Unsteady Computational Fluid Dynamics in Aeronautics

432 Pages·2014·12.21 MB·English

by  P.G. Tucker (auth.)

Unsteady Computational Fluid Dynamics
in Aeronautics
FLUID MECHANICS AND ITS APPLICATIONS
Volume104
SeriesEditor: AndreTHESS
DepartmentonMechanicalEngineering
IlmenauUniversityofTechnology
98684Ilmenau,Germany
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P.G. Tucker
Unsteady
Computational
Fluid Dynamics
in Aeronautics
P.G.Tucker
DepartmentofEngineering
WhittleLaboratory
UniversityofCambridge
Cambridge,UK
ISSN0926-5112 FluidMechanicsandItsApplications
ISBN978-94-007-7048-5 ISBN978-94-007-7049-2(eBook)
DOI10.1007/978-94-007-7049-2
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To myFamily
Preface
In2001Ipublished‘ComputationofUnsteadyInternalFlows’.Thistextwaslargely
basedaroundincompressibleflowsolvermethodsandhencetypicallylowerspeed
flows. The key premise behind the original text was that, in some sense, most en-
gineeringflowsareintrinsicallyunsteady(evenifjustduetoturbulence).However,
becauseofcomputationalexpense,thisaspectisoftenignored.Ofcoursecomputing
powercontinuestorise.TheuseofGraphicalProcessorUnitsfornumberprocess-
ingisshowingpromisewithrivaltechnologiesbeginningtoemerge.
DetachedEddySimulationandrelatededdyresolvingmethodshaveaddedim-
petustotheuseofunsteadyComputationalFluidDynamics.Simulationsthatpoten-
tiallyrivaltremendouslyexpensiverig/windtunneltestsarenowappearing.Ano-
table shoot from this emerging era is work around 2007 at the US Airforce Lab-
oratory, who performed DES for a F/A-18 fighter configuration. Tail buffet was
exploredandsuccessfulcomparisonmadewithrealflightdata(intermsofspectral
shape of surface pressure data). This situation was not unforeseen. Around 1975,
Chapman, Director of Aeronautics at NASA, proposed, using well founded scien-
tific arguments,1 that when computers reached 1014 flops, eddy resolving simula-
tions that could rival aerodynamic tests would emerge. Modern high performance
computingprovisionnowexceedsChapman’sexpectations,reachingPetascaleand
beyond. Hence, now the ability to directly predict turbulence, for complex engi-
neeringsystems,withoutrecoursetoaccuracyreducingassumptionsbecomesever
closer—even if advances in solver technology have not been as extensive as per-
haps expected by Chapman. The current text focuses on aerospace. Hence, unlike
theformer,italsoincludesdiscussionofcompressibleflowtechnology.
With the projected demand for air transport set to double the world aircraft
fleet by 2020 it is becoming urgent to take steps to reduce environmental im-
pact with respect to noise and other emissions. Hence, the current text, hopefully,
will contribute, in some sense, to the quest to use computers to improve aircraft
1Note,Chapman’souterboundarylayerscalingsareoptimisticbutthisaspectislesscriticalthan
theinnerscalings.
vii
viii Preface
and thus impact on this pressing environmental need. To make major technologi-
calbreakthroughs,ultimately,extremelycloseairframeandengineintegrationwill
be needed. This gives the requirement for coupled engine-airframe simulations.
Also, increasingly multi-physics simulations will be required. Such endeavors do
not marry well with the obvious accuracy benefits provided by making turbulent
eddy-resolvingsimulations.Hence,thistextattemptstoexplorethesetensions.
Inpreparingthetext,greatefforthasbeenmadetoremoveerrorsofatypograph-
icalnature.Apologiesfortheerrorsthataredoubtlessfound.
I would like to express my gratitude to past Researchers who have helped run
manyofthesimulationscontainedinthistext.Especialthanksareduetomylongest
servingteammembers—Drs.R.Jefferson-LovedayandJ.Tyacke.
TheoriginaltextwaspreparedinWORD.ThenVadlamaniNagabhushanaRao
leadanintrepidteamwhokindlyconvertedthetexttoLATEX,properlylinkingrefer-
encesfiguresandequationstothetext.IamverygratefultotheLATEXteam:Ahmed
Al-Shabab;ZaibAli,JiahuanCui,MahakMahak;JamesPage;VadlamaniNagab-
hushanaRao,RobertWatsonandXiaoyuYang.
Cambridge,UK PaulG.Tucker
January2013
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 AerospaceChallenges . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 LargeScaleSimulations . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 ComputationalCost . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3.1 Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3.2 Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 UnsteadyFlowSources . . . . . . . . . . . . . . . . . . . . . . . 10
1.4.1 Turbomachinery . . . . . . . . . . . . . . . . . . . . . . . 10
1.4.2 UnsteadyFlowandAirframes . . . . . . . . . . . . . . . . 21
1.5 PredictiveAccuracyofRANS . . . . . . . . . . . . . . . . . . . . 25
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2 ComputationalMethodsforUnsteadyFlows . . . . . . . . . . . . . . 33
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.2 OverviewofTemporalDiscretizations . . . . . . . . . . . . . . . 33
2.3 TemporalProfileAssumptionsforVariables . . . . . . . . . . . . 34
2.3.1 DependentVariableChangeswithTime . . . . . . . . . . 34
2.3.2 SpatialVariationoftheTimeDerivative . . . . . . . . . . 35
2.4 Two-LevelSchemes . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.4.1 GeneralExplicitSchemes . . . . . . . . . . . . . . . . . . 36
2.5 Higher-LevelSchemes . . . . . . . . . . . . . . . . . . . . . . . . 37
2.5.1 GearSchemes . . . . . . . . . . . . . . . . . . . . . . . . 38
2.6 OtherTemporalDiscretizationMethods. . . . . . . . . . . . . . . 38
2.7 ElementarySolutionAdaptedTime-StepApproaches . . . . . . . 41
2.7.1 RelatingErrorEstimatetoNewTime-Steps . . . . . . . . 42
2.7.2 AlternativeTechniques . . . . . . . . . . . . . . . . . . . 43
2.8 UnsteadyAdjointandTimeStepAdaptation . . . . . . . . . . . . 43
2.8.1 AdjointMethodsforUnsteadyFlowDesignOptimization . 45
2.9 TemporalAdaptationUsingSpace-TimeElements/Volumes . . . . 45
2.10 ConvectiveSchemesforUnsteadyFlow. . . . . . . . . . . . . . . 47
2.11 ClassicalHigh-OrderApproaches . . . . . . . . . . . . . . . . . . 48
ix
x Contents
2.11.1 CompactSchemes . . . . . . . . . . . . . . . . . . . . . . 48
2.11.2 DiscontinuousGalerkinScheme. . . . . . . . . . . . . . . 50
2.11.3 SpectralDifference,VolumeandCPRMethods . . . . . . 51
2.11.4 ENO/WENO . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.12 HighResolutionSpatialSchemes . . . . . . . . . . . . . . . . . . 52
2.12.1 DRPSchemes . . . . . . . . . . . . . . . . . . . . . . . . 52
2.12.2 CABARET . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.13 ConvectiveSchemesforDensityBasedSolvers
andRelatedAspects . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.13.1 TheMUSCLScheme . . . . . . . . . . . . . . . . . . . . 56
2.13.2 Monotonicity. . . . . . . . . . . . . . . . . . . . . . . . . 58
2.14 Preconditioning . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.15 SpatialOrderandSolutionAccuracy . . . . . . . . . . . . . . . . 60
2.15.1 GridStretching. . . . . . . . . . . . . . . . . . . . . . . . 62
2.15.2 HighOrderUpwinding . . . . . . . . . . . . . . . . . . . 64
2.15.3 AliasingandNumericalOrder . . . . . . . . . . . . . . . . 64
2.16 SmoothingControl . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.16.1 ShocksandLES . . . . . . . . . . . . . . . . . . . . . . . 69
2.17 MeshRelatedTechniques . . . . . . . . . . . . . . . . . . . . . . 69
2.17.1 BodyFittedGrids . . . . . . . . . . . . . . . . . . . . . . 70
2.17.2 OversetGrids . . . . . . . . . . . . . . . . . . . . . . . . 72
2.18 TheSubstantialDerivative . . . . . . . . . . . . . . . . . . . . . . 73
2.19 SimultaneousEquationSolution. . . . . . . . . . . . . . . . . . . 75
2.20 EvaluationofthePressureField . . . . . . . . . . . . . . . . . . . 76
2.20.1 PressureSubcycling . . . . . . . . . . . . . . . . . . . . . 76
2.20.2 Pressure-VelocityCoupling . . . . . . . . . . . . . . . . . 77
2.20.3 CompressibleFlowSolversandPressureRecovery. . . . . 78
2.21 BoundaryConditions . . . . . . . . . . . . . . . . . . . . . . . . 79
2.22 ImpactofGridTopologyonSolutionAccuracy. . . . . . . . . . . 81
2.23 FrequencyofUseofDifferentNumericalApproaches . . . . . . . 85
2.24 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3 TurbulenceandItsModelling . . . . . . . . . . . . . . . . . . . . . . 93
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.2 AveragingProcedures . . . . . . . . . . . . . . . . . . . . . . . . 94
3.2.1 TimeBasedAveraging. . . . . . . . . . . . . . . . . . . . 94
3.2.2 SpatialAveraging/Filtering . . . . . . . . . . . . . . . . . 96
3.2.3 DiscreteSpatialFilters. . . . . . . . . . . . . . . . . . . . 98
3.3 GoverningAveragedEquations . . . . . . . . . . . . . . . . . . . 99
3.3.1 (U)RANSEquations . . . . . . . . . . . . . . . . . . . . . 99
3.3.2 LESEquations . . . . . . . . . . . . . . . . . . . . . . . . 99
3.4 VLES/URANSModelling . . . . . . . . . . . . . . . . . . . . . . 100
3.5 (I)LESandDNS . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
3.5.1 FunctionalModels . . . . . . . . . . . . . . . . . . . . . . 103
3.5.2 StructuralModels . . . . . . . . . . . . . . . . . . . . . . 107