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

^{in}

^{the}

^{relative}

^{veloity}

^{when}

^{adding}

^{the}

induedveloities (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

^{Prop}

ellerplane

### θ

(a)Without

### ~v ind

### ~v _{ind} Ωr

### V _{∞} sin α sin ψ V _{∞} cos α

### W

### β + ∆β

### x y

### b

### z

^{Prop}

ellerplane

### 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}

^{the}

^{}

rota-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)

^{ontinuous}

^{in}

^{all}

^{the}

### [a, b]

^{interval.}

^{The}

^{rst}

^{integral}

^{is}

^{improper}

but 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.