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8/2/2019 Lecture A8 - Hydro Cyclone
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The Hydrocyclone
A classifying device which utilises centrifugal force to accelerate thesettling rate of particles
One of the most important device in the mineral industry
Extremely efficient in fine size separation Use in closed-circuit grinding operation; de-slimming, de-gritting and
thickening
A typical hydrocyclone
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A conical shaped vessel, open at the apex or underflow
A tangential feed inlet
A vortex finder which prevents short circuiting of feed.
Overflow
A particle in the hydrocyclone is subjected to two opposing forces; centrifugaland drag force.
Faster settling particles move to the wall where the velocity is lowest andmigrate to the apex opening.
The slower-settling particles move towards the zone of low pressure alongthe axis and are carried upward through the vortex-finder to the overflow.
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Fig: Forces acting on an orbiting particles in the hydrocyclone
The existence of an outer region of downward flow and an inner regionof upward flow necessitates a position at which there is no verticalvelocity.
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Particles thrown outside the envelope of zero vertical velocity by the greatercentrifugal force exit via the underflow while particles swept to the centre by
the greater drag force leave in the overflow.
The efficiency
The efficiency of separation or the imperfection I :
50
2575
2d
ddI
=
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Analysis of Hydrocyclone
o
0
S
X
,O
,O
f
f
S
X
,F
,F
u
uS
X
,U,U
Therefore for the feed
slurryofmass
solidsofmassX
sf
fs
f..
..
)1(
)1(=
=
and s is the density of solids and ml/gm1O2H=
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Underflow:
)1(
)1(
=
su
usuX
Overflow:
)1(
)1(
=
so
osoX
Dilution Ratio
In the feed ff
fy
X
X
solids
water=
==
1
Underflow uu
u yX
X=
=
1
Overflow oo
o yX
X=
=
1
Overall solids Balance
sss OUF +=
water balance
sosusf OyUyFy += Hence
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ou
of
s
s
yy
yy
F
U
=
and
uo
uf
s
s
yy
yy
F
O
=
ff
ss
slurry
sf
VV
mmX
==
wfs
wsf
VVV
VVV
=
+=
fw
wf
f
w
f
wf
f
s
m
m1
V
V1
V
VV
V
V
==
=
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ml/g0.1w = , ff
w X1m
m=
)X1(1V
Vff
f
s=
))X1(1(V
VX ff
f
s
ff
ssf ==
)1(
)1(X
)1()1(X
)1()11
(X
)1(XX
sf
fs
f
fs
s
ff
f
s
ff
ffff
s
f
=
=
=
=
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Example: Hydrocyclone classification
3
w m/kg1000= 3
s m/kg2700=
3
f m/kg1670=
3
u m/kg1890=
3
o m/kg1460=
637.0)7.21(67.1
)67.11(7.2
)s1(f
)f
1(s
fX =
=
=
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57.0637.0
637.01
fX
fX1
fy =
=
=
747.0)7.21(89.1
)89.11(7.2
)s1(u
)u1(suX =
=
=
34.0747.0
747.01
uXuX1
uy =
=
=
5.0)7.21(46.1
)46.11(7.2
)s1(o
)o1(soX =
=
=
0.1
5.0
5.01
o
XoX1
oy =
=
=
Now calculate:
ou
of
s
s
yy
yy
F
U
=
652.0134.0
157.0
F
U
s
s=
=
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Basis: solids.kg100Fs = ,
the solids in the underflow kg2.65Us =
and in the overflow kg8.34Os =
5.0X
ml/g46.1
kg5.0/8.34O
kg8.34O
o
0
S
=
=
=
=
637.0X
ml.g67.1
kg637.0/100F
,kg100F
f
f
S
=
=
=
=
747.0X
ml/g89.1
,kg747.0/2.65U,kg2.65U
u
u
S
=
=
=
=
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particle size (micron)
0 200 400 600 800 1000
PercentoffeedtounderfloworUs/F
s%
0
20
40
60
80
100
d75
d50
d25
I=(d75-d25)/(2*d50)
No enough data for imperfection calculation.
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Factor Affecting the cyclone Performance
Factors affecting cyclone parameters
Cut size:
Increases with cyclone diameter, feed % solids or viscosity, small apex, large vortex finder,
cyclone inclination to vertical
Decreases with flow rateClassification efficiency:
Increases with appropriate cyclone size, limiting water to underflow
Decreases with feed % solids or viscosity
Flow split of water to underflow (impacts short circuiting)
Increases with larger apex or smaller vortex finder, feed % solids or viscosity
Decreases with flow rate, inclined cyclones
Flow rate:
Increases with pressure, cyclone diameter
Decreases with feed % solids and viscosity
Several of the empirical relationships which are used to predict the cutpoint ina cyclone are as follows:
Plitt equation (1976)
large diameter cyclone
operating at high solids concentration
.
)(QhD
eDDDKd
Ls
45.038.071.0
u
063.021.1
o
6.0
i
46.0
c1
c50
s
=
1K = a constant (14.8)
=c50d cut-point of corrected 50d (m)
cD =inside diameters of hydrocyclone at the bottom of thevortex finder (cm)
iD = inside diameter of the hydrocyclone inlet (cm)
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oD =inside diameter of the overflow or vortex finder (cm)
uD =inside of the underflow or apex diameter(cm)
h = distance between bottom of vortex finder to the top ofthe underflow orificeQ =total flow rate (litres/ minutes)
S = density of solids (g.cm-3)
L =density of liquid (g.cm-3)
S = volumetric % of solids in the feed
And the volumetric flow rate eqn:
S0031.0
49.02
o
2
u
16.053.0
i
21.0
c
56.0
e
)DD(hDDP21.0Q
+=
where P is the pressure drop across the cyclone in kPa.
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The power:
kW
3600
PQPower=
Effect of pressure drop on capacity and cut-point
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The size of the apex or spigot opening determines the underflowdensity and must be large enough to discharge the coarse solids thatare being separated by the cyclone. The spigot must also permit theentry of air along the axis of the cyclone in order to establish the airvortex.