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COMPUTATIONAL FLUID DYNAMICS
FLUENT
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1 INTRODUCTION......................................4
1.1 FLUID DYNAMICS:............................................................4
1.2 TYPES OF FLOWS:.............................................................4
1.3 FLOW CLASSIFICATIONS:...............................................6
2 COMPUTATIONAL FLUID DYNAMICS
(CFD)..............................................................8
2.1 COMPUTATIONAL FLUID DYNAMICS:.........................82.2 CFD – Ho !" o#$%:............................................................8
2.3 APPLICATIONS OF CFD:...................................................&
2.4 AD'ANTAES OF CFD:....................................................&
2. LIMITATIONS OF CFD:....................................................1*
2.6 DISCRETI+ATION.............................................................11
2., TERMINOLOY:...............................................................1
2.8 MESH -UALITY:..............................................................1
2.& STRI'IN FOR -UALITY:..............................................1,
2.1* RID DESIN:..................................................................18
2.11 MAIN SOURCES OF ERRORS IN MESHIN:...............21
2.12 O'ERNIN E-UATION:...............................................212.13 CONTINUITY E-UATION:..............................................22
2.14 MOMENTUM E-UATION:..............................................23
2.1 NA'IERSTO/ES E-UATION:........................................23
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2.16 0OUNDRY CONDITIONS:...............................................24
2.1, MATERIAL PROPERTIES:...............................................2,
2.18 SOLUTION METHODS:...................................................28
2.1& PRESSURE 'ELOCITY COUPLIN:..............................3*
3 HEAT TRANSFER MODELLIN..........4*
4 TRANSIENT FLOW MODELLIN.......4,
CFD EERCISE.......................................2
.1 F! Fo 5 H75" T#5%7# ! 5 M!9! T77...................2
.2 L5;!5# P!5"!o.......................62
.3 F5" P5"7 0o5#? L5?7#...................................................6
.4 S"75? Fo P5%" 5 C?!7#...............................................6&
. U%"75? Fo P5%" 5 C?!7#...........................................,1
.6 S Fo O@7# 5 W77..........................................,4., Co;
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CHAPTER 1
1 INTRODUCTION
1.1.1 FLUID DYNAMICS:
F! ?5;!>% !% "B7 %>!7>7 o ! ;o"!o. F! o !% >o;;o? %"!7 ! o7
o "B#77 5?%:
• E95 ! ?5;!>%.
• N;7#!>5?: >o;% (CFD).
1. EXPERIMENTAL FLUID DYNAMICS (EFD)
• W! "7% (%=%o!> "#5%o!> % o"#=7>7 !#>5"!o >B57 >5@!"5"!o "7 ;7
2. THEORETICAL FLUID DYNAMICS
3. COMPUTATIONAL FLUID DYNAMICS (CFD)
N;7#!>5 5o#!"B;% Co; o%. TB7? 5#7: ! o #55# o.
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F!#71.2 #55# Fo
1.1.3 FLOW CLASSIFICATIONS:
1.3.1. LAMINAR FLOW:
I" !% "B7 o7 ! B!>B "B7 ! 7%%!@7 >#o%% %7>"!o o "B7 o
!!% o B5@! B!B @!%>o%!"?.
1.3.1.2. TURBULENT FLOW:
I" !% "B7 o7 ! B!>B "B7 ! 7% ;o@7 ! 5 "5=7 7% 5#7
"5"!o ! "B7 @7o>!"? 5
#% ! #!@7#% >55% %"#75;% 5"7#
%
I %"75? o @5#!o% >B5#5>"7#!%"!>% o o! !% %>B 5% @7o>!"? B5#5>"7#!%"!>% 5#7 !7>#% B7 5"7# o% "B#oB 5
B57 !"B #7%" "o "!;7. E. p = p(x,y,z,t). W5@7 ;o@7;7"% ! 5 %75 #7%7;=7% "B7
%"75? o >75#?.
1.3.1.5. NEWTONIANS FLUID:
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TB7 ! B!>B o=7?% NEWTONGS LAW OF 'ISCOSITY( %B75# %"#7%% !% !#7>"?
B o7% o" o=7?% NEWTONGS LAW OF 'ISCOSITY( %B75# %"#7%% !%
!#7>"? o;o%"5" ! 5 o !7. Fo#
5 "!>5 o;5%7 "B7 B57% B5@7 !""7 77>" o "B7!# @o;7.
1.3.1.#. COMPRESSIBLE FLOW:
A o !% %5! "o =7 >o;B57% #o; B57 o B57 o 57 ;"!
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CHAPTER 2
2 COMPUTATIONAL FLUID DYNAMICS (CFD)
2.1.1 COMPUTATIONAL FLUID DYNAMICS:
Co;% (CFD) !% "B7 %>!7>7 o "! ! o B75"
"#5%7# ;5%% "#5%7# >B7;!>5 #75>"!o% 5 #75"7 B o@7# "B7%7 7%%7% %! 5 ;7#!>5 7%%.
TB7 #7%" o CFD 55?%7% !% #77@5" 7!77#! 5"5 %7 !:
• Co>7o;5 ;o7 o 5 5 "5=7 (7.. %"75?%"5"7 !>o;! "o !;7%!o5). P#o@!7
5.
• TB7 >o7>"!o o >7% !% >57 "B7 #!.
• TB7 %7" o 57=#5!> 75"!o% 5#7 %o@7 ;7#!>5? (o 5 >o;
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• S?%"7; o 75"!o% 5#7 %o@7 %!;"57o%? "o
• A7#o?5;!>% o #o @7B!>7% 5!#>#5" ;!%%!7%.
• F!; >o5"! "B7#;oo#;! ! ;5"7#!5 7%%! 5oo! o% ! =!!%.
• CB7;!>5 @5"#!.
• H75" "#5%7# o# 77>"#o!>% $5! 5o;7 ;o#7 $ "#5#o ;75% 7!77#! 5"5 >5 =7 !"#o>7 75#? ! "B7
7%! 7%%.
& A++*- * +6*' 7' 08+*+8
• M5? o 5 B75" "#5%7# 7%%7% >5 o" =7 (75%!?) "7%"7 7..
B? o.
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• CFD o!"!o.
& A++*- * +6*' +' 08+*+8.
• CFD 5o% #75" >o"#o o@7# "B7 5 7%% 5 o%"5"
"7;.).
• CFD 5o% "B7 55?%" "o 795;!7 5 5#7 ;=7# o o>5"!o% ! "B7
#7!o o !"7#7%" 5 ?!7% 5 >o;B7;!%"#? ;"!5 o? =7 5% 5>>#5"7 5% "B7 5 ;o7% o
B!>B "B7? 5#7 =5%7.
& N6'7+0 '777:
• So@! 75"!o% o 5 >o;7% ;7#!>5 7##o#%.
• Roo 7##o#: 7 "o !!"7 o# %!7 5@5!5=7 o "B7
>o;5 =7 %;5
! ;o%" >5%7%).
• T#>5"!o 7##o#: 7 "o 55"!o 7##o#% ! o "o 7#o 5% "B7 #! !% #7!7. M7%B #7!7;7"
!% o7 5? "o 75 !"B "#>5"!o 7##o#.
& B687- 08+*+8:
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• A% !"B 5 ;o7% "B7 5>>#5>? o "B7 CFD %o"!o !% o? 5%
oo 5% "B7 !!"!5J=o5#? >o!"!o% 5
;o7.
• E95;" !"B %7 79
#5"B7# "B5 5%%;7 !o#; >o!"!o%.
2.1.$ DISC%ETI&ATION
TB7 5#" o %=!@!! 5 %"#>"#7 !"o 5 >o@7!7" ;=7# o %;57#
>o;7%. TB7 !%>#7"!7 o;5! !% >57 "B7 K#!G o# "B7 K;7%B.G 77#5
>o%7#@5"!o ("#5%. 5#7 !%>#7"!7 !"o
57=#5!> 75"!o%. TB!% !% 77#5? 5#7"!7 E7;7"
2.!.1. GRID:
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TB7 #! !% o"B! =" "B7 o;5! "B5" !% 7%>#7"!7 !"o 5 !!"7 %7" o >o"#o @o;7%
o# >7%. TB7 7#77 o #! #7%o"!o !% 5%o 7>7%%5#? "o ! %o"!o o# 5 B
#7!o o "B7 o;5!.
TB7#7 5#7 "B#77 !7#7" "?
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F!#7 2.3 T7"#5 M7%B
2.!.2.2. >UADRILATERAL MESH:
Fo# %!;7% "B5 5 >o;
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2.!.2.3. HYBRID MESH:
TB!% !% "B7 >o;=!5"!o o !7#7" "?? 5 5>>#5>? 5#7
7B5>7 #75"!@7 "o "7"#5B7#o 5 B795B7#5 ;7%B. I" >o%!%"% o =o"B ;7%B #o"7#% 5;7%B >!7"% ! B!>B =o"B "B7 "?7"7# >7"7# o 5 >7.
• E7 =o5#? o 5 5>7.
• F5>7 =o5#? o 5 >7.
• +o7 #o7% 5 >7%:
– W5 =o5#? o7.
– F! >7 o7.
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• Do;5! #o< o o7 5>7 5 >7 o7%.
F!#7 2.6 2D 3D C7 T7#;!oo?
2.1.( MESH )UALITY:
Fo# "B7 %5;7 >7 >o" B795B7#5 ;7%B7% ! !@7 ;o#7 5>>#5"7 %o"!o% 7%!5?
! "B7 #! !7% 5#7 5!7 !"B "B7 o. TB7 ;7%B 7%!"? %Bo =7 B!B 7oB "o
>5
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o7% 5 5>7 %B5
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F!#7 2.8 A%" #5"!o ! M7%B!
2.1.* ST%I!IN" FO% )UALITY:
A 7 %!7. Fo# 795;7" >7 %Bo o"
B5@7 +' 7*+ #75"7# "B5 2*. I %>B 77 *.8.• T#!%: %$77%% %Bo o" 79>77 *.8.• T7"%: %$77%% %Bo o" 79>77 *.&.
@6' '/8' @ C' >6+*-.
2.1.1+ "%ID DESI"N:
2.1%.1. GRID DESIGN GUILDLINES: RESOLUTION
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TB7 75"#7% o >#5>? >5 =7 ;57. RoB ;7%B! %#5>7 77;7" 75% "o !5>>#5>?.
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F!#7 2.1* S;oo"B7%% o# #!
I 5 ;7%B! 77;7" "B7 ;59!;; >B57 ! #! %! ;%" =7 7%% "B5 2*.
2.1%.3. GRID DESIGN GUILDLINES: TOTAL CELL COUNT
I "B7 ;=7# o #!% o# >7% 5#7 ;o#7 "B7 "B7 5>>#5>? o "B5" ;7%B! 77;7"
! =7 B!B7#. A" "B7 %5;7 "!;7 !" ! !>#75%7 ;7;o#? %57 5 CPU "!;7. TB7#7 5#7 "o
5?% %7 "o $77< >7 >o" o o7 !% U%7 5 o!o#; #! "o >%"7# >7% o? B7#7
"B7? 5#7 777 5 o"B7# o7 !% U%7 %o"!o 55o"% %Bo =7 "B7 o#7# o oo!
• 1E4 5#7 #75"!@7? %;5
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• 1E6 5#7 5#7. S>B 5 =7 7!>!7"? # %!
;"!o;;o ! 57#o%7 5 5"o;o"!@7 5o5#%7.
• H!B %$77%%.
• L5#7 ;7%.
• L5#7 5%" #5"!o%.
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• I"7#oo#;5 !"7#5>7%.
• I57 "B7 oo! >o%7#@5"!o 5% o %:
• Co%7#@5"!o o ;5%%.
• N7"o% %7>o 5: "B7 >B57 o ;o;7"; 75% "B7 %;
o o#>7% o 5 ! "#7 5 ;o"!o% ;5? =7 !o#7.
2.12.1. LAGRANGIAN DESCRIPTION:
TB!% 5B ! o%!%"% o "B7 %5;7 !
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>o%!7# Bo o 7%.
F!#7 2.13 E7#!5 Mo7
2.1.13 CONTINUITY E)UATION:
TB7 >o"!!"? 75"!o !% o@7#7 #o; "B7 7+80+' 08'7,*+8 . I"
%"5"7% "B5" *9' 6+ /+8 *9769 *9' +' * 07 '0*+8 7'+8
08*8* + *9'7' + 8 6+ + ' 7 7',' 7 *9' +'.
MASS BALANCE:
R5"7 o !>#75%7 o ;5%% ! ! 77;7" 75% "B7 7" #5"7 o
o o ;5%% !"o 77;7". R5"7 o !>#75%7 o ;5%% !% 79"!o !% 75 "o #5"7 o >B57 o ;o;7"; ! "B5" !#7>"!o.
L!75# !;B57 ! !75# ;o;7";.
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I 9!#7>"!o !!"!5 !75# !;B 5% #5@!"?
>7"#!5 Co#!o!% 5 77>"#o;57"!> o#>7%.
2.1.1# NA!IE%,STO-ES E)UATION:
TB7 75"!o% o ;o"!o% !"Bo" >o%!7#! o#>7 7 "o "#=7>7 5
>o%!7#! "B7 #5@!"? o%!"? o#>7% 5#7 $o 5% 5@!7#%"o$7% 75"!o.
F9 (F)9 V (F "!o.
FY (F)? V (F "!o.
F+ (F) V (F "!o.
B7#7 F – #5@!"? o#>7.
F o% o#>7.
A"BoB TB7 N5@!7#S"o$7% 75"!o% o#; 5 >oo%7#@5"!o o ;5%% ;o;7"; 5 77#? o# 5 !. Fo#
5 N7"o!5 ! ! o7 !;7%!o "B7? >5 =7 #!""7 5%
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ρ !% "B7 ! 7%!"? u !% "B7 @7o>!"? e !% "B7 "o"5 77#? o>"!@!"?. TB7
"o"5 77#? e !>7% !"7#5 77#? o!"!o% 5#7 5 #7!#7 >o;5 ;o7. TB7
=o5#!7% !#7>" ;o"!o o o. TB!% ! =7 %!? "B7 97% !"o "B7 >o;7
o7%. 0o5#? >o!"!o% 5#7 5 #7!#7 >o;5 ;o7.
0o5#!7% 5 !"7#5 %#5>7% 5#7 #7
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F!#7 2.14 P!B7" =o5#? >o!"!o o7 #!=7% "B7 @57 o 5 @5#!5=7 5"
"B7 =o5#? 7.. u(x) = "o#$ta#t . WB7 %! 5 N7;5 =o5#? >o!"!o o7
#!=7% "B7 #5!7" o#;5 "o "B7 =o5#? o 5 @5#!5=7 5" "B7 =o5#? 7.. #u(x) =
"o#$ta#t . WB7 %! 5 ;!97 =o5#? >o!"!o 5 >"!o o "B7 o#; au(x)%&u(x) =
"o#$ta#t !% 5o!"!o% "?5"7% o;5%7%. TB7 =o5#? 5"5 #7!#7 7"7. So;7 o "B7
!7!7% 5#7 ;7"!o7 =7o B!>B !% %7 o# >Boo%! !7" 5 o"7" >o!"!o%.
• S77>" =o5#? o>5"!o 5 %B5B "B5" o 7!"B7# o7% !
o# o". No" ;55"o#? =" ! "?5? #7%" ! =7""7#
>o@7#7>7.
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• SBo o" o=%7#@7 5#7 #5!7"% ! !#7>"!o o#;5 "o
=o5#? 75# !7"% 5 o"7"%. TB!% !!>5"7% 5 !>o##7>"
5"!o.
• M!!;!7 #! %$77%% 75# =o5#?
.
2.1!.3. PRESSURE BOUNDARY CONDITIONS:
P#7%%#7 =o5#? >o!"!o% #7!#7 %"5"!> 57 o!7 o 77% "o =7 7!7.
F!#7 2.1 P#7%%#7 7@7%
2.1!.4. @ELOCITY INLETS:
'7o>!"? !7"% 7!7% @7o>!"? @7>"o# 5 %>55# !"? o;o;5 75 "o o5 #7%"%. Do" $77< 5 @7o>!"? !7" "oo >o%7 "o 5
%o! o=%"#>"!o. TB!% ! 75 "B7 %o"!o "o =7 o5.
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2.1!.5. OUTFLOW BOUNDARY:
O"o =o5#? >o!"!o% 5#7 %7 "o ;o7 o 79!"% B7#7 "B7 7"5!% o "B7
o @7o>!"? 5 o7!>!7"% "o ;B 5% 7%!"? @!%>o%!"? ;o7>5# 7!B" "B7#;5 >o>"!@!"?
!%!o >o7!>!7"%. WB!>B o%"5" ( >o%"5"). I >5%7 o >o;!!7 >"!o%. Ho7@7# o# B!B M5>B ;=7# o% %! "B7 >o
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2.1.1( SOLUTION METHODS:
2.1#.1. FINITE ELEMENT METHOD:
TB!% !% 5 ;7#!>5 ;7"Bo o# %o@! 5
55?%!%. I "B!% ;7"Bo 5 =o? o# 5 %"#>"#7 ! B!>B "B7 55?%!% "o =7 >5##!7 o" !%
%=!@!7 !"o %;57# 77;7"% o !!"7 !;7%!o% >57 !!"7 77;7"%. TB7 "B7 =o? !%
>o%!7#7 5% 5 5%%7;=57 o "B7%7 77;7"% >o7>"7 5" 5 !!"7 ;=7# o o!"% >57
8' o# No5 B5!>% 5 %"#>"#5
;7>B5!>% o!"!o% 5@5!5=7. I" o#$% 7 o# "o !;7%!o5 #7!o% !"B
=o5#!7% oo#!5"7 597%.
TB7 o;5! !% !%>#7"!7 !"o 5 %7#!7% o #! "#7G ;7%B !% #7!#7.TB7 o@7#! 75"!o% (! !7#7"!5 o#;) 5#7 !%>#7"!7 (>o@7#"7 "o 57=#5!> o#;).
F!#%" 5 %7>o 7#!@5"!@7% 5#7 5"
"o #!"7 77#5 >o;
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2.1#.3. FINITE @OLUME METHOD:
TB7 =5%!> !75 o 5 !!"7@o;7 ;7"Bo !% "o %5"!%? "B7 !"7#5 o#; o "B7
>o%7#@5"!o 5 "o %o;7 7#77 o 5o"#o
@o;7% B!>B >o@7# "B7 o;5! o !"7#7%". TB!% ;7"Bo 5% 5""#5>"!@7 =7>5%7 B!7
@5#!5=7% ;5? o" =7 >o"!o%? !7#7"!5=7 5>#o%% %Bo>$% 5 o"B7# !%>o"!!"!7%
;5%% ;o;7"; 5 77#? 5#7 55?% >o%7#@7.
AD@ANTAGES:
• TB!% ;7"Bo o7% o" !;!" >7 %B5B57 ! "B7 @5#!5=7 #o; o7 !"7#5"!o "o
"B7 79" =7>o;7% %o %;5 "B5" "B7 %o"!o >5 =7 >o%!7#7 >o@7#7. A" >o@7#7>7 5
!%>#7"7 >o%7#@5"!o 75"!o% (;o;7"; 77#? 7">.) 5#7 o=7?7 ! 5 >7% "o 5%!!7 "o7#5>7 "B7 %o"!o o o7# >B57% !"B 5!"!o5 !"7#5"!o%. M5%%
;o;7"; 77#? 5 %>55# =55>7% 5#7 o="5!7. R7%!5% ;75%#7 !;=55>7 (o# 7##o#)
! >o%7#@5"!o 75"!o%. TB7 oo! "B!% %Bo =7 >o%!7#7 B!7 >o@7#7>7
• A5?% 7%#7 7 =7o#7 %! 5 %o"!o. >o@7#7
%o"!o% >5 =7 ;!%75!.
• So"!o% 5#7 >o@7#7 B7 "B7 o !7 5 %>55# !7% 5#7 o o7#
>B5!.
2.1#.5. MONITOR RESIDUALS:
I "B7 #7%!5% B5@7 ;7" "B7 %!!7 >o@7#7>7 >#!"7#!o =" 5#7 %"! 7>#75%!
"B7 %o"!o ;5? o" ?7" =7 >o@7#7. I "B7 #7%!5% 7@7# ;77" "B7 >o@7#7>7 >#!"7#!o
=" 5#7 o o7# 7>#75%! 5 o"B7# %o"!o ;o!"o#% o o" >B57 7!"B7# "B7 %o"!o !%
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>o@7#7. F!5 #7%!5% 5#7 o"7 B!B7# !"B B!B7# o#7# !%>#7"!5"!o %>B7;7% "B5
!"B !#%" o#7# !%>#7"!5"!o. TB5" o7% o" ;75 "B5" "B7 !#%" o#7# %o"!o !% =7""7#.
R7%!5% >5 =7 ;o!"o#7 #55? 5%o.
F!#7 2.16 Mo!"o# R7%!5%
2.1.1* P%ESSU%E !ELOCITY COUPLIN":
P#7%%#7 5 75"!o o#
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"B7 o##7>"!o p' !% 7#!@7 ! 5 o#; %!;!5# "o "B7 75"!o% 7#!@7 o# "B7
>o@7>"!o!%!o 75"!o%:
5
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TB7 !7#7>7% 5#7 ! %B 5o#!"B; !% 5%"7%" 7o
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WB7#7 * "!;7 %"7"7#!5"!o o T#=7" Fo%
F#o; N5@!7#S"o$7% E5"!o% "o R7?o%A@7#57 N5@!7#S"o$7% (RANS) Mo7%
R7?o% S"#7%% T7%o# 5 "B7 Co%#7 P#o=7;
T#=7>7 /!7"!> E7#? ( ) E5"!o
E? '!%>o%!"? Mo7% (E'M)
R7?o% S"#7%% Mo7 N75#5 T#75";7"% O7 Mo7! !7!7%
A% o T#=7>7
IB7#7"? %"75? "B#77 !;7%!o5 5 5 %!#! ;o"!o% (>"5"!o%)
#7%"! ! 7B5>7;7" o ;!9! B75" "#5%7# 5 %B75#.
I%"5"57o% >"5"!o% 5#7 #5o; ("5=7) =o"B ! %7 5 ! "!;7. 0"
%"5"!%"!>5 5@7#5! o "#=7>7 >"5"!o% #7%"% ! 5>>o"5=7 "#5%57% (@o#"!>7% o# 7!7%) 79!%" ! 5 "#=7" o% (#o; @7#?
%;5 "o @7#? 5#7).
'7#? %7%!"!@7 "o (o# 7o!"!o%.
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U%"75? 5 ;o"!o ! B!>B 5 "B#77 @7o>!"? >o;o;!"? !"o ;75 5 >"5"!
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2.21.2. TRANSITION IN KET FLOW:
F!#7 2.1& T#5%!"!o ! Z7" Fo
2.21.3. TURBULENT FLOW CORRELATIONS:
EXTERNAL FLOWS:
R79 [ \1* 5o 5 %#5>7.
R7D [ 2**** 5#o 5 o=%"5>7.
INTERNAL FLOWS:
R7D [ 122**
WB7#7 R7L ULJ ]
L 9 D DB 7">.
WB7#7 R7 – R7?o% ;=7#. ^ D7%!"? o !. U ^ '7o>!"? o !. L ^ L7"B o "=7. ^ '!%>o%!"? o !. D ^ D!5;7"7# o "=7.
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2.21.4. TURBULANT BOUNDARY LAYER:
I "#=7" o "B7 =o5#? 5?7# !% 7!7 5% "B7 "B! #7!o o "B7 %#5>7 o 5
=o? ! B!>B @!%>o% 77>"% 5#7 !;!"? U "o 5 @7o>!"? o 7#o 5" "B7 5. TB7 @7o>!"? >o;#o%% "B7 5?7# 5#7 ;>B #75"7# "B5 "B7 #5!7"% ! "B7 o !#7>"!o. TB7
=o5#? 5?7# "B!>$7%% !% 7!7 5% "B7 !%"5>7 55? #o; "B7 %#5>7 B7#7 "B7
@7o>!"? #75>B7% && o "B7 #77%"#75; @7o>!"?.
- /9'7' 6U %.$$.
WB7#7 5# ? 5"7# "B!>$7%%. 6@7o>!"? o !.
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F!#7 2.2* T#=7" 0o5#? L5?7#
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2.21.5. RANS M' D'07+*+8 8 B'9,+7 S67-
Mo7 D7%>#!o%!"?.
D7%!7 %!!>5? o# 57#o%7 5o5#%7# ;7%B7%.
O7 %"#5! #5"7 ! $ "!o "7#; !;5
o%.S"55# $–_ TB7 =5%7!7 "o"#5%!7"% 5#7 7;5? 7#!@7 @5! o# ? "#=7" o% o?.
O>o" o# @!%>o% B75"! =o?5>? 5 >o;B57% ! "B7 _ 75"!o !;5 >o%"#5!"% "o =7 o=7?7 B!>B "!;5"7? !; !%%!o9 (1&&8). TB!% !% "B7 75" $–` ;o7. D7;o%"#5"7% %o" o# "#5%!"!o5 #77 %B75# 5 >o;o9 ;o7 o# %7
75# 5% 5 "B7 %"55# $–_ ;o7 55? #o; 5% %! 5 =7! >"!o.
A%o !;!"% "#=7" @!%>o%!"? "o 5#5"77 "B5" aT b $. TB7 "#5%!"!o 5 %B75#!
oo;o%!"? 5%%;
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S %"!7%.RN $–_ S!"5=7 o# >o;@o#"!>7% 5 o>5? "#5%!"!o5 o% (7.. =o5#? 5?7# %7o;B!7#?). C5 =7 %7 o# "#5%!"!o5 o% ("BoB "7% "o "
75#? "#5%!"!o). S7"7 "o =7 79>7%%!@7 5 75#?.SST $–` O7#% %!;!5# =77!"% 5% %"55# $–`. D7? o 5 !%"5>7
;5$7% "B!% 7%% %!"5=7 o# #77 %B75# o%.R7?o% S"#7%% PB?%!>5? "B7 ;o%" %o RANS ;o7. A@o!% !%o"#o 7? @!%>o%!"?
5%%;o%7 >oo;
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3 HEAT TRANSFER MODELLING
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4 TRANSIENT FLOW MODELLING
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5 CFD EXERCISE
5.1.1 F6+ F/ 8 H'* T78'7 +8 M++8 T''
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5.1.2 L+87 P+' F/ P7' S'0++0*+8
• P7' S'0++0*+8
• Co%!7# ! o! "B#oB 5 >!#>5# o%"5" #5!% 5% !%"#5"75=o@7. TB7
• TB7 !7" @7o>!"? + z 1 ;J%. Co%!7# "B7 @7o>!"? "o =7 >o%"5" o@7# "B7!7" >#o%%%7>"!o.
• TB7 ! 79B5%"% !"o "B7 5;=!7" 5";o%B !% 5" 5 o7!>!7" o @!%>o%!"? - = 2 x 103 g! ($). TB7 R7?o% ;=7# /e =5%7 o "B7 !"? 5" "B7 !7" B!>B !% 1 ;J% ! "B!% >5%7.
So@7 "B!% B. Po" "B7 >7"7#!7 @7o>!"? 5%$!#!>"!o >o7!>!7" 5 @7o>!"? o%Mo7 OB57% 5#7 777. C!>$ Cancel "o 79!" "B7 ;7. No "B7 E7#? Mo7 Edit.... Fo# !>o;o!>$ Cancel "o 79!" "B7 ;7.
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D'+8' M*'7+ P7'7*+'
No "B7 #75"75 7 ! $Clic%& Materials > 'luid > Create(Edit...
I "B7 Create(Edit Materials ;7 %7" "B7 Density "o 1$J;c3 (>o%"5") 5 %7" "B7Viscosity "o 273 $J(;%) (>o%"5")
C!>$ C)ane(Create. Co%7 "B7 !o.
D'+8' B687- C8+*+8
A" "B!% o!"!o% o# "B7 o# *amed Selections ! =7 %!!7. TB7
=o5#? >o!"!o o# "B7 #et ! =7 %!!7 !#%".I8'* B687- C8+*+8
I o#7# "o %"5#" "B7 7%% $Clic%& +oundary Conditions > inlet > Edit...
No"7 "B5" "B7 +oundary Condition ,ype %Bo B5@7 =77 5"o;5"!>5? %7" "ovelocity-inlet . No "B7 @7o>!"? 5" "B7 #et ! =7 %!!7. I "B7 Velocity nlet ;7 %7""B7 Velocity Speci"ication Met)od "o Components 5 %7" "B7 Axial-Velocity $m(s& "o 1 ;J%
TB7 >!>$ ! "o >o%7 "B7 Velocity nlet ;7.
O6*'* B687- C8+*+8
F!#%" %77>" outet ! "B7 +oundary Conditions ;7
A% >5 =7 %77 ! "B7 !;57 5=o@7 "B7 ,ype %Bo B5@7 =77 5"o;5"!>5? %7" "o pressure-outlet . I "B7 ,ype !% o" %7" "o pressure-outlet "B7 %7" !" "o pressure-outlet . Noo #"B7# >B57% 5#7 777 o# "B7 outet =o5#? >o!"!o.
C'8*'7+8' B687- C8+*+8
S77>" "e#te#e ! "B7 +oundary Conditions ;7A% >5 =7 %77 ! "B7 !;57 5=o@7 "B7 ,ype B5% =77 5"o;5"!>5? %7" "o /all B!>B
!% o" >o##7>". CB57 "B7 ,ype "o axis
WB7 "B7 !5o =o97% 5$ 0es "o >B57 "B7 =o5#? "?!>$ ! "o 5>>7
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P+' W B687- C8+*+8
F!#%" %77>" ppea ! "B7 +oundary Conditions ;7
So"!o
S7>o O#7# S>B7;7
A %7>oo#7# !%>#7"!5"!o %>B7;7 ! =7 %7 "o 5!>$ o outo# eto$ "B7 >!>$ o oe#tu 5 %77>" e"o# :e ;p# .
S7" I!"!5 7%%
H7#7 "B7 o !7 ! =7 !!"!5!7 "o "B7 @57% 5" "B7 !7". I o#7# "o >5##? o" "B7!!"!5!5"!o >!>$ o Solution nitiali1ation "B7 >!>$ o Compute "rom 5 %77>" inlet .
TB7 >!>$ "B7 nitiali1e =""o . TB!% >o;
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5.1.3 F* P*' B687- L-'7
• Co%!7# 5 ! o! 5>#o%% 5 5" 7 "B7 o"7# =o5#?. A #7>"55# o;5! ! =7 %7 o# "B!% %!;5"!o.
• TB7 B7!B" o "B7 #7>"55# o;5! ! =7 7"7#;!7 =? "B7 79"7 =o5#?5?7# "B!>$7%%.
• Fo# 5 5" $7%%.
WB7 9 L *.*;.
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• TB7 B7!B" o "B7 o;5! ! =7 %7" "o "7 "!;7% "B7 =o5#? 5?7# "B!>$7%%. TB%"B7 B7!B" o "B7 =o5#? ! =7 %7" "o *.;. TB7 oo! !#7 %Bo% "B7
!;7%!o% o "B7 o;5! 5 "B7 =o5#? 5=7% B!>B ! =7 %7 "o %7" "B7 =o5#? >o!"!o%.
1.ef#e oe Popete$
I "B!% %7>"!o "B7 @5#!o% %o@7# $ o Solution Met)ods "B7 >!>$ o Momentum 5 %77>" Second !rder 6p/ind..
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https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flat+Plate+Boundary+Layer+-+Problem+Specificationhttps://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flat+Plate+Boundary+Layer+-+Problem+Specificationhttps://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flat+Plate+Boundary+Layer+-+Problem+Specification
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4.2 S'* C8,'7'80' C7+*'7+
FLUENT #7B o@7#!75"!o. W7 !"7#5"7 "B7 %o"!o "! "B7 #7%!5 o# 75>B 75"!o 5% =7o 176. I
o#7# "o %!? "B7 #7%!5 >#!"7#!5
$Clic%& Monitors > esiduals > Edit....
N79" >B57 "B7 #7%!5 7# Converence Criterion o# continuity x-velocity5 y-velocity 5 "o 176 5% >5 =7 %77 =7o.
L5%"? >!>$ ! "o >o%7 "B7 esidual Monitors ;7.
4.3 S'* I8+*+ G6'
H7#7 "B7 o !7 ! =7 !!"!5!7 "o "B7 @57% 5" "B7 !7". TB5" !% "B7 !!"!5 @57% o5 "B7 >7% ! =7 %7" "o 1 ;J% 5 * P5 o# 9 @7o>!"? 5 57 5##? o" "B7 !!"!5!5"!o >!>$ o Solution nitiali1ation "B7 >!>$ o Compute "rom 5 %77>" inlet 5% %Bo =7o.
5. R'6*
.1O"7" '7o>!"? P#o!7
I "B!% %7>"!o 7 ! !#%" o;!"? 5o "B7o"7". TB7 7 ! o; 5lots > 70 5lot... > Set 6p.. 5% %Bo =7o.
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W7 >#75"7 5 %"#5!B" @7#"!>5 !7 #o; (9*?*)(*.*) "o (91?1)(*.*.). S77>" Line,ool 7# !ptions. E"7# x8*. y8* x4*. y4*.. E"7# !71 7# *e/ Sur"ace *ame. Yo# Line(a%e Sur"ace ;7 %Bo oo$ 795>"? !$7 "B7 oo! !;57.
N79" >!>$ Create. No "B5" "B7 @7#"!>5 !7 B5% =77 >#75"7 7 >5 77 "o "B7 $ o 5lots "B7 o=7 >!>$ 70 5lot "o o"!o 5=o@7 79>7"!o%. M5$7 %#7 "B5" 9rite to 'ile!% o" %77>"7 "B7 >!>$ 5lot . Yo %Bo o="5! "B7 oo! o"
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5.1.4 S*'- F/ P* C-+8'7
P7' S'0++0*+8
• Co%!7# "B7 %"75? %"5"7 >5%7 o 5 ! o! o;o;!"? !% %7" "o 1 ;J% 5 "B7 7%!"? o "B7 ! !% %7" "o 1$J;c3. TB% "B7 ?5;!> @!%>o%!"? ;%" =7 %7" "o *.* $J;e% ! o#7# "o o="5! "B77%!#7 R7?o% ;=7#.
P7'A8-+ Q S*7*U
P#!o# "o oo!"!o% 5#7.
S6*+8 D+8
Fo# 5 79"7#5 o !#>5# o;5! ! =7 %7 o# "B!% %!;5"!o. TB7 77>"% "B5" "B7>?!7# B5% o "B7 o 79"7 5#. TB% "B7 o"7# =o5#? ! =7 %7" "o =7 64 "!;7% 5%
5#7 5% "B7 !5;7"7# o "B7 >?!7#. TB5" !% "B7 o"7# =o5#? ! =7 5 >!#>7 !"B 5!5;7"7# o 64 ;. TB7 %o"!o o;5!!%>%%7 B7#7 !% !%"#5"7 =7o.
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B687- C8+*+8
F!#%" 7 ! %!? 5 @7o>!"? !7" =o5#? >o!"!o. W7 ! %7" "B7 7" B5 o"B7 o"7# =o5#? 5% 5 @7o>!"? !7" !"B 5 @7o>!"? o 1 ;J% ! "B7 9 !#7>"!o. N79" 7! %7 5 o!"!o o# "B7 7" B5 o "B7 o"7# =o5#? !"B 5
57 ?!7#5. TB7 5o#7;7"!o7 =o5#? >o!"!o% 5#7 !%"#5"7 =7o.
S'*6 (P9-+0)
D6' P7'0++8:S77>" Dou3le 5recision.
S6*+8: S'08 O7'7 U/+8 M'8*6 S09''
Solution > Solution Met)ods > Spatial Discreti1ation.S7" Momentum "o Second !rder6p/ind
C8,'7'80' C7+*'7+8
Solution > Monitors > esiduals > Edit....S7" "B7 A3solute Criteria o# x-velocity 5 y-velocity 5 "o 176. C!>$ o%
Solution > Monitors > Dra > Edit....TB7 >B7>$ 5rint to Console 5 5lot . N79" >!>$cylinder/all B!>B !% o>5"7 7# 9all :ones. L5%"?>!>$ o%
R7%"%'o#"!>!"?:R7%"% f #5% 5 A!;5"!o% f Co"o#%f S7" U
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• Co%!7# "B7 %"75? %"5"7 >5%7 o 5 ! o! o;o;!"? !% %7" "o 1 ;J% 5 "B7 7%!"? o "B7 ! !% %7" "o 1 $J;c3. TB% "B7?5;!> @!%>o%!"? ;%" =7 %7" "o 8.33391*c3 $J;e% ! o#7# "o o="5! "B7 7%!#7R7?o% ;=7#.
• Fo# "B!% U%"75? C5%7 "B7 o@7#! 75"!o =7>o;7% o !75# 7 "o "B75!"!o o 5 "!;7 7#!@5"!@7 "7#;:
• TB7 ;7"Bo% !;5%7. I "B!% >5%7 "B7 o;5! 5 =o5#?>o!"!o% ! =7 "B7 %5;7 5% "B7 S"75? Fo P5%" 5 C?!7#.
• Ho7@7# =7>5%7 "B!% !% 5 "#5%!7" %?%"7; !!"!5 >o!"!o% 5" "* 5#7 #7!#7. To
%o@7 "B7 %?%"7; 7 77 "o !o@7#7>7 o# 5 !;!" o !"7#5"!o% !% #75>B7 "B7 ! 77 "o "B7 79" "!;7 %"7B!d "B#oB "!;7 "! "B7 7 "!;7 !% #75>B7.
1. S'*6 (P9-+0)
D5"7 S"75? Fo P#o7>"
F!#%" >o; Duplicate
L5>B F7".
$Dou3le Clic%& Setup ! "B7 5"7 ". S77>" Dou3le 5recision. TB7 >!>$ !
T#5%!7"
I "B!% %"7< B7#7 7 ! "7 FLUENT "o %o@7 o# "B7 %"75? o. A% ?o >5 %77 =?75" FLUENT ! %o@7 o# "B7 %"75? o.
Po&e etup > ?e#ea . S'* Te * Ta#$e#t .
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https://confluence.cornell.edu/display/SIMULATION/FLUENT+12.1+-+Steady+Flow+Past+a+Cylinder+-+Problem+Specificationhttps://confluence.cornell.edu/display/SIMULATION/FLUENT+12.1+-+Steady+Flow+Past+a+Cylinder+-+Problem+Specificationhttps://confluence.cornell.edu/display/SIMULATION/FLUENT+12.1+-+Steady+Flow+Past+a+Cylinder+-+Problem+Specification
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S!? M5"7#!5 P#o$ C)ane(Create "B7 >!>$ close
2. So"!oCo@7#7>7 C#!"7#!o: T# o D#5 T# o L!"
Solution > Monitors > Dra > Edit.... TB7 >B7>$ 5rint to Console 5 >B7>$ 5lot .C!>$ o% .
Solution > Monitors > Li"t > Edit.... TB7 >B7>$ 5rint to Console 5lot 5 9rite. C!>$ o% .TB7 5%" oo7!>!7" 5"5 "o 5 !7 "B5" !% =#!7 ! o7 o "B7 %=o7#%"B5" FLUENT >#75"7% ! "B7 o#$! o7#. Yo B5@7 "o ! 5#o "o ! !".
So"!o I!"!5!5"!o
Adapt > eion.... TB7 %7" 7 Min "o *. ; %7" 7 Max "o 32 ; %7" 0 Min "o * ; 5 %7" 0 Max "o 32;. C!>$ Mar% "B7 >!>$ Close.
Solution > Solution nitiali1ation. S7" Compute 'rom "o "ar"ield4.. C!>$ nitiali1e. N79">!>$ 5atc). Co;!>$ close.
S7""! U< D5"5 E95>5"7. To o %o 7 ! 77 "o 79!"?
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># o o. I "B!% >5%7 7 ! 79o;# o "B7@7o>!"? 7@7#? "!;7 %"77 So"!o ! T!;7
Solution > un Calculation. S7" ,ime Step Si1e "o *.2 %7>o% 5 %7" "B7 *um3er !" ,ime Steps "o 2**. No >!>$ Calculate. (Yo ;5? B5@7 "o B!" Calculate "!>7.) No B5@7 5 ><
o >o77. Co"!7 "B7 "!;7%"7
5.1.! S6'78+0 F/ O,'7 W''
P#o=7; S!!>5"!o
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• Co%!7# 5 1g 57 77 5" 7#o 57 o 5""5>$. TB7 !>o;! o >o!"!o%5#7: M13 !7" o "B7 77 %#5>7 !"B "B7 >o##7%$.
5ro3lem Setup > Models
Do=7 >!>$ o Viscous - Laminar
S77>" nviscid 7# Model .
C!>$ ! . TB!% ;75% "B7 %o@7# ! 77>" "B7 @!%>o% "7#;% ! "B7 o@7#! 75"!o%.
M' E8'7-
Do=7 >!>$ o Enery - !""
I >o;oo"!!"? 5 ;o;7";75"!o%. So 7 77 "o %o@7 "B7 77#? 75"!o o# o# !>$ ! .
5ro3lem Setup > Materials
M5$7 %#7 5!# !% %77>"7 7# 'luid . Do=7 >!>$ 5!# %7" Density "o ideal-as 5;5$7 %#7 Cp !% constant 5 75 "o 1**6.43 J$$. A%o ;5$7 %#7 "B7 Mo7>5# W7!B"!% >o%"5" 5 75 "o 28.&66 $J$;o. S77>"! "B7 ideal as o
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D'+8' O'7*+8 C8+*+8
To 7#%"5 B5" "B7 !peratin 5ressure !% #75 "B#oB "B7 %Bo#"5%77"
%7>"!o 8.14.2 ! "B7 %7#% !7. W7 %77 "B5" o# 5 o% FLUENT %7% "B7 57 5" @5#!5"!o ! "B7 5=%o"7 o;7 =7"77 "B7 57 5 5=%o"7 $ ! .
D'+8' B687- C8+*+8
S7" "B7 =o5#? >o!"!o o# "B7 pe$$uefafe %#5>7 (5$5 o7) "o "B7 =o5#? "?!>$! o "B7 #o
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