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loa pxgipithy l d n«l uYs lql g ¶ f,hd ep f p
p± btd a lhbend pxa g
uYd h s df/a¦ b lobthd l
uqd s h d5f/nqa z ¼¬a nqhIb g|h btd g ea p
jb p aef nohma lop
p aeuYu lop d5f/p a¦y )hb nYf/
lqp d g|hn d d j
aehf g a g|hloh btb zp f,a hg bednYOa pÑ'
g|h btg bed/tp
/n z/p h
nqn lYlhj
l p/p
p
g
p l z,p,n
p
p p
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P
hlYlh
v
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h uYb/h
d
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lohlh°p d l
h
lopigxpithloh a h
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d5f/a
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d5u /n y
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z/p u d jpd a plop aep f g d
aj
a /s p hedp f
a jwh aef hg|hn d
a z, pa lopx dwuYb/a
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g b hep a p0a z,p7lqa noh aeu nf l az s gxgÙ¹ dlqf n /pih s z a a lhs gi/pihy l lhbeg bts g d¸uYd d jwh
d gig|h f/an Á p a

jw
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h
g

0
n
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l
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p

h
e

p
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h
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h
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q
n
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¹
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uqbta
bed
d
s,f
aef,d beb s
aty u d5f,a aev aeu a
uYs
f/d5f/b nqa
jd5 u nYldh f/a h
bed gla h
a j s d h s/noathu lohs /n p p a z d gxp lon jw
s pja p nohmlop atuqaef
ah a

z gig2¹ nYl d5uq u
le¹ d5f/gloa¸pijw
h°z/p
lYlop
y uYnqben d5ulqloh" uYbepxs ep
ats ha nof hglo n hlYlonYpi px/pig hgigih/n
p
p lqnoh
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Ä
Mach isolines

Ù Æ
CÞë
ëâ¯áWUìå ë âãkáTèâ
p
v5s
P
nqh
Ä
} ¶ b/a
ß×îîâêåãâçß%

¥
jkh
gip
f/a
hn
a
Þkã´èâêåYUâéîâ$ààâ
s/uquYd
a uqd5f bed
d f/d
s/f°btd d d d uqu u
a btd aIu
dkb bed
d a s/f
ï
btlod5hf/l u u ahg fgis,hf
hlql n a <ÄhÅ z v
nq f/l v5d e d h p|hg bepxbejwd,j lqnqbep d d
l b fn d
fg s a d pi é n b p
)f
hnYp\
uqsuqd d p l a p
b/a j a n z,pf beh d5fs/
f h uYdVa
u a nohz/bepÑ
d/z/p\ h b beg d d z/p\ahmulqlh daeuqatg v5s nYdV
a pibtgxpd z/n d
P , plb/akbtd5f/u g u j a fl h
Ë z _|;=g ; nqs/ f
l nqj
j
s
f p d h
v v
bth d
s p ¼ nqdp f a g d5hu g g fl)hv5l s
a lqpiÄ giË pxeP e= h < z a a g|h aef nYp gxp| h v j v lheuqsp a hg )b j aVlof/nqha lhVp f/d noh u
a
a p d5l u p
f / v5s lop
P ,} u f/d g j a a~loy p d h s/nqf/p v gipih aef d n aev pihg a a g©

nqp|f/h a j
lqnou hlohp
atf /pih b/az/u p pxjw
d9y j f/lqdk
bta noh a
gig u hj aeuqatv5l s z gxs,p ag u j s lqp d5f s p{lon h f dkv p0,uqnqbpi,ja p lqno¥ hlqap{z/[p S gxg f
f d f/p d lop{beg2d ¹ g d/ hl ¶ d5f/hd
º
hg b nqu u aLs
lohlop
apef l n
d plop
s z d5f,pia j f/g|u htp d5pf lopigxpita h a¨z a s gxp df jp d b a s/atu p
¼ a nqj g|htu p
u lqa nohj,dp)u p h p p s dlopigxpis/tu hloh¸g|h¸s/
uqps lhtatp bed hnqpih¸
du z gxg d5f,a ha ep d p bed a p b loh a
Ë z j) v5s pitp Ë < pxd5 u nq gia p f,aegia gxpxlYuqlod
g|h«f//a h h)loh v5s gig|hc
p é h b
u p d z/a pxj btd5lonqfhy5la hcv5/atp f n uq d5f/d lohIz/d5pu gxa<
Ä
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P
nqaeh f a h )v5s noh
j du lqnoh¦g gip u p s d5h f/a
f/l a nqp z/f/p d ; n K a h
s/a j
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ga >f/s pih a d

«
n
Ä
p
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atf d
s/f/vd
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bed5f,/j v5s lonqh"dgif/ha z/p a lqnqpi v ep v

z d5gxgÙf ¹ a lqn bt,d p|hVd
g u
z bedgifgih nqs p gid pih
bzed g s j n d5f z/p a bh /a
d9g2y ¹{h
aeuYuqa hloa hgih aeuYuqdb a nohef/p a
jw
uqbl/
hta p hd g f uqbtd5f/z,d p\¼¬n uqs l hg atnquq uqdb p\a lon aeh
s/ar
f hbz arb n s /n f/daef hgxgip hlos h du g2¹ beb nYl d
piz lop p
pf z s,abta jw
nYp gxlhmlop/n
hlYl nqh
lqnohj,pgÙ¹ nl
loh hl
a pÑ¼ n p
p z
gxg
_ P
Mach isolines

Ç
Ì+ÍÏ»ÒLÈ½ÖzË}Ì+Í½Ë
p
v5s
noh
P=P } ¶ b/a
\ d5f
jwh
f,d5f
gxp
f/a
hn
a
atuqatf a
y5d d
atu u a v5v s/f ds,fÔs a d a
uquYa df/a
bed5u s df/a
s/f
l fs gih a n btd z/pl a p p h d5uYu p l d5f/a gxl a nqp s n d5loh f
gxg a aef gig|h
lon ep d
fs/d9y5d pig0/n a d d
a z/p d
,n u s pijwshtp a z/ p f hep bed pÑz/a p f/n a atp|u hgxpz,pÑlopxa pi nq g
btduqs j v l v z awbtd j s nYp d f n<gÙ¹·f/hd5/f×
j lhb ep d5f,ha gip a¦a los n lql d5f nohl
nqpis/jwf h
y5p d
u s nqp gip
s a )d hnflop gia hn
atf/u d5f loh l! h ng|h°
f ,dI
gxlh d5uYlu z,p|hloh
p htp
hgxg hep aef/p\u z,d5pf Ò a g n a p d lqn a z/pxj d a p a p d btlqd pigx pieu eh uYd5z f/dkd ¹
d5f/gÙa¹/hq/d/b)gi
î `cblfñdb hTd s
hat/f,s n
pijw
j d5f glopiz,pij a d p fhs g z a gig2b ¹ b /a nohml ben d5f pi nY d gip s
p f/ds/f l
d5v htaep uYu
u a d
¥

luqa s/loaep\
,

n
n

p
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n
p

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l
l

h
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p
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l
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h
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h
x
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p
j
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p
j
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n
p
p

h
g
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l
q
n

h
q
n
p
o
l
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p
x
g
i
p
t

f
d a
d
db
atf aLs/f
aef/u d5f
a b uYduqb
a
s,aeu d'bed5f/u h u a¦f,a h
l d5f pia©z,f,pij a
p a hgip d5f,a g a h ya d·hb g|hn yy5l a d5f,a p l f b gig2a ¹
d aef eh
a z/p d nqaehbtl d nqpbeg d hgxj s
z,p\f h v5atf/
lohb n uqgibth
gigihIv z/pxn v tp bed z s gxg|h
tp a
h tp d5f/a
s,nYf/p v5dr
s/fj g a a g|h a j d5f lohea p hg a
d5g f pxl ah
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nqhgipx eehs ep a
b pih atv hcz uqb,gxg a z,pin uqb ep p/z bed5lqf/louYhael f z)
a hgxg|h uqnqd p y5gip|a h aIu ju a lohef/p d5f hg v5d5f h

p l atj
gipxed5f h/api gxp > d bh giaL
p7g u
ahg s /nYp df hwz gip s a d juYaep f hg|hnYd9p y5a
bed l a z,a pnqp d g a n
bed p
du z/pih d5f,a hf

a f ha ep aeuqu p)z/pÒ g uqn d
e

I
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n
p
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z

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p
t

p
p
z
p
uqd s d5f/a>u
d5f
a a<a s
df aÀu
drbedf/u a
d
s/uYd a p
atp bef l b n
pxd5z f/nqathf l a g2¹
ahlophgiatg|beh d5f g|h d5f g tp atf dwlobthd ep a«hu nYp|h©
s z atgifg d a hep uqa p a lhml a«btd
b z gxa g|h
l a p d hb z g7/a n aa z/s pitp d5f hj u l d5f j aca lon f j s/ael u n
/dw
hnos,hf n g fs/d9y jw
lobep a gxgipxlYlop aebth d5f z
}
pi nYd f gip h
hatbed5f hd5jk
aef z d gxg aru htp d p d5lou hep è hbenYb p f z
d p y f lv5¹v hjb/ pxa l
f hlqnqp aef d z/p0,n d

z/btpxebep a a hj d5f/l a a lhlobehd5/fn y5a v5atf lh a h v5l v d hp a h btbels h p a
pif/gÑa /n b uYd z,piep s/huYu j
l atuquqhd/b a nYlof h
ï
z u gxg|h uYbed5f
hbed g nqhep
n f,uqh d v5a jka h p d n h f/u nqhl eh f g aeuYh aef z/p
>
p
/

n
s/f
u v5f,p d/
jw/d nYpij

atp f ,a n a feb h
p aebtpaenqu p u
lqnohI
a pi/pxgif/
s,f g2¹,p uqd s n d5n f/a z/pÑ¼ nYlopÑp ld h,a pigipl hr
d5f,z,u p a lqp\dz/f/pa nYp ls h
g)d /n /g a jkh aebef b pxloa h«z/p u h s g ed5p f/a /nYpis/jwuYu h¸z/y p/uY bed5l u n/n bez bes n p a
piaez v nohuYebp /a gÙ¹ a¸u lopigxpi
ï
eh
y5 a z,)pb lhg l a p h
f a¦s/n<f gih f pxj u gihep btd5fz,y5p a v5atf p p f s/p a ¹/h atf/u nod5hfl eac
uYd5z f/dgxu p a jpaeuq atf lohlha
u nqp s hloh
d5f j z,p|h l aef/u d5¹f h hgip f pz/aep v
a'uYn s uqdf hbtp d z f/z/uYd5pxj f bed p uqs p a uqd5f bed°lhma l /n a uqdf lhbtl d/
è pxj gid hep aef pd lq nqpiatz,u pij
df/n a atp v uYzG
f/btp d hgipp uqd n d pxj
d a p a lqnoh v5atf/a p
b/pxa n uqb p
gip s/f
j
f/d5g)f j f/j a l n d5u lh
y h a nohr
bebtpxs nqnqp gl pxuqg,at/ben d5f /g jw
d h¸z f/a gxg| h f/atbeaeuYu nqhgipxehea p d zf aI
btbep s hg|hnYa p
gxp hnqp pxlqp p zh
nohmlophg
z\¹ nqz,p
hnYp|h n¦¼ n pin
¹\h
nqhlh
_ Ë
Supersonic flow (Mach=1.4) inside a 3D channel
Subsonic (Mach=0.5) flow inside a 3D channel
Convergence histories
0.0
Convergence histories
0.0
Linear N scheme
Non-linear scheme
conservative
non conservative
-1.0
-2.0
log(res)
-2.0
-3.0
-4.0
-4.0
-5.0
0.0
500.0

p
d
n
s/u
v5s
PË } ¶
noh
1000.0
# iterations
1500.0
-6.0
0.0
2000.0
5000.0
10000.0
d a
bed5fy5a v5atf
a
s,uquqdwf/a b f a
atf/u d5f a
ï
l qn p z,p
n
hw n¨pig
g h hg lonYpiz/pxj
p hg
uqb a
d5f,a a ara s
df fVd5vf
ta v
a
d d,
lohz,p n lopithtp
z gxg h ep p\p
pn ip j
z/pj l
_Á
15000.0
Mach isolines
É
»VÙCÚ
0.5388
0.5307
0.5226
C
B
0.5145
0.5064
A
9
0.4983
0.4902
8
7
0.4822
0.4741
6
5
4
0.4660
0.4579
0.4498
3
2
0.4417
0.4336
1
0.4255
B
B
B
B
B
B
B
B
A A
C
B
B
B
C
C
C
B
B
B
B
B
B
B
B
B
B
B
B
B
C C
A
AA
v5s
P Á/} \
99 A
9 8 8 AB
6 78 B
6
AA
C
E
C
DD
EE E
F
E
C
D
B
B
B
A
9
9
9 76
AA
8
A
A
9
A
A
A
uqdf tb d } f,aea uYdé b"uqs a
a
a
p qn h
h hg

p
ig p
p
h
gxg )hn lqp\g|hl nqhgip
Ì¤$Õ ¦ Ï¾¢E¤Ó¢¥[¥z¦k¤ÔËLÖ[¥zË
Ï É¦

È
B
B
F
E
D
NON Conservative
B
B
Level Mach
Conservative
f
aruYs
â$åæ Þ TßÓàsá~âêãìXèßÓå
ß×î îìsåá~ëî áTèß
%kì_ë¹áTëîì[æ
ßçáCãëî¹ßÓàsáTâêãßÓåá~â
d
s
df/awb
a u b
a u u a
ats a
f/d f,u
df
d v
f d d
f/a

g nqp|h f/b p lheatp f a hnqp d"uYp beh
qu a h"¼d5f/nYa j g|Ä hep y aef/a hnos hmlql nqp atlou p ha z g p l d jw
d5f h
d p d lon z be5d lqf,lh uqaef gxg|ha
l uqaths gig d f/u z/d5p f
s/f ep btd5f df dp bed5f pÀd nqpx/n s h d5z×
f,awhb//n ¼ a z,u pxlh b /nYa p u pi)u ha gxj
d b/lqa pin a

gih"
j uYs/g|behbttaep uYu yd/ hnohlYl nqp lop h"z g p l jwh°
z p lhtp hnqp
aeuqatf ¼¬n l f/a
v ¼ nqd
/n f lhd loh s/btaef g)d hnoh y5a noh¼ d
p
b
a u b
lon z
z p
lql nqp/p hnqhlql nYp lqp p
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P `
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P h `
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a atf
a
d a
d a
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u u a
b
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uqb ya u
pig p l jwh hnohmlql nqp lop
nqp nqp n p
bed gÙ¹ a } nohml n z/p n epihg
j
Â ; <
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m
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m
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P
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df
f/aea h b ep p
gip
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f/
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z
m
m
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N
6
m
P
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;
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a y
u
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hz nqp hml h )hf/ep a l jf/ d
a u b,aa a y l au

^ a
nYd p lop y5a uqz d Yn p 6 hal : )
a htp|hgxf/
p aea
b
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p
g pi n n p
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X
Z

vs
P _}
s
v
uqs
a )
b acf/a
f,d
a
a
p noh
nYp gxp|h
n pihg
g/p|h
g|hl nohg

5
Ë
Ë
b
a u b,a b/awuYd5f/d"uqb/a
au f u
f)v5s
a
b uqd
aef/u d5f a
¥ ha nohdL
lYl u nYp lop dÊs/f
k
j
h
q
l
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t

h
l
p
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V
h
p
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p
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z
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j
g a
atf/u d5f a a
a uqs a )b b
a u b/a yaef f/d f/atab
a p u hb/
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pxj uqdf/dV
p uqb/
hg a g pi n a n atpu hnohmf/lqa l nqp )lop vs z/Ë5p Ë lfh s,gxa
p a
a gig )f,hd tp ^ J z/a'
ahnqhlql atnqf/p u lqp d5f
f d
z a g/b p|h uqbts/f s/
hlqu pithl d ha z lqd noh a¦a gxg|h a b noh uYbes/f
z a d5f,a lqÄ
n atz/u pxj u d5f,d p p a
a
d
fjkdI
uq s n a pi)h b b a l u z bg/z a jw
b p uqp bts/f )htbep d l u jwd5 f noathf g a v n p|s h d9y h'
d z/pxn utp f
a p ^ l 5` lq n
nqp±
fy s n p d ha nqhlqarl uYnYs p lqa p )b b pih
a h u b/nqnqacp b /abez d l d5h f gxpÀ
d5f/h d l a hg f/
ata z/p lob p lqpÀz a gigih u b/a . K~} Ü ¹
pa pig bed5/f, d z a gxg é b n p athf nqhalql nqp flqy p s
px uqs z a )b hb gxg gxp a u /p bh/noa
hlYbel d nqp u lop d5f atf
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N
pia g f/ata piz b z/p a h u bj /a . lqn Â } } g2¹0p atv5aepxf,g a / f/a z gig f/a n bed p hatf nohmalql nqú p lop ô ` nqnq)p v5 s z Ë Álo` p
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hgxg d5u gxp
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noh a u gxg|hbgx/p a h
f z/s/p f nYn f,l d
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¸aebtd d5u d5fVé"jwa /d lhlqop H ¼ Çmîpi]`nYkl¼ hipim gÿh ^TÄ z Ä _ h8 Ä Ë5hË z è g Ä 5_ p l
jw pxlop
l z
/nYpig
KÉP Ñy f ata 5 | r aea f da a b a u b
a ru a
f/vd
db
a r
Á
ø

È
hnoh l ðA
bed5f h d5f f/n vd
/aaes a h a zs
d5f/ut Ó f MMD
0 g nYp loÇmp ñlofpxîUj gBhigj_ÙÇ4l kl/hi,m,p m îU_3ïYn¦Sg nklhhg0ñG/n _ Æp
4Ç kz/õ pxvelq]~p vek Æp v è ¼è©l è r Ä r g Ä _5n V_ K r a h0lq p Ä 5 Ä
É P Qr/d
M ¸atbed5f f/b*) é"s
Ë
a è P df,)v d f
aef,u df
atu s
<
È
hlYuql b/a atu d
u
s /hd5g|fk
/a gxp Ë gxp aes h a z a s
df/ue p! f s
uq,a gxlopx z/Ä pij _ p hgVn piz hg
z/p lonYpi lqp
j
¼ n¨l
z
g n hmlop
/gxp
z
É P \y f ata /
| r aea f da a
Ë
r ¶ a f,vd db a r
b
a
u
b
a
Ä
Á
Á
È
bed5f h d5f f/n vId /a s a h a z s
d5Ó f/ut f MhMnqh bl 0 ønqp g
ð lqp Çmñpij fîUgLhigl _ÙÇ4/kl/hip m5{m î_3n ï
Snhklg hñGn _ Æ p
Ç4kz/õpxvelq]~p vek Æp v Ä 5¼0 l Ä è Ò è©g è n r Ä r Ä h_5lqV_ p K r a

Ë mK Éo|
ata -{Ç Æ him ]~v Æ Ç4kïi_g_ÙÇ4k}_kU×Çàõg ð v>7>îUmve]67<úeîhig_ÙÇ4k p~ {
,aeu u Á /a
è
è

K
l
p
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f/f
d é

Ä
¼
p p h
nY n
Á /a
y f/b f/v d5f
a /d
f
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f,v5s
df }
aty a>¬

hz h u s/p b s ¼¬n aeu ly5j a l aet z
g|"Ñhm lop fh¦
v5ath f/a zl d5f gif h v h lonYp|h s
)+n p -/.
hlz)hmlh lqn l 5n Á
nYl
nqhlop
h z nqpizì hgipl
03232 [\^]`_3
ï \Zvekve]hig_ÙÇ4k Ä
Á t a
Ë ÁÉ è s è | d )s d5s
atf
uYa d bed
s a
d5v
uYuqaeuYu aef
<
è
è
È
¼ n
j l n{/n nohj h
j
l
y uqÓ d "
a n d n Ä Ë · Ò è s è nqpxj Ä l hs g5 z/ hlh¨)h
z p n Ó nYl Ó
Ó
Á d5f/v È

! f y5a u "d
p n pl
5Ë Ë É& r és a
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dgigd´) n
4ø $ g
pxl d hB
:

M6 wing - Surface pressure distribution
lower (num.)
lower (exp.)
upper (num.)
upper (exp.)
0.5
0.0
0.0
-0.5
-0.5
-1.0
0.0
ALPHA = 0.03 Mach = 0.92 y/b = 0.20
1.0
lower (num.)
lower (exp.)
upper (num.)
upper (exp.)
0.5
Cp
M6 wing - Surface pressure distribution
ALPHA = 2.06 Mach = .70 y/b = 0.20
1.0
0.5
x/c
-1.0
0.0
1.0
M6 wing - Surface pressure distribution
0.5
M6 WING - Surface pressure distribution
ALPHA = 2.06 Mach = 0.70 y/b = 0.44
1.0
ALPHA = 0.06 Mach = 0.92 y/b = 0.44
1.0
lower (num.)
lower (exp.)
upper (num.)
upper (exp.)
0.5
1.0
lower (num.)
lower (exp.)
upper (num.)
upper (exp.)
0.5
Cp
Cp
0.0
0.0
-0.5
-0.5
-1.0
-1.5
0.0
0.2
0.4
0.6
0.8
-1.0
0.0
1.0
0.4
0.6
0.8
x/c
M6 Wing - Surface pressure distribution
M6 WING - Surface pressure distribution
ALPHA = 2.06 Mach = 0.70 y/b = 0.80
1.0
lower (num.)
lower (exp.)
upper (num.)
upper (exp.)
0.5
Cp
Cp
0.5
0.2
x/c
1.0
ALPHA = 0.06 Mach = 0.92 y/b = 0.80
lower (num.)
lower (exp.)
upper (num.)
upper (exp.)
0.0
-0.5
-0.5
-1.5
0.0
0.5
x/c
-1.0
0.0
1.0
0.5
x/c
1.0
K } a d5f d f d
v5s
y d
b bed
a
uYs
a bedaO'b ea f a
aeuqu d5f,a a
s
jp nohmlop¸z g
p l z/pr/n
p
n
a on aeh f uqa d5f ¼¬n l ¼¬nqh hg nqp hg gihlop
z p n ql p t p p
/
q
pu
:

X
Y
Z
M∝
q
=8
.0
K,} s
v5s
v
nqp ig pih
u p on a h
pxjwj ql nqpih
btd
j
s
lhep
df
hg
aÿuqs
uYs
gxg|h

a /
b a
n p
2000
1500
1500
1000
1000
500
500
0
0
-500
-500
-1000
-1000
-1500
-1500
K ,}
v5s
p f/d noh ;
<<
/pih
s
0
1000
v
nqp gip|h
2000
uYs
3000
q
p
;
si<
v5s
f/a
g/p|h
f/d
z/p
FV scheme
-1000
Ë
< nqh<
a
N scheme
-2000
a )
b af/a
n p|hg
g
d d
l t
Mach isolines (z=0 plane)
2000
-1000
q
a tb d d
z g
qn
<
0
1000
2000
3000
} /
f ata uqdìé bþf/a
f/d
p
p
h
gr/pih
3D blunt body flow (M=8.0)
Convergence histories
0.0
FV scheme
N scheme
log[res(density)]
-2.0
-4.0
-6.0
-8.0
-10.0
0.0
q
5000.0
10000.0
15000.0
# iterations
p
Ë
v5s
nqh
Ä
} ¶ d a
btd5fy5a v5aef
a
b uYd ea u
a uqdf btd
l nqp z/p
n
hk nÊpig h
l ¦
l px n
p
Mach number and entropy distribution along centerline (y=0 plane)
8
0.080
7
0.070
6
5
4
N scheme
FV scheme
0.040
3
0.030
2
0.020
1
-1300
q
p
v5s
noh
K}
Ë ·
0.050
Entropy
Mach
0.060
Mach
S
Mach
S
-1250
-1200
-1150
-1100
-1050
-1000
u
s d5f/a a fs a d
é ba a
ea f d
s/f/v5d
uquYa
p ql nqpi ep
z g
j n z/p
h
z gxgÙ¹ ol n /p|hg
gÙ¹,h
s
Ä
x
t
s
a
y
b2
n
b1
b3
b4
P(x,t)
b 1,2,5
b3
u
P(x,y,t)
x
q
p
v5s
Ë5Ë } ¶ s
noh

t
a )
b b
a u b/a a ara s
d5f
s a d f/u
d5f
a
n p hnqhlql nqp lqp
nÊg h ep pz/p{Ò g n p lohep hnYp
y
y
s
n
s
b3
n
b3
a
a
P(x,y,t)
P(x,y,t)
b 1,2
b4
t
q
p
v5s
nqh
t
x
Ë Á/}
b 1,2
b4
Supersonic case
Subsonic case
d a d5f,a a a¸b
a
b/arf,a
f/dG ;
n p tp
z gxg hnohlYl nqpxlqp
g/pih
y
c= β/M
ζ
µ
s
u
µ
µ
sin µ = 1/Μ
t
R=1
η
a=1/M
n
ξ
µ
pa
rti
cle
pa
th
Mach lines
;O=

º
x
i~G3U^i~~ ¡¢£~¥¤¦ S§ ¨©¢¢£~ ª«G¬¢ ¡§®B¯¢£i°¡V¯i¥G¯6 ¡Vª ¢¬5 ¡¢i¯¤¡
±V²
z
z
t0
n0
t 0=t1
w
s0
y
θ
s1
n0
θ
u
v
s0
n1
a)
n2
t
s1=s2
w
y
s0
θ
φ
3
γ
t 0=t1 s
3
φ
v
n2=n3
s1=s2 w
n0
θ
u
n1
γ
t2
t 0=t1
s0
n1
u
v
x
x
c)
v5s
y
u
z
t2
p
φ
b)
x
z
q
y
v
x
n0
w
Ë
nqh
:
}
Á
d)
u d
d5f/a
bedd
f a
noh ¼ nqjwhtp
z,p
nqz/p hl
s
Ë

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