Transcript Cyclone – Basic Principles - CNR

Air Pollution Control – Part A
Cyclone – Basic Principles
Yaacov Mamane
Visiting Scientist, CNR
Rome, Italy
7/7/2015
What is a Cyclone?
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Cyclone
Performance
for various
Application
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Standard Cyclone
Dimensions
General guidelines:
H<S
W < (D-De)/2
Lb+Lc > 3D
Cone angle = 7o ~ 8o
De/D = 0.4~0.5,
(Lb+Lc)/De = 8,
S/De = 1
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Conventional Cyclone
Symbol Nomenclature
D
H
W
S
De
Lb
Lc
K
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Body diameter
Inlet height
Inlet width
Outlet length
Outlet diameter
Cylinder length
Cone length
Configuration #
Conventional
1.0
0.5
0.25
0.625
0.5
2.0
2.0
402.9
Stokes Law
 Gravitational forces are balanced by
drag and buoyancy forces.
 This will lead to stokes law - settling
velocity of particles.
mp g = p
Fd
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
6
3
d g
= 3  d v
When Fd = Fg the
settling velocity is
given: as follows.

2 p
vt = g d
18 
Where
g – gravity acceleration
d – particle diameter
rp – particle density
m - air viscosity
For example Vt (1 m) = 0.006 cm/s
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For a particle moving at high speed Vc in a circle, the centrifugal
acceleration is given by Vc*Vc/r. The centrifugal force is similar to the
gravity forces
v c2
Fc = m
r
Vc
,
Fg = mg
v c2
g
r
But Fc >> Fg
The equivalent “settling velocity” of the
centrifugal forces is taken from Stokes
Law and is given by the following
Equation:
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vc
w=
r
v c2 2 p
vt 
d
r
18
Example
For a particle of 1 m moving in a 0.3 diameter circle at 18.3
m/s:
vt
2

18.3 m/s 2
-6
10 m
=
0.3 m
vt = 0.68 cm/s
 = 1.8  10
-5
kg
m s
While Vt stokes is only 0.006 cm/s!!!
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2000 kg/m 3
18 
Settling Chamber
W
v
Vt
h
Particle is entering a chamber at
height h an horizontal speed V and
settling velocity Vt, may fall inside
the chamber. Time (Tl) to cross the
chamber is L / V . Time (Th) to fall
inside the chamber is h / Vt, thus we
could define a collection efficiency
h = Tl / Th = L Vt / H V
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H
L
The Collection Efficiency of a settling chamber used to collect large
particles is given by the simple expression:
h = L Vt / H V
or
h = L g d2 p / H V 18 
But V = Q / WH where Q is the flow through the
settling chamber, and thus
h = L g d2 p / H V 18  = L W g d2 p / Q 18 
= L W g d2 p / Q 18 
This collection efficiency may be applied to a Cyclone
where
H and L of the chamber are equivalent to
W and ND0 of a cyclone
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h = L Vt / H V for a cyclone may be written as:
NDo  g d 2 p
hc =
W  v 18 
Since a cyclone is an
elongated settling chamber
NDo v t
hc =
W
vc
4W = Do = 2r
2
vc
d 2 p
vt =
18 r
For centrifugal forces
N  2r v c2 d 2 p
h=
W v c 9  2r
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After rearranging the parameters the equation is now given by:
N v c d 2 p
hlam =
9W
And for a turbulent flow it is then expressed by the general term:
h turb = 1 - exp  - h lam 
Example:
Calculate efficiency for a cyclone to collect 1 mm particles of density 1.
Cyclone width – 15 cm, Vc – 18.3 m/s and N – 5.
The efficiency is h = 0.023
And for a particle of 10 mm diameter h is larger than 1.
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Let define a parameter of importance in particulate control, d cut , used to
describe the properties of the cyclone,
dcut =
Where
Dcut  NVc p W-
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9 W
2 Nv c p
cut diameter in mm
is viscosity
number of rotations
tangential velocity
particle density
entrance width of the cyclone
Pressure Drop
Number of gas inlet velocity head
HW
Hv  K 2
De
K = 16 for normal tangential inlet
= 7.5 for one with an inlet vane
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Static pressure drop
1
P   gVi 2 H v
2
Power requirement
 f  QP
w
Lapple Theory (laminar flow)
Number of effective turns
1
Ne 
H
Lc 

 Lb  2 


Gas residence time
t   DNe / Vi
Terminal velocity
Vt  W / t 
d p2  p   g Vi 2
9D
Smallest collected diameter
9 W
dp 
N eVi  p   g 
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50% cut size
d pc 
9 W
2 N eVi  p   g 
The collection efficiency
of any size dpj
1
hj 
2
1  d pc / d pj 
h (%)
Overall efficiency
h  h j f j
Penetration
P  1 h
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Particle size ratio dp/dpc

h  1  exp Ad


1
n 1
p
n  1  1  0.67D0.14



 KQ p (n  1) 
A  2

3
18

D



 T 


 283

 d pj

h j  1  exp0.693
d pc


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Licht Theory (turbulent flow)




0.3
1
n 1
(D in )
 0.693
d pc  

 A 




n 1
1
2 ( n 1)
Arrangement
Parallel/
Battery
Series
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Air Pollution Control Equipment,
Theodore & Buonicore, CRC Press, 1988
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Discharge
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Handbook of Air Pollution Control Engineering
& Technology,
Mycock, McKenna and Theodore, Lewis
Publishers, 1995.
Advantages & Disadvantages
Advantages:



Low capital cost
Ability to operate at high
temperatures
Low maintenance
requirements because there
are no moving parts
Disadvantages:


Low efficiencies for fine
particles
High operating costs (due to
pressure drop)
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Cyclones used for removing wood dust