cfd manual fluent
TRANSCRIPT
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COMPUTATIONAL FLUID DYNAMICS
FLUENT
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1 INTRODUCTION.......................................3
2COMPUTATIONAL FLUID DYNAMICS(CFD)..............................................................7
3HEAT TRANSFER MODELLING............39
4TRANSIENT FLOW MODELLING.........46
5CFD EERCISE.........................................51P!"#$%& S'%*+,"-..........................................................................................................72
R%/$,76
P$", 0%$", 0%,"!...........................................................................................................76
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CHAPTER 1
1 INTRODUCTION
1.1 FLUID DYNAMICS:
F$/ -+& ,% %-% "* *$/ &","-. F$/ *$" "&&"-$ ,/% - "-%
"* ,!%% +
E'%!&%-,+$ *$/ -+&.
T%"!%,+$ *$/ -+&.
N/&%!+$$ "&'/,+,"-+$ *$/ -+& (CFD).
1. EXPERIMENTAL FLUID DYNAMICS (EFD)
W- ,/--%$ (/#"- ,!+-"- /'%!"- $"8,/!#/$%-% '!%/!%
:)
T"-; ,+-
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1.2.1. FLUID FLOW:
F$/ *$" %+$ , ,% *$" "* *$/("&'",,"- "* $>/ +- ;+). A *$/
"-, "* + $+!;% -/%! "* -=/+$ &"$%/$%.T%% "/$ - '!-'$% #% &"%$% +
-,%!+,-; "$ '+!,$%.
F;/!% 1.1 F$/ F$"
1.2.2. GRANULAR FLOW:
I, %+$ , *$" "* "$ '+!,$%. T% -,%!+,"- #%,%%- +?+%-, +$, ;!+- +-
+?+%-, *$/ '+!,$% >/,% **%!%-,.
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F;/!%1.2 G!+-/$+! F$"
1.3 FLOW CLASSIFICATIONS:
1.3.1. LAMINAR FLOW:
I, ,% "-% - ,% *$/ '+!,$% &"=% - $+%! ("! $+&-+) , "-% $+%! "**$/ $-; &"",$ "=%! +- +?+%-, $+%!. F$/ '+!,$% &"=% - %$$ %*-% '+, +-
,% !%,+- ,% +&% !%$+,=% '","- +, /%=% !" %,"- "* ,% *$" '++;%. T
,'% "* *$" "/! ;%-%!+$$ - &"", ''% %- ,% =%$", "* *$" $" +- +$" -
$>/ "* +=-; ; =",.
1.3.1.2. TURBULENT FLOW:
I, ,% "-% - ,% *$/ '+!,$% - +- %-,!%$ +'++! "! %!!+, &+--%!.
F$/ '+!,$% &"=% - +- /-'!%,+#$% '+, ,+, !%/$, - + !+' +- "-,-/"/ &-; "*
,% *$/ $%+-; ," &"&%-,/& ,!+-*%! + *$" "/!. I- / + *$" %% "! ="!,% +!%
'!%%-,. T%% %% +- ,%! !+-"& &"=%&%-, ;=% !% ," *$/,/+,"- - ,% =%$", +-
'!%/!% +, +- '"-, - ,% *$" *%$. T ,'% "* "/! - !=%! +-+$ ,!%+& +,%!
/''$ ''%.
1.3.1.3. STEADY FLOW:
I- ,%+ *$" =+!"/ +!+,%!, "* *$"-; *$/ / + =%$", '!%/!%
%-, ,%&'%!+,/!% %,.. +, + '"-, " -", +-;% , ,&%. I- ",%! "! + ,%+ *$"
&+ #% %*-% + ,+, - ,% =+!"/ +!+,%!, +!% -%'%-%-, "* ,&%. E;. p =
p(x,y,z) T
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T% *$/ "#% NEWTON@S LAW OF 0ISCOSITY( %+! ,!% !%,$
'!"'"!,"-+$ ," %+! ,!+-) +$$% N%,"-+- *$/.
1.3.1.!. NON NEWTONIANS FLUID:
T% *$/ "% -", "#% NEWTON@S LAW OF 0ISCOSITY( %+! ,!%
!%,$ '!"'"!,"-+$ ," %+! ,!+-) +$$% N"- N%,"-+- *$/.
1.3.1.". INCOMPRESSIBLE FLOW:
A *$" + ," #% -"&'!%#$% *$" * ,% %-, "-,+-, - + *$" *%$. F"!
+$$ '!+,+$ '/!'"% $>/ +- #% !%;+!% + -"&'!%#$% #%+/% ,% '!%/!% +-
,%&'%!+,/!% +-;% +=% $,,$% %**%, "- ,%! ="$/&%.
1.3.1.#. COMPRESSIBLE FLOW
A *$" + ," #% "&'!%#$% * ,% %-, +-;% *!"& '"-, ," '"-, /%
'!%/!% +- ,%&'%!+,/!%.
M+,%&+,+$$ -", %>/+$ ," "-,+-,.
1.3.1.$. SINGLE PHASE FLOW:
T% *$" - ,%!% -" +-;% "* '+%. I- , ,%!% "-$ "-% '+% "*
*$/ *$"(%,%! $>/ "! ;+).
1.3.1.1%. MULTI PHASE FLOW:
T% *$" - ,%!% +-;% "* '+% +$$% &/$,'+% *$". I- , ,%!%
+ &,/!% "* '+% *$"($>/8;+ $>/8"$ ;+8"$).
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CHAPTER 2
2 COMPUTATIONAL FLUID DYNAMICS (CFD)
1.4 COMPUTATIONAL FLUID DYNAMICS:
C"&'/,+,"-+$ *$/ -+& (CFD) ,% %-% "* '!%,-; *$/ *$" %+,
,!+-*%! &+ ,!+-*%! %&+$ !%+,"- +- !%$+,% '%-"&%-+ # "$=-; ,%
&+,%&+,+$ %>/+,"- ;"=%!- ,%% '!"%% /-; + -/&%!+$ '!"%.
T% !%/$, "* CFD +-+$% !%$%=+-, %-;-%%!-; +,+ /% -
C"-%',/+$ ,/% "* -% %;-.
D%,+$% '!"/, %=%$"'&%-,.
T!"/#$%"",-;.
R%%;-.
CFD +-+$ "&'$%&%-, ,%,-; +- %'%!&%-,+,"-.
R%/% ,% ,",+$ %**"!, !%>/!% - ,% $+#"!+,"!.
1.5 CFD How it wor!:
A-+$ #%;- , + &+,%&+,+$ &"%$ "* + '+$ '!"#$%&. C"-%!=+,"- "*
&+,,%! &"&%-,/& +- %-%!; &/, #% +,*% ,!"/;"/, ,% !%;"- "* -,%!%,. F$/
'!"'%!,% +!% &"%$% %&'!+$$. S&'$*-; +/&',"- +!% &+% - "!%! ," &+/+,"- +$;%#!+.
T% "$$%,"- "* %$$ +$$% ,% ;!.
T% %, "* +$;%#!+ %>/+,"- +!% "$=% -/&%!+$$ ("- + "&'/,%!) *"!
,% *$" *%$ =+!+#$% +, %+ -"% "! %$$.
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S,%& "* %>/+,"- +!% "$=% &/$,+-%"/$ ," '!"=% "$/,"-.
T% "$/,"- '",8'!"%% ," %,!+, >/+-,,% "* -,%!%, (%.;. $*, !+;
,"!>/% %+, ,!+-*%! %'+!+,"- '!%/!% $" %,.).
1." APPLICATIONS OF CFD:
A''$+,"- "* CFD +!% -/&%!"/B
F$" +- %+, ,!+-*%! - -/,!+$ '!"%% (#"$%! %+, %+-;%!
"/,"- %>/'&%-, '/&' #$"%! ''-; %,.).
A%!"-+& "* ;!"/- =%$% +!!+*, &$%.
F$& "+,-; ,%!&"*"!&-; - &+,%!+$ '!"%-; +''$+,"-.
F$" +- %+, ,!+-*%! - '!"'/$"- +- '"%! ;%-%!+,"- ,%&.
0%-,$+,"- %+,-; +- ""$-; *$" - #/$-;.
C%&+$ =+'"! %'","- (C0D) *"! -,%;!+,% !/, &+-/*+,/!-;.
H%+, ,!+-*%! *"! %$%,!"- '+
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CFD '!"=% ,% +#$, ," ,%"!%,+$$ &/$+,% +- '+$
"-,"-.
& A++*- * +6*' +' 08+*+8.
CFD +$$" ;!%+, "-,!"$ "=%! ,% '+$ '!"% +- '!"=% ,%
+#$, ," "$+,% '%* '%-"&%-+ *"! ,/.E+&'$% + %+, ,!+-*%!
'!"% +- #% %+$% , ++#+, "-,+-, %+, *$/ "! "-,+-,
,%&'%!+,/!% #"/-+!%.
& C7'9'8+,' +87*+8.
E'%!&%-, "-$ '%!&, +,+ ," #% %,!+,% +, + $&,% -/%! "*
$"+,"- - ,% ,%& (%.;. '!%/!% +- ,%&'%!+,/!% '!"#% %+, *$/
;+/;% LD0 %,.).
CFD +$$" ,% +-+$, ," %+&-% + $+!;% -/%! "* $"+,"- - ,%
!%;"- "* -,%!%, +- %$ + "&'!%%-=% %, "* *$" '+!+&%,%! *"!
%+&-+,"-.
1.& LIMITATIONS OF CFD:
& P9-+0 ':
CFD "$/,"- !%$ /'"- '+$ &"%$ "* !%+$ "!$ '!"%% (%.;.
,/!#/$%-% "&'!%#$, %&,! &/$,'+% *$" %,.).
T% CFD "$/,"- +- "-$ #% + +/!+,% + ,% '+$ &"%$ "-
,% +!% #+%.
& N6'7+0 '777:
S"$=-; %>/+,"- "- + "&'/,%! -=+!+#$ -,!"/% -/&%!+$ %!!"!.
R"/-8"** %!!"! /% ," *-,% "! % +=+$+#$% "- ,%
"&'/,%!.R"/-8"** %!!"! $$ +$+ %, (,"/; ,% +- #% &+$$
- &", +%).
T!/-+,"- %!!"! /% ," +''!"&+,"- - ,% -/&%!+$ &"%$.
T!/-+,"- %!!"! $$ ;" ," %!" + ,% ;! !%*-%. M% !%*-%&%-,
"-% + ," %+$ , ,!/-+,"- %!!"!.
& B687- 08+*+8:
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A , '+$ &"%$ ,% +/!+ "* ,% CFD "$/,"- "-$ +
;"" + ,% -,+$#"/-+! "-,"- '!"=% ," ,% -/&%!+$
&"%$.
E+&'$% *$" - + /, , /%- %'+-"-. I* *$" /''$% ,"
"&+- # + ''% "/ "/$ /% + */$$8%=%$"'% '!"*$% *"! =%$",
!+,%! ,+- +/&% /-*"!& "-,"-.
1.' DISC(ETI)ATION
T% +!, "* /#=-; + ,!/,/!% -," + "-=%-%-, -/%! "* &+$$%!
"&'"-%-,
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T% ;! -",-; #/, ,% "&+- ,+, %!%,% -," + *-,% %, "* "-,!"$ ="$/&%
"! %$$. T% %;!%% "* ;! !%"$/,"- +$" -%%+! ," *- "$/,"- *"! + '!"#$%& - %+
!%;"- "* ,% "&+-.
T%!% +!% ,!%% **%!%-, ,'% "* ;! - ;%-%!+$
F"!&+$ ;!.(,!+-;$% ,%,!+%!"- '!+& '!& %+%!"-
>/+!$+,%!+$ )
H#! ;!.
N"- *"!&+$ ;!.
2.!.2. TYPES OF CELL SHAPES OR GRIDS:
F;/!% 2.2 T'% "* G!
2.!.2.1. TETRAHEDRON MESH: T% &'$%, ,%, &% % ,%!& +- "!%! 4 "! $-%+! &% /% *"/!
'"-, , %*-% %+ ,%,!+%!"-. F"! "&'$% ;%"&%,!% >/+% &%% " -"
-/&%!+$ +=+-,+;% +- % +- +=% &%-; %**"!, # /-; + ,!,%, &%.
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F;/!% 2.3 T%,!+ M%
2.!.2.2. >UADRILATERAL MESH:
F"! &'$% ;%"&%,!% >/+% &%% +- '!"=% ;8>/+$,"$/,"- ,
*%%! %$$ ,+- + "&'+!+#$% ,!,%, &%.
F;/!% 2.4 /+ M%
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2.!.2.3. HYBRID MESH:
T ,% "-+,"- "* **%!%-, ,'% "* *"!&+$ ;! *"! + ="$/&% "* #". I- , +
'%* !%;"- &%% , **%!%-, ;! "! %$$ ,'%. T% %**%- +- +/!+ +!%
%-+-% !%$+,=% ," ,%,!+%!"- +- %+%!+$ &%. I, "-, "* #", &% !"/,%! +-&% $%-, - #", ,% ,'% "* -"% '%!*"!&-; !"/,-; +- *"!+!-;
*/-,"-+$,. T
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D"&+- ;!"/' "* -"% *+% +- %$$ "-%.
F;/!% 2.6 2D J 3D C%$$ T%!&-"$";
1.11 MESH +UALITY:
F"! ,% +&% %$$ "/-, %+%!+$ &%% $$ ;=% &"!% +/!+,% "$/,"- %'%+$$
* ,% ;! $-% +!% +$;-% , ,% *$". T% &% %-, "/$ #% ; %-"/; ,"
+',/!% +$$ !%$%=+-, *$" *%+,/!%. T% &% +?+%-, ," ,% +$$ "/$ #% *-% %-"/; ,"!%"$=% ,% #"/-+! $+%! *$". I- #"/-+! $+%! >/+ % +- '!&%;% %$$ +!%
'!%*%!!% "=%! ,! ,%, "! '!+&.
T%!% +!% ,!%% ,'% "* &% >/+$, SKEWNESS SMOOTHNESS (CHANGE IN SIE) ASPECT RATIO
2.#.1. MESH >UALITY: S?EWNESS
T" &%," *"! %,%!&--; UILATERAL @OLUME:
S
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"',&+$ %$$ %
T +''$+#$% "-$ ," ,!+-;$% +- ,%,!+%!"-. T ,% %*+/$, &%," *"!
,!+-;$% +- ,%,!+%!"-.
2.B' 8 *9' ',+*+8 7 87+' '6+*'7 8':
S/+$,
+$+ /% *"! '!& +- '!+&.
2.#.2. MESH >UALITY : SMOOTHNESS C+-;% - % - +- %$%&%-, "/$ #% ;!+/+$. I* ,% &%-; /!*+%
&"", ;"" +/!+ +- #% &+%. R"/; &%-; /!*+% %$%&%-, $%+ ,"
-+/!+.
F;/!% 2.7 S&"",-% - M%-;
2.#.3. MESH >UALITY : ASPECT RATIO
T %*-% + ,% !+," "* $+!;%, &%-"- "* ,% %$%&%-, ," ,% &+$$%,
&%-"-. I- &+- +% + ,% +'%, !+," -!%+% ,% -+/!+ "* ,% "$/,"-
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-!%+%. T% "-$/"- "* &+- !%%+!% ,+, ,% +'%, !+," "/$ #% $"% ,"
/-, + '"#$%. E>/+$ ," 1 (%+$) *"! +- %>/$+,%!+$ ,!+-;$% "! + >/+!%.
F;/!% 2. A'%, !+," - M%-;
1.12 ST(I$IN% FO( +UALITY:
A '""! >/+$, ;! $$ +/% -+/!+,% "$/,"- +-"! $" "-=%!;%-%. T" ;%, +
#%,,%! >/+$, &-&% $"+$ =+!+,"- - %$$ %. F"! %+&'$% +?+%-, %$$ "/$ -",
+=% Q+' 7*+ ;!%+,%! ,+- 2. I* / '""! >/+$, %, %$%,% ,% &%-;
;%"&%-,! " -%%+! %"&'","- +- "! '!% &% ,% %;% +- *+% +- !%&% ,%
%$%&%-,.
MINIMIUIANGLE S?EW:
H% +- >/+ %$$
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1.13 %(ID DESI%N:
2.1%.1. GRID DESIGN GUILDLINES: RESOLUTION
T% *%+,/!% "* '%!,-%-,(!%$%=+-,) *$" "/$ #% +%>/+,%$ !%"$=%. W%- ,%
*$" &/$, &%-"-+$ Q0' '0* 7*+ (!+," "* $+!;%, &%-"- ," ,% &+$$%,
&%-"-) "/$ #% -%+! "-%. A$" /+% +- #% ,!%,% %!% ,% *$" */$$
%=%$"'% +- %%-,+$$ "-%8&%-"-+$.
F;/!% 2.9 D%;- *"! G!
2.1%.2. GRID DESIGN SOLUTIONS:SMOOTHNESS
C+-;% - % - +- %$%&%-, "/$ #% ;!+/+$. I* ,% &%-; /!*+% &"",
;"" +/!+ +- #% &+%. R"/; &%-; /!*+% %$%&%-, $%+ ," -+/!+.
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F;/!% 2.1 S&"",-% *"! G!
I- +- &%-; %$%&%-, ,% &+&/& +-;% - ;! '+-; &/, #% $% ,+- 2.
2.1%.3. GRID DESIGN GUILDLINES: TOTAL CELL COUNT
I* ,% -/%! "* ;! "! %$$ +!% &"!% ,%- ,% +/!+ "* ,+, &%-; %$%&%-,
$$ #% ;%!. A, ,% +&% ,&% , $$ -!%+% &%&"! /+;% +- CPU ,&%. T%!% +!% ,"
+ /% ,"
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1E6 +!% $+!;%. S/ '!"#$%& +- #% %**%-,$ !/- /-;
&/$,'$% CPU #/, &% ;%-%!+,"- +- '",8'!"%-; &+
#%"&% $".
1E7 +!% /;% +- "/$ #% +="% * '"#$%. H"%=%! ,%
+!% "&&"- - +%!"'+% +- +/,"&",=% +''$+,"-.
1E +- &"!% +!% %'+!,&%-, "* %*%-% ,$% +''$+,"-.
2.1%.4. ADOPTION EXAMPLE: FINAL GRID AND SOLUTION
F;/!% 2.11 F-+$ G! *"! +- E$%&%-,
1.14 MAIN SOU(CES OF E((O(S IN MESHIN%:
M% ,"" "+!%.
H;
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I-,%!'"$+,"- %!!"! +, -"-8"-*"!&+$ -,%!*+%.
I-+''!"'!+,% #"/-+! $+%! &%.
1.15 %O$E(NIN% E+UATION:
T% ;"=%!--; %>/+,"- -$/% ,% *"$$"-; "-%!=+,"- $+ "* '
C"-%!=+,"- "* &+.
N%,"- %"- $+ ,% +-;% "* &"&%-,/& %>/+$ ,%
/& "* *"!% "- + *$/ '+!,$%.
F!, $+ "* ,%!&"-+& ("-%!=+,"- "* %-%!;) !+,% "*
+-;% "* %-%!; %>/+$ ,% /& "* !+,% "* %+, +,"- ," +-
"!< "-% "- *$/ '+!,$%.
T% *$/ ,!%+,% + + "-,-//&. F"! $%-;, +$% "* + 1 & +- $+!;%!. T% &"$%/$+! ,!/,/!% +- &","- &+ #% ;-"!%.
2.12.1. LAGRANGIAN DESCRIPTION:
T +''!"+ ",%!% +$$% + Q7*+0' 709. A *$/ *$" *%$ +- #%
,"/;, "* + #%-; "&'!% "* + $+!;% -/%! "* *-,% % *$/ '+!,$% +=%
&+ &"&%-,/& -,%!-+$ %-%!; +- ",%! '!"'%!,%. M+,%&+,+$ $+ +- ,%- #%
!,,%- *"! %+ *$/ '+!,$%. F$/ - &+,%!+$ ="$/&% (,%&) $$ &"=% ,"!, +-
+-;% % +- +'% #/, +$+ "-, "* ,% +&% *$/ '+!,$%.
'+,$-%
F;/!% 2.12 L+;!+-;+-
M"%$
2.12.2. EULERIAN
DESCRIPTION:
T ",%!% +$$% + Q+' 709. I- , &"%$ -=/+$ +!% -", $+#%$%
+- -", ,-;/% *!"& "-% +-",%!. I- ,% E/$%!+- %!',"- "* *$/ &","- %
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"-%! " *$" '!"'%!,% +-;% +, + *$/ %$%&%-, ,+, *% - '+% +- ,&%
(,) !+,%! ,+- *"$$"-; -=/+$ *$/ '+!,$%.
F;/!% 2.13 E/$%!+- M"%$
1.1" CONTINUITY E+UATION:
T% "-,-/, %>/+,"- ;"=%!-% *!"& ,% Q7+80+' 08'7,*+8 . I,
,+,% ,+, Q*9' 6+ /+8 *9769 *9' +' * 07 '0*+8 7'+8
08*8* + *9'7' + 8 6+ + ' 7 7',' 7 *9' +' .
MASS BALANCE:
R+,% "* -!%+% "* &+ - *$/ %$%&%-, %>/+$ ,% -%, !+,% "*
*$" "* &+ -," %$%&%-,. R+,% "* -!%+% "* &+ %'!%% +
1.1# MOMENTUM E+UATION:
T -",-; #/, QN'/*8 S'08 L/ M*+8 (F&+). T% -%, *"!% *"!% +,-; -
+- !%,"- %>/+$ ," !+,% "* +-;% "* &"&%-,/& - ,+, !%,"-.
L-%+! &'/$%+-;% - $-%+! &"&%-,/&.
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I- 8!%,"- -,+$ $-%+! &'/$%$-%+! &'/$%*-+$ $-%+! &"&%-,/&. R+,% "*
-!%+% "* 8 8 +- 8&"&%-,/&
T% *"$$"-; *"!% +,-; "- *$/ '+!,$% +!%
S/!*+% *"!% / + '!%/!% +- ="/ *"!%.
V" *"!% +, "- + ="$/&% / + ;!+=,
%-,!*/;+$ C"!"$ +- %$%,!"&+;-%, *"!%.
1.1& NA$IE(,STO-ES E+UATION:
T% %>/+,"- "* &","- ,"/, "-%!-; *"!% /% ," ,/!#/$%-% +-
"-%!-; ,% ;!+=, '!%/!% +- =", *"!% +!%
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,% *$/ %-, u ,% =%$", e ,% ,",+$ %-%!; '%! /-, ="$/&% p ,% '!%/!%
T ,% ,%&'%!+,/!% ,% "%**%-, "* =", +- ,% ,%!&+$ "-/,=,. T%
,",+$ %-%!; e -$/% -,%!-+$ %-%!; '%! /-, ="$/&% e (%!% e ,% -,%!-+$ %-%!;
'%! /-, &+) +- /!% "&'"-%-, "* ,% &+,%&+,+$ &"%$.
V"/-+!% +- -,%!-+$ /!*+% +!% !%'!%%-,% # *+% "-%. V"/-+! +,+ +!% +;-%
," *+% "-%.
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F;/!% 2.14 P'% *$" , "!*% '$+,%.
2.1!.1. NEUMANN AND DIRICHLET BOUNDARY CONDUTIONS:
W%- /-; + D!$%, #"/-+! "-,"- "-% '!%!#% ,% =+$/% "* + =+!+#$% +,
,% #"/-+! %.;. u(x) = "o#$ta#t. W%- /-; + N%/&+-- #"/-+! "-,"- "-%
'!%!#% ,% ;!+%-, -"!&+$ ," ,% #"/-+! "* + =+!+#$% +, ,% #"/-+! %.;. #u(x) =
"o#$ta#t. W%- /-; + &% #"/-+! "-,"- + */-,"- "* ,% *"!& au(x)%&u(x) =
"o#$ta#t +''$%. N",% ,+, +, + ;=%- #"/-+! **%!%-, ,'% "* #"/-+! "-,"-
+- #% /% *"! **%!%-, =+!+#$%.
2.1!.2. FLOW INLETS AND OUTLETS:
A % !+-;% "* #"/-+! "-,"- ,'% '%!&, ,% *$" ," %-,%! +- %, ,%
"$/,"- "&+-. I- ;%-%!+$ ,% %-,! '"!,"- -+,% '!%/!% -$%, +- %, '"!,"-
-+,% '!%/!% "/,$%,. F"! -"&'!%#$% *$" %-,! '"!,"- $$ #% &%-,"- + =%$",
-$%, +- %, + "/,*$". I- +% "* "&'!%#$% *$" %-",% + &+ *$" -$%, +-
'!%/!% *+!8*%$. I-$%, =%-, "/,$%, =%-, -,+
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S"/$ -", "#%!=% $+!;% ;!+%-, - !%,"- -"!&+$ ,"
#"/-+! -%+! -$%, +- "/,$%,. T -+,% +- -"!!%,
'!"#$%& '%*+,"-.
M-&% ;! /!% ,+, ;+/;% '!%/!% -'/,. T% "'%!+,-;
'!%/!% -'/, %, %'+!+,%$. T #"/-+! "-,"- $$ #% /%*/$ %- N%,%! ,%
*$" !+,% -"! ,% =%$", +!%
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2.1!.5. OUTFLOW BOUNDARY:
O/,*$" #"/-+! "-,"- +!% /% ," &"%$ *$" %, %!% ,% %,+$ "* ,%
*$" =%$", +- '!%/!% +!% -", /!% -*"!&+,"- *!"& -,%!"!.
2.1!.!. POROUS MEDIA CONDITIONS:
P"!"/ "-% &"%$ + '%+$ ,'% "* *$/ "-%. I- , '!%/!% $" - *$"
%,%!&-% =+ /%! -'/, "* !%,+-% "%**%-, ," $/&'% '+!+&%,%! &"%$. T /%
," &"%$ *$" ,!"/; '"!"/ &%+ +- ",%! ,!#/,%@ !%,+-% %.; '+
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1.21 SOLUTION METHODS:
2.1#.1. FINITE ELEMENT METHOD:
T + -/&%!+$ &%," *"! "$=-; '!"#$%& "* %-;-%%!-; +- &+,%&+,+$
+-+$. I- , &%," + #" "! + ,!/,/!% - ,% +-+$ ," #% +!!% "/,
/#=% -," &+$$%! %$%&%-, "* *-,% &%-"- +$$% *-,% %$%&%-,. T%- ,% #"
"-%!% + +- +%$+;% "* ,%% %$%&%-, "--%,% +, + *-,% -/%! "* ?"-, +$$%
Q8' "! N"+$ '"-,. V+% "- +''$+,"- ,% %$%&%-, '!"#$%& +!% $+*% +
*"$$"
S,!/,/!+$ '!"#$%&.
N"-8,!/,/!+$ '!"#$%&.
AD@ANTAGES:
H;%, +/!+ "- "+!% ;!.
E%$$%-, *"! **/"- "&-+,% '!"#$%& ="/ +- *!%% /!*+%
'!"#$%&.
DISAD@ANTAGES:
S$" *"! $+!;% '!"#$%&.
N", %$$ /,% *"! ,/!#/$%-, *$".
2.1#.2. FINITE DIFFERENCE METHOD:
T &%," /%*/$ *"! "$=-; %+, ,!+-*%! *$/ &%+- +- ,!/,/!+$
&%+- '!"#$%&. I, +''$+#$% ," +- '%-"&%-"- *"! **%!%-,+$ %>/+,"-
+$"-; , ,% #"/-+! "-,"- +=+$+#$%. I, "!/!%.T% ;"=%!--; %>/+,"- (- **%!%-,+$ *"!&) +!% !%,% ("-=%!,% ," +$;%#!+ *"!&).
F!, +- %"- %!=+,=% +!% +''!"&+,% # ,!/-+,% T+$"! %!% %'+-"-. T%
!%/$,-; %, "* $-%+! +$;%#!+ %>/+,"- "$=% %,%! ,%!+,=%$ "! &/$,+-%"/$. T
&%," **/$, ," /% %- !%;"- +=% /!=% "! !!%;/$+! #"/-+!% +- , **/$,
," !,% ;%-%!+$ "&'/,%! '!";!+&.
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2.1#.3. FINITE @OLUME METHOD:
T% #+ %+ "* + *-,%8="$/&% &%," ," +,* ,% -,%;!+$ *"!& "* ,%
"-%!=+,"- $+ ," "&% %;!%% "* +''!"&+,"- *"! %+ "* &+- "-,;/"/ "-,!"$
="$/&% "=%! ,% "&+- "* -,%!%,. T &%," + +,,!+,=% #%+/% $%
=+!+#$% &+ -", #% "-,-/"/$ **%!%-,+#$% +!" "/+,"- (&"&%-,/& %-%!; %,.) +!% "#%% - +$$ %$$ ," +'%*% ,"$%!+-% ,% "$/,"- -" $"-;%! +-;% , +,"-+$ ,%!+,"-. M+
&"&%-,/& %-%!; +- +$+! #+$+-% +!% "#,+-%. R%/+$ &%+/!% +$+-% ("! %!!"!)
- "-%!=+,"- %>/+,"-. T% *"$$"-; ,-; "/$ #% "-%!% $% "-=%!;%-%
A$+ %-/!% '!"'%! "-=%!;%-% #%*"!% /-; + "$/,"-. /-"-=%!;%
"$/,"- +- #% &$%+-;.
S"$/,"- +!% "-=%!;% %- ,% *$" *%$ +- +$+! *%$ +!% -" $"-;%!
+-;-;.
2.1#.5. MONITOR RESIDUALS:
I* ,% !%/+$ +=% &%, ,% '%*% "-=%!;%-% !,%!"- #/, +!% ,$$ %!%+-;
,% "$/,"- &+ -", %, #% "-=%!;%. I* ,% !%/+$ -%=%! &%%, ,% "-=%!;%-% !,%!"-
#/, +!% -" $"-;%! %!%+-; +- ",%! "$/,"- &"-,"! " -", +-;% %,%! ,% "$/,"-
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"-=%!;%. F-+$ !%/+$ +!% "*,%- ;%! , ;%! "!%! !%,+,"- %&% ,+-
, *!, "!%! !%,+,"-. T+, "% -", &%+- ,+, ,% *!, "!%! "$/,"- #%,,%!.
R%/+$ +- #% &"-,"!% ;!+'+$$ +$".
F;/!% 2.16 M"-,"! R%/+$
1.22 P(ESSU(E $ELOCITY COUPLIN%:
P!%/!% +''%+! - +$$ ,!%% &"&%-,/& %>/+,"-. T% =%$", *%$ +$" + ,"
+,* ,% "-,-/, %>/+,"-. S" %=%- ,"/; ,%!% -" %'$, %>/+,"- *"! '!%/!% %
" +=% *"/! %>/+,"- *"! *"/! =+!+#$% +- ,% %, "* %>/+,"- $"%. S" '!%/!%8
=%$", "/'$-; +$;"!,& +!% /% ," %!=% %>/+,"- *"! ,% '!%/!% *!"& ,%
&"&%-,/& %>/+,"- +- ,% "-,-/, %>/+,"-. T% &", "&&"-$ /% +$;"!,& ,%
SIMPLE (S%&8I&'$, M%," *"!P!%/!%8L-/+,"-). A- +$;%#!+ %>/+,"- *"!
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,% '!%/!% "!!%,"- p' %!=% - + *"!& &$+! ," ,% %>/+,"- %!=% *"! ,%
"-=%,"-8**/"- %>/+,"-
+''X +-#'X #X.
%!% ' '!%/!% "!!%,"-. # "-,-/, +$+-%.
E+ ,%!+,"- ,% '!%/!% *%$ /'+,% # +''$-; ,% '!%/!% "!!%,"-. T%"/!% ,%!& &' ,% "-,-/, +$+-%. T% ",%! "%**%-, %'%- "- ,% &% +- ,%*$" *%$.
2.1$.1. PRINCIPLE BEHIND SIMPLE:
T% '!-'$% #%- SIMPLE >/,% &'$%. I, #+% "- ,% '!%&% ,+, *$/
*$" *!"& !%;"- , ; '!%/!% ," $" '!%/!%. I- , *!, S,+!, , +- -,+$
'!%/!% *%$ ,%- L""< +, + %$$. I* "-,-/, -", +,*% #%+/% ,%!% &"!% &+
*$"-; -," ,+, %$$ ,+- "/, "* ,% %$$ ,% '!%/!% - ,+, %$$ "&'+!% ," ,%
-%;#"!-; %$$ &/, #% ,"" $". T/ ,% '!%/!% - ,+, %$$ &/, #% -!%+% !%$+,=% ,"
,% -%;#"!-; %$$. T% !%=%!% ,!/% *"! %$$ %!% &"!% &+ *$" "/, ,+- -. R%'%+,
, '!"% ,%!+,=%$ *"! +$$ %$$. T% ,!< - *--; + ;"" %>/+,"- *"! ,% '!%/!%
"!!%,"- + + */-,"- "* &+ +$+-%.
2.1$.2. IMPRO@EMENTS ON SIMPLE:
SIMPLE ,% %*+/$, +$;"!,& - &", "&&%!+$ *-,% ="$/&% "%. I&'!"=%
=%!"- +!%
SIMPLER (SIMPLE R%=%).
SIMPLEC (SIMPLE C"-,%-,).
PISO (P!%/!% I&'$, , S'$,,-; "* O'%!+,"!).
A$$ ,%% +$;"!,& +- '%% /' "-=%!;%-% #%+/% ,% +$$" *"! ,% /% "* $+!;%! /-%!
!%$++,"- *+,"! ,+- SIMPLE. A$$ "* ,%% $$ %=%-,/+$$ "-=%!;% ," ,% +&% "$/,"-.
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T% **%!%-% +!% - '%% +- ,+#$,. W +$;"!,& *+,%, %'%- "- ,% *$" +-
,%!% -" -;$% +$;"!,& ,+, +$+ *+,%! ,+- ,% ",%! "-%.
2.2*. SOLUTION P(OCEDU(E:
2.2%.1. SEGREGATED SOLUTION PROCEDURE:
F;/!% 2.17 S%;!%;+,% S"$/,"- P!"%/!%
2.2%.2. COUPLED SOLUTION PROCEDURE:
W%- ,% "/'$% "$=%! /% *"! ,%+ ,+,% +$/$+,"- , %%-,+$$ %&'$" +
&"*% ,&% %'%-%-, "$/,"- +$;"!,& /-; + ,&% ,%'
Z, CFL(UL).
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W%!% * 8 ,&% ,%'. CFL C"/!+-,8F!%!8L%= -/%!. 6 L"+$ =%$",.
L % "* ,% %$$.
2.21. TU(ULANCE MODELLIN%:
C+!+,%!+,"- "* T/!#/$%-, F$"
F!"& N+=%!8S,"/+,"- ," R%-"$8A=%!+;% N+=%!8S,"
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U-,%+ +'%!" &","- - +$$ ,!%% =%$", "&'"-%-, *$/,/+,% &-;
&+,,%! &"&%-,/& +- %-%!;. D%"&'"% =%$", -," &%+- +- *$/,/+,-; '+!,
U+(*) U+ J 6+(*).
2.21.1. TRANSITION IN BOUNDARY LAYER FLOW O@ER FLAT PLATE
F;/!% 2.1 T!+-,"- - V"/-+! $+%!
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2.21.2. TRANSITION IN KET FLOW:
F;/!% 2.19 T!+-,"- - [%, F$"
2.21.3. TURBULENT FLOW CORRELATIONS:
EXTERNAL FLOWS:
R%\ 5]15 +$"-; + /!*+%.
R%D \ 2 +!"/- +- "#,+$%.
INTERNAL FLOWS:
R%D \ 122
W%!% R%L UL ^
L D D %,.
W%!% R% R%-"$ -/%!. _D%-, "* *$/. U _0%$", "* *$/. L _L%-;, "* ,/#%. _0", "* *$/. D _D+&%,%! "* ,/#%.
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2.21.4. TURBULANT BOUNDARY LAYER:
I- ,/!#/$%-, *$" ,% #"/-+! $+%! %*-% + ,% ,- !%;"- "- ,% /!*+% "* +
#" - ="/ %**%, +!% &'"!,+-,. T% #"/-+! $+%! +$$" ,% *$/ ," ,!+-,"-
*!"& ,% *!%% ,!%+& =%$", U ," + =%$", "* %!" +, ,% +$$. T% =%$", "&'"-%-,-"!&+$ ," ,% /!*+% &/ &+$$%! ,+- ,% =%$", '+!+$$%$ ," ,% /!*+%. T% ;!+%-,
"* ,% *$" +!" ,% $+%! +!% &/ ;!%+,%! ,+- ,% ;!+%-, - ,% *$" !%,"-. T%
#"/-+! $+%! ,
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F;/!% 2.2 T/!#/$%-, V"/-+! L+%!
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2.21.5. RANS M' D'07+*+8 8 B'9,+7 S67-
M"%$ D%!',"-
S'+$+!,
A$$&+!+
A -;$% ,!+-'"!, %>/+,"- &"%$ "$=-; !%,$ *"! + &"*% ,/!#/$%-, =",.
D%;-% '%*+$$ *"! +%!"'+% +''$+,"- -="$=-; +$$8#"/-% *$" "- +
*-% -%+!8+$$ &%. FLUENT &'$%&%-,+,"- +$$" ,% /% "* "+!%! &%%.
O',"- ," -$/% ,!+- !+,% - < '!"/,"- ,%!& &'!"=% '!%,"- "* ="!,+$
*$".S,+-+! /+,"- &"%$ "$=-; *"! < +- `. T ,% %*+/$,
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S'+$+!,
A$$&+!+
E"-"&+$ *"! $+!;% &%%. P%!*"!& '""!$ *"! 3D *$" *!%% %+!
*$" *$" , ,!"-; %'+!+,"-. S/,+#$% *"! &$$ "&'$% (>/+82D)
%,%!-+$-,%!-+$ *$" +- #"/-+! $+%! *$" /-%! '!%/!% ;!+%-,
(%.;. +!*"$ -; +!'$+-% */%$+;% &$% ' /$$).
S,+-+!
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3 HEAT TRANSFER MODELLING
E/0r Etio/ I/tro67tio/
E/0r tr/!8ort 034tio/:
E/0r E 80r 4/it 9!! i! 60i/06 !:
Pr0!!4r0 wor /6 i/0ti7 0/0r r0 ;w! 77o4/t06 or wit0
iro/90/t w07tio/ /6 (6itio/
=o4/6r 7o/6itio/!.
W;; 9t0ri; /6 t
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Co/t0 H0t Tr/!0r E@98;0
Cir74it =or6 0@t0r/;; 7oo;06B *.1 W9G-
< 1.5 W92G-
T 2'& -
Air i/;0t
$ *.5 9!
T 2'& -
E;07tro/i7 Co98o/0/t
o/0
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M0!!. T
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Sritio/.
Wit t0r9 i! i/7;4606?
8r0!!4r0 r6i0/t /6 =o6 or70 t0r9
i/ t
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Ntr; Co/>07tio/ t07tio/ ;ow! t0r? o4!!i/0!3 9o60; 94!t =0 4!06.
For 4/!t06 !o;>0r? o4!!i/0!3 9o60; or i60; ! ;w 7/ =0 4!06.
U!0r I/84t! or Nt4r; Co/>07tio/
D0i/0 tittio/; 770;0rtio/ 6o/0i/ O80rti/ Co/6itio/! 8/0;.
D0i/0 60/!it 9o60; !0>0r; o8tio/!r0 >i;=;0B.
o4!!i/0! 9o60;
E/=;0 r>it. S0t O80rti/ T0980rt4r0? T*.
S0;07t o4!!i/0!3 ! t
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(6itio/
(6itio/ 007t! !
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4 TRANSIENT FLOW MODELLING
Tr/!i0/t CFD A/;!i! Si94;t0 tr/!i0/t ;ow i0;6 o>0r !807ii06 ti90 80rio6
I So;4tio/ 9 88ro7ri=;0! !to8 70ri=;0! ;47t4t0 wit< r080ti/ 8tt0r/
IYo4r o; 9 ;!o =0 !i98; to /;0 t0r 8r0!7ri=06 ti90
i/t0r>;.
Fr00 !4r70 ;ow!
Mo>i/ !0!
Et7.
E@tr7t 34/titi0! o i/t0r0!t
I Nt4r; r040/7i0! 0.. Stro40r06 /6or (MS >;40!
I Ti90,r0;t06 8r90t0r! 0.. ti90 r04ir06 to 7oo; it w>0!? !0!B
For706 tr/!i0/t!
I Ti90,6080/60/t =o4/6r 7o/6itio/!? !o4r70 t0r9! 6ri>0 ti/,H0;9
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Tr/!i0/t F;ow Mo60;i/ Wor;ow
E/=;0 t0r.
S0t 48 8
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S0;07ti/ t
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Tr/!i0/t F;ow Mo60;i/ A/i9tio/!
Yo4 94!t !0t 48 / /i9tio/! EFO(E 80ror9i/ it0rtio/!.
I A/i9tio/ r90! r0 writt0/!tor06 o/,t
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P0ror9i/ It0rtio/!
T/7090/t!7
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5 CFD EXERCISE
1.23 F6+ F/ 8 H'* T78'7 +8 M++8 T''
Strt i/ Wor=0/7asic initiali+ation imposes the same
&alues in all cells" #ou can impro&e on this in &arious 'ays for
e-ample% $y patchin! different &alues into different +ones"
Se&eral features% includin! patchin! and post.processin!% are
not a&aila$le until after initiali+ation"
This computes a &alue
for each &aria$le% $ased
on a&era!e conditions in
the select +one" This
&alue is used in e&ery
cell 'hen you press
;Initiali+e"
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C;7;ti/
Wi0w r0!i64;! /6 9o/itor!
I 7
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1.24 L+87 P+' F/ P7' S'0++0*+8
P7' S'0++0*+8
C"-%! *$/ *$"-; ,!"/; + !/$+! ''% "* "-,+-, !+/ + $$/,!+,%+#"=%. T% ''% +&%,%! .2 & +- $%-;,* &.
T% -$%, =%$", +z 1 &. C"-%! ,% =%$", ," #% "-,+-, "=%! ,%-$%, !"8%,"-.
T% *$/ %+/, -," ,% +%-, +,&"'%!% +, + '!%/!% "* 1
+,&. T+ Enery-!"" > Edit.... F"! -"&'!%#$% *$" ,% %-%!; %>/+,"- %"/'$% *!"& ,% "-,-/, +- &"&%-,/& %>/+,"-. W% -%% ," "$=% ,% %-%!;%>/+,"- "-$ * % +!% -,%!%,% - %,%!&--; ,% ,%&'%!+,/!% ,!#/,"-. W% $$ -",%+$ , ,%&'%!+,/!% - , %+&'$%. S" $%+=% ,%Enery E#uation%, ," "** +- $ 'luid > Create(Edit...
I- ,% Create(Edit Materials&%-/ %, ,%Density," 1 inlet > Edit...
N",% ,+, ,% +oundary Condition ,ype "/$ +=% #%%- +/,"&+,+$$ %, ,"velocity-inlet. N" ,% =%$", +, ,% #et$$ #% '%*%. I- ,% Velocity nlet&%-/ %,,% Velocity Speci"ication Met)od," Components +- %, ,%Axial-Velocity $m(s&," 1 &
T%- $< !," $"% ,% Velocity nlet&%-/.O6*'* B687- C8+*+8
F!, %$%, outet- ,%+oundary Conditions&%-/
A +- #% %%- - ,% &+;% +#"=% ,% ,ype"/$ +=% #%%- +/,"&+,+$$ %, ,"pressure-outlet. I* ,% ,ype -", %, ,"pressure-outlet ,%- %, , ,"pressure-outlet. N"-" */!,%! +-;% +!% -%%% *"! ,% outet#"/-+! "-,"-.
C'8*'7+8' B687- C8+*+8
S%$%, "e#te#e- ,%+oundary Conditions&%-/
A +- #% %%- - ,% &+;% +#"=% ,% ,ype+ #%%- +/,"&+,+$$ %, ," /all -", "!!%,. C+-;% ,% ,ype," axis
W%- ,% +$"; #"% +''%+! $< 0es," +-;% ,% #"/-+! ,'%. T%- $< !," +%', e%-,%!$-%e + ,% "-% -+&%.
Page 62 of 81
https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Laminar+Pipe+Flow+-+Problem+Specificationhttps://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Laminar+Pipe+Flow+-+Problem+Specification -
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P+' W B687- C8+*+8
F!, %$%,ppea- ,%+oundary Conditions&%-/
S"$/,"-
S%"- O!%! S%&%
A %"-8"!%! !%,+,"- %&% $$ #% /% ," +''!"&+,% ,% "$/,"-. I-"!%! ," &'$%&%-, ,% %"- "!%! %&% $< "- outo# eto$,%- $< "-oe#tu+- %$%, e"o# :e ;p#.
S%, I-,+$ G/%
H%!% ,% *$" *%$ $$ #% -,+$% ," ,% =+$/% +, ,% -$%,. I- "!%! ," +!! "/, ,%-,+$+,"- $< "-Solution nitiali1ation,%- $< "- Compute "rom+- %$%, inlet.
T%- $< ,%nitiali1e#/,,"- . T "&'$%,% ,% -,+$+,"-.
S'* C8,'7'80' C7+*'7+
FLUENT !%'"!, + !%/+$ *"! %+ ;"=%!--; %>/+,"- #%-; "$=%. T% !%/+$ + &%+/!% "* " %$$ ,% /!!%-, "$/,"- +,*% ,% !%,% *"!& "* %+ ;"=%!--;%>/+,"-. W%X$$ ,%!+,% ,% "$/,"- /-,$ ,% !%/+$ *"! %+ %>/+,"- *+$$ #%$" 1%86. I-"!%! ," '%* ,% !%/+$ !,%!+ $Clic%& Monitors > esiduals > Edit...
N%, +-;% ,% !%/+$ /-%! Converence Criterion*"! continuityx-velocity+-y-velocity +$$ ," 1%86
L+,$ $< !," $"% ,%esidual Monitors&%-/.
E%/,% C+$/$+,"-
P!"! ," !/---; ,% +$/$+,"- ,% &+&/& -/%! "* ,%!+,"- &/, #% %,. T"'%* ,% &+&/& -/%! "* ,%!+,"- $< "-un Calculation,%- %, ,%*um3er o"terations," 1.
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1.25 F* P*' B687- L-'7
C"-%! + *$/ *$"-; +!" + *$+, '$+,% + $$/,!+,% +#"=%. O#,+- ,% =%$",
+- '!%/!% ,!#/,"- %- ,% R%-"$ -/%! #+% "- ,% '$+,% $%-;, 1.
T R%-"$ -/%! "#,+-% # /-; ,% *"$$"-; %,,-;.
o T% '$+,% $%-;, 1 &.
o T% -"&-; *$/ *$"-; - ,% 8!%,"- , + =%$", "* 1 &.
o T% %-, "* ,% *$/ 1
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T% %;, "* ,% "&+- $$ #% %, ," ,%- ,&% ,% #"/-+! $+%! ,
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4.2 S'* C8,'7'80' C7+*'7+
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