Calculation of Aerodynamic Noise of Wing Airfoils by Hybrid Methods

240 Pages·2016·9.97 MB·English

by  Rabea Matouk

Calculation of Aerodynamic
Noise of Wing Airfoils by Hybrid
Methods
Rabea Matouk
Department of Aero-Thermo-Mechanics
Brussels School of Engineering, Université Libre de Bruxelles
This dissertation is submitted for the degree of
Doctor of Engineering Sciences and Technology
Promotors:
Prof. Gérard Degrez
Prof. Jean Louis Migeot Academic year: 2016-2017

Acknowledgements
First,IwouldliketothankalotmysupervisorProf. GérardDegrez(ULB)forthedirection
ofthiswork,forhisvaluableadviceandsupportduringtherealizationofthisthesisandfor
hisavailability.
Next, I want to thank my co-supervisor Prof. Jean Louis Migeot (ULB,FFT) and the
FFT Company for providing ACTRAN, for their permanent support and for giving the
opportunityforaninternshipinthecompany.
IwanttothankDr. ChristopheJulien(thevonKarmanInstituteforFluidDynamics)for
hishelpandrichdiscussionsaboutmywork,forsendingmehisresultstocomparewithmy
resultsandforthehelptorealizemyfirstpaper.
IalsowanttothankalotDr. YvesDetandt(FFT)forhishelpandsupporttorealizethe
secondpaperandforhisadviceduringthethesiscommitteemeetings.
IwouldalsoliketoacknowledgemycommitteemembersandthePhDthesiscommission
members:
Prof. GérardDegrez
Prof. JeanLouisMigeot
Prof. HermanDeconinck
Dr. YvesDetandt
Prof. ChristopheSchram
Prof. GhaderGhorbaniasl
Myfamilyand bestfriendshavebeen encouraging,supportingand showing beliefinme
andmywork. Sothanksalottoallyou.
IacknowledgetheUniversitéLibredeBruxelles(ULB)andinparticulartheSchoolof
Engineering, Department of Aero-Thermo-Mechanics to welcome my research and all its
iv
membersespeciallyDr. XavierDeschamps(ULB)andShirleyWaynefortheirsupport.
I gratefully acknowledge the University of Aleppo (Syria) for the financial support of
this research, and in particular the mechanical engineering faculty and all its professors
particularlyProf. MustafaTaki,mysupervisorinSyria.
Finally,IwouldliketothankaswelltheConsortiumdesEquipementsdeCalculIntensif
en Fédération Wallonie Bruxelles CECI for providing the supercomputing resources funded
byFRS-FNRS(Belgium).
Abstract
This research is situated in the field of Computational AeroAcoustics (CAA). The thesis
focusesonthe computationoftheaerodynamic noise generatedbyturbulent flowsaround
wing, fan or propeller airfoils. The computation of the noise radiated from a device is the
firststepfordesignerstounderstandtheacousticalcharacteristicsandtodeterminethenoise
sources in order to modify the design toward having acoustically efficient products. As a
casestudy,thebroadbandortrailing-edgenoiseemanatingfromaCD(Controlled-Diffusion)
airfoil, belonging to a fan is studied. The hybrid methods of aeroacoustic are applied to
simulateandpredicttheradiatednoise. Thenecessarytoolswereresearchedanddeveloped.
Thehybridmethodsconsistintwostepssimulations,wherethedeterminationoftheaerody-
namicfieldisdecoupledfromthecomputationoftheacousticwavespropagationtothefar
field,sothefirstpartofthisthesisisdevotedtoanaerodynamicstudyoftheconsideredairfoil.
Inthispartofthethesis,acompleteaerodynamicstudyhasbeenperformed. Someaspects
havebeen developedinthe used in-housesolverSFELES, includingtheimplementationof
a new SGS model, a new outlet boundary condition and a new transient format which is
usedtoextractthenoisesourcestobeexportedtotheacousticsolver,ACTRAN.Thesecond
partof thisthesisis concernedwiththe aeroacousticstudywhere fourmethodshavebeen
applied,amongthemtwoareintegralformulationsandthetwoothersarepartial-differential
equations. ThefirstmethodappliedisAmiet’stheory,implementedinMatlab,basedonthe
wall-pressurespectrumextractedinapointnearthetrailingedge.
The second method is Curle’s formulation. It is applied proposing two approaches; the
first approach is the implementation of the volume and surface integrals in SFELES to be
calculated simultaneously with the flow in order toavoid the storage of noise sources which
requiresahugespace. Inthesecondapproach,thefluctuatingaerodynamicforces, already
obtained during the aerodynamics simulation, are used to compute the noise considering
justthesurfacesources. Finally,LighthilandMöhringanalogieshavebeenappliedviathe
acoustic solver ACTRAN using sources extracted via SFELES. Maps of the radiated noise
aredemonstratedforseveralfrequencies. Therefractioneffectsofthemeanflowhavebeen
studied.

Table of contents
Listoffigures xi
Listoftables xix
Nomenclature xxi
1 Introduction 1
1.1 Fannoise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 Airfoiltrailing-edgenoisemechanisms . . . . . . . . . . . . . . . 3
1.2 ComputationalmethodsofAeroacoustics . . . . . . . . . . . . . . . . . . 5
1.2.1 Thedirectnumericalacousticsmethod: . . . . . . . . . . . . . . . 5
1.2.2 Thehybridmethodsofaeroacoustics: . . . . . . . . . . . . . . . . 6
1.3 Objectivesofthedissertation . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Thesisorganization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5 Maincontributionsandoriginalwork . . . . . . . . . . . . . . . . . . . . 8
2 Reviewofaeroacousticstheories,soundsourcesdefinition 11
2.1 Lighthill’sanalogy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.1 ApproximationofLighthill’sstresstensor . . . . . . . . . . . . . . 13
2.1.2 IntegralsolutionofLighthill’sanalogy . . . . . . . . . . . . . . . . 13
2.2 Curle’sformulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 FfowcsWilliamsandHall’stheory . . . . . . . . . . . . . . . . . . . . . . 16
2.4 Möhring’sanalogy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.5 Amiet’saeroacoustictheory . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.5.1 Derivationofthegeneralizedtrailing-edgenoiseformulation . . . . 20
2.6 Soundsourcesdefinition: Monopole,dipole&quadrupole . . . . . . . . . 27
viii Tableofcontents
3 Solversandnumericalmethods 31
3.1 TheCFDsolver,SFELES . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.1.1 Turbulencemodeling . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2 Theacousticsolver,ACTRAN . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2.1 The variational FE formulation of the acoustic analogies as imple-
mentedinACTRAN . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2.2 Theinfiniteelements . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2.3 Mappingmethods . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3 Flowandacousticcharacteristicscales,meshesbuildingcriteria . . . . . . 46
4 FlowregimesofControlled-DiffusionAirfoils 49
4.1 Descriptionoftheconfiguration . . . . . . . . . . . . . . . . . . . . . . . 49
4.1.1 ThecomputationaldomainandCFDmeshes . . . . . . . . . . . . 50
4.1.2 TheBoundaryconditions . . . . . . . . . . . . . . . . . . . . . . . 52
4.1.3 PreviousexperimentalandnumericalstudiesoftheCDairfoil . . . 53
4.2 FlowpatternsaroundtheCDairfoilaccordingtoflowReynoldsnumber . . 55
4.2.1 Attachedflow(creeping)0<Re<270 . . . . . . . . . . . . . . . . . 56
4.2.2 Steady,separatedflow270<Re<1300 . . . . . . . . . . . . . . . . 56
4.2.3 2-dunsteadylaminaroscillatingflow(vortexstreet)1300<Re<6450 57
4.2.4 3-dunsteadylaminaroscillatingflow6450<Re<14000 . . . . . . . 57
4.2.5 3-dturbulentwake,2-dlaminarboundarylayerregime
14000<Re<47500 . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.2.6 Recirculation bubble appearance near the leading edge, laminar
boundarylayerRe=47500 . . . . . . . . . . . . . . . . . . . . . . 59
4.2.7 Recirculation bubble explosion, 3-d laminarperiodic boundarylayer
andturbulentwake50000=<Re<52000 . . . . . . . . . . . . . . . 60
4.2.8 FullyturbulentregimeRe>=52000 . . . . . . . . . . . . . . . . . . 60
4.2.9 Pressureandfrictioncoefficientsdistribution . . . . . . . . . . . . 61
4.2.10 EvolutionoftheliftanddragcoefficientswithReynoldsnumberand
theflowregime . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.2.11 EvolutionoftheStrouhalnumberwithReynoldsnumber . . . . . . 65
5 TurbulentflowoverCDairfoil(Re=160000) 69
5.1 EvolutionofGhorbaniasl’smodelconstantC . . . . . . . . . . . . . . . . 70
s
5.2 Flowtopology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.3 Pressureandfrictioncoefficientsdistributionontheairfoilsurface . . . . . 73
5.4 Boundarylayervelocityprofiles . . . . . . . . . . . . . . . . . . . . . . . 75
Tableofcontents ix
5.5 Wallpressurespectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.6 Theaveragevelocityprofilesinthewake . . . . . . . . . . . . . . . . . . . 79
5.7 Stressesintheturbulentboundarylayerandthelawofthewall . . . . . . . 84
5.8 Spanwisepressurecoherencefunctionandlength . . . . . . . . . . . . . . 87
5.9 Spatialconvergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.9.1 Flowtopology,pressureandfrictioncoefficientsdistribution . . . . 90
5.9.2 Boundarylayervelocityprofiles . . . . . . . . . . . . . . . . . . . 93
5.9.3 Stressesintheturbulentboundarylayer . . . . . . . . . . . . . . . 93
5.9.4 Wallpressurespectra . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.9.5 Spanwisepressurecoherencefunctionandlength . . . . . . . . . . 94
5.10 Spanwiseextensioneffects,z/C=0.2 . . . . . . . . . . . . . . . . . . . . . 96
6 Aerocousticsresults 101
6.1 BroadbandnoiseatReynoldsnumberof160000 . . . . . . . . . . . . . . . 101
6.1.1 Amiet’saeroacousticstheory . . . . . . . . . . . . . . . . . . . . . 101
6.1.2 Curle’sintegralformulation . . . . . . . . . . . . . . . . . . . . . 106
6.1.3 Lighthill’sanalogy . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.2 Comparisonoftheappliedhybridmethods,conclusions . . . . . . . . . . . 131
7 Conclusionsandperspectives 139
References 145
AppendixA Theleading-edgenoiseorturbulenceimpactnoiseformulation[29] 155
AppendixB Amiet’stheory: transferfunctionsderivation[29,31–33,99] 163
B.1 Leadingedgecase(turbulence-interactionnoise): . . . . . . . . . . . . . . 163
B.1.1 TheanalyticsolutionusingSchwarzschild’stechnique . . . . . . . 165
B.2 Trailingedgecase: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
B.2.1 Supercriticalgust: . . . . . . . . . . . . . . . . . . . . . . . . . . 170
B.2.2 Subcriticalgust: . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
AppendixC Ghorbaniasl’sSGSmodelderivation[50] 173
Appendix D The spatial discretization of the 2D NS equations by Galerkin finite
elementsmethods[43] 177
AppendixE EnsightGoldformatasimplementedinSFELES 181
x Tableofcontents
AppendixF Hydrodynamicsreflectionsatthemeshoutlet,thephysicalboundary
condition 183
F.1 Thephysicalboundarycondition . . . . . . . . . . . . . . . . . . . . . . . 186
F.1.1 Thegoverningequations . . . . . . . . . . . . . . . . . . . . . . . 186
F.1.2 AdaptationforastructuredpolargridandaCartesiangrid . . . . . 189
F.1.3 Implementation in SFELES for unstructured grids, generalization
for3Dflows,proposingapressureequationfortheoutletBC . . . 190
F.1.4 Validationofthephysicalboundarycondition: Velocitiesapproach . 191
F.1.5 Validationofthephysicalboundarycondition: Pressureapproach . 196
Appendix G Tonal noise corresponding to the vortex shedding at Reynolds num-
berof12000 203
G.1 ThesoundradiatedoftheCDairfoilina2dlaminarunsteadyregime,Re=12000204
G.1.1 ResultsforLighthill’sanalogy . . . . . . . . . . . . . . . . . . . . 204
G.1.2 ResultsforMöhring’sanalogy . . . . . . . . . . . . . . . . . . . . 208
G.1.3 ResultsforCurle’sformulation . . . . . . . . . . . . . . . . . . . . 212
G.2 ThesoundradiatedoftheCDairfoilina3dlaminarunsteadyregime,Re=12000215