8/16/2019 CFD Lecture 2007
1/52
Introduction toComputational FluidDynamics (CFD) Tao Xing and Fred Stern
IIHR—Hydroscience & Engineering
C !a"#ell Stanley Hydraulics $a%oratory
Te 'niersity o Io#a
*+,-./ Intermediate !ecanics o Fluids
ttp,00cssengineeringuio#aedu01me2-./0
Sept 34 5//3
8/16/2019 CFD Lecture 2007
2/52
2
6utline
- 7at4 #y and #ere o CFD85 !odeling
9 :umerical metods
; Types o CFD codes
* CFD Educational Interace
. CFD
8/16/2019 CFD Lecture 2007
3/52
3
7at is CFD8= CFD is te simulation o >uids engineering systems
using modeling (matematical pysical pro%lemormulation) and numerical metods (discreti?ationmetods4 solers4 numerical parameters4 and gridgenerations4 etc)
= Historically only @nalytical Fluid Dynamics (@FD) andE"perimental Fluid Dynamics (EFD)
= CFD made possi%le %y te adent o digital computerand adancing #it improements o computerresources
(*// >ops4 -A;3
5/ tera>ops4 5//9)
8/16/2019 CFD Lecture 2007
4/52
4
7y use CFD8
= @nalysis and Design- SimulationB%ased design instead o %uild & test!ore cost eectie and more rapid tan EFDCFD proides igBdelity data%ase or diagnosing >o#
eld
5 Simulation o pysical >uid penomena tat are
diGcult or e"perimentsFull scale simulations (eg4 sips and airplanes)Enironmental eects (#ind4 #eater4 etc)Ha?ards (eg4 e"plosions4 radiation4 pollution)
8/16/2019 CFD Lecture 2007
5/52
5
7ere is CFD used8
= 7ere is CFDused8
= Aerospace
= Automotive
= Biomedical = Cemical
8/16/2019 CFD Lecture 2007
6/52
6
7ere is CFD used8
Polymerization reactor vessel - prediction
of flow separation and residence time
effects.
Streamlines for workstation
ventilation
= 7ere is CFD used8= @erospacee
= @utomotie
= Kiomedical
= ChemicalProcessing
= HVAC
= Hydraulics
= !arine
= 6il & Jas
=
8/16/2019 CFD Lecture 2007
7/527
7ere is CFD used8
= 7ere is CFD used8= @erospace
= @utomotie
= Kiomedical
= Cemical
8/16/2019 CFD Lecture 2007
8/528
!odeling= !odeling is te matematical pysics
pro%lem ormulation in terms o a continuousinitial %oundary alue pro%lem (IK
8/16/2019 CFD Lecture 2007
9/529
o e ng geome ry andomain)
= Simple geometries can %e easily created %y e#
geometric parameters (eg circular pipe)= Comple" geometries must %e created %y te partial
dierential eLuations or importing te data%ase ote geometry(eg airoil) into commercial sot#are
= Domain, si?e and sape
= Typical approaces= Jeometry appro"imation
= C@D0C@E integration, use o industry standards suc as
8/16/2019 CFD Lecture 2007
10/5210
!odeling (coordinates)
x
y
z
x
y
z
x
y
z
(r,θ,z)z
r θ
(r,θ,φ)
r θ
φ(x,y,z)
Cartesian Cylindrical Spherical
General C!r"ilinear C##rdinates General #rth#$#nal
C##rdinates
8/16/2019 CFD Lecture 2007
11/5211
eLuations)
= :aierBStoOes eLuations (9D in Cartesian coordinates)
∂
∂
+∂
∂
+∂
∂
+∂
∂
−=∂
∂
+∂
∂
+∂
∂
+∂
∂2
2
2
2
2
2%
z
u
y
u
x
u
x
p
z
u
w y
u
v x
u
ut
u µ ρ ρ ρ ρ
∂
∂+
∂
∂+
∂
∂+
∂
∂−=
∂
∂+
∂
∂+
∂
∂+
∂
∂2
2
2
2
2
2%
z
v
y
v
x
v
y
p
z
vw
y
vv
x
vu
t
v µ ρ ρ ρ ρ
( ) ( ) ( )0=∂
∂+∂
∂+∂
∂+∂
∂
z
w
y
v
x
u
t
ρ ρ ρ ρ
RT p ρ =
L
v p p
Dt
DR
Dt
R D R
ρ
−=+
2
2
2
)(2
3
C#n"ecti#n &iez#'etric press!re $radient isc#!s ter's#cal accelerati#n
C#ntin!ity e*!ati#n
+*!ati#n # state
-aylei$h +*!ati#n
∂
∂+
∂
∂+
∂
∂+
∂
∂−=
∂
∂+
∂
∂+
∂
∂+
∂
∂2
2
2
2
2
2%
z
w
y
w
x
w
z
p
z
w
w y
w
v x
w
ut
w
µ ρ ρ ρ ρ
8/16/2019 CFD Lecture 2007
12/5212
!odeling (>o# conditions)= Kased on te pysics o te >uids penomena4
CFD can %e distinguised into dierentcategories using dierent criteria
= iscous s iniscid (Re)= E"ternal >o# or internal >o# (#all %ounded or not)
= Tur%ulent s laminar (Re)= Incompressi%le s compressi%le (!a)
= SingleB s multiBpase (Ca)
= Termal0density eects (o# (Fr) and surace tension (7e)= Cemical reactions and com%ustion (
8/16/2019 CFD Lecture 2007
13/5213
!odeling (initial conditions)= Initial conditions (ICS4 steady0unsteady
>o#s)
= ICs sould not aect nal results and onlyaect conergence pat4 ie num%er oiterations (steady) or time steps
(unsteady) need to reac conergedsolutions
= !ore reasona%le guess can speed up teconergence
= For complicated unsteady >o# pro%lems4CFD codes are usually run in te steadymode or a e# iterations or getting a%etter initial conditions
8/16/2019 CFD Lecture 2007
14/5214
o e ng oun aryconditions)
=Koundary conditions, :oBslip or slipBree
on #alls4 periodic4 inlet (elocity inlet4 mass >o#rate4 constant pressure4 etc)4 outlet (constantpressure4 elocity conectie4 numerical %eac4 ?eroBgradient)4 and nonBre>ecting (or compressi%le >o#s4suc as acoustics)4 etc
.#/slip alls !0,"0
"0, dpdr0,d!dr0
nlet ,!c,"0 !tlet, pc
Periodic "oundary condition in
span!ise direction o# an air#oil#
r
xxisy''etric
8/16/2019 CFD Lecture 2007
15/5215
models)
= CFD codes typically designed or soling
certain >uid penomenon %y applying dierent models
= iscous s iniscid (Re)= Tur%ulent s laminar (Re4 Tur%ulent models)
= Incompressi%le s compressi%le (!a4 eLuation ostate)
= SingleB s multiBpase (Ca4 caitation model4 t#oB>uid
model)
= Termal0density eects and energy eLuation (o# (Fr4 leelBset & surace tracOingmodel) and
surace tension (7e4 %u%%le dynamic model)= Cemical reactions and com%ustion (Cemical
! d li (T % l d
8/16/2019 CFD Lecture 2007
16/5216
!odeling (Tur%ulence and ree suracemodels)
= Turbulent models,= D:S, most accurately sole :S eLuations4 %ut too e"pensie
or tur%ulent >o#s
= R@:S, predict mean >o# structures4 eGcient inside K$ %ute"cessie
diusion in te separated region
$ES, accurate in separation region and unaorda%le orresoling K$
= DES, R@:S inside K$4 $ES in separated regions= Free-surface models,= SuraceBtracOing metod, mes moing to capture reesurace4
limited to small and medium #ae slopes
= Single0t#o pase leelBset metod, mes "ed and leelBset
unction used to capture te gas0liLuid interace4 capa%le o
= Tur%ulent >o#s at ig Re usually inole %ot large and small
scale ortical structures and ery tin tur%ulent %oundary layer (K$) nearte #all
8/16/2019 CFD Lecture 2007
17/5217
E"amples o modeling (Tur%ulence andree surace models)
$%, -e105, s#/s!race # criteri#n (04) #rt!r:!lent l# ar#!nd .C12 ith an$le # attac; 60
de$rees
'A, -e105, c#nt#!r # "#rticity #r t!r:!lentl# ar#!nd .C12 ith an$le # attac; 60 de$rees
'A,
8/16/2019 CFD Lecture 2007
18/52
18
:umerical metods
= Te continuous Initial Koundary alue
8/16/2019 CFD Lecture 2007
19/52
19
Discreti?ation metods
= Finite dierence metods (straigtor#ard to apply4usually or regular grid) and nite olumes and niteelement metods (usually or irregular meses)
= Eac type o metods a%oe yields te samesolution i te grid is ne enoug Ho#eer4 somemetods are more suita%le to some cases tanoters
= Finite dierence metods or spatial deriaties #itdierent order o accuracies can %e deried using
Taylor e"pansions4 suc as 5nd order up#ind sceme4central dierences scemes4 etc
= Higer order numerical metods usually predictiger order o accuracy or CFD4 %ut more liOelyunsta%le due to less numerical dissipation
= Temporal deriaties can %e integrated eiter %y tee"plicit metod (Euler4 RungeButta4 etc) or implicit metod (eg KeamB7arming metod)
scre ?a on me o s
8/16/2019 CFD Lecture 2007
20/52
20
scre ?a on me o s(ContQd)
= E"plicit metods can %e easily applied %ut yieldconditionally sta%le Finite Dierent ELuations (FDEs)4#ic are restricted %y te time step Implicitmetods are unconditionally sta%le4 %ut need eortson eGciency
= 'sually4 igerBorder temporal discreti?ation is used#en te spatial discreti?ation is also o iger order
= Sta%ility, @ discreti?ation metod is said to %e sta%lei it does not magniy te errors tat appear in tecourse o numerical solution process
=
8/16/2019 CFD Lecture 2007
21/52
21
(e"ample)
0=∂∂
+∂∂
y
v
x
u
2
2
y
u
e
p
x y
uv x
uu ∂
∂+
∂∂
−=∂∂
+∂∂
µ
= 5D incompressi%le laminar >o# %oundary layer
'0'1
/1
y
x
'>>'>>?1
(,'/1)
(,')
(,'?1)
(/1,')
1l
l l mm m
uuu u u
x x
−∂ = − ∂ ∆
1
l l l mm m
vuv u u
y y +
∂ = − ∂ ∆
1
l l l mm m
vu u
y − = − ∆
@A Si$n( )B0l mv
l
mvA Si$n( )D0
2
1 12 22l l l m m m
uu u u
y y
µ µ + −
∂ = − + ∂ ∆
2nd #rder central dierence
ie, the#retical #rder # acc!racy
&;est 2
1st #rder !pind sche'e, ie, the#retical #rder # acc!racy &;est 1
8/16/2019 CFD Lecture 2007
22/52
22
(e"ample)
1 12 2 2
1
2
1
l l l l l l l m m mm m m m
FDu v v yv u FD u BD u
x y y y y y BD
y
µ µ µ + −
− ∆+ − + + + − ∆ ∆ ∆ ∆ ∆ ∆ ∆
1( )
l l l mm m
uu p e
x x
− ∂= −∆ ∂
2 3 1
4( )11 1 2 3 1 4 l l l l l m m m m m B u B u B u B u p e x−
− + ∂+ + = − ∂1
4 1
12 3 1
1 2 3
1 2 3
1 2 1
4
0 0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0 0
l
l
l
l l mm l
mm
mm
p B u
B B x eu
B B B
B B B
B B u p B u
x e
−
−
∂ − ÷∂ ••
× =• • • • •• •• ∂ − ÷∂
olve it using
homas algorithm
o "e sta"le* Matri+ has to "e
$iagonally dominant,
Solers and numerical
8/16/2019 CFD Lecture 2007
23/52
23
Solers and numericalparameters
= Solvers include, tridiagonal4 pentadiagonal solers4
8/16/2019 CFD Lecture 2007
24/52
24
umer ca me o s grgeneration)
= Jrids can eiter %e structured(e"aedral) or unstructured
(tetraedral) Depends upon type odiscreti?ation sceme and application
= Sceme Finite dierences, structured Finite olume or nite element,
structured or unstructured
= @pplication Tin %oundary layers %est resoled
#it iglyBstretced structuredgrids
'nstructured grids useul orcomple" geometries
'nstructured grids permitautomatic adaptie renement%ased on te pressure gradient4 orregions interested (F$'E:T)
str!ct!red
!nstr!ct!red
8/16/2019 CFD Lecture 2007
25/52
25
:umerical metods (gridtransormation)
y
x# #
&hysical d#'ain C#'p!tati#nal d#'ain
x x
f f f f f
x x x
ξ η
ξ η ξ η ξ η
∂ ∂ ∂ ∂ ∂ ∂ ∂
= + = +∂ ∂ ∂ ∂ ∂ ∂ ∂
y y
f f f f f
y y y
ξ η ξ η
ξ η ξ η
∂ ∂ ∂ ∂ ∂ ∂ ∂= + = +
∂ ∂ ∂ ∂ ∂ ∂ ∂
Erans#r'ati#n :eteen physical (x,y,z)and c#'p!tati#nal (ξ,η,ζ) d#'ains,i'p#rtant #r :#dy/itted $rids Ehe partial
deri"ati"es at these t# d#'ains ha"e the
relati#nship (2A as an exa'ple)
η
ξ
Erans#r'
Hi ti d t
8/16/2019 CFD Lecture 2007
26/52
26
Hig perormance computing and postBprocessing
= CFD computations (eg 9D unsteady >o#s) areusually ery e"pensie #ic reLuires parallel ig
perormance supercomputers (eg IK! .A/) #itte use o multiB%locO tecniLue= @s reLuired %y te multiB%locO tecniLue4 CFD codes
need to %e deeloped using te !assage
8/16/2019 CFD Lecture 2007
27/52
27
Types o CFD codes= Commercial CFD code, F$'E:T4 StarB
CD4 CFDRC4 CFX0@E@4 etc= Researc CFD code, CFDSHI
8/16/2019 CFD Lecture 2007
28/52
28
CFD Educational Interace
-a"./ Pipe 0lo! -a" 1/ Air#oil 0lo! -a"2/ $i##user -a"3/ Ahmed car
1 Aeiniti#n # FC@A &r#cess2 #!ndary c#nditi#ns3 terati"e err#r 4 Grid err#r 5 Ae"el#pin$ len$th # la'inar
and t!r:!lent pipe l#s6 eriicati#n !sin$ @A7 alidati#n !sin$ +@A
1 #!ndary c#nditi#ns2 +ect # #rder # acc!racy
#n "eriicati#n res!lts3 +ect # $rid $enerati#n
t#p#l#$y, FC and F>eshes
4 +ect # an$le # attac;t!r:!lent '#dels #n
l# ield5 eriicati#n and alidati#n
!sin$ +@A
1 >eshin$ and iterati"ec#n"er$ence
2 #!ndary layerseparati#n
3 xial "el#city pr#ile4 Strea'lines5 +ect # t!r:!lence
'#dels6 +ect # expansi#n an$le and c#'paris#n ith +S, +@A, and
-.S
1 >eshin$ and iterati"e c#n"er$ence2 #!ndary layer separati#n3 xial "el#city pr#ile4 Strea'lines5 +ect # slant an$le and c#'paris#n ith +S,
+@A, and -.S
8/16/2019 CFD Lecture 2007
29/52
29
CFD process= uid interactions or%u%%ly >o#s4 study o #ae induced massiely separated>o#s or reeBsurace4 etc
= Depend on te specic purpose and >o# conditions o tepro%lem4 dierent CFD codes can %e cosen or dierentapplications (aerospace4 marines4 com%ustion4 multiB
pase >o#s4 etc)= 6nce purposes and CFD codes cosen4 CFD process is
te steps to set up te IK< pro%lem and run te code,
- Jeometry 5
8/16/2019 CFD Lecture 2007
30/52
30
CFD #del
#!ndary
C#nditi#ns
nitial
C#nditi#ns
C#n"er$ent
i'it
C#nt#!rs
&recisi#ns
(sin$le
d#!:le)
.!'erical
Sche'e
ect#rs
Strea'lineseriicati#n
Geometry
Select
Ge#'etry
Ge#'etry
&ara'eters
Physics Mesh olve Post4
Processing
C#'pressi:le
.@@
@l#
pr#perties
Hnstr!ct!red
(a!t#'atic
'an!al)
Steady
Hnsteady
@#rces -ep#rt(litdra$, shear
stress, etc)
IJ &l#t
A#'ain
Shape and
Size
=eat Eranser
.@@
Str!ct!red
(a!t#'atic
'an!al)
terati#ns
Steps
alidati#n
'eports
8/16/2019 CFD Lecture 2007
31/52
31
Jeometry= Selection o an appropriate coordinate
= Determine te domain si?e and sape
= @ny simplications needed8
= 7at Oinds o sapes needed to %e used to%est resole te geometry8 (lines4 circular4oals4 etc)
= For commercial code4 geometry is usuallycreated using commercial sot#are (eiterseparated rom te commercial code itsel4 liOe
Jam%it4 or com%ined togeter4 liOe Flo#$a%)
= For researc code4 commercial sot#are (egJridgen) is used
8/16/2019 CFD Lecture 2007
32/52
32
uid properties - Flow conditions, iniscid4 iscous4 laminar4
or tur%ulent4 etc 5 Fluid properties, density4 iscosity4 and
termal conductiity4 etc
9 Flo# conditions and properties usuallypresented in dimensional orm in industrialcommercial CFD sot#are4 #ereas in nonBdimensional aria%les or researc codes
= Selection o models, dierent models usually
"ed %y codes4 options or user to coose= Initial and Koundary Conditions, not "ed%y codes4 user needs speciy tem or dierentapplications
8/16/2019 CFD Lecture 2007
33/52
33
!es= !eses sould %e #ell designed to resole
important >o# eatures #ic are dependentupon >o# condition parameters (eg4 Re)4 suc aste grid renement inside te #all %oundary layer
= !es can %e generated %y eiter commercial
codes (Jridgen4 Jam%it4 etc) or researc code(using alge%raic s
8/16/2019 CFD Lecture 2007
34/52
34
Sole
= Setup appropriate numerical parameters= Coose appropriate Solers
= Solution procedure (eg incompressi%le >o#s)
Sole te momentum4 pressure o# eld Luantities4 sucas elocity4 tur%ulence intensity4 pressureand integral Luantities (lit4 drag orces)
8/16/2019 CFD Lecture 2007
35/52
35
Reports= Reports saed te time istory o te
residuals o te elocity4 pressure andtemperature4 etc
= Report te integral Luantities4 suc as totalpressure drop4 riction actor (pipe >o#)4
lit and drag coeGcients (airoil >o#)4 etc= X plots could present te centerlineelocity0pressure distri%ution4 rictionactor distri%ution (pipe >o#)4 pressurecoeGcient distri%ution (airoil >o#)
= @FD or EFD data can %e imported and puton top o te X plots or alidation
8/16/2019 CFD Lecture 2007
36/52
36
8/16/2019 CFD Lecture 2007
37/52
< i ('@ i i )
8/16/2019 CFD Lecture 2007
38/52
38
8/16/2019 CFD Lecture 2007
39/52
39
ixed #scillat#ryc#n"er$ent
terati#n hist#ry #r series 60 (a) S#l!ti#n chan$e (:) 'a$niied "ie # t#tal
resistance #"er last t# peri#ds # #scillati#n (scillat#ry iterati"e c#n"er$ence)
(:)(a)
)(2
1
LU I
S S U −=
8/16/2019 CFD Lecture 2007
40/52
40
8/16/2019 CFD Lecture 2007
41/52
41
8/16/2019 CFD Lecture 2007
42/52
42
8/16/2019 CFD Lecture 2007
43/52
43
= @symptotic Range, For suGciently small ∆"O4te solutions are in te asymptotic rangesuc tat igerBorder terms are negligi%leand te assumption tat and are
independent o ∆"O is alid= 7en @symptotic Range reaced4 #ill %eclose to te teoretical alue 4 and tecorrection actor
#ill %e close to -= To aciee te asymptotic range or practical
geometry and conditions is usually notpossi%le and mY9 is undesira%le rom a
resources point o ie#
8/16/2019 CFD Lecture 2007
44/52
44
8/16/2019 CFD Lecture 2007
45/52
45
8/16/2019 CFD Lecture 2007
46/52
46
E"ample o CFD o#s (Re-;9) around ClarOy airoil
#it angle o attacO . degree is simulated= C sape domain is applied= Te radius o te domain Rc and do#nstream
lengt $o sould %e specied in suc a #ay tatte domain si?e #ill not aect te simulationresults
E"ample o CFD
8/16/2019 CFD Lecture 2007
47/52
47
E"ample o CFD
8/16/2019 CFD Lecture 2007
48/52
E l CFD < (S l )
8/16/2019 CFD Lecture 2007
49/52
49
E"ample o CFD
8/16/2019 CFD Lecture 2007
50/52
50
(Reports)
processing)
8/16/2019 CFD Lecture 2007
51/52
51
processing)
8/16/2019 CFD Lecture 2007
52/52