Inidene Eet

A high-speed run inthe windtunnel ampaign hasbeenhosento ompare

HOST-MINTsimulations withexperimental dataand CFDuRANSomputationsinelsA.

Table1.3presentsasummaryofthemainowonditions. Simulationsareperformed

at experimental thrust levels by hanging the blade pith in HOST-MINT and in

elsA simulations.

Propellerperformane. Anumberofparametersareomparedhereafter: thrust

oeient(

C

TH

(a)Loadtermsdenition (b)Momenttermsdenition

Figure1.10: Denition ofloads and moments

Notie rst the non-zero 1P loads modulus at

0 ^◦

^{inidene in the wind tunnel}

data. Asithasbeenexplained byOrtun[Ortun 2012℄thismayomefrom anerror

inthe balanesalibration. Hene,inthepresent study,1P loadsat zero inidene

have been onsidered as a onstant oset in the measurement of the balanes for

all thetest ases. Theplotted errorbars showthe upper and lower limit ofthe 1P

loads modulus andphase whenonsidering this oset.

ComparisonsinFig.1.11showagoodagreement between isolated HOST-MINT

simulations and wind tunnel test datain termsof thrust and power. However, we

an also notie an underestimation of the 1P load oeient (around

40%

^{) and a}

slight overestimation of the 1Pphase lag(from

5

^to

15 ^◦

^).

When installation eets are added in HOST simulations, an underestimation

of thrust is obtained. Consequently, the pith angle should be modied by

+0.7 ^◦

in order to obtain the experimental thrust levels. In those ases, as shown in the

upperleftplot inFig.5.1,thepoweris overestimated byabout

10%

^.

Several reasonsan explain these powerosets. First,only theoldCAD blade

shape was available for simulations, thus bladedeformationswerenegleted in

sim-ulations. Seond, asit has been explained in the Methods and Tools Chapter, the

tehnial report indiated that the rotating balanes usedin the wind tunnel tests

mayunderestimatetheshaftpower. Third,inordertoreahexperimentalthrust

lev-els,aninreaseof

0.7 ^◦

^{inpithanglewasneessaryinthe}simulations. Changingthe bladepithleadstoaninreaseinthebladeinideneandthustoaninreaseinthe

separated boundary layer near blade tips, whih are aerodynami onditions more

diult to be preditedorretly with RANSsimulations or withtwo-dimensional

airfoil data. Finally, neither in elsA CFD simulations nor in HOST airfoil data,

laminar-turbulent transition eets aretaken into aount.

Incidence [deg]

(a)Thrustoeient,

C

^TH

Incidence [deg]

(b)Poweroeient,

C

^PW

Incidence [deg]

1 P L o a d C o e ff ic ie n t, C 1 P

0 0.5 1 1.5 2 2.5 3

1 P M o m e n t C o e ff ic ie n t, C M 1 P

0 0.5 1 1.5 2 2.5 3

(e)1Pmomentoeient,

C

M1P

Incidence [deg]

1 P M o m e n t P h a s e L a g , M 1 P

0 0.5 1 1.5 2 2.5 3

Figure 1.11: Inidene eet on propeller performane and 1P loads. Comparison

between wind tunnel data, CFD uRANS omputations and HOST-MINT

simula-Propellerplane

Spinner

α _∞

V ∞ α _ind α V ⊥

α = α _∞ + α _ind

Figure1.12: Spinner eet sheme(side and front view)

islosertowindtunnelmeasurementsandverylosetoCFDsimulations. Asshown

bytheshemeinFig.1.12,onsideringtheperturbationveloitiesaroundthespinner

gives an additional indued inidene to theairow, whih inreases the inidene

asymmetrybetween downward and upward movingblades, andsoinreases the1P

load modulus.

When regarding 1P phase lag, while CFD omputations predit values within

theerror bars for all the inidenes,it an be notied thatHOST simulationstend

to overestimate thesephase lagsby

5 ^◦

^to

10 ^◦

^.

A very good agreement in terms of 1P moment oeient an be observed

be-tweenisolated HOSTsimulationsandexperimentaldata. However,whenaddingthe

installation eets, HOST-MINT tend to overestimate the norm of these in-plane

moments. On the other side, signiant osets areobserved in1P moments phase

lag. Even though,the levelsof mismatharesimilarto thoseobtained inelsA

om-putations. These mismathes in 1P moment preditions may ome from the fat

that thelifting-lineapproah is lessaurate inthe predition ofloads lose to the

bladetips. Astheontribution ofagivenbladesetionon1Pmomentsorresponds

to theamplitude ofthrust osillations multipliedby theleverarm, a slight errorin

thethrustpreditionnearbladetipsmayindueimportant1Pmoment mismathes.

Simulations onsidering installation eets and the hub model give results in

terms of thrust and power that are similar to the results of isolated simulations.

When the hubmodel isativated,no blade pith modiationis needed.

Notiethe important ontribution to the1Ploadnorm, when omparedto isolated

or installed HOSTsimulations. An overestimation ishowever observed in

ompari-sonwithexperimental data(around

+17%

^{). Ontheother side,a slight inreasein}

1P phase laganbe observed (

+2 ^◦

^).

Finally,1Pmomentoeientpreditionsarenotsatisfatorybothintermsofnorm

and phaselag.

Blade loading. In order to better understand the previous omparisons, load

Relative Radius

A m p li tu d e d /d r P h a s e l a g d /d r

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Figure 1.13: Blade load distribution modes in Case No. 1149. elsA omputations

are ompared to three HOST simulations: isolated, with installation eets, and

with installationeets andhub model.

this omparison isthe spanwise gradient of thethrust oeient

∂τ /∂ξ

^:

∂τ

∂ξ = ∂T

∂r

R

ρ _∞ N ² (2R) ⁴

^(1.3)

Figure 1.13shows theload distributionomparison between elsA and thesame

three HOST-MINT simulations exposed in the previous paragraph. Only the two

rst modesof the Fast-Fourier Transform areshown: zeromode(mean value) and

rst mode (one per revolution, 1/rev). All HOST-MINT simulations give similar

results in terms of mean blade loading (left-hand side plot), and predit orretly

the load evolution for theentral part of the blade. However, an underestimation

anbenotiedfromthe

0.7R

^{spantothetipoftheblade. Thisload}underestimation generates the already observed thrust mismathes. Moreover, notie that the load

nearthebladerootisnotwellpreditedbyisolated andinstalled HOSTsimulations,

while the hub eets gets loserto elsA.

When fousing onthe 1/rev mode,more important dierenes arenotied. On

oneside,thesolidredlineandthesymbolsarounditrepresentthenormofthe1/rev

mode, whih an belinkedto the normof 1P loads. Ontheother side, thedashed

redlineandthesymbolsarounditrepresentthephaselagofthe1/rev mode,whih

anbelinked tothe phaselagof1Ploads. Wheninstallationeetsareonsidered,

the1/revnorm getsloserto elsAresults,while keepingalmostthesame phaselag

thaninisolated simulations. However,important mismathesareinduedwhenthe

hub model isonsidered. Notie theoverestimation with respet to CFDresults of

both the modenorm and the mode phaselag. Theimplementedhubmodel,whih

should have only an important eet near the blade root, impats in fat all the

Table 1.4: Rotationalspeed sweep inAPIANexperimental high-speed tests

Test No. Mah No. Inidene RPM J

[℄ [

◦

℄ [min

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