Introdução ao CFD

8/3/2019 Introduo ao CFD

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Universidade Federal de ItajubUniversidade Federal de ItajubInstituto de Engenharia MecnicaInstituto de Engenharia Mecnica

Grupo de Estudos em Tecnologias de Converso de EnergiaGrupo de Estudos em Tecnologias de Converso de Energia

Coordenador: ProfCoordenador: Prof. Dr. Marco Antnio R. Nascimento. Dr. Marco Antnio R. Nascimento

INTRODUO DINMICA DOSINTRODUO DINMICA DOSFLUIDOS COMPUTACIONAISFLUIDOS COMPUTACIONAIS -- CFDCFD

SIMULAO COMPUTACIONALSIMULAO COMPUTACIONAL

[email protected]

Eraldo Cruz dos SantosEraldo Cruz dos Santos


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Eraldo Cruz dos SantosEraldo Cruz dos Santos 2/2/2012 2

TPICOS DA APRESENTAOTPICOS DA APRESENTAO

O QUE O CFD?;

MODELAGEM;

MTODOS NUMRICOS; TIPOS DE CDIGOS DO CFD;

INTERFACE EDUCACIONAL DO CFD;

PROCESSOS DO CFD;

EXEMPLOS DE PROCESSOS;


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O QUE O CFD?

CFD is thesimulationoffluidsengineeringsystemsusingmodeling

(mathematical physical problemformulation)andnumericalmethods (discretization methods,solvers,numerical parameters,andgridgenerations,etc.)

Historicallyonly Analytical Fluid Dynamics (AFD)andExperimental Fluid Dynamics (EFD).

CFD made possibleby theadvent ofdigitalcomputerandadvancing with improvementsofcomputerresources(500 flops, 194720 teraflops,2003)


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PORQUE USAR CFD?

Analysisand Design1. Simulation-baseddesigninsteadof build & test Morecost effectiveandmorerapid than EFD CFD provides high-fidelitydatabasefordiagnosingflow

field

2. Simulationof physicalfluid phenomena that aredifficult forexperiments Fullscalesimulations (e.g.,shipsandairplanes) Environmentaleffects (wind, weather,etc.)

Hazards (e.g.,explosions,radiation, pollution) Physics (e.g., planetaryboundarylayer,stellarevolution)

Knowledgeandexplorationofflow physics


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Aplicaes do CFD

Onde usadoo CFD? Aeroespacial Automotiva

Biomdica Processos qumicos HVAC Hidrulica Martimas

leo & Gs Geraode Energia Esportes

F18 Store Separation

Temperature and naturalconvection currents in the eyefollowing laser heating.

Aeroespacial

Automotiva

Biomdico


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Aplicao do CFD

Polymerization reactor vessel - predictionof flow separation and residence timeeffects.

Streamlines for workstation

ventilation

Onde usado o CFD? Aerospace Automotive

Biomedical Chemical Processing HVAC Hydraulics Marine

Oil & Gas Power Generation Sports

HVAC

Chemical Processing

Hydraulics


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Aplicaes do CFD

Where is CFD used?

Aerospace

Automotive

Biomedical

Chemical Processing HVAC

Hydraulics

Marine

Oil & Gas

Power Generation Sports

Flow of lubricating

mud over drill bitFlow around cooling

towers

Marine

Oil & Gas

Sports

Power Generation


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Modelagem

Modelingis themathematical physics problemformulationin termsofacontinuousinitialboundaryvalue problem (IBVP)

IBVPisin theformofPartial Differential Equations(PDEs) with appropriateboundaryconditionsandinitialconditions.

Modelingincludes:1. Geometryanddomain2. Coordinates3. Governingequations

4. Flow conditions5. Initialandboundaryconditions6. Selectionofmodelsfordifferent applications


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Modeling (geometryanddomain)

Simplegeometries canbeeasilycreatedbyfewgeometric parameters (e.g.circular pipe) Complex geometries must becreatedby the partial

differentialequationsorimporting thedatabaseof thegeometry (e.g.airfoil)intocommercialsoftware

Domain:sizeandshape Typicalapproaches

Geometryapproximation CAD/CAE integration: useofindustrystandardssuch asParasolid, ACIS, STEP,or IGES,etc.

The threecoordinates: Cartesiansystem (x,y,z),cylindricalsystem (r, ,z),andsphericalsystem(r, , )shouldbeappropriatelychosenforabetterresolutionof thegeometry(e.g.cylindricalforcircular pipe).


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Modeling (coordinates)

x

y

z

x

y

z

x

y

z

(r,U,z)

z

rU

(r,U,J)

rU

J(x,y,z)

Cartesian Cylindrical Spherical

General Curvilinear Coordinates General orthogonalCoordinates


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Modeling (governingequations)

Navier-Stokes equations (3D in Cartesian coordinates)

-

xx

xx

xx

xx!

xx

xx

xx

xx

2

2

2

2

2

2

zu

yu

xu

xp

zuw

yuv

xuu

tu QVVVV

-

x

x

x

x

x

x

x

x!

x

x

x

x

x

x

x

x2

2

2

2

2

2

z

v

y

v

x

v

y

p

z

vw

y

vv

x

vu

t

vQVVVV

0!xxxxxxxx zw

yv

xu

tVVVV

RTp V!

L

v pp

Dt

DR

Dt

RDR

V

!

2

2

2

)(2

3

Convection Piezometric pressure gradientViscous termsLocalacceleration

Continuity equation

Equation of state

Rayleigh Equation

-

x

xx

xx

xx

x!x

xx

xx

xx

x2

2

2

2

2

2

z

w

y

w

x

w

z

p

z

ww

y

wv

x

wu

t

wQVVVV


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Modeling (flow conditions)

Based on the physics of the fluids phenomena, CFDcan be distinguished into different categories usingdifferent criteria

Viscous vs. inviscid (Re) External flow or internal flow (wall bounded or not) Turbulent vs. laminar (Re) Incompressible vs. compressible (Ma) Single- vs. multi-phase (Ca)

Thermal/density effects (Pr, g, Gr, Ec) Free-surface flow (Fr) and surface tension (We) Chemical reactions and combustion (Pe, Da) etc


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Modeling (initialconditions)

Initialconditions (ICS,steady/unsteadyflows) ICsshouldnot affect finalresultsandonlyaffect convergence path,i.e.numberofiterations (steady)or timesteps (unsteady)needtoreach convergedsolutions.

Morereasonableguesscanspeedup theconvergence

Forcomplicatedunsteadyflow problems, CFDcodesareusuallyrunin thesteadymodeforafew iterationsforgettingabetterinitialconditions


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Modeling(boundaryconditions)

Boundary conditions: No-slip orslip-freeon walls, periodic,inlet (velocityinlet,massflow rate,constant pressure,etc.),outlet (constant pressure,velocityconvective,numericalbeach,zero-gradient),andnon-reflecting (forcompressibleflows,such asacoustics),etc.

No-slip walls: u=0,v=0

v=0, dp/dr=0,du/dr=0

Inlet ,u=c,v=0 Outlet, p=c

Periodic boundary condition inspanwise direction of an airfoilo

r

xAxisymmetric


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Modeling (selectionofmodels)

CFD codes typically designed for solving certain fluidphenomenon by applying different models

Viscous vs. inviscid (Re) Turbulent vs. laminar (Re, Turbulent models)

Incompressible vs. compressible (Ma, equation of state) Single- vs. multi-phase (Ca, cavitation model, two-fluid model) Thermal/density effects and energy equation

(Pr, g, Gr, Ec, conservation of energy) Free-surface flow (Fr, level-set & surface tracking model) and

surface tension (We, bubble dynamic model) Chemical reactions and combustion (Chemical reaction model) etc


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Modeling (Turbulenceandfreesurfacemodels)

Turbulent models: DNS: most accurately solve NS equations, but too expensive

for turbulent flows

RANS: predict mean flow structures, efficient inside BL but excessivediffusion in the separated region.

LES: accurate in separation region and unaffordable for resolving BL DES: RANS inside BL, LES in separated regions.

Free-surface models: Surface-tracking method: mesh moving to capture free surface,limited to small and medium wave slopes

Single/two phase level-set method: mesh fixed and level-setfunction used to capture the gas/liquid interface, capable of

studying steep or breaking waves.

Turbulent flows at high Re usually involve both large and small scale

vortical structures and very thin turbulent boundary layer (BL) near the wall


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Examplesofmodeling (Turbulenceandfreesurfacemodels)

DES, Re=105, Iso-surface of Qcriterion (0.4) for turbulent flow aroundNACA12 with angle of attack 60 degrees

URANS, Re=105, contour of vorticityfor turbulent flow around NACA12 withangle of attack 60 degrees

DES, Athena barehull


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Numericalmethods

Thecontinuous Initial Boundary ValueProblems(IBVPs)arediscretized intoalgebraicequationsusingnumericalmethods. Assemble thesystemofalgebraicequationsandsolve thesystem toget approximatesolutions Numericalmethodsinclude:1. Discretization methods2. Solversandnumerical parameters

3. Gridgenerationand transformation4. High Performance Computation (HPC)and post-processing


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Discretizationmethods

Finitedifferencemethods (straightforward toapply,usuallyforregulargrid)andfinitevolumes andfiniteelement methods (usuallyforirregularmeshes)

Each typeofmethodsaboveyields thesamesolutionifthegridisfineenough. However,somemethodsaremoresuitable tosomecases thanothers

Finitedifferencemethodsforspatialderivatives withdifferent orderofaccuraciescanbederivedusingTaylorexpansions,such as2nd orderupwindscheme,centraldifferencesschemes,etc.

Higherordernumericalmethodsusually predict higherorderofaccuracyfor CFD,but morelikelyunstabledue tolessnumericaldissipation Temporalderivatives canbeintegratedeitherby theexplicit method (Euler, Runge-Kutta,etc.)orimplicitmethod (e.g. Beam-Warmingmethod)


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Discretization methods (Contd)

Explicit methods canbeeasilyappliedbut yieldconditionallystable Finite Different Equations (FDEs),which arerestrictedby the timestep; Implicit methodsareunconditionallystable,but needeffortsonefficiency.

Usually, higher-order temporaldiscretization isusedwhen thespatialdiscretization isalsoof higherorder.

Stability: A discretization methodissaid tobestableifit doesnot magnify theerrors that appearin thecourseofnumericalsolution process.

Pre-conditioning methodisused when thematrix of thelinearalgebraicsystemisill-posed,such asmulti-phaseflows,flows with abroadrangeofMach numbers,etc. Selectionofdiscretization methods shouldconsiderefficiency,accuracyandspecialrequirements,such asshock wave tracking.


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Discretization methods (example)

0!x

x

x

x

y

v

x

u

2

2

y

u

e

p

xy

u

vx

u

u x

x

x

x!

x

x

x

x

Q

2D incompressiblelaminarflow boundarylayer

m=0m=1

L-1 L

y

x

m=MMm=MM+1

(L,m-1)

(L,m)

(L,m+1)

(L-1,m)

1l

l lm

m m

uuu u u

x x

x ! - x (

1

l

l lm

m mvuv u u

y yx ! - x (

1

l

l lm

m m

vu u

y ! - (

FD Sign( )0

2

1 12 22l l l

m m m

uu u u

y y

QQ

x ! - x (

2nd order central differencei.e., theoretical order ofaccuracyPkest= 2.

1st

order upwind scheme, i.e., theoretical order of accuracy Pkest= 1


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Discretization methods (example)

1 12 2 2

12

1

l l l

l l l l m m m

m m m m

FDu v vy

v u F D u BD u x y y y y y

BDy

Q Q Q

( ( ( ( ( ( ( - -

(-

1( / )

l

l lm

m m

uu p e

x x

x!

( x

B2 B3B1

B4 11 1 2 3 1 4 /ll l l l

m m m m m B u B u B u B u p e

x

x ! 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

pB u

B B x eu

B B B

B B B

B B u pB u

x e

x x

yy v !y y y y yy

yy - x-

x -

Solveit usingThomasalgorithm

To be stable, Matrix has to be

Diagonally dominant.


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Solversandnumerical parameters

Solvers include: tridiagonal, pentadiagonal solvers,PETSC solver,solution-adaptivesolver,multi-gridsolvers,etc.

Solvers canbeeitherdirect (Cramersrule, Gausselimination, LU decomposition)oriterative(Jacobimethod, Gauss-Seidelmethod, SOR method)

Numerical parameters need tobespecified tocontrolthecalculation. Underrelaxationfactor,convergencelimit,etc. Different numericalschemes

Monitorresiduals (changeofresultsbetweeniterations) Numberofiterationsforsteadyflow ornumberof

timestepsforunsteadyflow Single/double precisions


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Gridscaneitherbestructured

(hexahedral)orunstructured(tetrahedral). Dependsupon typeofdiscretization schemeandapplication Scheme

Finitedifferences: structured

Finitevolumeorfiniteelement:structuredorunstructured Application

Thinboundarylayersbestresolved with highly-stretchedstructuredgrids

Unstructuredgridsusefulforcomplex geometries Unstructuredgrids permit

automaticadaptiverefinementbasedon the pressuregradient,orregionsinterested (FLUENT)

Numericalmethods (gridgeneration)

structured

unstructured


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Numericalmethods (grid transformation)

y

xo oPhysical domain Computational domain

x x

f f f f f

x x x

\ L

\ L\ L \ L

x x x x x x x

! ! x x x x x x x

y y

f f f f f

y y y

\ L\ L

\ L \ L

x x x x x x x! !

x x x x x x x

Transformation between physical(x,y,z) and computational (\L^)domains, important for body-fitted grids. The partialderivatives at these two domainshave the relationship (2D as an

example)

L

\

Transform


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High performancecomputingand post-processing

CFD computations (e.g. 3D unsteadyflows)areusuallyveryexpensive

which requires parallel high performancesupercomputers (e.g. IBM

690) with theuseofmulti-block technique. Asrequiredby themulti-block technique, CFD codesneed tobe

developedusing theMassagePassing Interface (MPI) Standard totransferdatabetweendifferent blocks.

Post-processing: 1. Visualizethe CFD results (contour,velocityvectors,streamlines, pathlines,streaklines,andiso-surfacein 3D,etc.),and2. CFD UA:verificationandvalidationusing EFD data (moredetailslater)

Post-processingusually through usingcommercialsoftware


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Typesof CFD codes

Commercial CFD code: FLUENT, Star-

CD, CFDRC, CFX/AEA,etc. Research CFD code: CFDSHIP-IOWA Publicdomainsoftware (PHI3D,

HYDRO,andWinpipeD,etc.) Other CFD softwareincludes the Grid

generationsoftware (e.g. Gridgen,Gambit)andflow visualizationsoftware (e.g. Tecplot, FieldView)

CFDSHIPIOWA


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CFD Educational Interface

Lab1: Pipe Flow Lab 2: Airfoil Flow

CFD

1. Definition of CFD Process

2. Boundary conditions

3. Iterative error and grid convergence studies

4. Developing length of laminar and

turbulent pipe flows.

5. Validation using AFD/EFD

1. Inviscid vs. viscous flows

2. Boundary conditions

3. Effect of order of accuracy

4. Effect of angle of attack/turbulent

models on flow field

5. Validation and confidence of CFD


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CFD process

Purposes of CFD codes willbedifferent fordifferent

applications:investigationofbubble-fluidinteractionsforbubblyflows,studyof waveinducedmassivelyseparatedflowsforfree-surface,etc.

Dependon thespecific purposeandflow conditionsof theproblem,different CFD codes canbechosenfordifferentapplications (aerospace,marines,combustion,multi-phaseflows,etc.) Once purposesand CFD codeschosen, CFD process is thesteps toset up the IBVP problemandrun thecode:

1. Geometry2.Physics3.Mesh4. Solve5. Reports6.Post processing


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CFD Process

ViscousModel

BoundaryConditions

InitialConditions

ConvergentLimit

Contours

Precisions(single/double)

NumericalScheme

Vectors

StreamlinesVerification

Geometry

SelectGeometry

GeometryParameters

Physics Mesh Solve Post-Processing

CompressibleON/OFF

Flowproperties

Unstructured(automatic/

manual)

Steady/Unsteady

Forces Report(lift/drag,shear stress,etc)

XY Plot

DomainShape and

Size

HeatTransferON/OFF

Structured(automatic/

manual)

Iterations/Steps

Validation

Reports


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Geometry

Selectionofanappropriatecoordinate Determine thedomainsizeandshape Anysimplificationsneeded? What kindsofshapesneeded tobeused tobest

resolve thegeometry? (lines,circular,ovals,etc.) Forcommercialcode,geometryisusuallycreated

usingcommercialsoftware (eitherseparatedfrom thecommercialcodeitself,like Gambit,orcombinedtogether,like FlowLab)

Forresearch code,commercialsoftware (e.g. Gridgen)isused.


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Physics

Flow conditionsandfluid properties1.Flow conditions:inviscid,viscous,laminar,orturbulent,etc.

2.Fluid properties:density,viscosity,andthermalconductivity,etc.

3. Flow conditionsand propertiesusually presentedindimensionalforminindustrialcommercial CFDsoftware, whereasinnon-dimensionalvariablesforresearch codes.

Selectionofmodels:different modelsusuallyfixedbycodes,optionsforuser tochoose Initialand Boundary Conditions:not fixedbycodes,userneedsspecify themfordifferentapplications.


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Mesh

Meshesshouldbe welldesigned toresolveimportantflow features which aredependent uponflowcondition parameters (e.g., Re),such as thegridrefinement inside the wallboundarylayer

M

esh canbegenerated byeithercommercialcodes(Gridgen, Gambit,etc.)orresearch code (usingalgebraicvs.PDE based,conformalmapping,etc.)

Themesh, together with theboundaryconditionsneed tobeexportedfromcommercialsoftwareinacertainformat that canberecognizedby theresearch CFD codeorothercommercial CFDsoftware.


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Solve

Setup appropriatenumerical parameters Chooseappropriate Solvers Solution procedure (e.g.incompressibleflows)

Solve themomentum, pressurePoissonequationsandget flow field quantities,such asvelocity,turbulenceintensity, pressureand integralquantities (lift,dragforces)


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Reports

Reportssaved the time historyof theresidualsofthevelocity, pressureand temperature,etc. Report theintegral quantities,such as total

pressuredrop,frictionfactor (pipeflow),lift anddragcoefficients (airfoilflow),etc.

XY plotscould present thecenterlinevelocity/pressuredistribution,frictionfactordistribution (pipeflow), pressurecoefficientdistribution (airfoilflow).

AFD or EFD datacanbeimportedand put on top ofthe XY plotsforvalidation


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Post-processing

Analysisandvisualization Calculationofderivedvariables

Vorticity Wallshearstress

Calculationofintegral parameters:forces,moments

Visualization (usually with commercialsoftware) Simple2D contours 3D contourisosurface plots Vector plotsandstreamlines

(streamlinesare thelines whosetangent directionis thesameas thevelocityvectors)

Animations


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Post-processing (Uncertainty Assessment)

Simulationerror:thedifferencebetweenasimulationresult S and the truth T (objectivereality),assumedcomposedofadditivemodeling SM andnumerical SN errors:

Verification:processforassessingsimulationnumericaluncertainties U

SNand, whenconditions permit,estimating the

signandmagnitude Delta *SN of thesimulationnumericalerroritselfand theuncertaintiesin that errorestimate UScN

Validation:processforassessingsimulationmodelinguncertainty USM byusingbenchmarkexperimentaldataand,whenconditions permit,estimating thesignandmagnitudeofthemodelingerror SM itself.

SNSMSTS HHH !!

222

SNSMSUUU !

!

!!J

j

jIPTGISN

1

HHHHHHH 22222PTGISN UUUUU !

)(SNSMDSDE HHH !!

222

SNDV UUU !

VUE Validation achieved


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Post-processing (UA, Verification)

Convergencestudies: Convergencestudiesrequireaminimumof

m=3 solutions toevaluateconvergence with respective toinputparameters. Consider thesolutionscorresponding tofine ,medium ,andcoarsemeshes 1k

S

2kS

3kS

(i). Monotonic convergence: 0


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Post-processing (UA, Verification,contd)

Monotonic Convergence: Generalized Richardson Extrapolation

? A ? A

!

*

1

2

*

1

1.014.2

11

kREk

kREk

C

CkcU

H

H

Oscillatory Convergence: Uncertainties can be estimated, butwithoutsigns and magnitudes of the errors. Divergence

LUk SSU ! 21

1. Correctionfactors

2. GCI approach *1kREsk

FU H! *1

1kREskc

FU H!

32 21ln

ln

k k

k

k

pr

I I! 11

k

kest

p

kk p

k

rCr

!

1

* 21

1k k

k

RE p

kr

IH !

1

1

2

*

*

9.6 1 1.1

2 1 1

k

k

k RE

k

k RE

CU

C

H

H

- ! -

1 0.125kC

1 0.125kC u

1 0.25kC

25.0|1| u kC|||]1[|*

1kREkC H

In this course, only grid uncertainties studied. So, all thevariables with

subscribe symbol k will be replaced by g, such as Uk will be U

g

estk

p is the theoretical order of accuracy,2 for 2nd order and 1 for 1st orderschemes

kU is the uncertainties based on finemesh solution, is theuncertainties based on numericalbenchmark SC

kcUis the correctionfactor

kC


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Asymptotic Range: For sufficiently small (xk, thesolutions are in the asymptotic range such thathigher-order terms are negligible and theassumption that and are independent of (xkis valid.

When Asymptotic Range reached, will be close tothe theoretical value , and the correctionfactor

will be close to 1.

To achieve the asymptotic range for practicalgeometry and conditions is usually not possible andm>3 is undesirable from a resources point of view

Post-processing (Verification, AsymptoticRange)

ik

p ik

g

estkp

kp

kC


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Exampleof CFD Processusingeducationalinterface (Geometry)

Turbulent flows (Re=143K)around Clarky airfoil withangleofattack6degreeissimulated. C shapedomainisapplied Theradiusof thedomain Rc anddownstreamlength Lo

shouldbespecifiedinsuch a way that thedomainsizewillnot affect thesimulationresults


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Exampleof CFD Process (Physics)No heattransfer


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Exampleof CFD Process (Mesh)

Grid need to be refined nearthe foil surface to resolvethe boundary layer


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Exampleof CFD Process (Solve)

Residuals vs. iteration


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Exampleof CFD Process (Reports)


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Exampleof CFD Process (Post-processing)


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Produtos Ansys

Lista Completa de Produtos

Featured Products Pre-processing Stand-alone Solvers Application SpecificANSYS Mechanical ANSYS ICEM CFD ANSYS Multiphysics ANSYS AQWA

ANSYS Structural ANSYS MeshMorpher ANSYS Rigid Dynamics ANSYS ASAS

ANSYS Professional TGrid FLUENT for CATIA V5 ANSYS Icepak

ANSYS DesignModeler ANSYS POLYFLOW ANSYS TurboGrid

ANSYS SpaceClaim

Direct Modeler

ANSYS ICEM CFD Cart3D ANSYS BladeModeler

ANSYS Meshing ANSYS Fatigue Analysis ANSYS Vista TF

ANSYS DesignXplorer ANSYS Airpak

ANSYS CFD ANSYS Composite PrepPost

ANSYS CFX

ANSYS FLUENT

ANSYS CFD-Post

ANSYS Explicit STR

ANSYS AUTODYN

ANSYS LS-DYNA

ANSYS EKM


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E ld C d S tE ld C d S t 2/2/2012 48

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MUITO OBRIGADO!MUITO OBRIGADO!

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