The design parameters axial gap and stator count of highpressure turbine stages are evaluated numerically towards theirinfluence on the unsteady aerodynamic excitation of rotorblades. Of particular interest is if and how unsteadyaerodynamic considerations in the design could reduce the riskofhigh cycle fatigue (HCF) failures of the turbine rotor. A well-documented 2D/Q3D non-linear unsteady code (UNSFLO)is chosen to perform the stage flow analyses. The evaluatedresults are interpreted as aerodynamic excitation mechanisms onstream sheets neglecting 3D effects. Mesh studies andvalidations against measurements and 3D computations provideconfidence in the unsteady results. Three test cases areanalysed. First, a typical aero-engine high pressure turbinestage is studied at subsonic and transonic flow conditions,with four axial gaps (37% - 52% of cax,rotor) and two statorconfigurations (43 and 70 NGV). Operating conditions areaccording to the resonant conditions of the blades used inaccompanied experiments. Second, a subsonic high pressureturbine intended to drive the turbopump of a rocket engine isinvestigated. Four axial gap variations (10% - 29% ofcax,rotor) and three stator geometry variations are analysed toextend and generalise the findings made on the first study.Third, a transonic low pressure turbine rotor, known as theInternational Standard Configuration 11, has been modelled tocompute the unsteady flow due to blade vibration and comparedto available experimental data. Excitation mechanisms due to shock, potential waves andwakes are described and related to the work found in the openliterature. The strength of shock excitation leads to increasedpressure excitation levels by a factor 2 to 3 compared tosubsonic cases. Potential excitations are of a typical wavetype in all cases, differences in the propagation direction ofthe waves and the wave reflection pattern in the rotor passagelead to modifications in the time and space resolved unsteadypressures on the blade surface. The significant influence ofoperating conditions, axial gap and stator size on the wavepropagation is discussed on chosen cases. The wake influence onthe rotorblade unsteady pressure is small in the presentevaluations, which is explicitly demonstrated on the turbopumpturbine by a parametric study of wake and potentialexcitations. A reduction in stator size (towards R≈1)reduces the potential excitation part so that wake andpotential excitation approach in their magnitude. Potentials to reduce the risk of HCF excitation in transonicflow are the decrease of stator exit Mach number and themodification of temporal relations between shock and potentialexcitation events. A similar temporal tuning of wake excitationto shock excitation appears not efficient because of the smallwake excitation contribution. The increase of axial gap doesnot necessarily decrease the shock excitation strength neitherdoes the decrease of vane size because the shock excitation mayremain strong even behind a smaller stator. The evaluation ofthe aerodynamic excitation towards a HCF risk reduction shouldonly be done with regard to the excited mode shape, asdemonstrated with parametric studies of the mode shapeinfluence on excitability. <b>Keywords:</b>Aeroelasticity, Aerodynamics, Stator-RotorInteraction, Excitation Mechanism, Unsteady Flow Computation,Forced Response, High Cycle Fatigue, Turbomachinery,Gas-Turbine, High-Pressure Turbine, Turbopump, CFD, Design

<p>The design parameters axial gap and stator count of highpressure turbine stages are evaluated numerically towards theirinfluence on the unsteady aerodynamic excitation of rotorblades. Of particular interest is if and how unsteadyaerodynamic considerations in the design could reduce the riskofhigh cycle fatigue (HCF) failures of the turbine rotor.</p><p>A well-documented 2D/Q3D non-linear unsteady code (UNSFLO)is chosen to perform the stage flow analyses. The evaluatedresults are interpreted as aerodynamic excitation mechanisms onstream sheets neglecting 3D effects. Mesh studies andvalidations against measurements and 3D computations provideconfidence in the unsteady results. Three test cases areanalysed. First, a typical aero-engine high pressure turbinestage is studied at subsonic and transonic flow conditions,with four axial gaps (37% - 52% of cax,rotor) and two statorconfigurations (43 and 70 NGV). Operating conditions areaccording to the resonant conditions of the blades used inaccompanied experiments. Second, a subsonic high pressureturbine intended to drive the turbopump of a rocket engine isinvestigated. Four axial gap variations (10% - 29% ofcax,rotor) and three stator geometry variations are analysed toextend and generalise the findings made on the first study.Third, a transonic low pressure turbine rotor, known as theInternational Standard Configuration 11, has been modelled tocompute the unsteady flow due to blade vibration and comparedto available experimental data.</p><p>Excitation mechanisms due to shock, potential waves andwakes are described and related to the work found in the openliterature. The strength of shock excitation leads to increasedpressure excitation levels by a factor 2 to 3 compared tosubsonic cases. Potential excitations are of a typical wavetype in all cases, differences in the propagation direction ofthe waves and the wave reflection pattern in the rotor passagelead to modifications in the time and space resolved unsteadypressures on the blade surface. The significant influence ofoperating conditions, axial gap and stator size on the wavepropagation is discussed on chosen cases. The wake influence onthe rotorblade unsteady pressure is small in the presentevaluations, which is explicitly demonstrated on the turbopumpturbine by a parametric study of wake and potentialexcitations. A reduction in stator size (towards R≈1)reduces the potential excitation part so that wake andpotential excitation approach in their magnitude.</p><p>Potentials to reduce the risk of HCF excitation in transonicflow are the decrease of stator exit Mach number and themodification of temporal relations between shock and potentialexcitation events. A similar temporal tuning of wake excitationto shock excitation appears not efficient because of the smallwake excitation contribution. The increase of axial gap doesnot necessarily decrease the shock excitation strength neitherdoes the decrease of vane size because the shock excitation mayremain strong even behind a smaller stator. The evaluation ofthe aerodynamic excitation towards a HCF risk reduction shouldonly be done with regard to the excited mode shape, asdemonstrated with parametric studies of the mode shapeinfluence on excitability.</p><p><b>Keywords:</b>Aeroelasticity, Aerodynamics, Stator-RotorInteraction, Excitation Mechanism, Unsteady Flow Computation,Forced Response, High Cycle Fatigue, Turbomachinery,Gas-Turbine, High-Pressure Turbine, Turbopump, CFD, Design</p>

Les roues aubagées sont des composants dont le comportement dynamique est très sensible au désaccordage involontaire causé par les tolérances de fabrication qui rendent les aubes légèrement différentes les unes des autres. Cette sensibilité se traduit généralement par une amplification des vibrations. L’objectif de ce travail de recherche est de proposer de nouvelles méthodologies permettant d’optimiser la conception en vibration des roues aubagées vis à vis du désaccordage involontaire. L’optimisation est faite pour la réponse forcée et sous une contrainte de marge à la stabilité aéroélastique. Dans ce contexte, le désaccordage intentionnel par modification géométrique des aubes est utilisé. Pour réduire les temps de calcul, une nouvelle méthode de réduction de modèles de roues aubagées désaccordées intentionnellement par modification géométrique est développée et validée. La modélisation des incertitudes incluant le désaccordage involontaire, est faite avec une approche probabiliste non paramétrique. Une application à l’optimisation de la conception en vibration d’une roue réelle a finalement été effectuée en deux phases : (1) une optimisation de la répartition des différentes aubes désaccordées intentionnellement sur la roue aubagée et (2) une optimisation du niveau de modification géométrique de ces aubes. Les résultats montrent qu’une conception robuste par désaccordage intentionnel de la roue aubagée a été effectuée / Bladed disks are components which dynamic behaviour are very sensitive to mistuning induced by the manufacturing process which makes blades differ from one another. This sensitivity increases in general the vibrations. The objective of this research is to propose new methods for optimizing design in vibration of bladed disks with respect to mistuning. Optimization is done for the forced response while keeping a sufficient aeroelastic stability margin. In this context, detuning by modifying geometrically the blades’ shapes is used. To reduce numerical computational costs, a new reduction method for geometrically detuned bladed disks is developed and validate. Uncertainties modeling including mistuning is done with a non-parametric probabilistic approach. An application by optimizing the design in vibration of a realistic bladed disk is finally done in two steps : (1) An optimization of the different detuned blades arrangements around the disk and (2) an optimization of the geometric modification level of blades. The results show that a robust design of the bladed disks has been done using geometric detuning

Forced response which is blade vibration due to an external excitation can lead to blade failure. The estimation of the level of vibration is dependent on the determination of aerodynamic damping. This thesisinvestigates the determination of aerodynamic damping at high reduced frequencies in turbomachines. The aerodynamic damping was calculated by a linearized Navier-Stokes flow solver with exact 3D non-reflecting boundary conditions. The method was validated using the two-dimensional test cases (Standard Configuration 5 and 8). Thereafter, two 3D profiles were also investigated: an aeroelastic turbine rig (AETR) which is a subsonic turbine case, and a virtual integrated compressor (VINK) which is a transonic compressor case. In AETR case, the first bending mode with reduced frequency 2.0 was studied. The 3D acoustic modes were calculated and the rate of decay was plotted as a function of nodal diameter and radial order. This plot identified six acoustic resonant points which included two points corresponding to the first radial order. The six resonance points correspond to six peaks in the damping curve. In VINK case, the fifth mode (1854 Hz, reduced frequency 3.1) was investigated. Acoustic resonance was predicted to occur for the first and second radial orders at the inlet. It was concluded that the higher order resonance points are influencing the damping curve. There were some inconsistencies in the results and grid convergence was not achieved. These inconsistencies were due to the difficulty in calculating the acoustic modes at the transonic inlet with an impinging shock. / Aerodynamiskt påtvingade vibrationer, som är bladvibrationer på grund av en extern excitation kan leda till haveri. Prediktering av vibrationen är beroende av bestämning av aerodynamisk dämpning. I detta arbete undersöks bestämningen av aerodynamisk dämpning vid höga reducerade frekvenser i turbomaskiner. Den aerodynamiska dämpningen beräknades genom en linjäriserad Navier-Stokeslösare med exakta 3D icke-reflekterande gränsvillkor. Metoden validerades med hjälp av de tvådimensionella testfallen (Standardkonfiguration 5 och 8). Därefter undersöktes två 3D-profiler: en aeroelastisk turbinrigg (AETR), som är en subsonisk turbinenhet och en virtuell integrerad kompressor (VINK) som är ett transoniskt kompressorfall. I AETRfallet undersöktes det första böjningsformen med reducerad frekvens 2.0. 3D akustiska lägen beräknades och graden av förfall visades som en funktion av noddiameter och radiell grad. Denna metod identifierade sex akustiska resonanspunkter som innehöll två punkter som motsvarade den första radiella graden. De sex resonanspunkterna motsvarar sex toppar i dämpningskurvan. I VINK-fallet undersöktes den femte svängningsformen (1854 Hz, reducerad frekvens 3.1). Akustisk resonans förutspåddes inträffa för första och andra radiella graden vid inloppet. Slutsatsen drogs att de högre ordningens resonanspunkter påverkar dämpningskurvan. Det fanns vissa inkonsekvenser i resultaten och gridkonvergens uppnåddes inte. Dessa inkonsekvenser berodde på svårigheten att beräkna de akustiska svängningsformerna vid det transoniska inloppet med en stötvåg.

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The thesis comprises a collection of four papers with preceding summary and supplementary appendices. The core investigation solely is of experimental nature although reference and comparisons with numerical models will be addressed. The first admission stage in an industrial steam turbine is referred to as the control stage if partial admission is applied. In order to achieve high part load efficiency and a high control stage output it is routinely applied in industrial steam turbines used in combined heat and power plants which frequently operate at part load. The inlet flow is individually throttled into separate annular arcs leading to the first stator row. Furthermore, partial admission is sometimes used in small-scale turbine stages to avoid short vanes/blades in order to reduce the impact from the tip leakage and endwall losses. There are three main aspects regarding partial admission turbines that need to be addressed. Firstly, there are specific aerodynamic losses: pumping-, emptying- and filling losses attributed to the partial admission stage. Secondly, if it is a multistage turbine, the downstream stages experience non-periodic flow around the periphery and circumferential pressure gradients and flow angle variations that produce additional mixing losses. Thirdly, the aeromechanical condition is different compared to full admission turbines and the forcing on downstream components is also circumferentially non-periodic with transient load changes. Although general explanations for partial admission losses exist in open literature, details and loss mechanisms have not been addressed in the same extent as for other sources of losses in full admission turbines. Generally applicable loss correlations are still lacking. High cycle fatigue due to unforeseen excitation frequencies or due to under estimated force magnitudes, or a combination of both causes control stage breakdowns. The main objectives of this thesis are to experimentally explore and determine performance and losses for a wide range of partial admission configurations. And, to perform a forced response analysis from experimental data for the axial test turbine presented herein in order to establish the forced response environment and identify particularities important for the design of control stages. Performance measurements concerning the efficiency trends and principal circumferential and axial pressure distortions demonstrate the applicability of the partial admission setup employed in the test turbine. Findings reveal that the reaction degree around the circumference varies considerably and large flow angle deviations downstream of the first rotor are present, not only in conjunction to the sector ends but stretching far into the admission sector. Furthermore, it is found that the flow capacity coefficient increases with reduced admission degree and the filling process locally generates large rotor incidence variation associated with high loss. Moreover, the off design conditions and efficiency deficit of downstream stages are evaluated and shown to be important when considering the overall turbine efficiency. By going from one to two arcs at 52.4% admission nearly a 10% reduction in the second stage partial admission loss, at design operating point was deduced from measurements. Ensemble averaged results from rotating unsteady pressure measurements indicate roughly a doubling of the normalized relative dynamic pressure at rotor emptying compared to an undisturbed part of the admission jet for 76.2% admission. Forced response analysis reveals that a large number of low engine order force impulses are added or highly amplified due to partial admission because of the blockage, pumping, loading and unloading processes. For the test turbine investigated herein it is entirely a combination of number of rotor blades and low engine order excitations that cause forced response vibrations. One possible design approach in order to change the force spectrum is to alter the relationship between admitted and non-admitted arc lengths. / Denna sammanläggningsavhandling består av fyra artiklar och föregås av en sammanfattning med kompletterande bilagor. Kärnan av undersökningen är experimentell även om referenser och jämförelser med numeriska modeller förekommer där så bedöms lämpligt. Det första steget i en industriell ångturbin kallas reglersteg om partialpådrag tillämpas. Det används rutinmässigt i kraftvärmeanläggningar som ofta körs vid dellaster för att åstadkomma en hög dellastverkningsgrad och hög stegeffekt. Inloppsflödet delas in separata och individuellt strypreglerade pådragsbågar som leder till det första munstycksgittret. Ibland används partialpådrag i små turbiner för att undvika korta blad och på så sätt minska takläckage och ändväggsförlusternas inflytande på den totala förlusten. Det finns i huvudsak tre aerodynamiska/aeromekaniska egenheter som bör beaktas. Först det första är det speciella aerodynamiska förluster associerade till partialpådrag eller reglersteget: ventilations-, tömnings och fyllningsförluster. För det andra, om det är en flerstegsturbin påverkas också nedströms steg negativt av det asymmetriska flödet runt omkretsen som innefattar stora tryckvariationer och flödesvinkelvariationer. För det tredje är den aeromekaniska situationen speciell jämfört med ett fullpådraget steg. För partialpådrag existerar dynamiska krafter med snabba laständringar vid in och utpassering i pådragsbågen. Även om det existerar generella förklaringar i den öppna litteraturen angående förluster så har inte förlustmekanismerna utretts i samma omfattning jämfört med fullpådrag. Ingen generell förlustkorrelation finns. Utmattning på grund oförutsedda excitationsfrekvenser, underskattade kraftamplituder eller en kombination av båda orsakar reglerstegshaveri för ångturbinintressenter. De huvudsakliga målsättningarna med denna studie är att experimentellt utforska och bestämma prestanda och förluster för ett stort antal partialpådragskonfigurationer. Samt att genomföra en vibrationsanalys (relaterat till aerodynamiska kraftimpulser) utifrån mätdata från provturbinen avhandlad häri. Detta för att kartlägga de aeromekaniska förutsättningarna och om möjligt identifiera egenheter viktiga för konstruktion av reglersteg. Prestandamätningar rörande verkningsgradstrender och generella strömningsvariationer runt omkretsen bekräftar resultat från den öppna litteraturen och därmed demonstrerar dugligheten av den partialpådragskonfiguration som används i luftprovturbinen. Dessutom visar resultaten bland annat att reaktionsgraden varierar kraftigt runt omkretsen med stora variationer i rotorns utloppsvinkel inte enbart i anslutning till sektorändar utan långt in i pådragssektorn. Flödeskapacitetskoefficienten eller turbinkonstanten ökar med minskat pådrag och fyllningsprocessen genererar stora variationer i rotorns inloppsvinkel förknippade med höga förluster. Det är viktigt att beakta dellastförutsättningarna och verkningsgradsminskningen för nedströms steg. Genom att använda två pådragsbågar istället för en för ett givet pådrag av 52,4% minskar partialpådragsförlusterna för nedströmssteget med nästan 10 % vid designpunkten, härlett från mätningar. Samlade medelvärden från roterande instationära mätningar visar på en fördubbling av det relativa dynamiska trycket vid rotortömning jämfört med en opåverkad del av pådragsbågen. Vibrationsanalys (relaterat till aerodynamiska kraftimpulser) av mätdata avslöjar att partialpådrag orsakar en stor mängd kraftimpulser med låga varvtalsmultiplar, främst från ventilationen och påavlastningsprocesserna. För provturbinen så är det helt och hållet kombinationer mellan antalet rotorblad och dessa kraftimpulser som orsakar strömningspåverkade vibrationer. Ett möjligt tillvägagångssätt konstruktionsmässigt för att ändra kraftspektrumet är att ändra längförhållandet mellan pådragen och blockerad del. / QC 20120109

Forced response analysis of bladed disk assemblies plays a vital role in rotor blade design and has been drawing a great deal of attention both from research community and engine industry for more than half a century. However because of the phenomenon called &lsquo / mistuning&rsquo / , which destroys the cyclic symmetry of a rotor, there have been several difficulties related to forced response analysis ever since, two of which are addressed in this thesis: efficient non-linear forced response analysis of mistuned bladed disks and mistuning identification. On the nonlinear analysis side, a new solution approach is proposed studying the combined effect of non-linearity and mistuning, which is relatively recent in this research area and generally conducted with methods whose convergence and accuracy depend highly on the number of degrees of freedom where non-linear elements are attached. The proposed approach predicts nonlinear forced response of mistuned bladed disk assemblies considering any type of nonlinearity. In this thesis, special attention is given to the friction contact modeling of bladed disks which is the most common type of nonlinearity found in bladed disk assemblies. In the modeling of frictional contact a friction element which enables normal load variation and separation of the contact interface in three-dimensional space is utilized. Moreover, the analysis is carried out in modal domain where the differential equations of motions are converted to a set of non-linear algebraic equations using harmonic balance method and modal superposition technique. Thus, the number of non-linear equations to be solved is independent of the number of non-linear elements used. On the mistuning identification side, a new method is enclosed herein which makes use of neural networks to assess unknown mistuning parameters of a given bladed disk assembly from its assembly modes, thus being suitable for integrally bladed disks. The method assumes that a tuned mathematical model of the rotor under consideration is readily available, which is always the case for today&rsquo / s realistic bladed disk assemblies. A data set of selected mode shapes and natural frequencies is created by a number of simulations performed by mistuning the tuned mathematical model randomly. A neural network created by considering the number of modes, is then trained with this data set for being used to identify mistuning of the rotor from measured data. On top of these, a new adaptive algorithm is developed for harmonic balance method, several intentional mistuning patterns are investigated via excessive Monte-Carlo simulations and a new approach to locate, classify and parametrically identify structural non-linearities is introduced.

De nombreux éléments de structures de génie civil sont élancés et partiellement enfouis dans un milieu solide. Les ondes guidées sont souvent utilisées pour le contrôle non destructif (CND) de ces éléments. Ces derniers sont alors considérés comme des guides d’ondes ouverts, dans lesquels la plupart des ondes sont atténuées par des fuites dans le milieu environnant. D’autre part le problème est non borné, ce qui le rend difficile à appréhender sur le plan numérique. La combinaison d’une approche par éléments finis semi-analytique (SAFE) et de la méthode des couches parfaitement adaptées (PML) a été utilisée dans une thèse antérieure pour calculer numériquement trois types de modes (modes piégés, modes à fuite et modes de PML). Seuls les modes piégés et à fuite sont utilisés pour la représentation des courbes de dispersion. Les modes de PML sont non intrinsèques à la physique. L’objectif premier de cette thèse est d’obtenir, par superposition modale sur les modes calculés, les champs émis et diffracté dans les guides d’ondes ouverts. Nous montrons dans un premier temps que les trois types de modes appartiennent à la base modale. Une relation d’orthogonalité est obtenue dans la section du guide(incluant la PML) pour garantir l’unicité des solutions. La réponse forcée du guide peut alors être calculée rapidement par une somme sur les modes en tout point du guide. Des superpositions modales sont également utilisées pour construire des frontières transparentes au bord d’un petit domaine élément fini incluant un défaut, permettant ainsi de calculer le champ diffracté. Au cours de ces travaux, nous étudions les conditions d’approximation des solutions par des superpositions modales, limitées seulement aux modes à fuite, ce qui permet de réduire le coût des calculs. De plus, la généralité des méthodes proposées est démontrée par des calculs hautes fréquences (intéressantes pour le CND) et sur des guides tridimensionnels. Le deuxième objectif de cette thèse est de proposer une méthode d’imagerie pour la localisation de défauts. La méthode de l’imagerie topologique est appliquée aux guides d’ondes. Le cadre théorique général, de type optimisation sous contrainte, est rappelé. Le formalisme modal permet un calcul rapide de l’image. Nous l’appliquons pour simuler un guide d’onde endommagé, et nous montrons l’influence du type de champ émis (monomodal, dispersif,multimodal) ainsi que des configurations de mesure sur la qualité de l’image obtenue. / Various elements of civil engineering structures are elongated and partially embedded in a solid medium. Guided waves can be used for the nondestructive evaluation (NDE) of such elements. The latteris therefore considered as an open waveguide, in which most of waves are attenuated by leakage losses into the surrounding medium. Furthermore, the problem is difficult to solve numerically because of its unboundedness. In aprevious thesis, it has been shown that the semi-analytical finite-element method (SAFE) and perfectly matched layers(PML) can be coupled for the numerical computation of modes. It yields three types of modes: trapped modes,leaky modes and PML modes. Only trapped and leaky modes are useful for the post-processing of dispersion curves. PML modes are non-intrinsic to the physics. The major aim of this thesis is to obtain the propagated and diffracted fields, based on modal superpositions on the numerical modes. First, we show that the three types of modes belong to the modal basis. To guarantee the uniqueness of the solutions an orthogonality relationship is derived on the section including the PML. The forced response can then be obtained very efficiently with a modal expansion at any point of the waveguide. Modal expansions are also used to build transparent boundaries at the cross-sections of a small finite-element domain enclosing a defect, thereby yielding the diffracted field. Throughout this work, we study whether solutions can be obtained with modal expansions on leaky modes only, which enables to reduce the computational cost. Besides, solutions are obtained at high frequencies (which are of interest for NDE) and in tridimensional waveguides, which demonstrates the generality of the methods. The second objective of this thesis is to propose an imaging method to locate defects. The topological imaging method is applied to a waveguide configuration. The general theoretical framework is recalled, based on constrained optimization theory. The image can be quickly computed thanks to the modal formalism. The case of a damaged waveguide is then simulated to assess the influence on image quality of the emitted field characteristics (monomodal, dispersive or multimodal)and of the measurement configuration.

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