In order to prepare open rotor oupled simulations, the veloities indued by elsA
andHOSTareomparedinrepresentativepositionsoftheoweld. Twoplanes,one
upstreamandonedownstreamthepropellerareonsideredhere. InelsAsimulations,
theplanes area X-slieinthe mesh.
InlassialCFDomputationsthereisnodiretaessto theveloitiesindued
by the propeller blades. To estimate them, it must be assumed that the veloity
eldisthesuperpositionoftheveloityeldaround ablade-onaelleandtheeld
around the propeller blades without naelle. This hypothesis might be orret at
rstorder,butnegletstheinterationbetweenthehubandtheblade, anditseet
on the airow. Figure 7.19 shows the onsidered geometry and the two planes of
interest inred.
On the ontrary, inHOST, the veloities indued by the propeller are diretly
obtained. Indeed, singularity methods assume that the veloity eld is the
super-positionof the elementary elds generated byeah singularity. Thus,theveloities
indued by the propellerblades andtheir wakes ontheonsidered X-planesan be
alulated at eah timestepbyBiot-Savart'slaw.
The main goal of this omparison is to estimate the indued angle of attak
Figure7.19: Sideview of APIANpropeller andtwo onsidered X-planes(inred)
Figure7.20: InduedangleofattakontheupstreamX-plane. Comparisonbetween
elsA andHOST.
ordownstreamthe APIANpropeller. Theratio between therotor-to-rotor distane
andthe maximumbladehordhasbeenhosenfromageneriontra-rotating open
rotor geometry,AI-PX7:
(d/c) APIAN = (d/c) AIPX7
,d APIAN = 0.22
m .Figures 7.20and7.21showtheinduedangleof attakpreditedbyHOSTand
elsA at an X-plane upstream the propeller and downstream the propeller,
respe-tively. Itonsiders theangledierene
∆β
inthe relative veloity whenaddingtheinduedveloities (seeFig. 7.22). Thepoint of viewis infront of theX-planesand
thepropellerturns ounterlokwise.
A notieable underestimation of the indued angle of attak on the upstream
plane an be notied in HOST simulations. This indued angle of attak is
di-retly linked to the indued veloities. Remember that a similar phenomenon had
been alreadyobserved inthefront rotor of AI-PX7 open rotor ase. Inboth ases,
Figure 7.21: Indued angle of attak on the downstream X-plane. Comparison
between elsA and HOST.
Ωr
V ∞ sin α sin ψ V ∞ cos α
W β
x y
b
z
Propellerplane
θ
(a)Without
~v ind
~v ind Ωr
V ∞ sin α sin ψ V ∞ cos α
W
β + ∆β
x y
b
z
Propellerplane
θ
(b)With
~v ind
Figure7.22: Veloitytriangles onsidering ornot theindued veloities
hypothesisreduing all the bladeto its quarter-hord line.
On the ontrary, a good predition of the indued angle of attak is obtained
for the downstream plane. In this ase, the hord eets are less important than
the eet of the wake going through the X-plane. Notie however, that the main
dierenesaremainlyobservedneartherootand thetipoftheblade: elsApredits
moreimportant root andtipwake eetson theindued angleofattak.
Neverthe-less,theseomparisonsshowthatthe generalpatternsareverylose,andtherefore,
elsA and HOST simulations are expeted to present similar aerodynami angles of
attak.
7.6 Conluding Remarks
The urrent oupling strategy between the HOST-MESIRomprehensive odeand
theelsACFDodehasbeen analyzedanditsmainadvantages anddrawbakshave
been put forward. In order to overome with some of the main shortomings of
this method, a new oupling strategy using the MINT free-wake model has been
partially implemented andassessed rst withrespetto MESIR oupling strategy.
A numberofmodiations inthe extrationoftheinduedveloitieshavebeen
performedinorderto obtainresultsinMINTthatarelosertoMESIRpreditions.
The modiations have foused on the vortex and panel regularization tehniques
used in HOST-MINTsimulations, whih have shown to be unadapted for oupled
simulations.
The seond part of the validation proess has been a omparison between
full-annulus elsA simulationand a oupled HOST-MINT and elsA simulation.
Signi-ant dierenes have been observed mainly on thepredition of the1P load phase
lag, whihis largely underestimatedinthe oupledsimulation.
Finally, a omparison between the indued ows in thefull-annulus and in the
near-wallsimulationshasbeen performedinordertoprepare futureontra-rotating
open rotor oupled simulations. Two X-slies, one upstream and one downstream
the blade, in order to assess the angle of attak indued by the propeller. These
slies have been plaed at distanes that arerepresentativesof thease of an open
rotor. Therefore,theinduedangles ofattakarelikelyto represent theinteration
between both rotorsina real open rotor ase.
For this ase, enouraging results have been obtained as both, full-annulus and
redued-domainsimulations, yieldto very similarinduedangles ofattakforboth
theupstream andthedownstreamX-slies.
Due to the inrease in fuel pries, airframe and engine manufaturers are looking
for step-hanging tehnologies that might enable them to produe more eient
and leaner airraft by 2020 and later. Among a number of emerging onepts,
the ontra-rotating open rotor engine is likely to be an interesting option for the
signiant redution ofthe airraft fuelonsumption and polluting emissions.
Nev-ertheless, a numberof key aspetsare not still suiently masteredfrom theearly
development steps of theengine. Therefore,manufaturers areinvesting inthe
de-velopmentofmethodologiesadaptedforpreliminarydesignphasesinorderto assess
some ofthese keyparameters.
In thepresent thesis,theobjetivewasto providemoderate-ostmethodologies
forthe aerodynamisimulationofontra-rotatingopenrotors. Thekeyparameters
to be assessed inthe preliminary aerodynami design of an open rotor are, on one
side, the predition of the engine performane and, on theother side, the in-plane
loads generated by the engine installation or by the airraft inidene. Moreover,
duringthe rst designsteps, rapidand exiblesimulationtools shouldbeprovided
todesignersenablingthemtoexplorealargesopeofengineongurationsandtest
ases inareasonable omputational time.
Following these riteria, a study of the dierent available simulation methods
has been onduted. The main assets and drawbaks of eah method have been
put forward and the hoie of a method based on the unsteady lifting-line theory
has been justied. The HOSTomprehensive ode for aero-mehanial simulation
of rotorraft hasbeen hosen and adapted for thesimulation of single and
ontra-rotatingpropellers. Thesubsequenthapters have beendevoted,rst,to assessthe
HOST ode for the aerodynami simulation of propellers and CROR in inidene;
seond, to improvethe blade-element modelto aount forunsteadyaerodynamis;
third,to provide abetter insightinto the mehanisms governing thein-planeloads;
and fourth, toexplore HOST-elsA oupling strategiesfor propellers.
Chapter1 hasprovided arstassessment oftheHOSTode forsinglepropeller
test ases inminimum-bodyonguration andinhigh-speed onditions. A number
of bestpraties for future simulationshave been establishedand justied.
Then, wind tunnel data and more advaned CFD simulations have been used to
assessthe aurayofHOSTsimulationsinthepreditionofpropellerperformane
and in-plane loads. In addition, the blade load distributions have also been
om-pared. Moreover,twomodelstoaount forthe eetsofthespinnerhavealsobeen
tested and ompared to experimental dataandCFD simulations.
Despite the unertainties in experimental data, satisfatory results have been
ob-tained in HOST simulations when the eets of spinner were taken into aount.
HOST has shown to apture orretly the inidene eet (
α
-eet) and therota-tional speed eet (J-eet). Nevertheless, some osets were still notied in the
planeloadshasbeenneessaryastheseloadsareritialfor thedimensioningofthe
engineinstallation,fortheairafthandlingqualities,andforaeroelastiphenomena.
Previousworksfoundintheliteraturehadtriedtounderstandthein-planeloads
fromaglobalapproahprovidedbyexperimentaldataorCFDsimulations. However,
totheauthor'sknowledge,nodeepanalysisonthein-planeloadshasbeenpreviously
done based on singularity methods. This type ofapproahesis basedon thelinear
superpositionoftheeetofanumberofelementsinthespae(thesingularities)to
determine the globalairow. Thispropertyhasbeen usedinChapter2 toestimate
theontribution ofa numberofaerodynamimehanismsat theorigin ofpropeller
in-plane loads. This has led to a better understanding of these mehanisms and
provides a preious tool for engine designers aiming at mastering these undesired
loads.
The unsteadiness in the relative airow seen by the blade has been identied
as one of the main ontributors to predit orretlythe in-plane loads. Besides, it
hasalsobeenshownthattheunsteadyorretionsintheoialHOSTversiondoes
not implement rigorously the unsteady airfoil theory. Therefore, Chapters 3 and
4 have been devoted to the theoretial analysis, development, and implementation
of an unsteady airfoil model that enables, on one side, to orret the quasi-steady
airfoil data to inlude the loads due to airow unsteadiness and,on the otherside,
to aount for the loal blade sweep and urvature. In Chapter 3 a rst model
based on previous workshasbeen theoretially analyzedand hasshown important
shortomings. Hene, ithasbeen neessaryto re-developan unsteadyairfoilmodel
to be implemented in the HOST ode, asexposed in Chapter 4. Again, the main
shortomings of the implementedmodelhave been put forward.
The unsteadymodel implemented inHOST hasbeen assessed in Chapter5 by
omparison with previous HOST simulations, experimental data, and CFD
simu-lations. Very satisfatory results have been obtained in terms of propeller
perfor-mane, in-planeloads,and bladeload distributions. In partiular,an improvement
in thepredition of in-planeloads phase lagand blade loaddistribution have been
remarked thanksto theunsteadyairfoil model.
Asimilar study hasbeen onduted inChapter6 forthease ofa generiopen
rotor geometry (AI-PX7)inisolated onguration, in high-speed onditions andin
inidene. TheassessmentoftheHOSTodehasbeendonebyomparingitsresults
with CFD simulations. Again, satisfatory results have been obtained in terms of
global performaneandin-planeloads,aswellasintermsofbladeloaddistribution.
Takingintoaounttheeetsofthenaelleandinludingtheunsteadyairfoilmodel
hasprovidedmorein-planeloadsthatarelosertoCFDresults. Nevertheless,ithas
alsobeennotedtheimportaneofhordandvolumeeetsinopenrotorsimulations.
Indeed,duetothefatthattheseeetsarenegletedinHOST,anunderestimation
of thepotential interation between rotorshasbeen notied.
In order to omplete the insight into in-plane load mehanisms in Chapter 2,
theseond partofthe Chapter6hasbeen devotedto thestudy ofthemehanisms
behind open rotor in-plane loads. Again, this method provides a useful tool for
planeloads to an important number ofkey designparameters.
The last hapter of this thesis (Chapter 7) is devoted to an exploratory study
oftheoupling between theelsA CFDodeand theHOSTomprehensive odefor
propeller simulations. The interest of this type of simulations lies in thefat that
theCFD simulation domain is redued to a small volume around one blade of the
propeller. Theeetof the otherbladesis provided bytheindued veloities
alu-lated ina more rapid ode, HOSTin the present study. This approah is likely to
redueomputationalostswithrespettofullCFDsimulations,whilemaintaining
a largesopeof appliations, inludinginstalled ongurationsor inidene eets.
Thestate-of-artinthiseldissummarizedanditsshortomingsareexposed. Then,
a new oupling strategy is proposedand partially implemented. First omparisons
between both oupling strategies on a single propeller test ase show similar
re-sults, although a numberof modiations in the omputation of indued veloities
have been neessary. On the ontrary, when omparing this new oupling
strat-egy with CFD simulations of a omplete propeller, important mismathes an be
notied. Further studies should be onduted to better understand the origin of
these mismathes and to solve them. Moreover, for the moment, only a one-way
oupling strategy has been implemented. Future HOST versions are likely to be
more adaptedfor omplete oupledHOST-elsA simulations.
Tosumup,thisthesishasprovidedabetterinsightintotheomprehensionofthe
in-planeloadmehanisms,aswell asa preliminarydesign toolfor theaerodynami
simulationofopenrotors. Thesearetwokeystepsfortheintegrationofopenrotors
on futureAirbusairraft.
Moreover, this thesis hasopened a number of elds to be explored: (1)HOST
simulations have shown a lak of auray in the predition of loads lose to the
blade root. Therefore, a hub model based on singularity methods might be a way
to improve the preditions in this area. (2) The unsteady airfoil model urrently
implemented still neglets the singularity of the spanwise vorties in the wake. A
more rigorous model allowing a orret regularization of the wake should improve
the stability of HOST simulations (3) In order to redue the omputational time,
fastmultipole tehniquesare being investigated at Onerafor the integrationof the
indued veloities, promising important gainsin omputationaltime. (4)Continue
with the development of a full HOST-elsA oupling strategy for the simulation of
propellers and ontra-rotating open rotors. (5) Inreasing the number of HOST
appliations: inluding aeroelasti simulations, or using theMINT wake for rapid
aeroaoustisimulations.
Finite Part Integrals
This hapter details the theory behind nite part integrals as used by Gallois
[Gallois2003℄andMuller[Muller 2007℄intheirrespetivePh.D.thesis. Thehapter
startswitha denitionof Cauhy'sPrinipal Valueintegral. Then, theFinite Part
integral dened by Hadamard as the generalization of Cauhy's Prinipal Value is
detailed.
A.1 Prinipal Value of a Singular Integral
Fromtheformalizationofthelifting-lineproblem,Prandtl[Prandtl 1923℄has
disov-eredthe importane of the orretomputation of singular integrals. In partiular,
he hadto onsider thePrinipal Value ofthefollowing integral: PV
Z b
In amoregeneral ase, the PrinipalValueintegrals areusedinintegrals ofthe
form:
forafuntion
ψ(x)
ontinuousinallthe[a, b]
interval. Therstintegral isimproperbut onvergent. Theseond integral hasbeensolvedbyPrinipalValues asfollows:
Z b
Toalulate the Prinipal Valueintegral, itis imposedthat
ε 1 = ε 2
,thus yielding:PV
The singularterm inthe integral hasdisappeared.