Aerodynami Mehanisms behind 1P Loads

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The last setionof this study isdevotedto theanalysisof theaerodynami

meha-nisms behindopen rotor 1P loads. Singularity methods like the lifting-linetheory

are partiularly well adapted to this type of study. Theyallow a deomposition of

theindued veloities indierent termsand, byremoving one termat eah

simula-tion, its impatan be quantied.

Desription ofthe method. Fromapurelygeometrial approah,1Ploadsan

beattributed to a dierene inthe relative veloities of the downward and the

up-wardmoving blades,whihgeneratesa diereneintheir loadsandthusanetfore

inthepropellerplane. However, the impatof induedveloities,

~v ind

,on 1Ploads

annotbe negletedasit hasbeen shown insetion6.2. To analyze their

ontribu-tion,

~v ind

are going to be deomposed in several omponents. A quantiation of theimpatofonesingle

~v ind

omponent onthrustand1Ploadsshouldbeestimated

by removing that omponent from a HOST simulation and omparing the results

with respetto theoriginal simulation.

The indued veloities

~v ind

represent the inuene of the potential wakes, the

installation eets and the airfoil motion relative to the airow. These dierent

ontributions are added in the lifting-line methods to alulate the total

~v ind

on

eahbladesetionandthereforetoobtainthe aerodynamibehaviorofthedierent

bladesetions of the propeller.

Hene adeomposition of the

~v ind

an be done as follows: (a)unsteady orretions

due to the airfoil motion; (b) installation eets due to the hub; () auto-indued

veloities,

~v ind

bythe wake of a propelleron the propeller itself;and (d)

mutually-indued veloities,

~v ind

bythewakeoftheotherpropeller. Both, auto-andm

utually-induedveloitiesaredeomposedinmeanvalue(mode0),1/revorinidenemode

(mode 1), and the Blade Passing Frequeny mode (mode BPF). Figure 6.7 shows,

foragivenradialposition(

r = 0.75R

),thedeompositionoftheaxialand

irumfer-Azimuth (deg)

(a)Frontrotoraxial

~v

ind

Azimuth (deg)

(b)Rearrotoraxial

~v

ind

Azimuth (deg)

() Frontrotorirumferential

~v

ind

Azimuth (deg)

(d)Rearrotorirumferential

~v

ind

Figure 6.7: Deomposition of the indued veloities

~v

ind

for thefront and therear

rotors.

ential omponents of the

~v

ind into its dierent terms. Notethat negative axial

~v

ind

tend to diminish the aerodynami inidene of theblade setion, whereas negative

irumferential

~v

ind

tendto inrease it.

Figure6.8plotstheontributionofeah

~v ind

omponentonthrust,1Ploadnorm,

and1Ploadphase. Notiethatthe perentagevalueaountsfortheimportaneof

theimpatofeahomponent,whereasthesignaountsforitspositiveornegative

ontribution. Moreover, perentages in redshould be onsidered arefully, asthey

are a onsequene of non-linear eets, as it will be explained hereafter. These

resultshavebeenobtainedbystoringthe

~v ind

eldforaompleteCRORsimulation

and then removing one

~v ind

omponent at eah simulation, inorder to quantify its

T h ru s t F R

Figure6.8: Contribution ofthe

~v ind

termsonthethrust,the1Ploadnorm, andthe

1P loadphaselag offront and rearrotors.

Aerodynami mehanisms of Thrust. The mean value of

~v ind

is omposed

mainly of an axial and a irumferential omponent, i.e. the swirl. In the present

methodboth omponentsareonsidered together. Notiethemeanvalueof

~v ind

is

themain mehanism impating thepropeller thrust. However, the impatof

auto-indued and mutually-indued veloities is not the same. On one side,in thease

ofauto-induedveloities,bothaxialandswirlomponentsdereasetheloalangle

of attak and henethethrust. Onthe otherside, inthease of mutually-indued

veloities,theswirl inreasestheangleofattakwhereasaxialomponentdereases

it, but the overall eet tendsto inreasethe angleof attak.

The front rotor thrust predited by HOST is almost not aeted by the rear

rotor wake. Thus we an onsider that its response will be similar to the ase

of a single propeller in inidene. On the ontrary, the rear rotor thrust is more

impatedbythefrontrotormean

~v ind

(bar5)thanbyitsauto-induedveloity(bar 2). Furthermore, the ontribution of the swirl of thefront rotor wake inreases the

bladeinidene and thus therear rotorthrust.

Finally,asthehub tendstoaelerate theairowintheaxialandupward

dire-tions,ithasanegativeimpaton thethrust ofboth rotors(bar1),though itisless

important than the wake omponents (

−9%

).

Aerodynami mehanisms of 1P load norm. The main

~v ind

mehanism

im-pating 1P load norm is the rst mode of the wake (bars 3 and 6), due to the

propellerinidene. Indeed,the vortiityshedinthewakeislinked totheevolution

aninreaseintheangleofattakgeneratesawakewithmorevortiityandmore

~v ind

whih tend to redue the angle of attak. As the 1P load norm is diretly related

with the osillation of the angle of attak of the blades, both auto- and

mutually-indued veloities tend to redue this 1P load norm. As for the thrust, the most

important ontribution on the 1P load norm of the rear rotor is the rst mode of

the front rotor wake. This helps to explain what was notied in setion 6.2: that

front rotor wake redues the rear rotorinidene andthus the1P loadnorm.

Notie the important ontribution of the mean

~v ind

(bar 2). As plotted inthe

shemeof Fig.6.9,thisis dueto non-linear airfoil data,whih isnot desiredinthe

present linearanalysis ofthe 1P loads. Indeed,when removing the mean

~v ind

from

theinputperturbationles,theloalinideneinreasesuptovaluesaftertheairfoil

stall angle. As itis shown inthegure, for a given inideneosillation and when

removing the mean

~v ind

ontribution, the lift oeient does not almost osillate.

Consequently, the method predits a very important but unphysial ontribution

of themean

~v ind

on the 1P load norm and phase lag. Thiswould not be the ase

if the angle of attak remained around the working point and inside the range of

inidenes where theairfoildataislinear. Therefore,theperentagesof theimpat

of mean auto-indued and mutually-indued veloities on the 1P load norm and

phase lag(bars 2and 5) shouldbeonsidered arefully.

Finally, similar to what has been obtained for the single propeller, the hub in

inidenehasapositiveontributiononthe1Ploadnormasitaeleratestheairow

upwards,inreasingthediereneinrelativeveloityseenbythedownwardmoving

bladeandtheupward movingblade,andthusinreasingtherotorvertialforeand

onsequently inreases the 1Pload norm(bar1).

Aerodynami mehanisms of 1P load phase. One of the most important

ontributions omes from the installation eets (bar 1). Indeed, as it has been

explained inthe previousparagraph, thehubinreases thevertial foregenerated

by the propeller without modifying its side fore. This is why installation eets

tendto redue 1P loadphaselag.

Notiealso that theunsteady airfoilmodelhasan important positive

ontribu-tion on the phase lag (bar 8). Inaddition to the

~v ind

fromthe airfoil motion, this

modelinludes theeet ofthenearwake. Therstone tendstoaelerate thelift

evolution when the inidene is modied, whereas the seond one tends to lag it.

The overall ontribution isan inrease inthelag between inideneand lift, whih

generates an inreasein1P loadphaselag.

As explained before, the mean

~v ind

has a non-linear impat on 1P load norm and

phase lag,and should be onsideredarefully (bars 2 and5).

Therstmodeof

~v ind

(bars3and6)tendtodereasetheamplitude andlagthe

blade loading osillation due tothe propeller inidene. Thisexplains why1P load

phaselagoftherearrotorisaroundtwotimestheoneofthefrontrotor. Figure6.10

tries to illustrate howthe front rotor indued veloities ontribute to lag theangle

Incidence, [ ] L if t C o e ff ic ie n t, C L

-4 0 4 8 12 16

-0.4 0 0.4 0.8 1.2

w/o mean v ind C L

C L ~ 0

Figure 6.9: Example of two-dimensional airfoil dataand theosillation ofangle of

attak dueto theinidene alongablade yle. Comparisonbetween theasewith

and the asewithout meanindued veloities.

angleofattakofasinglepropellerinduedbyitswake;itsminimumvalueisfound

in the downward moving blade zone, beause there the wake has more vortiity.

Seond, the dash-dotted urve represents the angle of attak indued by the front

rotor wake; its minimum value is plaed around

270

, where the front rotor wake

hasmorevortiity. Finally,thesolidurveshowstheadditionofbothontributions,

asin the ase of a CROR. It presents a redutionof the amplitude of the

∆α

and

an inreaseinits phasewithrespetto thesinglepropellerase.

Finally, the ontribution of the BPF modes in HOST simulations is negligible

(bars 4and 7). However, ananalysisof thesensitivity of1P phaselag totimestep

presented by François et al. [François2013b℄, puts forward that the BPF modes

have animpat ofaround

3.5

for the front rotor (

−17%

) and

3

for therearrotor

(

−7%

). Theseosets an be a onsequene of thethree reasonsexposedin setion

6.2: usingdierent timesteps,negletingvisouseetsinHOST,andreduingthe

bladeto its quarter-hord line inHOST.

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