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h
efi
r stf
acto r to co n si d
e ri
sw h
eth
e rM
cK
e r n a n a nd D
u n n ap p l i
ed
th
el
aw
s of
s
i m i l
a ri
ty to s c al
e th
ei
r e xpe ri m
e ntsf
r om C
a rl
to n's e xpe ri m
e ntO
n e of
th
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te ri
a of
s
i m i l
a ri
ty
, sp
e ci f
i c al l y g
eom
etri
c si m i l
a ri
ty, r eq
ui
r e s al l b
od
yd i m
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o n si
n al l
th
reec o o r
d i
n ate s toh
a v e th
e s am
el i
n e a r-s c a
l
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ob
etw
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em
od
el
a nd p
r ototyp
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s o, a
l l
a n
g l
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etw
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em
od
el
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th
resp
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a rlt
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od
el i
n th
eB
ai
tyB
ui l d i
ng
w i
nd
tu n n el
u si
ng
a ch i l d m
a n n eq
ui
nM
cKe r n a n a nd D
u n n t ested
th
eH V L P
spr ayp
ai
ntg
u ni
n th
e sam
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nd
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n th
el
a rg
e rR
o s e n a u Bui l d i
ng p
ai
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o oth
u si
ng
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d
, ad
ult
m
an n eq
ui
nF
o r exam p l
e, th
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o of m
a n n eq
ui
n a r e a(
h
ei g h
t xb
r e ad
th
)
tot
h
ew i
nd
tu n n el
a r e aw
a s v e ryd i f f
e r e ntf
o rM
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toC
arl
ton 's
w
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T h
er ef
or e,b
et ter c o
m p
ari
s ons c anb
em
ad
eb
etw
een exp
e ri m
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enT he s e c o nd fa ctor to c o nsi
d
er is the de si gn d i f fe r en c e betw
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o spr ay paintg
u nsA
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ai
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ai
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ow
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ep
ai
nt and
o
p
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um
ai
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)
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c o n v e nt
i
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sp
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ai
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pr e s s u r e to atom i
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ep
ai
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op
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pr e s s u r e o
f
5 0 to 6 0 psi
g Th
e r e s ul
ta nt e xi
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o ci
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cf
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sp
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s oni
cf
o r th
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PC
arlt
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se x
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e Th
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L P Th
ej
et e xi
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o ci
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s a ni m
po rt antc r
it
eri
a si
n c eK i m
^' "^d
ete rm i
n ed
th
at th
em
om
entum f
r om
a n o z zl
e,w h i
ch i
s th
em
as sf l
ow
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e si
ts v el
o ci
ty, af f
e cts th
e r e v e r s ef l
ow
r egi
o nd
ow
nw i
nd
of
th
em
a n n eq
ui
ni
n af
r eestr e am
, and
th
u s th
e c o n c e ntr ati
o n of
c o ntam i
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n th
eb
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ng
z o n eK i m d
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op
ed
t
h
em
om
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ch i
s th
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om
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e sp
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om
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'
s
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, th
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om
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ota
k
e si
nto ac cou nt th
ed i f f
e rent e xit
v el
o ci
ti
e s of
th
e spr ayp
ai
ntg
u n s a nd
c o ul d b
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t op
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ct th
e e xp
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aw
ork
e r.I f
th
eC
a rl
to n n u mb
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s r epl
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th
th
em
om
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u xto
p
r ed i
ct exp
o s u re, th i
s n ew m
od
el
a ss um
e s th
at th
el i q
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r op
ertie sh
a v el i
t tl
ei
nf l
u e n ceo n co nta
m i
n a nt tr a n sp
o rt to th
eb
reath i
ng
z o n eC
pnye r si
on of
th
ed
ataf
r om C
a rlt
on,
M
cK
e r n a n^ a n
d D
u n ni
nto th
em
om
e ntum f l
u x r ati
og i
v e s ap
r el i m i
n a ryi
nd i
c ati
o n as am
o r ec o n s
i
ste ntp
r ed i
cto r of
e x posu r e th
an th
eC
a rl
t on n um b
e r1
.2 Proj
ectO b
j
e cti
v e sT
h i
sp
r oj
e ct te sts th
eh
yp
oth
e si
s th
at th
em
om
e ntum f l
u x r ati
om
ay pr ed i
ct th
ea n
d H
V L P sp
r ay pai
ntg
u n sA
n a nth
r op
om
etri
cm
a n n eq
ui
n a nd
a n em
p ha si
s o n ge om
etri
cs
i m i l
a ri
tyw
e r e u s ed d
u ri
ng
th
e e xp
e ri m
e ntal
r u n si
n th
e 9 0° a nd
1 8 0° o ri
e ntati
o n sn
.T H
EO R Y
D EV
E LO
PM
E N T2.1 Ex
po s u r e
M
od
el De v elop m
e n tC
arl
to n^ '*^
d
e v e
l
op
ed
a n em p
eri
cal
-c o n -ce
p
tu al
mod
el
top
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ct th
eb
r eath i
ng
zon econ c e ntr at
i
o n of
pai
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stsd
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ng sp
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ai
nti
ng
ta sk
sH
ei
ntr od
u c ed
th
ef
ol l
ow i
ng th
r e es equ e nt
i
al p
r o c e s s e s c om m
o n to al l
spr ayi
ng ta sk
s a nd
r el
ated
to e x po s u r e s :(
1)
d
r opl
etf
o rm
ati
on,
(
2
)
d
rop l
et tr ansf
e r, a nd
(
3
)
d
r op l
et tr a n sp
o rt/
e v ap
o r ati
o nI
n a sp
r ayp
ai
ntg
u n, th
e ai
r str e am d i
s ch
a rg
ed
th
r o u gh
th
e a n n ul
u s s u r r o u nd i
ng th
el i q
ui d
str e am
c a u s e sd
r op l
etf
o rm
ati
o nb
y e x e rti
ng sh
earf
o r c e s o n th
el i
qui d
Th
e tw
ostr e a
m
sm i
x aw
ay f
r om
th
e n o z zl
ei
n ap
roc e s s c al l
ed
tw i
n-f l
ui d
atom i
z ati
o n ^' '^
A d d i
ti
o n al
a
i
r th
r o ug h
th
e tw
oh
o r n s at ta ch
ed
to th
e c ap
r egul
ate s th
ed
e si
r ed
spr ay pat te r n Th
ere su
l
ti
ng m i
st c a n c o ntai
n pa rti
cl
e sl
e s s th
a n 5 0 ^m i
nm
a s sm
ed i
a nd i
am
ete r(M
M
D)
th
atc an
b
e easi l
yi
nh
al
ed
^ ^ *^C
a rl
to nd
ete rm i
n ed
th
at n o z zl
ep
r e s s u r e(
p
n)
,l i q
ui d p
ai
ntv
i
sco si
ty
(
m)
, a nd
th
e r ati
o of
ai
r tol i q
ui d m
a s sf l
ow
r ate s(
m
j
m
\)
a r e sal i
e ntp
a r am
eter s of
d
r opl
etf
orm
ati
on . ^'*^
D
r op l
et tr a nsf
e r o c cu r s aft
e r th
ed
r op l
eti
sf
o rm
ed
at th
e n o z zl
eT h
e ai
rj
ets of
th
es
p
r ay p
ai
ntg
u ni m p
a rt am
om
e ntum
to th
ed
r op l
ets Th
ed
r op l
ets a r e ei
th
e r tr a n sf
e r red
tot
h
e ob
j
e ctb
ei
ng p
ai
nted
o r th
eyb
ec om
e th
e o v e r sp
r ay ob
s e r v ed d
u ri
ng
sp
r ayp
ai
nti
ng
.D
r op l
etsw i
th
s uf fi
ci
e nt si
z e a nd m
om
e ntum w i l l i m p
a ct th
e ob
j
e ct; oth
e rwi
se, th
ed
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etsw i l l f
ol l
ow
th
e ai
r str eam
s c r eated b y
th
ep
ai
nti
ng
op
e rati
o nC
a rl
to nd
ete rm i
n ed
th
at n o z zl
ep
r e s su r e(
p
n)
a nd
o v e r sp
r ay(
m
o)
af f
e ctd
r op l
et tr a n sf
e r. ^"*D
r op let tr a n spo rt a nd
e v apo r atio n af fe cts the o v er spray from
the painting operatio nT r j i n s
p
o rtm
ayi
n v ol
v e c o ntr ol l i
ng
th
e o v e r sp
r ayw i
th
e xh
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ch i
sf
o u nd i
na
p
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n ed p
ai
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o oth
Ev apo r ati
o n of
sm
al l d
r op l
ets a nd
th
e s ol
v e nts u s ed i
n th
ep
ai
ntm
ay al
s o o c c u r. B oth p
r o c e s s e sm
ay c a u s e e x po s u r e to the em p l
oy e e Th
e o ri
e ntati
o no
f
th
ew
o rk
e r, a s s
h
ow
ni
n Fi
gu r e1
,m
ayi
n c r e a s e/ d
ecr e a s e th
ew
o rk
e r 's e x
p
o s u r eC
a rlt
o nu s e
d
th
efr
eestream
v el
o cit
y
(
U
)
,w
o rk
e r ori
e ntati
o n(
9 0° o r 1 8 0° to th
ei
n c om i
ng
fr
e e stream
)
,b
r e ath i
n
g
z o n e c o n c e ntr ati
o n(
C
)
, a nd
th
eh
ei
gh
t(
H
)
a nd b
r e adt
h
(
B)
of
th
ew
o rk
e rf
o rh i
s e xp
o s u r em
od
el
^ ''^
U
si
ngd i m
en si
o n al
a n al
ysi
s,
C
a rlt o
n
d
e v el
op
ed
th
ef
ol l
ow i
ng m
od
el
to r el
atee x
p
o s u r e a nd
th
e op
e r ati
o n of
a c o n v e ntio n al
spr ayg
u n :C H U D
= <
t
>m
„
—
-,^-^
—
, o n entati o n
m
, n,U
0 )
W
h
en th
ed i m
e n si
o nl
e s s c o n c e ntr ati
o n,C H U D / m
o,i
sp l
o t ted
a s af
u n cti
o n of
th
eC
a rlt
o nn u
m b
er,
p
nH /
|a iU
, th
ed i m
e n si
o nl
e s s c o n c e ntr ati
o n v a ri
ed
a s a c om p l
e xf
u n cti
o n of
th
ed i m
e n si
o nl
e s sl i q
ui d p
r operti
e si
nb
oth
th
e 9 0°o r 1 8 0°
w
o r
k
e r o ri
e ntati
o n to th
ef
r e e str e am2.2
E
xp
o s u r eM
od
el ing w i
thM
om
e n tum
F lu xA i
r e xi
ti
ng
th
e c o n v e nti
o n al
a nd H V L P
sp
r ay p
ai
ntg
u n sw i
th
s o ni
c a nd
sub
s oni
ce x
it
i
ng vel
o ci
ti
e s, r e spe cti
v el
y,i m
pa rtm
om
e ntum
to th
e
f
r e e str e am
v el
o ci
tyf
i el d L i
qui d
d
rop l
etsf
orm
ed f
rom atom i
zatio
nh
av ei
n si g
ni fi
c ant mom
e ntum
a s c om p
a r ed
to th
e ai
r;t
h
u s, s ub
s eq
u e ntd i
scu s si
o n of
mom
e ntum
r ef
e r s o nl
y to the ai
r mom
e ntum
T h
em
om
e ntumI
-9
0
°O R I E N T A T IO N
1 8 0
°O R
I
E N
T A
T
I
O N
F i g
u re1
:W
ork
e rO
ri
entati
o n to th
eF
re estr eam
^ '*R
e v e r s efl
ow
o c c u r sd
ow
n str e am f
r om
aw
o rk
e r a s thef
r e e str e am
lo o s e si
tsk
in eti
ce n e r
g
y to the
f
ric
tio n a
l fo r c e s o
f
th
ei m m
ed i
at eb
o u nd
a ryl
aye r of
th
ew
o rk
e r Th
e r e v e r s efl
ow i
s r el
ated
to the
e xp
o s u re of
aw
o rk
e r/
^ ^^T h
em
om
entum
of
the
r e v e r s efl
ow
c a u s ed b
yt
h
ew
o rk
eri
s r ef
e r r ed
to a s Fm.K i m
^^ °^d
ete rm i
n ed
th
at th
e r atio
of
th
em
om
e ntum fl
u x of
a n o z zl
e to th
e r e v e r s efl
ow m
om
e ntum i
s r el
ated
to th
e e xp
o s u r e of
th
ew
o rk
e rI
n c o rp
o r ating
th i
sk
n ow l
edg
ein
toe
q
ua tio n
(
1)
, th
ef
ol l
ow i
ng
r el
ati
o n sh i p i
sd
e v el
op
ed
:C H U D
,=
O
m
„—^
, o r
ie n
tati m
m(
2)
T h
eb
r eath i
ng
z o n e co n c e ntr atio n
is n o
w
af
u n ctio n
of
th
em
om
e ntum fl
u x r atio
T
h
em
om
e ntum fl
u x r a tio
c a nb
ew
ri
t t en a s :Z
g_ ^ PnA
nV
n^
+
(
Pn
'Pa
)
A
n .
3.
F, p.
H D U
^w h
e r e pis
th
ed
e n si
t y of
th
e gas at the n o z z
le
e xi
t(
n)
o r am b ie n
t(
a)
,A
„i
s th
e n o z zl
e a r ea of
t
h
e c ap and h
o r n,V
ni
s th
e ai
r e xi
t v el
o ci
t y at th
e n o z zle
, pi
s th
ep
res s u re at th
e n o z zle e x
i
tor a
m b i
ent,H i
sth
e
w
ork
erh
ei g h
t,D is
th
ew
ork
erd ia
m
ete r(
br e a
d
th
)
, a nd U i
s the
v el
oci
ty
o
f
th
ef
r e e str e am
Th
e n um
e ra to rin
Eq
u atio n
(
3)
i
s them
om
e ntum fl
u xf
r om
th
e sp
r ay pai
ntg
u n a nd
paH
DU
^is
th
em
om
e ntum fl
ow
th
r o ug h
th
ep
r oj
e cted
a r e a of
th
ew
o rk
e rT he
t erm
(
P
n -P
a)
A
n ad
j
u stsf
o rp
r e s s u r ed i f f
e r e n c eb
etw
e e n th
e c ap
a nd
am b i
e nt air
th
e c o n v e nti
o n al
T
h
e Fg/ F
m r ati
oi
s a ni
nd
ex th
at c ani
nf
orm
th
e re search
e rw h
eth
e r th
eg
u nm
om
e ntum
or th
e vorte x sh
ed d i
ng
ef f
e ctdo
m i
n ate s th
ef lo
w
r eg i m
e a r o u nd
th
e sp
rayp
ain
ter.B
y u n
d
er st and i
ng w h i
ch m
om
e ntum f l
u xd
om i
n atesd
u ri
ng
ap
ain
ti
ng p
r o c ess, anex
p
o s u r ep
r ed i
c ti
o n c a nb
em
ad
em
.M
ET H O
DO
LO
G
Y
3.1 E x
p
e ri m
e ntS
et -up
T h i
sp
r oj
ectf
ol l
ow
ed
th
e ob
j
e ctiv e s
of S
ecti
o n1
2 so th
atd
ata ob
tai
ned i
n th i
se x
p
e ri m
e nt c o ul d b
e c om p
a r ed
tod
ata ob
tain e
d b y C
a rl
tonT h
e r atio
of
th
e ad
ul
tm
a n n eq
ui
n' s 1 4i
n ch
ch
e std i
am
ete r to th
e ch i l d m
a n n eq
uin
's 8i
n ch
ch
e std ia
m
ete r(
u s ed i
nC
a rl
to n's e xp
e ri m
e nts)
i
s1
75
. Th
e r ef
o r e, t
h
e n ew p l
ate u s ed i
n t
h i
sp
r oj
ectis
42 i
nch
esw i d
e a nd
6 3i
n ch
e si
nh
ei g h
tC
a rl
to n u s ed
ap l
ate2
4i
n ch
e sb
y 3 6i
n ch
es Th
e ad
ul
tm
a n n equi
ni
s 7 3i
n ch
e si
nh
ei g h
t a nd
th
e chi l d m
a n n eq
ui
ni
s4
1in c
h
e si
nh
ei g h
tT h
e ad
ul
tm
an n eq
uin
w
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ai
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w i
th
th
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eV i l b is
sH V L P
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s e e F ig
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A)
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9,T
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s 7 5i
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ai
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s e e Fi
gu r eA
9,A
p pe nd i
xA
)
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xA
2)
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pp
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xA
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r a n sf
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h
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yw
a s ob
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o steps T heb
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PM
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b
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th
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ped
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tain
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e r ed
r ate Th
e o v e r sp
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(
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i
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etr a nsfe r e
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rate to th
el i
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r ateD
ataf
o rt
h
e r u ns a r ein
A p p
e nd ix
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in ati
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eth
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