hovering

第61卷，2019年第5期

.61，2019,No.5

ChineJournalofTurbomachinery

RapidAerodynamicDesignofProp-rotorBladewith

Optimization

YincheangNgHai-xinChen

(SchoolofAerospaceEngineering,TsinghuaUniversity,China,)

Abstract：Aeroddoffocusona

designcondition,prop-rotorarerent

work,tofurtherimproveperformanceofprop-rotorundereachoperatingcondition,theconceptofvariable-pitchprop-

r,acompromisingaerodynamicdesignofprop-rotorisinevitable,duetodiscrepancy

uently,s

whichhassignificantlyinfluencedonae

avoidexpensivelycomputationalcost,twotheorieshasbeenimplementedandvalidatedwhileitabletoprovidea

ally,veraldesignedindividualswithindifferent

uentlyacalculationofaerodynamiccharacteristicwithhigh-

fidelitysolverhasbeenconductedasvalidationfordesignedindividual.

Keywords：AerodynamicDesign,Optimization,Prop-Rotor,PreliminaryDesign,BEMT,VortexTheory

DOI:10.16492/.2019.05.0004

Nomenclature

PL

hov

FM

DL

η

p

P

0

T

κ

P

∞

Hoveringpowerloading

Figureofmerit

Diskload

Propulsiveefficiency

Profilelosscoefficient

Statictemperature

Factorofinducedloss

Environmentalpressure

0Introduction

Conceptoftiltrotoraircrafthascombinedcapabilityof

pulsivesystemre-

liesonapairofconvertiblerotor,duetoadvantageofaero-

dynamiccharacteristicsofrotor,itspropulsivesystemisable

toprovidecapabilityofhoveringinreasonablehighefficien-

rastwiththeconventionalhelicopter,tiltrotorair-

craftareabletocruiinhigh-speedwithinhighpropulsive

ore,itisanattractiveapproachtoachieve

bothverticalandshorttake-off/landing(STOL).However,a

significantchallengeforconvertiblerotoraircraftwhichisto

designaprop-rotorwithgoodperformanceundereachoper-

rast,helicopterrotorandpropeller

hasonlyoperatedoptimallyataspecifiedconditionwithnar-

operatesunderoff-designcondi-

tion,

anaerodynamicanalysisofprop-rotor,inducedlossdomi-

natesthehoveringperformancewhileprofilelossplaysa

ult,prop-rotorre-

T

∞

V

∞

C

T

C

p

C

i

r

ˉ

ρ

Vnd

Environmentaltemperature

Cruivelocity

Thrustcoefficient

Powercoefficient

Parameterofmultinomialequation

Dimensionlessradialposition

Density

Advancedratio

··19

ChineJournalofTurbomachinery

questsalargediskareaandsoliditytoattainagoodperfor-

manceinhoveringoperationwhileprop-rotorrequestsalow-

erdiskareatoreduceprofilelossandemployedairfoilwith

highlift-dragratiotoprovidedemandingthrustaswellasre-

eofthediscrep-

ancyofdesignphilosophybetweenhoveringandpropelling

condition,acompromisingdesignhastobeconducted.

1RelatedWork

InthedesignprocedureofXV-15,McVeighetal(1983)

[1]firstlydesignanadvancedcompositereplacementblade

foreachcrucialflightconditionbycompromidchordand

twistdistributionofbladestoachieveanacceptablehovering

uently,Paisleyetal

(1987)[2]investigatedinaderivativeoftheV-22Ospre,who

hasimplementedanaerodynamicoptimizationfordesignof

bladeshapetoincreaflyingspeedunderoperationoffor-

wardflyunderconsiderationtomaintainagoodpropelling

atively,Liuetal(1990)[3]suggesteda

non-linearprogrammingtechniquesasanapproachforaero-

ultipleoperating

condition,aerodynamicdesignofprop-rotorismuchmore

b-

lemofaerodynamicdesignisformedasamulti-objectiveop-

herunderstandtheproblemof

aerodynamicdesignofprop-rotor,astudyhasbeenconduct-

edandadescriptionofpossibledesignparametersanditsin-

fluenceonaerodynamicperformanceofprop-rotorhave

beengivenbyLeishmanetal(2011)[4].Modernapproachto

conductamulti-objectiveoptimizationarecommonlyem-

ployagradient-bastedalgorithmwithlinearsuperpositionof

multi-objectivewithinweightcoefficienttotransforma

multi-objectionoptimizationtosingleobjectiveoptimizing

r,gradient-badalgorithmcommonlyre-

-

lethisproblem,atypeofstochasticoptimizingmethodsuch

ketal(2013)

[5]hasimplementedamulti-objectiveoptimizationbyadopt-

edgeneticalgorithmtofurtherimprovehoveringandpropul-

siveperformancebyoptimizedtwistandchorddistribution

tion,multi-objectiveoptimizingapproach

willproducetheiroptimalresultasPareto-optimalsolution.

Itwillallowdesignertolectandcompareeachcompro-

middesignfromfrontier-edge.

2NumericalApproach

2.1Geneticalgorithm

Convertiblerotoraircrafthasawiderangeofoperating

hoperatingstate,whichimpoaverydif-

ferentinflowconditionfortheprop-rotoraswellasblade

eveoptimalperformanceoneachstates,

whichrequestadifferentaerodynamicdesignfortheblade.

Therefore,acompromisingdesignhastobeconductedto

achievelowestrequirementofaerodynamicloadingtothe

aircraftaswellasmaximumitfficiencyateachoperating

signproblemleadstoamulti-objectiveoptimi-

achobjectiveareconflicted,solution

prentwork,FastandElitistMulti-ObjectiveGeneticAlgo-

rithm(NSGA-II)whichpropodbyDebetal(2002)[6]is

employed.

2.2Aerodynamicsolver

Toavoidexpensivelycomputationalcostofdirectly

solvetheRANSequationintheoptimizingprocess,Blade

ElementMomentumTheory(BEMT)andClassicalVortex

Theoryareimplementedforprovidingaerodynamiccharac-

teristicsofprop-rotorandacomparisonofaccuracyarecon-

Tareatheorywhicharecombinationof

oryconsiders

prop-rotorwhichconsistofveralbladeelementandits

aerodynamiccharacteristicsaredeterminedbyfluidflow

-

tion,tipeffectofprop-rotorisintroducedwithPrantalloss

functionandinducedvelocitytoeachbladeelementwhich

therhand,the

VortexTheoryassumetherotorconsistofadiskandawake

ingtoBiot-SavartLaw,every

vortexfilamentwillinduceavelocityandeventuallyimple-

mentanintegrationtovortexfilamentwithBiot-SavartLaw.

-

fore,theaerodynamiccharacteristicsofprop-rotorcanbecal-

culated.

3ChallengesandPerformanceMetric

Thechallengeofaerodynamicdesignforconvertible

prop-rotorwhichistomaintainagoodhoveringperfor-

manceaswellaspropulsiveperformanceoverawiderange

ore,amulti-objectiveoptimiza-

herunderstandthedesigning

philosophyofprop-rotor,aninvestigationoffactorswhich

willsignificantlyinfluencetheaerodynamicperformance

sively,thofactorscanderiveas

1）Solidity

2）TwistDistribution

3）ChordDistribution

4）Airfoil

5）RotorTipSpeed

Accordingtothedefinitionofsoliditywhichreprent

irectly

ndChord

distributionhasaffectedprofilelossandinducedlossrespec-

tivelyandanairfoilwithhighlift-drag-ratioaredemanded.

Toavoidanadditionalreductionofrotorperformancewhich

inducedbycompressibleeffect,thetipspeedofrotorhasto

work,afurtherimprovementofbothperformancesunder

hoveringandpropellingconditionhasbeenimplementedby

geneticalgorithm.

3.1Hoveringmetric

Regradingtohoveringoperatingstate,PowerLoading

andFigureofMeritarecommonlyadoptedasobjectivein

rastbetweenPowerloading

andFigureofMerit,PowerLoadingisanabsolutemetricof

aerodynamicefficiencywhichstraightforwardmeasure

RapidAerodynamicDesignofProp-rotorBladewithOptimization

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第61卷，2019年第5期

.61，2019,No.5

ChineJournalofTurbomachinery

thrust-power-ratioofrotorwhileFigureofMeritarethemet-

ricwhichmeasurebetweenidealandactualpowerrequire-

er,PowerLoadingcanbederivedasaform

whichconsistofFigureofMeritanddiskloadasfollowing:

PL

hov=

2ρFM

DL

（1）

Fromtheequation,toattainagoodhoveringperfor-

mance,agoodFigureofMeritandlowdiskloadwasre-

therhand,Leishmanetal(2011)[4]indicat-

edthatarotorwithingreathoveringperformancearenot

ore,

anabsolutemetricimployedasobjectivefunctionforopti-

mizationinthiswork.

3.2Propellingmetric

Astraightforwardapproachtomeasurepropulsiveeffi-

ciencyisratioofshaftpoweroverpropellingpower,itcan

simplyderiveasfollowing:

η

p=PropellingPower

PropellingPower+InducedLoss+ProfileLoss

（2）

Subquently,shaftpowercanbedividedasPower

whichudforpropelling,resistinducedlossandprofile

ropelleroperateunderhighspeedconditionthe

propulsiveefficiencycanderiveasfollowingform:

η

p=

1

1+κDL2ρV2

∞

+P

0

TV

∞

（3）

Fromtheequation,powerudforresistinginduced

lossarediminishingwithinfactorof1

V

2

∞

.Therefore,profile

herimprove

propulsiveperformance,profilelosswillbetheobjectto

atively,amorepowerfulmetrictomeasureair-

craftpropulsiveperformancewhichispropulsivepowerload-

iderspropellerasaprocedurewhichisinsidethe

loopofaircraftdesignandgenerallyconsidertheentireair-

craftaerodynamicperformancewhileaircraftarecruising.

4ValidationofLow-fidelitysolver

Inthispartofwork,atheoreticalapproachhasbeen

studiedforavoidingexpensivelycomputationalcostbydi-

-fidelitymethodisimple-

mentedforpredictingaerodynamicperformanceofprop-ro-

ork,VortexTheo-

ryandBladeElementMomentumTheory(BEMT)areimple-

hervalidatetheaccuracyof

thelow-fidelitymethods,avalidationwhichcomparebe-

tweencalculationoflow-fidelitymethodandexperimental

alidation,theexperimentaldata

arechonfromEdwinetal(1938)[7]andtheexperimental

datatwith2blades-RAF6-airfoilpropellerarechon.

Thecomparingresulthaveshowedbelow:

Inthisvalidation,wewerecomparingthrustandpower

thefigure,itindicatedthatVortexTheoryandBEMThas

showedapromisingpredictionofthrustcoefficientandboth

ofthetheoryhasaworpredictioninpowercoefficient,

nd,wedecid-

edtoemployBEMTassolverforpredictingaerodynamic

performanceintheoptimizingprocess.

5Validationofhigh-fidelitysolver

Inthisction,anumericalsolverwhichhasbeenvali-

-fidelity

solverwhichisCFD++areudforvalidationbycalculated

thecaofCaradonnaTungrotoranditscomputationalre-

erimental

nnaetal(1981)[8].

Thisarticlehascontainedvariousofdatatwhichhasbeen

conductedwithindifferentexperimentaltupandcondition.

Tovalidatethesolver,adatatwhichisCaradonnarotorop-

erateinhoveringconditionwithin1250RPMrotatingspeed

ailofthege-

ometryhasshowedbelow:

Inthisvalidation,threetofstructuralgirdwithindif-

ferentnumberofmeshelementhasbeengeneratedforthe

hreetofmeshhassharedasametopol-

ogyandfivetypeofboundaryconditionhasbeentforin-

put,output,sideboundary,

detailoftheboundarytuphasshowedas

Fig.2Comparisonofpowercoefficientalongadvancedratio

Fig.1Comparisonofthrustcoefficientalongadvancedratio

Tab.1Summaryofgeometricalandflowcondition

Geometry&OperatingCondition

ChordLength/m

AspectRatio

CollectivePitch/deg

TipMach

RPM

P

∞/Pa

T

∞/K

C

t

0.1905

6

8

0.4390

1250

103027

286.75

0.00459

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ChineJournalofTurbomachinery

Inthecalculation,Inflowboundaryconditionaregiven

astotalpressureandtotaltemperatureboundarycondition

whileoutflowboundaryandsideboundaryaregivenasstat-

ueofthetotalpressure,

staticpressure,totaltemperatureandstatictemperatureare

givenasambientpressureandtemperaturewhichis103027

ore,

theflowisinducedbytheworkwhichwasproducedbythe

rotor,partoftheworkisudtoproducethrustwhiletheoth-

idflowthroughthecalculation

domainwithininflowandsideboundaryandleavethedo-

ical-

ly,thesinglerotatingframewithinrotatingspeed1250RPM

areemployedandtheRANSequationwithSSTturbulent

modelwithinwallfunctionhasbeensolvedinthecalcula-

tion,thesteadyRANSequationhasbeendiscret-

edwithcondorderTVDschemewithminmoidlimiter.

Threetofmeshwith3,6and12millionofgridelement

er,thrustcoefficient

andpressuredistributionindifferentradialpositionofblade

hasbeencomparedfordeterminingapromisingelement

numberofmeshforfurthercalculationunderconsideration

ofbothcomputationalcostandaccuracy.

Thegraphwhichshowedabovehavecomparedthecap-

tureofpressuredistributionatradialpositionwithin50%,

60%,89%and90%with3,6,and12millionofmeshele-

irstgraph,itshowedthreemeshhaslittlediffer-

enceinpredictionofpressuredistributionwhiletheother

threeofgraphsindicatedthatthemeshwithin6and12mil-

lionofelementareabletoaccuratelycapturethepeakof

pressuredistributionwhilethenumericaldissipationarede-

creasingwhenthenumberofmeshelementareincread.

Bycontrastwiththrustcoefficient,thedifferencebetween12

lusion,themeshwith-

in6millionofelementareappropriateforcomputationun-

dertheconsiderationofbothcomputationalcostandaccura-

cy.

Fig.3Experimentalt-upofCaradonnaTungrotor

Fig.4Computationaldomainandboundary

Fig.6OgridforCaradonnarotor

Fig.5SurfacemeshofCaradonnarotor

BoundarySurface

Inflow,SideBoundary

Outflow,SideBoundary

PeriodicBoundary

Blade

BoundaryCondition

TotalPressure&TotalTemperature

StaticPressure&StaticTemperature

PeriodicBoundaryCondition

ViscousSurface

Tab.2Boundaryconditionforcaradonnatungrotor

Fig.7Independenceanalysisofgrid

RapidAerodynamicDesignofProp-rotorBladewithOptimization

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第61卷，2019年第5期

.61，2019,No.5

ChineJournalofTurbomachinery

6ProcedureofOptimization

Inthisction,apairofprop-rotorhasbeendemanded

forMAVtoachievecapabilityofShortTake-OffandLand-

ing(STOL).Therequirementtotheprop-rotorhasbeen

madeandobjectiveofoptimizationwhichistoimprovehov-

eringpowerloadingandpropulsiveefficiencyasmuchas

ailofrequirementhasshowedas

Optimizingvariableandoriginalrotor

Duringoptimizingprocess,aprop-rotorwhichisorigi-

nallydesignforhoveringstatehasbeenemployedasoriginal

ofblades,chorddistribution,twistdistribution,

hoveringandpropellingrotatingspeedinRPMareconsider

asdesignvariablewhichhavesignificantlyinfluencedpro-

pulsiveandhoveringefficiencywithinthofactorswhich

theprocedureof

optimization,amultinomialequationisudtoparameterize

chordandtwistdistributionas

C()r=C

0+C1

()r

ˉ

-0.75+C

2

()r

ˉ

-0.75

2+C3

()r

ˉ

-0.75

3

(4)

especially

C

iaredesignvariableand

r

ˉ

isdimension-

tion,tofurtherimprovebothper-

formanceateachstate,avariablepitchanglehasbeenintro-

ducedtoprop-rotorforfurtheradaptingdifferenceofinflow

odynam-

iccharacteristicandgeometryoforiginalprop-rotorhaspro-

videdasbelow:

Inthispartofwork,aproblemofaerodynamicoptimi-

zationwithmulti-objectivehasbeensolvedwithNSGA-II

geneticalgorithmandBEMThasbeenemployedasasolver

absolutemetricofperformancewhichishoveringpower

loadingandpropulsiveefficiencyhasbeenemployedasob-

optimization,therotorwhichshowedabovehavebeenem-

ployedasoriginaldesign,11variablesareinvolvedintheop-

Fig.8Pressurecoefficientdistributionatradialr/R=0.5,0.8,0.89,0.9

Requirement

HoveringCondition

BladeNumber

Radius

RotatingSpeed

Thrust

PropellingCondition

FlySpeed

VariablePitch

RotatingSpeed

Thrust

3

0.55m≤R≤0.65m

2000≤RPM≤4000

500N≤T≤900N

15m/s

2°≤Pitch≤25°

500≤RPM≤2500

50N≤T≤90N

Tab.3Designrequirementforrapidaerodynamicdesign

Fig.9Originalrotorfortheoptimization

··23

ChineJournalofTurbomachinery

timizingprocessand120individualshasbeentforagener-

ulationofindividu-

i-

cally,theflowgraphoftheoptimizingprocesshasshowed

below:

7Constraint

Thediscrepancybetweenhoveringandpropellingun-

deroperatingstate,whichhaveverydifferentinflowcondi-

tionanditrequiresdifferenttwistdistributionforeveryair-

foilelementtoworkunderangleofbestLift-Drag-ratio.

Therefore,twistdistributionofprop-rotorhastobecompro-

midtoattainagoodperformanceundereachdesignpoint.

Duetodiscrepancyofinflowcondition,rootpartofprop-ro-

torisinevitablyworkwithineitherstallingornegativeangle.

Toavoidnegativethrust,aconstraintoflift-coefficientisin-

troducedwhichconstraineveryairfoilelementtoproduce

positivethrust,thereforefurtherimprovehoveringperfor-

manceaswellasacceleratetheoptimizingprocess.

Ontheotherhand,profilelossdominatespropellingef-

idealforthe

designprocessistorequireallairfoilelementofprop-rotor

r,thisidealwillbe

anextremelystrongconstraintforprop-rotorandeventually

noneofthedesignindividualwillfulfiltheconditionwhile

thediscrepancyofinflowanglebetweenhoveringandpro-

ore,acompromidstrat-

egyistoconstrainmediumandtippartofprop-rotorwhich

produceslargepercentageofthrustoverthetotalthrustto

workwithinhighlift-dragratioandlowertherestrictionat

rootpartofpropellerasillustrateasFig11.

8ResultandDiscussion

Resultofmulti-objectiveoptimization

Aprop-rotorwithreasonablehighhoveringperfor-

mancehasbeenemployedasinitialgeometryandamulti-ob-

jectiveoptimizationwhichconsiderbothhoveringandpro-

pellingperformancewasconductedwithgeneticalgorithm.

Someconstraintsareemployedforeithersatisfyingdesign

objectiveoraccelerateoptimizingprocess.

Bothfigurewhichhaveshowedaboveindicatehover-

ingpowerloadingandpropulsiveefficiencyofeachindividu-

egraphswhich

gure12

and13,itindicatesthathoveringperformancearesacrificed

whilethepropellingperformanceareimprovingintheopti-

strateachobjectiveunderhovering

nd,acollec-

tionofindividualwhichcontainallofqualifiedindividual

vidualwhicharelocatedataverage

levelofbothconvergedobjectivesarelectedasdesignindi-

vidualandthedesignindividualhascomparedwithtwoindi-

vidualswhichhavebestperformancerespectivelyunderhov-

eringandpropellingstate.

OriginalPerformance

HoveringCondition

BladeNumber

RotatingSpeed/

RPM

Thrust/

N

ShaftPower/

kW

PowerLoading/(

NkW

)

PropellingCondition

FlySpeed/(m/s)

RotatingSpeed/

RPM

Thrust/

N

ShaftPower/

kW

PropulsiveEfficiency

3

3000

498.54

11.425

43.635

15

3000

260.1

8.099

0.48

Tab.4Performanceoforiginalrotor

Fig.10Procedureofoptimization

fig.11Lift-dragratioconstraint

Fig.12Converginghistoryofpropulsiveefficiency

RapidAerodynamicDesignofProp-rotorBladewithOptimization

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第61卷，2019年第5期

.61，2019,No.5

ChineJournalofTurbomachinery

Fromfigure,itindicatedlectedbladeandtheblade

withhighhoveringpowerloadingshareasimilargeometri-

ydiscrepancythetwobladesisthe

rotatingspeedatpropellingcondition,itdirectlyaffectthe

descentofpropulsiveefficiencywithinprofilelosswhen

P

0≈ρπR2

C

p0

V

3

tipasmentionedbyLeishmanetal(2011)[4].

Ontheotherhand,thebladewithbestpropulsiveperfor-

mancehavealargetwistangleontherootpartofrotor

arisonwiththeothertwoblade,thetwistdis-

tributionallowsthebladeworkneartotheangleofbestlift-

ore,itshowedabetter

performancethanotherinthecondition.

Inthiswork,tofurtherimprovepropulsiveefficiencyof

o-

ducedavariable-pitchmechanismtoallowprop-rotorto

switchbetweeneachoperatingconditionbychangeitstotal

efigurewhichshowedabove,itindi-

catesthepropulsiveefficiency,thrustcoefficientandpower

coefficientoflectedbladewhicharecalculatedbyBEMT.

Thelectedbladeisoperatingwithindifferentoperating

conditionwhileitchangeitstotalpitchangletoattainagood

eline

indicatedthebestpropulsiveperformanceandaerodynamic

characteristicsofthelectedbladewhichareabletoattain

underdifferentoperatingconditionwhileitstotalpitchangle

phsshowedthemechanismofvariable

pitchangleareprovidingasufficientwaytoachievethede-

signgoalwhichrequireprop-rotorareabletoattaingoodper-

formanceoverwiderangeofoperatingcondition.

9ValidationWithCFDAnalysis

Inordertovalidatethelectedoptimizedindividual,a

numericalsolverwhicharedirectlysolvetheRANSequa-

tionareintroducedandANSYSICEMCFDareemployed

ithin6millionelementsare

handdetailofthecomputa-

validation,five

typeofboundaryconditionareinvolvedineachoperating

condition,singlerotatingframeandSSTturbulencemodel

adyRANShas

beendiscretizedwithcondorderTVDschemewithmin-

ingtothemesh,anOmeshhasbeengen-

eratearoundtheblade,andthefirstlevelhighofmeshhas

beentas

y

+=1

whiletheReynoldsnumberatbladetip

are7.84

×10

6

inhoveringstateand2.60

×10

6

inpropelling

state,itwillensurefirstlevelhighofmeshalongtheradial

positionarebelowas

y

+=1

.

Inthecalculation,wehaveconductedasimulationin

ically,the

prop-rotorrotatewith3518.03RPManditwillflipwithin

9.735degwhileitchangesitsoperationbetweenhovering

overingstate,theinflow

boundaryisgivenastotalpressureandtotaltemperature

withinambientpressure101325Paandtemperature287K

whileoutflowboundaryconditionisgivenwithstaticpres-

ther

hand,theprop-rotorflyforwardwithin15m/s,inflow,out-

flowandsideboundaryaregivenasstaticpressure101325

Pa,temperature287Kandvelocitycondition.

Inthisca,asinglerotatingframehasbeenemployed

culationhascarriedoutforhovering

hebladerotatewith3518

RPMinhoveringstate,itsMachNumberonbladetip

achieve

M

tip=0.55,while

M

tip=0.19underpropellingcond-

7

whichshowedabovehascomparedthepredictionofthrust

Fig.13ConverginghistoryofHoveringPowerLoading

HoveringCondition

Individual

SelectedBlade

Best

PL

hov

Best

η

p

PropellingCondition

Individual

SelectedBlade

Best

PL

hov

Best

η

p

RPM

3518.03

3519.00

3491.50

RPM

1139.63

1212.50

1026.00

Radius/m

0.5574

Radius/m

0.5574

VariablePitch/(deg)

0

0

0

VariablePitch/(deg)

9.738

9.738

7.944

C

p

0.0533

0.0515

0.0610

C

p

0.0989

0.0952

0.0971

C

T

0.1079

C

T

0.1026

0.0946

0.1045

PL

hov

30.979

NkW

31.881

NkW

27.684

NkW

η

p

0.735

0.716

0.782

Tab.5Comparisonbetweenlectedblade,bladewithbesthoveringandpropulsiveperformance

Fig.14Geometryoflectedblade

··25

ChineJournalofTurbomachinery

Fig.15Chorddistributionofthreelectedblade

Fig.16Twistdistributionofthreelectedblade

Fig.17Propulsiveefficiencyoflectedbladeworkwithindiffer-

entvariablepitchangleindifferentadvancedratio

Fig.18Thrustcoefficientoflectedbladeworkwithindifferent

variablepitchangleindifferentadvancedratio

Fig.19Powercoefficientoflectedbladeworkwithindifferent

variablepitchangleindifferentadvancedratio

HoveringState

BoundarySurface

Inflow,SideBoundary(inflow)

Outflow,SideBoundary(outflow)

PeriodicBoundary

Blade

ConeStone

PropellingState

BoundarySurface

Inflow,Outflow,SideBoundary

PeriodicBoundary

Blade

ConeStone

BoundaryCondition

TotalPressure&TotalTemperature

StaticPressure&StaticTemperature

PeriodicBoundaryCondition

Viscouswall

Inviscidsurface

BoundaryCondition

Pressure,Temperature&Velocity

PeriodicBoundaryCondition

Viscouswall

Inviscidsurface

Tab.6Boundaryconditiont-upforhoveringandcruistate

Fig.20Computationaldomainandrelatedboundary

RapidAerodynamicDesignofProp-rotorBladewithOptimization

··26

第61卷，2019年第5期

.61，2019,No.5

ChineJournalofTurbomachinery

andshaftpowerwhichcalculatedbyBEMTandhighfidelity

etable,inbothoperatingcondi-

tionthepredictionofthrustindicatedaninconsistentresult

betweenlowandhighfidelitysolverwhileshaftpoweris

heless,theinconsistencyofthrust,but

thediscrepancyofcalculationbetweenBEMTandCFDare

aroundandbelow10%.Itisanacceptableresultfortherap-

iddesignofprop-rotorinpreliminarystageofdesign.

10Conclusion

Inthisprentwork,arapidaerodynamicdesignplat-

formwithoptimizingapproachisimplementedforproviding

apreliminarydesignofprop-rotorwhileademandofMAV

mplishthetask,NS-

GA-IIgeneticalgorithmareemployedforsolvingproblem

lementMomentum

TheoryandVortexTheoryarevalidatedandimplemented

foracceleratingtheoptimizingprocesswhilemodernCFD

eevaluationof

BEMTandVortexTheory,whichindicatedthatboththeories

areabletoprovidedpromisingthrustpredictionfortheopti-

mizationandBEMTaremuchmorerobustthanVortextheo-

-

fore,BEMThasbeenlectedasanaerodynamicsolverfor

herunderstandthechallengeofde-

sign,astudyhasbeenconductedandveraldesignparame-

terswhichwillsignificantlyinfluencetheaerodynamicper-

formanceofbladeundereachstatehasbeenintroducedfor

-ob-

jectiveoptimizationhasbeenconductedfordesigningaprop-

rotor,veralconstraintsareintroducedintotheoptimizing

processforeithertofulfiltherequirementofdesignoraccel-

eratetheoptimizingprocessbyintroducedthepriorideal

-rotorwithgoodhoveringperformance

hasbeenudasinitialgeometryandtheoptimizingprocess

showedawellconverginginbothobjectiveswhilethehover-

ingperformancearescarifiedtoattainagoodpropulsiveper-

imizationshowedasignificantimprove-

mentofpropulsiveperformanceanditshowafastconverged

nislectedfromthecollectionof

hervalidatethelecteddesign,a

validatedCFDsolverhasbeenadoptedforthevalidation.

ThevalidationindicatedthattheBEMTareabletoprovidea

consistentpredictioninshaftpowerwhilethepredictionof

thrustisrelativelyinaccuratebutitstillacceptableforprelimi-

narydesign.

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HoveringCondition

SelectedBlade

CFD

ErrorAnalysis

PropellingCondition

SelectedBlade

CFD

ErrorAnalysis

Thrust

699.80

810.69

13.68%

Thrust

69.82

63.65

8.84%

ShaftPower

22.589kW

22.689kW

0.44%

ShaftPower

1.424kW

1.433kW

0.63%

Tab.7Comparisonanderroranalysisofthrustandshaftpower

prediction

··27