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
~v indare going to be deomposed in several omponents. A quantiation of theimpatofonesingle
~v indomponent onthrustand1Ploadsshouldbeestimated
by removing that omponent from a HOST simulation and omparing the results
with respetto theoriginal simulation.
The indued veloities
~v indrepresent 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
bladesetions of the propeller.
Hene adeomposition of the
~v indan be done as follows: (a)unsteady orretions
due to the airfoil motion; (b) installation eets due to the hub; () auto-indued
~v indbythe wake of a propelleron the propeller itself;and (d)
~v indbythewakeoftheotherpropeller. Both, auto-andm
(mode 1), and the Blade Passing Frequeny mode (mode BPF). Figure 6.7 shows,
r = 0.75R),thedeompositionoftheaxialand
Figure 6.7: Deomposition of the indued veloities
for thefront and therear
ential omponents of the
~vind into its dierent terms. Notethat negative axial
tend to diminish the aerodynami inidene of theblade setion, whereas negative
tendto inrease it.
and1Ploadphase. Notiethatthe perentagevalueaountsfortheimportaneof
ontribution. Moreover, perentages in redshould be onsidered arefully, asthey
are a onsequene of non-linear eets, as it will be explained hereafter. These
and then removing one
~v indomponent at eah simulation, inorder to quantify its
T h ru s t F R
Figure6.8: Contribution ofthe
~v indtermsonthethrust,the1Ploadnorm, andthe
1P loadphaselag offront and rearrotors.
Aerodynami mehanisms of Thrust. The mean value of
~v indis omposed
mainly of an axial and a irumferential omponent, i.e. the swirl. In the present
methodboth omponentsareonsidered together. Notiethemeanvalueof
themain mehanism impating thepropeller thrust. However, the impatof
auto-indued and mutually-indued veloities is not the same. On one side,in thease
of attak and henethethrust. Onthe otherside, inthease of mutually-indued
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
~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 (
Aerodynami mehanisms of 1P load norm. The main
im-pating 1P load norm is the rst mode of the wake (bars 3 and 6), due to the
propellerinidene. Indeed,the vortiityshedinthewakeislinked totheevolution
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
stall angle. As itis shown inthegure, for a given inideneosillation and when
removing the mean
~v indontribution, the lift oeient does not almost osillate.
Consequently, the method predits a very important but unphysial ontribution
~v indon 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
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 indfromthe 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 indhas a non-linear impat on 1P load norm and
phase lag,and should be onsideredarefully (bars 2 and5).
~v ind(bars3and6)tendtodereasetheamplitude andlagthe
blade loading osillation due tothe propeller inidene. Thisexplains why1P load
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.
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
asin the ase of a CROR. It presents a redutionof the amplitude of the
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 (
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.