A B S T R A C T
B
E T T Y L
.G A T A N O
.D
ete rm in
in
g
th
eT
r a n sf
e rE fl
i cie n c
y of
aH
V
L PSp
r ayG
u n(
U
nde r t he dir e c
t io n of DR
.M
IC
H
A
E LR
. F LY N N
)
In t
hi
sw
o rk
, am
ath
em
ati
c al
r ela
tio n
shi
pb
etw
e e n th
e tr a n sf
e r effi
ci
e n cy of
ah i g h
v o
lu
m
el
ow p
r e s s u r e(
H V
LP
)
sp
r ay g
u n a nd it
s op
e r ati
o n al p
a r am
ete r sw
a sd
e v elo
p
ed
.Sp
r ayp
ain
t op
erati
onsw
e r e si m
ul
ated b
y am
a n n eq
uin
sp
r ay i
ng
a n o n v ola
til
e oil fr
om
theH
V L P g
u n o nto afl
atp l
ate. Th
e tr an sfe r efl Bc
ie n c
y w
a s cal
c ula
ted fr
om
th
e am
o u nt of
oil
s
p
r ayed fr
om
the
g
u n a nd
th
e am
o u nti m p
acted
o n the
pla
te.M
a n n equi
nm
oti
o n a nd
o r
i
e ntati
o n, a
ir
p
r ess u r e of
th
e sp
r ayg
u n, and
air
vel
oci
t yin
the
w i
nd
tu n n el w
e r e v a ri
ed
to a s ses s th
eir
ef f
ect o n transf
er effi
ci
e n cy
T h
em
e as u r ed
tr a n sf
er effi
ci
enci
es r a ng
ed fr
om
0.
6
6 to 0.8 7.T
r a n sf
e r effi
ci
e n cy d
e c r e a s ed l i
n e a rl
y a s af
u n cti
o n of
the
m
a s s of
ai
r to th
em
a s s of l i q
ui d
sp
r ay
ed
(
m
a/m
i)
M
a n n eq
ui
nm
otio n
al
s od
e cr e a s ed
th
e tran sf
e r effi
cie n c
y
att
he
h ig h
e st v al
u e s of m
./ m
i.A
the
oreti
c al m
od
el f
o rp
red i
ctin
g
transf
er effi
ci
ency b
as ed
on th
ei
nerti
al
im p
acti
on of p
a rti
cl
e s o nto aw
o rk p i
e c ew
as al
s od
e vel
op
ed
A lt
h
o ug h
th
em
od
el
ov e re st
i m
ated
th
e tran sfe r
effi
cie n c
ie s
,
g
o od
ag
r e em
e ntw
a s n oted b
etw
een th
ep
r ed i
cted
tran sfe r
effi
ci
en cie
s and m
e a s u red
v al
ue s. Th
e th
eo re ti
c al m
od
el h
a s th
ep
otenti
al
tob
e aI l l
A C
K
N O
W
LE
DG
M
EN T S
T
hi
sw
o rk w
o ul d h
a v e no tb
e e n po s si b l
ew i
th
o ut thefi
n a n ci
al
s up po rt of N
IO SH
g
r a nt# 5 R 0
1O H
02
8 58
, "C
om p
utati
o nal
M
eth
od
si
nI
nd
u stri
al V
enti l
atio
n. "M
anyp
e op l
e co ntri b
uted
to th
e c om pl
etio n of
thi
s r ep
ort.F i
r st of
al l
,I
ow
em
a ny
t
h
ank
s tom
y ad
vi
sor.D
rM
i
ch
ael F l
yn n,w h
o s e sup p
ort, u nd
e r sta nd i
ng
, a nd g
ui d
an c ew
a sa
p p
r eci
ated m
ore th
anI
c an s ay h
e re.A l
s o,I w
ant to th
a nk D
rD
a vi d L
ei
th
a nd D
r.M
i
ch
a el Sym
on sf
o r read i
ng m y
r ep
o rt and p
r o vi d i
ng
th
ei
ri
n v al
u ab l
ei
np
utT
h
reep
eop l
ew
ere e sp
e ci
al l y im p
ortanti
nh
el p i
ng m
efi
nish
th is rep
ort.I
ow
e ab
i g d
eb
t toJ
oh
nM
cK
em
a n,m y l
ab p
a rtn e r a nd fi i
e nd
W
i
th
o uth i m
,I
n e v e rw
o ul d h
a veu n
d
erstood h
ow
toh
o ok
up
th
at sp
ray g
u n .H i
sp
atie
n c e a nd
s up p
ortd
u ri
ng m y
n u
m
e r o u sp
a ni
c at ta ck
sw
e r em
u ch
ap p
re ci
ated
I
al
s ow
ant to th
a nk J
ord
a nK
ovit
zf
o rhi
sw
o rk i
nd
e v el
op i
ng
th
ei
n e rtia
l im p
acti
o nm
od
el
a nd f
or try i
ng
tim
e a nd
ti m
e ag
ai
n toex
p l
ai
nit t
om
e. Fi
n al l
y, Iw
a nt to th
a nk K
evi
n Du n nf
o r alw
ays a n sw
e ri
ng m
yq
u e sti
o nsa
b
o ut sp
r ay p
ai
nting
a nd m
ak i
ng m
el
a ug h
at th
e s am
e ti m
e.T h
ere arem
a ny m
orep
e opl
e th
atI w
ant to ack
n ow l
ed g
e.I w
oul d l i k
e to th
a nk
ev e r
y
o nei
n th
eB
ait
y L
ab
or ato ry
(
esp
eci
al l
yf
o r al l
th
ei
rh
el p
tod
ayw h
enm y
c om p
ute r atem y
th
e si
s)
. Th
a nk
s al
s o toK
e nd
al l
a nd L
au ri
ef
o r th
ei
rfi i
e nd
sh i p d
u ri
ng m
y ti m
ei
ng
r ad
u ate s ch
o ol
I
ow
e ab i
g th
a nk
s toN
a n cyf
o r e v e ry
th i
ng
th
at sh
ed i d f
o rm
e th
ep
a stt
w
oy
e ar sT h
ank
sf
o r th
e c ook i
es! L
astly
,I w
a nt to th
a nk m y b
e stfi i
end
,C
arol y
n,w h
oh
a s al w
ays e n c o u r ag
ed m
e tod
om
o r e th
a nI
e v e r th
o ug h
t I c o ul d
E D
.O B !
T
h
em
o sti m p
orta ntp
e op l
e tom
e a nd
th
e o n esw h
od
e s e r ve th
eb i g g
est th
a nk
s a rem
yp
ar e nts and
si
ste rsT h
eyb
el i
e v ed i
nm
e e v e nw he
n Id id
n 't
b
el i
e vei
nm y
s elf
T h
ey
I V
T
A B
LE O F C O
NT
EN
TS
U
S
TO
FT
AB
L ES
vU
S
TO
FF
IG U
R ES
viL I ST O F SY
M
B O L S
vi i
I
I N
TR O D U C T
IO
N
1I
I
.T H E O R E T I C A L C O
N
SI D E
RA
T IO N
2
2
.1 A
tom
izat ion 22
.2
M
om
en tum
4
2
.3 I
mp
a ct ion 52
.4 O
v e r sp
ray
6
I I I
.M
E T H O D O L O G Y
7
3
.1 L
ab
o ra to ry S
etUp
73
.2 E
xp
e ri m
en tal D
e sig
n9
I V
.R E SU L T S
10
4
.1 E
xp
e rim
e nt al R
e s ul
ts1
04
.2
M
od
el R
e s ul
ts1
1V
.D I SC U SSI O N
12
5
.1 Ex p
e rim
en t al R
e s ul
ts1
25
.2 L
im
i ta tio n s of
th
eR
el
a tio n sh
ip b
et we e nm
j
m
iand T
r an sf
e rE
ff
icie n cy
12
5
.3
D
is c u s sio n of
I mp
actionM
od
el
13
5
.4 L
im
it at ions of
I mp
act io nM
od
el
1
45
.5 I mp l
icat io n s of
I mp
acti
o nM
od
el
14
V I C O N C L
U
S
IO N S A N D
R EC O
M M
EN D A
T IO N S
1
5V
I I R E FE
R EN C E S
2 2
A P
P EN D I X A
:I
n str um
e ntC
al ib
rati
o n, Exp
eri m
e ntal
R e s ul
ts, and S
am p l
eC
al
c ul
ati
o n s2
3A P P
EN D I X B
:S
um m
a ry
of S
tati
sti
c al
M
eth
od
s 4 1A P
PE N D I X C
.C
al
c ul
ati
on of T
r a n sf
e rE f fi
ci
e n cL I
S
TO
FT A B
LE S
T
ab l
e1
.O
ver vi
ew of
N
oz zle
P
r e s s ure and F
r e e str e am V
el
o ci
ty
*10
T
ab l
e 2.R
egr e s si
o n E qu atio n s
f
o r Tr a n sf
e r Ef fi
cie n c
y a s a Fu n ctio n
of
n ia/ m
i*
VI
L I ST O F
F IG U R E S
F ig
u r e 1.S
ch
em
ati
c of
th
eH V
LP S p
r ay
N
oz zl
e 1 6F i
gu r e 2S
ch
em
ati
c of
th
e In e rti
al
lm
pa cti
o nM
od
el
1 7F ig
u re 3.S
ch
em
ati
c of
th
e Pr ess u ri
z ed Sp
r ay PotS
ystem
1 8 Fi
gu r e 4.O
ri
e ntati
o n of
M
am
i eq
ui
nw i
th
Fr e e str e am
1 9F i g
u re5
.T
r a n sf
e rE f fi
ci
e n cy
as aF
u n cti
o n of
n ia/ m
i2 0
F ig
u r e6
.T
ran sf
erE ffi
ci
ency P
red
i
cted fi
"o
m Si m p l
eI m p
a cti
o nM
od
el C
om p
a red
tov u
L I ST O F SY
M
BO L S
Ac ap
B
C
C
c L'n o z zled
j og
cH
K
m
n i a ,
m
i n igu ii
M M
D
P
,P
nP
oQ
jetR
eST
K
5 0U gu n
L'l io z zle
X
* X
Y
a rea o
f
ai
rd i
s ch
arg
e of
c ap
(
sq
u a ref
e et)
b
r e ad
th
of w
o rke r(
ft
)
C
o n c e ntr ati
o ni
n aw
o rk
e r'sb
r e ath i
ng
z o n e(
m
g/m
^)
C
unni
ng h
am
c or re cti
onf
a ctor(
u nit
l
es s)
d i
am
eter of h y p
oth
eti
c al
noz zl
e and
d
i
stanc efr
om
th
ehy p
oth
eti
c al
noz zl
e to th
ew
ork p i
e c e(
m
)
i m p
a cto r c ut si
z e(
m
)
g
r a vi
tati
o n al
c o n sta nt of
3 2.1 7 4ft
-l b/ l b
^- s^
h
ei g h
t of w
o rk
e r(
ft
)
k i
nem
ati
cm
om
e ntum
(
m
V
s ^)
s u
p
e r s c ri p
t u s ed i
nK i m
a nd
M
a r sh
al l E q
uati
on(
u ni
tl
e s s)
m
as s e s of
ai
r a nd l i q
ui d
, resp
e cti
v el y
(
Ib / m i
n)
m
ass of
ai
rf
r om g
u n,
b
ased
on c ap
a nd h
or n(
k g /
s)
m
a s sm
ed i
a nd i
am
eter(
|im
)
n o z zl
ep
r e s s u r e(
Ib
f/ft
^
)
p
r e s s u r ei
n res e rv oi
r(
Ib
/
ft
^
)
vo
l
um
etri
cfl
ow
r atefr
om
ci
r c ul
a rj
et(
m
^/
s)
R
ey
nol d
sn um b
e r(
u nit
l
e ss)
S
tok
e s n um b
e r c o r r e sp
o nd i
ng
to 5 0%
c ol l
ecti
o n eff i
ci
e n cy
of
a ni m p
a cto r(
u ni
tl
e s s)
p
r ed i
ct ed
a nd m
e a s u red
tr a n sf
e r eff i
ci
e n cy
, r e sp
e cti
v el y
(
u ni
tl
e s s)
ai
r vel
o ci
ty
of
th
ew i
nd
tu n n el
(
ft /
s)
ve
l
oci
ty
of
ai
rfr
om H V
L P sp
ray g
u n(
m /
s e c)
r e
l
ati
v e v el
o ci
ty of
ai
r tol i
qui d fr
om
sp
r ayg
u n(
ft /
s e c)
v el
oci
ty
of
ai
r athy p
oth
eti
c al
n o z zl
e(
m /
s)
d i
sta n c ed
ow
n str e am f
rom
th
eh yp
oth
eti
c al
ci
r c ul
arj
et(
m
)
re
d
uc ed d i
am
eter,d
s o/
M
M
D
V l l l
L I
S
TO
FSY
M
BO
LS
(
c o n t in u ed)
G
r e ek L
et te r so s u r
f
a c e te n si
o n of l i
qui d
(
d
yn e s/
cm
)
O
v c um
ul
ati
v e v olu
m
efr
eq
u e n cy f
o r ap
a rti
cl
e si
z ed is
trib
uti
o n(
u ni
tle s s)
Ht, ixi v
i
s c o sit
i
e s of
ai
r and l i q
ui d
, re sp
e ctiv e
l y
(
c ent
i p
oi
s e)
y
ratio o
f
sp
e cifi
ch
e ats : c onstant at1
.4 fo
r air
(
u ni
tl
e ss)
P
a,p
id
e n sit
i
e s of
ai
r a nd l i q
ui d
, resp
e ctiv e
ly
(
Ib /ft
^
)
P
airp
a rtic
le
of
air
fr
om
sp
r ayg
u n(
k g / m
^
)
Pp
p
a rtic
le
d
e n si
t y(k g / m
^
)
P
od
e n si
ty
of
air
in
the r e s e r v oi
r(
Ib/ ft
^I
.I N
TR O
DU C T
IO N
T
h
eh i g h
v ol
um
elo
w p
re s su re(
H
V L P)
sp
ray g
u nis a
sp
eci
al i
zed p i
e c e of
sp
r ay
p
ai
nti
ng
eq
uip m
e nt th
at op
e r ate s atl
ow
e rg
u np
r ess u r e s a nd
pr od
u c e sg
r e ate r ai
rf lo
w
rates th
a n c o n v enti
o n al
sp
r ayg
u n s.W
hi l
e c o n v e nti
o n al g
u n s op
e r ate at t y pi
c al
cap
pr e s s u r e s
i
n th
e r a nge of
5 0 to 6 0 psi
g, th
eH
V L P spr ay gu ni
sl i m it
ed
to am
a xi m
um
of
1 0p
si g
at th
eg
u n c ap
.A i
rfl
ow
r ate sf
o r th
eH V L P
sp
ray g
u n c a n ex c e ed 2
0 s cfm
at10 p
si g
.C
o n v e nti
o n al g
u n s o nl
yp
r od
u c e a r o u nd
1 4 to 1 6 s cfi
n at th
ei
rm
a xi m
um p
r e ssu r e r a ng
e. ^'^H V
L P sp
r ayg
u n sh
a v e al
s ob
e e n r ep
o r ted
toh
a veh i g h
e r tr a n sf
e r ef fi
ci
e n ci
e s th
anc o n v e nt
i
o n al
sp
r ayg
u n s ^ *^T h
e tr a n s
f
e r eff i
ci
e n cy of
a sp
r ay g
u n r ep
r e s e nts th
ef
r a cti
o n of
m
a s s spr ayed fr
om
th
e gu n th
atd
epo si
ts o nto th
ew
o rk p i
e c e.D
r op l
ets n otd
ep
o sit
ed
o ntot
h
ew
o rk
pi
e c e a r e te rm
ed
o v e r sp
r ay a nd h
a v e th
ep
ote nti
al
t ob
e tr a n spo rted i
nto th
ew
o rk
e r'
s
b
r e ath i
ng
z o n e Th
u s, sp
r ayg
u n sw it
h hi g h
e r tran sf
e r eff i
ci
en cy, s u ch
a s th
eH V
L Pg
u n,h
a v el
ow
e r r ates of
o v e r sp
ray
a nd
a r ed
u c ed p
ote ntial f
o rw
ork
e r e xp
o s u r e tom i
stsR
ec entw
o rk h
a sd
o c um
e nted
th
e r el
ati
o n shi p b
etw
e e n tr a n sf
e r efl H
ci
e n cy a nd w
ork
erex
p
o su re. ^^ ^^C
a rl
to n a nd
Fl
yn n(
1
9 96
)
ha
ved
e v elo
p
ed
am
od
el
th
atp
r edi
cts th
ec o n c e ntr at
io
n of p
a rti
cle s
i
n aw
o rk
e r'sb
r eathi
ng
z o ne a s af
u nc ti
on of
th
e o v e r sp
r ay
g
e n e r ati
o n r ateH
ei
tb
ri
nk
et al
(
19 9 6)
h
a v e sh
ow n e xp
eri m
e ntal l y
th
at th
eh i gh
e r tr a n sf
ere
ffi
ci
e n ci
e s a ssocia
ted w i
th H
V L Pg
u n s c o r r e sp
ond
tol
ow
erw
o rk
e r exp
osu r e top
ai
ntm is
ts a sco
m p
a r ed
to th
e tr a nsfer effi
ci
e n ci
e s of
a con v enti
o n al
sp
r ay g
u nFr o
m
a n e n vi
ronm
e ntal p
e r sp
e cti
v e,h ig h
e r tr a n sf
e r effi
ci
e n ci
e s c a n r ed
u c e th
e am
o u nto
f p
ai
nt c o nsum
ed
a nd
th
e am
o u nt of
v ol
ati l
e o rg
a ni
c c om p
o u nd
s(
V O C
s)
em i
t ted fr
om
sp
r ay
p
ai
nt op
e r ati
o n s ^ '^F
or th
es e r e a s o n s,H V L P g
u n s c a nb
e u s ed
a s c o ntr ol
te ch
n ol
og
y.O
n es u c
h
c a s ei
si
n th
eS
tate of C
al if
o r ni
a,w h i
ch
r eq
ui
r e s th
atH V L P
sp
r ay g
u ns(
o r oth
e r sp
ray
e
q
uip m
ent c ap
abl
e of
ach i
e vi
ng
a6 5
%
transfer effi
ci
e n cy)
b
e u s ed i
n su rf
a c e c o ati
ng
ap p
li
c ati
o n s ^^' *^B e c a u s e o
f
th
ep
ote nti
al b
e n efi
ts of
a chi
e vi
ng hi g h
e r tr a nsfe r effi
cie
nci
e si
n sp
ray
p
ai
nting
ope r ati
o n s,m
eth
od
sf
o r qu a ntif
yi
ng tr a n sf
e r effi
ci
e n cym
ayb
ei m p
o rta nt to sp
r ay2
e x a
m i
n e th
ef
a cto r s th
at aff
e ct tr a n sf
e r effi
ci
e n cy a nd
tod
e v el
op
a th
eo reti
cal m
od
el
top
red i
ct tr a n sf
e r effi
ci
e n cyb
a s ed
o n th
ei
n e rti
al i m p
a cti
o n of p
a rti
cl
e s o nto aw
o rk p i
e c en
. TH
EO R
E T IC A
LC O N S
m
ER A
T IO N
T
h
e ap pl i
c ati
o n of
pai
ntfr
om
a sp
r ayg
u n to a s u rf
a c e c a nb
em
od
el
ed
a s a ni m p
a cti
o np
ro c e s s. Ini
ti
al l
y, a spr ay g
u n a tom i
z e sl i q
ui d i
ntod
r op l
ets,w hi
ch
a r e th
e n transp
orted
to aw
o rk p i
e c e vi
am
om
entum
of
th
e ai
rj
etP
ai
ntd
rop l
etsw i
th
suffi
ci
enti
nerti
ai m p
act up
o n and
c o at th
ew
ork p i
e c e,w h i l
ep
arti
cl
e sw i
th l
es si
n e rti
af
ol l
ow
th
ea
i
r str e am
a nd b
e c om
ep
art of
th
e o v e r sp
r ay Fr om
th i
s si m p l i fi
ed
o v e r vi
ew
of
th
e c o ati
ng
p
r o c e s s, am
od
el w
a sd
e v el
op
ed
top
r ed i
ct th
e tr a n sf
e r effi
ci
e n cy
of
th
eH V
L P sp
r ay g
u n Th
e v a ri
o u s step
s of
th
ei m p
a cti
o nm
od
el
-ato
m i
z ati
o n, tr a n sp
o rt vi
am
om
e ntum
,i m p
a cti
o n, a nd
o v e r sp
r ay
- a r ed i
s c u s s ed i
nd
etail i
n thi
s s e cti
o n.
2
. 1A
tom
iza tio nT h
ep
e rf
o rm
a n c e of
a n atom i
z e r, s u ch
a s th
eH V L P
sp
r ayg
u n,d
ep
e nd
s oni
ts si
z e,t
h
eg
eom
etry
of
th
e n o z zl
e, th
ep h
ysi
c al p
rop
e rti
e s of
th
el i q
ui d b
ei
ng
atom i
z ed
, a nd
th
em
ed i
um
e n v el
op i
ng
th
e atom i
z ed l i q
ui d
^ '^B
e c au s e of
th
el
ow p
re s su re s as s o ci
ated w i
th
aH V L P
sp
r ay g
u n,i
tsg
e om
etry m
ay
b
em
o r e c ri
ti
c al i
n atom i
zati
on th
an th
at of
a c on venti
onal
sp
r ay g
u n ^ '' *^
F i g
u re1
sh
ow
s as c
h
em
ati
c of
th
eH V
L P sp
r ay g
u n noz zl
eA
s s e e ni
n th
efi g
u r e, ai
ri
sd i
sch
a rg
ed
th
r o ug h
an an n ul
u s s u r r o u nd i
ng
th
el i q
ui d
noz zl
e.A
tom i
zati
o n of l i q
ui d fr
om
th
eH V L P
sp
ray g
u noc c u r s a s t
h
e str e am
of l i q
ui d i
sd i
s ch
a rged i
nto th
e s u r r o u nd i
ng
c ol
um
n of
r el
ati
v el
yf
a stm
o vi
ng
ai
r.B
e c a u s e tw
ofl
ui d
s a r ei
n v ol
v ed
, t
h i
s ty p
e of
atom i
z ati
o ni
s te rm
ed
tw i
n -fl
ui d
ato
m i
z ati
o nT h
eH V L
Pg
u ni
s r ef
e r r ed
to a s a n e xte r n al
-m i
xi
ng
atom i
z e r,m
e a ni
ng
th
at th
eh i g h
v el
o ci
ty ai
r stre am i m p i
ng
e s on th
el iq
ui d
outsi d
e th
el i q
ui d d i
s ch
a rg
e noz zl
e ^'^
l i q
ui d i
nto sm
al l
e rd
r op l
ets.V i
s c o si
t y af f
e ctsb
oth
th
ed
r op
si
z ed i
stri b
utio
n and
th
efl
ow
rate of l i q
ui d
.A
ni
n c r eas ei
n vi
s c o si
ty w i l l d
e c re ase th
eR
ey
n ol d
s n um b
e r(
R
e)
a nd
p
r e v e nti
ns tab i li
ti
e si
n th
el i q
ui d
j
etD i
si
nteg
r atio
n of
thel i
qui d
o c c u r sw h
e n a e r od
yn am i
cf
orc es ex ce ed
th
e s e c o n s ol i da
ti
ng f
o r c e s. ^^^T h
ep
a rti
cl
e si
z ed i
stri b
uti
o n of l i q
ui d d
r opl
ets atom i
z ed b y
th
eH V
L P spr ay gu nd
efi
n e s th
efi
"a ctio n of pa rticle s that
w
i ll impa ct aw
o rk p ie c e S in c e the atom
iz atio np
r o c e s si
s com p l
e x,p
r ed i
cti
o n of p
a rti
cl
e si
z ed i
s tri b
uti
o n s r e s ul
tsp
ri m
a ri l
yfi
-o
m
em p i
ric a
l
c o r r e
l
atio n s. ^'^O
n e s u c
h
c o r r el
ati
o n,d
e v el
op
ed b
yK i m
a nd
M
a r sh
all
(
1 9 7 1)
,w
a s u s ed
h
ere top
r ed ic
t th
em
a s sm
ed
i
and ia
m
eter(M
M
D
)
of
th
ep
a rti
cl
e si
z ed i
stri b
utio
n .T h
ef
ol l
ow i
ng
eq
u ati
o np
r es e nts th
eK i m
a nd
M
a r sh
all
c or rela
tio
n^ '^:
MM
D
=2 4 9
0 4 1 „ 0 3 2
a
H
i(
t T ^ ^V
"
J 0 3 6 ^ (
W
r elP
a)
A
apP
i0 3 6 „ 0 16
+
1 2 6 (
> " /■\ 0 17
.
A
^
J
1
rO 5 4 '-'
r el
y
f "l
J
(
1)
T h
eK i m
a nd
M
a r sh
al l m
od
el
c or r el
ate s th
eM
M
Df
r om
a sp
r ayg
u n top hy
si
c al p
r op
e rti
e so
f
th
el i q
ui d
a nd
ai
r, th
e r el
ati
v e v el
o ci
t yb
etw
e e n th
e tw
ofl
ui d
str e am
s, th
e a r e a of
th
e ai
rn oz z
l
e, and
th
e rati
o of
th
em
as s of
ai
r tom
a s s of l i q
ui d
sp
r ayed
^ '^A
s s e e ni
nF i g
u r e1
, th
eH V L P
sp
r ay g
u n c and i
s ch
a rg
e ai
rf
rom b
oth i
tsh
or ns a nd
i
ts c ap
.H
ow
ever, onl y
th
e ai
rfl
ow fi
-o
m
the a
n n ul
a r noz zle
i
n th
e c ap w
a s as s um
ed
toato
m i
z e th
el i q
ui d
Fl
ow fi
-o
m
th
eh
o r n sw
as as s um
ed
t od
eterm i
n e th
e sp
r ayp
at ter n.A p p ly i
ng
th
eK i m
a nd
M
a r sh
al l
c o r r el
atio
n top
r ed i
ct th
ep
a rti
cl
e si
zed i
stri b
utio
n req
ui
r ed
t
h
at ad i
sti
n cti
o nb
em
ad
eb
etw
een th
e tw
o ai
rfl
ow
sT h
u s, o nl y
th
ep
a r am
etersa s so c
ia
ted w i
th
ai
rfl
ow fi
-o
m
th
e c ap w
e re u s ed i
nE q
uatio
n 1S i
nce ad i
r ec tm
e a s u r em
e nt of
th
e ai
rfl
ow f
r om
th
e c ap w
a sd if fi
c ult
, th
em
a s sfl
ow
r ate of
air thr o u gh
the c ap w
a s e stim
ated fi
-o m t
h
e v elo ci
tyi
n th
e c ap
A
s s um i
ng
th
att
h
efl
ow fi
-o
m
th
e noz zl
ei
sfi i
cti
o nl
e s s and
s ub
s o ni
c, th
ef
ol l
ow i
ng
eq
u ati
o n c a nb
e u s ed
toc a
l
c ul
ate th
e v el
o cit
y^ *^u =
2
r
g
cP
o{
r
- i)
P
o1
-/ N(i
-i / r )
—
\P
oJ
0 5
(
2
)
T
h
e r e s e r v oir
d
e n si
ty of
ai
r(
po)
i
n th
e ab
o v e equ atio n
w
a s c al
c ul
ated fr
om
th
ep
ow
e rl
aw
re
la
ti
on sh i p
sfo r
c om p
r e s sib l
efl
ow
thr
oug h
a noz zl
e/
^^A i
r vel
o ci
t yf
o rb
oth
th
e c ap
a nd
th
eh
o r n sw
a s c al
c ul
ated fr
om E q
u atio n
2f
o r th
eran
g
e of
exp
eri m
e ntal p
r e ssu r es.M
a s sfl
ow
r atesw
e r e th
e n e s ti m
at ed b
a s ed
o n th
e s ev e
lo
cit
i
es, th
e air
d i
s ch
arg
e ar e as of
the c ap
a nd h
o r n s, a nd
th
ed
en si
t y of
air
w h
e nd i
s ch
a rg
ed
.T h
e res uh i
ng m
as sfl
ow
r ate of
air
w
as sh
ow
n t ob
ed i
vi d
ed
eq
u al l
yb
etw
ee nt
h
e c ap
a nd
th
eh
o r n s Thu s
, the
m
a s sfl
ow
r ate te rm
(
m
,)
a s u s ed i
n E qu ati
o n 1w
a sest
i m
ated
a sh
al f
th
e total
ma s s of
air
f
rom
th
eH
V L
P sp
r ay g
u n.2. 2
M
om
e ntum
A i
rfl
ow fr
om
th
eH V L P
sp
r ayg
u nw
asm
od
el
ed
a s an eq
uiv
al
entm
om
entum
ai
rfl
ow
d is c
ha r
g
ed fr
om
a cir c u
la r
o ri fi
c eA
s the ai
rj
etin c r e a s e s
i
nd i
sta n c efr
om i
tsd i
s ch
arg
e o ri fi
ce, th
em
a ss of
air
i
n th
ej
etin c r e a s e s
a nd
th
e ai
r v el
oci
ty d
e c r e a se sC
on seq
u entl y
, th
em
om
entum
of
th
e ai
rj
et r emai
ns co n sta ntU
si
ng
th i
sp
ri
nci p l
e of
c o n sta nt
m
om
e ntum
a nd i g
norin
g
th
ep
res e n c e of p
a rti
cle s
in
th
e ai
r str e am
, th
e v olu
m
etri
cfl
ow
rate of
ai
r c a nb
ep
r ed i
cted
at a s om
ed i
sta n c e,X
,d
ow
n str e am f
r om
th
ej
et.T he
v o
lu
m
etri
cfl
ov i o-ate o
f
aj
et atp
oin
tX
is
g i
ven a s the
f
ol l
ow in
g
^^ *'^
a
,, = 0 4 0 4-
X
-y
f
K
=0 4 0
4 •X
- .I
^ " ^ "
(
3
)
S i
n c e th
em
om
e ntum
of
th
eH V
L P sp
r ayg
u nd
ep
end
s o n air
fl
ow f
r om
th
eh
o r n s a nd
th
ec a
p
, th
e total m
a s sfl
ow
r ate of
ai
rf
r om
th
eH V L P
sp
ray g
u nw
a s u s ed i
nE q
uati
on3
.S i
nc e th
e cir
cul
arj
etd
oe s not exi
sti
n real i
ty
,i
ti
s rep
r e sented b y
th
ehy p
oth
eti
cal
j
et sh
ow
nin
Fig
u r e 2. Th
elo c a
tio n
of
theh yp
oth
etic a
l
j
etw it
h
r e s5
(
ref
er r ed
to a sd i
stan c eY i
n Fi g
u r e 2)
w
a sd
ete rm i
n ed fr
om b
a si
c trig
o n om
etry
,
g i
v e n th
es
p
r ay p
at ter n of p
a rti
cl
e s on th
ew
o rk p i
e c e a nd
th
e sp
r ay
ang l
efr
om
th
eh
yp
oth
eti
c al
j
et.S
pr ay a ng l
e sfr
om
ci
r c ul
a rj
ets a r e r epo rted i
nl i
te r atu r e, a nd
a v al
u e of
2 9 °w
a s u s ed
h
e r e/
" ^ Th
e a ctu al
sp
r ay p
at te r nf
o rm
ed by
th
eH
V L Pg
u nw
a s el l i p
ti
c al
a nd d if f
e r ed
fr
om
th
e ci
r c ul
a rp
atte r n th
atw
o ul d b
ef
o rm
ed b y
th
ehy p
oth
eti
c al
j
et. T o c om p
e n s atef
o rth is
d
if fe r e n c e, the spr ay pat te r n
fr
om
theH
V L P gu nw
a sm
od
eled
a si
fi
tw
e r e a cir cleh
a vi
ng
an eq
ui
v al
e nt a r e a a s th
e el l i p
s e.T h
e r ad i
u s of
th
em
od
el
ed
ci
rcl
ew
as u s ed
, al
o ng
w i
th
th
e sp
r ay a ng l
e, to c al
c ul
ate th
el
o c ati
on o
f
th
ehy p
oth
eti
cal
j
et2
.3
I mp
a ct io nW
h
e n a n ob
j
e cti
sp l
a c ed i
n th
ep
ath
of
a n ai
r str e am
th
e r eb
y c a u si
ng
th
e str e am
toc
h
a ng
ed i
r e cti
o n s, a ny p
arti
cl
e sw i
th
suff
i ci
enti
n e rti
aw i l l f
oll
ow
th
ei
r ori g i
n al p
ath
and
i m
pact up
o n th
e ob
j
e ct. Pa rti
cl
e sw i
th l
e s si
n e rti
aw i l l f
ol l
ow
th
e ai
rpat
h
.F
o r a ni d
e al
i m
pacto r, a parti
cl
e si
ze exi
sts th
at repre s ents th
e poi
ntw h
e r eh
al f
of
th
ep
a rti
cl
e si m p
a cta n
d h
al f p
a s s al
o ng w i
th
th
e ai
r str e am
Thi
sp
a rti
cl
e si
zei
s ref
er r ed
to a s th
e cut si
ze ord
so of
a nim p
a ct or and
ca nb
e c al
cul
a t ed fr
om
th
ef
ol l
ow i
ng
eq
u ati
o n^ ^ ^^:
^
5 0 =9
ju.D
„^.u(
S T
K
, ,)
P
p ' - ' n o z zle ^ c0 5
(
4)
U
si
ng E q
u ati
on4
to c al
cul
ate th
ed
s of
or th
eH
V L P
sp
ray g
u n r eq
ui
red
th
at a s sum p
ti
o n sb
em
ad
e reg
a rd i
ng
th
ep
arti
cl
e si
zed i
stri b
uti
on and
th
e ai
rf l
ow
.T h
eC
u n ni
ng h
am
c o r r e ct
i
o nf
a cto ri
nE q
u ati
o n4 w
a s a s s um
ed
to eq
u al 1
.T h
e ai
rf l
ow w
as a s s um
ed
tob
ei
n th
eS
tok
e s r eg i m
e(
i
e , 5 0 0 < Re < 3 0 0 0)
W
i
th
thi
s a s s um p
ti
o n, th
e th
e o r eti
c al l
yd
eri
ved S
tok
e s n um b
er c or r e sp
o nd i
ng
to 5 0%
col l
e cti
on ef fi
ci
e n cy
(
i
eS
TK
50)
c oul d b
e6 T
h
ei m p
a cti
o n of p
a rti
cl
e s o nto th
ew
o rk p i
e c e c a nb
em
od
el
ed
a si f
th
e ai
r str e am
fr
om
th
eH V
L P sp
r ay g
u nw
a sd i
s ch
a rg
ed f
r om
a ni m p
a cto r n o z zl
e.Si
n c e th i
si m p
a cto rn o z z
l
ed
o e s n ot e xi
sti
n r e al i
ty,i
ti
s r epr e s e nted b
y ah
y poth
eti
c al
n o z zl
e, a s sh
ow
ni
nF
i g
u re2
.T h
ed i
sta ncefr
om
th
eh
yp
oth
eti
c al
j
et to th
eh
yp
oth
eti
c al
noz zl
e(
ref
e r r ed
to a sdi
stanc e xi
nF i g
u re2
)
w
a sb
a s ed
o n th
ed i
am
eter of
th
eh
yp
oth
eti
c al
n o z zl
e.T h
ed
iam
ete r a nd
thed
ista n c efr
om
the h y pothetic al n o z zl
e to th
ew
o rk
p ie c e(
Y
-x)
w
e r e s ete
q
u al
, a nd
th
el
eng
th
sw
e r ed
ete rm i
n ed fr
om i
terati
ve c al
cul
ati
o n sO
n c e th
ed i
stanc efr
om
th
eh
yp
oth
eti
c al
j
et to th
eh
yp
oth
eti
c al
noz zl
ei
sk
now
n,t
h
en th
e vel
oci
ty
of
th
e ai
r stre am
at th
eh y p
oth
eti
c al
noz zl
e ca nb
e c al
c ul
ated fr
om
th
ev o
l
um
etri
cf l
ow
r ate gi
v e ni
n Eq
u ati
o n 3 a nd
th
e a r e a of
th
eh
yp
oth
eti
c al
n o z zl
e. Th
e c uts
i
z e of
th
e pa rti
cl
e si m
pa cti
ng th
ew
o rk
pi
e c e a r e c al
c ul
ated fr
om E
qu ati
o n 4, gi
v e n th
ec a
l
c ul
ated
v el
o ci
t y2
.4
O
v e r sp
r ay
K i m
a nd
M
a r sh
al l
(
19 7 1
)
d
ete rm i
n ed
th
at th
e c um
ul
ati
v e v ol
um
efr
eq
u e n cy of
th
ep
a rti
cl
e si
z ed i
stri b
uti
o nfr
om
a tw i
n-fl
ui d
sp
r ayg
u nw
a sl
og
n o rm
al l
yd i
stri b
uted
a nd
c o u
l d b
ed
e s c rib
ed b
y th
ef
ol l
ow i
ng l
ogi
sti
c eq
u ati
o n^'^
:
1.
1
5O
, =7 7\ - 0 1
5
(
5
)
1
+6 6 7
exp
(
-2 18
x]
A
ss um i
ng
th
at th
ed
en si
ty
of p
a rti
cl
e si
s c on sta nt,E q
uati
on5
al
so rep
re s ents th
ec u
m
ul
ati
v em
a s sfr
eq
uen cy .T h
e X term i
n th
e ab
ov e eq
uati
oni
s th
e r ed
uc ed d i
am
ete r,w h i
ch i
sd
efi
ned
a s th
er at
i
o of
th
ep
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cl
ed i
am
eter to th
em
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ed i
and i
am
eter of
th
e si
zed i
stri b
uti
o nW
h
ent
h
ed
j oi
s u s ed i
n th
e r ed
u c ed d i
am
ete r, th
e nO
^ r e
p
r e s e nts th
efr
a cti
o n of p
arti
cl
es sm
al l
er7
overs
p
r ayfr
a cti
o n.T
r a n sf
er ef fi
ci
e n cy, o r th
efr
a cti
o n of
p
a rtic
le s
i m p
a cti
ng
th
ew
o rk
pi
e ce,i
s si m p l
y 1-
O
^
m
.M
E
TH O D O
LO G Y
3. 1 L a
b
o r a to ryS
etUp
A l
ab
o r atorym
od
el
of
a sp
r ayp
ain
ti
ng
op
e ratio n
w
a s u s ed
tod
ete rm i
n e th
e tr a n sf
e re
fl S
ci
ency
of
th
eH V L P
sp
rayg
u n.T h
em
od
el
c o n si
sted
of
am
a nneq
uin
sp
rayi
ng
va cu um
p
um p
oil w i
th
th
eH V
L P sp
ray g
u n Th
em
an neq
ui
nw
as autom
ated
s o th
ati
ts arm
c oul d b
esta t
i
onary
ori
nm
oti
o nw hi le
i
t sp
r ayed
Sp
r ayi
ng
o ccu r r ed i
n aw in
d
tu n n el
th
at r ep
resented
ap
ai
nt sp
r ay b
o oth
Th
ew i
nd
tu n n el w
a s 5-f
e et-by
-5
-f
eetw i
th
a r e s ul
tin
g
cros s-s e cti
o n al
ar e a of
2 5
sq
u a ref
e et.T h
ed
ep
th
of
th
ew i
nd
tu n nel w
as 8f
e et Fl
a r ed
entranc efl
ang
e s and
ap
eg b
o a rd
o n the
r e a rw
al l
of
the
w i
nd
tu n n el
c reated
a u nif
o rm
v el
o ci
typ
r ofi le
.A b
a nk
of
d is
po s ab le
p
a rtic
le
fi l
te r sm
o u nted
o n th
e r e a r pegb
o a rd h
el
ped
to e stabl is
h
a n u ni f
o rm
ai
rve
l
o ci
ty p
r ofi l
ein
th
ew in
d
tu n n el
,w h i le
p
rovi d i
ng
am
e ch
ani
sm fo r
cl
ea ni
ng
th
e exh
austed
air
.T h
eg
u n u s ed i
n th
e sp
r ayp
ai
ntin
g
op
erati
onsw
a s aD
eV i l bi
s sM
SV
-5 3 3-4-F F m
od
el
H
V
L P sp
r ay g
u nfi
tted w i
th
a#
3 3A
mr c ap
.T his
p
n e um
atic
, e xte r n al
-m ix
i
ng
sp
rayg
u no
p
e r ated
atp
re s su re sfr
om
0 1 to1
0p
sig
, a sm
e a s u red
at th
e noz zl
e c ap
.A
tw
o-sta
g
ec o
m p
re ssorp
um p p
r o vi de
d p
r es su riz e
d
air
f
o r th
e sp
ray g
u nT h
ep
re s su riz e
d
ai
rw
a sf
ed
to ag
alv
ani
zed
ste el p
ot,w he r
e the
l iq
ui d
tob
e sp
r ayed w
a sp
r e s s u riz e
d
to 1 0p
si
g.A i
rp
res su r e sin
th
ep
ot r a ng
ed fr
om 16
to5 3 p
si g
,d
ep
e nd in
g
o n th
e r eq
ui
r ed
c ap p
res s u r eT h
e air
p
r es s u r ew
a s redu
c ed
to th
e r eq
ui
red
c ap p
re ss u r ew i
thi
n th
eg
u nF ig
u r e 3 sh
ow
s a s ch
em
atic
of
th
ep
r e s s u riz e
d p
otT h
eH
V L
Pg
u n al lo
w
sfo r
fa n
p
at te r n tob
e v a rie
d by
ad
j
u stin
g
th
e am
o u nt of
air
e
m i
t ted f
o r th
eg
un 's
h
or ns.F
o r thi
sw
ork
, a r eal i
sti
cf
a np
at ter nw
a s s el
e cted
a nd
r em
ain
ed
c on sta nt
f
o r th
ed
u r ati
o n of
the
e xp
erim
e ntT h
e r e s ul
ti
ngf
a np
a t te r nw
a s a2
:1 el li p
s e,8
V
a c u um p
um p
oil w
a s u s ed
to si m
ul
ate th
ep
ai
nt,w hi
ch
c o ul d
n otb
e u s ed i
n thi
sex
p
e rim
entd
ue to th
e expl
o si
onp
ote nti
al
a s s o ci
ated w it
h
th
ep
mnt sol
vents.I
nste ad
, v a c u u
m
p
um p
oil w
a s s el
ected b
e c a u s ei
ti
s n o n v ol
atil
e,i
n e xp
e n si
ve, a nd h
a sph
ysi
c al p
r op
e rti
e s sim i l
a rto
p
ai
nt.T h
eli q
ui d
vi
sc o sit
y
of
the v acu um p
um p
oil w
a sd
ep
e nd
ent o n tem p
e r atu r e a nd
r a nge
d fr
om
ar o u nd
64 to6 8
ce ntip
oi
s e th
r o ugh
o ut th
e e xp
e rim
e ntT h
e s u rf
a c e te n si
o n of
th
eo
il w
a s no t a v ai l
ab l
efr
om
th
em
a n uf
a ctu r e rb
utw
a s e sti m
ated
a s 4 0 7d
yn e s/cm
.T
h
em
a n neq
ui
n u s ed i
n the e xp
erim
ent sto od 5 1 i
n ch
e sh i gh
and m
e a su red 14 i
n ch
e sa c ro s s the c
h
e stT h
em
ann eq
ui
nw
a s n ot a nth
r op
om
etri
cb
utw
a s tr u ncated
at th
e th ig h
s tofi
ti
n th
ew i
nd
tu n nel
.A
s sh
ow
ni
nF i g
u r e 4,
m
a n n eq
ui
n o ri
entati
o ni
n th
ew i
nd
tu n n el w
a se
i
th
e rp
a r al l
el
(
1 80
°)
orp
erp
e ndi
cul
a r(
9 0°)
w i
th th
e ai
rfl
ow i
n th
ew i
nd
tu n nel
.I
nb
oth
or
i
e ntati
o n s, them
a n n eq
ui
nw
a sp l
a c ed
at ad
ep
th
of
48 i
n ch
e si
n thew i
nd
tu n n el
.I
n th
e18 0
°
p
o sit
i
o n, the4 8 i
n ch
e sw
asm
e a s u r ed fr
om
th
em
a n n eq
ui
n'
s
b
a ck
to th
efr
o nt of
thew i
nd
tu n n e
l
In th
e 9 0 °p
o sit
i
o n, th
e 4 8i
n ch
e sw
a sm
e a s u r ed fr
om
th
e c e nte r of
th
em
a n n equi
n' s
l
eg
to t
h
efr
o nt of
th
ew i
nd
tu n n el
T
h
eH
VL P
sp
ray g
u nw
a sp l
a c ed i
n th
em
a n n eq
ui
n 's r
i g h
t(
d
ow
n str e am
)
h
a nd
, eig h
ti
n ch
e sfr
om
afl
atpl
ate.T h
efl
atpl
ate c r e ated
a u ni f
o rm
ai
rj
et r eb
ou nd
and f
o rm
ed
are
p
rod
u cib l
e o v e rsp
r ay g
e n e r ati
on r at eW
h
e n th
em
a n n eq
ui
nw
as stati
o n a ry
, th
e sp
r ay p
at te r nw
a s cente red
o n afl
atp l
ate3 f
e eti
nh
ei g h
tb y 2 f
e eti
nw i d
th
.A l
a rg
e rp l
at ew
as req
ui
red
w h
en th
em
an neq
ui
nw
asi
nm
otionb
e c aus e, as them
ann eq
ui
nm
oved
th
e sp
r ay
g
unh
o ri
z o ntall
y a c ro s s th
epl
a te, th
ep
ath
of
th
em
a n n eq
ui
n 's a r
m
e x c e ed
ed
th
ew i d
th
of
th
es
m
al l
erp l
ateA 3
-by
-3-f
ootfl
atp l
atew
a s u s ed
to a s s e ssm
oti
o n.