Reynolds Stress Modeling of Flow Separation on Curved Surfaces
Post on 18-Aug-2015
225 Views
Preview:
DESCRIPTION
Transcript
34 5760'/8
"!$#&%&'(#*),+'(.-'/0'12
9 :=A@CBEDGFIHJBEKMLONPFQK"< S;: MRT UVFQK?T">WATMUG{ a*skd[_gaX[`,cfHenbadhgi`s,X$qop/^$\1q rbX&stgi\1m4Z
=?~"$$Ab J?AP? viP~ "$~A J"$AW
ef"&bP~
rG
HenbaZ\1Zc`,d|[nbaMqba4da4aM`,c>\/m4aX[_\1sk[ha?`,cBXb\/Xbaa4dh\1Xb
U `tR [ha `,d&*@Csr
!"!$#%%&!$!(')& !+*,%.-!$&0/10*,132451/ 65#87:9&')';%9/65')#%&%!M!%-9aJO!,W.5%+5DE#&B>P%&P/19#%&B>:% &b*J&Y; !!$#%%&!$!+')P&c/1!K-P!%&@GCdTPB/1!$9&!$/ #FZ')P&1!5%L!%-$>%/ !%/ W
99&-%5#576&b*JP&Z#J"!$/1'e-15#f6g*h/ 9& -!K9&')>1jiB>Jk!%/ 9&!76!%&XV')Dl$!nmopq3rUsutvw 7 sxtPyw GV1P!!$#%%!%!z')P&1!{$,>:%&|#Je&PP(/ !%9&!%/ #FX')P&1!|/ (#%')!D-P';N2/ 9\!$#a5}/1 / #FG~U6#-%@/3[@-P!%/1!$#}/1 /1&/1!C>$&!$&k#V/1^#%J"';';_#%-'&_-65#%/1P!&7
P^#J_-!M!%')U!$>\9&/1:#%%&5#')&k#M'e-!$#M}:+/1')>:!%8GzdzB!%7_#JP+!$#}/ 1/ #Fe>%>:&N#/ &!
D+!$!$#%&'DU&_-6#/1!&';65#%/1WDl$'#%JB-!$O5D] !!$#%%&!$!;')&K5%*M%!$]#J65#J!$+#J5#C';%WV*J&Z-!$/1W5&^/1!$9&!$/ #F)';\/ !,-!$&8GIFB';k!$/ #-5#/ !&7#J/ !D59#1&!K#./3%W9&L*J&b-!%/ W;)&P1!!N#%!%!V';4GzHKJ/ !/1!!%>:&9&/113#$-n/ t Ae7*J&$e!%&$e!$#}/ 1/ #F^>%}1';!J6n}\&Y9&-k#&$&8GUcg* !I_-'e}:&+Pb!%K/ ';>:!%!$/1} M#%X-P!%/1';knf6g*!%/ #%-65#%/1!z87k#J_-!7k#J-!%WX/1!K /1')/ #;#%.*, 32RDl-P9#%/12R}6!$&B')1!KC#F*M52R:N#ak#7V$ /15}1Z1g*1!)_-'e}:&U J6!^}:&>$>\!%&/155#$#&')>P#.#!%3>65$#D#J!N#a}/ 1/3#Fn>$} &')!&7k!%/ 9&C#%J9&$%!%>:/ WLJ/1WJ) !I_-'e}:&T')}k|-P&I5.c/ suw !$Jg*,;!$'),>:#_#%/$}1';!GHKJ99&-%99aJ/ }_#JPV1P!!$#%%&!$!B';U/ 9&')>6$/1!$*/ #%J
P/1!%9!%/3#F0';&T/ !L#(!%-P)9&/ &k#30$}6}P B5#}\L-!$&Z*/1 B/ B/1-P!$#NG
I'W$5#$Dl-#T$D GI|%!,A"g/ !%^BA]GIY5#%!CV')Dl$!DlM#JP&/1!%-P>\$/1!$/1
PY!%-P>>\$#V#J$-WJ-P#U#%JX9&-$!%(D#%J/1!!$#%-PGKK1!$^5>>%9&/15#"#JP(9>:&%5#/
DeA]&G YW-P! U1 } 9aSDl%' #%J0VgLF!$#%/ #-#D(H`9aJ W/1 #%9aS_J1'OG=, PGX#%/1G( GXG(GXGXGXGXG(G(GXGXG(G(GLGLGXGXG(G(GXGXGXGXG(G(GXGXG(G(GXGXGXGXG(G(GXGXGLGLG(G(GXGXG(G(GXGXGXGXG(G(GXGXG(G(GXGXGXGXGG % )863
' >$ ?;=P( G y ? * !%9&$/1>P#%/1 GXGXG(GXG(GLGXG(GXGXG(GXG(GXGXG(GXGLG(GXG(GXGXG(GXG(GXGXG tkP( G HKJX';!%J GXG(GXG(GXGXG(GXG(GLGXG(GXGXG(GXG(GXGXG(GXGLG(GXG(GXGXG(GXG(GXGXG tkP( G t H{-%}-P1&P9&X';& ! GXG(GXG(GLGXG(GXGXG(GXG(GXGXG(GXGLG(GXG(GXGXG(GXG(GXGXG ttP( G t G y HC*,52R&_-65#%/1O')1!BGXG(GXGXG(GXG(GXGXG(GXGLG(GXG(GXGXG(GXG(GXGXG ttP( G t G VP1!U#%%!%!+bP&1!MG(GXGXG(GXG(GXGXG(GXGLG(GXG(GXGXG(GXG(GXGXG ttP( G 3 =,k9#%/1b!%9aJ';!^GXG(GXG(GLGXG(GXGXG(GXG(GXGXG(GXGLG(GXG(GXGXG(GXG(GXGXG tt(PG 6 &!%-P #!7 A U/1 8? g*G(GXG(GLGXG(GXGXG(GXG(GXGXG(GXGLG(GXG(GXGXG(GXG(GXGXG ttP( G 6 G y =,-$55#%-%X[\&9#! G(GLGXG(GXGXG(GXG(GXGXG(GXGLG(GXG(GXGXG(GXG(GXGXG t (P( G7( =,91-!$/1P!&7 A U / 18?`1g* GLGXG(GXGXG(GXG(GXGXG(GXGLG(GXG(GXGXG(GXG(GXGXG tS8U M T$:? S{ M gAV$l $`
H'8 G y A]&!$9&$/1>P#%/1ZD{#J"#%&!$#%9!$ GLGXG(GXGXG(GXG(GXGXG(GXGLG(GXG(GXGXG(GXG(GXGXG 3 (8 GG H{=,-%k}-P91%P/19&bX';!%9aJ';& ! !^GXGXG(G(GXGXG(G(GLGLGXGXG(G(GXGXGXGXG(G(GXGXG(G(GXGXGXGXG(G(GXGXGLGLG(G(GXGXG(G(GXGXGXGXG(G(GXGXG(G(GXGXGXGXGG 3 (8 G t &!%-P #!K5D`#%J"!%/ 'e- {T TE_ 5
3 #JbdIK= " ?GXH GX =GX5GX G(UGX G(GX GXG(%S_GX!$JG(GL>YGXYG(GXGX6G(P&GXG(?`GX1gGX* G(OGXGLG(1GX /1G(WGX7GXL# G(%GX !%%G(-PGXJ GXG yG%G%6#6 J^dIK= " ?H = + $S_!%J>^B6Z?1g*O1 /1W7=,J5#- yG%G ( %\G L1 g$/1655#%/1)>\/1k# 5 /157DlI/1P!$#a59&57/ !P#,!$-P)9&/ &k#3)9&9-5#%7_*J/19aJ/ #%-%!$/1W/ 695_#% Y5[\&9#%!"#J)99&-%95D,5G WGnWZ>$&/ 9#%/1!GeHKJ)/ ' D#JP/1!>$ $&9#(*,!L#J_-!L#Z/1P9&%&!%.#JP)-P&$!$#/ Wb5DCJg* 1!L!$#%%!%!(#%-%}P-19&')P&1!+>\$Dl$' / P59&0/1-P!$#$/:/1;*/ #%J I3A"#a +7_*J&$+#J+';& !J6n !%.}:&&Z#!$#%&Y/ OZ/1-P!$#$/Jk!%/ 9_%P%#%& !.>%-9#/ %&. 7/1!$!%/ >65#/ , j7@#-P%}- &k#L/3[@-!$/1 . U/1!%9-!"/3[@-P!%/1 G! /1!+#%Je')!N#5/1##%&!$&G 1#%&$';!Ii9&>P##JC/ !%9&-!MP/ [\-!%/ e#%' -!$-6 ( &;#L}:K';1&@GHKJ>$P-9#%/1B#%'/ !KiP9#U*JJnV1P!]!$#%%&!$!%!(5%e5/ \$#]_-65#/ YDlV#J(/1!$!%/ >65#/ %5#57 ,7P9O}\"*$/ #%#%&876!$& s y ( w 7*J%
* ) , , % $
" # " # " # & '( ' (' !" . ' .'
" '. '.
" +$ # . ' . ' ' ' '
& . . ' '
. . 8
4
G7)
) ' ' ' ' '' ' ' !HKJe#%&$';!]9&}:e/1k#/ &!]>P%-9#%/1Y%&15#Y##%Je')bf6g* " y t j7>) $P-9#%/1B$&\5#%&/ _#%(#%JU>P%} &'O7k#J_-!,$&_-/ %/1PW(')P&1!GF;&P./1!$9&!$/ #F)')1!I')1/ WL1$
}:&W/ !e/ #JPBV1P!e&_-65#%/1P!&7 4 G 3 2 G 6 j7}k Y';DlX#JVP1!(!$#%%&!$!%!#%J65#L&';6#&!]!L/3#/3e-PSP*P!(/ #J-5#/ !&G(?6+#%J/1!]';5#$#&7@#F*MO!$91
-5#/ !.$B-!%Dle9&')>-P#%/1W & /1!%9!%/3#F7T*J/ 9aJ/ #-$ /1!e-P!%&/1#J')P&D:#JPVP1!I!N#%!%!$&!&GIHKJ!$91%!I$K-!%-13n#JP#%-%}P-1_#IS_/ #%/19K&P&%W57*\7#%W#J*/3#JB#JPXPZ/ !%!$/1>65#%/1B%5#557 ,GV1P!b!N#%!%!')& !OP#b&P9&-k#%&k')1/ W De#%J#%&%')!O/1#J !&_-65#%/1P!&7 4 G 3 2 G 6 7!%/1P9&"#JX !!$#%%&!$!%!]$X!$ &ZDl>HKJPX')21/1PWO/ !"/1!N#&P/1%9#%g*C5%#%J.!$#%%&!$!(_-65#/ #J.9&';> &')&k#a5$!$91
-5#/ 8GIHKJL';!$#K*/1P& ^-!%Y!$91K/1OUb!/1!C#%JL&PZP/1!%!$/1>6#/1B5#%7 ,G
"O
=b~b
J?f
HKJ/ !B!$#%-P/ !^Dl9-!% +O!&7]5d "b!O%-P!%&!%1&3 Dl9&')>6$/1!$%&2!$!&GuHKJ;9&')';%9/6 /1W su% 6w GHKJ/ !`/ !{UJ/ WJn1!_-'n}\V')&c5b-P!%&!*,1@Dl-P9#%/1!V5#K*, 1!&G HKJP *_02 ,V')_}_e|-TJ6$'^ suO 3w GHKJP/1!z *1!`-P'e}\z')511g*!Z/ _#%&W%5#/ #JP%-WJO#%JL}\-P6NB$k9aJ}k.=,J) #& 7s 8gw *,!I1!$]9&;5-!%./1n#%J/1!z!N#-G
&$ "!$#&%S'A)(
HKJ;!$#6$*k20,')&T/ !L#%J.';!$#L*/1 Y-!% ';z/10/1P-!$#%%/> /19&5#/ !&GHKJZ';/1%&!% Dl(/ #%!e>\>-$/1!%/ W3B99&-%5#LDlK';kB/1P-!$#%%/> /19&5#/ !>HKJP(')P&|b
#%J&Vd LO!+$L}-/13#K->:B#J ,-!%!$/1!% s ( w Jk>:#%J&!$/1!&7 + # # t * 4 G G
MZP/1')&!$/165865 !%/ !&7P#%JL&P^/ !%9 !% /3#FB9 O}:! LDl%'e-15#Z9&9%P/1W#
+*-,)
*,
G ygv
KH J(#5!%>:$#+&_-65#%/1P!UDl *\7\_-65#/ G 8 7\+,7:&_-65#%/1 G7) 7\%(!%/ ';> / 6#% * * %&. , G yy .
, &% ., ! , , , +* * * * *J% # # !
#
%&. #65%Z51-!DlC#JL')89&!$#k#!U % ! .*-, v v%G * y 3%3 * y G y v y t A < $`{ $ * P ,
G y
1TDl-P9#/ !(%)-!$& 5#X#JP)*,1 !&GZ=,!%/ &nO9k#%
1-'))9&9%P/1WO# 6 W52PyW
? /1W-P% G y
m p p m6oIo)o6m pqEq3r-$ G y G"-k#/ #%/1!C5 -65#O5# % $"!%-}P!%9&$/1>P#%&O}kZ % Z_-6k#%/ #/ &!K51-65#%&5#+#Je*,1`}k G"HKJe#-P%}- &k#LS_/1#/ 9n&P&%W5/1!U!%3&Dl+5#]#%J
%59&&k##%#J^*, 47z5 #J;51-;DK#J*, M!$Jn!$#$&!$!'^}\51-6#&Dl%' * 4 G !$>\9&/P>%k59aJb/ !,#P+i *B5##%JLPL
%9&k##.#J"*,1c59&9&%/ W#* 4 +* , "! #$# G ygt *J% # # /1!C#SbDl$' #%JL1W1g*# 4 y 1 "&')( G 4y 3 ## %% v 73y ) 8& G 8 Gt G y 6 HKJ0&PP/1!$!%/ >65#/ #.7 ,7U/1! Pi&h5#B#JP0P0 %9&_#O# #%J*C "/1}:#J
>P>%k59aJ&!V}kB#JL%/ WeDl-9#/187 , 76/1!Kji>%!%!%!
*,
G y8
Gy )
G yG
t 73
i>
Ny 6v !
,
HKJL#%!$>\N#&_-65#%/1ZDl */1!
* * &% . , .
#%!$>\N#V&_-65#%/1BDl, , * / !K!%3&ZDl! ,, %&., ,
* * * *
!*J%L#JL65';>/ WeDl-9#/ Z/1!
PO#%JX/3#/ "!%-P%9&L#%'/ !
y
v t ji>
# . !
A ME$|C%$E{/ 9&O#J/ !;')& 1g*!Dl.#Jb/1k#W5#%/1D+#Jb}\-P6N}\-P6N9&P/ #/ /1!"51/ 8G I&19&/3#/ &!L0#J.#-P%}- &k#(S/ 2#/ 9"&%WB/ !K!%#K#.&%)5#K#JP]*C 4GzHKJP/1!K/1!C1!$e#%-PLDl,#J ,( *J/19aJ@769&k#%$;#,7*/1 @W#%)&$)*Jb#%J"*C 8/1!5>>%9aJ&@G
( "!$#&% 'A (
#F*M52R ' #- , * ' y ji> , *J% * '
#' * , 8v * % * , $ !+*
P ' /1!]#JP%';`/1!N#a9#B#Je*, 4GnHKJP;P2F_-65#/ ')z/1!L5>>1/ &&
#%J"*C 1!CDl ' # % 6v G $| C% $E { A MEHKJ/ !';&81!$.1 *!MDlC#JL2F!% /1>}:-P6$9&P/ #/ BB#JPL& 9/ #/ &!K5B#J#%-%}-P1&k#"S_/ #%/19X&%W
G"~U^*, `}:-$O9&/ #%/1b/1!U&&DlV#J(/1!$!%/ >65#/ %5#576!%/1P9&"#JLP2F_-65#/ Z';8/1!K-!$&b/1B#J/ !K%W/1@G
=?~".b$Ab
J?A
9&P2F')')&k#]91!$-%!"%(#J('^/ b#%>/19(DT#JP/1!+!N#-7cP!%&%z')P&1!VJ6}:&/1')> &')&k# 5#%&!N#&/1 #JY=C?zA 9&7C=C? 3 GHKJ%5%Z'^5_ ';& !5/11} n/1b#J.1/3#5#%-%n!%1&9#0')& !+*/1 `}:>%!%_#%&}\1g*LG(HKJP)jiP9#-5#/ )Dlz#JV !I!$#$&!$!%&!M/1!ID\9&-P%!%-!$&^!X!N#aN#/1PW">\/ k#TDlI1P';& !
Pb9&b}:L%*%/ #$#b!N'n}\ /19&13)9&9%/ W#7
* % , G
HKJLji59##%')!K%"!$Jg*b/ B&_-65#%/1 G7( , Z 9&Z}\"/ _#%&$>%#&O!7B#JP"1DE#N2
6J 5Y!$/15769&k9#%/187\@76O#%JL%/ WJk#$2FJZ!%/ 7>$-P9#/ 87P#%-%}P-1_#U/3[@-!$/1@7/1!$9&-P!/ [\-!$/187,>%!%!%-P%!$#%/ / _#%&%9#%/1/ !%!$/1>65#%/1@G 1K#%')!^'e-P!$#}:')P&1ji9&&>#eDl"#J;9&k&9#%/1@7z>%-9#/ 5/1!$9&-P!n/3[@-!$/1#%')!&7|*J/19aJ
$.iP9#&G.HKJ)#%-%}P-1_#X/3[@-P!%/1#&$' /1!"')& &-!%/ WB#J.W&%1/ &0W
/ &k#Jk>\5#J!%/1!V}kOA" ^
+5%1g* s ygw 7#J65#/ !
. * *, .
G t
*J%#J9!$#k# * v GzHKJ6 ')/1PW"9&kk#/1 ;! D:#JPU1!I!$#%%!%!';& !/ !e-!%-13}!% #J>P%>:!%';&IDlX#JB>$&!$!%-$&!.!$#%/ /1k#9#/ #%'O7
PO#%JL';& !K-!%b/ B#J/ !C*,$SB9O}:"!%-')'^5%/1&O!KDl 1g*! 9&'e}/15#/ D+#%JO1/1P$#-P% #%/ !%#%%>k #%&$'}_#$#a sutkgw #J /1&eF!$#$>/1&5#/ D T%-9#/ #&$' }k~U
#Ymo pq3rs ) w GHKJ/1!')&M/1!JP&%&5DE#U';Z /1B#JP/1!K!$#%-PG HKJP.*, z%f6&9#/1#%&$';!">$>:!%}k 1"/1}!$00|-P& s y 6w $-!%#%52W#JP&K*/ #%JO#%JL ';475B#JL9&'e}/15#/ B/1!KJ%&5DE#V';& 1LTG 2R1/ I>$>:!:}k^>\&/1157P5%S
M 1L5#!$S_/ sxtt5w /1!M-!%8GTHKJ/ !,')*/ 18}:"%Dl&$%&O#)!K#JPnP 1 ')4Gyy
HKJPB1/1PX';47z56>P#%& Dl(1g* V1P!n_-'e}:&eP 2R*,1%W/1P!&7z>$52>:!$&Y}k U
% / 9"5O{5- s y8w 76/1!K-P!%&@GMHKJL')P&@*/ 1@}:L9 1UTG 9&-}/ 9>%>\!%+}k=,5DE# s ygvw J6!B}:&-!%*/3#J9!N#ak#!O99&$/1PW #|-P&VPYc/ suw PO#%J-P!V/ !KJ&$5DE#%&V6')&O|caGHKJPeP/1#/1)5D8>$-P9#/ .#&$'}_;~U
#"mo pq3r@su ) w 7* 7
( * *, - t * * % t %&. G O3 021 / 3/ 021 3
56
56
*J% %&. % b#%JX9&!N#ak#%!U#a5S(#%JL51-!U>$>:!%Y/1b|-P&mo pq3rsut5w 7#%J65#V/1!7) * v (* y HKJ/ !"';`J65!]*,1`%f&9#%/1#%&$';!"5*/1 {#%J-P!"#">$>:&%3Y')/1')/19"#%Jn#-PN2}-P1&P9&X9&1!%]#;e*C514G/1P9&(#%J/1!+/1!]JP/1WJ1!]_-'n}\]';47#JeP/1!%!$/1>6#/1b#!%"/1!+')& &-!$/1W.#JP(5!%!%-P';>P#%/1B#%J65#K#JPX!$'^51@!$9 &!V$X/ !%#%%>P/19]/ O9aJ
9#U5O#%J_-!, t , G %6 HKJX/ !%!%/ >65#%/1B-5#/ Z/1!K!% ODlK /1B#J"Dl 1g*/1PWnDl%'
* * - ,,,%. , G (
+* * * * , ~V#]#%JL/ [\&$&9&!/1B9';>%/ !%^*/3#JZ&_ -6#/1 4 G y jGTHKJ! L/ [\ -! !%/ ^#%&%' /1!CW2
/1&876P#J">$P-9#%/187 %&. % 7/1!K')%+9&9-5#%&3!%9&$/1}:&O-!%/ W.UG> SCV{ N E_ 9 A < $`{
15Dl-9#%/1P!|%T-!$&n5#c#JT*,1}\-P6$/1&!7
"#J !|!$#%%&!$!%!$IJ6 &
99&$/1PWL#%X#%JK>$>\!6D@c/1;5)|!%9aJ/1 su%8 w 7_i#;#"#%J%U/ ';!%/ !GHKJ)/ !%!%/ >65#%/1#/1!L!$#n! , # # $ +%,' ]#"#J))
%9&k#L#Z#J*,1G;?6- 2#%J&$';$7P#%J"!$#%%!%!%!+5%]!$#V/1B 9&\!N#$' 1/ W&^9&%/ 65#%]!$!$#%&' */3#JB-P/ #}65!%9#%%! " ! n # $# % # # ! 7T*J&$ # /1!(#J-P/ #e*, ,$'^5
&9#%BP / !)#%Jb-P/ #)*C51K#aPW&k#/1C9#%;#%J65#;/1!;1/ W&*/ #%J#%Jbf*L7K!$&6W-% G GHKJ.#J/ %9&';>:_#L/ #J/ !"$#%JWz!%#XDC}65!%9#%!X/1!]#a5S& !#%J^9%!$!N2F>P%-9#eD& P # GZHKJ;!$#$&!$!%&!/ #%J/1!X19 Y!$';')#%%/ 9.f* $;!$#
99&$/1PW.#%
y
ntt
n
?/ W-$ G Eo pqPp "o p m6o pq m o r 6m,o p m m o qEq m # ' y v%G )S*\7 ' v O3 8 *O ' v %6 6 *\76*J&$ * # # *-, GU~U5##%J65#7M!.%!%-3#)DV!$';')#%$7 ' ' v G # # / !9&')>-P#%& Dl%'#JPO W1g*LG !$/1')>1"9%/ 65#]#%P!$Dl$'^5#%/1B*/ 1@#%J&b>%-9X#%JXDl11g*/ W)=C$#%&!$/$9&-$*/11 *,!"W/ e#J.>$>\"!%/ WDl / B%&9/1$9&-15#/ W#F*M52FP/1')&!$/165@f6g*LG
ygt
&
AA ( (~
HKJI1L0')P&8/ !.')/ 69&5#/ ^5D`#%J" ')4GzR#9!$/1!$#%!D`#%JL ')P&@#%&%')!
P^i#%"#&$';!T#%J65#9&$%9##J&$%P&-!}:&J6/1-P5D@#JPV 2R';&691!$K#L*C 1!GHKJX')8/1! G )
, " * ' * # # t + # # t # # ' ' t t *
'
* ' # # ' # # " # # 6 , ' G G *J% 5 $]#aS5&bDl$' #%JL 2F')cZ#JPXP* 9!N#ak#!U$"
''* v 6* v t# / !n#JPB-/ #*, ,$'^5M9#%&G RDU')%^#%J6*, C$'^Mi/1!N#!7MP 0#J91!$&!$#*,1c/ !K/19%>:%5#87!% 6W-$ G t G
n
? /1W-% G t pqPp o + Lo6m pqEq pq Eo m o rHKJ/ !%!%/ >65#%/1#%&!$&7V#JP/1!%!$/1>6#/15#%&_-65#%/15#J*,1U}\-6N9/3#/1!%L')P&1Z!/1B#JPX ';&@&!$9&%/ }\b/ b&9#/1 G t G y G
f !( f $
A
%S'A)(
KH Jn';&c5D>:&&/1157\P%S
U&1X#!%S_/ suttw /1!V)D/ %3B%9&&k#+';&c#%J65#U';& !#%JC>$&!%!$-%!N#5/1e/ _#%&%9#%/1X#&$' }kn]2R1/ |$&kL#!%&7 G
* , * # %&. * , . . ty . .
* * $ * $# * * * . . . . t . .
G tv * * . . . .
y43
*J%
6 5 65 6 5 65 5 6 . . 5 6 HKJ(51 ')\!$&'; !C#%e*,$S;D/ %3*,1\*/3#J-P#C*,1 \ %f&9#%/1#%&$';!7P*J/19aJB/ !K
/ ';>:$#k#]Dl#-$eDl]#J.!$-9&9&!%!XD,k')z/1k#%&0#%B}\.-!$&0f6g*!(/
$-^P59&W&')#%%/1!I/191-/ WL!%&%\*, 6%'; !z*/ #JP/1.#JV';/1@GHKJ9!$#k#!U%)#* t 73 * y * 3 ) #* $ v * $ y t * * y % 6 * v 73HKJe 1 ')c/1!V !%;)J/ WJbVP1!V_-'e}:&U';&76O#JX/ !%!%/ >65#%/1B#!%&7#%J;P/1!%!$/1>6#/10%5#.-5#/ P0#%J)*, T}\-P6N9&P/ #/ !L$;')& &0!X/1#%JL ';&@&!$9&%/ }\b/ b&9#/1 G t G y G
(
f (
%S'A)(
HKJ)1g* V1P!(_-'e}:&L')P&z>$>:!%}k +5%1/90|-P& s y8w -!$&!L#J /1&C>$&!%!$-%(!$#%/ O')&8>P%>:!%b}kZ|-P&mo pq3r`sutw 7 * *, - t * 025 61 3 /
* ) % %&. ( v * 3 ) * %&./ yy t 6%025 661 yy t 3, - * v vPy6 % * $ !
v
gy%
6* t
,'3/0 25 61 G tPy *J% ' /1!C#%JL$'^@/1!N#a9"##J"*,18
+. # .
HKJ(';{9!N#ak#! * * # SX#JL51 -P&!
. # .
y G 6 v ! G 3 7%&!$>\9#%/ GVHKJPn/ !%!%/ 2>6#/1Z#%&!$/1!K')P&1O!, , Ny * * G tk t
t
*J%C#%JC6')>/ WUDl-P9#/ e/ !9aJ!$&)! y ygv ! 7!%& s y8 w GTO/ 69#/1!
$X1!$/1k#$-P9&&O/1#%JL/1!$!%/ >65#/ B&_-6#/187P*J/ 9aJb/ Z#%J/1!K g* !K_-'e}:&
>$>:!cJ!K#J"Dl$'
,,
,%.**
.
# # , , ** * * % $ , . .
, * * . , ! ! . , !
y6
G tt
*J%
y %8%6 * y ) * %$ v ji> (
y G
..
, , *
A ME$|C%$E{/ 9&"#%J/1!')8/1!V1g* VP1!_-'e}:&')P&47/ #/ _#%&W%5#!K#JL}:-65$Z^}:-65$)9&P/ #%/1;/1!M5 /18G J';W&-!CA]/ %/ 9aJ1#}:- $.9/3#/1;/ !/ ';>:!$&.;& 9/ #/ &!)!$#%%!%!%!&GHKJV/1!$!%/1>5#/ .5#%U/ !!$##% . #K#J"*,1G
( (
%S'A)(
HKJ/ !e')M/ !nPDKDl* $ /15}1)>%!%!$-%B!N#5/1 ')P&1!(/10#J / #%-$GR#n/1!9-}/19>P%>:!5`Dl%' +bNH #J65#&7c/1Y#%JeDl$' >$>:!%}_{5-"0c/ suw 7!$&&')!e#O*,%S _-/3#)*,1I*/ #JP-P#n*, M$f69#/ #%&%')!&GbHKJB>$&!%!$-%B!N#%/10#&$'$! G t 3
"*J% * , * ' . . ty , Ny G tS6
v ( % t % . v ( % .
. # . #v
. -. # . #
* . *
t ! %
! !
%
* ' ' ) ' 8 % %&. '
* y6 3 t yy v . . t %&. v vS6 . % . - % % %v y* ' ' * ' ' t * ' ' #. . y . ( . ygt * #v y* t
'* ' .
! ! G ( . v * . % . ty(
*J%
- * $ *
'* y * v 6%6
* t3y $ ' . . ( y G ) $ * v v
KH J;|c+')z/1!XBJ/ WJ0VP1!L_-'e}:&X')47c50#%J./1!$!%/ >65#/ #!%&7|#J/ !%!$/1>65#%/1Y5#%n&_-6#/1
#JPn*C51}:-P6$b9&/ #%/1P!]$e';1&Y9&9%P/1W#%)#%JL ';8&!$9&$/1}:&O/1Z!%9#/ G t G y G
& ( (+( f % 'A ( "
f ( %
KH J/ !./1!.';/ i 5DU#F*M5#J';& !e!%9&$/1}:& }:
7, #J_-!.#JB>P%&!$!%-$b!N#%/1/ _#%&%9#%/1Y#%&$' Dl$' #%J|c';&{/1!U9&'n}/1Y*/ #%J#Jn/1!$!%/1>5#/ b#%&!$+Dl%'#%J+';4G0')')P/ 69&5#/ !X'e-!$#e}\B';)#';/1k#a5/1 $ /1&}/1 / #FGYHKJ!$1g*>%!%!$-%!N#%/10#&$' 'e-!$#n-!%^b65';>/ WZDl-9#%/1@7 7_-6I#Y#%J65#(-!% /1#%J(P/1!%!$/1>6#/1^#!%7!%/1P9&LLD{#JL$ /15}/1 / #F.'^P !/1!C#J5##JL!%-P'D{#J/ !%!$/1>65#%/1e#%&$'b7 , 7_#%JK!% * >$&!%!$-%V!$#%/ e#%'O7 7k!%J-1.W"#"&$(/3D6#J9%$&!%>:P/1W" 1!{!$#%%&!$!zW&!|#U&&$GHKJP/1!{%&_-/ %'; _#`*/1 #`}\Dl- 11L-2 &!%!|#JPM65';>/ WDl-9#%/1X/1!{ !%-!$&eX#J!% g* >$&!%!$-%,!$#%/1L#%'OG`HKJPM65';>/ WDl-P9#/ Y/ !9aJ!%! O/1!V-!%/1Z-5#/ ! 4 G tk K 4 G tS6 jGC?6-N#JN2')%57@#JP9&!N#ak#%!X/ #J%>/ >6$#]DI#J>$&!$!%-$)!N#%/1#%&%'O78-5#/ 4 G t ( j7/ !V')/ 6875!V!$-WW!$#%&Y}kO=,%5DE#UO|-P& s yyw 7#%';/ v 6%6 $ ! * ' ';/ v ( $ ! *
y8
h i/ !$';')#%%/ 9}\P*/3#J !%')5#J%&B&*,!b9aJP!% !Z 6%!N#Z#&!N#O9!$Gdi>\%/ ';_#V65#a0i/1!N#!7 U-6PW mo pq3r+s y ) w 7CDl#F*M !^_-'e}:&$!&7K65'; _yg*Cv !(P5 /11
} 15 7@5) ) 0k#%yJv% G,.HKJP/ [\($&!$k#U#"9#-!$$X}*,- &!V99&)')')>-P#%&& b!+*,}\Dl%)%X-!%k8ZG;D`/1P#J9&!$
- %9 ;96 7GPe#%J&$]/1!';%+ji>\%/1')&k#65#ang5/ %>:!%`}kY|-"J6$'^ suO3w 7\!%&)&9#%/1 G G G U*,!" !%-!$&876*J/ 9aJb/ !K#JL ')P&8!%9%/1}:&O/1b9#%/1 G t G y GJ
?
A
HKJ)W$/1!"-!$&/1#J.9';>P-P#a5#%/1P!"%)Bj2F} 9aSb!$#%%-9#-$& ')&!$J9!$/1!$#%/1WZD9&1 !cDlc#JT#F*M+J/ WJn1!|_-'e}:&{';1!|X9&1 !|Dl8#J1g* 1!|_-'e}:&')P&47\!% W-% t G y GLHKJ9&k#%!XDI#Jn/1%')!$#]9&& 1!+*M&$195#%&5#]/1!N#a9&!
D ' ( tv ' ( v y 7P%&!$>\9#%/ GJ
~~AbP~
b ?
KH J.J/ WJ+$&]-P>_*/ !%9aJ';57+ !$& sxt5w 7@/1!]-!$&*J0P/1!%9%#/1/1W;#J92
&9#%/1O#%')!U/ Z#%JX';')&k#%-'&_-6#/1!&GCHKJP 6$!$#N2F$&U9&9-#XJ_$/1O!%9aJ';y)
100 x 40 cells
100 x 50 cells
3.0
3.0
2.5
2.5
2.0
2.0
1.5
1.5
1.0
1.0
0.5
0.5
0.0
0.0
100 x 40 cells0.25
0.20
0.15
0.10
0.05
0.00
2
3
4
5
2
3
4
5
2.90
3.00
3.10
3.20
?/ W-$ t G y H ^m p m pqEq o + ep p ! ^m p m
m $m Eo^ o 6 m q VmK* ,
m q3r (o6m o p m q3p m^m6oVo6m m + Uo 6m m p r/ !V-P!%&ZDlK/3#%#%)/ O1:#-$}-19&L-5#/ !&G
J
|"""lb
|""z$P~"
F #O9&/ #%/1P!^*,%0}P#/1-!%/ W #J%!%-3#!BDn >%/1-!Z9';>P-P#a5#%/15De9/1%9-:&$/1')&k#!GzHKJ & 9/ #Fn*,!D\9&-$!%!$#]#%^&%7\O#-$}- &k#]_-6k#%/ #/ &!*,%e!$#U#^ g* >\!%/ #%/ X5 -&!7:ji9&&>#]Dl#J 2F!N#%!%!7M*J/ 9aJ *,!.!%#)#&%PG HKJbi/1!N';')#%%/19^9aJ6Kf6g**C5!)9')>-P#87Dl$' *JP/19aJ>$ 61X*C5!]#}:!%1&9#8GLHKJ/1 #V*C5!"9aJ!%#B}:5# v (P7*J%( ^#JX!%S_/1ZDl%/ 9#%/1Z9&)9/1&k#V*C5!+5/11} +Dl%' ';&!%-$&')&k#! G,HKJ_-!V#J/ 1#M>P% 6 &!D| 5%/1}1!I9&- ;}:#aS5&^*J%+#%JV9aJ6\f6g*$9aJPJP/1!!%S_/1Dl$/19#%/1B9)9&/1k#G]-P# #M9&P/ #/ !T*M&%+!%#K!MJP';W&-!,~U&-P'^^9&P/ #/ !TDlM165$/6%5#8GTF#JK9';>P-P#a5#%/1P!z-!%/ W"#JK g*1!_-'e}:& *_02 ,.')&{
) ) ygv 7\;!N#a} (!$1-#/1Y/1!V%&9aJY!$&>655#%/19&9-%!(5# v GPyg 78!% W-% t G 3 GHKJP)JP/1WJ0 !"_-'e}:&L';1!]/ #!$&>6%5#LDl C#%J/1! !_-'e}:&&GyG
0.006k-epsilonIPexp
Cf
0.003
0
0.6
?/ W-% t G
*
, 6 Gkygv r
po
1
x/L
0.3
0Cp
k-epsilonIPexp-0.3
-0.60.6
?`/1W-$ t G t
*
po
v
, 6 7G kygv r
x/L
1
0.006low Re k-epsilonexp
Cf
0.003
0
J
?/ W-% t G 3
~"W"bP~"
o* p
, ) ) k ygvgrx/L
R #9&B}\+9&91-P&B#J6#KU *,$S_!K}\#%#,#J#J *k20,X';@P#J65#,*C \Dl-P92#%/1!V)#V*,%S$Z*M&1c*J.!%&>5#%/1O!%JP-1b99&-G >P>%k59aJ/1W.#JP(!$&>2
%5#/ B>:/1k#7*C51@Dl-P9#/ !K5%".1W&M51/1B#J_-!W/3"%/ !%+#%./1!$9&%>69/1!&GHKJ+1g* *_-2 ,L';6!%&';!M#(*M$S)B}\#%##%J6^#%J]UG_HKJUf6g*!%&>5#%&!5#
) ) yv */ #%J#%J/1!X';47c*J/19aJ !n5#n9&9-(*J #J)#%J&(';& !
$-!$&8G Ug*M&7#J/ !n9&';>65%/1!$ / !n#n&N $&15k#!%/ 9%JBU *C5!e*C Dl-P9#/ 2R}6!%8G ')%X/1k#%&%!$#%/1W;9&')>6$/1!%O*M- }\L#)#!$#+#%J/1!V1g* 1!_-'e}:&. *_-2 ,e')P&@&%!$-!+!$')"1g* 1!_-'e}:&VUG 51%f&9#%/1"#%&%')!c/1]#%JT>$&!%!$-%j2F!N#5/1"#%' $zi91-(/ X=C?zAL_2F?z t AeGHKJ/ !]/1!U}\9-P!%/ #U/1!+1')!N#+/ ';>:!%!$/1} "#/ ';> &')&k#V#J!%n#%&%')!]/ W&%`*,GHKJ/ !CD9#/ !K !%.e!%-%9"DP/1!%9%>69/1&!K/ *C5132R}\-^f6g*!VB*/1 \}:"/1k!$#%/32Wk#&O}:&1g*LG
y
F# *M52R/1')&!$/1|9aJ6`f6g* *,!]9&';>-#&9aJP/1fPbDlV}-WW/ W>-P%>:!%!L!]!$/1')>1(= K2F[@9#/3n#%&!N#"9!$GUdiP>:&$/1')&k#!+}_b|-PDl suyw $e5/11}15GCHKJ !I_-'e}:&T}6!$&)#J';i/1'e-P' &19&/3#FP)J D#JPKJ&/ WJk#ID\#%JK9aJ6P&/ ! ! tv ) vv G?
"""PA"
?
~~AbP~
b ?
?
Ab" b
J?f
!,!N#$&!%!K')& !I*M&$]-!$&Z;#JU';& !,5%7_#JP+ ';47k#J 1X')&7#%J. 1 ')47#Je{cK')P&`Y#%J T%!%&k#L')P&4G `')& !+$(#%J%-WJ3!%9%/1}:&b/1Z!%9#%/1 G t G
HKJVJ/ WJ&T%-P>_*/ ^!$9aJ&')7 + !$& sut5w 7_/1!T-!$&;/1#J')')&k#-' &_-65#%/1P!&7
PO#%JLJ_$/1O!%9aJ';X/1!K-P!%&b/1O \#-P%}- &9L&_-65#%/1!G
""?AM
KH J0 ')&]W/ !Z&$%-!Z$'^5+!$#%%!%!O/1!N#%/ }-P#%/187K*J/ 9aJ 9&}\!$&/ %9#3^Dl$' #JPX>P%&!$!%-$(!N#%/1Z/1k#%&59#/ B#%'O7&_-65#%/1 G @3 GTHKJL>$P-9#%/1#%&%')!Dle#JP !$#$&!$!^P#%J !N#%!%!;%B&$7CP#%J_-!;_-65#/ ! 4 G ( e5%/ &k#/ 9\DlK}\5#JO!$#$&!$!%&!+B#J_-!
- !$/1W)#J/ !';&G,HKJ !$#%%&!$!+/ !Vg&%>P%&P/19#%&91!$X#%)#%JX*, `5b*/ 18W/3X%/ !%#%)#%JL&$>%/19#& !$#%%!%!&7!$& 6W-$ 3 G y G 51$f69#/ ^#%&%')!T*/1 6!%3#J/ !M>$} &'!/1.#J/1L';&7k!% 6W-P%&! 3 G 23 G 3 GC/19"*C c%f6&9#/1b#%')!/191-"*,1cP%';8/ !$#9&!]PO*,1cP%';8-P/ #
&9#%%!7,#JP&!%O$B#&$-P!%Dl-PK/1 9&!)5D]k W& / #FG b& !e#J65#.')/1')/19#%J]>$&!%9&LD{X*C :*/3#J-P#,*,1:/ !$#a59&!%U/1!N#5>%Dl&$%&@7!%-9aJO!M#JLP 1')P&4GHKJ/1!C9&>P#%-%!,#J"!N#$&!%!KP/1!$#%%/ }-P#/ ^/ ^!%!%9&57!%& W-%! 3 G 2 3 G 3 GHKJL||')P&T*,%S_!e& }:#$#&n!%Jg*!e}:#$#&n9&9-590 #%J A 9aJ6P&Mf* #%J6
k#JP&n')&G #%-P95#%& Dl$' DC#JP/1!n')&T*,! !%b#%&!N#& */3#J 9!N#ak#!
!
0.50.4
0.3
0.2
0.2
0.1
0.1
!
ygv ' #0.5
00
1
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
00
##?/ W-% 3 G y 0.5
compo exp
0.4
0.3
00
0.5
compo exp
00
1
comp+ exp
yv ' #U ygv ' #0.5
ygv * # 5
10
1
15
20
^o6m
m q3r
99&$/1PWZ#%O=,5DE# s ygvw 78#%J65#"/ ! * v (BP * ' v /1_-65#/ G t (PGXHKJ/1!"')&79&1 &B#Jn=KB';&7Wk(b9&9-59Z9&';>65} ]##J5#V}P#a5/1b-!$/1W#%JeP 1 p @m q
)' P&47P!%& 6W-%! 3 G 2 3 G 3 G~U!$/1WP/ 69&k#e}:& #!.$^Wk5/1 }k -!$/1Wb1g* V1P!e_-'e}:&e')P&47!*,1Dl-9#/ !C5%+P&!%/ W^DlC5^*M%S$;*,1:^#JP/1!IDl-13.&1>\}\-6N1g&GHKJ.9aJ6Tf6g* *,!L-!%Dl+#%J.9&P!$#a5_#%!(/ #J T%!%_#(')47c5#J$&!%-P #!KDl$' #J5#';c%L!$Jg*Y/1 W-%! 3 G 6 3 7G (PG
t
!
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
00
0.2
?`/1W-$ 3 G
0.4
0.6
0.8
00
1
2
4
6
# #
8
10
#
12
14
16
18
20
q m o6m p @m q &r m q Eo p
0.90.140.8
!
GL
0.7
0.12
SSG0.6
0.1CS
0.5
0.08
LLI
0.4
o
exp0.06
0.30.040.20.02
0.100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
' #
?/ W-% 3 G t ' q m o6m
O3
00
0.1
0.2
0.3
p @ m q
0.4
0.5
0.6
0.7
' #
0.8
0.9
1
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
00
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
00
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
' # ' #?/ W-$ 3 G 3 ' p ' q m o 6m p @ m q &r m m p ;o a m r
Reh/2=3080030.0PresentExp. Laufer
+
20.0
u
!
0.9
10.0
0.0 110
0
10
1
2
10
10
3
10
4
10
+
y
?/ W-% 3 G 6
p @ m q
;o6m%6
m m6o m 3q r m q Eo
q m r
7
0.1
0.080.060.040.0200
0.1
0.2
0.3
0.4
0.5y/(d/2)
0.6
0.7
0.8
0.9
1
0.1
0.2
0.3
0.4
0.5y/(d/2)
0.6
0.7
0.8
0.9
1
0.2
ygvv
0.150.10.0500
? / W-$:q
oo m p '
3 XoG ( 6m p@ m @m q X o 6 m 0o6m am m 6(oo 6 m$
m q3r 6m oam @ m (o o6 m o + r ' q q p
q 'p q p
q
)o 6m p 6m
ooFm q @m p ^o6m 3q r
(
HKJ(f6g* g&"^}9aSk*C$2RD59&/1PW!$#%&>Y*,!]9';>P-P#-!%/ WB^ g* V1P!+_-'e}:&UG6HKJ%(%XA"~+B5#a}kOc b/ su ( w Ge
"""PA"
J?f
!K!$#%%!%!';1!,*M&$"-!%b')P&1 /1WL#JP]#-$}-19&"Z#%J"}69aSk*,%2RD9/1W!N#&>@GMHKJL')P&1!K-P!%&Y% HKJP( ')&8P&!%9%/ }\b/ O!$&9#/1 G t G y G 1L')P&8!%9%/1}:&O/1Z!$&9#%/1 G t G G HKJP2 HKJPn|cM')&8P&!%9%/ }\Y/1Z!$&9#%/1 G t G 6 G HKJP T%!%_#U')8!%9&$/1}:&b/1B!%9#%/1 G t G (Ge
~~AbP~
e
b ?
HKJVJ/ WJ&T%-P>_*/ ^!$9aJ&')7 + !$& sut5w 7_/1!T-!$&;/1#J')')&k#-' &_-65#%/1P!&7
PO#%JLJ_$/1O!%9aJ';X/1!K-P!%&b/1O \#-P%}- &9L&_-65#%/1!G?AbW&O$ |
KH J(9&')>-P#5#/ 6@';/1Z/1!V!%JP*Y/1 6W-$ 6 G y 7:Z#JPe !U_-'n}\U}65!%&b#J(!$#>J&/ WJk#"PYDl%n!$#%%&' & 9/ #FZ/1!6Cygvv GF #U>% 61!]$(#a5S&Dl$'A"~]Z65#a7\5b#%J(/ 1#/1!V195#%& ygv !$#>J /1 WJk#!V->!N#$'D`#J(!$#>8GKHKJjiP>!%/ %5#/ / ! y G 7C #%JY-P# #)/1!)>%!%_#')P&$5#$#a9aJP&!%')*J5#]#15#57@!% 6W-$ 6 G t 7@}:&9&-!$)5D-%>$&/ 9#%/1
D`#JL!$J!N#%!%!7 76/ Z#%JL!%J&%W/1@7!% 6W-% 6 G 3 G
)
k-epsilon-model
y/h
IP-model
y/h
7
7
6
6
5
5
4
4
3
3
2
2
1
1
0
00
2
4
6
8
x/h 10
0
GL-model
y/h
2
4
7
6
6
5
5
4
4
3
3
2
2
1
1
8
x/h 10
LLI-model
y/h
7
6
0
00
2
4
6
8
0
x/h 10
2
4
6
Pr esent - model
y/h7654321
00
2
4
6
8
10 x/h
?/1W-P% 6 G o m p q @m Lo6m p p p Fo m @r
G
8
x/h 10
3o2.5
( t
DNSIPGLLLIPresent
2.5
2
y/h
y/h
2
1.5
1.5
1
1
0.5
0.5
00
##
0.5
00.5
1.5
2
2
1.5
1
0.5
0.5
3
0.5
00
1
2
y/h
2
1.5
1
0.5
0.5
?/ W-$ 6 G tq %p o + &r
0.4
##0.5
0.6
0.7
0.8
0.9
1
00
6m p p p o m r
tv
0.3
## yG
0.4
0.5
0.6
0.7
0.8
0.9
1
0.6
0.7
0.8
0.9
1
1.5
1
0.3
0.2
3
2.5
0.2
0.1
y6
2.5
0.1
1
1.5
1
0.5
ygv
3
##
##
2.5
0
0
(
2.5
00.5
y/h
1
y/h
y/h
3
00
3
3
0.1
0.2
0.3
m q Eo
##0.4
0.5
q m p o ]mm6o
3
( t
o2.5
DNSIPGLLLIPresent
2.5
2
y/h
y/h
2
1.5
1
0.5
0.5
#
00.01 0.008 0.006 0.004 0.002
0
0.002
0.004
0.006
0.008
00.02
0.01
2
2
y/h
2.5
1.5
1
0.5
0.5
3
# 0.005
0.005
3
2.5
2.5
2
2
1.5
1
0.5
0.5
# 0
0.002
0.004
0.006
0.008
?`/1W-$ 6 G 3 6 m p p p o m
0.01
tPy
0
0.005
0.01
ygv
# yG
0
0.002
0.004
0.006
0.008
0.01
0.002
0.004
0.006
0.008
0.01
1.5
1
00.01 0.008 0.006 0.004 0.002
0.005
00.01 0.008 0.006 0.004 0.002
0.01
y6
0
#
1.5
1
0.01
0.01
3
2.5
0.015
0.015
(
y/h
y/h
3
y/h
1.5
1
00.02
3
3
#
00.01 0.008 0.006 0.004 0.002
0
r q m (p o ]mm6o q %p o+ &r
HKJ.ji#X#%&!N#L9!$9aJ!% / !+#Jef* g( AJP/117\!$& 6W-P% (PG y 7@*J/ 9aJ/ !"^#!$#9&!%L/1#%JLdIK= "?H = 5 U p o p p m Xp m o pq q3p o + 0mo
q m 6o q 7 #L$1!$%-J y4G%G 3 7 s y&w 7*JP&%T#%J&!$$&!$- #%!8*,%I>%!%_#%&8GHKJ/ !,#!$#9&!%]J!C}:&&Z')!$-%B}k 1')&/1Zmo pq3rcs 6w 7PZBji#&P!%/ "_-'e}:&CDjiP>:&$/1')&k#a5c65#a/ !g5/
')#%&$!% =,J{JP&/1WJ_#&7 y8v ')' V/1 @J/1WJk#7 )')'HKJ(#>bDz#JPnJ/ 1c!%JP-1b}\(195#%& ygvv ';'5DE#%&V#J(/1 #UO#J(-P# #U!%J-1}:X5#V)!$-P)9&/ &k#V/1!N#a9Lg*!$#%%5'bGM?6-$#%J&$';$7Pf*h>6%';#%!$ *C#& 7 A]!%/3#F7 ygvvv S_W 5' $
#"/ &';5#/ 9+/1!$9&!$/ #F7 y kygv ' 5! Ob9&&k#%&% /1]& 9/ #FZ5#K#%JL/1 #&7 # y 3 8 ' 5!HKJ/ !W/ &!V;1!K_-'e}:&DJ
?
)
#
( vIvvv
A
HKJLW$/1!K-P!%&Z*M&%X9&$5#%&Z-!$/1W#JPXN=CdZ2 =C?zA ';!%JZW&PGHKJPX')&!$JZ!%/1&!Dl/3[@%_#P 2R*,1@#%%&5#')&k#!V$ @Dl-9#/1O')& ! = B ! 76!$& 6W-$ (PG cg* 1!_-'e}:&')1! =F B 7!% 6W-% (PG ttk
Inlet
Outlet
Upper wall
Lower wall
?/1W-% P( G y p
J
"""PA"
qEq
r
J?f
!_ %S'A (
f ( 5
HKJ!N#aP6% *_20,.')P&{&!$9&%/ }\/1&9#/1 G G y *C5!]-!%#W#JU*/3#JY#%Jn * !_-'e}:&KDl%'n--`8-$/@7')(+*,D-6%E,D-a,2F- 8/@78&:6%E&/)*e-0%E F-^E&(Mi1&7B-6:6%,DC Z "$#&/@7%:6:B(=:^/)7`-6#&%1 *(21jp2%*e-0%E 4sG&:B-6#&%:b2l
k- model
y/h3.02.5
2.5
2.0
2.0
1.5
1.5
1.0
1.0
0.5
0.5
0.0
0.00
1
\ /@~=G&:B% Hx Z l
2
RSM
y/h3.0
3
4
0
x/h
"
1
2
3
4
x/h
+
SSG model
y/h3.02.52.01.51.00.50.00
\ /@~=G&:B% Hx Z c
"
1
2
3
4
x/h
+
b>c
LS model
y/h3.0
HL model
y/h3.0
2.5
2.5
2.0
2.0
1.5
1.5
1.0
1.0
0.5
0.5
0.0
0.00
1
2
\ /@~=G&:B% xHZnx
"
3
4
0
x/h
1
2
3
4
x/h
+
E&(Mi1&7u-0:B%,2CkU`7B%%9~=GH:6%7 xHZ U xHZ ,21&E xTZ Z "$#H% '@(Mi %d+1&(2')E&7 1jG&CF5%:QC;(+E&%'@7,2:B%CG&*_# C(=:B%,2**G&:0,D-6%/)1 K L -0#&/@7KM:6b %~2/)(=1 Z K(Ml io%ep=%:Uv-0#&% C;(+E&%'o( p2%:B8&:6%E&/)*e-07-0#&%-6G&:6F&GH')%1>- j/@1&%-6/)*%1&%:6~2dX,D-o-6#&%a-6(=8 (24P-0#&%#H/)')' Z "$#H/)7o/@7o,D')76(!-0:BG&%a4s(=:]-0#&%a7B-0,21&E9,2:BE jt C(TEH%'hUV7B%%9~2G&:6% xHZ Z "$#H%:6%,276(214s(=:-6#&/)7/)7-0#&,D-`-6#&%,2**%')%:6,D-0/@(=1w(D4-0#&%%9(Mi ( p2%:-6#&%-0(=8k(=:v-0#H%F&')(+* .KM,2L ~=%(24 -0#&% %9(MiJ/)7 j1&(Mi1f-6(*:6%,D-0%^8&:B(=F&')%C;7U&*,DG&76/@1&~3-0(+(3#&/)~=#k,8&:B(TEHG&*-6/)(=13(2"4 j/)1H%-0/@*v%1H%:6~Ddi#&%'1 jt `C(+E&%'@7,2:B%$G&76%E Z 7A76GH*_#X,27-6#&% C(TE&%'E&(X,2**(=G&1>-4s(=:$-0#&/@78H#&%1&(2C;%1&(=1w7B/)1&*%!-6#&%!8&:6(+E&G&*e-0/)(21k-6%:6C7/)1Q-0#&%!7B-6:6%767% +G&,D-0/@(=1&7,2:B%%eRH,2*e- Z!\ /@~=G&:6% xHZ ,2'@76(X7B#&(Mi7-0#9,D-a-0#&%:6%3/@7`F-i/@-6#%eRT8-07i/q-0# -6#&% C(TEH%'vK -0L #&,21 -6#&% C;(+E&%'$/)1 -0#&%9:B7B-;89,2:B-(24a-0#&%k76%89,2:6,D-0%E :6%~=/)(=1PUi#&%:6%,27-0#&% C(+E&%' /)7aC;(=:B%,2**G&:6,D-0%/)1w-6#&%:6%,2:`8&,2:B-,21&E/)1f-0#&%4|,D:aio, 2% Z "$#H/)7/@719,D-6G&:0,D'o76/@1&*%-0#&'% %9(Mi ,.-6-_,D*_#&%E -6(T(%,2:6'qd G&76/@1&~w-0#H% C(TE&%'o,D1&E E&(Mi1&7u-0:6%,2CE&/@76*:6%8&,21&*/@%7-0#jG&7(T**G&:,27,*(=1H76% jG&%1&*% Z #&%,2:7B-0:B%7B7a8&:B(29'@%7,2:6%^7B#&(Mi1w/)1Q9~2G&:6%% 7,D1&E/)1&E&/@*,D-6%v:6%,276(219,2F&'qd3~=(+(TE,2~2:6%%C;%1>-Ai/@-0#%SRH8-07?%SRH*%8HxHZ Kl 4s(=:-6#&4s(=:$-6#&%^',D-B-0%:o89,2:B-(D4g-0#H%!7B%89,D:0,D-6%Ek:6%~2/)(=1k,27$E&/@76*G&767B%E,2F-6%:6%7B-6/)1&~-6(76%%$#H( i -0#H%$*G&:up2,.-0G&:B%$(249-0#&% %&( i ,5%*e-07-0GH:6F&G&'@%1&*%$/)1-6#&%$C(TE&%')7 Z G&:upD,D-0G&:B%*,21kF5%C%,27BG&:6%EwF>d -6#&%^*G&:up2,.-0G&:B%!:6,2E&/@G&7
&& ' &&K & K! ' #" %$ ! && '( *(=1&7u#&/)~2#Q*G&:up2,.-0G&:B%:6,2E&/)GH7*),+ ')(MiJ*G&:BpD,D-6G&:6%
z /@-6# . - 0/ '( *(21&7B2
K
.1 U&-0#&/@7$% jG9,D-6/)(=1kF-0/q-rdk*,21~=:6,28&/@*,2'@'@dXF5%!pT/@76G9,D')/ %E,D7`/)1k9~=G&:B% xHZ U,p=%/@C;8&:B%7B76/@p2%:B%7BG&'@-67 Z 1&%:6%K ,D76(=1fCX,dF-,D8&8&:6(=,2*_#w4s(=:$io,2')'}4sG&1&*e-0/@(=1&7 Z / P%:6%1j-~=:B/)E&7UVF5(=GH1&ETt,2:udk*(=1&EH/@-0/@(=1&7a,21&E*(=1>p=%*-0/@(=176*_#H%C%7C/)~=#>-a,2')7B(X~=/qp=%:6/)7B%-6(XE&/@7B-0/@1&*-6/)(=1H7aF-a76(='qp=%,D-`')%,D7B89,D:B-(24A-6#&%8&:B(=F&'@%C i/@-6#wiv,D')' 4sGH1&*-6/)(=1&7 Z (Mi%p2%:UC(=7B-`(24A-0#H%76%38H:6(=8-%eRT/q-76%*e-0/@(=1f/@7 L=c c Z
~=%(=C;%e-0:B/)*QE&%76*:B/)8H-6/)(=1 (24-0#H%kFp=%:6~=%E7B(=')GH-6/)(=1 Z "$#&/@7F5%#9,pT/@(=G&:F,2/@1&%E4s:6(2CNG&76/@1&~^-0#&%:6%,2')/ ,2F&'@% C;(+E&%'&io%:6%a-6%7u-0%E,21HE :B%7BG&'@-6%E /)1, C/qRf(24]C(TEH%')7a:6%e4s%:6:B%E-0(,D7-0#&% :B%76%1>-C(+E&%' Z "$#&/)7C(TEH%' E&/)E7B#&(Mi 76(2C;%$/@C;8&:B(Mp=%C%1>-A(211jG&C%:B/)*,2'H7u-_,2F&/@')/q-rd=U2FHGH-?7B-6/)')'T1&(*(21jp2%:B~=%E;76(='@GH-0/@(=1*(2G&')EFi/)1&E 7B*_#&%C%;/@7G&7B%E 4s(=:C;%,21p=%')(+*/q-0/)%7UP-6#&%#>dTFH:6/)E 7B*_#&%C%/)7G&7B%Ek4s(=: U ,21&EQ-0#H% %d+1&(2')E&77B-6:6%7676%7`/@1-6#&%^E&/ 5%:B%1>-0/),2'{7u-0:6%767C;(+E&%')7 Z
6
W
\> @_W X[ XA \ Y \ >@_W ]_W?WX\?d76%ep=%:0,2' ,2GH-6#&(=:B7U-*(2C;8>-_,D-6/)(=1&7,D:6%*(=C;8&,2:6%Efi/@-6#f%SRT85%:6/)C%1>-67aF>d #&%7619, .,27`,21&E /)C8&76(21 W mDY U `#&1 W Y ,D1&E :6%8&')/@1 l - ,2 ~=%:W Y[ZL2I
_%
87
9 W;: =< X\?Y \?> @_W W J A # W
"$#&%f*(=C8&GH-0,D-0/@(=19,2'oE&(=C;,2/)1 ,21&E C;%76# ,2:6%k76#&(Mi1 /@1 &~=G&:6% mHZ Uv,D1&E -6#&%%d+1&(2')E&71jG&CFi/)7B%Qp=%'@(T*/@-rd *(=C8-67U,2'@'$C;(+E&%')74|,2/@'v/)1 8&:6%E&/)*e-0/@1&~-0#&%k8&:6(285%:'@%p2%'hUo,2'@-6#&(=G&~2# -6#&%k76#9,28
top related