CFDNotes Introducion Course CFX Bueno

7/23/2019 CFDNotes Introducion Course CFX Bueno

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Computational Fluid Dynamics

Computational Fluid

Dynamics

Course Notes

Dr PK DysonSep 2004


2/68


CFD Overviewand

Introduction to CFX


3/68


Introduction

What do you want to know?

What do you need to define?

Whats the physics?


4/68


Solution of the Equations

Equations are so!ed nu"ericay# at a series ofdiscrete points in the fow do"ain$

% !aria&es at '00#000 points i"pies what ($?

)esuts can &e !iewed *raphicay and processedto pro!ide nu"erica outputs$

+or "ost packa*es# the data strea" is,

-eo"etry

.. /esh creation

.. +uid definition

.. Pro&e" definition

.. Soution

.. iewin* of )esuts

1D 3usuay

Pre5processor

So!er

Post5processor

/esh -enerator


5/68


ANSS ! CFX Overview "#$

Start . 6ni!ersity Software . 7S8S .7S8S '0

-eo"etry

Desi*n/odeer39$a*d& fie

1+:5/esh39$c"d& fie

-eo"etry fie39$*t"

/esh 1ontroPara"eters

;his starts the 7S8S Work&enchen!iron"ent fro" which the !arious

indi!idua co"ponents are aunched$

1D


6/68


ANSS ! CFX Overview "%$

=oundary

conditions

+uidproperties

Pro&e"type

Soutioncontro

Definitionfie 39$def

Session fie39$ses hods

record ofco""ands

entered durin*

session

>ourna fie 39$ouhods record ofco""ands for

particuardata&ase

1ase fie 39$cf@ 1+:5Pre

-eo"etry fie39$*t"


7/68


1+:5Post

So!er

ANSS ! CFX Overview "&$

Definition

fie 39$def

)esutsfie 39$res

Autputfie 39$out

eocities

Strea"ines

Pressures;ur&uence

+orces

3nu"erica datain te@t fie

See Bep,5 fro" d!anced 1+: Pane,

Bep . /aster 1ontents

7S8S 1+:# )eease '0$0,


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File 'ana(ement

1reate a C/y1+: foder on the oca hard dri!eand put each o& in a different su&5foder$

Do not leave spacesin foder or fie na"esanywhere in the path to your workin* foder$

Work fro" the oca hard dri!e or pen dri!e 3notacross the 7etwork fro" your 6, dri!e

t the end of the session# dra* and drop yourentire workin* foder to your pen dri!e$

W)7


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Contact with ANSS)CFX Staff

I'*O+,AN, NO,E


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,heory Overview


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/eneral *rinciples ) +evision

'omentum

'ass Continuity

u2u'

net force actin* on fuid

F rate of chan*e of "o"entu"F chan*e of rate of "o"" fowF

222''' !! =

how?

+or steady fow


12/68


'ass Continuity Equation "#$

@

y

@#u

y#!

"ass5!eocityF u

!G#w

7et rate of outfow of "ass Frate of depetion of "ass in contro !ou"e


13/68


'ass Continuity Equation "%$

( ) ( ) ( )

0

G

w

y

!

@

u

Dt

D

0G

w

y

!

@

u

Gw

y!

@u

t

0Gw

y!

@u

t

=

+

+

+

=

+

+

+

+

+

+

=+

+

+

Su&stantiaderi!ati!e

+or inco"pressi&e fow# this &eco"es,


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'omentum Equation "#$

@

yu

!

+orce on 1ontro ou"e

F )ate of 1han*e of /o"entu"

+orce on 1ontro ou"e

F )ate of 1han*e of /o"entu"

0elocity Chan(es across Control 0olume

yu

,"o"@2

( )@

@

yuyu

,"o"@2

2

+

@

@

uu

+

yy!!

+ ( ) yy @u!@u!

,"o"@

+

@u!

,"o"@


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'omentum Equation "%$

Forces Actin( in 1)Direction

on Control 0olume

@y


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'omentum Equation "&$

+ate of Chan(e of 'omentum in 1)direction

( ) ( )

( ) ( )

( ) ( )

y@y

u!

@

uu

y

!

@

uu

y@y

!u

y

u!

@

uu

@

uu

y@!uy

@yu@

2

+

=

+

+

+

+

=

+

=

F 0 for steady fow

3fro" continuity


17/68


'omentum Equation "2$

Net force in 1)direction


18/68


,he Navier)Sto3es Equations

steady state 25di"ensiona inco"pressi&e

++= +

+

+

=

+

2

2

2

2

2

2

2

2

y

!

@

!

y

P8y

!!@

!u

y

u

@

u

@

P:

y

u!

@

uu

+or,


19/68


Navier)Sto3es ) 0ector Notation

( )!P+Dt

!D 2+=


20/68


Navier)Sto3es ) Summation Convention

##ii#i#iuPfuu +=

;akin* u F u' ! F u2 w F uH

3separate equation for each of i F ' to H

where '# 2# H represent @# y# G directions a su&cripted co""a and inde@ represents a

deri!iti!e

repeated su&script "eans set it to '# 2# H inturn and su" resutin* !aria&es

( ) 22

H#H#22#' w!uIyuu$e$i ==

G

uw

y

u!

@

uu

uuuuuuuu$e$i H#'H2#'2'#''#'

+

+

=

++=

3so what does u#F 0 "ean?


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,he Ener(y Equation

@

yu

!1on!ection

with "ass transfer 1onduction&y te"perature *radient


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Analytical E1ample ) Couette Flow

Stationary pate

/o!in* Pate 5 !e F us

s


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Solutions to the Equations

;he set of equations for inco"pressi&e#

!iscous# 2D steady fow is,

0y

!

@

u=

+

+

+

=

+

+

+

=

+

2

2

2

2

2

2

2

2

y

!

@

!

y

P8

y

!!

@

!u

y

u

@

u

@

P

:y

u

!@

u

u

6nknowns are u# !# P which are to &e so!edin ter"s of @ and y 5 i$e$ across fow do"ain$

Soutions are typicay pots of !eocity!ectors# strea"ines# pressure contours 3andte"perature contours if ener*y equation isadded$

;hese "ay &e processed to produce suchdata as forces 3e* ift and dra* on a foi orpressure oss in pipes and fittin*s$


24/68


Computational /rid

Since anaytica soution is a!aia&e ony in

si"pest of cases# nu"erica techniques arerequiredI thus a *rid across fow do"ainneeds to &e defined

6nknowns are deter"ined at each *rid point

1oncept "ay &e e@tended into ti"e do"ain,

@ y

t


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,ypical /rid Notation

i#

i# J'

i# 5'

i5'# J'

i5'#

i5'# 5'

iJ'# J'

iJ'#

iJ'# 5'

@

y


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Solution ,echniques

=roady speakin*# one of three techniques is

adopted for the soution of the *o!ernin*equations,

finite difference# in which the differentiater"s are discretised for each ee"ent

finite volume# in which the *o!ernin*equations are inte*rated around the "eshee"ents

finite element# in which !ariation of!aria&es within ee"ents is appro@i"ated&y a function# and a residua 3or error ter"is "ini"ised$

;he first of these is perhaps the easiestconceptuay# and thus we wi use this tooutine a typica soution procedure$

1+: uses the finite !ou"e "ethod$


27/68


Differencin( Formulae "#$

u

@

uiJ'

ui

i iJ',aylor E1pansion

( ) ( )

( )

( )2'i'i

i

H

iH

H

i'i'i

H

i

H

H

2

i

2

2

i

i'i

H

i

H

H2

i

2

2

i

i'i

@A@2

uu

@

u

$$$$

@

@

u

2@@

u

2uu

,*Su&tractin

$$$$@

@u

2

@

@

u@

@

uuu

so

$$$$

@

@

u

2

@

@

u@

@

uuu

+

=

+

+

=

+

+

+

+=

+

+

+

+=

+

+

+

3second ordercentra difference


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Differencin( Formulae "%$

ddin* the ;ayor Series equations,

( )22

'ii'i

i

2

2

4

i

4

42

i

2

2

i'i'i

@A@

uu2u

@

u

$$$$'2

@

@

u@

@

uu2uu

+

+=

+

+

+=+

+

+

;hus# if we take# say# the @ direction75S equation 3steady for si"picity,

+ +

+

=

+

+

+

=

+

++

+++

2 '#i#i'#i2 #'i#i#'i

#'i#'i'#i'#i

#i

#'i#'i

#i

2

2

2

2

y

uu2u

@

uu2u

@2

PP

y2

uu!

@2

uuu

&eco"es

yu

@u

@P

yu!

@uu


29/68


,he Equation Set


30/68


,he *ressure Correction Approach

Se"i5


31/68


4oundary Conditions "#$

=oundaries "ust &e defined# &ut care "ust &e

taken not to, under5define &oundaries 3insufficient data

for soution o!er5define &oundaries 3creatin* a

physicay i"possi&e situation

e*$ With para"eters defined on &oundaries asfoows ($$

uF!aue!F0PF!aue

uF0#!F0

uF0#!F0

wa

wa

((( "ode is over)definedsince!eocity and pressure are stipuated

at inet and outet$ aues "ay thusnot satisfy the continuity and"o"entu" equations$

uF!aue!F0PF!aue


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4oundary Conditions "%$

+or e@a"pe# for steady# inco"pressi&e#!iscous fow# so!ed &y pressure correction"ethod# &oundaries conditions "ay &e,

! F 0

PF !aue PF !aue

0!#0u ==

0!#0u ==

=oundaries defined wi depend on natureof equations to &e so!ed 3steady Nunsteady# inco"pressi&e N co"pressi&e#in!iscid N !iscous


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/rids "#$

Computational

Space

Structured 'esh

usuay co"prisin* quadriatera ee"ents

*hysical Space

e*$ circuar duct


34/68


/rids "%$

erofoi Section 3E@a"pe of structured"esh# refined in critica re*ions


35/68


/rids "&$

.nstructured 'esh

usuay &ased on trian*uar pyra"ids3e* 1+: %

Important 'odellin( Considerations -rid refine"ent in critica areas -rid independent soution 5 checks required 1o"putationay econo"ic "ode

coarse *rid in non5critica areas

"ake use of sy""etry and periodic&oundary conditionsuse 25D and a@i5sy""etric "odeswhere possi&e


36/68


,ur-ulence

u

6

!e ata point

ti"e


37/68


Introduction to ,ur-ulence 'odellin(

La"inar +ow /o"entu"

diffusion&y !iscosity

;ur&uent +owdditiona "o"entu"

diffusion due to tur&uence

1oncept oftur&uent 3or eddy!iscosity#

tt is not a fuid property# &ut dependson e!e of tur&uence in fow

concept eads to "athe"atica "odesto dea with tur&uenceI each "ode isan appro@i"ation to what is reayhappenin*

one popuar "ode 3k5epsion "odeintroduces two further unknowns,

KEtur&uentofndissipatioratethe

2

w!uene*ykinetictur&uentthek

222

++=

KEtur&uentofndissipatioratethe

2

w!uene*ykinetictur&uentthek

222

++=


38/68


,ur-ulence 'odellin( ! the 'aths

;hink of u#!#w and p as co"prisin* of two parts,ense"&e a!era*e !aues and tur&uent fuctuations$

Superscript&ar denotes the ensem-le avera(eor

the "ean !aue$Dashdenotes the fluctuatin( part$

;ur&uence fuctuations usuay ha!e s"a en*th andti"e scaes co"pared to the "ean fow$

Su&stitutin* this deco"position to the 7a!ier5Stokesequations and takin* the ense"&e a!era*e# we now*et

pppwwwvvvuuu +=+=+=+= ,,,

+

=

+

=

i

i

i

i

i

uu@

u

@@

p'

@

uu

t

u,"o"entu"

0@

u,continuity


39/68


Equations 3aso caed )eynods equations forense"&e a!era*e !aues are identica to the 7a!ier5Stokes equation e1cept for the cross)productsofthe fuctuation ter"s$

Since these ter"s ha!e si"iar functions as !iscousstresses# they are caed Otur&uent stresses or)eynods stresses$

;o propery cose the syste"# we ha!e to define the&eha!iour for tur&uence cross5product ter"s$

,ur-ulence Closure

( ) ( ) ( ) ( ) ( ) ( )w!#wu#!u#w#!#u 222

;his is where "any different types and e!es oftur&uence "odein* co"e in$

t the hi*hest e!e# transport equations can &e

set up for each of these ter"s$ ;his wi increasethe nu"&er of equations to so!e &y si@$;ur&uence "odes &ased on this approach arecaed )eynods stress equation "ode 3)S/ orthe second5order cosure "ode$

co""ony used tur&uence "ode inen*ineerin* differs fro" this approach &yreducin* the nu"&er of e@tra equations to onytwo and is known &y the na"e k- "ode$


40/68


3)5 'odel ) ,heory


41/68


;he 3e"pirica constants in the k5Q "odeare usuay,

R2$'c#44$'cH0$'I0$'#0R$0c

2'

k

=====

Where

( )

( ) ( )k$$H

2P

kc

@

u

@

ueIee2

w!u2

'k

;tk

2

t

i

iiii

222

++=

=

+

==

++=

UUUUU.t

3

3)5 'odel ! ,heory "continued$


42/68


3) ,ur-ulence 'odel ) Summary

requires two further equations# si"iar to

7a!ier5Stokes equations for k and thus requires

inet !aues for k and initia *uesses for k and

esti"ates for these "ay &e o&tained fro"equations such as the foowin*# a!aia&e inthe iterature

( )26%$'k =

sensiti!ity to inet tur&uence quantities

shoud &e checked# and "ay point tothe need for e@peri"entay deri!ed!aues for use in the 1+D "ode$

( )

= 6

uensityinttur&uencetheiswhere

2'

2

fowshearfreefor3k

L

2H

=

widthayershearsticcharacteritheisand

'$0en*theddysticcharacteriiswhere L


43/68


CFD 6ealth 7arnin( 8

We ha!e &arey scratched the surface of the

theory of 1+D$ few of the possi&e areasfor further fruitfu readin* are,

nature of the equations under different

conditions 5 hyper&oic# para&oic# eiptic$ transient pro&e"s choice of &oundary and initia conditions coupin* &etween "o"entu" and ener*y

equations 3especiay in &uoyancy dri!en

fows supersonic fows and shock capture tur&uence "odein* 5 what aternati!e

"odes are a!aia&e? wa &oundary conditions 3o* aw of the

wa

;reat 1+D with respect 5 a itte knowed*e isa dan*erous thin* M


44/68


E1ercises


45/68


E1ercise #

1reate foder 'yCFXand a su&5foder ;utoria'

Start 7S8S 1+: '0$0$


46/68


E1ercise # "continued$

1ontinue with this tutoria# &ut note the instructions inpara 4 at the end of the Desi*n/odeer ;utoria,5

C( "issin* out the instructions in the section C1reatin* a7ew Si"uation$ 7ote that you do not need to copy thesa"pe fie Static/i@er/esh$*t" to your workin*

directory if you ha!e ust created the "esh in 1+:5/esh#since you wi want to use your new "esh and not theone suppied with 7S8S 1+:$ +or the C


47/68


Now ma3e sure you understand :;;

Whats the difference &etween

Sketchin* "ode and "odein* "ode

Desi*n/odeer and 1+:5/esh

Surface /esh and ou"e /esh


48/68


Work throu*h ,utorial %? Static 'i1er"+efined

'esh$which wi show you,

"ore a&out the "esh *eneration process

"odifyin* *eo"etry

use of 1+: 1o""and Lan*ua*e 311L to a!oid

too "any repetiti!e keystrokes$

s &efore you wi need to start in theDesi*n/odeerN1+:5/esh 3Soid /odein*;utoria and switch to the 1+: 3+uid /odein*;utoria$

E1ercise %


49/68


)efine the "esh e!en further in the outet re*ion ofthe "i@er &y insertin* a "esh contro as foows$

)e5open Static/i@er in 1+:5/esh )i*ht cick Control. Insert*oint Spacin( 1ick *oint Spacin( #in Detai iew and chan*e

the settin*s to, Len*th scae 0$' "# )adius of


50/68


Findin( Out 'ore ! ,he 6elp *a(es

6elpon 1+: *re? Solver and*ostis accessed fro"the d!anced 1+D panes 35Pre# 5So!er# 5Post &ycickin*,

6elp


51/68


Findin( Out 'ore

ANSS 7or3-ench 6elp < CFX)'esh 6elp

What is the principe type of "esh utiised &y 1+:?What is its ad!anta*e o!er a quasi5rectan*uar"esh?What is "esh contro? Why use it?What is infation? Why use it?What is a "esh independent soution? 31arry out a

search usin* mesh NEA+ independentaskeywords$ /ake sure that pa*es referred to are for1+:5/esh or Desi*n/odeerI pa*es referrin* to# fore@a"pe# Desi*n:porer or Si"uation 3top eft ofpa*e are not ree!ant to you

CFX 6elp < CFX)*re < Fluid DomainsWhat options are a!aia&e for the fuid do"ain"odes?What standard fuids are a!aia&e?

CFX 6elp < CFX)*re < 4oundary ConditionsWhat &oundary conditions are a!aia&e?

CFX 6elp < CFX)*re < Initial ConditionsWhy are initia !aues set?

CFX 6elp < CFX)*re < Solver ControlWhat are con!er*ence criteria?


52/68


,reatment of 7alls and Flow

4oundaries

Near 7all 'odellin(

37S8S 1+:5So!er '0$0 /odein* . ;ur&uenceT 7ear Wa /odein* 5 /odein* +ow 7ear the

Wa

4oundary Condition 'odellin(

37S8S 1+:5So!er '0$0 /odein* 5 =oundary1ondition /odein*

+urther readin* fro" 1+: Bep pa*es,


53/68


E1ercise 2

thou*h this is an e@terna fow# 3as opposed tothe pre!ious pipe e@a"pe which was interna#we sti need to define a i"it to the do"ain$ ;hiswi effecti!ey &e a Cwind tunne in which thecyinder wi &e paced$

We wi treat this as a 25D e@a"pe &y "akin*the fuid do"ain thin in the @ direction andattachin* the cyinder to the wa at each side$

8ou shoud create a new foder for this pro&e"$

y

zx


54/68


'$ Sketch surface 3the ow5@ surface as arectan*e$

2$ Sketch the circe 3rectan*e and circe wi &oth&e part of sketch '

H$ E@trude in the @ direction$

0$H

2

'0

@ G

y

point 0 0 0

surface

.sin( Ansys Desi(n'odeller

'2 dia"eter 0$H

;he HD &ody for"ed &y the &o@ with the cyinder cutout# so"eti"es confusin*y referred to as the Csoid# iswhere the fuid wi fow$


55/68


.sin( Ansys CFX)'esh

4$ Apen 1+:5/esh and create a 25D re*ion for eachof the surfaces 3eft# ri*ht# inet# outet# cyinder ea!e top T &otto" undefined they wi for" theCdefaut 2D re*ion# *i!in* each a suita&e na"e3you wi use these ater to define &oundary

conditions$%$ Set "esh defaut &ody spacin* to a "a@i"u" of

0$H "$$ Set up


56/68


U$ Pace "esh contros to refine the "esh in there*ion of the cyinder and its wake$

V$ 1reate surface "esh# and check it to ensure it isrefined in the appropriate paces$

R$ 1reate the !ou"e "esh 3thus writin* the $*t" fieand start CFX)*re$


57/68


'0$ 1reate a fuid do"ain 5 use standard air or water#seect steady state# k5tur&uence "ode# scaa&ewa function# isother"a# non5&uoyant$ Setreference pressure at 0 Pa$

''$


58/68


'H$ 8ou can check and edit =oundary 1onditions &ydou&e cickin* on the ree!ant condition in CA&ectSeector$ 7ote that the CDefaut &oundarycondition 3a no5sip wa appies to any &oundarywhich is undefined$

'4$ ppy defauts for initia !aues$

'%$ ppy defauts for the so!er para"eters# e@ceptnu"&er of iterations which you shoud chan*e to

%0$

'$ Write definition fie and *o to So!er$


59/68


'U$ )un the so!er$ Does it con!er*e within the %0iterations which ha!e &een set?


60/68


2'$ Draw !ectors and a pressure profie &ased on one ofthe side was$ E@peri"ent with differentarran*e"ents of strea"ines# different en*ths of!ector arrow# and with a shaded pressure pot 3&ycheckin* the CDraw +aces &o@ on the C)enderpane$

22$ Print one of the pots to a >PE- fie usin* +ie 5 Print#

and check the CWhite &ack*round &o@$ ;his coudater &e incuded in a report$

2H$ 6se the ine which you created earier to produce achart 3ie a *raph showin* how the G5direction!eocity !aries across the wake at a position ust

downstrea" of the cyinder$

24$ 6se the cacuator to find the tota force on thecyinder in the G5direction$ 1o"pare this with thedra* shown in the $out fie 3you wi need to add 2!aues fro" $out to*ether to *et the dra* 5 why?$1acuate the dra* coefficient 5 is it anywhere nearcorrect?


61/68


With a &it of cunnin*# and udicious use "esh contros

and 1+:5Post# this is possi&e ($$


62/68


'odifyin( the 'odel

;ry pacin* an e@tra cyinder in cose to the first$What is the effect on the fow and the dra* on thecyinders?


63/68


uestions

What is the effect of ha!in* a !ery narrow 3say0$0' or a !ery wide 3say H$0 &o@?

Bow does the pro@i"ity of the top and &otto"was affect the soution?

Bow does the position of the upstrea" anddownstrea" &oundary affect the soution?

1oud a pane of sy""etry ha!e &een used toreduce the co"putationa ti"e?


64/68


E1tractin( Numerical Data

;he "ost usefu ways of e@tractin* nu"erica data are,

Output File;9$out fie contains te@t &ased data on &othsoution and resuts$


65/68


Definin( *olylines

Intersection @ine ine of intersection &etween a &oundary 3defined in1+:5Pre and a pane 3defined in 1+:5Post "ay &eused$

File Input

te@t fie is written 3outside 1+: containin* co5ordinates of the points required# in a for"at shown &ythe foowin* e@a"pe$

1oordinates "ay define a strai*ht or cur!ed ine$ Data

3e* pressures wi ony &e potted at the points youdefine# so if you want *ood resoution# you need pentyof points# e!en if its a strai*ht ine$


66/68


*olyline Data File

0 0 0

0$00% 0$0''RH 0

0$00U% 0$0'4H 0

0$0'2% 0$0'V'% 00$02% 0$02%0V 0

0$0% 0$0H4UU 0

0$0U% 0$04202 0

0$' 0$04URR 00$'% 0$0%UH2 0

0$2 0$042H 0

etc

@ y Gcoodinates#dei"ited &yta&s or

spaces$

;he Poyine is oadedusin* the CPoyineicon


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E1portin( Data from CFX)*ost

Ance a poyine has &een defined a chart"ay &e

produced$

so the !aria&es "ay &e e1portedfor points defined&y the poyine usin* +ie E@port$

Seect the !aria&es required 3e* @# y# G# pressure3hod down Ccontro to "ake "utipe seections andocator 3e* poyine' and *i!e an appropriate fiena"e$

;he data is for"atted as a series of @5y5G co5

ordinates# and !aues for the para"eters potted$

;he e@a"pe o!ereaf shows @# y# G co5ordinatesto*ether with !aues for P# u# !# w$ ;his has &eentidied up &y oadin* the fie into E@ce# usin* Cspaceand C3C characters to dei"it data# and then carryin*

out a search and repace to *et rid of C characters$


68/68


E1portin( Data ) E1ample File

X@ 5 1oordinates "

Xy 5 1oordinates " XG 5 1oordinates " X' 5 Pressure k*"Y5'sY52 X2 5 eocity "sY5'5$'2E5' 0$00EJ00 2$00EJ0' 5H$2RE50%'$VRE50U U$22E50U '$VVE505%$4VE5' 0$00EJ00 '$VREJ0' U$VE50UU$R2E50V %$0%E50U '$VUE50H54$VHE5' 0$00EJ00 '$UREJ0' $24E50%2$4VE50 $U0E50U '$R4E50H

X@ 5 1oordinates "

Xy 5 1oordinates " XG 5 1oordinates " X' 5 Pressure k*"Y5'sY52 X2 5 eocity "sY5'5$'2E5' 0$00EJ00 2$00EJ0' 5H$2RE50%

'$VRE50U U$22E50U '$VVE505%$4VE5' 0$00EJ00 '$VREJ0' U$VE50UU$R2E50V %$0%E50U '$VUE50H54$VHE5' 0$00EJ00 '$UREJ0' $24E50%2$4VE50 $U0E50U '$R4E50H

7ote, data here for each point stretches across 2 ines as!eocity has H co"ponents$

*ressure around a Cylinder

0 00EJ00

%$00EJ0'

An(le "de($

fter "anipuation in E@ce# a chart can &e potted,

CFDNotes Introducion Course CFX Bueno

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