Unformatted text preview: Electrostaticcontrol of particle deposition
and
HIROAKI
MASUDA
YAMAGUCHI
KENICHIRO MAKOTO
TANOUE,
YoshidaHonmachi,
University,
Sakyoku,
Department Engineering,
of Chemical Kyoto
6068501,
Kyoto Japan
1998
Received 1998; 17
17
September
July accepted
inan
AbstractA
twodimensionalhas conductedelectrostatic
simulation
been
powdercoating
most
flow
In absent
the
boothcontrolling deposition. ofelectrostatic of
for
forces, particles
particle
andmage
forces
steamlines deposit target. electrostatic
and
cannot on
the When
(coulombic
i
along
the
near
the It
are inthe ofthe
forces)added motion particle,rajectoriessignificantlytarget.
t
change
From calculated
isfound image hardly the
that force affectsdeposited ofthe
position particle. the
near
the region
the coulombic found larger drag
force to
is
be than
force
distribution aimed on target,
when particle close t Particlessmall number small
force the isvery tothearget. with Stokes having
the regions.
the
width
the region
charge exactly
specific deposit on aimed Furthermore of aimed also
the
of
the deposition.
affects ccuracyparticle
a
Stokes specific
Electrostaticparticle 2D
simulation;
number; charge.
Keywords: control; deposition;
NOMENCLATURE
coefficient
()
cc
Cunningham's
slip
coefficient
CD
()
drag
deviation
ofparticle
Di
deposited ()
position
size
Dp
particle (gm)
E
electric (V/m)
field
electric definedequation ()
dimensionless field
(7)
by
Eê
electric defined
dimensionless field
(8)
byequation ()
Q
Eê,o
dimensionless field
electric definedequation ()
(9)
by
E*
coulombic (N)
force
Fc
force
FD
drag (N)
force
FG
gravity (N)
force
Fj
image (N)
Froude
number
Fr
() 120
g
H
Lo
All
i
L2
Lw
mp
NP
q/mP
(q / mp)o
(q / mp)*
Rein
Rep
St
Stopt
u
Uo
U
v
Z
W
X
Xp,
T'
Greek
sj
,r
A
pp
pG
r
or
(D acceleration 2)
(m/s
gravity
width nozzle
of
(m)
ofinlet (m)
length region
o
widthfaimed (m)
region
ofaimed (m)
intervals
region
distance
between and wall
particle the (m)
o
mass fparticle
(kg)
()
injected number
particle
specific (C/kg)
charge
reference
ofspecific (C/kg)
charge
dimensionless charge
specific ()
dimensionless value specific (–)
charge
optimum of
number
Reynolds ()
= HpGuo/>
number
Reynolds ()
particle
number
Stokes
()
number
value
()
optimum ofStokes
airvelocity
(m/s)
inlet velocity
air
(m/s)
airvelocity
dimensionless
()
(m/s)
particle
velocity
dimensionless velocity
()
particle
o
widthftarget
(m)
axial
coordinate
(m)
o aimed (m)
region
edge fthe
most
particles
departed from ofdeposited (m)
position Xe.;
coordinate
transverse
(m)
definedequation (m)
(11)
by
ratio
permittivity ()
of
viscosityair(kg/m/s)
of
densityparticle
(kg/m3)
of
densityair(kg/m3)
dimensionless
time
()
ofaimed (V)
electric
region
potential
electric
dimensionless potential
() 121
1.INTRODUCTION
toget
their
Recently, ridofpollution,
pollutionfree areincreasing market
paints
share ear year.The
method electrostatic [1]is
force
y by
powder
coating
using
remarkable andis applied thecoating automobiles,
to
of
themost
railroad
one,
etc.
d
electrostatic coating consists
of
articles, Because
cars, omestic
[1]
powder
ofparticles, transportcharged
of
to
as
(i)electrification
(ii)
particlesthetarget an
ofinternalexternal field, particle
or
electric (iv)
aerosol, formation
(iii)
deposition
and(v)fusion particles, research each
of
much
of
has conducted
process been
andnumerically.
has
experimentally
Transporting to thetarget been
particles
studied
external work theparticles,it is
forces on
so
[26].
numerically Various
difficult
todiscuss individual experimentally. asmost them
the
force
Besides, of are
limited only and
for big simple there noreports are
which concerned
with
targets, is
selective exact
and deposition
ofparticlesinelectrophotographics
as
and
coating
ofimage
elementsaBraun
on
tube.
inwhicharticles ontheaimed
Inthepresent fortheprocess
work,
p
deposit
ina
wehave
simulation tworegion tribocharge, conducted particle
by
charged
dimensional booth discuss accuracy particle
the
ofthe
under
coating and
deposition
various
conditionsvelocity, size specific
(air
operating
charge).
particle and
2.CALCULATION
DOMAIN
1shows calculation Gas fed the region = W) y
the
domain. is into inlet (Lo b
Figure
the
with
a expands
(H
velocity (u
using nozzle = 0.06W) constant profile = uo) nd
into particle booth S W 8 W. target W 0.1 )isplaced W
the
The ( x W
3
coating of x
ofthe
downstream nozzle The regionsparticle
exit. aimed
of
are
depositionsettled
atintervals Each the
ofL2. of aimed has width L 1. surface
of The
regions a
potential
onthe
aimed is1>T theallother are
walls grounded Particles
are
(0V).
region and
into booth
the
as
flow.
injected the through nozzle anaerosol
3.NUMERICAL
AND
PROCEDURE ONDITIONS
C
3.1. flow field
and
electric field
Air
intwodimensional coordinates.
Numerical
simulation
isconducted
Cartesian
The
are
to derive governing
the
(i)
following
assumptionsintroduced
equations:the
field
and
in
is
air,(ii)
gas incompressible thevelocity istwodimensional steady
the
booth uniform
state,iii)gasenters coating with
(
(iv)
velocity, theelectric
not
is
to
i (
potentialequal 0 Vat theboothnlet, v)gasdoes sliponthewall,
surface
electric
is
a
walls
(vi)
regionndallother are
potentialOrontheaimed
(0V), flow
(viii)
grounded (vii) isturbulent, thespace effect negligible,
charge is
and both gradients
ofmomentumelectric
and
are
to
(ix) the
potential equal 0 at
thebooth
inthis
outlet.
thestandard model was
ks
Furthermore,
[7] adopted 122 1.Calculationin electrostaticbooth.
domain
the
Figure
coating 2.
meshes calculation near target.
domainthe
FigureStaggered inthe 123
NavierStokes kequation,
simulation.
(continuity,
Governing
equations
equations,
and
and
conditionsrewritten
are
innonequation) boundary
sequation Laplace's
over
mesh
dimensional and discretized acontrol ona staggered
forms then
volume
of
method
and
solved
numerically
bymeans theSIMPLE [8].The
typical of
grid
isshown Fig. ,where x 100
in 2
inthe
this
simulation the
near target
130
meshes
axial transverse
and
directionsused.
are
3.2.
Particle
motion
field determined,
thetrajectoriescalculated
are
After gas and
the field electric are
with equation
the
ofparticle
motion.
Including force, force,
drag gravity coulombic
force imageorce theexternal ontheparticle, dimensionless
and
f as
forces
the
ofparticleexpressed
is
as
equation The
fourth ofthe
term righthand isthe
side image [1]. here,
force W the
concentration
is
The
to
interaction
isignored
because particle
particleparticle
low. the
When distance particle the isless Dp/2, assume
between and target than we 124
the
is
on target
surface. 1shows condition
Table
the
ofthis
particledepositedthe
simulation.
Stokes
(St) the
By
changing number and dimensionless charge
specific
we studied accuracy particle
the
ofthe
[(q/mP)*],have
deposited
position.
4.RESULTS DISCUSSIONS
AND
4.1. flow and
Gas field electric
field
3shows calculated inthe
the
air
flow whole The velocity
isequal
Figure
region. inlet
to10 Arrows the
m/s.
show velocity The and ofthe scale
vectors. light shade gray
shows axial
the equivelocity Intheinlet
profiles.
region, flow develops
gas fully
booth. o
flows
around
and into coating Apair flarge
enters the
circulating isformed
1.
Table
Conditions
of
simulation 3.Calculated inthe region = 3333).
air
flows whole (Rein
Figure 125
that
From velocity itisfound ajetstream
the inthe
profiles,
region
target booth. the
exit.
axial
small.
exists thenozzle Inother
near
Ux
regions, velocities arevery
area.
in 4
value
Inparticular, have negative intheblack Asshown Fig. ,a
they a
from center the along
to edge the
near target the
new
boundary isformed the
layer
itis
that
transverse
direction.
Therefore, anticipatedtheparticles not eposit
may d
force
on
the if attractive (electrostatic isabsent. 5
force)
Figure
effectively targetthe
of target
Arrows
electric in vicinitythe surface. show
shows calculated field the
the
force
The a shade thegray shows
of
scale equipotential
electric vectors. light nd
on
and
If particles charged
are
negativelyapositive isapplied
voltage
profiles.the
and repulsive
force on
theaimed the
regions the
region, attractive works theaimed
w at
between
force orks intervals them.
4.2. rajectories
T
I
near
6a b
the
ofparticles thetarget = 102).n
(Fr
Figure and shows trajectories
flow
and
force drag are
6
Fig. a,only
gravity and force considered theparticles
The
which
from center the
of booth,
the
along steamlines. particle, isinjected the
In 6
coulombic and
force image
on
surface. Fig. b,including
deposits thetarget
the
and
the
force, trajectories dramatically particles near aimed
deposit the
change
region, cannot
deposit
region.
Although 2and are tothe
particles 3 close aimed they
o
On
force at
onit because repulsive works theedge fthem. theother
the
hand,
of nozzle ishardly
affected
is
from
wall,
4,
particlewhich injected thevicinitythe vectors.
C
of
4.
air
flows the (Rein
(a)
FigureCalculated near target = 3333).Velocity (b) ontours
axial (lJx).
velocity 126 5.Calculated potential near target = 0.00133, +L2) =
electric profilesthe
Figure
LI/(LI
electric (b)
of
electric (<1».
0.2]. Lines force.Contours potential
(a) of 6.
near
the (a)
+ (b) = + + +
FigureTrajectoriestarget.YF= FD FG. Y F FD FG FC FI. 127 = I,
7. curves the [Rein St
(q/mp)* ' = 0.00133,
FigureForce near target = 3333,= 0.25,
Table
2.
The
influenceimage on particle position =
of the forcethe deposition (Rein
St= (q/mp)* =
3333, 0.25, = I,Eê.o 0.00133, +L2) 0.2)
L)/(Li = the
force it
flows s
Therefore,particle
bycoulombic and almost alongteamlines.
on inject
under conditions stronglythe positions.
trajectories these
depend
surface.
we
how forces the
on particle near target
Next investigate the
change the
the
between particle
ofthe
7
the
LW distance
Figureshows distribution forces. isthe
from
the
distance the
axes respectively,
wall. horizontal vertical show,
and
and The
force. particles
surface theaxial normalized gravity The
and
force
bythe
target
and
decelerated
at the
inthenozzleLw> 3W) immediately
areaccelerated
(
than
the force
When
nozzle Therefore,drag isnegative. Lwisless 0.02W,
exit.
value
the
and
coulombic affects trajectorieshasmaximum atLw =0.01 W
force
atthe o aimed For
avery coulombic isinduced edge fthe
force
because large
region.
If is than
force
constant.LW less
O.OOO1Lw< O.O1 coulombic isalmost
< W
W,
ofthe
The
O.OO1 W, force
position
image increases
gradually. deviation deposited
W
in
2.
due image isabout
to
force
0.00001asshownTable Therefore, force
image
isnegligible applications.
inactual
4.3.
Evaluationparticle
deposition
of
Stokes
of
atvarious numbers
8
the
(St).
Figureshows ranges particle
deposition
axis
The
horizontal isthe
axis positionparticle
of
and vertical isthe
depositionthe
The
of
The gray show
Stokes
number. three areas theaimed
regions. deviation 128 8.
ofparticle
inconnection number =
with
Stokes [Rein 3333,
Figure Ranges
deposition
(D;)
particle
deposition isevaluated
(10) (11).
byequations and where e,; theedge ftheaimed and is themost
o
X is
region XP.;
departed
position
ofdeposited
from Ifall
inthe
particles Xe, ;. particles
deposited aimed
region,
wedefined < 0, and other D; > 0. For
the case,
ifSt
D;
example, = 0.5and
then =
W Xe,
Therefore 1.5.
L= 0.02W, Xp, j O.15 and l = 0.12 W .
D=
4.3.1.
number.
9
the
between
Influence
ofStokes
Figureshows relationship St
andD ;.The
dimensionless charge / mp)* to 1.0.This
is equal
specific (q
figure
means thesmaller inother
that
thesmaller
size
St,
words,
particle orthesmaller
airvelocity the
ofthe
IfSt
small,
yields higher
accuracy deposition. istoo
particles
cannot onthe
So optimum
condition inthe
exists particle or
size
deposit target. the
airvelocity.
the coulombic (Fc,,) hanges inallofthe
force
little
Although axial
c
aimed
the
than
regions, transverse force atthe ofthe islarger
drag (Fp,y) edge target
that thecenter it. Asaresult, particle beyond aimed and
at
of
the
flows
the
region
on
the
value
the
deposits theinterval Then shows largest among three
region. D3
aimed
regions. 129 in
with
Stokes [Rein =
9.
ofthe
deposition
FigureDeviationparticle = connection number 3333,
= 1,
Lj /(L j
(q/mp)* =0.00133, + L2) 0.2]. with charge =
ofthe
10.
s
Figure Deviationparticle inconnectionpecific [Rein3333,
deposition
=
= (q/mp)p C
St 0.25, = 103 /kg, + L2) 0.2].
between
10
the
4.3.2.
charge.
Figure shows relationship
Influencespecific
of
=
In figure, larger
the
a St
and
(q/mp)*
(q/mp)* D;atRein 3333nd = 0.245. this
are
causes greater The
the
DL. reasons asfollows;
force
is
of particleaffectedthe
area the
by coulombic is
(1)The where motionthe
wider that small / m p) * .
than for (q
from
at
region
(2)Transverse velocitythedeparted
position theaimed is
particle
for (q/mp)*, particle
the
than for
Therefore,large
higher that small
(q/mp)*.
the
onthe
flows
region.
region deposits interval
beyond aimed and
cannot on
Then ¡enlarges. specific istoo
Ifthe
small,
D
particles deposit the
charge
that
than gravity Itisfound
force.
the
force
because coulombic issmaller the
target
the
the
conditions incontrolling
exist
particle
deposition.
optimum
operation
the
W have
4.3.3.
region. e discussedaccuracy
Influence width the
ofthe of aimed
under
width aimed (LI) itsinterval
ofparticle
region and
deposition constant ofthe 130 11.
ofthe
with
Stokes [Rein
Figure Deviationparticle inconnection number = 3333,
deposition
= 1,
+ =
(q/mp)* LII(LIL2) 0.333]. 12.
ofthe
with charge =
Figure Deviationparticle inconnectionpecific [Rein3333,
deposition
s
=
St=0.25, + L2) 0.333]. 13.
between
normalized the regionoptimumof
width aimed and
of
value
Figure Relationshipthe
St,
atthe region
(q/mp)* aimed 1. 131
i previous
sections.fact,tisnecessary
In i
tochangeaccordingthe
to
L,
(L2)nthe
inelectrophotographics,
For
the
objects. example, are size a character
they the of
size image
of
elementsaBraun etc.
on
we studied accuracy
the
tube, Thereforehave
ofparticle
for
widths
11
depositionvarious oftheaimed
region.
Figuresand 12
=
show calculated forthecase L I I(L LZ) 0.333. tendency
the
results
of
The
+
t accuracy
isenhanced orspecific becomes isthe as
asSt
smaller same
thathe
charge
in previous
shownthe
sections.
However, isless 0.5 any
Dihere than in conditions;
<
at0.025 St < 0.075, hasa negative The shows
value. fact
that
D3
especially
inthe
We
the
particles perfectly internal ofthe
deposit
region aimed
region. define
which inimize and variationthem shown a
and
m
of is
as
D;, the
Stopt
function
of
i
1
the of
b
+ LZ)nFig. 3.For case L,/(L¡+ L2)> 0.2, oth
= 0.08],
and
have constant [Stopt 0.022,
a
value =
Stopt
(q/mp.opt)*
This
the
respectively.iswhy particles
perfectly onthe
deposit aimed under
region
the
condition L I / i +Lz).
oflarge
(L
in order
the
of
inan
Consequently, tocontrol position thedeposited
particles
electrostatic process, necessary (i)thewidth the
itis
toset
of aimed
coating
region,
and t optimum
t optimum size optimumvelocity (iii)he
air
(ii) he
particle or
specific
charge.
5.CONCLUSION
For ontrolling
the
we
have
aerosol
ina
c
particle
deposition, conducted simulations
twodimensional
electrostatic booth. absenceelectrostatic
of
forces,
coating Inthe
almost along
and the
theparticles flow thesteamlinesonly particles
from
injected
thecentral ofthenozzle
on
surface. thecoulombic
If
region
deposit thetarget
and
forces included, trajectories dramaticallythe
the
near aimed
image are
change
Force
near target calculated. shown thedrag
are
Itis
that
region. distributionsthe
force coulombic play
and
force important inthe
roles trajectoriesimage
but
force
israrelyffective. theparticlevery totheaimed
e
When
is close
coulombic
region,
than drag The
force greater the force. accuracy deposit
is
ofthe
isa
position function
ofairvelocity, size specific and
we optimum
particle and
charge, therefore have
conditions.
When consider
we
the
itis
touse
particle
deposition,necessary asmall
controlling
Ifwe
inthe
Sthavingsmall
a
one
specific
charge. useonly nozzle electrostatic
the
flow
the
coating, deposited isaffectedthe
position
by circulating around target.
ofthe
we
t
Then, guesshattheaccuracy deposited
position beimproved
may
ifmany
are which the
to
considerably nozzles used, spray particles
perpendicular
whole ofthe under condition <0.6.
ofSt
the
region target the
Acknowledgement
Ltd. a
This was supported
work partly
Co.,
bySamsung
DisplayDeviccs, and Grantof
inAid Scientific
for
Research 10555265) theMinistry Education,
from
(No.
of
Science, and
Culture, Sports Japan. 132
REFERENCES
Powder Research Press
1.J.F.
ElectrostaticCoating. Studies ( 1984).
Hughes,
in
electrostatic
L. and J.
ofcharged trajectories
2.M. Ang P. Lloyd,
Investigation particle
powder
J.
Flow 823836
1
(1987).
coating Int. Multiphase3,
system,
metal in
and
K.
Adhesion powders surface coating
3.S.
powder
Banerjee Mazumder, of
charged on
IEEE
(1993).
process, 18971901
ofparticle
intribopowderin:Conf.
4.K.
Adamiak Mao,
and Simulation trajectories
J.
coating,
Annu. Orlando,
Record IEEE Applications Meet., FL, 12731279
the Industry
Society
pp.
of
( 1995).
K.
Electric modeling
ofelectrostaticcoating
5.D.E.Woolard Ramani, field
and
powder ofa
continuous J.Electrostatic. (1995).
fiber
373387
bundle,
35,
6.K.Adamiak, modeling
Numerical oftribochargecoating J.Electrostatic.
powder systems,
40/41, 395400
(1997).
7.C.
Suuchi Kougaku. shyuppan
Arakawa, Ryuutai Daigaku kai, (1995)
Tokyo (in
Japanese).
New
York
8.S. Patanker, Heat and luid Hemisphere, (1980).
V.
Numerical
F
Transfer Flow.
S.Morooka
H.
Shintaikei Kougaku/Biryuusi
9.K.Okuyama, and Masuda, Kagaku
Kougaku.
(1992)
Ohmushya, (in
Tokyo Japanese). ...
View
Full Document
 Spring '11
 Prof.Ramachandran
 Electrostatics, Force, Magnetic Field, Particle, Electric charge

Click to edit the document details