Introdução 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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    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)

    -

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    )(2

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    Convection Piezometric pressure gradientViscous termsLocalacceleration

    Continuity equation

    Equation of state

    Rayleigh Equation

    -

    x

    xx

    xx

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    x!x

    xx

    xx

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    x2

    2

    2

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    z

    w

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    w

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    p

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    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

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    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

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    1

    l

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    1

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    FD Sign( )0

    2

    1 12 22l l l

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    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

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    m m m m

    FDu v vy

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

    x

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    4 1

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    0 0 0 0 0

    0 0 0 0 0

    0 0 0 0 0 0

    l

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    B B B

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    x e

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    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.

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    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

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

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    * 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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