Management and Minimisation of Uncertainties and Errors in Numerical Aerodynamics: Results of the German collaborative project MUNA

342 Pages·2013·44.2 MB·English

by  E. Mazlum

Notes on Numerical Fluid Mechanics
and Multidisciplinary Design 122
SeriesEditors
Prof.Dr.WolfgangSchröder
(GeneralEditor),RWTHAachen,LehrstuhlfürStrömungslehreundAerodynamisches
Institut,Wüllnerstr.5a,52062Aachen,Germany
E-mail:offi[email protected]
Prof.Dr.Ir.BendiksJanBoersma
ChairofEnergytechnology,DelftUniversityofTechnology,Leeghwaterstraat44,
2628CADelft,TheNetherlands
E-mail:[email protected]
Prof.Dr.KozoFujii
SpaceTransportationResearchDivision,TheInstituteofSpaceandAstronautical Science,
3-1-1,Yoshinodai,Sagamihara,Kanagawa,229-8510,Japan
E-mail:fujii@flab.eng.isas.jaxa.jp
Dr.WernerHaase
HöhenkirchenerStr.19d,D-85662Hohenbrunn,Germany
E-mail:[email protected]
Prof.Dr.MichaelA.Leschziner
AeronauticsDepartment,ImperialCollegeofScienceTechnologyandMedicine,
PrinceConsortRoad,LondonSW72BY,UK
E-mail:[email protected]
Prof.Dr.JacquesPeriaux
38,BoulevarddeReuilly,F-75012Paris,France
E-mail:[email protected]
Prof.Dr.SergioPirozzoli
DipartimentodiMeccanicaeAeronautica,UniversitàdiRoma“LaSapienza”,
ViaEudossiana18,00184,Roma,Italy
E-mail:[email protected]
Prof.Dr.ArthurRizzi
DepartmentofAeronautics,KTHRoyalInstituteofTechnology,Teknikringen8,
S-10044Stockholm,Sweden
E-mail:[email protected]
Dr.BernardRoux
L3M-IMTLaJetée,TechnopoledeChateau-Gombert,F-13451MarseilleCedex20,France
E-mail:[email protected]
Prof.Dr.YuriiI.Shokin
InstituteofComputationalTechnologies,SiberianBranchoftheRussianAcademy
ofSciences,Ac.LavrentyevaAve.6,630090Novosibirsk,Russia
E-mail:[email protected]
Forfurthervolumes:
http://www.springer.com/series/4629
Management and
Minimisation of Uncertainties
and Errors in Numerical
Aerodynamics
Results of the German Collaborative
Project MUNA
Bernhard Eisfeld, Holger Barnewitz,
Willy Fritz, and Frank Thiele (Eds.)
ABC
Editors
Dr.BernhardEisfeld WillyFritz
InstituteofAerodynamicsand EADSDeutschlandGmbHCassidian
FlowTechnology Manching
GermanAerospaceCenter(DLR) Germany
Braunschweig
Germany Prof.Dr.FrankThiele
InstitutfürStrömungsmechanik
Dipl.-Phys.HolgerBarnewitz undTechnischeAkustik
AirbusOperationsGmbH Berlin
Bremen Germany
Germany
ISSN1612-2909 e-ISSN1860-0824
ISBN978-3-642-36184-5 e-ISBN978-3-642-36185-2
DOI10.1007/978-3-642-36185-2
SpringerHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2012956291
(cid:2)c Springer-VerlagBerlinHeidelberg2013
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Preface
Continuousdevelopmentofnumericalmethodsoverthelastdecadestogetherwith
increasing available computer power has made Computational Fluid Dynamics
(CFD)akeytechnologyinmodernaircraftdevelopment.Theresultsobtainedover
thelastdecadesgiverisetothevisionthatfutureaircraftdesignmayalmostentirely
rely on numerical simulations. This shift in paradigm will not only dramatically
changetheengineeringprocessinitself,butalsotherequirementsonthesimulation
data. In particular, safe estimates of the errors and uncertainties of the simulation
resultswillhavetobeprovided,similartoerrorbarsinexperimentaldatafromthe
windtunnel.
Inorderto meetsuchfutureneeds,thecollaborativeresearchprojectMUNA –
Managementand Minimisationof Errorsand Uncertaintiesin NumericalAerody-
namics – has been initiated within the 4th German Aeronautics Research
Program(Luftfahrtforschungsprogramm).FollowingthepredecessorprojectsME-
GAFLOWandMEGADESIGN,altogether12partnersfromindustry(Airbus,Cas-
sidian, Eurocopter), research organisations (DLR, Institute of Aerodynamics and
FlowTechnology)anduniversities(RWTHAachen:InstituteofAerodynamicsand
Institute of ComputationalAnalysis of TechnicalSystems; TU Berlin: Institute of
Fluid Mechanics and Technical Acoustics; TU Braunschweig: Institute of Fluid
Mechanics, Institute of Aircraft Design and Lightweight Structures and Institute
ofScientific Computing;UniversityStuttgart:Instituteof AerodynamicsandGas-
dynamics;UniversityTrier:DepartmentofMathematics)havebeendevelopingand
applyingmethods,addressingerrorsanduncertaintiesofvariouskind,typicallyen-
counteredinCFDsimulations.Forthispurpose,theDLRTAUcodewasprovided
asmajorsimulationtool.
Inafirststepthepartnersjointlycollectedpossiblesourcesoferrorsanduncer-
tainties,wherethecomputationalgrid,turbulencemodeling,thenumericalaccuracy
andgeometricalissuesinthecontextofcoupledmultidisciplinarysimulationshave
beenidentifiedasimportant.Consequently,theresearchactivitiesofthefirstproject
phasehavebeenconcentratingontherespectiveareas,whichisalsoreflectedbythe
organisationofthebook.
VI Preface
Inthesecondphaseoftheproject,stochasticuncertainties,alsocalledaleatory,
havebeenaddressed.Thereforethefinalpartofthebookisdevotedtovariousactiv-
itiestowardsefficientlycomputingstatisticaloutputquantitiesduetouncertainties
intheinputparameters,includingmethodsfortherobustdesignundergeometrical
uncertainties.
The results of the project have been presented to the public during two Work-
shops held on March 23th and 24th 2010 and on October 25th 2012. The current
bookdocumentstheresultsachievedbythepartners.
Theeditorisindebtedtoallco-workersoftheproject,inparticulartothemem-
bersofthesteeringcommittee,HolgerBarnewitz(Airbus),WillyFritz(Cassidian)
andProf.Dr. FrankThiele(TU Berlin),fortheircontributionsandinevitablesup-
portinmakingMUNAasuccess.Furthermoretheeditorwantstothankthegeneral
editoroftheSpringerseries“NotesonNumericalFluidMechanicsandMultidiscip-
linary Design”,Prof. Dr. W. Schröder,and the staff of the Springer-Verlagforthe
opportunitytopublishthetechnicalresultsoftheMUNAproject.
FinallythefundingofthepartneractivitiesbytheGermanMinistryofEconomics
withinthe4thGermanAeronauticsResearchProgramisgratefullyacknowledged.
Braunschweig BernhardEisfeld
November2012
Contents
PartI MeshGenerationandManipulation
MethodsandStrategiesfortheDetectionandManagementofGrid
InducedUncertaintiesinNumericalAerodynamics ................... 3
E.Mazlum,R.Radespiel
1 IdentificationofSourcesofErrorInducedbyGeometryand
Discretisation ............................................ 3
1.1 NumericalMethod ................................ 4
1.2 Analysisin2D.................................... 4
1.3 UncertaintiesInducedbyVariationoftheTrailing-Edge
Geometry ........................................ 5
1.4 UncertaintiesInducedbytheGridTopology ........... 6
1.5 EffectsoftheHybridBorderontheFlowSolution...... 8
2 Methodsfor the Detectionof ImproperlyDiscretised Grid
Regions ................................................. 12
2.1 ErrorIndicatorBasedontheArtificialDissipationof
CentralConvectionSchemes ........................ 12
2.2 ApplicationoftheErrorIndicator.................... 14
3 GridImprovementStrategiesandTechniques.................. 18
3.1 Enlargementof the Hexahedra Layer via Grid
Manipulation ..................................... 18
3.2 LocalRefinementofHexahedratoImprovetheWake
Discretisation..................................... 24
References..................................................... 27
Quantification and Reduction of Numerical Uncertainties by
ImprovementoftheTAUGridAdaptationToolandAdjointMethods ... 29
MatthiasOrlt,NicolasR.Gauger
1 Introduction.............................................. 29
2 ImprovementsUsingtheDecomposabilityofElements.......... 31
VIII Contents
3 ModificationofAdaptedGridsontheBase
ofaGeometricalElementQuality............................ 36
3.1 AGeometricQualityMeasurefortheElementTypesof
TAU ............................................ 36
3.2 ModificationofAdaptedGrids ...................... 40
3.3 ResultsonModifiedGrids .......................... 42
4 Adjoint-BasedErrorEstimationandFunctionalCorrection ...... 46
5 ErrorIndicationBasedontheAdjointSolution ................ 48
6 ConclusionsfortheApplication ............................. 51
References..................................................... 52
ApplicationofMeshModificationsandAdjointErrorEstimates........ 55
S.Albensoeder
1 Introduction.............................................. 55
2 Methods................................................. 56
2.1 AdjointErrorEstimationMethod .................... 56
2.2 MeshManipulation................................ 57
3 Results .................................................. 59
3.1 AdaptationbyanAdjointErrorEstimate .............. 59
3.2 MeshManipulation................................ 65
4 Conclusion............................................... 69
5 Outlook ................................................. 72
References..................................................... 72
PartII TurbulenceModeling
MinimizationandQuantificationofErrorsandUncertaintiesinRANS
Modeling ...................................................... 77
TobiasSchmidt,CharlesMockett,FrankThiele
1 Introduction.............................................. 77
2 ClassificationofErrorsandUncertainties ..................... 78
3 DevelopmentoftheSensors ................................ 79
3.1 DevelopmentoftheErrorSensors.................... 79
3.2 DevelopmentoftheUncertaintySensors .............. 84
4 ApplicationoftheSensors.................................. 92
4.1 ErrorSensors..................................... 92
4.2 UncertaintySensors ............................... 94
5 ApplicabilityonMixedErrors............................... 96
6 IndustrialApplication...................................... 97
7 FieldofApplicationandItsLimits........................... 99
References.....................................................100
Contents IX
SensorControlledZonalRANS-LESMethod ........................ 101
BenediktRoidl
1 Introduction..............................................101
2 NumericalMethods .......................................103
2.1 Large-EddySimulation.............................103
2.2 SensorDevelopment...............................103
2.3 SyntheticTurbulenceGenerationMethods(STGM).....104
3 Results ..................................................107
3.1 SensorValidation..................................107
3.2 ValidationofSTGM ...............................108
3.3 ObliqueShockonFlatPlate(SWBLI) ................114
3.4 DRA2303TransonicProfile.........................117
4 Conclusion...............................................124
References.....................................................125
PartIII NumericalMethods
The Application of IteratedDefect CorrectionsBased on WENO
Reconstruction ................................................. 129
AlexanderFilimon,Claus-DieterMunz
1 Introduction..............................................129
2 TheMethodofIteratedDefectCorrection.....................130
2.1 IDeCforInhomogeneousProblems ..................134
3 WENOReconstructiononUnstructuredGrids .................135
4 NumericalResults.........................................138
4.1 ConvergenceStudies...............................138
4.2 ApplicationTestCases .............................147
4.3 Conclusion.......................................152
References.....................................................153
PartIV GeometryandDeformation
Uncertainties of Numerical Structural Models in the Frame of
Aeroelasticity................................................... 157
P.Reich,A.Reim,M.Haupt,P.Horst
1 Finite Element Models and Analysis Methods Used for
UncertaintyQuantification..................................158
1.1 ParametricFiniteElementModel ....................158
1.2 QuantificationofUncertainty........................160
2 PartI:ModelUncertainties .................................163
2.1 Introduction ......................................163
2.2 DesignoftheWingStructure........................164
2.3 UncertaintiesduetoModelingSimplifications .........165
3 PartII:StochasticSimulations ..............................171
3.1 Introduction ......................................171
X Contents
3.2 FirstOrderReliabilityMethod.......................172
3.3 Combinationof the FORM-Routine with Fluid-
StructureInteractionCodeLibrary ...................173
3.4 SensitivityAnalysisbyaGlobalVariationinStructural
Parameters .......................................174
3.5 ResultsoftheFORMAnalysis ......................177
3.6 Conclusions ......................................179
References.....................................................180
A Comparisonof Fluid/Structure Coupling Methods for Reduced
StructuralModels............................................... 181
GeorgWellmer,LarsReimer,HorstFlister,MarekBehr,JosefBallmann
1 Introduction..............................................181
2 CouplingMethodology ....................................183
2.1 FlowSolver ......................................185
2.2 StructuralSolver ..................................186
2.3 FlowGridDeformation ............................186
3 SpatialCoupling..........................................187
3.1 FiniteInterpolationElementMethod .................188
3.2 AdditionalInterpolationSchemesforFIE .............190
3.3 GlobalSpline-BasedInterpolation(GSB) .............192
3.4 Moving-Least-SquaresInterpolation(MLS) ...........194
3.5 InsertionofAdditionalSupportPoints ................195
4 ErrorSourcesinSpatialCoupling............................197
4.1 CFDMeshSpacingandLoadDistribution.............197
4.2 InfluenceofProjectionParameters ...................204
5 CoupledSimulations ......................................212
6 Conclusion...............................................215
References.....................................................217
ImprovedMeshDeformation...................................... 219
HolgerBarnewitz,BerndStickan
1 Introduction..............................................219
2 CFDMeshDeformationModule ............................221
2.1 RadialBasisFunctionsinMeshDeformation ..........222
2.2 Algorithm........................................224
3 WallDistanceModule .....................................227
4 BasePointReductionMethods..............................228
4.1 EquidistantReductionMethod ......................229
4.2 WeightedDistances................................229
4.3 ErrorCorrection ..................................232
5 InterpolationQualityComparison............................234
6 Applications .............................................237
6.1 WingShapeDesign................................237
6.2 Multi-disciplinaryWingOptimization–SFB-401-Wing ..238
6.3 ApplicationtoComplexConfiguration................239
Contents XI
7 Summary ................................................240
References.....................................................242
PartV StochasticUncertainties
StatisticalAnalysisofParameterVariationsUsingtheTaguchiMethod .. 247
A.Wolf,D.Henes,S.Bogdanski,Th.Lutz,E.Krämer
1 Introduction..............................................247
2 TheTaguchi-Method ......................................248
2.1 OrthogonalArrays.................................249
2.2 ANOVA-Analysis .................................249
2.3 ParameterInteraction ..............................252
2.4 ErrorDetermination ...............................252
3 SimulationSetup..........................................253
4 Results ..................................................255
5 TAUImplementation ......................................262
6 SummaryandConclusion ..................................263
References.....................................................264
Numerical Methods for Uncertainty Quantificationand Bayesian
UpdateinAerodynamics ......................................... 265
AlexanderLitvinenko,HermannG.Matthies
1 Introduction..............................................265
2 StatisticalModellingofUncertainties ........................266
2.1 ModellingofUncertaintiesinParameters .............267
2.2 ModellingofUncertaintiesintheAirfoilGeometry .....268
3 DiscretisationTechniques ..................................269
4 Low-RankResponseSurface................................270
4.1 Update of the Low-Rank Response Surface via
ComputingtheResidual............................273
5 DataCompression.........................................274
5.1 ConcatenationofTwoLow-RankMatrices ............276
6 BayesianUpdateoftheUncertainAirfoilGeometry ............276
7 Numerics ................................................277
References.....................................................281
Efficient Quantification of Aerodynamic Uncertainties Using
Gradient-EmployingSurrogateMethods............................ 283
DishiLiu
1 Introduction..............................................283
2 TestCase ................................................285
3 Methods.................................................287
3.1 Quasi-MonteCarloQuadrature ......................287
3.2 Gradient-EnhancedRadialBasisFunctions ............288
3.3 Gradient-EnhancedKrigingMethod..................289