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The seventh lecture in the module Particle Technology, delivered to second year students who have already studied basic fluid mechanics. Centrifugal Separation covers both sedimenting and filtering centrifuges as well as hydrocyclones. Adaptation of the gravity settling and conventional filtration models, to account for the conceptual centrifugal acceleration, is included. Examples of industrial equipment for centrifugal separation are included.
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Centrifugal Separation
Chapter 8 in Fundamentals
Professor Richard Holdich
[email protected] Course details: Particle Technology, module code: CGB019 and CGB919, 2nd year of study.
Watch this lecture at http://www.vimeo.com/10203052
Visit http://www.midlandit.co.uk/particletechnology.htm
for further resources.
Centrifugal separation
Sedimenting centrifuges Particle motion in a centrifugal field Sigma theory Hydrocyclones Grade efficiency & cut size Filtering centrifuges Adaptation of filtration equations Washing (ratio) & Drying
Scroll Discharge Decanter
Archimedian screw to convey solids out of the centrifuge
Imperforate bowl, i.e. sedimenting not filtering
Image courtesy of Thomas Broadbent & Sons Limited Image courtesy of Siebtechnik GmbH
Scroll Discharge Decanter
Screw rotates at only slight differential speed to the centrifuge - solids leave at one end, centrate at the other.
Image courtesy of Siebtechnik GmbH
Tubular bowl centrifuge
This one is vertical axis - simple design with no internals for clarification or liquid/liquid separation - a more complicated design is the chamber bowl.
Image removed for copyright reasons. For an example product please see
http://www.sharpenntechnologies.com/pcat-gifs/products-large2/high-speed-centrifuge1111-2.jpg
.
Disc stack centrifuge
Like a lamella clarifier: internal surfaces to encourage settling - usually used in oil/water separation and cream
Sedimenting Centrifuges –
Let’s confine our analysis to a simple geometry - ignoring the complicated internal structures required to remove deposited solids and oil concentrates.
Air core
Inner radius
Outer radius
Liquid flow out
Gravity settling
Field force (weight) is:
Drag force is:
gx
s )(6
3
xU3
Giving:
18
)(2 gxU s
t
Centrifugal settling
Field force (weight) is:
Drag force is:
23
)(6
r
xs
xU3
Giving:
18
)(
d
d 22 rx
t
r s
Centrifugal settling
i.e. U = f(r)
r
18
)(
d
d 22 rx
t
r s
i.e. U = dr/dt
Sedimenting Centrifuges
Centrifugal settling
i.e. the radial residence time in the machine
limits: r=r1 at t=0 to r=r2 at t=t
Giving:
18
)(
d
d 22 rx
t
r s
2212
)(
)/ln(18
sx
rrt
Horizontal/axial residence time
where
Qt
Volume
LrrV )( 21
22
Sedimenting Centrifuges
Critical trajectory model
Residence time axially and radially is the same.
Q
V
x
rrt
s
22
12
)(
)/ln(18
Critical trajectory model
Multiply through by ‘g’:
)/ln(18
)(
12
22
rrg
gx
V
Q s
Critical trajectory model
Multiply through by ‘g’:
)/ln(18
)(
12
22
rrg
gx
V
Q s
Square bracketed term is the terminal settling velocity of a particle of size x.
Critical trajectory model- Eq 8.10 & 5.28!
Rearrange:
)/ln( 12
2
rrg
V
U
Q
t
c.f. a gravity settling basin
m2
Machine parameters
)/ln( 12
2
rrg
V
The theoretical settling basin equivalent PLAN area given the dimensions of the machine in question and its operating conditions.
m2
Process parameters
tU
Q
The measured value given the process flow rate and operating performance for the 100% cut-off.
m2
Sigma values
)/ln( 12
2
rrg
VSigma machine m2
tU
QSigma process m2
The two sigma values are equal for 100% efficient machines - normally 40 to 60% may be achieved.
Uses of sigma values
To compare between different machines of same geometry
Attempts to compare between different types of machines
Estimate of machine size required to replace gravity settling clarifier
You need a density difference!
Flue gas desulphurisation
Feed:CaSO4 - 35water - 65 100%
Cake:CaSO4 - 70water - 30 100%
Centrate:CaSO4 - 2.7water - 97.3 100%
All concentrations as mass percent
Hydrocyclone
Single unit and array:
Defined by diameterof cylindrical section
Image showing "Krebs gMAX® Hydrocyclones" courtesy of FLSmidth Krebs Inc.
Means of separation
Centrifugal: 800 g in 300 mm hydrocyclone 50000 g in 10 mm hydrocyclone
Type of separator: a classifier (i.e. splits into sizes) a thickener (i.e. concentrates
suspensions)
Operating data
Diameters: 0.01 to 1 metre
Solid (cut) sizes: 2 to 250 microns
Flow rates (single unit):0.1 - 5000 m3
h-1
Pressure drop: 6 to 0.4 barU/F solid content: up to 50% v/v
(claimed)
Principal features
Note: primary & secondary vortex, air core, U/F, O/F, tangential feed
Tangential velocity
Radial velocity
Axial velocity
Grade efficiency – Cut Point
Feed distribution is split into two fractions: Overflow
Underflow
Grade efficiency
Fraction by mass of each grade entering the U/F of the hydrocyclone.
Recovery is the overall fraction entering the U/F - usually by volume.
Grade efficiency
Equation:
feedin gradein mass
underflowin gradein massE
Grade efficiency
What is the grade efficiency of the following?
Overflow50 kg/h
Underflow50 kg/h
Grade efficiency
Equation:
feedin gradein mass
underflowin gradein massE
100%
Rf
0%
Grade efficiency
i.e. we need to correct for effect due to flow split in order to reliably record the ability of the device to act as a classifier.
The reduced grade efficiency.
Grade efficiency
Reduced grade efficiency:
fREE '
Normalised reduced grade efficiency:
f
f
R
REE
1
''
<100%
100%
Equilibrium Orbit Theory
A particle orbiting on the LZVV has no net tendency to move into the primary vortex (then O/F) or secondary vortex (then U/F).
It must be equal to the cut size x50%.
Equilibrium Orbit Theory
Force balance: centrifugal
23 )(6
is rx
Tangential velocity:i
i
r
v
Liquid drag: Ux3 FD FC
Hydrocyclones - types and configurations
Oil/water separation - often offshore
Filtering Centrifuges
A perforated bowl - similar to a spin dryer
See box on page 83 for descriptions
Filtering Centrifuge – Section 8.3
Pusher generally coarse solids > 50 microns (semi)-continuous solids output careful balance of slurry in
Image courtesy of Siebtechnik GmbH
Filtering Centrifuge
Peeler generally solids > 5 microns usually intermittent solids output - slow to
50 rpm
Image removed for copyright reasons.
Please search online for an image of a peeler centrifuge.
Filtering Centrifuge
Inverting Bag generally solids > 5 microns intermittent solids output
Image removed for copyright reasons.
Please search online for an image of an inverting bag centrifuge.
Filtering centrifuge - full cycle
Function Time(s) Time(%) Accelerate from 50 to 500 rpm 40 5Load/Filter at 500 rpm 277 32Accelerate to 1050 rpm 90 10Spin dry at 1050 rpm 119 14Wash at 1050 rpm 10 1Spin dry at 1050 rpm 236 27Slow down to 50 rpm 90 10Unload at 50 rpm 15 2
Total cycle time 877 100Basket load per cycle of solids 140 kgProductivity 575 kg/hour
Centrifuge - simple analysis – Fig 8.9
Definitions:
Ptotal = Pcake + Pmedium
Centrifuge - simple analysis
- same as for conventional filtration
However, the radius at which the cake forms is continually moving inwards and the geometry is not planar.
hrA oo 2where:
AQRA
cVP m /)(
om A
QR
A
cVP
Centrifuge - simple analysis
Centrifugal head - the driving pressure:
2/)( 222Lo rrP
where omega is in seconds-1 = (2 pi/60)RPMDensity is that of the slurry or liquid depending upon the operation: filtering or washing
Centrifuge - washing
but rc remains constant during the washing stage. The time to wash with Vw m3 of solvent is:
hrR
rr
hC
rrQ
o
m
c
os
Lom
2ln
2
2/)( 222
wo
m
c
os V
r
R
r
rC
Pht
ln2
Centrifuge - washing
Typical washing performance:
Wash volumes
Solute concn.Initial concn.
0
1
0.5
1 2 3
Flooded cake
Dewatered cake
Centrifuge - drainage
Time or dimensionless drainage time
Relative saturation
0
1
0.5
0.2 0.4
0.6
Irreducible saturation
SS* = S
Sinitial
This resource was created by Loughborough University and released as an open educational resource through the Open Engineering Resources project of the HE Academy Engineering Subject Centre. The Open Engineering Resources project was funded by HEFCE and part of the JISC/HE Academy UKOER programme.
Slide 3 (Left). Image of a decanter centrifuge provided courtesy of Thomas Broadbent and Sons Ltd. See http://www.broadbent.co.uk/en/about for details.
Slides 3 (right), 4, and 42. Images courtesy of Siebtechnik GmbH. See http://www.tema.co.uk/images/products/7_1.jpg for details.
Slide 24. Image of"Krebs gMAX® Hydrocyclones" photo courtesy of FLSmidth Krebs Inc. See http://www.flsmidthminerals.com/Products/Classification/Hydrocyclones/Hydrocyclones.htm for details.
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