are from 1 degree to 90 degrees. theta=(1:1:90); % Mc = mass
flow rate for a circular outlet (kg/s)
Mc=rho*A*sqrt((B*g)./(2*(1+1)*tan(theta*pi/180))); % Ms = mass flow
rate for a slot-shaped outlet (kg/s)
Ms=rho*A*sqrt((B*g)./(2*(1+0)*tan(theta*pi/180)));
plot(theta,Mc,'-b',theta,Ms,'--r') title('Comparison of Outlets')
xlabel('mass flow hopper angle measured from vertical (deg.)')
ylabel('mass flowrate (kg/s)') legend('Circular','Slot-shaped') THE
PREVIOUS PLOT COMPARES THE TWO SHAPES OF OUTLETS AND ALSO THE MASS
FLOW WITH RESPECT TO A CHANGING HOPPER ANGLE. AS THE PLOT SHOWS,
THE SLOT-SHAPED OUTLET HAS A LARGER MASS FLOW FOR ALL VALUES OF THE
HOPPER ANGLE THAN THE CIRCULAR OUTLET. THE PART OF THE GRAPH
BETWEEN 20 AND 70 IS WHERE A REALISTIC HOPPER ANGLE WOULD EXIST. IN
THIS REGION, AN INCREASING LEADS TO A DECREASE IN MASS FLOW.
ESSENTIALLY AS THE SLOPE OF THE BIN DECREASES, LESS MASS EXITS THE
BOTTOM OF THE BIN PER UNIT TIME. THE CODE THAT CREATED THE PLOT IS
GIVEN BELOW: 17
Slide 18
The main factors for funnel flow are making the hopper slope
steep enough to be self-cleaning, and sizing the hopper outlet
large enough to overcome arching and ratholing. For the bin to
capable of self-cleaning, the hopper slope must be 15-20 degrees
steeper than the wall friction angle, assuming that a rathole has
not formed. Knowledge of the materials cohesive strength and
internal friction is needed in order to determine the minimum
dimensions to overcome ratholing and arching. For funnel flow, the
design of the mass-flow bins is independent of scale, but the
overall size matters. Thus, large funnel flow bins have a higher
ratholing tendency, while mass flow bins have no chance of
ratholing. DESIGNING FOR FUNNEL FLOW Flow Channel Non-flowing
region
http://research.che.tamu.edu/groups/Seminario/numerical-topics/Bin%20Design.pdf
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Slide 19
Unfortunately, some fluids have properties that can make flow
calculations difficult. In these cases, collecting experimental
data and interpolating can be the next best thing. For example,
this data was generated to simulate storing a very viscous,
shear-thickening, non Newtonian fluid. This liquid rapidly thickens
and becomes more adhesive when exposed to a high pressure gradient.
While the exact calculations are beyond the scope of this project,
the data shows that at any angle less than 30 degrees from
vertical, flow rate drops rapidly as the fluid hardens into a gooey
solid. The question is, how do we model this flow and find a
theoretical maximum rate? EXPERIMENTAL FLOW CALCULATIONS: Angle
From Vertical Flow (in^3/s) 54.1 104.7 156.1 208.2 2527.3 Angle
From Vertical Flow (in^3/s) 3086.2 3560.3 4076.4 4566.1 5054.1
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Slide 20
We use splines to interpolate the data and provide a model fit.
Our matlab code was: Our graph provides estimated flow values at
any angle from 5 to 50 from vertical. It shows our theoretical
maximum flow is around 90 in^3/s at approx 32 degrees from
vertical. EXPERIMENTAL FLOW CONT. AN=[5 10 15 20 25 30 35 40 45
50];F=[4.1 4.7 6.1 8.2 27.3 86.2 80.3 76.4 66.1 54.1];
EF=spline(AN,F,linspace(5,50,250)); ANE=linspace(5,50,250);
plot(ANE,EF);hold on;plot(AN,F,'*k'); xlabel('Angle from
vertical'),ylabel('flow rate (in^3/s)'),title('Experimental flow
calculations') legend('Experimental fit','Table values') 20
Slide 21
Ratholes can cause serious problems with flow. To better
understand the issues they cause, this function calculates the
fraction of usable flow area left by a rathole, and the fraction of
the total volume of the bin the rathole takes up. It makes the
assumption that you are using an economically designed (H=(1:4)*max
diameter) cylindrical hopper with a centered cylindrical rathole
and a circular outlet. Additionally, it assumes the material is not
significantly large and has negligable tendency to clump together.
The function is as follows: RATHOLE CALCULATIONS function [FA,FV]=
Rathole(DI,DO,Hbin,DR,BA); %Inputs: %DI is the input diameter, or
the diameter of the cylindrical bin %DO is the output diameter, or
the diameter of the circular outlet %Hbin is the height of the
cylindrical bin area %DR is the diameter of the rathole %BA is the
bin angle in degrees. %Outputs %FA is the usable fractional area of
the outlet for flow %FV is the fraction of the total volume of the
bin the rathole takes up %In function %AI,AO,RA are the input,
output, and rathole area %HC and HT are the height of the conical
bottom section and the total area %Vtotal and VR are the total
volume of the bin and the rathole volume 21
Slide 22
if Hbin 4*DI, error('Bin height should be 1 to 4 times bin
diameter to be economical.') end if DR > DO | DO > DI,
error('Diameters should be: DI>DO>DR') end %Our article
stated that H should be DI*(1-4); this step checks that condition
and other logical conditions
AI=pi.*DI.^2./4;AO=pi.*DO.^2./4;RA=pi.*(DR.^2)./4; %This step
calculates the input, output, and rathole area. UA=AO-RA; %This
step computes the usable area by subtracting rathole area from
output area. FA=UA./AO; %The fractional area is computed by
dividing the usable area by the output area.
HC=(DI-DO)./2.*tand(BA);HT=HC+Hbin; %The height of the bottom
section is computed by the slope of the bin and the difference of
the %input and output diameters, assuming the bottom section is
approximately a frustrum of a cone.
Vtotal=pi.*HC./3.*(DI.^2+DO.*DI+DO.^2)+AI.*Hbin; %The volume total
is a combination of the formula for the volume of a %cylinder for
the top combined with the volume of the bottom frustrum. VR=HT.*RA;
%The volume of the rathole is calculated by multiplying the bins
total height by the ratholes area. FV=VR./Vtotal; %The fractional
volume of the rathole is calculted by dividing the rathole volume
by the total volume. RATHOLE FUNCTION CONTINUED: 22
Slide 23
Assuming a bin with a 10 foot diameter inlet, a cylindrical bin
height of 25 ft before the conical section, a bin angle of 60
degrees from horizontal, and a varying output diameter, this graph
shows the effect of ratholes on fractional output area. As you can
see, even small ratholes cause immediate drops in the usable flow
area, even when the output diameter is very large (1/2 inlet
diameter) While it is not shown, the fraction of the total volume
taken up by these ratholes is very low; the maximum was just over
20% for a rathole that was 5 ft across, or half the diameter of the
input. For outlets that are small fractions of the inlet diameter,
less than 5% of the total volume will cause near complete loss of
usable flow area EXAMPLE RATHOLE CALCULATIONS 23
Slide 24
The Janssen equation, as seen in (CITE OTHER POWERPOINT HERE),
calculates the pressure on a bin as a factor of bin major diameter,
bin height, gravity, material density, Janssen coefficient, and bin
angle from vertical. *INSERT FIGURE WITH EQUATION HERE* But what if
we know the maximum pressure our bin can support, but want to
figure out the minimum deviation from vertical our bin can support?
We can use Matlabs fzeroes function, the Janssen equation, and our
maximum pressure to solve for the minimum angle from vertical.
JANSSEN CALCULATIONS: function AD = Amin(D,H,y,g,K,pmax); %This
function calculates the minimum angle from the vertical a hopper
must be using the Janssen equation. %The function calculates angle
using US units. % We use.8 pmax in our calculations as a safety
factor, so that fluctuations during use do not go over our maximum
tolerance. %D=Diameter, H=Height, y=density, g=gravitational
acceleration %K=Janssen coefficient,pmax=max pressure %AD is the
minimum bin angle from vertical in degrees. AD=fzero(@(x)
((y.*g.*D./(4.*tand(x).*K)).*(1-exp(-4.*H.*tand(x).*K./D))-.8.*pmax),45);
%This finds the zeroes of an anonymous Janssen function of angle,
minus the (practical) pmax. %It guesses an intermediate angle of 45
degrees to start. if AD>70, error('Pmax is too low to be
practical') elseif AD