Forced and Aeroelastic Responses of Bird-Damaged Fan Blades

17 Pages·2016·1.82 MB·English

JOURNALOFAIRCRAFT
Vol.53,No.2,March–April2016
Forced and Aeroelastic Responses of Bird-Damaged Fan Blades:
A Comparison and Its Implications
EricR.Muir∗andPeretzP.Friedmann†
UniversityofMichigan,AnnArbor,Michigan48109
DOI:10.2514/1.C033424
Theaeroelasticresponseofabird-damagedfanstageattheinletofahigh-bypassratioturbofanengineisexamined
usingacombinedcomputationalfluiddynamicsandcomputationalstructuraldynamicsframework.Thedamaged
fan sector consists of five blades obtained from accurate numerical simulation of the bird impact. Forced and
aeroelastic response calculations are performed and compared to assess the role of aeroelastic coupling. The
4 calculationsareperformedat100,75,and60%throttlesettingstoinvestigatetheroleofenginespeedonthefan
2
34 response.Resultsfromtheforcedresponseandaeroelasticresponsecalculationsindicatethattheundamagedblades
3
C0 oppositethedamagedsectorexhibitthehighestlevelofstructuralresponse.Comparingtheforcedresponsewiththe
4/1. aeroelasticresponseshowsincreasedparticipationofthehigherstructuralmodes,especiallyforthedamagedblades,
51 thatgrowintimeorexhibitbeating.Examinationoftheworkperformedbytheaerodynamicforcessuggeststhatthe
2
10. growthinbladeresponseisduetoaeroelasticphenomenaandcancauseapotentialinstability.Theresultsillustrate
OI: theimportanceofaeroelasticeffectswhenpredictingthepost-bird-strikefanresponse.
D
org | Nomenclature ς^ = radial basis function interpolant of the computational
a.
aia C = radialbasisfunctioninterpolantcoefficientvector fluiddynamicsmeshdeformation
arc. D = numberofradialbasisfunctiondriverpoints τ = aerodynamicviscouswallshearstress
7 | http:// FFaΩero == aasssseemmbblleeddaceernotrdiyfungaamlifcorfcoercveevcetocrtor ΩϕΦm === emrandogidianelesbhraoastpiasetifdouennfcsotpriomeneadtionofthemthmode
01 K = globalstructuralstiffnessmatrix
2
4, M = globalstructuralmassmatrix
er 1 m_ = massflowrate Subscripts
emb m_R = referredmassflowrate m = modenumber
Dec n = elementnormalvector STD = standardatmosphereconditions
n P = aerodynamictotalpressure
o
enter PpR == taoetraoldpyrneasmsuircesrtaattiiocpressure Superscripts
C
dt Qj = aerodynamicforcevectoronjthnodeofcomputational j = referencetonodejinthecomputationalfluiddynamics
udersta qm = fgleuniderdaylinzeadmdicesgmreeesohffreedomofthemthmode (cid:2)_(cid:3) = dm∕edsth;differentiationwithtime
an - D ST == caoermodpyuntaatmioincatloftlaulidtedmypnearmatiucrseelementsurfacearea
g
chi t = time I. Introduction
Mi U = assemblednodaldisplacementvector
versity of WWx AFRR === aaneeorrdooaddlyypnnoaasmmitiiioccnwwvooerrckktoffrrroommafoerrcoeedlarsetiscpocanlsceuclaatlicounlsations BdurinIbgRotDtahksectoirvifkfileaianondnaljanentddemningigliindteaurfeyatnaoibrtlhcaredatefets.niBdseiirnmdcpysotorritfkabneistrdfooscrtcotuhcreopdnregismriegagnraioltyef
Uni xd = radialbasisfunctiondriverpoint inthevicinityoftheground[1].Thelowaltitudeatwhichbirdstrikes
by xe = radialbasisfunctionevaluationpoint occurlimitsrecoveryoptionsandenhancestheriskduetobirdstrike.
ded Γ = computationalfluiddynamicsmeshdiffusivity Theturbofanenginesusedincommercialandmilitaryaircrafthavea
ownloa δΛ == ccoommppuuttaattiioonnaallfflluuiiddddyynnaammiiccssmeleemshednitsvpolalucemmeent lbairrgdestirnitkaekse.Darueraincgobvierrdedstrbiykef,atnhebblaidrdeshitthsatthienfcarneabsleasdeths,efrcahgamnceentosf,
D Λref = referencecomputationalfluiddynamicselementvolume andpropagatesthroughtheenginecoreandbypassduct.Theimpact
ς = computationalfluiddynamicsmeshdeformationvector cancausesubstantialdeformationofthebladeleadingedgeovera
largeregionofthebladespan,accompaniedbyglobalbendingand
twist of the blade [2]. Furthermore, the thin low-aspect-ratio low-
camber fan blades used in modern turbofans are structurally and
aerodynamically optimized for efficiency at normal operating
Presented as Paper 2015-0174 at the 56th AIAA/ASCE/AHS/ASC
conditions,andbirddamageinducesoffdesignoperation[3].
Structures,StructuralDynamics,andMaterialsConference,Kissimmee,FL,
5–9January2015;received2March2015;revisionreceived26May2015; The Federal Aviation Administration (FAA) mandates compre-
accepted for publication 7 June 2015; published online 18 August 2015. hensive standards for bird-strike resistance. Engine certifica-
Copyright©2015byEricR.MuirandPeretzP.Friedmann.Publishedbythe tionrequiressuccessfuldemonstrationofcompliancewithFederal
AmericanInstituteofAeronauticsandAstronautics,Inc.,withpermission. AviationRegulationCodeofFederalRegulation33.76inwhicha
Copiesofthispapermaybemadeforpersonalorinternaluse,oncondition birdisfiredwithanaircannonatateststandmounted,runningengine
thatthecopierpaythe$10.00per-copyfeetotheCopyrightClearanceCenter, [4].Foramodern,commercialturbofanengine,threetestsareman-
Inc.,222RosewoodDrive,Danvers,MA01923;includethecode1533-3868/
dated:thesinglelargebirdimpacttest,themediumflockingbirdtest,
15and$10.00incorrespondencewiththeCCC.
andthesinglelargestmediumbirdtest.Thesinglelargebirdimpact
*Postdoctoral Research Fellow, Department of Aerospace Engineering;
testverifiesthatanenginecanbesafelyshutdownafteringestionofa
currently Structural Engineer, The Boeing Company, Seattle, WA 98124.
MemberAIAA. 6 lb (2.72 kg) bird without endangering the airworthiness of the
†François-Xavier Bagnound Professor of Aerospace Engineering, aircraft.Theaerodynamicandaeroelasticresponseofthedamaged
DepartmentofAerospaceEngineering.FellowAIAA. fan is not a factor for single large bird tests, since there exist no
561
562 MUIRANDFRIEDMANN
requirements for continued operation after ingestion. The medium orone-waycoupledapproachtocalculatetheeffectoftheunsteady
flockingbirdtestsimulatesaflockencounterandrequiresingestion flowfieldonthe structural response [17–19]. In this approach, the
ofone2.5lb(1.13kg)birdandthree1.5lb(0.68kg)birds.The2.5lb aerodynamic calculations areperformed first for arigid geometry.
birdisaimedattheflowpathleadingtothecoreduct,oneofthe1.5lb Subsequently, the unsteady aerodynamic forces are extracted and
birds is aimed at the most critical exposed location of the fan as appliedonthestructuraldynamicmodeloftheblade.Theaerody-
determined by the engine manufacturer, and the remaining 1.5 lb namic model is not affected by the structural response; thus, the
birdsareevenlydistributedovertheengineface.Thesinglelargest feedback mechanism of the structural response on the unsteady
mediumbirdtestrequiresingestionofa2.5lbbirdatthemostcritical aerodynamicloadingisnotcaptured.Incontrast,aeroelasticresponse
location outboard of the flowpath leading to the core duct. The calculationsareperformedusinganintegratedortwo-waycoupled
damagedenginesfromthemediumbirdtestsmustmaintain75%of approach that combines the aerodynamic and structural dynamic
themaximumratedthrustandmeetenginehandlingrequirementsfor modelsandfullycapturestheaeroelasticbehavior[17–20].
a series of post-bird-strike operating conditions that simulate an Despiteitsimportance,onlyalimitednumberofcomputational
emergency landing sequence. Figure 1 provides a throttle skyline studies have considered the aerodynamic behavior and aeroelastic
chartthatdescribesthesequenceofthrottlesettingsfortherun-on responseofabird-damagedfan.BohariandSayma[21]presenteda
demonstration. CFD approach for analyzing the aerodynamic characteristics of a
Assumingthefanbladeswithstandtheinitialimpact,theminimum bird-damagedNASArotor67containingasinglebladewithassumed
24 thrustrequirementandrun-ondemonstrationofthemediumbirdtests leading-edgedamage.Thesteady-stateCFDresultsconcludethatthe
4
33 are particularly challenging. Aerodynamic disturbances caused by stall margins deteriorate for the damaged fan, with stall occurring
0
C thebirddamage,suchasflowseparation,vortexshedding,andshock belowthedesignoperatingline.ImregunandVahdati[14]andKim
1.
4/ oscillations,canresultinsustainedthrustloss.Theseaerodynamic etal.[15]conductedtwouniquestudiesthatexaminedtheaeroelastic
1
25 disturbancesalsointroducesignificantunsteadyaerodynamicforces responseandstabilityofabird-damagedbladeddiskcontainingtwo
0.
1 that can lead to high levels of vibratory stressand eventual fatigue damaged blades using a fully coupled CSD/CFD formulation to
OI: failureofthebladesduringtherun-ondemonstration.Furthermore,the determine the time-dependent response. In [14], the fully coupled
D
g | unsteadyaerodynamicforcescancouplewiththestructuraldynamics analysis demonstrates instability of the first torsion mode of a
or toproduceacomplexaeroelasticresponseproblemthatcanleadto damagedblade;however,itisunclearifthegrowthinmodaldisplace-
a.
aia aeroelastic instability [5,6]. Predicting the aeroelastic behavior of a mentistheresultofafluttermechanismorthestrongwakeshedby
arc. bird-damagedfanbladerepresentsasignificantdesignbarrierinthe theupstreamdamagedblade.Thesefindingsareinconclusive,since
p:// developmentofimproved-efficiencyturbofanengines[1]. thefullycoupledcalculationswereonlyperformedforone-thirdofa
htt Numericalsimulationsprovideacost-effectivemeansforasses- fanrevolutionduetolimitationsontheavailablecomputerresources.
17 | singtheaerodynamicloadingandaeroelasticbehaviorofadamaged Inafollow-upstudy[15],theaeroelasticstabilitywasalsofoundtobe
0
4, 2 fan. However, the combined aerodynamic and structural dynamic sensitive to flight conditions with flutter margins reduced at low-
er 1 modeling of a bird-damaged fan assembly, where the damage is pressureratiosandrotatingstalloccurringathigh-pressureratios.
b typicallylimitedtoasectorofblades,isacomplexproblem.Compu- Thesestudiesprovidedinsightintotheaerodynamicbehaviorand
m
ce tational structural dynamics (CSD) based on the finite element aeroelasticresponseofabird-damagedfan.However,thedamaged
e
n D method (FEM) are typically used to model the bird impact and sectorwaslimitedtooneortwoblades,andtheformofthedamage
nter o rbeeshualvtiinogrsatnrudctnuornallirneesaprognesoe,mseintrciecidtecfaonrmreaptrieosnesnt[7co–m13p]l.eCxommapteurtiaa-l dtiiodnnotetsrtess.eFmubrltehearmcoonrfei,gutrhaetioanerroeeslualsttiincgrferospmonbsired-csatrlickuelacteiortnifsicoa-f
e
dt C tional fluid dynamics (CFD) is required to accurately capture the [14,15]wereperformedat70%enginerotationalspeed,andtheaero-
dersta c[1o4m–p1l7e]x.RfleolwiabplheeCnoSmDeannadaCssFoDciamteedthwoditshebxiirsdt-tdoacmoamgpedutetutrhbeofbainrds ecloansstiicdebreehda.vTihoerroeffothree,ditaimsaegveiddefnatnthaattoathceormenpguitnateiosnpaeledaesrwoealsasntoict
u
D impact, structural dynamic response, and unsteady aerodynamic studyofabird-damagedcommercialturbofan,withdamagerepre-
n - loadsofadamagedfanblade.However,duetothecomputational sentative of experimental bird-strike tests or accurate numerical
a
g
hi times required for CFD methods, the structural and aerodynamic simulation of the bird-strike event, is required to improve our
c
Mi computations are typically performed separately in an uncoupled fundamentalunderstandingofthebird-strikeproblem.
of manner.Therefore,theaeroelasticeffectsthatmaybeimportantinthe In [22], the authors presented an aerodynamic model that is
y
versit birTdw-sotrikperimpraorbylemmeathreodnsotapreropuesreldyatocccoouunpteledftohre. CSD and CFD ccaopmambleercoiaflctauprtbuorfianngetnhgeinbeehaanvdioirsosufitaabdlaemfoargemdofdaenlinsgecbtoorthotfhea
ni
U components: the classical approach, which ignores the interaction forcedandaeroelasticresponsesofthebird-damagedblades.Sub-
y
b betweenthefluidandstructure;andtheintegratedapproach,which sequently,in[23],theaerodynamicmodelandastructuraldynamic
d
de attemptstoaccountforit.Forcedresponsecalculationsuseaclassical modelwerecombinedtoproducetheforcedresponsebehaviorsoas
a
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nl
w
o
D
Fig.1 Throttleskylinechartforrun-ondemonstration.
MUIRANDFRIEDMANN 563
Fig.2 Fanbladesandbirdmodelforbirdimpactcalculation(directionofrotation:clockwise).
4 togaininsightintothiscomplexsystem.In[24],theforcedresponse II. DamagedFanConfiguration
2
334 framework was extended to accommodate two-way coupling TheLS-DYNAcodeisusedtosimulatethebirdimpactandobtain
C0 betweentheaerodynamicandstructuraldynamicmodelsofthebird- the bird-damaged configuration. The LS-DYNA code has been
4/1. damagedfanandpreliminaryaeroelasticresponsecalculationswere extensivelyusedtomodelbird-strikeproblemsandhasprovenitselfa
251 performed.Inthispaper,thecombinedCFDandCSDframeworkis reliabletoolforcomputingthedamagedbladeconfigurations[7,13].
10. implementedtocomparethebladeresponseresultingfromone-way Theturbofangeometryexaminedinthisstudyresemblesamodern,
OI: forcedresponseandfullycoupledaeroelasticresponsecalculations, commercialhigh-bypassratioturbofanenginewithaninletdiameter
D
g | and thus assess the role of complete aeroelastic coupling on the ofapproximately55in.(1.4m).Thesinglelargestmediumbirdtest
or response.Thecalculationswereperformedatthe100,75,and60% often results in the most substantial damage, since the 2.5 lb bird
aiaa. throttlesettings,ontheskylinechartinFig.1,toexaminetheeffectof impactsthebladeatanouterspanlocation.Therefore,thebird-strike
arc. engine speed on the fan response. The specific objectives of the conditionsfortheLS-DYNAanalysiscorrespondtothesinglelargest
p:// currentstudyareasfollows: mediumbirdtestinwhichasingle2.5lbbirdisingestedattakeoff
htt 1) Present a coupled CFD/CSD framework for one-way forced conditions with an impact velocity of 270ft∕s (82.4m∕s) and a
17 | response and fully coupled aeroelastic response calculations of a strikelocationof70%bladespan.
20 bird-damagedfan. The LS-DYNA bird-strike simulation computes a typical bird-
14, 2)Studyindetailtheforcedandaeroelasticresponsesofabird- strike experimental test sequence performed in vacuum. The test
ber damaged turbofan stage with damage that is representative of an sequenceconsistsofseveralsteps:spinthefanstageataspecified
m
ce experimentalbirdstrikeinvolvingasectoroffiveblades.Performthe enginerotationalspeed,fireabirdatthefanstage,continuetospinthe
De computationsat100,75,and60%throttlesettingsasrequiredbythe engineuntilthetransientresponseofthebladessubsides,andslow
nter on FA3A),Cthoumspeaxrpelothriengbltahdeeenretisrpeoonpseerarteisnuglteinnvgefloropmeoofnthe-eweanygifnoer.ced trhesetrfiacntedsttaogaesteoctozerrcoonesnigstiinnegrooftfaitvieonbalaldsepseceadn.tiTlehveerceadlcautltahteiornooits,
Ce responseandfullycoupledaeroelasticresponsecalculationstoassess and the remaining blades are assumed to be undamaged. The fan
adt the importance of complete aeroelastic coupling in predicting the bladesaretitaniumandaremodeledasanelastoplasticmaterialwitha
erst post-bird-strikefanresponse. piecewise linear stress-strain relationship where the yield stress is
d
Du 4)Comparetheaerodynamicworkcalculatedfromtheforcedand dependentonthestrainrate.Thebirdmodelisanellipsoidandusesa
n - aeroelastic response calculations to identify the potential for aero- Lagrangianformulation.Aviscousmaterialmodelwitherosionin
a
hig elasticinstability. tensionandcompressionisemployedtocapturetheimpactproperties
Mic Itisimportanttoemphasizethat[14,15]assumedtwodamaged ofthebird.Figure2depictsafrontalviewandisometricprojectionof
of bladesinthefanthatwasoperatingata70%enginerotationalspeed. thefivefanbladesandbirdmodelusedinthebirdimpactcalculation.
ersity Iannd[1o4n]l,ythoenceo-tmhiprdutoaftiaonresvwoeluretioanlsowpasercfoonrmsiedderaetd7d0u%eteonlgiimneitastpioeends blaFdiegsuraere3ahsighholwigshttheeddianmoargaendgfeanancdontfhiegubrlaatdioens,awrehenruemthbeedraemd.aTgehde
v
Uni oncomputationalresources.Thus,thepresentstudymakesseveral bladedamageincludessubstantialleading-edgedeformationinallfive
by originalcontributionsthathavenotbeenpublishedintheavailable blades,aswellasglobalbendingandtwist.Furthermore,thedamage
ed literatureonbirdstrike. coversasignificantportionofthebladespan,withthelargestdeforma-
d
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Fig.3 Bird-damagedfanresultingfromthebird-impactsimulation(directionofrotation:clockwise).
564 MUIRANDFRIEDMANN
tionoccurringforblade2.Figure3bdepictsthefiveundamagedblades upstreamofthefanblades.Thereferredmassflowrate,calculated
(coloredinblue)overlaidwiththefivedamagedblades(coloredin usingEq.(1),isthemassflowratethroughthedomaincorrectedfor
orange). nonstandarddayinflowconditionsandrepresentsthemassflowthat
would pass through the fan if the inflow total pressure and total
temperaturecorrespondedtostandarddayconditions:
III. AerodynamicModel
moTdheeltAheNcSoYmSprCesFsXiblceoumnmsteearcdiyalflaoewrogdoyvnearmneicdsboylvtehreiRseuysneodldtso- m_ (cid:4)m_ s(cid:2)(cid:2)(cid:2)(cid:2)T(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:3)PSTD(cid:4) (1)
averagedNavier–Stokesequations[25].ANSYSCFXusesafinite R TSTD P
volume approach that yields a near-second-order accurate spatial
discretizationandminimizesnumericalreflectionsattheboundaries. Afanmapdepictstheoperatingpointsofanisolatedfanstagefora
Asecond-order-accuratebackwardEulertime-integrationschemeis varietyofoperatingconditions.Theoperatingpointsobtainedata
usedfortheunsteadycalculations.Thefluidisassumedtobeideal fixedenginespeedareconnectedtoformcharacteristiccurves.The
andcaloricallyperfect.Thek-ϵturbulencemodel,whichisanindus- stall point is identified by the peak in total pressure ratio along a
trystandardeddyviscositymodel,isemployedduetoitscompat- characteristic curve and indicates the onset of stall. Stall is an
ibility with scalable wall functions used to efficiently resolve the undesirable,unsteadyflowphenomenaproducedbyflowseparation
4 near-wall boundary layer. Other two-equation turbulence models, that typically occurs at low mass flow rates and high-bypass duct
342 suchasthek-ωandshear-stresstransportmodels,maycaptureflow staticpressure.Astalllineconnectsthestallpointsoneachcharac-
3
C0 separation more accurately; however, the near-wall discretization teristic curve and identifies the boundary of steady flow, where
4/1. requiredbythesemodelsprohibitedtheirpracticaluseinthisstudy. operatingpointstotheleftofthestalllineareunsteady.Afanmap
51 Furtherdetailsoftheaerodynamicmodelareavailablein[26]. alsoincludesthefanoperatinglinethatconsistsoftheuniquesetof
2
0. TheCFDcalculationisrestrictedtoanisolatedfanstagesuitable operating points produced by the fan stage when installed in a
1
OI: forpredictionoftheunsteadyaerodynamiccharacteristicsofabird- completeengine.Arepresentativefanmapthatincludesanoperating
D damagedfan.Thefanstagestartsdownstreamoftheengineinlet, line,severalcharacteristiccurves,andtheassociatedstallpointsis
org | extendsintothebypassductandcoreduct,andincludesasetoffan showninFig.5.
aa. blades,arotatinghub,astationaryshroud,andastationarysplitter,as Theoperatingpointsattheintersectionoftheoperatinglineandthe
c.ai illustratedbyFig.4.Aclearancebetweenthebladetipandshroudis characteristiccurvesaresignificantbecausetheyrepresentoperation
http://ar slopsesceisfieadndtosahcoccukrastterulyctaucrceo.untfortheinfluenceofthetipgaponflow opfretshseuirseoblaotuenddfaarnysctoagnediitnioanciosmsppelceitfeieedngsointeh.aTththeebpyrpeadsicstdeudcotpsetaratitc-
7 | At the domain inflow, the total pressure, total temperature, tur- ingpointcoincideswithapointontheoperatingline.Thebypassduct
201 bulenceintensity,anddirectionoftheincomingflowareenforced. staticpressurenecessarytoachievethedesiredoperatingpointatthe
4, The mass flow rate is specified at the core duct outflow with the intersection of the characteristic curve and the operating line is
1
er assumptionthattheenginecorepullsafixedmassflowratethrough unknownapriori.Therefore,aniterativeprocedureisusedtomapthe
b
em thecoreductforagivenenginerotationspeed.Theaveragestatic characteristiccurveanddeterminethebypassductstaticpressurethat
Dec pressure is enforced at the bypass duct outflow using a radial- yieldsanoperatingpointwithin∼3%erroroftheoperatingline.The
on equilibriumconditionthatpermitsthestaticpressuretovaryradially erroriscalculatedusingEq.(2)wherethepredictedoperatingpointis
nter and minimizes physical reflections. For the unsteady calculations, denotedby(cid:2)m(cid:2)_R;PR(cid:3);andΔm_RandΔPRdenotethehorizontaland
Ce ANSYSCFXusesanonreflectiveconditionatthedomainoutflowto verticaldistance of the operating point from the operating line, as
dt minimizereflectionofacousticwaves[27,28].Solidwallboundary showninFig.5:
a
erst conditionsareenforcedatthefanblades,hub,shroud,andsplitter,
Dud suchthatthevelocityoftheflowmatchesthatofthewallthrough s(cid:2)(cid:3)(cid:2)(cid:2)(cid:2)Δ(cid:2)(cid:2)(cid:2)(cid:2)m(cid:2)_(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:4)(cid:2)(cid:2)(cid:2)2(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:3)(cid:2)(cid:2)(cid:2)Δ(cid:2)(cid:2)(cid:2)(cid:2)P(cid:2)(cid:2)(cid:2)R(cid:2)(cid:2)(cid:2)(cid:2)(cid:4)(cid:2)(cid:2)(cid:2)2(cid:2)(cid:2)
an - sapttehceifsicharotiuodnaonfdasnpol-itstleipr,caonnddaitnioonn.zAerozewroalwlvaelllovceiltoyctihtyatisrepsruelstcsrfirboemd %ΔOL(cid:4) m(cid:2)_ R (cid:5) PR ×100 (2)
g R
chi enginerotationisprescribedatthebladesandhub.
Mi
of
y A. OperatingCondition
ersit The operating point of a fan stage is characterized by the total B. ComputationalMesh
v
Uni pressureratioandreferredmassflowrate.Thetotalpressureratiois TheANSYSTurboGridprogramisemployedtogenerateahigh-
by definedastheratioofthemassflowaveragedtotalpressureatthe quality structured CFD mesh of hexahedral elements for an un-
ed bypass duct outflow to the mass flow-averaged total pressure just damagedbladepassage.Properresolutionoftheboundarylayerand
d
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Fig.4 Meridionalcrosssectionofthefanstagecomputationaldomain. Fig.5 Representativefanmap.
MUIRANDFRIEDMANN 565
Fig.6 Constant-spanandmeridionalcrosssectionsoftheCFDmesh.
4
2
4
3
3
C0 tipgapisessentialtocapturetheshockstructureandflowlossesdue Mesh sensitivity studies were conducted in [26] for steady-
4/1. toviscosityintheboundarylayerandflowleakagethroughthetip stateCFDcalculationsoftheundamagedanddamagedfans.Itwas
51 gap.In[26],threemeshresolutionswereconsidered:coarse,medi- concluded that the coarse mesh identified in [26] was sufficiently
2
0. um,andfine.Theoveralltopologyofthecoarse,medium,andfine accuratefortheobjectivesofthecurrentstudy.Thefullwheelcoarse
1
OI: meshescorrespondstotheCFDmeshinFigs.6aand6b.Theprimary meshconsistedof10.4millionnodesand9.7millionelements.Cross
org | D danifdfetriepngcaepbreetswoeluetniothne.Ttharbeleem1elisshtsesthisetnhuembobuenrdoafrnyo-dlaeyseirnreeaficnhemCFenDt ssepcatnioanrseosfhtohwenunidnaFmigag.e7d.aTnhdeddaammaaggeeddcfoaanrsperCodFuDcemdebshyetshaetR75B%F
aa. mesh;thenumberofnodesintheradialdirectionbetweentheblade meshdeformationprocedureretainedthehighmeshqualityofthe
c.ai tipandtheshroud;andtheminimum,maximum,andarea-averaged originalmesh,particularlyneartheleadingedge,asdemonstratedfor
http://ar y(cid:5)TvhaeluAeNsSoYftSheTfuirrbstonGordidetforopmolothgeybislandoetsauprpfaliccea.bleforfullwheel blade2inFigs.7cand7d.
7 | geometriesthatincludeasetofdamagedblades.Toextendthehigh
1
0 meshqualityproducedbytheANSYSTurboGridmeshtopologyto
2
4, thedamagedfangeometry,theautomatedmeshdeformationscheme IV. StructuralDynamicModel
1
er presented in [26] is used. This procedure employs a radial basis The structural dynamic model is implemented in ANSYS
b
em functionnetwork(RBFN)tointerpolatethedeformationfieldofthe MechanicalAPDL,whichisacommerciallyavailablefiniteelement
c
De bird-damaged blades to the CFD mesh of the undamaged wheel. (FE)-basedstructuralsolverthataccommodatesone-wayandtwo-
on RBFNinterpolationisaneffectivetoolformultivariateinterpolation way coupling with ANSYS CFX for the forced and aeroelastic
nter andhasbeensuccessfullyusedforlarge-amplitudemeshdeforma- response calculations performed in this study. Details of ANSYS
Ce tioninaeroelasticapplicationsandCFD-basedaerodynamicshape Mechanical APDL are available in ANSYS’s Mechanical APDL
adt optimizationstudies[29–34]. Theory Reference Guide — Version 14.5 [35]. The computational
erst ARBFNconsistsofalinearcombinationofradialbasisfunctions domainforthestructuraldynamicmodelconsistsof24individual
Dud (RBFs)usedtomapthedeformationprescribedatthefluiddomain blades,witheachcantileveredatthebladeroot.Fanbladesofmodern
n - boundariestotheinteriorCFDmesh.ARBFϕisascalarfunctionfor high-bypass-ratio commercial turbofans are significantly more
Michiga wpohiincthxtehetovtahleueordiegpine,nsduscohntlhyatonϕt(cid:4)heϕd(cid:2)ikstxaenkc(cid:3)e.PfrroomvidtheedeavsaelutaotfioDn fslteruxcibtuleratlhacnouthpelihnugbbdeitswkese;nthtehreeffoarne,bthlaedheusbisdiisgknoisrendot[m15o]d.eTlehdeafnand
of driverpointsatwhichthedeformationisknown,theRBFinterpolant bladesaretitaniumandaremodeledwithalinearlyelastic,isotropic
ersity oTfhtehReBdeFfofirtmtinagtiocnoeffiefilcdieinstcsoCnsatrruecutnediqiuneltyhedfeotermrmginiveednbbyyeEnsqu.r(i3n)g. mthaetderaimalalgaewdtbhlaatdneesgrleescutsltitnhgefrreosmidutahlesbtrierdssimanpdacstt.rainhardeningof
niv the deformation evaluated with the RBF interpolant at the driver
U
y pointsisequaltotheprescribeddeformation,asgiveninEq.(4).The
d b choiceofRBFisimportanttoensurethebestpossiblerepresentation A. EquationsofMotion
ade ofthedeformationfieldandresultingmeshquality.Reference[34] Theequationsofmotionareformulatedfromtheprincipleofvirtu-
nlo demonstratedthatthevolumesplinedefinedbyϕ(cid:2)kxek(cid:3)(cid:4)kxekis alworkandsolvedbyANSYS’sMechanicalAPDL.Theequations
w
Do an ideal RBF for CFD mesh deformation; therefore, the volume ofmotionaregivenbyEq.(5),whereFΩrepresentsthecentrifugal
spline is used in this study where the norm is evaluated as the effectsduetoenginerotation,andFaerorepresentstheaerodynamic
Euclideandistancekxek(cid:4)p(cid:2)x(cid:2)(cid:2)2(cid:2)(cid:2)(cid:2)(cid:5)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)y(cid:2)(cid:2)(cid:2)2(cid:2)(cid:2)(cid:2)(cid:5)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)z(cid:2)(cid:2)(cid:2)2(cid:2)(cid:2): forcetransferredfromtheCFDmesh.Theglobalmassandstiffness
matricesareassembledfortheentirestructuralmeshusingconven-
D
ς^(cid:2)xe(cid:3)(cid:4)XCϕ(cid:2)kxe−xdk(cid:3) (3) tionalfiniteelementmethods.Forsimplicityofthestructuraldynamic
l l model, no structural damping is implemented. The assembled dis-
l(cid:4)1
placementvectorUcontainsthetranslationaldegreesoffreedomfor
eachnode:
D
ς (cid:4)ς^(cid:2)xd(cid:3)(cid:4)XCϕ(cid:2)kxd−xdk(cid:3)1≤s≤D (4)
s s l(cid:4)1 l s l MU(cid:3) (cid:5)KU(cid:4)FΩ(cid:5)Faero (5)
Table1 Detailsofthecoarse,medium,andfinemeshes
No.oftip
Mesh No.ofnodes nodes Minimumy(cid:5) Maximumy(cid:5) Averagey(cid:5) y(cid:5)>2,% y(cid:5)>10,% y(cid:5)>50,% y(cid:5)>150,% y(cid:5)>250,%
Coarse 435,546 4 1.76 400.86 101.6 100 98.1 73.1 15.0 1.62
Medium 625,485 9 0.91 129.0 24.6 99.2 81.3 13.8 0.0 0.0
Fine 1,278,743 43 0.08 15.2 2.6 48.3 0.63 0.0 0.0 0.0
566 MUIRANDFRIEDMANN
4
2
4
3
3
0
C
1.
4/
1
5
2
0.
1
OI: Fig.7 ComparisonoftheundamagedanddamagedCFDmeshesat75%span.
D
g |
or
a.
a
c.ai B. ComputationalMesh
http://ar eleTmheenftsan(AbNlaSdYesSaSreOmLIoDd1e8le5deulesminegnetitgyhpte-)nowdiethdtshorelied,trhanexslaahtieodnraall
7 | degreesoffreedomateachnode.Ameshsensitivitywasconductedin
1
20 [26]toidentifythemeshresolutionsuitablefortheobjectivesofthis
4, study.Thestructuralmeshconsistsof5712nodesand4020elements
1
er perbladeforatotalof137,088nodesand96,480elementsforthe
b
em full wheel model. Figure 8 shows the structural mesh of an un-
c
De damagedblade.
n
o
er
nt C. RotatingModeShapes
e
C
dt Thefirstfivemodeshapesofarotating,undamagedfanbladeata
dersta Fig.8 Structuralmeshforanundamagedblade. 1sh0a0p%estaokfeaorffoteantgininge,urontdaatimonagaledspbeleaddearaets7h5owanndin60F%ig.ta9k.eTohfeftmhroudset
u
D aresimilarinshape.Thefirstfivemodeshapesofthedamagedblades
an - are similar to those of the undamaged blade. Differences between
g
hi TheimplementationofthestructuraldynamicmodelinANSYS’s the modeshapesof theundamaged anddamagedblades aremore
c
Mi Mechanical APDL includes a large deflection formulation that is significant for higher-frequency modes; however, the blade re-
y of limitedtogeometricnonlinearity.Thisisaccomplishedbyageometric sponsesofthedamagedbladesaredominatedbythefirstfivemodes.
ersit stiffness matrix, where the radial loading depends on the speed of NotethatthefrequenciesandmodeshapesdescribedinFig.9have
niv rotation and distance of the element from the axis of rotation. A been identified as first bending (1B), second bending (2B), first
y U Newton–Raphson iterative procedure is implemented to update the torsion(1T),thirdbending(3B),andsecondtorsion(2T).However,
d b stiffness matrix within each time step. The Hilber–Hughes–Taylor duetothebuilt-intwistofthebladeandtheeffectofrotation,these
de (HHT)-α[36]time-integrationschemeisusedtointegrateEq.(5)in modesarecoupledwhereallthreedegreesoffreedom(bendingoutof
a
nlo time.FurtherdetailsontheNewton–RaphsonalgorithmandtheHHT- theplaneofrotation,bendingintheplaneofrotation,andtorsion)
w
o α scheme are available in ANSYS’s Mechanical APDL Theory participate. By identifying the mode as 1B, it is implied that the
D
ReferenceGuide[35]. primarycontributiontothemodeshapecomesfrombending.
Fig.9 Firstfivemodeshapesofarotating,undamagedblade.
MUIRANDFRIEDMANN 567
V. CoupledFluid–StructureFramework
FE Mesh CFD Mesh
TheANSYSmultifieldsolverisusedtocoupletheANSYSCFX
aerodynamicsolverandANSYSMechanicalAPDLstructuralsolver ANSYS MFX
fortheforcedandaeroelasticresponsecalculationsperformedinthis
Establish Fluid-Structure Interface
study.FurtherdetailsoftheANSYSmultifieldsolverareavailablein
ANSYS’s Mechanical APDL Coupled-Field Analysis Guide [37].
Thecomputationalframeworksandcouplingalgorithmfortheone-
Apply Steady-State Aerodynamic
way and fully coupled fluid–structure interaction calculations,
Loads to Structural Model
including the aerodynamic load transfer and mesh displacement
ANSYS Mechanical ANSYS CFX
scheme,areprovidednext.
Transfer Structural Displacements
A. One-WayForcedResponseFramework to CFD Mesh
Forone-wayforcedresponsecalculations,thecomputedunsteady
aerodynamicloadsareappliedtothestructuralmodelateachtime
Calculate CFD Mesh Deformation
steptoobtaintheresponse.Forthiscase,theCFDmeshisnotde-
and Update Aerodynamic State
33424 foofrtmheedstrausctthuerasltrruescptuornesdeeofnortmhes;utnhsetereafdoyrea,etrhoedyfeneadmbiacclkomadeicnhgainsinsmot me Step
C0 captured. The aerodynamic load for the forced response is time Transfer Aerodynamic Loads Ti
0.2514/1. dloeapdeinndge.nEt;quthautiso,nit(c6a)pgtouvreesrntshethterafnosriceendtrneastpuorensoefcthalecuaelartoidoynns:amic to FEM Mesh Advance
1
DOI: MU(cid:3) (cid:5)KU(cid:4)FΩ(cid:5)Faero(cid:2)t(cid:3) (6) Calculate Structural Response
g |
a.or AflowchartoftheforcedresponseframeworkisshowninFig.10. No Convergence of Aerodynamic Loads Yes
aia ThemappingbetweentheFEmeshandtheCFDmeshatthewetted and Structural Displacements
arc. surfaceisperformedtoestablishthefluid–structureinterface(FSI).A
p:// steady-state CFD calculation is carried out to generate the initial Aeroelastic Calculation
htt conditionsfortheunsteadyCFDcalculationsneededfortheforced Fig.11 Flowchartoftheaeroelasticframework.
17 | responsecalculation.Duringeachtimestepoftheforcedresponse
0
4, 2 calculation, the aerodynamic pressure and viscous loads from the performed to establish the FSI at the wetted surface. Next, the
er 1 unsteadyCFDanalysisaretransferredtothesurfaceoftheFEmesh aerodynamic forces from a steady-state CFD calculation of the
b andthestructuraldynamicresponseiscalculated.
em damagedfanareappliedtoastaticstructuralmodeltoinitializethe
c
De aerodynamicloadandstructuraldynamicmodelfortheaeroelastic
on B. FullyCoupledAeroelasticFramework response calculations. Within each time step of the aeroelastic re-
nter To obtain the coupled fluid–structure aeroelastic response, an sponse calculation, the aerodynamic state is calculated and the
Ce implicitcouplingalgorithmisemployedwheretheaerodynamicand associated aerodynamic loads are transferred to the FE mesh.The
adt structuralcomponentsrepresentingthefanaresolvediterativelyin resulting structural displacements are then transferred to the CFD
erst eachtimestep.TheCFDmeshisdeformedwiththestructuresuch meshbladesurface,andtheinteriorCFDnodesaredisplacedbythe
Dud thatthetime-varyingdisplacementatthebladesurfaceinfluencesthe amountdictatedbythestructuraldisplacement.
n - aerodynamic loads on the structure. The aerodynamic load varies
chiga wcaiuthsetdimbyebdoutehtthoetbhierdtrdaanmsiaegnet aenffdecthtseibnlatdheemaoertoiodny.nTahmeiecqluoaatdioinngs C. AerodynamicLoadandStructuralDisplacementTransfer
Mi Theaerodynamicforces,orloads,havetobetransferredfromthe
y of governingtheaeroelasticresponsearegivenbyEq.(7): CFD mesh to the FE mesh at the blade surface to obtain Faero in
versit MU(cid:3) (cid:5)KU(cid:4)FΩ(cid:5)Faero(cid:2)t;U;U_;U(cid:3)(cid:3) (7) Ethqe.(c5o)u.pTlhedisiasearoreelqaustiircemcaelnctufloartiboontsh.tThheefoarecreoddryensapmonicsefaosrcweesllaares
ni
U calculatedateachCFDnodeonthebladesurfaceusingEq.(8)and
y Aflowchartofthefullycoupledaeroelasticframeworkisshownin
ded b Fig.11.ThemappingbetweentheFEmeshandtheCFDmeshis iwnaclllusdterescsoenst.rTibhuetifoonrcsefsraormetrtahnesfaeerrroeddyfnroammitchepCreFsDsunreodaensdtovtihsceoFuEs
a
nlo nodesonthebladesurfaceusingtheconservativeinterpolationscheme
w
o availableinANSYSMFX.WhenthebladesurfaceontheCFDmesh
D
FE Mesh CFD Mesh andtheFEmeshmatchexactly,theconservativeinterpolationscheme
guaranteestheconservationoftheoverallforcetransfer:
Steady-State CFD Z Z
Calculation Qj(cid:2)t(cid:3)(cid:4) pndS(cid:5) τdS (8)
Establish Fluid-Structure Interface ANSYS CFX
ANSYS MFX Unsteady CFD For the aeroelastic calculations, the structural displacements are
Calculation transferred from the FE mesh to the CFD mesh using the profile-
preservinginterpolationschemeavailableinANSYSMFX.EachCFD
At Each Time Step:
nodeonthebladesurfaceismappedtoastructuralelementontheblade
Transfer Aerodynamic Loads surface.TheshapefunctionsoftheassociatedFEelementareusedto
to FEM Mesh
interpolate the displacement at the corresponding CFD node. This
interpolationschemepreservesthelocaldistributionsofdisplacements
transferredfromthecoarserFEmeshtothefinerCFDmesh.
Calculate Structural Response
The CFDmesh displacement isprescribed onthe bladesurface
ANSYS Mechanical APDL basedonthestructuraldisplacementandissettozeroontheinlet,
Forced Response Calculation outletbypass,outletcore,andsplittersurfaces.TheCFDnodesonthe
Fig.10 Flowchartoftheforcedresponseframework. hubandshroudarepermittedtoslideontheboundariessothatthe
568 MUIRANDFRIEDMANN
originalsurfacesofrevolutionaremaintained.Thedisplacementof
the interior CFD nodes is governed by the displacement-diffusion
equationprovidedbyEq.(9).InEq.(9),Γisthemeshdiffusivity,
which is analogous to the mesh stiffness; and δ is the mesh
displacementrelativetothemeshpositionattheprevioustimestep:
∇·(cid:2)Γ∇δ(cid:3)(cid:4)0 (9)
Aspatiallydependentmeshdiffusivityisusefulforpreservingthe
initialmeshdistributionandelementquality.Alargemeshdiffusivity
restrictsmovementofthenodesrelativetoeachother,withregionsof
lower mesh diffusivity absorbing a larger amount of the mesh
displacement.Ameshdiffusivitythatisinverselyproportionaltothe
elementvolumeisspecifiedsothatthelargerelementsintheblade
passages absorb most of the displacement and the small elements
nearthebladesurfacedonotbecomehighlydistorted.Equation(10) Fig.12 Damagedfanmapfor100,75,and60%throttlesettings.
4 provides the expression for mesh diffusivity, where the exponent
2
34 controls how quickly the mesh diffusivity changes with element
C03 volume: solution.Furthermore,steady-stateconvergenceoftheCFDsolution
1. atoperatingpointsneartheoperatinglinewasdifficulttoachieve,
14/ (cid:3)Λ (cid:4)2 indicatingthatthedamagedfanisoperatinginthevicinityofstall
0.25 Γ(cid:4) Λref (10) whereunsteadyflowisdominant.Thisimpliesthatunsteadyflowcan
1
OI: influence the aerodynamic behavior of the bird-damaged fan to a
D significantextent.
org | Thedamagedfanmapclearlyillustratesthesignificantinfluence
aa. VI. Results of the bird damage on the steady aerodynamic behavior of the
c.ai damagedfan.Thedamagedfancharacteristiccurvesaremuchflatter
p://ar damThaegesdtefaadnyoapnedratuinngsteaatdthyea1e0ro0d,y7n5a,manicdc6a0l%cultahtriootntlseosfettthinegbsiardre- neartheoperatingline,indicatingthatthedamagedfanisoperating
17 | htt paereroseenlatsetdicirnestphoisnsseecotfioanb.iSrdu-bdsaemquagenedtlyf,anthaettfhoercseedthrreesepoopneseratainngd vsiegrnyifniceaanrtt.hTehsetaollpeproaitnintgwphoeirnetuonfsttheeaddyamfloagwedphfaennoimsaelnsaomsiagynibfie-
4, 20 conditionsarepresentedandcomparedtodeterminetheroleofaero- caanndtldyaamffaegcetdedobpyertahteinbgirpdodinamts,angoe.rmTaablilzee2dcboymtphaeroepsethraetiunngdpamoiangteodf
er 1 elasticcoupling. Theaerodynamicworkcalculated from theforced theundamagedfanatthe100%throttlesetting.Table2alsoprovides
mb responseandaeroelasticresponsecalculationsarecomparedtoiden-
ce tifythepotentialforaeroelasticinstability.Forbrevity,theforcedand the percent mass flow loss relative to the undamaged fan at the
nter on De arseeeptroroeefslaebnslattiadcteivrreeessbpploaodnnessesesthcfaratolcbmuelstathtiielolsunessctraaaltcreeutlhapetrieofasnnesnritesesdpproofnovsried.eaTdhhienacn[o2dm6fu]p.lleotef ctfhlooerwrtehlsorpusossntfdoloirnstgshetrhe7rs5outlattlniendgs6ef0trt%ionmgth,trwhoehttelberiersdethtsteitnrmigksae,s.tshTfeoloccwhaallrcoausclstaeitrseisrttehilceatcmeudravstoes
Ce is extrapolated to the operating line assuming a constant pressure
adt ratio(i.e.,flatcharacteristiccurve).Thelargestmassflowlossoccurs
erst A. AerodynamicCalculationsoftheDamagedFan forthe100and60%throttlesettingsfollowedbythe75%throttle
Dud Steady-state andunsteady aerodynamic calculations are used to setting.
n - provide insight into the aerodynamic characteristics of the bird- Togaininsightintotheflowbehaviorresultingfromthedamaged
Michiga d(cid:5)a2m7a°gFecdofnadni.tiTohnes,farenedstthreeafmreecsotnredaitmiofnlsigchotrMresapcohnndumtobsetarnisdzaerdrod.aIny foafnthseectwohr,etehleaMreacehxacmonintoeudrsanatdaccoomnsptaarnetd-sptoanthceircuunmdafmereangteidalcsaliscee.
ersity of [bin2ad6su]e,dsstrtayeeaCrdoFyd-Dystnsaaotemlvaiecerrfomodroydannealmunwicdearcmealacvgueelradiftiifeoadnns.aTogbhateianaisneterodredwsyunitlahtsmthifcreocCmaFlcDaun-- Fd1a0igm0u%areget1hd3rofapttnrlosevasitde7tet5sin%Mg.sapTcahhnen(utdhmaembleoargcaectdoionMntooaucfrshgrocefoantthetsoetuudrnsadmaaramegaeog)beftodarinatnhedde
Univ lationsfromtheindustryCFDsolverwereperformedindependentof usingthecoarse,medium,andfinemeshestodemonstratethemesh
ed by tchailscustluatdiyo.nRseffoerreancdea[m2a6g]eadlsofainncwluidthesdaatcaomfrpoamristohneoinfdsutesatrdyyCCFFDD s1etnhsriotiuvgithy5p,ewrfhoermreetdheinb[l2a6d]e.nTuhmebfievresdcaomrraegspedonbdlatdoetshaorseelainbeFliegd.a3s.
ad solver.Overall,steadyCFDcalculationsshowedgoodagreementfor
o WhencomparedwiththeMachnumbercontourat75%spanforthe
wnl thecomplexflowfieldassociatedwiththedamagedfansectorand undamagedfan,Figs.13b–13dclearlyillustratethesignificanteffect
o confirmthecapabilitiesoftheaerodynamicmodelforthistypeof
D of the bird damage on the flowfield. The moderate leading-edge
calculation.
deformationofblade5createsaseparationbubbleonthesuctionside
ofthebladethatpartiallyblockstheflowthroughthedownstream
B. Steady-StateAerodynamicCalculations
passage.Thelargerleading-edgedeformationandglobalbendingof
Steadyaerodynamiccalculationswereperformedatthe100,75,
blade2andblade4resultinamoresubstantialflowdisruptionin
and60%throttlesettingstogaininsightintotheaerodynamicbehav-
iorofthedamagedfanandtoprovidetheinitialconditionsforthe
unsteadyaerodynamiccalculations.Thecharacteristiccurvesofthe Table2 Comparisonofoperatingpointsfortheundamagedand
damagedfanweremappedforeachthrottlesettingbyvaryingthe damagedfans
bypass duct static pressure. The bypass duct static pressure was
Throttle Normalized Normalized Flow ΔOL,
graduallyincreasedtoreachanoperatingpointneartheoperatingline
setting,% Configuration m_ PR loss,% %
thatrepresentsoperationofthedamagedfaninstalledinacomplete R
100 Undamaged 1.000 1.000 N/A 0.22
engine. Figure 12 provides the fan map of the damaged fan and
100 Damaged 0.931 0.933 7.33 0.63
includesthe fanoperating lineandthe characteristic curves corre-
75 Undamaged 0.881 0.889 N/A 0.70
sponding to the 100, 75, and 60% throttle settings. The values in
75 Damaged 0.847 0.850 5.90 3.3
Fig.12arenormalizedbytheundamagedfanoperatingpointatthe 60 Undamaged 0.793 0.822 N/A 0.74
100%throttlesetting.Itisimportanttonotethatthesteadycalcu- 60 Damaged 0.752 0.791 7.20 2.5
lationsconvergeatasnapshotoftheunsteadybehaviorthatmaynot
represent completely the time-averaged behavior of the unsteady Note:N/Adenotesnotapplicable;OLdenotesoperatingline.
MUIRANDFRIEDMANN 569
24 Fig.13 ComparisonofsteadyMachnumbercontoursofthedamagedfanat75%span.
4
3
3
0
C
1.
14/ which the flow through several downstream passages is blocked. passages,asisevidentfromtheincreasedMachnumberdistribution
5
0.2 Furthermore,themassflowthroughthebladepassagesdownstream throughthesebladepassages.
DOI: 1 ocrfetahseeddaanmgalegsedofsaetctatocrkeaxnpdefrlioewncseespaaralotisosnso.fHmoawsesvfelro,wthedupeastsoagiens- C. UnsteadyAerodynamicCalculations
g | upstream of the damaged sector compensate for this loss with an Theunsteadyaerodynamiccalculationsforthe100,75,and60%
a.or increasedmassflowandastrongerpassageshock. throttlesettingsareinitializedfromthecorrespondingsteadysolution.
a
ai Figure 14 provides Mach number contours on a constant-axial Aphysicaltimestepcorrespondingto500timestepsperrevolutionis
c.
ar sliceofthewheelatthemidbladechordfortheundamagedfanand specified,andthreeCFDsolversubiterationsareperformedateach
p:// thedamagedfanobtainedwiththecoarse,medium,andfinemeshes. timestepforconvergenceofthesolution.Theunsteadycalculations
htt
7 | The significant effect of the damaged sector on the aerodynamic wereperformedfor5000timestepscorrespondingto10revolutionsof
01 environmentoftheentirefanwheelisevident.Thedamagedsector thefan.
2
4, producesstalledflow,identifiedbytheblueregionsinFig.14,fora The unsteady operating point is plotted on the fan map in
er 1 largespanwiseportionofthedamagedbladepassages.Stalledflowis Figs.15a–15c,wherethevaluesarenormalizedbythereferredmass
b
m alsopresentattheundamagedbladetipsoverapproximatelyhalfof flowrateandtotalpressureratiooftheundamagedfanatthesame
e
ec thefanwheel.Theflowlossassociatedwiththestalledbladetipsis throttlesetting.Considerableunsteadinessintheoperatingpointis
D
n compensated by the increased flow through the unstalled blade evident.Forthe100and60%throttlesettings,theunsteadyoperating
o
er
nt
e
C
dt
a
erst
d
u
D
n -
a
g
hi
c
Mi
of
y
ersit
v
ni
U
y
b
d
e
d
a
o
nl
w
o
D
Fig.14 ComparisonofsteadyMachcontoursatmidchord(directionofrotation:clockwise).
570 MUIRANDFRIEDMANN
a) Fan map with characteristic curve and steady and b) Fan map with characteristic curve and steady and
unsteady operating points at the 100% throttle setting unsteady operating points at the 75% throttle setting
4
2
4
3
3
0
C
1.
4/
1
5
2
0.
1
OI:
D
g |
or
a.
a
ai
c.
http://ar cu)n Fstaena dmya opp weriathti nchg aproaicnttesr iastt itch ceu 6r0v%e a tnhdr ostttelaed sye tatinndg dti)m Ree hfeisrtroerdy mata tshs e f1lo0w0% ra tthe raontdtl et osteatlt ipnrgessure ratio
7 | Fig.15 Unsteadytotalpressureratioandreferredmassflowrate.
1
0
2
4,
1
er pointoscillatesaboutthesteadyoperatingpoint,andtheunsteady unsteady solution at the 100% throttle setting. The corresponding
b
m operatingpointforthe75%throttlesettingoscillatesaboutapoint totalpressureratioandreferredmassflowrateatthesetimestepsare
e
ec belowthesteadyvalue.Themeanflowlossisapproximately8%for indicatedbythefineverticallinesinFig.15d.Onlyasmallamountof
D
n eachcase,anditisgreaterthanthatpredictedbythesteadycalcu- unsteadinessisobservedinthevicinityofthedamagedbladeswhere
o
er lationsforthe75and60%throttlesettings.Furthermore,the75% theflowremainslargelyseparated,andtheflowthroughthedamaged
ent throttle setting exhibits the largest flow loss of 8.4% and is con- blade passagesis partially or totallyblocked. Bycontrast, consid-
C
dt siderably greater than the 5.9% flow loss predicted by the steady erableunsteadinessisevidentinmuchoftheundamagedsector,with
a
erst solution.Therefore,itisclearthatunsteadyeffectsareimportantin thegreatestlevelofflowunsteadinessoccurringinthebladepassages
ud predictingtheflowlossofthedamagedfan,andthesteadyaerody- betweenblade16clockwisetoblade21.
D
n - namic calculation of the damaged fan tends to underpredict the Thestalledflowemanatingfromthedamagedsector,denotedasa
ga flowloss. stallcellandidentifiedbytheblueregions,isthedominantunsteady
chi Machcontoursatmidchordareexaminedtoprovideinsightinto floweffectinFig.16.At0.8revolutions,thestallcellcoversroughly
Mi
of the unsteady behavior of the damaged fan. Figure 16 depicts the one-thirdofthefanwheel,fromblade21clockwisetoblade5,and
y unsteady Mach number contours at the midchord for 10 equally the mass flow rate is near its maximum. From 1.4 revolutions to
ersit spaced time steps spanning one representative oscillation of the 3.8 revolutions, the stall cell regresses slightly before propagating
v
ni
U
y
b
d
e
d
a
o
nl
w
o
D
Fig.16 UnsteadymidchordMachnumbercontoursofthedamagedfanatthe100%throttlesetting(directionofrotation:clockwise).