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DOCTORAT DE L'UNIVERSITÉ DE TOULOUSEDélivré par :

Institut National Polytechnique de Toulouse (INP Toulouse)Discipline ou spécialité :Energétique et Transferts

Présentée et soutenue par :M. THOMAS LIVEBARDON

le vendredi 18 septembre 2015

Titre :

Unité de recherche :

Ecole doctorale :

MODELISATION DU BRUIT DE COMBUSTION DANS LES TURBINESD'HELICOPTERES

Mécanique, Energétique, Génie civil, Procédés (MEGeP)

Centre Européen de Recherche et Formation Avancées en Calcul Scientifique (CERFACS)Directeur(s) de Thèse :

M. THIERRY POINSOT

Rapporteurs :M. CARLO SCALO, PURDUE UNIVERSITY EU

M. CHRISTOPHE BAILLY, ECOLE CENTRALE DE LYON

Membre(s) du jury :1 M. STÉPHANE MOREAU, UNIVERSITE DE SHERBROOKE QUEBEC, Président2 M. ALEXIS GIAUQUE, ECOLE CENTRALE DE LYON, Membre2 M. ERIC BOUTY, TURBOMECA, Membre2 M. THIERRY POINSOT, INP TOULOUSE, Membre

Résumé

L’augmentation du trafic aérien à proximité des zones à forte densité démographiqueimpose aux constructeurs aéronautiques de développer des appareils de plus enplus silencieux. Les systèmes propulsifs figurent parmi les principaux contribu-teurs du rayonnement acoustique des aéronefs. Plus particulièrement, il est ad-mis que la chambre de combustion est responsable d’une génération acoustiquelarge-bande et basse fréquence. Deux principaux mécanismes générateurs de bruitont été identifié dans les moteurs d’avions dans les années 70. Le premier cor-respond à l’émission d’ondes acoustiques par le dégagement de chaleur instation-naire induit par la combustion turbulente au sein de la chambre, bruit qualifiéde direct. Le second mécanisme est la génération acoustique dans les étages deturbine par l’accélération des fluctuations de températures et de vorticité créespar la flamme et l’écoulement turbulent dans la chambre, bruit qualifié d’indirect.Ces deux mécanismes ont été largement mis en évidence au travers de travauxacadémiques analytiques, expérimentaux et numériques. Par contre, l’importancedu bruit de combustion sur des moteurs réels a été peu étudiée. Dans ce tra-vail, une méthodologie de calcul basée sur des simulations aux grandes échelles dechambres de combustion couplées à une méthode analytique pour calculer le bruitde combustion dans une configuration réelle est évaluée. Cette châıne de calculnommée CONOCHAIN est comparée aux résultats expérimentaux analysés danscette thèse et issus du projet TEENI (projet européen FP7) où un moteur completTURBOMECA a été instrumenté pour identifier les sources de bruits large-bandes.Dans un premier temps, un secteur de la chambre TEENI est calculée pour deuxpoints de fonctionnements expérimentaux. Ensuite, la chambre annulaire complèteest simulée au point de fonctionnement maximal pour évaluer l’apport du champaérodynamique complet sur la prédiction du bruit. Enfin, les niveaux de bruitsdirect et indirect sont calculés, à partir des fluctuations extraites des précédentessimulations en sortie de brûleur, dans les étages de turbines et comparés auxdonnées expérimentales.

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The growth of air traffic at the vicinity of areas at high population density im-poses to make quieter aircrafts on aeronautical manufacturers. The engine noiseis one of the major contributors to the overall sound levels. Furthermore, thecombustion is known to be responsible for a broadband noise generation at low-frequency. The combustion noise can be put into two main mechanisms. Thefirst one is the emission of sound pulses by the unsteady heat release of the com-bustion process and is called the direct combustion noise. The second one is thegeneration of acoustic waves within the turbine stages by the acceleration of thetemperature inhomogeneities and vorticity waves induced by the combustion andthe turbulent flow within the combustor. This noise is the indirect combustionnoise. These mechanisms were fully investigated in academic cases using exper-imental, analytical and numerical approaches contrary to the combustion noisewithin real engines. In this work, a hybrid approach called CONOCHAIN andbased on LES of combustion chamber and an analytical disk theory to computethe combustion noise in a real turboshaft engine is evaluated. The predicted noiselevels are compared with the experimental results obtained from a TURBOMECAengine in the framework of TEENI project (European project FP7) and analysedin this work where a turboshaft engine was instrumented to locate and identify thebroadband noise sources. Two LES of a single sector of the TEENI combustionchamber representative of two experimental operating points are performed as wellas a LES of the full-scale combustor at high power. The unsteady fields providedby the LES are used to compute direct and indirect combustion noise within theturbine stages in both cases and compared with the experimental results.

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Remerciements

Je tiens à remercier chaleureusement Carlo Scalo, Christophe Bailly, Alexis Gi-auque et Stéphane Moreau pour avoir accepté d’évaluer mon travail et assisté àma soutenance de thèse. Avoir l’opportunité de présenter mes travaux devant untel jury fut pour moi un véritable honneur.

Un grand merci à mes encadrants de thèse, et, en premier lieu, Thierry Poinsotpour m’avoir accueilli au CERFACS et guidé tout au long de ces trois années (et enparticulier pendant la dernière ligne droite où son aide et ses conseils avisés furentprécieux pour rédiger ce manuscrit). Merci à Laurent Gicquel pour son aide dansla mise en place des calculs et sa grande capacité d’écoute, à Stéphane Moreaupour son suivi hebdomadaire, sa très grande disponibilité et enfin son soutien. Jeveux remercier également Eric Bouty pour m’avoir accueilli à Turbomeca pendantles essais TEENI et suivi durant toutes ces années. Merci aussi à toutes les équipesde Bordes qui ont rendu ce passage en entreprise très agréable!

Merci également à toutes les personnes au CERFACS qui nous permettent dese concentrer uniquement sur nos thèses, Chantal Nasri, Michèle Campassens etMarie Labadens pour l’administratif, l’équipe CSG toujours souriante et superefficace pour l’informatique. Il faut aussi remercier les stagiaires, doctorants, post-doctorants et seniors au CERFACS. Je tiens à remercier particulièrement Charlieavec qui j’ai traversé ces trois années, merci pour nos fous rires, notre séjour enBéarn, nos repas ”maisons” et merci à Dorian pour avoir eu le courage (et il enfaut) de partager mon bureau. Enfin, je remercie mes parents, ma soeur Marieet Pierre, pour avoir cru en moi durant ces trois ans et m’avoir soutenu dans lesmoments difficiles. Un grand merci à Charlène qui a toujours su trouver les motsdans les nombreux moments de doute.

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Contents

Introduction 1

I Experimental investigation of combustion noise in aturboshaft engine and presentation of CONOCHAIN method-ology 19

1 Localisation and identification of broadband acoustic sources in aturboshaft engine 201.1 Signal post-processing techniques . . . . . . . . . . . . . . . . . . . 22

1.1.1 Correlations and signal breakdown techniques . . . . . . . . 271.2 Experimental set-up . . . . . . . . . . . . . . . . . . . . . . . . . . 31

1.2.1 Signal processing parameters . . . . . . . . . . . . . . . . . . 331.3 Acoustic analysis of engine experimental data . . . . . . . . . . . . 38

1.3.1 Acoustic far-field data . . . . . . . . . . . . . . . . . . . . . 381.3.2 Unsteady pressure within the engine . . . . . . . . . . . . . 381.3.3 Unsteady temperature in the combustor and the high-pressure

turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401.3.4 Tracking combustion noise inside the engine . . . . . . . . . 41

1.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

2 CONOCHAIN: Numerical method to predict combustion-generatednoise in aero-engine 542.1 The actuator disk theory : CHORUS . . . . . . . . . . . . . . . . . 56

2.1.1 Linearised Euler equations . . . . . . . . . . . . . . . . . . . 582.1.2 Wave classification . . . . . . . . . . . . . . . . . . . . . . . 602.1.3 Jump relations across a blade row . . . . . . . . . . . . . . . 632.1.4 Computation of a turbine stage . . . . . . . . . . . . . . . . 742.1.5 Selection of higher azimuthal modes computed with CHORUS 752.1.6 Literature test cases . . . . . . . . . . . . . . . . . . . . . . 76

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2.2 Post-processing the waves at the end of a combustion chamber sim-ulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

2.3 A Helmholtz solver : AVSP-f . . . . . . . . . . . . . . . . . . . . . . 862.3.1 Solving the Phillips’ equation . . . . . . . . . . . . . . . . . 862.3.2 AVSP forced Helmholtz solver . . . . . . . . . . . . . . . . . 872.3.3 Analytical description of a low-Mach number hot jet . . . . 88

2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

II Large-Eddy simulations of the TEENI combustionchamber dedicated to the combustion noise evaluation 93

3 Numerical tools for the Large-Eddy Simulations 953.1 Large Eddy Simulation with AVBP . . . . . . . . . . . . . . . . . . 95

3.1.1 The governing equations . . . . . . . . . . . . . . . . . . . . 963.1.2 Equations for compressible Large Eddy Simulations . . . . . 98

4 Operating points and numerical set-up 1014.1 Configuration and operating points . . . . . . . . . . . . . . . . . . 102

4.1.1 Description of the geometry . . . . . . . . . . . . . . . . . . 1024.1.2 Operating points . . . . . . . . . . . . . . . . . . . . . . . . 103

4.2 Numerical parameters . . . . . . . . . . . . . . . . . . . . . . . . . 1044.2.1 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . 1044.2.2 Chemistry and combustion model . . . . . . . . . . . . . . . 1044.2.3 Modelling of multi-perforated plates in AVBP . . . . . . . . 105

5 Single-sector LES of the TEENI combustion chamber 1085.1 Mesh description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1095.2 Mean flow description . . . . . . . . . . . . . . . . . . . . . . . . . 110

5.2.1 Mean velocity in the combustion chamber . . . . . . . . . . 1155.2.2 Mean Temperature field . . . . . . . . . . . . . . . . . . . . 115

5.3 Unsteady activity in the combustion chamber . . . . . . . . . . . . 1215.3.1 Unsteady pressure within the combustor . . . . . . . . . . . 1215.3.2 Generation of temperature fluctuations . . . . . . . . . . . . 124

5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

6 Full-scale LES of the TEENI combustion chamber 1306.1 Mesh description for full engine . . . . . . . . . . . . . . . . . . . . 1316.2 Mean flow features . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

6.2.1 Mean flow description . . . . . . . . . . . . . . . . . . . . . 1316.2.2 Outlet mean temperature . . . . . . . . . . . . . . . . . . . 135

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6.3 Unsteady field in the full annular chamber . . . . . . . . . . . . . . 1396.3.1 Unsteady pressure within the chamber . . . . . . . . . . . . 1396.3.2 Unsteady temperature in the combustion chamber . . . . . . 1446.3.3 Entropy planar mode filtering . . . . . . . . . . . . . . . . . 148

6.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

III Combustion noise computation in the turbine stagesand in the far-field with CONOCHAIN tool 151

7 Combustion noise computation within the turbine stages of TEENIengine 1527.1 Acoustic characterisation of the turbine stages . . . . . . . . . . . . 153

7.1.1 Acoustic-to-acoustic transfer functions . . . . . . . . . . . . 1557.1.2 Vorticity-to-acoustic transfer functions . . . . . . . . . . . . 1557.1.3 Entropy-to-acoustic transfer functions . . . . . . . . . . . . . 1557.1.4 Entropy wave distortion through the turbine . . . . . . . . . 156

7.2 Extracted waves from the LES entering the turbine stages . . . . . 1617.2.1 Downstream-propagating acoustic waves . . . . . . . . . . . 1617.2.2 Vorticity waves . . . . . . . . . . . . . . . . . . . . . . . . . 161

7.3 Noise predictions within the turbine stages . . . . . . . . . . . . . . 1657.3.1 Noise predictions with a single-sector LES . . . . . . . . . . 1667.3.2 Noise predictions using a full-scale LES and comparisons

with a single-sector LES for the high power case . . . . . . . 1707.3.3 Comparisons between noise predictions using a full-scale LES

and a filtered single-sector LES . . . . . . . . . . . . . . . . 1737.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

8 Propagation of combustion-generated noise within the far-field 1768.1 Computational methodology . . . . . . . . . . . . . . . . . . . . . . 177

8.1.1 Numerical domain . . . . . . . . . . . . . . . . . . . . . . . 1778.1.2 Wave injection . . . . . . . . . . . . . . . . . . . . . . . . . 1798.1.3 Mean temperature field of the exhaust jet . . . . . . . . . . 1818.1.4 Scaling of the acoustic pressure in the far-field . . . . . . . . 182

8.2 Predictions of the acoustic far-field . . . . . . . . . . . . . . . . . . 1838.2.1 Numerical verification of far-field noise tool . . . . . . . . . . 1838.2.2 Comparison with experimental far-field spectra . . . . . . . 183

8.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

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General conclusion 191

Appendices 195

A Analytical transfer function of experimental pressure probe inharsh conditions 195A.1 Sketch of the sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . 195A.2 Acoustic modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

B Acoustic propagation and generation in a low-Mach number jet 199

C Acoustic wave propagation within annular and cylindrical ducts 202C.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202C.2 Acoustic pressure field within the duct . . . . . . . . . . . . . . . . 202

D Geometrical method to build a nozzle from a blade vane 206

E Preliminary results about LES of a single sector of the TEENIcombustion chamber 210E.1 Impact of the multi-perforated plates on the acoustic activity . . . . 210

E.1.1 Mean flow predictions . . . . . . . . . . . . . . . . . . . . . 210E.1.2 Unsteady features within the combustion chamber . . . . . . 212

E.2 Impact of the sub-grid scale models . . . . . . . . . . . . . . . . . . 213E.2.1 Mean flow predictions . . . . . . . . . . . . . . . . . . . . . 213E.2.2 Unsteady features within the combustion chamber . . . . . . 216

E.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

F Acoustic analysis of the TEENI combustion chamber with AVSP224F.1 Acoustic analysis of a single sector . . . . . . . . . . . . . . . . . . 224

F.1.1 Numerical parameters . . . . . . . . . . . . . . . . . . . . . 224F.1.2 Impact of secondary dilution holes . . . . . . . . . . . . . . 226

F.2 Acoustic analysis of the full-scale combustor . . . . . . . . . . . . . 226

Bibliographie 229

Publications 245

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List of Figures

1 Reference projection of global primary energy consumption up to2050 (Mtoe: Million Tonnes of Oil Equivalent). . . . . . . . . . . . 1

2 Projection of CO2 emissions until 2050 (MtCO2: Millions of tonnesof CO2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

3 The main contributing noise sources for take-off and approach for aturboshaft engine [Rolls-Royce, 2005]. . . . . . . . . . . . . . . . . . 5

4 Schematic view of the ARDIDEN gas generator and the two powerturbines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

5 Schematic view of RQL combustion chamber. . . . . . . . . . . . . 66 Ideal sound pressure level spectrum in the far-field of a turboshaft

engine with broadband and tonal components. . . . . . . . . . . . . 77 Ratio η between indirect and direct combustion noise calculated by

the compact theory. M1 is the combustion chamber Mach numberat the nozzle inlet and M2 us the Mach number at the nozzle exit[Leyko et al., 2009]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

8 Flowchart of the manuscript. . . . . . . . . . . . . . . . . . . . . . . 18

1.1 Signal sampling representation where the blue colored line is thecontinuous signal and the red dots are the discrete samples . . . . . 23

1.2 Sketch of averaged periodograms computation for a pair of signalsX and Y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

1.3 Representation in the complex plane C of the computation of co-herent components of two signals X and Y using an averaged cross-spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

1.4 Sketch of signal decomposition used in three-sensors technique . . . 291.5 Aerial picture of Uzein test bench and rear view of TEENI instru-

mented engine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321.6 Schematic view of an internal pressure sensor proposed by DLR. . . 331.7 Sketch of TEENI experimental set-up and location of internal pres-

sure and temperature sensors . . . . . . . . . . . . . . . . . . . . . 341.8 Schematic view of TEENI test-bench with far-field microphones lo-

cation (•) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

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1.9 TEENI engine with the silencer mouted on the air-intake . . . . . . 351.10 PSD of far-field acoustic pressure from minimum power ( ) to

maximum power ( ) at 120o (Fig. 1.8). . . . . . . . . . . . . . . 361.11 Radiation maps of acoustic far-field according to microphone loca-

tions (Fig. 1.8) and maximum of SPL ( ). . . . . . . . . . . . . . . 371.12 PSD of pressure fluctuations from minimum power ( ) to max-

imum power ( ) measured in different locations within the engine. 401.13 PSD of temperature fluctuation in the combustion chamber at 904kW. 411.14 Coherence spectrum γ2 (equation 1.7) between a HPT pressure

probe and a twin thermocouple in the combustion chamber. . . . . 421.15 Averaged coherence spectra of unsteady pressure computed with

the equation 1.7 applied between nozzle and combustion chamber, high-pressurized turbine (•) and power turbine ( ). . . . . . 43

1.16 PSD of an exhaust probe ( ) and PSD of three-sensors techniquedefined in equation 1.17 and applied between combustion chambersensors (position A in Fig. 1.7) and the nozzle probe (position D1in Fig. 1.7) ( ). . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

1.17 PSD of an exhaust probe ( ) and PSD of three-sensors techniquedefined in equation 1.17 and applied between high-pressure turbinesensors (position B in Fig. 1.7) and the nozzle probe (position D1in Fig. 1.7) ( ). . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

1.18 PSD of an exhaust probe ( ) and PSD of three-sensors techniquedefined in equation 1.17 and applied between power turbine sen-sors (position C in Fig. 1.7) and the nozzle probe (position D1 inFig. 1.7) ( ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

1.19 Dimensionless dot products of cross-spectra between a far-field mi-crophone probe and a probe located either in the combustion cham-ber ( ) or in the high-pressure turbine ( ) or in the powerturbine (�). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

1.20 Three-sensors technique defined in equation 1.17 and applied be-tween pair of combustor pressure probes (position A in Fig. 1.7)and far-field microphones according to their locations (Fig. 1.8). . . 49

1.21 Three-sensors technique defined in equation 1.17 and applied be-tween pair of HPT pressure probes (position B in Fig. 1.7) andfar-field microphones according to their locations (Fig. 1.8). . . . . 50

1.22 Three-sensors technique defined in equation 1.17 and applied be-tween pair of power turbine pressure probes (position C in Fig. 1.7)and far-field microphones according to their locations (Fig. 1.8). . . 51

1.23 Identification and location of broadband noise sources within theTEENI engine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

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2.1 Description of the CONOCHAIN methodology . . . . . . . . . . . . 562.2 Sketch of unwrapped annular duct according to CHORUS modeling 582.3 Two-dimensional modeling of a rotor stage . . . . . . . . . . . . . . 652.4 Sketch of the computation of the delays using the axial velocity

profiles accross a blade row . . . . . . . . . . . . . . . . . . . . . . . 672.5 Analytical entropy transfer functions ( ) and numerical results (•)

[Leyko et al., 2010, Duran et al., 2013]. . . . . . . . . . . . . . . . . 692.6 Modal distribution of the normalized entropy wave through a blade

row carried by planar entropy mode (•), the Nblade azimuthal mode(�) the 2N thblade (×) and the 3N thblade (+) and sum of the modal powersof these entropy transfer functions (-). . . . . . . . . . . . . . . . . 70

2.7 Kutta’s condition applied at the trailing edge of a blade. . . . . . . 712.8 Sketch of a subsonic blade row with no deviation (first test case). . 762.9 Acoustic transmission and reflexion coefficients for an incident upstream-

propagating acoustic wave according to the wave angle ν computedwith CHORUS ( ) and compared with Kaji’s results (•) - M = 0.1and θ = 60o (Fig. 2.8). . . . . . . . . . . . . . . . . . . . . . . . . . 77

2.10 Sketch of a subsonic blade row with no deviation (second test case). 772.11 Acoustic transmission and reflexion coefficients for an incident upstream-

propagating acoustic wave according to the wave angle ν computedwith CHORUS ( ) and compared with Kaji’s results (•) - M = 0.5and θ = 60o (Fig. 2.10). . . . . . . . . . . . . . . . . . . . . . . . . 78

2.12 Sketch of a subsonic blade row with deviation (third test case). . . . 782.13 Acoustic transmission and reflexion coefficients for an incident downstream-

propagating acoustic wave according to the wave angle ν computedwith CHORUS ( ) and compared with Kaji’s results (•) and Cum-spty’s results (�) (Fig. 2.12). . . . . . . . . . . . . . . . . . . . . . 79

2.14 Sketch of a subsonic nozzle. . . . . . . . . . . . . . . . . . . . . . . 802.15 Acoustic transmission and reflexion coefficients according to Mach

number computed with CHORUS ( ) and compared with one-dimensional theory (•) for an incident acoustic wave through a sub-sonic nozzle (Fig. 2.14). . . . . . . . . . . . . . . . . . . . . . . . . . 80

2.16 Acoustic transmission and reflexion coefficients according to Machnumber computed with CHORUS ( ) and compared with one-dimensional theory (•) for an incident entropy wave through a sub-sonic nozzle (Fig. 2.14). . . . . . . . . . . . . . . . . . . . . . . . . . 81

2.17 Entropy-to-acoustic transfer functions for an incident azimuthal en-tropy wave according to the inverse azimuthal wave numberKy com-puted with CHORUS ( ) and compared with Cumpsty’s results (•)for a subsonic blade row (Fig. 2.12). . . . . . . . . . . . . . . . . . . 83

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2.18 LES domain and two-dimensional interpolating planes at the exitof the combustion chamber. . . . . . . . . . . . . . . . . . . . . . . 84

2.19 Sketch of a low-Mach number jet flow . . . . . . . . . . . . . . . . . 892.20 Dimensionless radial velocity profiles in the potential core of the jet

flow at different abscissae: x = 0 (-), x = 0, 5xp (•), x = xp (�). . . 902.21 Dimensionless temperature profiles Tx according to dimensionless

radius R/D and axial coordinate x/D - D the nozzle diameter. . . . 91

4.1 LES domain of a 1/N thsectors of TEENI annular combustion chamber 1024.2 Sketch of the swirlers for liquid and gaseous injections . . . . . . . . 103

5.1 Tetrahedral mesh of the LES domain. . . . . . . . . . . . . . . . . . 1095.2 Stagnation pressure within the combustion chamber according to

the exit mass flow rate for reactive ( ) and non-reactive cases ()and stabilized operating points (�). . . . . . . . . . . . . . . . . . 110

5.3 Sketch of the multiperforated plate locations. . . . . . . . . . . . . . 1125.4 Sketch of the different planes locations. . . . . . . . . . . . . . . . . 1135.5 Sketch of the probes locations within the combustion chamber. . . . 1145.6 Streamlines of the mean projeted velocity in plane ∆1 (Fig. 5.4). . . 1155.7 Streamlines of the mean projeted velocity in plane ∆2 (Fig. 5.4). . . 1165.8 Mean dimensionless velocity magnitude w

Uinletwith white isolines of

mean heat relase (W/m3) in plane ∆1 (Fig. 5.4). . . . . . . . . . . . 1165.9 Mean dimensionless velocity magnitude w

Uinletwith white isolines of

mean heat relase (W/m3) in unwrapped plane ∆2 (Fig. 5.4). . . . . 1175.10 Mean dimensionless temperature field T−Tinlet

Tadiab−Tinletwith an isoline of

stochiometric mixture fraction in plane ∆1 (Fig. 5.4). . . . . . . . . 1185.11 Mean dimensionless temperature field T−Tinlet

Tadiab−Tinletwith an isoline of

stochiometric mixture fraction in unwrapped plane ∆2 (Fig. 5.4). . 1195.12 Mean dimensionless temperature field T−Tinlet

Tadiab−Tinletin unwrapped plane

∆3 (Fig. 5.4). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1205.13 Root-mean-squared pressure in plane ∆1 (Fig. 5.4). . . . . . . . . . 1215.14 Power spectral densities of pressure fluctuations within the flame

tube a the locations 1( ), 4 ( ) and 5 ( ) in Fig. 5.5. . . . . . 1225.15 Coherence spectra between unsteady heat release integrated over

the LES domain and exit pressure signals (plane 5 in Fig. 5.5) -344kW ( ) and 904kW ( ). . . . . . . . . . . . . . . . . . . . . . . 123

5.16 Dimensionless modulus (right) and normalised phase φπ

(left) of thefirst acoustic longitudinal mode computed with AVSP over the plane∆1 in Fig. 5.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

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5.17 Dimensionless modulus (right) and normalised phase φπ

(left) of thesecond acoustic longitudinal mode computed with AVSP over theplane ∆1 in Fig. 5.4. . . . . . . . . . . . . . . . . . . . . . . . . . . 125

5.18 Phase-shift of cross-spectra between pressure probes in plane 1 andplane 5 (Fig. 5.5). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

5.19 Normalized modal power distribution of the pressure signal at theexit of the combustion chamber over the exit plane ∆4 (Fig. 5.4),(mode = 0 : H, mode = -Nsectors : N, mode = Nsectors : •, highermodes : �). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

5.20 Power spectral densities of pressure fluctuations (position A in Fig.5.5)- LES ( • ) Experiment ( ). . . . . . . . . . . . . . . . . . . . . 126

5.21 RMS temperature in plane ∆1 (Fig. 5.4). . . . . . . . . . . . . . . . 1275.22 Instantaneous fluctuating temperature in plane ∆2 (Fig. 5.4). . . . . 1275.23 Power spectral densities of unsteady temperature in flame tube -

Plane 2 (�) Plane 3 (•) Plane 4 (+) in Fig. 5.5. . . . . . . . . . . . 1285.24 Normalized modal power distribution of the entropy fluctuations

signal at the exit of the combustion chamber over the exit plane ∆4(Fig. 5.4), (mode = 0 : H, mode = -Nsectors : N, mode = Nsectors :•, higher modes : �). . . . . . . . . . . . . . . . . . . . . . . . . . . 128

6.1 LES domain and mesh of a single-sector. . . . . . . . . . . . . . . . 1316.2 Vertical slices of mean dimensionless velocity magnitude w/Uinlet

with isolines of mean heat release (W/m3) (6.2(a)) and mean di-mensionless temperature field T−Tinlet

Tadiab−Tinlet(6.2(b)) with an isoline of

the stochiometric mixture fraction over plane ∆1 (Fig. 5.4) in thefull annular combustion chamber to compare with single-sector LES(Fig. 5.8(b) left and 5.10(b) right). . . . . . . . . . . . . . . . . . . 132

6.3 Mean dimensionless temperature field T−TinletTadiab−Tinlet

over the meridianplane ∆2 (Fig. 5.4) with an isoline of the stochiometric mixturefraction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

6.4 Time-evolution of the azimuthal velocity (m/s) extracted from thesingle sector ( and mean value ) and the full-scale LES ( andmean value ) over the exit plane ∆4 (Fig. 5.4). . . . . . . . . . . . 134

6.5 Mean dimensionless velocity magnitude w/Uinlet with isolines ofmean heat release (W/m3) over the meridian plane ∆2 (Fig. 5.4). . 135

6.6 Mean dimensionless temperature fields TTmean

over the exit plane ∆4(Fig. 5.4). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

6.7 Mean temperature profiles T/Tmean at the exit of the combustionchamber over the exit plane ∆4 (Fig. 5.4) for different azimuthalpositions for the single sector computation (�) and the full com-bustion chamber ( ). . . . . . . . . . . . . . . . . . . . . . . . . . 137

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6.8 Mean temperature profiles T/Tmean at the exit of the combustionchamber ver the exit plane ∆4 (Fig. 5.4) for different azimuthal posi-tions for the single sector computation (�) and the full combustionchamber ( ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

6.9 Comparisons between the RMS pressure field extracted from thefull-scale LES and the dimensionless acoustic pressure computedwith AVSP corresponding to the first azimuthal mode (Appendix F)over the plane ∆2 (Fig. 5.4). . . . . . . . . . . . . . . . . . . . . . . 140

6.10 Radial integration of the RMS pressure field over the exit plane ∆4(Fig. 5.4). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

6.11 Power spectral densities of pressure fluctuations over the Nsectorssectors (6.11(a)) and cross-spectrum between pressure probes withinsectors 5 and 12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

6.12 Modal power distribution of the pressure signal at the exit of thecombustion chamber over the exit plane ∆4 (Fig. 5.4), (mode = 0 :H, mode = -1 : N, mode = 1 : •, higher modes : �) . . . . . . . . . 143

6.13 Power spectral densities of pressure fluctuations within the flametube at the location A (Fig.5.5) for single sector computation (�),full scale simulation ( ) and experimental spectrum ( ). The grayerrorbars on the full LES spectra corresponds to the extrema of theNsectors PSDs circumferentially extracted at the location A. . . . . . 143

6.14 RMS temperature fields over the meridian plane ∆2 (Fig. 5.4). . . . 1456.15 Modal power distribution of the entropy signal at the exit of the

combustion chamber over the exit plane ∆4 (Fig. 5.4), (mode = 0 :H, mode = -1 : N, mode = 1 : •, the higher modes : �) . . . . . . . 145

6.16 Averaged power spectral densities of temperature fluctuations forthe single sector computation (�) and the full scale simulation ( ). 146

6.17 Phase-shifts φi,i+1 of cross-spectra Ci,i+1 (Eq.6.1) between the en-tropy planar modes extracted from adjacent sectors of the full-annular combustion chamber (Sectors 1 to 3: N - • - �, sectors4 to 6 : N - • - �, sectors 7 to 9 : N - • - �, sectors 10 to 12 : N -• - �). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

6.18 Power spectral densities of the planar entropy modes extracted fromthe ”single-sectors” ( ) and the full-annular combustion chamber (�).149

6.19 Power spectral densities of the planar entropy modes extracted fromthe different sum of sectors ( ) and the full-annular combustionchamber (�). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

7.1 Sketch of TEENI experimental set-up and location of internal pres-sure and temperature sensors. . . . . . . . . . . . . . . . . . . . . . 154

xiv

7.2 Sketch of TEENI turbine stages corresponding to Fig. 7.1 and wavenotation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

7.3 Analytical acoustic-to-acoustic transfer functions at different loca-tions within the turbine stages (Fig. 7.2). . . . . . . . . . . . . . . . 157

7.4 Analytical vorticity-to-acoustic transfer functions at different loca-tions within the turbine stages (Fig. 7.2). . . . . . . . . . . . . . . . 158

7.5 Analytical entropy-to-acoustic transfer functions at different loca-tions within the turbine stages (Fig. 7.2). . . . . . . . . . . . . . . . 159

7.6 Entropy-to-entropy transfer functions (ws)hp / (ws)cc: , (ws)p1 / (ws)cc:• and (ws)p2 / (ws)cc: � (Fig. 7.2). . . . . . . . . . . . . . . . . . . . 160

7.7 Power spectral densities of downstream-propagating acoustic waveamplitude ((w+)cc in Fig. 7.2) extracted from single-sector LES ofthe chapter 5 (planar mode ( ), ±N thsectors azimuthal modes (•)). . . 162

7.8 Power spectral densities of downstream-propagating acoustic waveamplitude ((w+)cc in Fig. 7.2) extracted from full-scale LES of thechapter 6 (planar mode ( ), ±1th azimuthal modes (H), ±2th az-imuthal modes (•) for the high power case to compare with thesingle-sector results of Fig. 7.7(b). . . . . . . . . . . . . . . . . . . . 162

7.9 Power spectral densities of vorticity wave amplitude ((wv)cc in Fig. 7.2)extracted from single-sector LES of the chapter 5 (planar mode ( ),±N thsectors azimuthal mode (•)). . . . . . . . . . . . . . . . . . . . . . 163

7.10 Power spectral densities of vorticity wave amplitude ((wv)cc in Fig. 7.2)extracted from the full-scale LES of chapter 6 (planar mode ( ),±1th azimuthal mode (H), ±2th azimuthal mode (•)). . . . . . . . . 164

7.11 Power spectral densities of entropy wave amplitude ((ws)cc in Fig. 7.2)extracted from single-sector LES of the chapter 5 (planar mode ( ),±N thsectors azimuthal mode (•)). . . . . . . . . . . . . . . . . . . . . . 164

7.12 Power spectral densities of entropy wave amplitude ((ws)cc in Fig. 7.2)extracted from the full-scale LES of the high power case of the chap-ter 6 (planar mode ( ), ±1th azimuthal mode (H), ±2th azimuthalmode (•)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

7.13 Computed combustion noise corresponding to the planar mode com-ing from single-sector LES in the high-pressurized turbine (positionB in Fig. 7.1). Total predicted noise: �, indirect noise: •, directnoise: H and experimental PSD of wall-pressure fluctuations ( )from the pair of probes. . . . . . . . . . . . . . . . . . . . . . . . . 167

7.14 Computed indirect noise corresponding to the planar vorticity mode(•) and experimental PSD of wall-pressure fluctuations ( ) fromthe pair of probes in the high-pressurized turbine (position B inFig. 7.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

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7.15 Computed combustion noise corresponding to the planar mode inthe power turbine (position C in Fig. 7.1). Total predicted noise:�, indirect noise: •, direct noise: H and experimental PSD of wall-pressure fluctuations ( ) from the pair of probes. . . . . . . . . . 168

7.16 Computed combustion noise corresponding to the planar mode atthe turbine exit (position D in Fig. 7.1). Total predicted noise: �,indirect noise: •, direct noise: H and experimental PSD of wall-pressure fluctuations ( ) from a pair of probes. . . . . . . . . . . 169

7.17 Computed combustion noise using longitudinal and azimuthal modesextracted from a full 360o LES (up to mode index = 2) in differentlocations within the engine (Fig. 7.1). Total predicted noise: �,indirect noise: •, direct noise: H and experimental PSD of wall-pressure fluctuations ( ) from the pair of probes in high powercase. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

7.18 Computed total combustion noise using full 360o LES (longitudinaland azimuthal modes (up to mode index = 2), •) and single-sectorLES (raw longitudinal mode, �) in different locations within theengine (Fig. 7.1) in high-power case. . . . . . . . . . . . . . . . . . . 172

7.19 Computed total combustion noise using full 360o LES (longitudinaland azimuthal modes (up to mode index = 2), •) and filtered single-sector LES (longitudinal mode, �) in different locations within theengine (Fig. 7.1) in high-power case. . . . . . . . . . . . . . . . . . . 174

8.1 Schematic view of the TEENI test-bench with far-field microphoneslocation (•). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

8.2 Schematic view of the TEENI test bench and the computational do-main AVSP-f with the location of experimental microphones (Fig. 8.1)projected over sphere around the engine (dotted lines). . . . . . . . 178

8.3 Schematic view of the computational domain AVSP-f and location ofan experimental microphone (Fig. 8.1) and his projection in AVSP-fdomain (dotted line). . . . . . . . . . . . . . . . . . . . . . . . . . . 179

8.4 Sketch of the AVSP-f domain and the boundaries. . . . . . . . . . . 1808.5 Mesh of the AVSP-f domain with a zoom of the mesh refinement in

the nozzle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1808.6 Mean temperature field through the jet flow scaled with the exit

temperature in the high power case. . . . . . . . . . . . . . . . . . . 1818.7 Mean sound velocity field through the jet flow scaled with the exit

sound velocity in the high power case. . . . . . . . . . . . . . . . . . 1828.8 Acoustic pressure fields at different frequencies in the high power

case induced by an unitary acoustic forcing through the turbine exit.184

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8.9 Acoustic pressure from 90o/90o to 130o/129,4o (θTEENI/θAV SPf inFig. 8.3) in the far-field for the high power case computed withCONOCHAIN (combustion noise with the entropy filtering (sec-tion 6.3.3): � , combustion noise without the entropy filtering: •)and experimental acoustic pressure ( ). . . . . . . . . . . . . . . . . 186

8.10 Acoustic pressure from 140o/148,8o to 180o/171,1o (θTEENI/θAV SPfin Fig. 8.3) in the far-field for the high power case computed withCONOCHAIN (combustion noise with the entropy filtering (sec-tion 6.3.3): � , combustion noise without the entropy filtering: •)and experimental acoustic pressure ( ). . . . . . . . . . . . . . . . . 187

8.11 Acoustic pressure from 90o/90o to 130o/129,4o (θTEENI/θAV SPf inFig. 8.3) in the far-field for the low power case computed withCONOCHAIN (combustion noise with the entropy filtering (sec-tion 6.3.3): � , combustion noise without the entropy filtering: •)and experimental acoustic pressure ( ). . . . . . . . . . . . . . . . . 188

8.12 Acoustic pressure from 140o/148,8o to 180o/171,1o (θTEENI/θAV SPfin Fig. 8.3) in the far-field for the low power case computed withCONOCHAIN (combustion noise with the entropy filtering (sec-tion 6.3.3): � , combustion noise without the entropy filtering: •)and experimental acoustic pressure ( ). . . . . . . . . . . . . . . . . 189

A.1 Sketch of a pressure probe . . . . . . . . . . . . . . . . . . . . . . . 196A.2 PSD of pressure fluctuations in the combustion chamber and the

power turbine (positions A and C in Fig. 1.7 respectively) ( )and analytical transfer functions ( ). . . . . . . . . . . . . . . . 198

B.1 Sketch of jet flow modelling. . . . . . . . . . . . . . . . . . . . . . . 200B.2 Modelling of the exhaust jet and acoustic ray path diagram ( ). 201

C.1 Sketch of the infinite annular duct . . . . . . . . . . . . . . . . . . . 203

D.1 Geometrical definition of the cones associated with the turbine ge-ometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

D.2 Sketch of the radial projection of a three-dimensional blade profileover the mediator cone. . . . . . . . . . . . . . . . . . . . . . . . . . 208

D.3 Osculating circles according to the curvilinear abscissae along theircenter points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

E.1 Mean dimensionless temperature field T−TinletTadiab−Tinlet

with an isoline ofstochiometric mixture fraction in plane ∆1 (Fig. 5.4). . . . . . . . . 211

E.2 Mean dimensionless velocity magnitude uUinlet

in plane ∆1 (Fig. 5.4). 211E.3 Sketch of the velocity plane locations and the swirler vanes. . . . . . 212

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E.4 Mean swirl numbers computed with the Eq. E.1 in the outer and theinner vane of the swirler (Fig. E.3) - Coupled ( ) and Uncoupledmulti-perforated plates ( ). . . . . . . . . . . . . . . . . . . . . . 213

E.5 Mean dimensionless axial velocity profiles ux/Uinlet over differentlines just after the lips of the swirler (Fig. E.3) according to thedimensionless radius - Coupled ( ) and Uncoupled multi-perforatedplates ( ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

E.6 RMS pressure within the flame tube in plane ∆1 (Fig. 5.4). . . . . . 215E.7 Power spectral densities of pressure and temperature fluctuations at

the exit of the combustion chamber (plane 5 in Fig. 5.4) - Coupled( ) and Uncoupled multi-perforated plates ( ). . . . . . . . . . . 215

E.8 Mean dimensionless temperature field T−TinletTadiab−Tinlet

with an isoline ofstochiometric mixture fraction in plane ∆1 (Fig. 5.4). . . . . . . . . 216

E.9 Mean dimensionless velocity magnitude uUinlet

in plane ∆1 (Fig. 5.4). 217E.10 Mean swirl numbers computed with the equation E.1 in the outer

and the inner vane of the swirler (Fig.E.3) - Classical Smagorinsky(×) - Dynamic Smagorinsky (�) - Fitlering Smagorinsky (•). . . . . 218

E.11 Mean dimensionless axial velocity profiles ux/Uinlet over differentlines just after the lips of the swirler (Fig. E.3) according to the di-mensionless radius - Classical Smagorinsky (×) - Dynamic Smagorin-sky (�) - Fitlering Smagorinsky (•). . . . . . . . . . . . . . . . . . 219

E.12 Mean dimensionless azimuthal velocity profiles uθ/Uinlet over thefirst line just after the lips of the swirler (Fig. E.3) according tothe dimensionless radius - Classical Smagorinsky (×) - DynamicSmagorinsky (�) - Fitlering Smagorinsky (•). . . . . . . . . . . . . 220

E.13 RMS pressure within the flame tube in plane ∆1 (Fig. 5.4). . . . . . 221E.14 Power spectral densities of pressure and temperature fluctuations at

the exit of the combustion chamber (plane 5 in Fig. 5.4) - ClassicalSmagorinsky (×) - Dynamic Smagorinsky (�) - Fitlering Smagorin-sky (•). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222

F.1 Mesh used in AVSP computation. . . . . . . . . . . . . . . . . . . . 225F.2 Mean dimensionless sound velocity field c−cmin

cmax−cmin over plane ∆1(Fig. 5.4). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

F.3 Dimensionless modulus of acoustic pressure field for the first longi-tudinal mode 1-L (Table F.1) in the combustion chamber with andwithout secondary dilution holes. . . . . . . . . . . . . . . . . . . . 228

F.4 Normalised phase Φπ

of acoustic pressure field for the first longitu-dinal mode 7-L (Table F.1) in the combustion chamber with andwithout secondary dilution holes. . . . . . . . . . . . . . . . . . . . 229

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F.5 Dimensionless modulus of acoustic pressure field for the seventhlongitudinal mode 1-L (Table F.1) in the combustion chamber withand without secondary dilution holes. . . . . . . . . . . . . . . . . . 230

F.6 Normalised phase Φπ

of acoustic pressure field for the seventh longi-tudinal mode 7-L (Table F.1) in the combustion chamber with andwithout secondary dilution holes. . . . . . . . . . . . . . . . . . . . 231

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List of Tables

1.1 Windowing wave-functions over a period T . . . . . . . . . . . . . . 25

2.1 Relations used to build linearised jump conditions across a blade row. 64

4.1 Dimensionless combustion parameters at low and high powers. . . . 1034.2 Laminar flame characteristics for the DTLES model . . . . . . . . . 105

5.1 Mean mass flow rate distribution within the flame tube (Fig. 5.3)and pressure losses for the operating points. . . . . . . . . . . . . . 111

F.1 Cut-on frequencies of the acoustic longitudinal modes (Hertz) ac-cording to the presence of secondary dilution holes. . . . . . . . . . 226

F.2 Cut-on frequencies of the acoustic modes (Hertz) within the full-scale combustion chamber. . . . . . . . . . . . . . . . . . . . . . . . 228

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Introduction

In 2050, the world population should reach 9.5 billions followed by an increasingenergy demand. The world power consumption would be multiplied by 3 to exceed50 MW [UE, 2006] (equal to 40 000 millions tonnes of oil equivalent) where fossilenergies count for 70% of the primary energies total as shown in Fig. 1.

0

5000

10000

15000

20000

25000

30000

35000

40000

1990 2001 2010 2020 2030 2040 2050

Household, serviceagricultureTransport

Industry

Power Plants

Figure 1: Reference projection of global primary energy consumption up to 2050(Mtoe: Million Tonnes of Oil Equivalent).

There are several reasons for this situation: the new oil discoveries (shale gasreserves, oil sands, available artic oil reserves), low-cost of petroleum products and

1

their ease-of-use to generate mechanical or electrical power. Consequently, fossilfuels will play a major role in long-timer global economic development especially incase of developing and newly industrialized countries (Brazil, China, India, Russia,...).

Four main sectors compose most of the fossil energy consumption [UE, 2006]:agriculture, transportation, industry and power plants (electricity generation) asshown in Fig. 1. Up to 2050, electricity production represents the largest part ofthe total energy consumption. Consequences of the growing dependence in fossilenergies are numerous. Indeed, many environmental problems result from hydro-carbons burning. First of all, combustion products are mainly composed of waterand carbon dioxyde which are well-known greenhouse gases. As shown in Fig. 2,

1990 2000 2010 2020 2030 2040 20500

5000

10000

15000

20000

25000

CoalOilNatural GasNuclearHydro and geothermalBiomass and wastesWind and solar

Figure 2: Projection of CO2 emissions until 2050 (MtCO2: Millions of tonnes ofCO2).

CO2 emissions will double by 2050 [EPA, 2010]: climate scientists predict thatif carbon dioxyde levels continue to increase, the planet will become warmer toreach 4oC global average temperature growth per century. Projected temperatureincreases will most likely result in a variety of impacts. In coastal areas, sea-levelrises due to the warming of the oceans and the melting of glaciers may lead to the

2

inundation of wetlands, river deltas, and even populated areas. Altered weatherpatterns may result in more extreme weather events. In addition to CO2 emissions,combustion process releases nitrogen and sulfur oxides which are important con-stituents of acid rain. As the acids accumulate, lakes and rivers become too acidicfor plant and animal life. Combustion products are responsible for air pollutionwhich can cause headaches, additional stress and heart diseases.

Transportation sector is more dependent on the fossil fuels than others becausecluttering and weight are known to be key constraints in design process of engines.Combustion-driven engines have these advantages because of the easy conversionof fossil energy into mechanical power, the high energy density and the ease of fuelstorage of petroleum products.

Furthermore, in order to satisfy the growth of global transport demand anddeal with climate changes, transport industry is facing unprecedented challenges :

• Reduction of fuel consumption

• Increase in engine thermo-mechanical efficiency

• Reduction of pollutant emissions : greenhouse gases, nitrogen oxides andnoise.

Even if hybrid and full-electrical engines are used on ground vehicles thanks to ad-vanced technologies in electricity storage, the majority of vehicles especially in airtransport will be fitted with combustion-driven engines. In particular, air trafficwill be multiplied by four in 2050 [UE, 2013] and aero-engine manufacturers are an-ticipating these challenges under international regulations [ICA, ACA]. Significantefforts are directed to develop new technologies in terms of composite materials,engine fuel efficiency and pollutant emissions (combustion products and noise).

Noise and aircraft

Noise regulationsThe International Civil Aviation Organization’s (ICAO) role is to lead the de-velopment of commonly-agreed solutions to limit aircraft emissions. Particularly,ICAO, through the Committee on Aviation Environmental Protection (CAEP),is setting the standards for noise [ICAO, 2006] by monitoring research and tech-nology developments. As announced during the seventh meeting of the CAEP in2007, ’the prime purpose of noise certification is to ensure that the latest availablenoise reduction technology is incorporated into aircraft design demonstrated by pro-cedure which are relevant to day to day operations, to ensure that noise reductionoffered by technology is reflected in reductions around airports.’ For helicopters,

3

noise regulations are summarized in the chapter 8 of the Annex 16 where specifica-tions about the take-off, overflight and approach reference noise measurements arespecified, as well as the noise level limits for these three reference points dependingon the helicopter take-off mass.

Health impact of noise pollutionNoise reduction is not only a comfort issue for aircraft passengers but also a healthproblem [enHealth Council, 2004] associated to a long list of symptoms related tonoise exposure. The most known effect is sound annoyance for airport neighbour-hood population. Hearing loss and sleep disturbance can happen above 45 dBnoise level. Furthermore, noise levels above 70 dB can induce cardiovascular ef-fects, hypertension and myocardial infarction. These effects are related to stressgenerated by noise which rises blood pressure and leads to vasoconstriction. Fi-nally, U. S. Environmental Protection Agency found that noise pollution can affectchild physical development.

Sources of aircraft noiseSound radiated from an aircraft is the result of many individual and separatenoise sources. Contribution of these sources in the overall radiated sound pressuredepends on the flight phases. Indeed, different engine elements are involved innoise generation like engines, airframe or landing gears. As shown in Fig. 3, manyaircraft components are responsible for noise emissions and the relative share ofeach contribution differs significantly from take-off to approach.

Noise of a helicopter engine

Description of a turboshaft engineA turboshaft engine is divided into two main parts : a gas generator and a powersection [Rolls-Royce, 2005]. A gas generator is composed of three distinct compo-nents :

• Compressors

• Combustion chamber

• High-pressure turbine.

Compressors raise the pressure of the working fluid passing through it and aredriven by the high-pressure turbine as seen in Fig. 4. Combustion takes place

4

Figure 3: The main contributing noise sources for take-off and approach for aturboshaft engine [Rolls-Royce, 2005].

Centrifugal compressor stages CombustionchamberPower turbines

High-PressureTurbine

Fresh air

Flame Tube

Burnt gases

Figure 4: Schematic view of the ARDIDEN gas generator and the two powerturbines.

in the annular combustor where liquid fuel is injected through circumferentiallyinjectors and burns with the pressurized air coming from the compressors stages

5

in a primary zone as shown in Fig. 5. This technology is called Rich burn, quickmix, lean burn (RQL) concepts to reduce pollutant emissions. Flame stabiliza-tion is ensured in the swirling flow generated by the injector. Dilution holes andmultiperforated plates are distributed along the flame tube to mix fresh air andburnt gases reducing mean temperature at the outlet of the combustor. Turbinesstages produce rotational power along a shaft to drive compressor stages. On theother hand, the power section converts kinetic energy of the hot gases to propulsivework. For turboshaft engines, several turbine stages are located downstream ofthe gas generator to extract energy from the hot flow and connected to a centralshaft providing mechanical work to the main gear box of the helicopter.

Compressor inlet

Combustor outlet

Injector andswirler

Flame tube

Casing

Fresh Air

FuelMultiperforatedplates

Reaction zone

Burnt gases

Figure 5: Schematic view of RQL combustion chamber.

Noise sources within a turboshaft engineIn a turboshaft engine, there are many acoustic sources over a wide frequencyrange. Several classification criteria can be used like the location of acousticsources, the frequency band or the main directivity angles as shown in Fig. 6. Amajor noise source is induced by the rotating devices within the engine like power

6

shafts or blade rows. It is possible to characterize the sound pressure frequencieswith the Blade Passing Frequency (BPF) which corresponds to the revolution rateper second multiplied by the number of compressor or turbine blades. This tonalnoise is mainly present at high frequency and radiates through the air intake incase of compressors and through the exhaust in case of turbine stages [Tyler andSofrin, 1962, Griffiths, 1964]. Moreover, an other narrowband noise results fromthe blade-to-blade interactions: wakes induced by turbulent flows around eachblade are convected across the blade-to-blade spacing and impact the next bladerows generating acoustic waves [Posson et al., 2010, Wang et al., 2000, Verdon andHuff, 2001, Kazin and Matta, 1975, Krejsa and Valerino, 1976, Hanson, 2001a,b,Envia, 1998, Atassi et al., 2004]. For turboshaft engines, turbulence generated

Directcombustion

noiseIndirect

combustionnoise

High pressureturbine induced

noiseSPL (dB)Power turbineinduced noise

20 kHzFrequency

Figure 6: Ideal sound pressure level spectrum in the far-field of a turboshaft enginewith broadband and tonal components.

noise within the low-Mach number jet is not significant.The last contributor of the engine-radiated noise is the combustion chamber.

Even if it is commonly admitted as a low-frequency and broadband noise, theimportance of combustion noise in the overall radiated noise of a turboshaft engineis not well-known. Engine manufacturers are not able to discriminate combustionnoise from exhaust noise and it is often called ”core-noise” but they know thatlow-Nox emissions engines are noisier than standard designs [Gliebe et al., 2000].

7

Actually, engine manufacturers estimate sound pressure levels generated by thecombustor using scaling laws [Harper-Bourne, 2001] based on previous enginesafter removing all the identified acoustic components out of the engine soundpressure spectra where the jet noise is often the most contributor. So, combustionnoise is often modelled with a broadband component from 100 Hz to 1200 Hzwhere two main mechanisms can be distinguished :

• Direct combustion noise : the turbulent combustion process in the com-bustor generates acoustic waves propagated through the turbines [Thomasand Williams, 1966, Hurle et al., 1968, Strahle, 1972, Clavin and Siggia, 1991,Bailly et al., 2010].

• Indirect combustion noise : it consists of acoustic waves induced by theconvection of combustion-generated heterogeneities like temperature fluc-tuations or turbulence through mean velocity gradients through the bladerows [Candel, 1972, Marble and Candel, 1977, Marble and Broadwell, 1977,Cumpsty and Marble, 1977, Pickett, 1975].

Especially for helicopter engines, combustion noise is suspected to be a majorcontributor in the overall radiated core-noise. Contrary to tonal noise, installationof passive devices to reduce low-frequency core-noise is impossible because of theirimpact on the helicopter engine weight.

Direct combustion noise

Because of the inherent unsteadiness within a free flame, direct combustion noisewas the first investigated over the last century. Phenomenological rules were es-tablished by Bragg [1963] to evaluate the acoustic power generated by a sphericalpremixed flame: the sound pressure levels produced by the combustion were relatedto the volume expansion linking the acoustic mass flux of a monopolar acousticsource with the mass flow rate fluctuation of fresh gases. These conclusions wereconfirmed experimentally by Thomas and Williams [1966] where the experimen-tal temporal variation of free radical combustion products were correlated withthe acoustic pressure signals. However, a dependence was found between the fueltype and the sound pressure levels. For turbulent flames, Bragg [1963] consid-ered the combustion zone as a collection of acoustic monopolar sources to buildscaling laws. Turbulent flames were also addressed by Strahle [1971, 1972] wherethe same monopolar behaviour of the acoustic sources generated by combustionwere considered. However, Strahle estimated the sound pressure level of turbulentflames based on an adapted Lighthill’s analogy. Using Doak’s analogy, Hassan[1974] found a similar result for turbulent premixed flames at low-Mach number.

8

The Lighthill’s analogy To deal with noise emission by a isothermal turbulentjet in a free space, Lighthill [1952] proposed an exact formulation of the Navier-Stokes equations to build a wave equation and operate the different source terms.This formulation divides the domain into two main zones : a source zone (the jetflow) and the quiescent space containing the listener.

∂2ρ′

∂t2− c20

∂2ρ′

∂x2i= ∂

2Tij∂xi∂xj

(1)

where Tij isρvivj − τij + (p′ − c20ρ′)δij, (2)

and ρ is the density, p the pressure, vi a velocity component, δij the Kroneckerfactor, t the time, c the sound velocity and the subscripts ′ and 0 denote thefluctuating variable and the reference state respectively. The right-hand-side of theequation 1 is detailed in 2 where three main aero-acoustic processes are involvedin noise generation :

• ρvivj are the non-linear convective forces described by the Reynold stresstensor

• τij are the viscous forces

• (p′ − c20ρ′)δij is the deviation from an isentropic behaviour [Rienstra andHirschberg, 2011].

Eq. 1 is useful to compute the acoustic field of a turbulent jet and shows thatthe turbulent noise source is of quadripolar type.

For combustion noise, Dowling re-writes the multi-species Navier-stokes equa-tions [Crighton et al., 1992] similarly to the Lighthill’s analogy to deal with thethermo-acoustic source terms :

1c20

∂2p

∂t2−∇2p = ∂

2

∂xi∂xj(ρuiuj − τij)

+ ∂∂t

[ρ∞ρ

(γ − 1)c2

(ω̇T +

∑k

hk∂Jk∂xk− ∂qi∂xi

+ τij∂ui∂xj

+ Q̇)

+ ρ∞D

Dt(lnr)

]

+ 1c∞

∂

∂t

[(1− ρ∞c

2∞

ρc2

)Dp

Dt− p− p∞

ρ

Dρ

Dt

]+ ∂

2

∂xj∂t(ρeuj) (3)

where γ is the ratio of specific heats, ω̇T the heat release, hk the specific enthalpyfor species k, Jk the diffusive molecular flux for species k, qi the j-th componentof the diffusive heat flux and ρe is the excess density and corresponds to the

9

difference between the overall mass density fluctuation and the one generated bythe isentropic transformation such as an acoustic wave [Morfey, 1973]. Eq. 3displays the effect of all the thermoacoustic sources and it is more general thanthe Lighthill’s analogy. Consequently, the first term of the right-hand side of Eq. 3corresponds to the quadripolar source of Eq. 1. The second term is responsible forthe direct combustion noise: it is of monopole nature and is related to the soundgenerated by irreversible flow process especially combustion and heat release. Thethird term contributes in case of unsteady flow with different mean density andsound speed form the ambient fluid. Finally, the last term can correspond to theindirect combustion noise where density inhomogeneities are accelerated and it isof dipole type.

Bailly et al. [2010] simplified the Eq. 3 using classical assumptions of turbulentcombustion such as a constant molecular weight of the mixture, negligible diffusionflux terms, a quasi-isobaric flow at low Mach number and a heat ratio which isindependent of temperature. The main acoustic source term is related to theunsteady heat release and the far-field acoustic pressure is equal to

p(x, t) ∼=(γ − 1)4πc2∞x

∂

∂t

∫Vω̇T

(y, t− ||x− y

c∞

)dy. (4)

which is the expression found by Strahle [1971, 1972].Analytical works used the Philip’s analogy [Phillips, 1960] extended to the

reacting zones to compute the direct combustion noise [Chiu and Summerfield,1974, Kotake, 1975, Bailly et al., 2010] which provides a better identification ofcombustion noise source terms. Interactions between turbulence and flame in thescope of noise generation was also addressed by Clavin and Siggia [1991], Lieuwenet al. [2006], Rajaram and Lieuwen [2009] showing that sound intensity is scaledwith the volume of flame brush and proportional to the fourth power of the Machnumber and the flame dilatation. Furthermore, scaling laws were proposed to takeinto account turbulent velocity fluctuations which exhibits frequency-dependencerelation between sound generation and turbulence. Using numerical approaches,several studies investigated the direct combustion noise to assess these results.Sound pressure generated by a laminar premixed flame was computed by Taleiet al. [2011] using Direct Numerical Simulations (DNS) where two mechanisms wereidentified in direct combustion noise generation. It was found that the wrinklingand surface variation of the flame are responsible for the direct combustion noise aswell as flame pitch-off when the flame is acoustically excited. For turbulent cases,Large-Eddy Simulations (LES) coupled with Computational AeroAcoustics (CAA)methods are used to capture the interactions between turbulence and combustionon the one hand and acoustic sources generation and propagation in the free spaceon the other hand. Good agreements were found between these simulations and

10

the experiments [Flemming et al., 2007, Ihme et al., 2009a] in terms of soundpressure levels and directivity patterns.

Indirect combustion noise

The acoustic analogies presented in the last paragraph highlight the mechanismresponsible for indirect combustion noise generated by the convection of inho-mogeneities through accelerating flows. Acoustic generation through acceleratingflows was first investigated in the scope of combustion instabilities in rocket engineswhere hot spots were convected by the main flow through the exit nozzle whichgenerated a reflected acoustic waves and strong pressure fluctuations within theengine [Tsien, 1952]. Acoustic behavior of one-dimensional nozzles was firstly ad-dressed by Marble and Candel [1977]. In this work, an one-dimensional isentropicmean flow was considered through subsonic or supersonic nozzles. Linearisation ofquasi one-dimensional linearised Euler equations highlighted acoustic generationinduced by a mean velocity gradient.

D

Dt

(p′

γp

)+ u ∂

∂x

(u′

u

)= 0,

D

Dt

(u′

u

)+ c

2

u

∂

∂x

(p′

γp

)=

[s′

cp− 2u

′

u+ (γ − 1)

(p′

γp

)]du

dx,

D

Dt

(s′

cp

)= 0 (5)

where u is the axial velocity, cp the specific heat at constant pressure, s the entropyand the entropy fluctuation s′

cpwas equal to

s′

cp= p

′

γp− ρ

′

ρ. (6)

The left-hand side of the momentum equation in the system 5 shows that an ac-celerating entropy disturbance is an acoustic source. Then, Marble and Candelcomputed entropy-to-acoustic transfer functions of subsonic and supersonic noz-zles. Considering that combustion noise was very low-frequency, the characteristicaxial length of the nozzle was smaller than entropy or acoustic wavelengths. Conse-quently, the nozzle could be consider as ”compact” and was similar to an interfacewhere jump relations could be applied between upstream and downstream zones.Linearisation of mass, total temperature and entropy conservation across the noz-zle provided these jump relations between fluctuating and mean variables of theflow. However, these transfer functions were only valid at low-frequency. In order

11

to extend this theory at low-frequency, Marble and Candel considered a linear ve-locity profile in the nozzle which allowed computing frequency dependent transferfunctions but was not representative of a realistic mean flow.

Bloy [1979] used a characteristic method to solve acoustic generation inducedby the temperature disturbance convection through subsonic nozzles

Different approaches for dealing with non-compact effects were used. At low-frequency, Stow et al. [2002] proposed an asymptotic analysis to compute thefirst-order correction of acoustic-entropy transfer functions for choked nozzles.

To remove this frequency limit, several authors divided an arbitrary nozzleinto several segments for which the mean velocity was linearly distributed alongthe nozzle axis [Giauque et al., 2012a,b, Moase et al., 2007]. Thus, reflectionand transmission coefficients of each segment were computed using the hyper-geometric solution proposed by Marble and Candel [1977]. Acoustic behaviour ofthe complete nozzle was computed by combining the analytical coefficients. Morerecently, Duran and Moreau [2013] solved analytically the quasi one-dimensionalEuler equations using a Magnus expansion. This powerful method provides reflec-tion and transmission coefficients for any nozzle geometry and any mean flow.

Indirect noise has been thoroughly studied by DLR in an experiment calledEntropy Wave Generator [Bake et al., 2008, 2009]. This experiment was a singlenozzle where entropy waves were generated by an electrical device at the upstreamof the nozzle and different flow regimes were tested. Consequently, this work wasthe aim of numerous analytical and numerical studies [Muhlbauer et al., 2009,Giauque et al., 2012b, Leyko et al., 2008]. Howe [2010] suggested that a significantpart of generated acoustic waves in the EWG experiment could be induced byvorticity generation in the divergent part of the nozzle at high-Mach number.Particularly, the compact theory of Marble and Candel [1977] was validated withEuler simulations and analytical works [Leyko et al., 2008]. Leyko [Leyko et al.,2009] proposed an evaluation of the ratio between direct and indirect combustionnoise according to the nozzle exit Mach number. Fig. 7 shows the importanceof indirect combustion noise for supersonic nozzles compared to the direct noise.In modern aero-engines, the first turbine stage at the combustion chamber exitis often choked. Consequently, indirect combustion is expected to be dominantcompared with direct combustion noise.

The acoustic behaviour of turbines was investigated for several decades. Asturbine blades are the place of complex physics, noise mechanisms are numerousand are characterized by their frequency range. Consequently, numerous analyti-cal works deal with the acoustic generation and are dedicated to one kind of noisemechanism. Combustion noise mechanisms within turbine blades are quite sim-ilar to the nozzle case even if the mean flow structure is more complex becauseof deviation induced by the turbine blades and the rotating devices. Particu-

12

Figure 7: Ratio η between indirect and direct combustion noise calculated by thecompact theory. M1 is the combustion chamber Mach number at the nozzle inletand M2 us the Mach number at the nozzle exit [Leyko et al., 2009].

larly, the compact assumption used in nozzle cases can also be applied in turbinestages. Indeed, the axial blade chord is smaller than characteristic wavelengthsof combustion noise. Different studies proposed a compact approach to deal withturbine stages in the scope of low-frequency noise. Kaji and Okazaki [1970a]proposed a two-dimensional semi-actuator disk theory able to take into accountacoustic resonances within the blade rows with a finite axial chord but infinitesi-mal blade spacing for isentropic flows. Jump relations were written at the leadingand trailing edges. As this approach was two-dimensional, only azimuthal modeswere considered. Mach number, flow deviation and blade loading effects were in-vestigated in terms of acoustic transmission and reflection coefficients in case ofnon-reflecting boundary conditions at the turbine exit. To remove the infinitesimalblade spacing assumptions, Kaji and Okazaki [1970b] wrote a second analyticalmethod based on the acceleration potential method. Muir [1977a,b] extended thismethod to deal with three-dimensional acoustic waves where radial components

13

of the acoustic modes were taken into account. Matta and Mani [1979] proposeda two-dimensional approach where a finite-length of blade rows was taken intoaccount. Each blade spacing was modeled by a wave guide similar to a ”linear”nozzle defined by Marble and Candel [1977] in the one-dimensional case. Con-sequently, this model was able to capture acoustic resonances within the bladerows. However, it was found that an actuator disk theory was sufficient to mimicthe acoustic behaviour of turbine stages at low-frequency. The actuator disk the-ory was used by Pickett [1975] dealing with temperature disturbances convectedthrough turbine stages. Linearised Euler equations were written in blade vanes.Then, jump relations across blade rows were determined by computing the limit ofthese equations when the axial chord length tended to zero. Cumpsty and Marble[1977] developed a similar two-dimensional approach based on the actuator disktheory where linearised conservation laws across blade rows provided the jumprelations. Leyko used this theory [Cumpsty and Marble, 1977] coupled with LESof a turbulent reactive flow in an aero-engine to compute core-noise induced by acombustion chamber. Using also numerical simulations of a two-dimensional tur-bine stage, Leyko proved the ability of this analytical method to predict indirectcombustion noise generated by entropy fluctuations, the direct combustion noisegenerated through a stator [Leyko et al., 2010, Duran et al., 2011] or a rotor [Du-ran and Moreau, 2012] and through a complete turbine stage [Duran and Moreau,2013, Duran et al., 2013]. Entropy wave scattering induced by the turbine stageswas also addressed. In the same way, this actuator disk theory is investigated bycomparing two-dimensional numerical simulations of a subsonic stator with an in-jection of entropy spots against analytical predictions [Mishra and Bodony, 2013]showing the validity of this theory for low-frequency cut-on acoustic modes. Fewstudies deal with combustion noise generation within a real aero-engine becauseof the lack of experimental measurements especially within the engine. Tam et al.[2012] investigated combustion noise generation within auxiliary power units butthe separation of indirect part from the combustion noise is still a challenge.

The present work used the actuator disk theory proposed by Cumpsty andMarble [1977] to compute combustion-generated noise in a real turboshaft engine.This theory will be fully described in the first part of this document.

Motivations and objectives of the thesisNew designs of combustion chamber start emerging with the main objective ofreducing NOx emissions and fuel consumption. Unfortunately, these new conceptsgenerate unwanted effects like combustion instabilities or extinction and are sensi-tive to side effects as broadband noise generation at low-frequency. Consequently,Turbomeca was involved in the European project SILENCE(R) where efficient

14

technologies were developed to reduce significantly broadband noise around 2kHzby 5 dB but low-frequency core-noise was not addressed, nor well-known, in areal engine. To fill this gap, Turbomeca launched the Turboshaft Engine ExhaustNoise Identification (TEENI project) in the seventh European Framework of pro-gramme research with European partners. This project focused on several majorobjectives:

• identification and location of broadband noise sources within a real tur-boshaft engine,

• development of sensors able to measure unsteadiness of the flow from thecombustion chamber to the engine exit despite the harsh conditions,

• building of a database composed of simultaneous internal and external acous-tic measurements of stabilized operating points,

• development of broadband noise source breakdown techniques.

In parallel to these experimental investigations, significant efforts were made toprovide analytical and numerical tools dedicated to the combustion noise analysis:thanks to the growth of High-Performance Computing resources, computationalfluid dynamics are now a powerful tool to design the low-NOx combustors andanticipate the unstable behaviour of combustion process. Particularly, LES is be-coming a reliable method to predict turbulent and reactive flows within combustionchambers. Consequently, this method should provide a realistic estimation of noisesources within the combustion chamber. However, in order to deal with indirectcombustion noise generated in the turbine stages, Leyko [2010] and Garcia-Rama[2013] applied an actuator disk theory [Cumpsty and Marble, 1977] called CHO-RUS on realistic aero-engines coupled with LES. This thesis is the outcome ofthese previous and fruitful works and aims at the evaluation of a hybrid methodcalled CONOCHAIN combining LES simulations of combustion chamber, com-bustion noise computation using CHORUS and the far-field propagation with theHelmholtz solver AVSP. Using TEENI’s results, validation of this hybrid approachwill be made by comparing with experimental results from combustion chamberto the far-field .

First of all, the analysis of the experimental database provided by the TEENIproject will be made in the scope of combustion noise. In parallel, LES of a sector ofTEENI combustion chamber will be performed for two operating points to capturethe unsteadiness of the turbulent reactive flow and the acoustic sources withinthe combustor. To estimate the loss of information induced by the computationof only one sector of the chamber in the scope of combustion noise, the full-scale combustion chamber will be computed and compared to the single-sector

15

case. Using instantaneous LES fields, acoustic power generated by the combustionprocess will be computed using CHORUS and compared with internal experimentalmeasurements. Finally, the acoustic footprint of the computed combustion noisesources will be analysed and compared with the experimental far-field database.

This manuscript is organized into three different parts. The first contains theexperimental analysis of TEENI’s results and the description of CONOCHAINtool dedicated to combustion noise computation in realistic aero-engines. Thesecond part deals with LES of the TEENI’s combustion chamber and the last partconsists of the application of the CONOCHAIN method followed by a comparisonbetween experimental and numerical results:

• Part I : This part contains two chapters dealing with the experimental anal-ysis using TEENI’s database to investigate the combustion noise in a realengine on the one hand and a numerical approach called CONOCHAIN tocompute combustion noise generation within a modern aero-engine on theother hand. The first chapter focuses on the experimental set-up and the ded-icated signal processing techniques used to analyse the acoustic role of eachengine module from the combustion chamber to exhaust at low-frequency.The description of the numerical hybrid method used in this thesis to com-pute combustion noise is addressed in the second chapter. The actuator disktheory proposed by Cumpsty and Marble [1977] called CHORUS to mimicacoustic behaviour of turbine stages is described followed by the Helmtozsolver AVSP used to propagate the combustion-generated acoustic waves inthe far-field.

• Part II : This second part focuses on the Large Eddy simulations of theTEENI combustion chamber performed with AVBP. First simulations arebased on a axi-symmetric single sector of the TEENI’s annular combus-tor computed for two experimental operating points. After a descriptionof the LES solver AVBP, the numerical set-up is presented in which simu-lation parameters are detailed. Mechanisms of combustion-generated noiseare identified by analysing single-sector LES representative to two computedoperating points (low and high power cases). Finally, the LES of the fullannular combustion chamber is performed to estimate the benefits of a com-plete simulation compared with single-sector LES in terms of mean flow andunsteady features at the exit of the combustor.

• Part III : This last part is dedicated to the computation of combustionnoise propagation and generation within the turbine stages of the TEENIengine using LES results and the analytical method CHORUS: the com-puted acoustic powers at different locations within the turbine are compared

16

with the experimental database. Results show that indirect combustion noiseis mainly induced by the first turbine stages and is an important broadbandnoise source at low-frequency for turboshaft engines. Experimental trendsidentified in the first part are well-predicted with the hybrid approach. Thefull-scale simulation provides a better estimation of combustion noise thanthe single-sector calculations because of a better prediction of spatial un-steadiness description at the exit of the combustion chamber. Finally, theacoustic far-field is also computed using the Helmholtz solver AVSP-f andinteresting properties of the experimental acoustic footprint of the engine arewell-captured.

Fig. 8 depicts the flowchart and the main steps of the present work.

17

Part I: Experimental investigation of combustion noise in a turboshaft engineand presentation of CONOCHAIN methodology

Part II : Large-Eddy simulations of the TEENI combustion chamberdedicated to the combustion noise evaluation

Part III : Combustion noise computation in the turbine stages and in thefar-field with CONOCHAIN tool

Chap. I: Localisation and

identification of broadband acoustic

sources in a turboshaft engine

Chap. II: CONOCHAIN: Numerical

method to predict combustion-generated

noise in aero-engine

Chap. V: Single-sector LES of the

TEENI combustion chamber

Chap. VI: Full-scale LES of the

TEENI combustion chamber

Unsteady fields at the exit of the

combustor

Chap. VII: Combustion noise computation

within the turbine stages of TEENI engine

Chap. VIII: Propagation of

combustion-generated noise within the

far-field

Internal measurements

Acoustic far-field

Acoustic waves at the exit of the

engine

CONOCHAIN

Figure 8: Flowchart of the manuscript.

18

Part I

Experimental investigation ofcombustion noise in a turboshaft

engine and presentation ofCONOCHAIN methodology

19

Chapter 1

Localisation and identification ofbroadband acoustic sources in aturboshaft engine

Abstract This chapter deals with the study of broadband noise generation ina real helicopter engine. A full turboshaft engine is instrumented from the com-bustion chamber to the exhaust to capture unsteady pressure and temperaturefluctuations for several stabilized operating points. In addition to the internal mea-surements, the acoustic far-field is characterized by a set of microphones placed ona radius of 19.2m from the engine. The noise sources within the engine are iden-tified by applying breakdown techniques between different locations inside andoutside the engine. It was found that a narrowband at 200Hz corresponds to thedirect combustion noise and a large hump from 200Hz to 1200Hz can be attributedto the indirect combustion noise mainly generated by the high-pressure turbine inthe acoustic footprint of the engine. Moreover, the experimental acoustic direc-tivity pattern is qualitatively explained with a simple analytical model involvingtemperature gradients through the exhaust jet flow in the acoustic rays propaga-tion showing that this pattern is controlled to first order by the temperature fieldof the hot jet issuing into the atmosphere.

20

IntroductionIn aeronautical engines, the experimental characterisation of the generation of com-bustion noise remains a challenge because of the harsh conditions imposed by thecombustion chamber making the discrimination of direct and indirect combustionnoise sources in the radiated core noise difficult.

Few attempts have already been made to track combustion noise in real aero-engines. Using a ducted combustor with an exhaust subsonic nozzle where the jetvelocity range was 140-200 m/s, internal pressure and temperature fluctuationswere analysed to identify direct combustion noise [Plett et al., 1976] in the far-fieldacoustic footprint. It was found that a narrowband component close to 150-200 Hzin far-field acoustic spectra correlated with internal pressure fluctuations. Contrar-ily, temperature measurements were not sufficient to identify indirect combustionnoise component. The overall noise levels were 14 to 20 dB higher than from thesame experiment without combustion which showed the importance of combustionnoise. To ease our understanding, separation of entropy induced noise from thepure acoustic waves generated by combustion in a real gas turbine combustor wasalso addressed by Strahle [Strahle, 1978]. To do so, an aero-engine burner coupledwith a subsonic nozzle to induce mean pressure gradient at the outlet of the com-bustion chamber was used to generate indirect combustion noise. However, thelow-Mach number at the outlet of the nozzle was not sufficient to discriminate in-direct combustion noise generation. In the absence of turbine stages at the end ofthe combustion chamber, this experiment did not mimic perfectly the combustionnoise generation within an aero-engine. Krejsa [1987] proposed an identification ofcombustion noise components in the far-field acoustic footprint of a turbojet usinga noise breakdown technique between internal pressure signals in the combustionchamber and far-field microphones but high levels of jet noise made combustionnoise identification impossible. However, this method will be described and usedin this chapter with more success.

In regards to the difficulties encountered in these works, the identification ofcombustion noise mechanisms in a real engine aircraft requires :

• reduction of the other acoustic sources radiated at low-frequency,

• simultaneous measurements within the engine and in the far-field,

• dedicated noise breakdown techniques.

Jet noise is known to be a major contributor of core-noise at low-frequency inturbojet acoustic footprint. As presented in the introduction , Lighthill [1952]proposed a quadrupole source term due to turbulence generated noise. In thecase of homentropic flow, acoustic power produced by a turbulent jet followed

21

is proportional to a 8-th power law Mach number. Contrarily, when the low-velocity jet has a temperature different from the environment which correspondsto a turboshaft engine case, mixing and convective effects are dominant and lead todipole acoustic source generation [Morfey, 1973]. Then, the acoustic power scalesat 6-th power law of Mach number. For turboshaft engines, the acoustic powergenerated by the jet is then negligible because the Mach number never exceeds0,15. Finally, in the scope of broadband noise at low-frequency, these engines arethen good candidates because the absence of jet noise limits core-noise to twomajor components :• turbomachinery noise

• combustion noise.However, turbomachinery tonal noise are known to contribute at higher frequen-cies.

More recently, to improve our understanding in core-noise generation withinturboshaft engines, in the seventh European framework of programme for research,the Turboshaft Engine Exhaust Noise Identification (TEENI) project was dedi-cated to the location of acoustic sources in a realistic helicopter engine. Internaland external measurements were made to cover the entire downstream sectionfrom the combustion chamber to the far-field in real operating conditions. Theexperimental analysis of combustion noise presented in this chapter is based onthe TEENI’s database.

Characterisation of core-noise requires broadband noise breakdown techniques.In this work, different signal post-processing methods based on Discrete FourierTransform [Wirsching et al., 2006, Bendat and Piersol, 1971] are used. Particularly,the method used by Krejsa [1987] is used to identify combustion noise from internaland far-field measurements. Then, the experimental set-up of TEENI experimentis presented where a dedicated instrumentation was installed on a real engine torecord pressure and temperature fluctuations while preserving probes from burntproducts. Next, a discrimination of acoustic sources is made within the enginefrom the combustion chamber to the exhaust and in the far-field. Finally, thedirectivity properties of these acoustic sources are investigated.

My contribution to this study was the participation to the tests, the analysis ofTEENI data and the development of the processing techniques required to identifynoise sources due to combustion.

1.1 Signal post-processing techniquesThis first part describes signal post-processing techniques used in the experimentalanalysis of TEENI’s database: the extraction of relevant information contained in

22

experimental time series requires adapted signal processing techniques to limitsignal-to-noise ratio. Correlations techniques presented in the following sectionare rely on discrete Fourier transform and are briefly introduced here.

Discrete Fourier Transform

To deal with discrete periodic time signals known at N instants separated by asample duration T , Discrete Fourier Transform is the equivalent of the continuousFourier transform [Wirsching et al., 2006, Bendat and Piersol, 1971]. Let s(t) bethe continuous time signal which is the source of the data. The continuous Fouriertransform of s is

S(jω) =∫ ∞−∞

s(t)e−jωtdt (1.1)

where ω is the pulsation. Knowing N samples of s noted s[0], ..., s[N ] (Fig. 1.1),the DFT of s is

S(jω) =N−1∑k=0

s[k]e−jωkT . (1.2)

The constant sampling step over a time period T gives

TN−1

s(t)

s[k]

t

0N

Figure 1.1: Signal sampling representation where the blue colored line is the con-tinuous signal and the red dots are the discrete samples

S(n) =N−1∑k=0

s[k]e−jnk 2πN , (1.3)

23

The finite duration T of the signal s imposes the smallest computed frequencywhich is equal to 2π/T while the highest computed frequency is imposed byNyquist–Shannon sampling theore

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