low-pressure turbine separation control— comparison · pdf filehelp from dr. richard...
TRANSCRIPT
Vija
y K
. Gar
gU
nive
rsit
y of
Tol
edo,
Tol
edo,
Ohi
o
Low
-Pre
ssur
e Tu
rbin
e Se
para
tion
Con
trol
—C
ompa
riso
n W
ith
Exp
erim
enta
l Dat
a
NA
SA/
CR
—20
02-2
1168
9
July
200
2
GT
–200
2–30
229
The
NA
SA S
TI P
rogr
am O
ffic
e . .
. in
Pro
file
Sinc
e it
s fo
und
ing,
NA
SA h
as b
een
ded
icat
ed to
the
adva
ncem
ent o
f aer
onau
tics
and
spa
cesc
ienc
e. T
he N
ASA
Sci
enti
fic
and
Tec
hnic
alIn
form
atio
n (S
TI)
Pro
gram
Off
ice
play
s a
key
part
in h
elpi
ng N
ASA
mai
ntai
n th
is im
port
ant r
ole.
The
NA
SA S
TI P
rogr
am O
ffic
e is
ope
rate
d b
yL
angl
ey R
esea
rch
Cen
ter,
the
Lea
d C
ente
r fo
rN
ASA
’s s
cien
tifi
c an
d te
chni
cal i
nfor
mat
ion.
The
NA
SA S
TI P
rogr
am O
ffic
e pr
ovid
es a
cces
s to
the
NA
SA S
TI D
atab
ase,
the
larg
est c
olle
ctio
n of
aero
naut
ical
and
spa
ce s
cien
ce S
TI i
n th
e w
orld
.T
he P
rogr
am O
ffic
e is
als
o N
ASA
’s in
stit
utio
nal
mec
hani
sm fo
r d
isse
min
atin
g th
e re
sult
s of
its
rese
arch
and
dev
elop
men
t act
ivit
ies.
The
se r
esul
tsar
e pu
blis
hed
by
NA
SA in
the
NA
SA S
TI R
epor
tSe
ries
, whi
ch in
clud
es th
e fo
llow
ing
repo
rt ty
pes:
•T
EC
HN
ICA
L PU
BL
ICA
TIO
N. R
epor
ts o
fco
mpl
eted
res
earc
h or
a m
ajor
sig
nifi
cant
phas
e of
res
earc
h th
at p
rese
nt th
e re
sult
s of
NA
SA p
rogr
ams
and
incl
ude
exte
nsiv
e d
ata
or th
eore
tica
l ana
lysi
s. In
clud
es c
ompi
lati
ons
of s
igni
fica
nt s
cien
tifi
c an
d te
chni
cal d
ata
and
info
rmat
ion
dee
med
to b
e of
con
tinu
ing
refe
renc
e va
lue.
NA
SA’s
cou
nter
part
of p
eer-
revi
ewed
form
al p
rofe
ssio
nal p
aper
s bu
tha
s le
ss s
trin
gent
lim
itat
ions
on
man
uscr
ipt
leng
th a
nd e
xten
t of g
raph
ic p
rese
ntat
ions
.
•T
EC
HN
ICA
L M
EM
OR
AN
DU
M. S
cien
tifi
can
d te
chni
cal f
ind
ings
that
are
pre
limin
ary
orof
spe
cial
ized
inte
rest
, e.g
., qu
ick
rele
ase
repo
rts,
wor
king
pap
ers,
and
bib
liogr
aphi
esth
at c
onta
in m
inim
al a
nnot
atio
n. D
oes
not
cont
ain
exte
nsiv
e an
alys
is.
•C
ON
TR
AC
TOR
RE
POR
T. S
cien
tifi
c an
dte
chni
cal f
ind
ings
by
NA
SA-s
pons
ored
cont
ract
ors
and
gra
ntee
s.
•C
ON
FER
EN
CE
PU
BL
ICA
TIO
N. C
olle
cted
pape
rs fr
om s
cien
tifi
c an
d te
chni
cal
conf
eren
ces,
sym
posi
a, s
emin
ars,
or
othe
rm
eeti
ngs
spon
sore
d o
r co
spon
sore
d b
yN
ASA
.
•SP
EC
IAL
PUB
LIC
AT
ION
. Sci
enti
fic,
tech
nica
l, or
his
tori
cal i
nfor
mat
ion
from
NA
SA p
rogr
ams,
pro
ject
s, a
nd m
issi
ons,
ofte
n co
ncer
ned
wit
h su
bjec
ts h
avin
gsu
bsta
ntia
l pub
lic in
tere
st.
•T
EC
HN
ICA
L T
RA
NSL
AT
ION
. Eng
lish-
lang
uage
tran
slat
ions
of f
orei
gn s
cien
tifi
can
d te
chni
cal m
ater
ial p
erti
nent
to N
ASA
’sm
issi
on.
Spec
ializ
ed s
ervi
ces
that
com
plem
ent t
he S
TI
Prog
ram
Off
ice’
s d
iver
se o
ffer
ings
incl
ude
crea
ting
cus
tom
thes
auri
, bui
ldin
g cu
stom
ized
dat
a ba
ses,
org
aniz
ing
and
pub
lishi
ng r
esea
rch
resu
lts
. . .
even
pro
vid
ing
vid
eos.
For
mor
e in
form
atio
n ab
out t
he N
ASA
ST
IPr
ogra
m O
ffic
e, s
ee th
e fo
llow
ing:
•A
cces
s th
e N
ASA
ST
I Pro
gram
Hom
e Pa
geat
htt
p://
ww
w.s
ti.n
asa.
gov
•E
-mai
l you
r qu
esti
on v
ia th
e In
tern
et to
help
@st
i.nas
a.go
v
•Fa
x yo
ur q
uest
ion
to th
e N
ASA
Acc
ess
Hel
p D
esk
at 3
01–6
21–0
134
•Te
leph
one
the
NA
SA A
cces
s H
elp
Des
k at
301–
621–
0390
•W
rite
to:
N
ASA
Acc
ess
Hel
p D
esk
N
ASA
Cen
ter
for
Aer
oSpa
ce In
form
atio
n
712
1 St
and
ard
Dri
ve
Han
over
, MD
210
76
Vija
y K
. Gar
gU
nive
rsit
y of
Tol
edo,
Tol
edo,
Ohi
o
Low
-Pre
ssur
e Tu
rbin
e Se
para
tion
Con
trol
—C
ompa
riso
n W
ith
Exp
erim
enta
l Dat
a
NA
SA/
CR
—20
02-2
1168
9
July
200
2
Nat
iona
l Aer
onau
tics
and
Spac
e A
dm
inis
trat
ion
Gle
nn R
esea
rch
Cen
ter
Prep
ared
und
er C
ontr
act N
AS3
–001
80 a
nd C
oope
rati
ve A
gree
men
t NC
C3–
926
Prep
ared
for
the
Turb
o E
xpo
2002
cosp
onso
red
by
the
Am
eric
an S
ocie
ty o
f Mec
hani
cal E
ngin
eers
and
the
Inte
rnat
iona
l Gas
Tur
bine
Inst
itut
eA
mst
erd
am, T
he N
ethe
rlan
ds,
June
3–6
, 200
2
GT
–200
2–30
229
Ack
now
led
gmen
ts
The
aut
hor
wis
hes
to th
ank
Dr.
Ray
mon
d G
augl
er, C
hief
, Tur
bine
Bra
nch,
at t
he N
ASA
Gle
nn R
esea
rch
Cen
ter
for
his
supp
ort o
f thi
s w
ork.
Hel
p fr
om D
r. R
icha
rd R
ivir
of t
he A
ir F
orce
Res
earc
h L
abor
ator
y an
d M
ajor
Jeff
rey
Bon
sof
the
Air
For
ce In
stit
ute
of T
echn
olog
y re
gard
ing
the
expe
rim
enta
l dat
a is
als
o gr
atef
ully
ack
now
led
ged
.
Ava
ilabl
e fr
om
NA
SA C
ente
r fo
r A
eros
pace
Info
rmat
ion
7121
Sta
ndar
d D
rive
Han
over
, MD
210
76
Nat
iona
l Tec
hnic
al In
form
atio
n Se
rvic
e52
85 P
ort R
oyal
Roa
dSp
ring
fiel
d, V
A 2
2100
Thi
s re
port
con
tain
s pr
elim
inar
yfi
ndin
gs, s
ubje
ct to
rev
isio
n as
anal
ysis
pro
ceed
s.
Ava
ilabl
e el
ectr
onic
ally
at h
ttp:
//
gltr
s.gr
c.na
sa.g
ov/
GLT
RS
Trad
e na
mes
or
man
ufac
ture
rs’ n
ames
are
use
d in
this
rep
ort f
orid
enti
fica
tion
onl
y. T
his
usag
e d
oes
not c
onst
itut
e an
off
icia
len
dor
sem
ent,
eith
er e
xpre
ssed
or
impl
ied
, by
the
Nat
iona
lA
eron
auti
cs a
nd S
pace
Ad
min
istr
atio
n.
LO
W-P
RE
SS
UR
ET
UR
BIN
ES
EP
AR
AT
ION
CO
NT
RO
L-
CO
MP
AR
ISO
NW
ITH
EX
PE
RIM
EN
TA
LD
AT
A
AB
STR
AC
T
The
pres
ent
wor
kde
tails
aco
mpu
tatio
nals
tudy
,usi
ngth
eG
lenn
-H
Tco
de,
that
anal
yzes
the
use
ofvo
rtex
gene
rato
rje
ts(V
GJs
)to
cont
rol
sepa
ratio
non
alo
w-p
ress
ure
turb
ine
(LPT
)bl
ade
atlo
wR
eyno
lds
num
bers
.T
heco
mpu
tatio
nal
resu
ltsar
eal
soco
mpa
red
with
the
expe
rim
enta
lda
taof
Bon
set
al.
[1]
for
stea
dyV
GJs
.It
isfo
und
that
the
code
dete
rmin
esth
epr
oper
loca
tion
ofth
ese
para
tion
poin
ton
the
suct
ion
surf
ace
ofth
eba
selin
ebl
ade
(with
out
any
VG
J)fo
rR
eyno
lds
num
bers
of50
,000
orle
ss.
Als
o,th
eco
defi
nds
that
the
sepa
rate
dre
gion
onth
esu
ctio
nsu
rfac
eof
the
blad
eva
nish
esw
ithth
eus
eof
VG
Js.
How
ever
,th
ese
para
ted
regi
onan
dth
ew
ake
char
acte
rist
ics
are
not
wel
lpr
edic
ted.
The
wak
ew
idth
isge
nera
llyov
er-p
redi
cted
whi
leth
ew
ake
dept
his
unde
r-pr
edic
ted.
NO
ME
NC
LA
TU
RE
Bje
tbl
owin
gra
tio=
(ρu)
jet/(
ρu) lo
cal
Cp
blad
epr
essu
reco
effi
cien
t=
(po,
in-
p s)/
0.5(
ρu2 ) in
Cx
axia
lch
ord
ofth
ebl
ade
din
ject
ion
hole
diam
eter
ktu
rbul
ence
kine
ticen
ergy
turb
ulen
cele
ngth
scal
ep
pres
sure
PrPr
andt
lnu
mbe
rR
ein
let
Rey
nold
snu
mbe
r=
Cx(
ρu/µ
) inT
ufr
eest
ream
turb
ulen
cein
tens
ityu
stre
amw
ise
mea
nve
loci
tyv*
shea
rve
loci
tyx,
yC
arte
sian
coor
dina
tesy
stem
with
orig
inat
the
blad
ele
adin
ged
gey+
dist
ance
inw
all
coor
dina
tes
=ρy
v*/µ
αth
erm
aldi
ffus
ivity
∆ydi
stan
ce(f
rom
the
wal
l)of
the
firs
tpo
int
off
the
wal
lε
turb
ulen
cedi
ssip
atio
nra
teγ
wak
elo
ssco
effi
cien
t=
(po,
in-
p o,e
x)/(
p o,in
-p s
,in)
µdy
nam
icvi
scos
ityρ
dens
ityτ
shea
rst
ress
ωsp
ecif
ictu
rbul
ence
diss
ipat
ion
rate
=ε/
k
Subs
crip
ts
efef
fect
ive
valu
eex
valu
eat
casc
ade
exit
inva
lue
atca
scad
ein
let
jet
vort
exge
nera
tor
jet
cond
ition
sla
min
arva
lue
loca
llo
cal
blad
em
id-c
hann
elco
nditi
ons
ost
agna
tion
valu
es
stat
icva
lue
ttu
rbul
ent
valu
ew
valu
eat
the
wal
l
INT
RO
DU
CT
ION
For
the
flow
over
anai
rfoi
l,th
ere
isan
adve
rse
pres
sure
grad
ient
regi
onov
era
larg
epa
rtof
the
suct
ion
surf
ace.
Thi
sca
nca
use
the
flow
tose
para
teon
the
suct
ion
surf
ace,
espe
cial
lyat
low
Rey
nold
snu
mbe
rs,
inw
hich
case
the
boun
dary
laye
rov
erth
ebl
ade
may
bela
min
ar.
Itis
wel
lkn
own
that
ala
min
arbo
unda
ryla
yer
can
with
stan
don
lya
min
orad
vers
epr
essu
regr
adie
ntbe
fore
sepa
ratio
nw
hile
atu
rbul
entb
ound
ary
laye
rca
nw
ithst
and
am
uch
stro
nger
adve
rse
pres
sure
grad
ient
regi
on.
Flow
sepa
ratio
nre
duce
slif
tan
din
crea
ses
drag
.It
isth
usun
desi
rabl
ean
dne
eds
tobe
cont
rolle
d.
Flow
sepa
ratio
nca
nbe
cont
rolle
dby
both
pass
ive
and
activ
ete
chni
ques
.T
hefo
rmer
empl
oys
smal
lvo
rtex
gene
rato
rs(r
ecta
ngul
aror
delta
shap
edw
ingl
ets)
whi
char
eim
bedd
edin
abo
unda
ryla
yer
ahea
dof
alin
eof
flow
sepa
ratio
n[2
].Sp
anw
ise
arra
ysof
vort
exge
nera
tors
are
ofte
npl
aced
alon
ga
win
gup
stre
amof
the
flap
hing
eor
insi
deth
elip
ofa
jet
engi
nein
let
diff
user
.T
helo
ngitu
dina
lvo
rtic
esge
nera
ted
inth
ebo
unda
ryla
yer
incr
ease
cros
s-st
ream
mix
ing
ofst
ream
wis
em
omen
tum
and
supp
ress
orel
imin
ate
sepa
ratio
n.T
hese
fixe
dvo
rtex
gene
rato
rsha
veth
ead
vant
ages
ofsi
mpl
icity
,ru
gged
ness
and
low
cost
.H
owev
er,
they
add
para
sitic
drag
infl
owsi
tuat
ions
whe
rese
para
tion
cont
rol
isno
tne
eded
,e.
g.,
take
-off
and
land
ing.
*NA
SA R
esid
ent R
esea
rch
Ass
ocia
te a
t Gle
nn R
esea
rch
Cen
ter.
Vija
y K
. Gar
g*U
nive
rsity
of
Tole
doTo
ledo
, Ohi
o 43
606
vija
y.ga
rg@
grc.
nasa
.gov
1N
ASA
/CR
—20
02-2
1168
9
Inon
eof
the
activ
ete
chni
ques
,sm
all
jets
blow
nth
roug
hho
les
inth
eso
lidsu
rfac
eca
nge
nera
telo
ngitu
dina
lst
ream
wis
evo
rtic
esin
abo
unda
ryla
yer.
The
sevo
rtic
esin
crea
secr
oss-
stre
amm
ixin
gof
stre
amw
ise
mom
entu
m.
The
surf
ace
hole
sar
epi
tche
dan
angl
eto
the
surf
ace
(gen
eral
lylo
wpi
tch
angl
eof
30-4
5°),
and
incl
ined
rela
tive
toth
em
ain
flow
dire
ctio
n(s
kew
angl
eva
ryin
gfr
om45
-90°
),m
uch
like
the
com
poun
d-an
gled
hole
son
the
show
er-h
ead
offi
lm-c
oole
dbl
ades
.T
his
met
hod
isca
lled
the
vort
exge
nera
tor
jet
(VG
J)m
etho
d.T
his
met
hod
was
firs
tex
amin
edby
Wal
lis[3
,4]
,an
dby
Wal
lisan
dSt
uart
[5]
prim
arily
for
the
purp
ose
ofde
layi
ngsh
ock-
indu
ced
sepa
ratio
nof
turb
ulen
tbou
ndar
yla
yers
.B
all[
6]em
ploy
edV
GJs
alon
ean
dto
geth
erw
ithfi
xed
gene
rato
rsfo
rst
all
supp
ress
ion
inin
let
diff
user
sof
jet
engi
nes.
Hen
ryan
dPe
arce
y[7
]sh
owcl
earl
yth
ede
velo
pmen
tof
asi
ngle
,do
min
ant
vort
exfo
ra
VG
Jat
high
skew
angl
es.
Itha
sbe
ensh
own
byJo
hnst
onan
dN
ishi
[8]
that
this
vort
exen
ergi
zes
the
sepa
ratin
gbo
unda
ryla
yerb
ybr
ingi
nghi
ghm
omen
tum
free
stre
amfl
uid
dow
nto
the
wal
l.E
xper
imen
tal
data
onth
ebe
nefi
cial
effe
cts
ofV
GJs
are
avai
labl
ein
[9].
The
flow
requ
irem
ents
for
the
jets
inth
eV
GJ
met
hod
isa
very
smal
lfr
actio
nof
the
tota
lje
ten
gine
flow
,and
com
pres
sor
blee
dai
ris
suff
icie
ntto
pow
erth
esy
stem
.T
heje
tsca
nbe
turn
edon
and
off
asde
sire
d.W
ithje
tsof
f,th
ere
isno
para
sitic
drag
.T
hepo
tent
ial
appl
icat
ions
ofth
eV
GJ
met
hod
are
num
erou
sfo
rex
tern
alfl
owov
erai
rcra
ftan
dm
issi
les.
Inte
rnal
flow
sin
diff
user
sca
nal
sobe
impr
oved
and
pres
sure
loss
esre
duce
d.T
heV
GJ
met
hod
can
beus
edw
ithap
prop
riat
efl
owdi
rect
ion
sens
ors
and
afe
edba
ckco
ntro
lsy
stem
tosu
ppre
sssu
rge
and
rota
ting
stal
lin
com
pres
sors
ofje
ten
gine
s.
The
oper
atin
gR
eyno
lds
num
ber
for
the
low
-pre
ssur
etu
rbin
ein
anai
rcra
ftga
stu
rbin
een
gine
can
drop
belo
w25
,000
duri
nghi
ghal
titud
ecr
uise
.A
tsu
chlo
wR
eyno
lds
num
bers
,th
ebo
unda
ryla
yers
onth
eL
PTbl
ades
are
larg
ely
lam
inar
,m
akin
gth
emhi
ghly
susc
eptib
leto
flow
sepa
ratio
nne
arth
eaf
tpo
rtio
nof
the
blad
esu
ctio
nsu
rfac
e,w
ithas
soci
ated
incr
ease
inlo
sses
and
drop
inpe
rfor
man
ce.
Alte
ring
the
blad
esh
ape
toav
oid
this
low
Rey
nold
snu
mbe
rse
para
tion
prob
lem
isno
tfe
asib
lesi
nce
such
am
odif
icat
ion
will
likel
yim
pair
the
engi
neop
erat
ion
athi
gher
(des
ign)
Rey
nold
snu
mbe
rs.
As
such
,an
activ
efl
owco
ntro
lst
rate
gy,
such
asth
eus
eof
VG
Js,
has
been
test
edex
peri
men
tally
atth
eA
irFo
rce
Res
earc
hL
abor
ator
yre
cent
ly[1
,10
].T
his
pape
rai
ms
tous
eth
eG
lenn
-HT
code
inor
der
toan
alyz
eth
eus
eof
VG
Jsat
low
Rey
nold
snu
mbe
rs,
and
toco
mpa
reth
eco
mpu
tatio
nal
pred
ictio
nsw
ithth
eex
peri
men
tal
data
ofB
ons
etal
.[1
].
AN
AL
YSI
S
The
num
eric
alsi
mul
atio
nha
sbe
enpe
rfor
med
usin
gth
eN
ASA
Gle
nnR
esea
rch
Cen
terG
ener
alM
ulti-
Blo
ckN
avie
r-St
okes
Con
vect
ive
Hea
tT
rans
fer
code
,G
lenn
-HT
.B
rief
ly,
the
code
,fo
rmer
lykn
own
asT
RA
F3D
.MB
[11]
,is
anex
plic
it,m
ultig
rid,
cell-
cent
ered
,fi
nite
volu
me
code
with
ak-
ωtu
rbul
ence
mod
elw
ithou
tan
yw
all
func
tions
.T
his
isa
gene
ralp
urpo
sefl
owso
lver
desi
gned
for
sim
ulat
ions
offl
ows
inco
mpl
icat
edge
omet
ries
.T
heN
avie
r-St
okes
equa
tions
ina
rota
ting
Car
tesi
anco
ordi
nate
syst
emar
em
appe
don
toa
gene
ral
body
-fitt
edco
ordi
nate
syst
emus
ing
stan
dard
tech
niqu
es.
The
mul
tista
geR
unge
-K
utta
sche
me
deve
lope
dby
Jam
eson
etal
.[12
]is
used
toad
vanc
eth
efl
owso
lutio
nin
time
from
anin
itial
appr
oxim
atio
nto
the
stea
dyst
ate.
Asp
atia
llyva
ryin
gtim
est
epal
ong
with
aC
FLnu
mbe
rof
4is
used
tosp
eed
conv
erge
nce
toth
est
eady
stat
e.E
igen
valu
e-sc
aled
artif
icia
ldi
ssip
atio
nan
dva
riab
le-c
oeff
icie
ntim
plic
itre
sidu
alsm
ooth
ing
are
used
alon
gw
itha
full-
mul
tigri
dm
etho
d.T
heov
eral
lac
cura
cyof
the
code
isse
cond
orde
r.N
ow
all
func
tions
are
used
,thu
sav
oidi
ngan
ybi
asto
the
com
plex
thre
e-di
men
sion
alfl
owst
ruct
ures
near
the
blad
eor
any
othe
rsu
rfac
e.W
hile
the
Gle
nn-H
Tco
deis
basi
cally
aco
mpr
essi
ble
code
,th
epr
esen
tpr
oble
min
volv
esin
com
pres
sibl
efl
owat
rath
erlo
wR
eyno
lds
num
bers
.T
hus,
ther
ew
ere
som
equ
estio
nsre
gard
ing
the
use
ofG
lenn
-HT
code
insu
cha
situ
atio
n.N
eedl
ess
tosa
y,su
chqu
estio
nsab
out
getti
ngco
nver
ged
solu
tion
from
the
Gle
nn-H
Tco
defo
rsu
cha
case
have
been
put
tore
st.
How
thes
ere
sults
com
pare
with
expe
rim
enta
lda
tais
anot
her
mat
ter.
Whi
leth
eG
lenn
-HT
code
has
the
orig
inal
k-ω
mod
el[1
3],
the
shea
rst
ress
tran
spor
t(S
ST)
mod
elof
Men
ter
[14]
,an
dth
ek-
ωm
odel
ofW
ilcox
[15]
wer
eim
plem
ente
din
itby
Gar
gan
dA
mer
i[1
6].
The
SST
mod
elen
com
pass
esbo
thth
ek-
ωan
dth
ek-
εm
odel
s,w
ithth
eor
igin
alk-
ωm
odel
ofW
ilcox
[13]
activ
ated
inth
ene
ar-w
all
regi
onan
dth
est
anda
rdk-
εm
odel
[17]
activ
ated
inth
eou
ter
wak
ere
gion
and
infr
eesh
ear
laye
rs.
Mor
eove
r,th
ede
fini
tion
ofed
dyvi
scos
ityis
mod
ifie
dto
acco
unt
for
the
tran
spor
tof
the
prin
cipa
ltu
rbul
ent
shea
rst
ress
.T
here
ader
isre
ferr
edto
Men
ter
[14]
for
anel
ucid
atin
gdi
scus
sion
ofth
eSS
Tm
odel
.M
ore
deta
ilson
the
rele
vant
equa
tions
and
thei
rim
plem
enta
tion
are
avai
labl
ein
Gar
gan
dA
mer
i[1
6].
The
SST
mod
elw
asus
edfo
rth
epr
esen
tco
mpu
tatio
ns.
Itis
assu
med
that
the
effe
ctiv
evi
scos
ityfo
rtu
rbul
ent
flow
sca
nbe
wri
tten
as
whe
reth
ela
min
arvi
scos
ityµ
isca
lcul
ated
usin
ga
pow
er-l
awfo
rits
(1)
depe
nden
ceon
tem
pera
ture
[18]
.T
hetu
rbul
ent
visc
osity
µ tis
com
pute
dus
ing
the
SST
mod
el.
The
turb
ulen
tth
erm
aldi
ffus
ivity
isco
mpu
ted
from
whe
rea
cons
tant
valu
eof
0.9
isus
edfo
rth
etu
rbul
entP
rand
tlnu
mbe
r,
(2)
Prt.
Bou
ndar
yC
ondi
tion
s
Att
hem
ain
flow
inle
tbou
ndar
ylo
cate
dat
anax
iald
ista
nce
equa
lto
the
blad
eax
ial
chor
dup
stre
amof
the
blad
ele
adin
ged
ge,
the
tota
lte
mpe
ratu
re,
tota
lpr
essu
re,
whi
rl,
and
mer
idio
nal
flow
angl
ear
esp
ecif
ied,
and
the
upst
ream
-run
ning
Rie
man
nin
vari
ant
base
don
the
tota
lab
solu
teve
loci
tyis
calc
ulat
edat
the
firs
tin
teri
orpo
int
and
extr
apol
ated
toth
ein
let.
The
velo
city
com
pone
nts
are
then
deco
uple
dal
gebr
aica
lly,
and
the
dens
ityis
foun
dfr
omto
tal
tem
pera
ture
,to
tal
pres
sure
and
tota
lve
loci
tyus
ing
anis
entr
opic
rela
tion.
For
the
turb
ulen
cem
odel
,th
eva
lue
ofk
and
ωis
spec
ifie
dus
ing
the
expe
rim
enta
lco
nditi
ons,
nam
ely
whe
reT
u in
isth
ein
tens
ityof
turb
ulen
ceat
the
inle
t(t
aken
tobe
0.01
(3)
aspe
rex
peri
men
tal
data
for
the
PakB
blad
e),
u in
isth
eab
solu
teve
loci
tyat
inle
t,an
dis
the
inte
gral
leng
thsc
ale
repr
esen
ting
the
size
ofth
een
ergy
cont
aini
nged
dies
.T
his
leng
thsc
ale
need
sto
beas
sum
ed,
ifno
tre
port
edas
part
ofth
eex
peri
men
tal
cond
ition
s,as
inth
epr
esen
tca
se.
Itw
asas
sum
edto
be5%
ofth
ebl
ade
axia
lch
ord.
At
the
mai
nfl
owex
itpl
ane
loca
ted
atan
axia
ldi
stan
ceeq
ual
to80
%of
the
blad
eax
ial
chor
ddo
wns
trea
mof
the
blad
etr
ailin
ged
ge,
2N
ASA
/CR
—20
02-2
1168
9
the
stat
icpr
essu
reis
spec
ifie
dan
dth
ede
nsity
and
velo
city
com
pone
nts
are
extr
apol
ated
from
the
inte
rior
.A
tth
eso
lidsu
rfac
eof
the
blad
e,th
eno
-slip
cond
ition
isen
forc
ed,
and
tem
pera
ture
issp
ecif
ied
aspe
rex
peri
men
tal
data
.T
hebo
unda
ryco
nditi
ons
for
turb
ulen
cequ
antit
ies
onth
ew
alls
are
k=
0,an
d
for
ahy
drau
lical
lysm
ooth
surf
ace.
An
uppe
rlim
itis
impo
sed
onth
e
(4)
valu
eof
ωat
the
wal
l,as
sugg
este
dby
Men
ter
[19]
and
foun
def
fect
ive
byC
him
a[2
0],
The
grid
arou
ndth
ebl
ade
exte
nds
tom
id-w
aybe
twee
ntw
o
(5)
adja
cent
blad
esw
ithpe
riod
icfl
owco
nditi
ons
inte
rms
ofcy
lindr
ical
velo
city
com
pone
nts
set
ona
dum
my
grid
line
outs
ide
this
boun
dary
.Fo
ra
linea
rca
scad
e(w
hich
istr
uefo
rth
eex
peri
men
tal
data
),it
ispo
ssib
leto
cons
ider
only
asl
ice
ofth
ere
alsp
anfo
rco
mpu
tatio
nal
purp
oses
with
ape
riod
icbo
unda
ryco
nditi
onat
both
ends
ofth
eco
mpu
tatio
nal
span
.Fo
rth
eba
sic
blad
ew
ithno
VG
J,th
issl
ice
can
beof
any
reas
onab
lew
idth
,bu
tw
ithV
GJs
,th
ew
idth
ofth
esl
ice
ison
esp
an-w
ise
pitc
hof
the
hole
s.
The
effe
ctof
VG
Jsha
sbe
enin
corp
orat
edin
the
form
ofap
prop
riat
ebo
unda
ryco
nditi
ons
atth
eho
lelo
catio
nson
the
blad
esu
rfac
e.E
ach
hole
exit
inits
true
oval
shap
eis
repr
esen
ted
by22
4co
ntro
lvo
lum
es.
Dif
fere
ntve
loci
tyan
dte
mpe
ratu
repr
ofile
sfo
rth
ein
ject
edfl
uid
can
besp
ecif
ied
atth
eho
leex
its.
For
the
pres
ent
stud
y,po
lyno
mia
ldi
stri
butio
n[2
1]of
velo
city
and
tem
pera
ture
ofth
ein
ject
ant
atth
eho
leex
itw
assp
ecif
ied.
The
inje
ctan
tan
gle
was
take
nto
beth
esa
me
asth
eho
lean
gle.
Tur
bule
ntin
tens
ityat
the
hole
exit
was
assu
med
tobe
1%(s
ame
asfo
rth
efr
eest
ream
),w
hile
the
turb
ulen
cele
ngth
scal
eat
the
hole
exit
was
take
nto
beth
esa
me
asth
eho
ledi
amet
erd.
EX
PE
RIM
EN
TA
LD
ET
AIL
S
Mea
sure
men
tsw
ere
mad
eby
Bon
set
al.[
1]in
anin
duct
ion
win
dtu
nnel
atth
eU
.S.A
irFo
rce
Res
earc
hL
abor
ator
y.T
helin
ear
casc
ade
cons
iste
dof
eigh
t0.8
8m
(34.
5in
)sp
an,0
.18
m(7
in)
axia
lcho
rd(C
x)bl
ades
plus
two
part
ial
blad
een
dwal
ls.
The
blad
esw
ere
fabr
icat
edfr
omm
olde
dpo
lyur
etha
nere
sin.
The
2-D
blad
esh
ape
stud
ied
isth
ePr
att
&W
hitn
ey"P
akB
"re
sear
chde
sign
,w
hich
isa
Mac
hnu
mbe
rsc
aled
vers
ion
ofa
typi
cal
high
lylo
aded
LPT
blad
ede
sign
.T
heca
scad
eha
da
solid
ity(a
xial
chor
dto
blad
esp
acin
g)of
1.13
,an
inle
tfl
owan
gle
of55
°(m
easu
red
from
the
plan
eof
the
casc
ade)
,an
da
desi
gnex
itan
gle
of30
°.B
lade
s4
and
6w
ere
inst
rum
ente
dar
ound
both
pres
sure
and
suct
ion
surf
aces
(in
the
cent
er0.
2m
ofth
eir
span
)w
ithfo
rty
1m
mdi
amet
erst
atic
pres
sure
taps
.U
ncer
tain
ties
inth
epr
essu
rem
easu
rem
ent
tran
slat
edto
aner
ror
of±
0.18
inth
eC
pda
taat
Re
=10
0,00
0[1
].
Bla
de#5
ofth
eca
scad
eha
dth
eac
tive
sepa
ratio
nco
ntro
l.It
was
man
ufac
ture
dw
itha
hollo
wca
vity
runn
ing
the
span
ofth
ebl
ade
and
cove
ring
the
regi
onfr
om40
%to
90%
axia
lch
ord.
Ane
edle
valv
elo
cate
dup
stre
amof
the
feed
port
allo
ws
fine
cont
rol
ofth
em
ass
flow
rate
into
the
blad
eca
vity
.A
irex
haus
tsfr
omth
isva
lve
into
a1.
2cm
diam
eter
capp
edco
pper
tube
runn
ing
the
span
ofth
ebl
ade
insi
deth
eca
vity
.H
oles
of1.
5m
mdi
amet
eran
dsp
aced
ever
y2.
54cm
alon
gth
e
copp
ertu
bepr
oduc
edan
even
dist
ribu
tion
ofai
rfl
owto
the
VG
Js.
The
1m
mdi
amet
er(d
)cy
lindr
ical
VG
Jho
les
wer
edr
illed
from
the
exte
rior
surf
ace
ofth
ebl
ade,
thro
ugh
the
4m
mth
ick
wal
l,an
din
toth
eca
vity
with
a30
°pi
tch
angl
ean
da
90°
skew
angl
e.T
heV
GJ
hole
sha
vea
leng
thof
8dan
dar
esp
aced
ever
y10
dal
ong
the
cent
er0.
46m
ofth
isbl
ade
span
.T
hero
wof
VG
Jsw
aspl
aced
at0.
73C
x.T
his
loca
tion
isw
ithin
the
sepa
rate
dre
gion
onth
eba
selin
e,un
cont
rolle
dbl
ade
ata
Rey
nold
snu
mbe
rof
50,0
00[1
].T
heje
tbl
owin
gra
tio(B
)w
asco
mpu
ted
asth
era
tioof
the
jet
exit
velo
city
toth
elo
cal
free
stre
amve
loci
tyas
calc
ulat
edfr
omth
elo
cal
pres
sure
coef
fici
ent.
Whi
leth
ein
let
Rey
nold
snu
mbe
rw
asva
ried
betw
een
25,0
00an
d10
0,00
0,B
was
take
nas
0,1,
2or
4.
Stan
dard
pito
tan
dho
t-w
ire
prob
esm
ount
edon
ala
rge
Dan
tec
3-ax
istr
aver
selo
cate
dat
opth
etu
nnel
faci
lity
wer
eus
edto
map
a0.
6m×
0.6m
plan
arcr
oss-
sect
ion
ofth
efl
owdo
mai
n.W
ake
velo
city
prof
iles
wer
em
easu
red
usin
ga
sing
le4µ
mdi
amet
ertu
ngst
enho
t-w
ire.
Asi
ngle
TSI
sub-
min
iatu
reho
t-fi
lmpr
obe
was
used
for
boun
dary
laye
rpr
ofile
mea
sure
men
ts.
The
hot-
film
sens
ordi
amet
erw
as25
µman
dth
ese
nsin
gel
emen
tlen
gth
was
0.25
mm
.T
heer
ror
inth
eho
t-w
ire
and
film
prob
esw
asw
ithin
±2%
atfl
owra
tes
ofin
tere
st.
Mor
ede
tails
are
avai
labl
ein
[1].
CO
MP
UT
AT
ION
AL
DE
TA
ILS
The
com
puta
tiona
lsp
anex
tend
edov
era
part
ofth
ebl
ade
span
with
ape
riod
icbo
unda
ryco
nditi
onat
both
ends
.In
the
axia
ldir
ectio
n,th
eco
mpu
tatio
nal
dom
ain
exte
nded
from
the
inle
tpl
ane
loca
ted
one
axia
lcho
rdup
stre
amof
the
blad
ele
adin
ged
geto
the
exit
plan
elo
cate
d80
%of
the
axia
lcho
rddo
wns
trea
mof
the
blad
etr
ailin
ged
ge.
Aro
und
the
blad
e,th
egr
idex
tend
sto
mid
-way
betw
een
two
adja
cent
blad
esw
ithpe
riod
icbo
unda
ryco
nditi
ons.
Figu
re1
show
sa
span
wis
ese
ctio
nof
the
mul
ti-bl
ock
visc
ous
grid
arou
ndth
ebl
ade.
The
visc
ous
grid
isob
tain
edfr
oman
invi
scid
grid
bycl
uste
ring
the
grid
near
all
the
solid
wal
ls(b
lade
here
).T
hecl
uste
ring
isdo
nein
such
aw
ayas
toen
sure
that
inth
evi
scou
sgr
id,
the
dist
ance
ofan
yce
llce
nter
adja
cent
toa
solid
wal
l,m
easu
red
inw
all
units
(y+ ),
isle
ssth
anha
lffo
rth
eca
ses
stud
ied
here
,fo
llow
ing
Boy
lean
dG
iel
[22]
.T
hein
visc
idgr
idw
asge
nera
ted
usin
gth
eco
mm
erci
alco
deG
ridP
ro/a
z300
0[2
3].
For
com
puta
tiona
lac
cura
cyth
era
tioof
two
adja
cent
grid
size
sin
any
dire
ctio
nw
aske
ptw
ithin
0.8-
1.25
.A
sca
nbe
obse
rved
from
Fig.
1,th
egr
idqu
ality
isve
rygo
odes
peci
ally
near
the
blad
esu
rfac
e.Fi
gure
1al
sosh
ows
the
grid
over
the
blad
esp
anne
aran
dw
ithin
the
inje
ctio
nho
leex
its.
Initi
ally
,the
grid
for
the
blad
ew
ithin
ject
ion
hole
sco
nsis
tsof
136
bloc
ksbu
tbe
fore
the
solv
eris
used
,it
can
bem
erge
din
toju
st10
bloc
ksus
ing
the
Met
hod
ofW
eake
stD
esce
nt[2
4].
The
fina
lvi
scou
sgr
idco
nsis
tsof
1601
28ce
lls,f
orm
edby
clus
teri
ngne
arth
ebl
ade
from
anin
visc
idgr
idw
ith92
928
cells
.T
here
are
224
cells
with
inth
eho
leex
iton
the
blad
esu
rfac
e.T
hein
visc
idgr
idha
s14
4ce
llsar
ound
the
blad
e(f
orth
eO
-gri
dar
ound
the
blad
e),
28ce
llsin
the
blad
e-to
-bla
dedi
rect
ion
from
the
blad
eto
the
peri
odic
boun
dary
in-b
etw
een
the
two
blad
es,a
nd24
inth
esp
anw
ise
dire
ctio
n.A
fter
clus
teri
ng,t
henu
mbe
rof
cells
inth
ebl
ade-
to-b
lade
dire
ctio
nin
crea
ses
to48
.T
wo
mor
egr
ids
wer
ege
nera
ted
for
agr
id-i
ndep
ende
nce
stud
y.O
nein
visc
idgr
idha
d1.
5tim
esth
enu
mbe
rof
cells
inea
chdi
rect
ion
asco
mpa
red
toth
eba
sic
grid
desc
ribe
dab
ove.
For
the
seco
ndgr
id,t
heba
sic
invi
scid
grid
was
clus
tere
dne
arth
ebl
ade
with
agr
idsp
acin
gha
lfof
that
for
the
basi
cvi
scou
sgr
id.
All
thes
eva
riat
ions
ofth
eba
sic
grid
yiel
ded
near
lyth
esa
me
valu
esfo
rth
esk
infr
ictio
nco
effi
cien
ton
the
entir
ebl
ade
surf
ace
asth
eba
sic
grid
;an
yva
riat
ions
wer
ew
ithin
±2%
.T
here
sults
pres
ente
dhe
reco
rres
pond
toth
eba
sic
grid
show
nin
Fig.
1.
3N
ASA
/CR
—20
02-2
1168
9
Com
puta
tions
wer
eru
non
the
16-p
roce
ssor
C90
supe
rcom
pute
rat
NA
SAA
mes
Res
earc
hC
ente
r.T
heco
dere
quir
esab
out
26m
illio
nw
ords
ofst
orag
ew
ithal
lblo
cks
inm
emor
yfo
rth
eca
sew
ithin
ject
ion,
and
take
sab
out
7s
per
itera
tion
for
two
leve
lsof
mul
ti-gr
id.
Aca
sere
quir
esab
out
4000
itera
tions
toco
nver
gefo
ra
case
with
inje
ctio
n.T
his
unus
ually
larg
enu
mbe
rof
itera
tions
for
conv
erge
nce
isdu
eto
the
com
puta
tion
ofin
com
pres
sibl
efl
owat
low
Rey
nold
snu
mbe
rs.
Rec
allin
gth
atth
eG
lenn
-HT
code
ises
sent
ially
aco
mpr
essi
ble
code
,th
eco
dew
asin
itial
lyru
nto
near
-con
verg
ence
for
one
case
with
and
with
out
inje
ctio
nfo
ran
exit
Mac
hnu
mbe
rof
0.6.
The
exit
Mac
hnu
mbe
rw
asth
ensu
bseq
uent
lyre
duce
din
step
sof
0.1
toa
fina
lva
lue
of0.
2,w
hich
ises
sent
ially
anin
com
pres
sibl
efl
owco
nditi
on.
Thi
sob
viat
edth
eus
eof
any
low
Mac
hnu
mbe
rpr
econ
ditio
ning
.Fo
rsu
bseq
uent
case
s,re
sults
for
this
case
serv
edas
the
star
ting
poin
t.
RE
SUL
TS
and
DIS
CU
SSIO
N
Seve
ral
expe
rim
enta
lca
ses
for
the
PakB
blad
e,av
aila
ble
in[1
],w
ere
anal
yzed
for
com
pari
son.
The
seca
ses
cove
rth
ree
inle
tRey
nold
snu
mbe
rva
lues
,25
000,
5000
0an
d10
0000
for
afr
eest
ream
turb
ulen
tin
tens
ityof
1%.
Mos
tof
the
data
in[1
]ar
efo
rT
u=
1%.
Val
ues
ofB
for
whi
chco
mpu
tatio
nsw
ere
done
are
0,1
and
2.Fi
gure
2sh
ows
the
com
pute
dsh
ear
stre
sson
the
basi
cbl
ade
surf
ace,
with
outa
nyV
GJ,
for
thre
eva
lues
ofth
ein
let
Rey
nold
snu
mbe
r.In
this
figu
re,t
heze
rosh
ear
stre
sslin
eis
show
nfo
rre
fere
nce.
Cle
arly
,th
esh
ear
stre
ssis
nega
tive
beyo
ndth
ese
para
tion
poin
ton
the
suct
ion
surf
ace
ofth
ebl
ade.
The
sepa
ratio
npo
int
onth
esu
ctio
nsu
rfac
e,co
rres
pond
ing
toτ w
=0,
islit
tleaf
fect
edby
the
Rey
nold
snu
mbe
r;it
isat
0.71
Cx
for
Re
=50
,000
and
100,
000,
but
at0.
73C
xfo
rR
e=
25,0
00.
The
reap
pear
sto
bea
smal
lre
gion
onth
epr
essu
resu
rfac
eas
wel
lth
atha
sse
para
ted
flow
for
Rey
nold
snu
mbe
rs≥
50,0
00.
The
smal
lse
para
ted
regi
onon
the
pres
sure
surf
ace
isov
er0.
22≤
x/C
x≤
0.25
for
Re
=50
,000
,an
dov
er0.
18≤
x/C
x≤
0.29
for
Re
=10
0,00
0.T
here
isno
sepa
rate
dre
gion
over
the
pres
sure
surf
ace
for
Re
=25
,000
.T
helo
catio
nof
sepa
ratio
npo
int
onth
esu
ctio
nsu
rfac
em
atch
esve
ryw
ell
with
the
expe
rim
enta
lda
ta[2
5]fo
rR
eyno
lds
num
bers
of50
,000
orle
ss.
Bon
set
al.
[1]
give
noin
dica
tion
whe
ther
they
obse
rved
any
sepa
rate
dre
gion
over
the
pres
sure
surf
ace.
We
may
note
that
the
boun
dary
laye
rov
erth
een
tire
blad
eis
lam
inar
,as
evid
ence
din
Fig.
3.T
his
figu
resh
ows
the
dim
ensi
onle
sstu
rbul
ent
visc
osity
,µt,
with
ina
narr
owra
nge
from
0to
1.0
inth
efl
owfi
eld
for
Re
=50
,000
and
B=
0an
d1.
Not
ing
that
the
dim
ensi
onle
ssla
min
arvi
scos
ity,
µ,
isne
arly
unity
(dim
ensi
onle
sslo
cal
tem
pera
ture
isne
arun
ity),
itis
clea
rth
atth
eef
fect
ive
visc
osity
with
inth
een
tire
boun
dary
laye
rov
erth
ebl
ade
surf
ace
ises
sent
ially
lam
inar
.W
em
ayno
teth
epr
esen
ceof
sepa
ratio
non
the
suct
ion
surf
ace
inFi
g.3(
a),
whi
lew
ithth
eV
GJs
turn
edon
,th
efl
owge
tsat
tach
ed(c
f.Fi
g.3(
b)).
Sim
ilar
resu
ltsw
ere
obta
ined
for
Re
of25
,000
and
100,
000.
Figu
re4
show
sth
eve
loci
tyve
ctor
s,co
lore
dby
stat
icpr
essu
re,i
nth
efl
owfi
eld
arou
ndth
ebl
ade
for
inle
tR
eyno
lds
num
ber
of50
,000
,an
dfo
rB
=0
and
1.T
heth
ick
sepa
rate
dre
gion
,with
reve
rse
flow
,is
clea
rly
visi
ble
inFi
g.4(
a)fo
rth
eun
cont
rolle
dbl
ade,
whi
leth
ere
isal
mos
tno
sepa
ratio
non
the
suct
ion
surf
ace
for
the
cont
rolle
dbl
ade
(Fig
.4(
b))
with
B=
1.O
nth
epr
essu
resu
rfac
e,th
eve
loci
typr
ofile
sap
pear
tobe
clos
eto
sepa
ratio
nov
era
very
smal
lre
gion
,as
disc
usse
dab
ove
rega
rdin
gth
ere
sults
inFi
g.2.
Sim
ilar
resu
ltsw
ere
obta
ined
for
Re
of25
,000
and
100,
000.
Figu
re5
com
pare
sth
epr
esen
tcom
puta
tions
with
the
expe
rim
enta
lda
ta[1
]fo
rth
epr
essu
reco
effi
cien
ton
the
base
line
blad
eat
two
inle
t
Rey
nold
snu
mbe
rsan
dT
u=
1%.
The
com
pari
son
isve
rygo
odon
the
pres
sure
surf
ace
but
not
sogo
odon
the
suct
ion
surf
ace
due
toth
epr
esen
ceof
sepa
ratio
n.W
hile
the
expe
rim
enta
ldat
aex
hibi
tthe
clas
sic
plat
eau
indi
catin
gno
n-re
atta
chin
gla
min
arse
para
tion,
the
anal
ysis
pred
icts
sign
ific
ant
diff
usio
nth
roug
hth
ese
para
tion
regi
on.
Sim
ilar
disc
repa
ncy
was
obse
rved
byB
ons
etal
.[1
]be
twee
nth
eir
expe
rim
enta
lda
taan
dth
e2-
DN
avie
r-St
okes
Van
eB
lade
Inte
ract
ion
(VB
I)co
de.
Figu
re6
com
pare
sth
eco
mpu
ted
boun
dary
laye
rpr
ofile
sov
erth
eba
selin
e(n
oV
GJ)
blad
esu
ctio
nsu
rfac
eat
thre
ech
ordw
ise
loca
tions
with
the
expe
rim
enta
lda
tafr
omB
ons
etal
.[1
]fo
rR
e=
50,0
00an
dT
u=
1%.
At
67%
axia
lch
ord,
the
expe
rim
enta
lpr
ofile
was
note
dby
Bon
set
al.[
1]to
beun
stea
dyin
the
regi
ony
<3m
m.
Tha
tis
why
the
expe
rim
enta
lda
tafa
llin
toa
wid
eba
ndin
the
near
-wal
lre
gion
.A
t73
%an
d79
%ax
ialc
hord
,the
flow
isse
para
ted,
with
the
com
puta
tions
clea
rly
show
ing
reve
rse
flow
.Fo
rth
eex
peri
men
tal
data
,rev
erse
flow
dire
ctio
nco
uld
not
bere
solv
ed[1
]si
nce
asi
ngle
hot-
film
prob
ew
asus
ed.
How
ever
,se
para
tesm
oke
visu
aliz
atio
ndi
dco
nfir
mth
atfl
owre
vers
alw
aspr
esen
tin
side
the
sepa
ratio
nbu
bble
atth
e73
%ax
ial
chor
dm
easu
rem
ent
stat
ion.
The
com
pari
son
betw
een
the
com
pute
dan
dex
peri
men
tal
data
isno
tve
rygo
od,
spec
ially
at79
%ax
ial
chor
dlo
catio
n,w
here
the
expe
rim
enta
lda
tash
owm
uch
thic
ker
boun
dary
laye
rco
mpa
red
toth
eco
mpu
tatio
ns.
Thi
sim
plie
sth
atth
ese
para
ted
regi
onis
not
wel
lre
solv
edby
the
com
puta
tions
.
Asi
mila
rco
mpa
riso
nis
show
nin
Fig.
7fo
rin
let
Rey
nold
snu
mbe
r=
100,
000
and
B=
0.C
lear
lyat
this
high
Rey
nold
snu
mbe
r,th
ebo
unda
ryla
yer
isth
inne
rco
mpa
red
toth
atin
Fig.
6.H
owev
er,t
heex
peri
men
tal
data
show
ath
inne
rbo
unda
ryla
yer
com
pare
dto
that
from
the
com
puta
tions
atal
lth
ree
chor
dwis
elo
catio
ns.
Whi
leth
eco
mpu
tatio
nssh
owse
para
ted
(rev
erse
)fl
owat
both
73%
and
79%
axia
lch
ord
loca
tions
,B
ons
etal
.[1
]re
port
that
the
flow
was
clos
eto
sepa
ratio
nat
the
79%
axia
lch
ord
loca
tion
but
atta
ched
atth
e73
%ax
ialc
hord
loca
tion.
Figu
re8
com
pare
sth
eco
mpu
ted
velo
city
prof
iles
inth
ew
ake
at0.
62ax
ial
chor
ddo
wns
trea
mfr
omth
ebl
ade
trai
ling
edge
for
two
inle
tR
eyno
lds
num
bers
agai
nst
the
expe
rim
enta
lda
taof
Bon
set
al.[
1]w
ithno
VG
J.W
hile
the
com
puta
tions
show
little
effe
ctof
Re
onth
ew
ake
wid
than
dre
lativ
ely
smal
leff
ecto
nth
ew
ake
dept
h,th
eex
peri
men
tal
data
show
ala
rger
effe
ctof
Re
onbo
thth
ew
ake
wid
than
dde
pth.
At
Re
=50
,000
,th
eco
mpu
ted
and
expe
rim
enta
lw
ake
wid
ths
mat
chbu
tth
eco
mpu
ted
wak
ede
pth
ison
lyab
out
half
ofth
eex
peri
men
tal
valu
e.A
tR
e=
100,
000,
the
com
pute
dw
ake
dept
hco
mpa
res
wel
lw
ithth
eex
peri
men
tal
valu
ebu
tth
eco
mpu
ted
wak
ew
idth
isab
out
twic
eth
atof
the
expe
rim
enta
lva
lue.
Such
prob
lem
sw
ithco
mpu
ted
wak
esar
ew
ell
know
n,an
dpo
int
toth
ene
edfo
rm
ore
wor
kin
this
area
.M
oreo
ver,
inth
epr
esen
tca
se,
thes
epr
oble
ms
are
augm
ente
dby
the
larg
ese
para
tion
regi
onov
erth
esu
ctio
nsu
rfac
eof
the
blad
e.A
nyun
stea
dyef
fect
sow
ing
toth
efl
owse
para
tion
and
wak
esh
eddi
ngca
nnot
bere
solv
edby
the
stea
dyco
deth
atw
asus
edfo
rth
epr
esen
tco
mpu
tatio
ns.
Figu
re9
show
sa
com
pari
son
betw
een
the
pres
ently
com
pute
dlo
ssco
effi
cien
t,γ,
and
the
expe
rim
enta
lva
lues
prov
ided
byB
ons
etal
.[1
0].
Whi
leth
eex
peri
men
tal
data
show
asu
dden
drop
inlo
ssco
effi
cien
taro
und
Re
=50
,000
,the
com
puta
tions
show
only
agr
adua
lde
crea
sein
the
loss
coef
fici
ent
from
Re
=25
,000
to10
0,00
0.T
his
isag
ain
are
flec
tion
ofth
epo
orw
ake
pred
ictio
nno
ted
abov
e.Fi
gure
10co
mpa
res
the
com
pute
dbo
unda
ryla
yer
prof
iles
over
the
blad
esu
ctio
nsu
rfac
eat
thre
ech
ordw
ise
loca
tions
with
the
expe
rim
enta
lda
tafr
omB
ons
etal
.[1]
for
Re
=50
,000
and
B=
2.B
oth
the
com
puta
tions
and
expe
rim
ent
show
nose
para
tion
(rev
erse
flow
).H
owev
er,
the
4N
ASA
/CR
—20
02-2
1168
9
expe
rim
enta
lda
tash
owst
eepe
rpr
ofile
sth
anth
eco
mpu
ted
resu
ltsat
all
the
stat
ions
,sim
ilar
toth
ere
sults
inFi
g.7
for
Re
=10
0,00
0an
dno
VG
J.B
ons
etal
.[1
]at
trib
ute
the
doub
ly-i
nfle
cted
(but
atta
ched
)ve
loci
typr
ofile
at79
%ax
ial
chor
dst
atio
nto
the
ultim
ate
pene
trat
ion
dept
hof
the
vort
exje
tsin
toth
efr
eest
ream
.T
heco
mpu
ted
resu
ltsdo
not
show
any
such
anom
aly.
Figu
re11
com
pare
sth
eco
mpu
ted
velo
city
prof
iles
inth
ew
ake
at0.
62ax
ial
chor
ddo
wns
trea
mfr
omth
ebl
ade
trai
ling
edge
for
anin
let
Rey
nold
snu
mbe
rof
50,0
00ag
ains
tth
eex
peri
men
tal
data
ofB
ons
etal
.[1
]w
ithan
dw
ithou
tV
GJs
.W
em
ayno
teth
atth
eda
taco
rres
pond
ing
toB
=0
are
also
avai
labl
ein
Fig.
8;th
eyar
ein
clud
edhe
reto
com
pare
with
the
data
for
B≠
0.T
heco
mpu
ted
wak
ew
ithV
GJs
on(B
≠0)
issh
allo
wer
and
som
ewha
tnar
row
erth
anth
atw
ithou
tan
yV
GJ
(B=
0),
ason
ew
ould
expe
ctsi
nce
the
sepa
ratio
nre
gion
vani
shes
whe
nV
GJs
are
on.
How
ever
,th
eef
fect
isno
tso
dram
atic
,sp
ecia
llyfo
rth
ew
ake
wid
th,
asfo
rth
eex
peri
men
tal
data
.E
xper
imen
tally
the
wak
eis
very
narr
oww
hen
the
VG
Jsar
eon
com
pare
dto
the
case
whe
nth
eyar
eno
t.T
hew
ake
dept
hre
cove
ry,
ratio
ofth
ew
ake
dept
hfo
rB
≠0
toth
atfo
rB
=0,
isab
out
the
sam
efo
rbo
thth
eco
mpu
tatio
nal
and
expe
rim
enta
lda
ta.
Als
o,th
ere
islit
tledi
ffer
ence
betw
een
the
prof
iles
corr
espo
ndin
gto
B=
1an
dB
=2
for
both
the
com
puta
tiona
lan
dex
peri
men
tal
data
.
CO
NC
LU
SIO
NS
The
Gle
nn-H
Tco
dew
asus
edto
com
pute
the
flow
over
alo
w-
pres
sure
turb
ine
blad
eat
very
low
Rey
nold
snu
mbe
rsw
ithan
dw
ithou
tth
eus
eof
vort
exge
nera
tor
jets
.T
here
sults
are
com
pare
dw
ithth
eex
peri
men
tal
data
ofB
ons
etal
.[1
]fo
rst
eady
VG
Js.
Itis
foun
dth
atth
eco
dede
term
ines
the
prop
erlo
catio
nof
the
sepa
ratio
npo
int
onth
esu
ctio
nsu
rfac
eof
the
base
line
blad
e(w
ithou
tan
yV
GJ)
for
Rey
nold
snu
mbe
rsof
50,0
00or
less
.A
lso,
the
code
find
sth
atth
ese
para
ted
regi
onon
the
suct
ion
surf
ace
ofth
ebl
ade
vani
shes
with
the
use
ofV
GJs
.H
owev
er,t
hese
para
ted
regi
onan
dth
ew
ake
char
acte
rist
ics
are
not
wel
lpr
edic
ted.
The
wak
ew
idth
isge
nera
llyov
er-p
redi
cted
whi
leth
ew
ake
dept
his
unde
r-pr
edic
ted.
Thu
s,th
ere
isa
need
toim
prov
eth
epr
edic
tion
ofw
ake
char
acte
rist
ics,
espe
cial
lyin
situ
atio
nsw
here
larg
ese
para
ted
regi
ons
may
exis
tup
stre
amof
the
wak
e,as
inth
epr
esen
tca
se.
For
reso
lutio
nof
the
unst
eady
effe
cts
due
tofl
owse
para
tion
and
wak
esh
eddi
ng,
use
ofan
unst
eady
code
isre
com
men
ded.
RE
FE
RE
NC
ES
1.B
ons,
J.P.
,So
nder
gaar
d,R
.an
dR
ivir
,R
.B.,
1999
,C
ontr
olof
Low
-Pre
ssur
eT
urbi
neSe
para
tion
Usi
ngV
orte
xG
ener
ator
Jets
,A
IAA
Pape
r99
-036
7.2.
Pear
cey,
H.H
.,19
61,
Shoc
kIn
duce
dSe
para
tion
and
itsPr
even
tion,
Bou
ndar
yL
ayer
&F
low
Con
trol
,vo
l.2,
(Ed.
)G
.V.
Lac
hman
n,Pe
rgam
on,
NY
,pp
.11
70-1
344.
3.W
allis
,R
.A.,
1952
,T
heU
seof
Air
Jets
for
Bou
ndar
yL
ayer
Con
trol
,A
erod
ynam
ics
Res
earc
hL
abor
ator
ies,
Aus
tral
ia,
Aer
oN
ote
110
(N-3
4736
).4.
Wal
lis,
R.A
.,19
60,
APr
elim
inar
yN
ote
ona
Mod
ifie
dT
ype
ofA
irJe
tfo
rB
ound
ary
Lay
erC
ontr
ol,
Aer
onau
tical
Res
earc
hC
ounc
il,A
ustr
alia
,C
urre
ntPa
per
No.
513.
5.W
allis
,R
.A.
and
Stua
rt,
C.M
.,19
58,
On
the
Con
trol
ofSh
ock-
Indu
ced
Bou
ndar
y-L
ayer
Sepa
ratio
nw
ithD
iscr
ete
Jets
,A
eron
autic
alR
esea
rch
Cou
ncil,
Aus
tral
ia,C
urre
ntPa
per
No.
595
(N63
-101
38).
6.B
all,
W.H
.,19
84,
Tes
tsof
Wal
lB
low
ing
Con
cept
sfo
rD
iffu
ser
Bou
ndar
yL
ayer
Con
trol
,A
IAA
Pape
r84
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6.7.
Hen
ry,
F.S.
and
Pear
cey,
H.H
.,19
94,
Num
eric
alM
odel
ofB
ound
ary
Lay
erC
ontr
olU
sing
Air
-Jet
Gen
erat
edV
ortic
es,A
IAA
J.,
vol.
32,
pp.
2415
-242
5.8.
John
ston
,J.P
.and
Nis
hi,M
.,19
90,V
orte
xG
ener
ator
Jets
-M
eans
for
Flow
Sepa
ratio
nC
ontr
ol,
AIA
AJ.
,vo
l.28
,pp
.98
9-99
4.9.
Com
pton
,D
.A.
and
John
ston
,J.
P.,
1992
,St
ream
wis
eV
orte
xPr
oduc
tion
byPi
tche
dan
dSk
ewed
Jets
ina
Tur
bule
ntB
ound
ary
Lay
er,
AIA
AJ.
,vo
l.30
,pp
.64
0-64
7.10
.B
ons,
J.P.
,So
nder
gaar
d,R
.an
dR
ivir
,R
.B.,
2001
,T
heFl
uid
Dyn
amic
sof
LPT
Bla
deSe
para
tion
Con
trol
Usi
ngPu
lsed
Jets
,A
SME
Pape
r20
01-G
T-1
90.
11.
Stei
ntho
rsso
n,E
.,A
mer
i,A
.A.
and
Rig
by,
D.L
.,19
97,
TR
AF3
D.M
BA
Mul
ti-B
lock
Flow
Solv
erfo
rT
urbo
mac
hine
ryFl
ows,
AIA
APa
per
97-0
996.
12.
Jam
eson
,A
.,Sc
hmid
t,W
.an
dT
urke
l,E
.,19
81,
Num
eric
alSo
lutio
nsof
the
Eul
erE
quat
ions
byFi
nite
Vol
ume
Met
hods
Usi
ngR
unge
-Kut
taT
ime-
Step
ping
Sche
mes
,A
IAA
Pape
r81
-12
59.
13.
Wilc
ox,
D.C
.,19
88,
Rea
sses
smen
tof
the
Scal
e-D
eter
min
ing
Equ
atio
nfo
rA
dvan
ced
Tur
bule
nce
Mod
els,
AIA
AJ.
,vol
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pp.
1299
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0.14
.M
ente
r,F.
R.,
1994
,T
wo-
Equ
atio
nE
ddy-
Vis
cosi
tyT
urbu
lenc
eM
odel
sfo
rE
ngin
eeri
ngA
pplic
atio
ns,A
IAA
J.,v
ol.3
2,pp
.159
8-16
05.
15.
Wilc
ox,
D.C
.,19
98,
Tur
bule
nce
Mod
elin
gfo
rC
FD,
DC
WIn
dust
ries
,2n
dE
dn.
16.
Gar
g,V
.K.
and
Am
eri,
A.A
.,20
01,
Tw
o-E
quat
ion
Tur
bule
nce
Mod
els
for
Pred
ictio
nof
Hea
tT
rans
fer
ona
Tra
nson
icT
urbi
neB
lade
,In
t.J.
Hea
t&
Flu
idF
low
,vo
l.22
,pp
.59
3-60
2.17
.Jo
nes,
W.P
.an
dL
aund
er,
B.E
.,19
73,
The
Cal
cula
tion
ofL
ow-R
eyno
lds-
Num
ber
Phen
omen
aw
itha
Tw
oE
quat
ion
Mod
elof
Tur
bule
nce,
Int.
J.H
eatM
ass
Tra
nsfe
r,vo
l.16
,pp.
1119
-113
0.18
.Sc
hlic
htin
g,H
.,19
79,
Bou
ndar
yL
ayer
The
ory,
McG
raw
-Hill
,N
ewY
ork,
7thed
ition
,pp
.31
2-31
3.19
. M
ente
r,
F.R
., 19
92,
Impr
oved
T
wo-
Equ
atio
n k-
ω
Tur
bule
nce
Mod
els
for
Aer
odyn
amic
Flo
ws,
NA
SA T
M-1
0397
5.20
.C
him
a,R
.V.,
1996
,A
k-ω
Tur
bule
nce
Mod
elfo
rQ
uasi
-Thr
ee-
Dim
ensi
onal
Tur
bom
achi
nery
Flow
s,A
IAA
Pape
r96
-024
8.21
.G
arg,
V.K
.an
dG
augl
er,
R.E
.,19
97,
Eff
ect
ofV
eloc
ityan
dT
empe
ratu
reD
istr
ibut
ion
atth
eH
ole
Exi
ton
Film
Coo
ling
ofT
urbi
neB
lade
s,J.
Tur
bom
achi
nery
,vo
l.11
9,pp
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3-35
1.22
.B
oyle
,R.J
.and
Gie
l,P.
,199
2,T
hree
-Dim
ensi
onal
Nav
ier
Stok
esH
eat
Tra
nsfe
rPr
edic
tions
for
Tur
bine
Bla
deR
ows,
AIA
APa
per
92-3
068.
23.
Prog
ram
Dev
elop
men
tC
orpo
ratio
n,19
97,
"Gri
dPro
TM
/az3
000
-U
ser’
sG
uide
and
Ref
eren
ceM
anua
l,"W
hite
Plai
ns,
NY
.24
.R
igby
,D.L
.,St
eint
hors
son,
E.a
ndC
oiri
er,W
.J.,
1997
,Aut
omat
icB
lock
Mer
ging
Usi
ngth
eM
etho
dof
Wea
kest
Des
cent
,A
IAA
Pape
r97
-019
7.25
.R
ivir
,R
.B.,
2001
,pr
ivat
eco
mm
unic
atio
n.
5N
ASA
/CR
—20
02-2
1168
9
-25
0
25
50
75
00.20.40.60.81.0
Re=100000Re=50000Re=25000
pressure
suction
x/cx
τw
Fig. 2 Computed shear stress on the blade surface at various inlet Reynolds numbers (Tu = 1%; B = 0)
(a)(b)Fig. 3 Dimensionless turbulent viscosity within 0 and 1 in the flow field for Re = 50,000; Tu = 1%. (a) B = 0; (b) B = 1.
Fig. 4 Computed velocity vectors, colored by static pressure, around the blade for Re = 50,000; Tu = 1%. (a) B = 0; (b) B = 1.
(a)(b)
periodicboundary
periodicboundary
periodicboundary
0
1
2
3
4
5
00.20.40.60.81.0
expt, Re=50000expt, Re=100000comp, Re=50000comp, Re=100000
x/cx
Cp
Fig. 5 Comparison of pressure coefficient for baseline blade at two inlet Reynolds numbers and Tu = 1%
Fig. 1 Spanwise section of the multi−block viscous grid around the blade, with detail of grid over the blade span near and within the hole exits
0.9
1.0p/po
6N
ASA
/CR
—20
02-2
1168
9
0
0.5
1.0
1.5 -0
.20.
20.
61.
0
expt
0.7
9ex
pt 0
.73
expt
0.6
7co
mp
0.79
com
p 0.
73co
mp
0.67
u/m
id-c
hann
el v
eloc
ity
y (cm)
Fig
. 6 C
ompa
rison
of b
ound
ary
laye
r pr
ofile
s of
str
eam
line
velo
city
norm
aliz
ed b
y m
id−c
hann
el v
eloc
ity a
t thr
ee c
hord
wis
e st
atio
ns:
0.67
, 0.7
3 an
d 0.
79 a
xial
cho
rd o
n th
e su
ctio
n si
de.
Re
= 50
,000
; Tu
= 1%
; B =
0
0
0.5
1.0
1.5 -0
.20.
20.
61.
0
expt
0.7
9ex
pt 0
.73
expt
0.6
7co
mp
0.79
com
p 0.
73co
mp
0.67
u/m
id-c
hann
el v
eloc
ity
y (cm)
Fig
. 7 C
ompa
rison
of b
ound
ary
laye
r pr
ofile
s of
str
eam
line
velo
city
norm
aliz
ed b
y m
id−c
hann
el v
eloc
ity a
t thr
ee c
hord
wis
e st
atio
ns:
0.67
, 0.7
3 an
d 0.
79 a
xial
cho
rd o
n th
e su
ctio
n si
de.
Re
= 10
0,00
0; T
u =
1%; B
= 0
0.80
0.85
0.90
0.95
1.00
1.05
3.4
3.8
4.2
expt
, Re=
1000
00co
mp,
Re=
1000
00ex
pt, R
e=50
000
com
p, R
e=50
000
4.4
y/bl
ade
spac
ing
streamwise velocity/mid-channel velocity
Fig.
8 C
ompa
rison
of w
ake
velo
city
pro
file
at 0
.62
axia
l cho
rd d
owns
tream
from
the
blad
e tra
iling
edg
e fo
r tw
o in
let R
eyno
lds
num
bers
. Tu
= 1
%
an
d B
= 0
0
0.15
0.30
0.45
0.60
0.75
00.
4x10
50.
8x10
51.
2x10
5
expt
com
p
Re in
loss coefficient
Fig
. 9 C
ompa
rison
of l
oss
coef
ficie
nt v
s. in
let R
eyno
lds
num
ber
for
Tu
= 1%
0
0.5
1.0
1.5
00.
30.
60.
91.
2
expt
0.7
9ex
pt 0
.73
expt
0.6
7co
mp
0.79
com
p 0.
73co
mp
0.67
u/m
id-c
hann
el v
eloc
ity
y (cm)
Fig
. 10
Com
paris
on o
f bou
ndar
y la
yer
prof
iles
of s
trea
mlin
e ve
loci
ty
n
orm
aliz
ed b
y m
id−c
hann
el v
eloc
ity a
t thr
ee c
hord
wis
e st
atio
ns:
0.6
7, 0
.73
and
0.79
axi
al c
hord
on
the
suct
ion
side
.
R
e =
50,0
00; T
u =
1%; B
= 2
0.80
0.85
0.90
0.95
1.00
1.05
3.4
3.8
4.2
expt
, B=
2co
mp,
B=
2ex
pt, B
=1
com
p, B
=1
expt
, B=
0co
mp,
B=
0
4.4
y/bl
ade
spac
ing
streamwise velocity/mid-channel velocity
Fig
. 11
Com
paris
on o
f wak
e ve
loci
ty p
rofil
e at
0.6
2 ax
ial c
hord
dow
nstr
eam
fro
m th
e bl
ade
trai
ling
edge
for
Re
= 50
,000
; T
u =
1%; B
= 0
, 1, 2
7N
ASA
/CR
—20
02-2
1168
9
Thi
s pu
blic
atio
n is
ava
ilabl
e fr
om th
e N
ASA
Cen
ter
for A
eroS
pace
Inf
orm
atio
n, 3
01–6
21–0
390.
RE
PO
RT
DO
CU
ME
NT
AT
ION
PA
GE
2.R
EP
OR
T D
AT
E
19.
SE
CU
RIT
Y C
LA
SS
IFIC
AT
ION
OF
AB
ST
RA
CT
18.
SE
CU
RIT
Y C
LA
SS
IFIC
AT
ION
OF
TH
IS P
AG
E
Pub
lic r
epor
ting
burd
en f
or t
his
colle
ctio
n of
inf
orm
atio
n is
est
imat
ed t
o av
erag
e 1
hour
per
res
pons
e, i
nclu
ding
the
tim
e fo
r re
view
ing
inst
ruct
ions
, se
arch
ing
exis
ting
data
sou
rces
,ga
ther
ing
and
mai
ntai
ning
the
dat
a ne
eded
, an
d co
mpl
etin
g an
d re
view
ing
the
colle
ctio
n of
inf
orm
atio
n.
Sen
d co
mm
ents
reg
ardi
ng t
his
burd
en e
stim
ate
or a
ny o
ther
asp
ect
of t
his
colle
ctio
n of
inf
orm
atio
n, i
nclu
ding
sug
gest
ions
for
red
ucin
g th
is b
urde
n, t
o W
ashi
ngto
n H
eadq
uart
ers
Ser
vice
s, D
irect
orat
e fo
r In
form
atio
n O
pera
tions
and
Rep
orts
, 12
15 J
effe
rson
Dav
is H
ighw
ay,
Sui
te 1
204,
Arli
ngto
n, V
A
2220
2-43
02,
and
to t
he O
ffice
of
Man
agem
ent
and
Bud
get,
Pap
erw
ork
Red
uctio
n P
roje
ct (
0704
-018
8),
Was
hing
ton,
DC
20
503.
NS
N 7
540-
01-2
80-5
500
Sta
nd
ard
Fo
rm 2
98
(R
ev.
2-8
9)
Pre
scrib
ed
by A
NS
I S
td. Z
39
-18
298-1
02
For
m A
ppro
ved
OM
B N
o. 0
704-
0188
12b
.D
IST
RIB
UT
ION
CO
DE
8.P
ER
FO
RM
ING
OR
GA
NIZ
AT
ION
RE
PO
RT
NU
MB
ER
5.F
UN
DIN
G N
UM
BE
RS
3.R
EP
OR
T T
YP
E A
ND
DA
TE
S C
OV
ER
ED
4.T
ITL
E A
ND
SU
BT
ITL
E
6.A
UT
HO
R(S
)
7.P
ER
FO
RM
ING
OR
GA
NIZ
AT
ION
NA
ME
(S)
AN
D A
DD
RE
SS
(ES
)
11.
SU
PP
LE
ME
NT
AR
Y N
OT
ES
12a.
DIS
TR
IBU
TIO
N/A
VA
ILA
BIL
ITY
ST
AT
EM
EN
T
13.
AB
ST
RA
CT
(M
axim
um
200
wo
rds)
14.
SU
BJE
CT
TE
RM
S
17.
SE
CU
RIT
Y C
LA
SS
IFIC
AT
ION
OF
RE
PO
RT
16.
PR
ICE
CO
DE
15.
NU
MB
ER
OF
PA
GE
S
20.
LIM
ITA
TIO
N O
F A
BS
TR
AC
T
Unc
lass
ifie
dU
ncla
ssif
ied
Fina
l Con
trac
tor
Rep
ort
Unc
lass
ifie
d
1.A
GE
NC
Y U
SE
ON
LY
(L
ea
ve b
lan
k)
10.
SP
ON
SO
RIN
G/M
ON
ITO
RIN
G A
GE
NC
Y R
EP
OR
T N
UM
BE
R9.
SP
ON
SO
RIN
G/M
ON
ITO
RIN
G A
GE
NC
Y N
AM
E(S
) A
ND
AD
DR
ES
S(E
S)
Nat
iona
l Aer
onau
tics
and
Spac
e A
dmin
istr
atio
nW
ashi
ngto
n, D
C 2
0546
–00
01
Ava
ilabl
e el
ectr
onic
ally
at h
ttp://
gltr
s.gr
c.na
sa.g
ov/G
LTR
S
July
200
2
NA
SA C
R—
2002
-211
689
GT
–200
2–30
229
E–
1341
9
WU
–708
–73–
43–0
0N
AS3
–001
80N
CC
3–92
6
13
Low
-Pre
ssur
e T
urbi
ne S
epar
atio
n C
ontr
ol—
Com
pari
son
With
Exp
erim
enta
l Dat
a
Vija
y K
. Gar
g
Low
-pre
ssur
e tu
rbin
e; S
epar
atio
n co
ntro
l; V
orte
x ge
nera
tor
jets
Unc
lass
ifie
d-U
nlim
ited
Subj
ect C
ateg
orie
s: 0
7 an
d 34
Dis
trib
utio
n:
Non
stan
dard
Uni
vers
ity o
f To
ledo
Tole
do, O
hio
4360
6
Vija
y K
. Gar
g, U
nive
rsity
of
Tole
do, T
oled
o, O
hio
and
NA
SA R
esid
ent R
esea
rch
Ass
ocia
te a
t Gle
nn R
esea
rch
Cen
ter.
Prep
ared
for
the
Tur
bo E
xpo
2002
cos
pons
ored
by
the
Am
eric
an S
ocie
ty o
f M
echa
nica
l Eng
inee
rs a
nd th
e In
tern
atio
nal
Gas
Tur
bine
Ins
titut
e, A
mst
erda
m, T
he N
ethe
rlan
ds, J
une
3–6,
200
2. P
roje
ct M
ange
r, R
.E. G
augl
er, T
urbo
mac
hine
ry a
ndPr
opul
sion
Sys
tem
s D
ivis
ion,
NA
SA G
lenn
Res
earc
h C
ente
r, or
gani
zatio
n co
de 5
820,
216
–433
–588
2.
The
pre
sent
wor
k de
tails
a c
ompu
tatio
nal s
tudy
, usi
ng th
e G
lenn
HT
cod
e, th
at a
naly
zes
the
use
of v
orte
x ge
nera
tor
jets
(VG
Js)
to c
ontr
ol s
epar
atio
n on
a lo
w-p
ress
ure
turb
ine
(LPT
) bl
ade
at lo
w R
eyno
lds
num
bers
. The
com
puta
tiona
l res
ults
are
also
com
pare
d w
ith th
e ex
peri
men
tal d
ata
for
stea
dy V
GJs
. It i
s fo
und
that
the
code
det
erm
ines
the
prop
er lo
catio
n of
the
sepa
ratio
n po
int o
n th
e su
ctio
n su
rfac
e of
the
base
line
blad
e (w
ithou
t any
VG
J) f
or R
eyno
lds
num
bers
of
50,0
00 o
rle
ss. A
lso,
the
code
find
s th
at th
e se
para
ted
regi
on o
n th
e su
ctio
n su
rfac
e of
the
blad
e va
nish
es w
ith th
e us
e of
VG
Js.
How
ever
, the
sep
arat
ed r
egio
n an
d th
e w
ake
char
acte
rist
ics
are
not w
ell p
redi
cted
. The
wak
e w
idth
is g
ener
ally
over
-pre
dict
ed w
hile
the
wak
e de
pth
is u
nder
-pre
dict
ed.