Simplified design of axial-flow cyclone mist eliminators


Brunazzi, E.; Paglianti, A.; Talamelli, A.

AICHE Journal 49(1): 41-51

2003


models that are essential for the design and optimization of complex separation units.

Simplified
Design
of
Axial-Flow
Cyclone
Mist
Eliminators
E.
Brunazzi
and
A.
Paglianti
Laboratory
of
Process
Equipment,
Dept.
of
Chemical
Engineering,
Industrial
Chemistry
and
Materials
Science
A.
Talamelli
Dept.
of
Aerospace
Engineering
University
of
Pisa,
1-56126
Pisa,
Italy
Mist
eliminators
have
widespread
application
in
many
processes,
and
a
large
number
of
different
types
of
mist
eliminators
are
available
on
the
market.
Wire-mesh
mist
elimi-
nators,
vane-type
eliminators,
and
cyclones
are
used
extensively
in
many
industrial
plants.
Unfortunately,
these
separators
present
some
significant
drawbacks
when
they
are
used
in
high-pressure
applications
or
in
any
application
in
which
a
reduction
in
the
diameter
of
the
vessel
containing
the
separator
is
necessary
and
high
separation
efficiency
is
re-
quired.
Therefore,
over
the
last
several
years
some
important
suppliers
have
developed
new
axial
flow
separators
(such
as
Axiflow,
Swirl
Tube,
or
Vico-Spin).
Despite
the
broad
range
of
entrainment
removal
applications,
open
literature
on
this
topic
is
scarce.
So
far,
design
of
these
axial-flow
separators
can
only
be
performed
by
suppliers
using
proprietary
design
criteria
or
using
semiempirical
equations
with
an
uncertain
range
of
applicability.
This
work
presents
new
experimental
data
obtained
at
atmospheric
condi-
tions
on
three
different
axial
separators
and
a
new
design
model.
Introduction
Entrained
liquid
may
be
required
to
be
removed
from
gas
or
vapor
streams
for
many
reasons
in
industrial
plants,
for
example,
to
recover
valuable
products
dispersed
in
the
pro-
cess
stream,
to
increase
the
vapor-
or
gas-stream
purity,
to
protect
downstream
equipment
from
corrosive
liquids,
or
to
improve
emission
controls.
Selection
of
the
proper
collection
equipment
depends
mainly
on
the
size
distribution
of
the
en-
trained
liquid
droplets
and
has
been
the
subject
of
many
arti-
cles
(Holmes
and
Chen,
1984;
Fabian
et
al.,
1993;
Svrcek
and
Monnery,
1993;
Capps,
1994;
Ziebold,
2000).
Unfortunately,
most
of
the
works
published
so
far
for
the
selection
neglect
the
existence
of
axial
flow
cyclones.
This
absence
may
have
been
acceptable
up
until
a
few
years
ago,
but
nowadays
this
is
no
longer
the
case.
Due
to
the
development
of
new
axial
flow
separators
and
their
increasing
presence
on
the
market,
design
criteria
for
these
new
types
of
separator
are
needed.
Axial
flow
separators
impart
a
very
high
centrifugal
force
on
the
entering
gas
stream.
This
allows
a
high
separation
effi-
ciency
and
increased
handling
capacity,
which
permits
a
re-
Correspondence
concerning
this
article
should
be
addressed
to
A.
Paglianti.
duction
in
the
vessel
diameter
compared
to
that
for
vane-type
or
wire-mesh
mist
eliminators.
The
maximum
superficial
gas
velocity
through
a
mist
elimi-
nator,
and,
therefore,
the
vessel
diameter,
has
usually
been
evaluated
using
the
Souders—Brown
relation
a
=
K
Pi
P
g
P
g
where
u
sg
,,
nax
is
the
maximum
superficial
gas
velocity
and
p
i
and
p
g
are,
respectively,
the
density
of
the
liquid
and
gas
phases.
The
K
values
have
to
be
experimentally
determined
because
they
depend
on
the
physical
properties
of
the
work-
ing
fluids,
on
the
deentrainment
height,
and
somewhat
on
the
system
pressure
(Ludwig,
1995).
For
vertical
flow
in
vane-type
and
wire-mesh
mist
eliminators,
Holmes
and
Chen
(1984)
and
York
and
Poppele
(1963)
give
an
average
design
K-factor
of
0.35
ft/s
(0.11
m/s).
Use
of
Eq.
1
permits
evalua-
tion
of
the
superficial
gas
velocity,
and,
therefore,
the
vessel
dimension
of
a
separator
equipped
with
either
a
vane-type
or
(1)
AIChE
Journal
January
2003
Vol.
49,
No.
1
41
t
io
n
Effic
ien
cy,
Ti
100
80
60
40
20
Drop
diameter,
d
(micron)
Figure
1.
Separation
efficiency
vs.
drop
diameter.
Theoretical
trend
according
to
Brunazzi
and
Paglianti
(1998).
Packing
characteristics:
270
m
2
/m
3
,
wire
diameter
270
gm,
pad
thickness
150
mm.
Working
conditions:
air—water
sys-
tem,
pressure
7
MPa,
temperature
20°C,
superficial
gas
ve-
locity
0.37
m/s.
a
wire-mesh
mist
eliminator.
If,
for
instance,
we
assume
that
mist
has
to
be
removed
from
100,000
kg/h
of
air
at
7
MPa
and
20°C,
Eq.
1
suggests
that
the
maximum
allowable
gas
velocity
is
about
0.37
m/s,
which
implies
that
a
vessel
diame-
ter
of
1070
mm
is
needed.
It
is
important
to
point
out
that
this
vessel
diameter
is
the
minimum
diameter
because,
as
shown
by
Ludwig
(1995),
the
K-factor
slowly
decreases
with
increasing
working
pressure.
In
this
case,
if
a
wire-mesh
mist
eliminator
is
used,
it
is
possible
to
predict
separation
perfor-
mance
using
the
model
by
Brunazzi
and
Paglianti
(1998).
Fig-
ure
1
shows
the
separation
efficiency
that
can
be
obtained
with
a
commonly
used
wire-mesh
mist
eliminator
with
a
spe-
cific
surface
area
of
270
m
2
/m
3
and
a
wire
diameter
of
270
microns.
Figure
1
also
shows
that
the
value
of
dp
i
,
which
is
the
smallest
droplet
diameter
that
can
be
separated
with
a
100%
efficiency,
is
about
20
microns.
The
low
separation
efficiency
in
the
5-10
micron
range
of
drop
diameter
and
the
large
vessel
diameter
required
to
con-
tain
the
wire-mesh
mist
eliminator
both
explain
why
some
new
separators
have
been
designed
especially
for
high
gas
density
applications
in
the
last
few
years.
In
addition,
the
new
separators
are
easily
cleaned,
they
continue
operating
even
if
some
solids
are
present
in
the
inlet
flow,
and
they
are
easily
inserted
through
manholes.
The
present
work
examines
three
different
types
of
axial
flow
separators
experimentally
at
atmospheric
working
condi-
tions.
The
experimental
investigation
considered
droplet
size
from
around
1
micron
upwards,
particular
attention
being
fo-
cused
on
the
overlapping
size
region
between
the
coarsest
mist
particles
and
the
finest
spray
particles.
A
model
for
the
collection
performance
of
the
tested
axial
flow
cyclones
has
been
developed,
using
a
number
of
simplifying
assumptions.
Two
different
approaches
concerning
droplet
behavior
in
the
axial
flow
separator
have
been
considered.
For
the
one
based
on
the
complete
radial
mixing
concept,
it
is
assumed
that,
because
of
the
turbulent
mixing,
the
concentration
of
uncol-
lected
droplet
is
uniform
across
any
horizontal
cross
section
of
the
separator
and
that
removal
occurs
across
a
thin
layer
at
the
outer
wall.
For
the
other
approach,
which
is
based
on
the
absence
of
a
radial
mixing
concept,
it
is
assumed
that
droplets
behave
as
if
they
are
in
a
laminar
flow
and
move
as
To
fan
Transmitter
unit
Receiver
unit
[Kern
Axial
Flow
separator
Containing
box
=RD
Compressed
air
Water
Carrier
gas
Figure
2.
Experimental
test
apparatus.
a
plug
toward
the
outer
wall.
The
results
of
the
model
using
either
the
former
or
the
latter
approach
are
compared
with
the
experimental
data.
Experimental
Loop
Experimental
collection
efficiencies
were
determined
as
a
function
of
droplet
size
and
gas
velocity
at
atmospheric
work-
ing
conditions
in
an
experimental
loop
designed
and
built
at
the
Chemical
Engineering
Department
of
the
University
of
Pisa.
For
this
purpose,
different
types
of
axial
flow
mist
elimi-
nators,
furnished
by
Costacurta
S.p.A.
VICO,
were
tested.
Air
and
water
were
used
as
working
fluids.
The
experimental
rig
mainly
consisted
of
a
spray-generation
circuit
and
an
air-
carrier
circuit.
The
spray
was
generated
using
an
ultrasonic
nozzle
fed
by
a
volumetric
pump,
giving
liquid
flow
rates
of
between
0
and
2,600
L/h,
and
by
a
compressor
supplying
air
at
0.6
MPa
at
flow
rates
of
up
to
280
m
3
/h
at
standard
condi-
tions.
The
test
section,
shown
in
Figure
2,
consisted
of
a
3-m-long
metal
measuring
section
with
a
rectangular
cross
section,
120
mm
wide
and
190
mm
high.
The
separator
was
installed
verti-
cally
with
respect
to
the
upflow
of
gas.
A
Malvern
Particle
Sizer
instrument,
based
on
measurements
of
the
diffraction
of
a
He—Ne
laser
beam
of
droplets
moving
through
the
mea-
suring
section,
was
used
to
accurately
measure
the
total
droplet
concentration
and
volumetric
droplet
distribution
(Brunazzi
and
Paglianti,
1998,
2000).
Acquisitions
were
car-
ried
out
both
upstream
and
downstream
of
the
separator.
10
15
20
25
42
January
2003
Vol.
49,
No.
1
AIChE
Journal
D
out
3-A
D
out
3~
4-C
2-A
4-B
3-B
H
H
3-C
1-A
2-B
1-B
1-C
1‘,
V
E
E
D
out
A
>
L
D
D
Figure
3.
Tested
cyclones.
Each
data
point
represents
the
average
of
six
different
acqui-
sitions.
The
accuracy
of
the
measured
efficiency
is
quite
high
and
the
maximum
uncertainty
of
the
measured
efficiency
is
below
5%.
This
article
analyzes
three
axial
flow
separators,
plotted
in
Figure
3,
whose
main geometrical
characteristics
are
shown
in
Table
1.
The
axial
separator
shown
in
Figure
3A
is
formed
by
a
swirler
170
mm
in
length
made
up
of
six
flat
deflected
vanes.
This
swirler
is
located
inside
a
tube
that
has
an
inner
diameter
of
110
mm
and
is
500
mm
long;
the
collected
liquid
is
drained
off
into
a
separate
external
concentric
tube
through
four
4-mm-wide
vertical
slits.
The
axial
flow
separator
shown
in
Figure
3B
is
formed
from
a
continuous
single-threaded
he-
lix
670
mm
in
length
located
inside
a
tube
with
an
inner
di-
ameter
of
135
mm.
The
drainage
system
is
formed
from
a
100-mm-long
vent
that
allows
the
separated
liquid
to
drain
into
an
external
concentric
tube.
The
top
of
the
separator
shows
an
external
concentric
tube
around
the
helix,
with
an
inner
diameter
of
210
mm,
that
has
the
goal
of
increasing
the
gas-velocity
limit
before
reentrainment
occurs.
The
axial
flow
separator
shown
in
Figure
3C
is
quite
similar
to
that
shown
in
Figure
3B;
the
helix
is
single-threaded
and
the
only
differ-
ence
is
the
presence
of
the
230-mm-long
filled
cone
at
the
bottom.
Model
to
Simulate
Axial
Flow
Separator
The
gas
flow
in
axial
cyclones
is
intrinsically
three-dimen-
sional
and
turbulent.
Unfortunately,
even
though
in
the
last
few
years
the
computational
fluid dynamic
(CFD)
approach
has
made
important
progress,
so
far
it
can
only
be
used
to
obtain
a
proper
evaluation
of
pressure
drops
across
these
Table
1.
Geometric
Characteristics
of
the
Cyclones
Cyclone Cyclone
Discharge
Hole
Vane
Blade
Outlet
Cone
Dia.
D
Hgt.
H
Hgt.,
E
Vertical
Angle
Dia.
D,,„
t
Total
Rev.
Hgt.,
B
Type
(mm) (mm)
(mm)
(deg)
(mm)
No.
(mm)
3.A
110
500
30
54
1.8
3.B
135
670
100
70
210
6
3.0
135
670
100
70
210
6
230
AIChE
Journal
January
2003
Vol.
49,
No.
1
43
r
2
r
o
Gas
streamlines
iv
0,0
A
A
A
A
A
v
Drop
trajectory
separators,
but
cannot
provide
a
good
prediction
of
separa-
tion
efficiency
(Babbore,
2000).
It
is,
therefore,
necessary
to
develop
simplified
approaches
based
on
the
study
of
droplet
trajectories.
By
using
simple
models
for
the
particle
mechan-
ics
and
the
gas
flow
through
the
cyclone,
it
is
possible
to
cal-
culate
the
particle
trajectories
and,
hence,
collection
efficien-
cies.
This
simplified
approach
was
applied
by
Licht
(1980)
for
the
study
of
common
cyclones,
with
interesting
results.
The
present
work
presents
an
approach
based
on
the
study
of
droplet
trajectories.
In
particular,
depending
on
the
de-
scription
of
droplets
mixing
on
any
horizontal
cross
section
of
the
axial
cyclone,
the
present
approach
leads
to
two
different
models.
In
fact,
the
mixing
of
droplets
inside
the
gas—liquid
separator
is
still
an
open
question.
One
of
two
cases
can
be
assumed:
either
(1)
perfect
mixing
in
any
horizontal
cross
sec-
tion
of
the
separator,
as
has been
considered
by
Carpenter
and
Othmer
(1955)
for
wire-mesh
separators
and
by
Dietz
(1981)
for
cyclones,
among
others
,
or
(2)
the
absence
of
mix-
ing,
as
considered
by
Brunazzi
and
Paglianti
(1998)
for
wire-
mesh
separators,
and
by
Verlaan
(1991)
for
axial-flow
cy-
clones.
Therefore,
the
present
work
will
analyze
both
perfect
mixing
and
the
absence
of
mixing
hypotheses.
This
will
lead
to
two
different
models
that
can
take
the
different
fluid
dy-
namic
behaviors
into
account.
Both
models
that
will
be
presented
are
based
on
the
fol-
lowing
two
hypotheses:
(1)
no
reentrainment
into
the
gas
stream
of
already
collected
liquid,
and
(2)
no
buildup
of
liq-
uid
inside
the
separator.
The
present
models
are
based
on
the
simplifying
hypothe-
sis
that
while
the
velocity
vector
of
a
liquid
drop
can
have
both
tangential
and
radial
components,
as
well
as
the
axial
one,
the
gas
stream
has
only
axial
and
tangential
velocity
components.
In
other
words,
it
has been
assumed
that
the
radial
component
of
the
gas
velocity
vector,
u,.,
is
nil
in
the
whole
separator.
A
droplet
with
a
tangential
velocity
equal
to,
v
o
,
o
,
at
time
t
=
0,
flows
in
the
separator
as
shown
in
Fig-
ure
4.
Another
widely
used
simplifying
hypothesis
is
to
ne-
glect
the
tangential
slip
velocity
between
gas
and
droplets.
Thus,
the
gas
and
the
droplet
tangential
velocities
are
the
same,
that
is,
u
0
=
v
0
.
As
regards
the
gas
flow
through
the
cyclone,
it
has been
assumed
that
the
ratio
between
tangential
and
axial
velocity
depends
only
on
the
swirling
element
and
does
not
change
along
the
length
of
the
separator.
This
simplifying
hypothesis
is
strictly
valid
only
for
"short"
cyclones.
The
present
work
analyzes
only
cyclones
with
length-to-diameter
ratios
below
5.
Therefore,
according
to
Biirkholz
(1989),
in
this
case
the
ro-
tational
moment
decreases
less
than
10%.
It
is
obvious
that
the
present
simplified
analysis
cannot
be
used
for
"long"
cy-
clones,
in
which
the
decrease
of
angular
momentum
as
a
function
of
the
tube
length
has
to
be
taken
into
account.
Several
earlier
workers
who
studied
common
cyclones
as-
sumed
that
the
gas
flow
constituted
a
form
of
vortex
such
that
the
tangential
gas
velocity
is
a
function
of
the
distance
from
the
center
and
can
be
computed
as
u
e
•rn
=
C
(2)
where
C
is
a
constant,
depending
on
the
geometry
of
the
equipment,
and
n
depends
on
the
geometry
and
on
the
work-
Figure
4.
Drop
trajectory.
ing
temperature.
For
ideal
flow
in
a
vortex,
n
=1,
whereas,
for
real
flow,
n
can
be
computed
using
semiempirical
equa-
tions.
The
present
work
uses
the
relation
by
Licht
(1980),
which
is
based
on
experimental
data
by
Alexander
(1980).
This
gives
T
-5
V
3
n
=1—
[1
0.67.(2.r2)
A
,41
i•
283
(
3
)
where
T
is
the
working
temperature
in
degrees
kelvin,
and
r
2
is
the
outer
radius
of
the
cyclone,
in
meters.
As
regards
the
flow
of
the
liquid
drops,
the
force
balance
in
the
radial
direction
on
the
single
drop
has
been
simplified
by
considering
only
the
centrifugal
force
and
the
shear
force.
Assuming
that
the
drop
is
spherical,
the
force
balance
as-
sumes
the
following
form
d
3
dv,.
d
3
ve
Pe•
dt
=
(
Pg)
1
0
2
(
7(12
)
CD
g
Vr
4
)
where
v
r
=
dr/dt
and,
due
to
the
low
value
of
the
radial
veloc-
ity,
the
drag
coefficient,
C
D
,
has
been
evaluated
using
the
Stokes'
law.
Therefore,
Eq.
4
can
be
rewritten
as
d
e
r
Pg
u
e
jag
(
dr\
dt
2
r
18
p
i
d
2
dt
Nevertheless,
if
the
Reynolds
number
is
more
than
unity,
the
influence
of
the
Reynolds
number
on
the
drag
coefficient
has
to
be
taken
into
account.
(
5
)
44
January
2003
Vol.
49,
No.
1
AIChE
Journal
2
r
o
t=
2.(n
+
1)
4
,0
d
2
—1
(
p
i
p
g
)
r
o
18•Ag
)
[
(r
2.(n+1)
dr
(p
i
p
g
)•d
2
td,
o
rg"
_
dt
18•
µg
r
2r•n+1
(6)
0
.
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
o
0
0
0
0
0
0
0
0
0
A
good
approximation
is
achievable
by
neglecting
the
sec-
ond-order
terms
in
Eq.
5.
This
enables
it
to
be
simplified,
which,
together
with
the
insertion
of
Eq.
2,
results
in
the
fol-
lowing
Integrating
the
previous
equation
from
t
=
0
to
a
generic
in-
stant
in
time,
t,
the
following
is
derived
r
2
2
18•
µg
2.(n
+
1)
6
2
d
2
.(
p
i
p
g
)
.
[
(r
)
2.(n
+1)
(
ro
)
2.(n
+
al
r
2
r
2
Figure
5A
shows
a
generic
horizontal
cross
section
of
a
separator.
In
an
infinitive
time,
dt,
only
the
droplets
whose
distances
from
the
wall
are
less
than
dr
can
be
effectively
collected.
As
previously
anticipated,
two
different
numerical
approaches
are
now
possible.
The
key
difference
between
these
concerns
droplet
behavior
in
the
separator.
We
can
ei-
ther
consider
that,
because
of
the
turbulent
flow
field
in
the
separator,
the
droplets
in
each
sector
of
the
cyclone
are
per-
fectly
mixed
along
the
radius,
and,
therefore,
no
concentra-
tion
gradient
of
droplets
exists
in
any
horizontal
cross
sec-
tion,
or
we
can
assume
that
no
mixing
occurs,
and
so
the
droplets
behave
as
if
they
were
in
a
laminar
flow
and
move
as
a
plug
toward
the
wall.
When
the
former
approach
is
used,
assumption
is
made
that
in
a
thin
layer
at
the
separator
outer
wall,
where
droplet
removal
occurs,
droplet
motion
can
be
considered
under
laminar
flow
conditions
and
the
Stokes'
law
is
applicable.
This
assumption
was
applied
with
interesting
results
in
the
study
of
common
cyclone
separators
(Flagan
and
Seinfeld,
1988).
Complete
radial
mixing
The
assumption
of
complete
radial
mixing
supposes
that
the
droplets
are
well-mixed,
due
to
turbulence
and
eddies
in
the
gas
stream;
therefore,
a
uniform
concentration
of
uncol-
lected
droplets
is
maintained
in
any
horizontal
cross
section
of
the
separator.
Droplet
removal
occurs
across
a
thin
layer
at
the
separator's
outer
wall.
Plug
flow
is
assumed
along
the
axial
direction.
Under
these
hypotheses,
the
mass
balance
on
a
sector
with
thickness
dz
and
angle
dO
can
be
written
as
r
dN
=
2
e
[
r2
[tq—(r
2
dr)l•
dz
X
(8)
where
N
is
the
total
number
of
droplets
in
the
control
vol-
ume
and
X
is
the
numerical
droplet
concentration.
The
total
(
7
)
r
dO
r
2
r
(A)
(B)
Figure
5.
Cyclone
cross
section:
(A)
flow
in
the
whole
cross
section;
(B)
flow
in
an
annulus
cross
section.
AIChE
Journal
January
2003
Vol.
49,
No.
1
45
[2.(n+1)•
2
d
*(
Pe
Pg)
42
,,
)1
—(2.n
+4(2
.n
+2)
(
18•
µg
r
2
d
2
(
p
g
)
2
18•A
g
11
0,2
t
res
r
2.
n
+2)
(15)
number
of
droplets
contained
in
the
control
volume
is
dO
N
=
X.-
2
dz
and
the
fraction
of
captured
droplets
is
dN
2.r
2
.
dr
dr
2
2.
dr
r
2
N
2
r
2
Equation
7
gives
the
relationship
between
time
and
radial
position
of
the
single
droplet.
Therefore,
introduction
of
Eq.
7
into
Eq.
10
permits
the
fraction
of
collected
droplets
to
be
expressed
as
a
function
of
time.
In
addition,
under
the
hy-
pothesis
of
complete
mixing,
each
as
yet
uncollected
droplet
is
remixed
uniformly
at
each
instant
over
the
horizontal
cross
section
of
the
cyclone,
despite
the
fact
that
the
total
number
of
droplets
decreases
with
increasing
residence
time.
Thus,
the
mass
center
of
the
droplets
not
captured
coincides
with
the
vortex
center
at
each
instant
t,
and
we
can,
therefore,
assume
that
r
o
=
0
in
Eq.
7.
Thus,
Eq.
10
can
be
rewritten
as
dN
d
2
*(
P
g
)
u;,2
2•
N
18•A
g
r
2
2
t
(2•
n
+
n
+
2).
dt
(11)
Finally,
integration
of
Eq.
11
over
a
residence
time,
t
rev
in
the
separator
gives
[ n
=1—
exp
—212.(n
+1)
2
1
=
1
exp
,2
,.2
r2
[2
(n
+1)
2)
—(2.n
+
1)A2
n
+
'2
'1
Absence
of
radial
mixing
When
using
the
absence
of
the
droplet
mixing
approach,
the
present
model
assumes
that
all
the
droplets
are
uniformly
distributed
across
the
inlet
cross
section
of
the
separator
and
that
the
trajectories
of
all
droplets
with
the
same
size
make
up
a
family
of
parallel
curves.
Therefore,
in
the
absence
of
mixing,
the
separation
efficiency
of
the
droplets
with
diame-
ter,
d,
can
be
easily
evaluated
from
the
knowledge
of
position
r'
of
the
innermost
particle
that,
after
a
time
equal
to
the
residence
time,
t
res
,
arrives
at
a
radial
position
equal
to
the
outer
radius
of
the
cyclone,
r
2
.
Analyzing
the
case
of
a
separator
whose
geometrical
char-
acteristics
are
shown
in
Figure
5B,
and
by
inserting
Eq.
2
into
Eq.
6,
we
get
dr
d
2
•(
p
g
)
C
2
dt
18•µ
g
r
2.n+1
Integrating,
it
is
possible
to
evaluate
r'
r
,
=
2
2.(n
+1)
[
'
d
2
'(
A
P
g
)
18.
lag
C
2
.
t
res
.2.(n
+1)
and,
therefore,
the
efficiency
(9)
(10)
(16)
(17)
r
2.
n
+2)1
d
2
(
Pg)
(
42
(12)
18.µ
g
r2
2
)
t
res
2
,2
r
2
r
2 2
r
2
(18)
Equation
12
can
be
used
if
the
whole
cross
section
of
the
axial
flow
cyclone
is
available
for
the
two-phase
flow,
whereas,
if
the
mixture
flows
in
an
annulus,
as
shown
in
Figure
5B,
Eq.
9
assumes
a
different
form
dO
N
=
X
2
(r?
-
r0
dz
(13)
and,
therefore,
Eqs.
11
and
12
assume
the
following
form
dN
d
2
•(
A
P
g
)
,2
,2
=-2•
`
.
6
1
N
18
iug
(r1-
q)
2.
4,2
—(2.n
+1)K2
.11
+
2)
(1
(
pi
p
g
)
(
ly(2
.n
+2).
dt
(14)
Equation
18
also
allows
the
separation
efficiency
to
be
evalu-
ated
for
a
cyclone
with
geometrical
characteristics
shown
in
Figure
5A.
In
this
case,
it
is
sufficient
to
substitute
r
1
=
0
in
Eq.
18.
The
flow
field
Both
in
the
case
of
perfect
radial
mixing
and
in
the
ab-
sence
of
mixing,
in
order
to
evaluate
the
separation
effi-
ciency,
it
is
necessary
to
know
the
mean
residence
time,
tres)
in
the
cyclone
and
the
tangential
velocity,
11
0
,
2
at
the
wall
of
the
cyclone
or,
equivalently,
the
value
of
the
constant
C.
Strictly
speaking,
the
value
of
u
0
,
2
is
nil
because
of
the
pres-
ence
of
the
boundary
layer.
Licht
(1980)
suggested
using
the
average
gas
inlet
velocity
for
a
conventional
cyclone;
in
the
present
work,
a
value
of
u
0
,
2
will
be
used,
which
will
derive
from
the
mass
balance
on
the
gas
phase
and
from
the
use
of
Eq.
2.
The
mass
balance
on
the
gas
phase
assumes
the
following
[
2.(n+1)•
18•A
g
yi
46
January
2003
Vol.
49,
No.
1
AIChE
Journal
We
need
to
know
a
o
to
evaluate
C.
Thus,
focusing
attention
on
the
tangential
velocity,
and
assuming
a
constant
value
of
the
angular
momentum
along
the
cyclone
length,
it
is
possi-
ble
to
evaluate
the
mean
residence
time,
t
o
,
as
7F
.(d
-
r0
N
to
_
u
.(r
2
r
i
)
where
N
is
the
number
of
revolutions
inside
the
separator.
On
the
other
hand,
if
we
focus
attention
on
the
axial
veloc-
ity,
it
is
possible
to
evaluate
the
residence
time,
t
a
,
as
L
t
a
=
Q
7F
(r?
(22)
where
Q
is
the
gas
volumetric
flow
rate
and
L
is
the
separa-
tor
length.
By
imposing
the
condition
that
the
residence
times
computed
using
either
the
tangential
or
the
axial
velocities
are
identical,
that
is,
tres
=
t
o
=
t
a
,
we
get
N
n
o
Q
L
(r
2
r
1
)
(23)
Therefore,
knowledge
of
the
geometrical
characteristics
of
the
cyclone
and
the
gas
volumetric
flow
rate
allows
us
to
com-
pute
the
average
tangential
velocity
and
the
residence
time.
These,
in
turn,
allow
us
to
evaluate
C
from
Eq.
20,
and
fi-
nally
to
calculate
u
0
,
2
,
which
is
required
for
evaluation
of
the
separator
efficiency.
(21)
100
80
60
40
20
-
••
.6460
0
,
o•
0
o
Axial
separator
type
IA
Axial
separator
type
3.B
Axial
separator
type
3.0
10
15
20
25
Drop
diameter,
d
(microns)
Figure
6.
Separation
efficiency
of
tested
cyclones
vs.
drop
diameter.
Working
conditions:
Air-water
system,
pressure
0.1
MPa,
temperature
20°C,
superficial
gas
velocity
5
m/s.
Sep
ara
t
ion
e
ffic
iency,
form
r
2
n
o
.(r
2
r
=
f
u
o
dr
r
t
(19)
where
Fl
o
is
the
mean
value
of
the
tangential
gas
velocity.
Using
Eq.
2
and
integrating
Eq.
19,
we
get
(r
2
r
1
)
C=
Fl
o
n)
yl—n
2
.
1
(20)
100
80
60
40
20
ion
e
ffic
iency,
t/
—Wire
mesh,
Brunazzi
and
Paglianti
(1998)
1
Experimental
data
Axial
separator
type
3.0
0
2
4
6
10
Drop
diameter,
d
(microns)
Figure
7.
Separation
efficiency
vs.
drop
diameter.
Comparison
between
present
experimental
measurements
on
cyclone
type
3.0
and
wire-mesh
mist
eliminator.
Wire-
mesh
packing
characteristics:
270
m
2
/m
3
,
wire
diameter
270
microns,
pad
thickness
150
mm.
Working
conditions:
air—water
system,
pressure
0.1
MPa,
temperature
20°C,
su-
perficial
gas
velocities
of
3.18
m/s
for
wire-mesh
mist
elimi-
nator
(the
maximum
allowable
according
to
Holmes
and
Chen,
1984),
and
5
m/s
for
cyclone
type
3.C.
Analysis
of
Experimental
Results
It
is
now
possible
to
analyze
the
experimental
separation
efficiency
of
the
axial
flow
cyclones
described
in
the
previous
paragraphs.
Figure
6
shows
the
measured separation
efficien-
cies
of
these
axial
flow
cyclones
as
a
function
of
droplet
di-
ameter;
in
all
cases,
the
superficial
velocity
of
the
gas
phase
was
5
m/s.
The
figure
shows
that
the
axial
cyclone
labeled
3.A
presents
a
dp
wo
value
of
about
15
microns,
whereas
the
separators
labeled
3.B
and
3.0
show
dp
ioo
values
of
about
5
microns.
The
figure
also
shows
that
the
separator
labeled
3.0
performs
somewhat
better
than
the
3.B
configuration.
It
is
important
to
point
out
that
all
three
types
of
cyclone
show
a
good
separation
efficiency
for
droplet
diameters
in
the
range
of
1-2
microns.
This
result
is
important
when
these
experi-
mental
results
are
compared
with
the
separation
efficiency
of
common
wire-mesh
mist
eliminators.
Figure
7
shows
the
sep-
aration
efficiency
of
cyclone
3.C,
measured
under
a
superfi-
cial
gas
velocity
of
5
m/s,
compared
with
the
efficiency
of
a
common
wire-mesh
pad,
computed
at
3.18
m/s,
according
to
the
model
by
Brunazzi
and
Paglianti
(1998)
[the
maximum
allowable
gas
phase
superficial
velocity
at
atmospheric
condi-
tions
and
with
an
air—water
system,
according
to
Holmes
and
Chen
(1984)].
The
specific
surface
of
the
wire-mesh
mist
eliminator
is
270
m
2
/m
3
,
the
thickness
is
150
mm,
and
the
wire
diameter
is
equal
to
270
microns.
The
figure
shows
that
axial
flow
separators
permit
the
highest
separation
efficiency
to
be
obtained
even
for
small
droplets.
Moreover,
it
must
be
emphasized
that,
because
of
their
geometrical
characteristics,
axial
flow
cyclones
can
also
be
used
in
the
presence
of
solid
particles,
which
is
a
field
where
the
use
of
wire-mesh
mist
eliminators
is
not
advisable.
It
is
now
possible
to
compare
the
experimental
data
ob-
tained
in
this
work,
with
the
computed
values
obtained
using
both
of
the
models
previously
shown
and
also
the
semiempir-
ical
equation
suggested
by
Biirkholz
(1989).
To
our
knowl-
edge,
the
equation
suggested
by
Biirkholz
(1989)
is
the
only
one
available
so
far
in
the
open
literature.
Cyclone
type
3.A
has
been
divided
into
three
parts
for
computational
reasons:
1-A,
2-A,
3-A
(see
Figure
3);
the
lower
AIChE
Journal
January
2003
Vol.
49,
No.
1
47
F
Sep
ara
t
io
n
e
ffic
iency,
100
r
5
m/s
Present
model
-
Burkholz
(1989)
0
Present
data
100
80
60
40
Burkholz
(1989)
—Present
model,
perfect
mixing
20
-
-
-
Present
model,
no
mixing
o
Experimental
data
80
60
40
20
10
15
Drop
diameter,
d
(microns)
0
5
20
25
0
100
Figure
8.
Separation
efficiency
vs.
drop
diameter.
Comparison
between
experimental
measurements
and
the
Biirkholz
(1989)
equation,
and
with
models
suggested
in
the
present
work.
Cyclone
type
3.A.
Working
conditions:
air—water
system,
pressure
0.1
MPa,
temperature
20°C,
su-
perficial
gas
velocity
5
m/s.
part,
1-A,
contains
the
swirling
element;
the
middle
part,
2-A,
contains
the
drainage
system;
and
the
upper
part,
3-A,
con-
tains
the
outlet.
The
separation
efficiency
of
the
lower
part
was
computed
as
the
separation
efficiency
of
a
cyclone
where
the
gas
phase
flows
through
an
annulus.
Because
of
the
pres-
ence
of
the
cone
in
the
bottom
part,
the
inner
radius
of
the
annulus
has been
assumed
equal
to
half
the
radius
of
the
cone
(that
is,
r
i
=
17.5
mm
and
r
2
=
55
mm).
The
number
of
revolutions,
N,
inside
part
1-A
is
0.5.
The
efficiencies
of
parts
2-A
and
3-A,
on
the
other
hand,
have
been
computed
by
con-
sidering
that
the
gas
phase
flows
through
an
empty
tube
with
radius,
r
2
,
equal
to
55
mm
and
27
mm,
respectively;
the
num-
ber
of
revolutions
is
1
in
part
2-A
and
0.3
in
part
3-A.
The
experimental
data
shown
in
Figure
8
refer
to
the
axial
flow
separator
type
3.A
working
with
a
superficial
gas
veloc-
ity
of
5
m/s.
The
figure
clearly
shows
that
the
present
model,
under
the
hypothesis
of
absence
of
mixing,
is
not
able
to
pre-
dict
the
experimental
data,
whereas,
both
the
present
model,
under
the
hypothesis
of
perfect
radial
mixing,
and
the
equa-
tion
suggested
by
Biirkholz
(1989)
seem
to
properly
predict
the
trend
of
the
experimental
data.
This
result
is
particularly
interesting
because,
contrary
to
the
Biirkholz
relation
(1989),
the
present
model
does
not
introduce
any
adjustable
parame-
ters.
Figure
9
shows
the
comparison
between
three
sets
of
ex-
perimental
data
obtained
by
testing
the
behavior
of
separator
type
3.A,
and
values
computed
using
the
present
model
and
the
Biirkholz
equation
(1989).
The
figure
shows
that
under
the
hypothesis
of
perfect
radial
mixing,
the
present
model
seems
to
predict
the
separation
efficiency
with
acceptable
ac-
curacy
for
all
of
the
working
conditions
analyzed.
Figure
10
shows
the
contribution
of
each
zone
of
the
sepa-
rator
toward
the
capture
efficiency
as
predicted
by
the
pre-
sent
model,
under
the
hypothesis
of
perfect
radial
mixing.
The
results
refer
to
separator
3.A
working
with
a
superficial
gas-phase
velocity
of
15
m/s.
For
instance,
the
model
pre-
dicts
that
drops
of
6
Am
are
captured
with
an
efficiency
of
about
65%
in
the
lower
zone,
1-A.
Then,
the
efficiency
in-
creases
up
to
80%
after
the
second
part,
and
eventually
reaches
95%
at
the
end
of
the
third
zone,
3-A,
that
is,
at
the
separator
outlet.
0
100
80
60
40
20
'
I
'
0
5
10
15
20
25
Drop
diameter,
d
(microns)
Figure
9.
Separation
efficiency
vs.
drop
diameter.
Comparison
between
experimental
measurements
and
the
Biirkholz
(1989)
equation,
and
with
the
present
model
un-
der
perfect
mixing
hypothesis:
cyclone
type
3.A.
Working
conditions:
air—water
system,
pressure
0.1
MPa,
tempera-
ture
20°C,
superficial
gas
velocity
(A)
5
m/s,
(B)
10
m/s,
(C)
15
m/s.
40
--Exit
zone
1-A
20
—/
—Exit
zone
2-A
Exit
zone
3-A
(separator
outlet)
0
0
Figure
10.
Separation
efficiency
vs.
drop
diameter,
computed
with
the
present
model
under
per-
fect
mixing
hypothesis.
Contribution
of
each
zone
of
cyclone
type
3.A
to
separa-
tion
efficiency.
Working
conditions:
air—water
system,
pressure
0.1
MPa,
temperature
20°C,
superficial
gas
veloc-
ity
15
m/s.
80
60
40
20
U
sg
=
10
m/s
/
u
sg
=
15
mis
Separator
type
3.A
Sep
ara
t
io
n
e
ffic
iency
,
100
ao
10
15
20
25
Drop
diameter,
d(microns)
48
January
2003
Vol.
49,
No.
1
AIChE
Journal
100
80
60
40
0.1
MPa
20
1
MPa
--
10
MPa
0
5
10
15
20
25
Drop
diameter,
d
(microns)
Figure
11.
Separation
efficiency
vs.
drop
diameter,
computed
with
the
present
model
under
per-
fect
mixing
hypothesis.
Effect
of
system
pressure
on
separation
efficiency
of
cy-
clone
type
3.A.
Working
conditions:
air—water
system,
temperature
20°C,
F-factor
16
Pa
°-5
.
The
extension
of
the
model
to
high
pressures
is
shown
in
Figure
11,
where
separation
efficiencies
vs.
drop
diameter
are
shown
for
system
pressures
of
0.1,
1
and
10
MPa.
An
F-factor
of
16
Pa'
has
been
assumed,
as
suggested
by
experiments
carried
out
at
atmospheric
pressure.
The
extension
to
high-
pressure
application
has been
made
by
assuming
that
the
F-
factors,
and,
hence,
the
shear
stresses,
have
a
constant
value,
as
suggested
by
Perry
and
Green
(1997).
This
assumption
im-
plies
that,
in
relation
to
the
properties
of
the
fluids
to
be
used,
a
higher
mass
flow
rate
and
lower
volumetric
flow
rate
are
permitted
with
an
increase
in
pressure.
The
figure
shows
that
for
a
given
drop
diameter,
the
efficiency
decreases
with
an
increase
in
pressure.
This
behavior
is
mainly
due
to
two
factors.
First,
the
diminished
difference
in
density
between
the
liquid
and
the
gas
phases,
which
renders
the
separation
more
difficult.
The
other,
and
more
important,
factor
is
the
lower
permitted
volumetric
flow
rate,
which
in
turn
means
that
a
lower
centrifugal
force
is
imparted
to
the
droplet
when
the
system
pressure
increases.
For
example,
the
model
pre-
dicts
that
a
drop
with
a
diameter
of
6µm
is
separated
with
an
efficiency
of
95%
at
0.1
MPa,
of
90%
at
1
MPa,
and
75%
at
10
MPa.
Cyclone
type
3.B
was
divided
into
four
parts
for
computa-
tional
reasons:
1-B,
2-B,
3-B,
4-B.
Parts
1-B
and
3-B
were
considered
in
the
same
way:
as
a
gas
phase
flowing
through
an
annulus,
the
inner
radius
is
equal
to
the
radius
of
the
helix
core
(that
is,
13.5
mm),
whereas
the
outer
radius
is
equal
to
D/2
(that
is,
67.5
mm).
In
parts
2-B
and
4-B
the
gas
phase
is
also
considered
to
be
flowing
through
an
annulus,
but
the
outer
radiuses
are,
respectively,
the
outside
radius
of
the
drainage
chamber
(96
mm)
and
the
radius
of
the
concentric
tube
(105
mm)
used
to
limit
the
reentrainment
phenomena.
The
number
of
revolutions
inside
the
separator
is
2.5
for
zone
1-B,
1
for
zone
2-B,
1.25
for
zone
3-B,
and
1.25
for
zone
4-B.
Figure
12
shows
the
comparison
between
the
present
ex-
perimental
data,
obtained
by
testing
the
type
3.B
separator,
and
the
computed
trends
evaluated
using
the
present
model
under
the
hypothesis
of
perfect
radial
mixing.
The
figure
shows
that
even
if
the
geometry
of
the
swirling
element
is
changed,
the
model
seems
to
predict
the
separation
effi-
ciency
properly.
0
1
-I
'-'
u
=
4
m/s
sg
Present
model
D
Present
data
070.___Med
,
R--'
u
=
5
m/s
sg
1
R.le-.
Fl
pi
El
' '
U=
6
m/s
sg
0
U=
8.6
m/s
sg
Separator
type
3.B
5
10
15
20
25
Drop
diameter,
d
(microns)
Figure
12.
Separation
efficiency
vs.
drop
diameter.
Comparison
between
experimental
measurements
and
the
present
model
under
perfect
mixing
hypothesis:
cyclone
type
3.B.
Working
conditions:
air—water
system,
pressure
0.1
MPa,
temperature
20°C,
superficial
gas
velocity
(A)
4
m/s,
(B)
5
m/s,
(C)
6
m/s,
(D)
8.6
m/s.
Figure
13
shows
the
comparison
between
experimental
data
and
the
computed
trends,
evaluated
using
the
present
model
under
the
hypothesis
of
perfect
radial
mixing,
for
the
type
3.0
cyclone.
For
computational
reasons,
cyclone
type
3.0
was
divided
into
four
parts,
the
same
as
the
type
3.B
cyclone.
The
only
difference
between
the
two
cyclones
is
the
presence
of
the
cone
in
the
type
3.0
cyclone.
Therefore,
in
the
latter
case,
the
flow
of
the
gas
phase
through
part
1-C
has
been
consid-
ered
to
be
the
flow
though
an
annulus
of
the
inner
radius
equal
to
half
the
cone
radius,
that
is,
r
1
=
32.5
mm.
Figure
13
shows
that
the
present
model
tends
systematically
to
under-
estimate
the
separation
efficiency.
This
behavior
is
probably
due
to
the
simplifying
hypothesis
used
to
simulate
the
part
1-C.
In
fact,
it
has
been
assumed
that
the
separation
effi-
ciency
of
the
cone
is
equal
to
the
separation
efficiency
of
a
cylinder,
with
the
inner
radius
equal
to
half
the
cone
radius.
This
assumption
allows
us
to
simplify
the
mathematical
model
but,
as
shown
in
figure,
it
introduces
systematic
errors.
The
potentialities
of
the
axial
flow
cyclone
are
evident
from
the
analysis
of
the
Figure
14,
which
shows
a
comparison
be-
tween
an
axial
flow
cyclone
and
a
wire-mesh
mist
eliminator.
The
example
refers
to
a
flow
rate
of
100,000
kg/h
of
air
at
7
MPa
and
20°C.
In
order
to
avoid
reentrainment
phenomena,
Sep
a
ra
t
io
n
e
ffic
ie
ncy,
1
(
%)
100
80
60
40
20
0
100
80
60
40
20
0
100
80
60
40
20
0
100
80
60
40
20
Sep
ara
t
ion
e
ffic
ie
ncy,
77
0
0
AIChE
Journal
January
2003
Vol.
49,
No.
1
49
dairom
sg
=
4
mis
Present
model
Present
data
u
sg
= 5
m/s
rrrM
tv
6
m/s
Separator
type
3.0
0
5
10
15
20
25
Drop
diameter,
d
(microns)
Figure
13.
Separation
efficiency
vs.
drop
diameter.
Comparison
between
experimental
measurements
and
the
present
model
under
perfect
mixing
hypothesis:
cyclone
type
3.C.
Working
conditions:
air—water
system,
pressure
0.1
MPa,
temperature
20°C,
superficial
gas
velocity
(A)
4
m/s,
(B)
5
m/s,
(C)
6
m/s.
100
80
60
20
±'
—Wire
mesh,
Brunazzi
and
Paglianti
(1998)
Axial
separator
type
3.A
0
the
superficial
gas
velocity
for
wire-mesh
mist
eliminators
has
been
assumed
equal
to
0.37
m/s,
which
corresponds
to
an
F-factor
of
3.37
Pa".
Similarly,
an
F-factor
equal
to
16
Pa"
has
been
assumed
for
the
axial
flow
type
3.A
cyclone,
as
ex-
plained
previously.
Figure
14
shows
a
comparison
between
the
computed
performances;
the
axial
flow
separator
shows
a
higher
separation
efficiency
for
droplets
smaller
than
10
mi-
crons;
whereas,
somewhat
higher
efficiencies
are
shown
by
the
wire-mesh
mist
eliminator
above
this
limit
up
to
about
30
microns,
above
which
the
efficiencies
become
comparable.
Moreover,
it
is
worth
pointing
out
that
when
using
a
wire-
mesh
mist
eliminator,
a
vessel
with
a
1070-mm
internal
diam-
eter
is
necessary,
whereas
if
a
separator
consisting
of
21
ax-
ial-flow
type
3.A
cyclones
arranged
in
parallel
is
used,
the
vessel
diameter
reduces
to
900
mm.
Finally,
the
use
of
axial-
flow
cyclones
allows
high
separation
efficiencies
to
be
ob-
tained
across
a
broad
range
of
droplet
sizes,
and
also
allows
the
vessel
diameter
to
be
sometwhat
reduced,
which
is
very
important
for
high-pressure
applications.
Conclusions
The
experimental
data
on
droplet
removal
efficiency
pre-
sented
in
this
article
were
obtained
using
a
laser-based
droplet
sizer,
the
Malvern
Particle
Sizer.
This
article
has
presented
not
only
different
sets
of
separation
efficiency
of
axial
flow
separators
but
also
a
new
model
for
predicting
their
removal
efficiency.
Analysis
of
the
experimental
data
obtained
in
this
article
shows
that
this
new
model
can
be
used
for
predicting
the
separation
efficiency
of
this
new
family
of
separators.
The
proposed
model
allows
the
measured
efficiency
to
be
pre-
dicted
with
sufficient
accuracy
without
the
need
of
introduc-
ing
any
adjustable
parameters.
This
result
is
significant
be-
cause
no
mechanistic
model
has
yet
been
published
in
the
literature
to
predict
the
separation
efficiency
of
this
family
of
separators.
This
could
be
an
important
improvement,
as,
es-
pecially
for
high
working
pressures,
an
increasing
quantity
of
industrial
separation
equipment
is
now
using
axial-flow
cy-
clones.
In
fact,
axial-flow
cyclones
permit
a
reduction
to
be
made
in
the
diameter
of
the
vessel
containing
the
separator,
thus,
allowing
an
important
reduction
in
investment
costs.
The
new
mechanistic
model
presented
in
this
article
could,
there-
fore,
be
used
for
the
design
and
the
optimization
of
complex
separation
units.
Acknowledgments
This
publication
is
based
on
work
supported
by
Costacurta
S.pA.
VICO,
Via
Grazioli
30,
20161
Milan,
Italy
and
by
the
"Ministero
dell'Universita
e
della
Ricerca
Scientifica."
The
authors
thank
Ing.
S.
Sagripanti
and
Ing.
A.
Babbore
for
their
helpful
assistance,
and
Ing.
B.
Mondello
and
Ing.
A.
Luongo
for
some
useful
discussions.
Sep
a
ra
t
ion
e
ffic
100
80
60
40
20
0
100
80
60
40
20
0
100
80
60
40
20
0
0
10
20
30
40
50
60
Drop
diameter,
d
(microns)
Figure
14.
Separation
efficiency
vs.
drop
diameter,
un-
der
high-pressure
working
conditions.
Comparison
between
theoretical
behavior
of
wire-mesh
mist
eliminators
(Brunazzi
and
Paglianti,
1998)
and
axial
flow
cyclones,
present
model.
Wire-mesh
packing
charac-
teristics:
270
m`/m
3
,
wire
diameter
270
microns,
pad
thick-
ness
150
mm,
superficial
gas
velocity
0.37
m/s.
Cyclone
characteristics:
type
3.A,
superficial
gas
velocity
1.7
m/s.
Working
conditions:
air—water
system,
pressure
7
MPa,
temperature
20°C.
Notation
C
=
constant
of
Eq.
2
C
D
=
drag
coefficient
d=
droplet
diameter
=
the
smallest
droplet
diameter
that
can
be
separated
with
an
efficiency
equal
to
100%
F-factor
=
u„
A
K=
constant
of
Eq.
1
L=
cyclone
length
N=
total
number
of
droplets
in
the
control
volume
50
January
2003
Vol.
49,
No.
1
AIChE
Journal
N=
number
of
revolutions
inside
the
separator
n
=
exponent
of
Eq.
2
r=
radius
Q=
gas
volumetric
flow
rate
T=
temperature
t=
time
tres
=
residence
time
u
=
gas
velocity
=
mean
tangential
gas
velocity
U
sg
=
superficial
gas
velocity
X=
droplet
concentration
z
=
axial
distance
Greek
letters
n=
capture
efficiency
µ.=
viscosity
v=
droplet
velocity
7r=
3.14159...
0=
angle
p=
density
Subscripts
and
superscripts
a
=
axial
g=
gas
phase
l=
liquid
phase
r=
radial
0=
tangential
Literature
Cited
Alexander,
R.
M.,
Air
Pollution
Control
Engineering,
Chap.
6,
Dekker,
New
York
(1980).
Babbore,
A.
"Fluidodinamica
ed
Efficienza
in
Separatori
Assiali
Centrifughi,"
(in
Italian),
MSc
Thesis,
Univ.
of
Pisa, Pisa,
Italy
(2000).
Brunazzi,
E.,
and
A.
Paglianti,
"Design
of
Wire
Mesh
Mist
Elimina-
tors,"
AIChE
J.,
44,
505
(1998).
Brunazzi,
E.,
and
A.
Paglianti,
"Design
of
Complex
Wire
Mesh
Mist
Eliminators,"
AIChE
J.,
46,
1131
(2000).
Biirkholz,
A.,
Droplet
Separation,
VCH,
Weinheim,
Germany
(1989).
Capps,
R.
W.,
"Properly
Specify
Wire-Mesh
Mist
Eliminators,"
Chem.
Eng.
Prog.,
90,
49
(1994).
Carpenter,
C.
L.,
and
D.
F.
Othmer,
"Entrainment
Removal
by
a
Wire-Mesh
Separator," AIChE
J.,
1,
549
(1955).
Dietz,
P.
W.,
"Collection
Efficiency
of
Cyclone
Separators,"
AIChE
J.,
27,
888
(1981).
Fabian,
P.,
P.
Hennessey,
M.
Neuman,
and
P.
Van
Dessel,
"Demys-
tifying
the
Selection
of
Mist
Eliminators,"
Chem.
Eng.,
100,
106
(1993).
Flagan,
R.
C.,
and
J.
H.
Seinfeld,
Fundamentals
of
Air
Pollution
Engi-
neering,
Prentice
Hall,
Englewood
Cliffs,
NJ
(1988).
Holmes,
T.
L.,
and
G.
K.
Chen,
"Design
and
Selection
of
Spray/Mist
Elimination
Equipment,"
Chem.
Eng.,
91,
82
(1984).
Licht,
W.,
Air
Pollution
Control
Engineering,
Dekker,
New
York
(1980).
Ludwig,
E.
E.,
Applied
Process
Design
for
Chemical
and
Petrochemical
Plants,
Vol.
1,
3rd
ed.,
Chap.
4,
Gulf
Pub.,
Houston,
TX
(1995).
Perry,
R.
H.,
and
D.
W.
Green,
Peny's
Chemical
Engineers'
Hand-
book,
7th
ed.,
Chap.
26,
McGraw-Hill,
New
York,
p.
26
(1997).
Svrcek,
W.
Y.,
and
W.
D.
Monnery,
"Design
Two-Phase
Separators
Within
the
Right
Limits,"
Chem.
Eng.
Prog.,
89,
53
(1993).
Verlaan,
C.
C.
J.,
"Performance
of
Novel
Mist
Eliminators,"
PhD
Thesis,
Delft
Univ.,
Delft,
The
Netherlands
(1991).
York,
0.
H.,
and
E.
W.
Poppele,
"Wire
Mesh
Mist
Eliminators,"
Chem.
Eng.
Prog.,
59,
45
(1963).
Ziebold,
S.
A.,
"Demystifying
Mist
Eliminator
Selection,"
Chem.
Eng.,
107,
94
(2000).
Manuscript
received
Manuscript
received
Feb.
15,
2001,
and
revision
received
May
28,
2002
AIChE
Journal
January
2003
Vol.
49,
No.
1
51