Les instabilités thermo-acoustiques résultent de l'interaction entre les oscillations de pression acoustique et les fluctuations du taux de dégagement de chaleur de la flamme. Ces instabilités de combustion sont particulièrement préoccupantes en raison de leur fréquence dans les turbines à gaz modernes et à faible émission. Leurs principaux effets indésirables sont une réduction du temps de fonctionnement du moteur en raison des oscillations de grandes amplitudes ainsi que de fortes vibrations à l'intérieur de la chambre de combustion. La simulation numérique est maintenant devenue une approche clé pour comprendre et prédire ces instabilités dans la phase de conception industrielle. Cependant, la prédiction de ce phénomène reste difficile en raison de sa complexité; cela se confirme lorsque les paramètres physiques du processus de modélisation sont incertains, ce qui est pratiquement toujours le cas pour des systèmes réels.Introduire la quantification des incertitudes pour la thermo-acoustique est le seul moyen d'étudier et de contrôler la stabilité des chambres de combustion qui fonctionnent dans des conditions réalistes; c'est l'objectif de cette thèse.Dans un premier temps, une chambre de combustion académique (avec un seul injecteur et une seule flamme) ainsi que deux chambres de moteurs d'hélicoptère (avec N injecteurs et des flammes) sont étudiés. Les calculs basés sur un solveur de Helmholtz et un outil quasi-analytique de bas ordre fournissent des estimations appropriées de la fréquence et des structures modales pour chaque géométrie. L'analyse suggère que la réponse de la flamme aux perturbations acoustiques joue un rôle prédominant dans la dynamique de la chambre de combustion. Ainsi, la prise en compte des incertitudes liées à la représentation de la flamme apparaît comme une étape nécessaire vers une analyse robuste de la stabilité du système.Dans un second temps, la notion de facteur de risque, c'est-à-dire la probabilité pour un mode thermo-acoustique d'être instable, est introduite afin de fournir une description plus générale du système que la classification classique et binaire (stable / instable). Les approches de modélisation de Monte Carlo et de modèle de substitution sont associées pour effectuer une analyse de quantification d'incertitudes de la chambre de combustion académique avec deux paramètres incertains (amplitude et temps de réponse de la flamme). On montre que l'utilisation de modèles de substitution algébriques réduit drastiquement le nombre de calculs initiales, donc la charge de calcul, tout en fournissant des estimations précises du facteur de risque modal. Pour traiter les problèmes multidimensionnel tels que les deux moteurs d'hélicoptère, une stratégie visant à réduire le nombre de paramètres incertains est introduite. La méthode <<Active Subspace>> combinée à une approche de changement de variables a permis d'identifier trois directions dominantes (au lieu des N paramètres incertains initiaux) qui suffisent à décrire la dynamique des deux systèmes industriels. Dès lors que ces paramètres dominants sont associés à des modèles de substitution appropriés, cela permet de réaliser efficacement une analyse de quantification des incertitudes de systèmes thermo-acoustiques complexes.Finalement, on examine la perspective d'utiliser la méthode adjointe pour analyser la sensibilité des systèmes thermo-acoustiques représentés par des solveurs 3D de Helmholtz. Les résultats obtenus sur des cas tests 2D et 3D sont prometteurs et suggèrent d'explorer davantage le potentiel de cette méthode dans le cas de problèmes thermo-acoustiques encore plus complexes. / Thermoacoustic instabilities result from the interaction between acoustic pressure oscillations and flame heat release rate fluctuations. These combustion instabilities are of particular concern due to their frequent occurrence in modern, low emission gas turbine engines. Their major undesirable consequence is a reduced time of operation due to large amplitude oscillations of the flame position and structural vibrations within the combustor. Computational Fluid Dynamics (CFD) has now become one a key approach to understand and predict these instabilities at industrial readiness level. Still, predicting this phenomenon remains difficult due to modelling and computational challenges; this is even more true when physical parameters of the modelling process are uncertain, which is always the case in practical situations. Introducing Uncertainty Quantification for thermoacoustics is the only way to study and control the stability of gas turbine combustors operated under realistic conditions; this is the objective of this work.First, a laboratory-scale combustor (with only one injector and flame) as well as two industrial helicopter engines (with N injectors and flames) are investigated. Calculations based on a Helmholtz solver and quasi analytical low order tool provide suitable estimates of the frequency and modal structures for each geometry. The analysis suggests that the flame response to acoustic perturbations plays the predominant role in the dynamics of the combustor. Accounting for the uncertainties of the flame representation is thus identified as a key step towards a robust stability analysis.Second, the notion of Risk Factor, that is to say the probability for a particular thermoacoustic mode to be unstable, is introduced in order to provide a more general description of the system than the classical binary (stable/unstable) classification. Monte Carlo and surrogate modelling approaches are then combined to perform an uncertainty quantification analysis of the laboratory-scale combustor with two uncertain parameters (amplitude and time delay of the flame response). It is shown that the use of algebraic surrogate models reduces drastically the number of state computations, thus the computational load, while providing accurate estimates of the modal risk factor. To deal with the curse of dimensionality, a strategy to reduce the number of uncertain parameters is further introduced in order to properly handle the two industrial helicopter engines. The active subspace algorithm used together with a change of variables allows identifying three dominant directions (instead of N initial uncertain parameters) which are sufficient to describe the dynamics of the industrial systems. Combined with appropriate surrogate models construction, this allows to conduct computationally efficient uncertainty quantification analysis of complex thermoacoustic systems.Third, the perspective of using adjoint method for the sensitivity analysis of thermoacoustic systems represented by 3D Helmholtz solvers is examined. The results obtained for 2D and 3D test cases are promising and suggest to further explore the potential of this method on even more complex thermoacoustic problems.

The predictive design of fuel injection hardware used for active combustion control is not well established in the gas turbine industry. The primary reason for this is that the underlying mechanisms governing the flow rate authority downstream of the nozzle are not well understood. A detailed investigation of two liquid fuel flow modulation configurations is performed in this thesis: a piston and a throttle-valve configuration. The two systems were successfully built with piezoelectric actuation to drive the prime movers proportionally up to 800 Hz. Discussed in this thesis are the important constituents of the fuel injection system that affect heat release authority: the method of fuel modulation, uncoupled dynamics of several components, and the compressibility of air trapped in the fuel line. Additionally, a novel technique to model these systems by way of one-dimensional, linear transmission line acoustic models was developed to successfully characterize the principle of operation of the two systems. Through these models, insight was gained on the modes through which modulation authority was dissipated and on methods through which successful amplitude scaling would be possible. At high amplitudes, it was found that the models were able to successfully predict the actual performance reasonably well for the piston device. A proportional phase shifting controller was used to test the authority on a 40-kW rig with natural longitudinal modes. Results show that, under limited operating conditions, the sound pressure level at the limit cycle frequency was reduced by about 26 dB and the broadband energy was reduced by 23 dB. Attenuation of the fuel pulse at several combustor settings was due to fluctuating vorticity and temporal droplet distribution effects. / Master of Science

Lean, premixed combustion has enjoyed increased application due to the need to reduce pollutant emissions. Unfortunately, operating the flame at lean conditions increases susceptibility to thermoacoustic (TA) instability. Self-excited TA instabilities are a result of the coupling of the unsteady heat release rate of the flame with the acoustics of the combustion chamber. The result is large pressure oscillations that degrade performance and durability of combustion systems. Industry currently has no reliable tool to predict instabilities a priori. CFD simulations of full-scale, turbulent, reacting flows remain unrealizable. The work in this paper is part of a study that focuses on developing compact models of TA instabilities, i.e. acoustics and flame dynamics. Flame dynamics are defined as the response in heat release to acoustic perturbations. Models of flame dynamics can be coupled with models of combustor enclosure acoustics to predict TA instabilities. In addition, algorithms to actively control instabilities can be based on these compact models of flame dynamics and acoustics. The work outlined in this thesis aims at determining the flame dynamics model experimentally. Velocity perturbations are imparted on laminar and turbulent flames via a loudspeaker upstream of the flame. The response of the flame is observed through two measurements. Hydroxyl radical (OH*) chemiluminescence indicates the response in chemical reaction rate. Tunable Diode Laser Absorption Spectroscopy (TDLAS), centered over two water absorption features, allows a dynamic measurement of the product gas temperature. The response in product gas temperature directly relates to the enthalpy fluctuations that couple to the acoustics. Experimental frequency response functions of a laminar, flat-flame burner and a turbulent, swirl-stabilized combustor will be presented as well as empirical low-order models of flame dynamics. / Master of Science

Increasing concerns over the condition of our environment and its long term health have led to the development of greener combustion techniques for use in turbomachinery applications. Lean Direct Injection is an active area of research for how fuel is introduced and burned in the combustor section of a jet engine or land based liquid fuel turbine. Overall lean combustion results in lower NOx emmisions while direct injection insures shorter combustor lengths. Lean Direct Injection and other lean burning combustor designs are susceptible to thermoacoustic instabilities. The SARA or Synchronously Actuated Response Atomizer is a liquid fuel atomizer and supply system designed to allow for the active control of droplet size, cone angle, and mass flow rate. These three parameters have been shown to be important in controlling combustion quality and heat release. This research investigates the capabilities of the SARA design in a series of non-reacting tests. Static and Dynamic tests were performed on the SARA nozzle with a maximum actuation of 400 Hz. Also, a novel use of hot-film anemometry was developed to measure the dynamic flow rate fluctuations. / Master of Science

In order to predict the linear stability of combustion systems in industrial-scale gas turbines, a stability analysis was completed using models generated for each of the major dynamic components. Changes in the combustion process of gas turbines to reduce emissions has resulted in large amplitude pressure oscillations associated with a coupling between the natural acoustic modes of the combustor and the unsteady heat release from the flame. Detailed models of the acoustics and the heat release processes were created and assembled, with a time delay element and the appropriate scaling, into a system block diagram to investigate the stability of the system using linear system theory. Wherever possible the analytical models were validated with experimental data. The main goal of this work was to create a design methodology which could be used by industry to predict where instabilities were likely to occur during the design phase. Results show that the system based stability analysis can predict some of the instability frequencies seen in the experimental data, but more refined models are needed to predict every instability. Future work will involve designing experiments to validate and refine the dynamic models already developed. / Master of Science

Lean premixed fuel-air conditions in large gas turbines are used to improve efficiency and reduce emissions. These conditions give rise to large undamped pressure oscillations at the combustor's natural frequencies which reduce the turbine's longevity and reliability. Active control of the pressure oscillations, called thermoacoustic instabilities, has been sought as passive abatement of these instabilities does not provide adequate damping and is often impractical on a large scale. Phase shift control of the instabilities is perhaps the simplest and most popular technique employed but often does not provide good performance in that controller induced secondary instabilities are generated with increasing loop gain. This thesis investigates the general underlying cause of the secondary instabilities and shows that high average group delay through the frequency region of the instability is the root of the problem. This average group delay is then shown to be due not only the controller itself but can also be associated with other components and inherent characteristics of the control loop such as actuators and time delay, respectively. An "optimum" phase shift controller, consisting of an appropriate shift in phase and a low order, wide bandwidth bandpass filter, is developed for a Rijke tube combustor and shown to closely match the response of an LQG controller designed only for system stabilization. Both the optimal phase shifter and the LQG controller are developed based on a modified model of the thermoacoustic loop which takes into account the change in density of the combustion reactants at the flame location. Additionally, the system model is coupled with a model of the control loop and then validated by comparison of simulated results to experimental results using nearly identical controllers. / Master of Science

The first part of the thesis focuses on developing a numerical methodology to simulate the acoustic properties of a hybrid liner consisting of a perforated plate, a porous layer and a Helmholtz cavity. Liners are always a standard way to reduce noise in today’s aeroengines, e.g. the fan noise can be reduced effectively through the installation of acoustic liners as wall treatments in the ducts. In order to optimize a liner in the design phase, an accurate and efficient prediction tool is of interests. Hence, a unified Linearized Navier-Stokes equations(LNSE) approach has been implemented in the thesis, combining the LNSE in frequency domain with the fluid equivalent model. The LNSE is applied in the vicinity of the perforated plate to simulate sound propagation including viscous damping effect, and the fluid equivalent model is used to model the sound propagation in the porous material including absorption. The second part of the thesis focuses on the prediction of thermoacoustic instabilities. Thermoacoustic instabilities arise when positive coupling occurs between the flame and the acoustics in the feedback loop, i.e. the flame acts as an amplifier of the disturbances (acoustic or fluid) at a natural frequency of the combustion system. Once the thermoacoustic instabilities occur, it will lead to extremely high noise levels within a relatively narrow frequency range, resulting in a huge damage to the structure of the combustors. Hence, a solution must be found, which breaks the link between the combustion process and the structural acoustics. The numerical prediction of thermoacoustic instabilities in the thesis is performed by two different numerical methodologies. One solves the Helmholtz equation in combination of the flame n − tau model with the low Mach number assumptions, and the other solves the Linearized Navier-Stokes equations in frequency domain with mean flow. The result show that the mean flow has a significant effect on the thermoacoustic instabilities, which is non-negligible when the Mach number reaches to 0.15. / <p>QC 20151221</p> / TANGO

The persistent thrust for a cleaner, greener environment has prompted air pollution regulations to be enforced with increased stringency by environmental protection bodies all over the world. This has prompted gas turbine manufacturers to move from non-premixed combustion to lean, premixed combustion. These lean premixed combustors operate quite fuel-lean compared to the stochiometric, in order to minimize CO and NOx productions, and are very susceptible to oscillations in any of the upstream flow variables. These oscillations cause the heat release rate of the flame to oscillate, which can engage one or more acoustic modes of the combustor or gas turbine components, and under certain conditions, lead to limit cycle oscillations. This phenomenon, called thermoacoustic instabilities, is characterized by very high pressure oscillations and increased heat fluxes at system walls, and can cause significant problems in the routine operability of these combustors, not to mention the occasional hardware damages that could occur, all of which cumulatively cost several millions of dollars. In a bid towards understanding this flow-flame interaction, this research works studies the heat release response of premixed flames to oscillations in reactant equivalence ratio, reactant velocity and pressure, under conditions where the flame preheat zone is convectively compact to these disturbances, using the G-equation. The heat release response is quantified by means of the flame transfer function and together with combustor acoustics, forms a critical component of the analytical models that can predict combustor dynamics. To this end, low excitation amplitude (linear) and high excitation amplitude (nonlinear) responses of the flame are studied in this work. The linear heat release response of lean, premixed flames are seen to be dominated by responses to velocity and equivalence ratio fluctuations at low frequencies, and to pressure fluctuations at high frequencies which are in the vicinity of typical screech frequencies in gas turbine combustors. The nonlinear response problem is exclusively studied in the case of equivalence ratio coupling. Various nonlinearity mechanisms are identified, amongst which the crossover mechanisms, viz., stoichiometric and flammability crossovers, are seen to be responsible in causing saturation in the overall heat release magnitude of the flame. The response physics remain the same across various preheat temperatures and reactant pressures. Finally, comparisons between the chemiluminescence transfer function obtained experimentally and the heat release transfer functions obtained from the reduced order model (ROM) are performed for lean, CH4/Air swirl-stabilized, axisymmetric V-flames. While the comparison between the phases of the experimental and theoretical transfer functions are encouraging, their magnitudes show disagreement at lower Strouhal number gains show disagreement.

La conception des turbines à gaz est aujourd'hui contrainte par des normes d'émissions de plus en plus draconiennes, couplées à l'urgente nécessité d'économiser les ressources en carburant fossile. Les choix technologiques adoptés pour répondre à ces exigences entraînent parfois l'apparition d'instabilités de combustion. Dans les chambres de combustion annulaires, ces instabilités prennent souvent la forme de modes azimutaux. Prédire ces modes reste un défi à l'heure actuelle et impose de considérer la totalité de la géométrie annulaire, ce qui n'est rendu possible, dans le domaine de la simulation numérique en mécanique des fluides, que par l'avènement très récent des supercalculateurs massivement parallèles. Dans ce travail de thèse, les modes azimutaux pouvant apparaître dans les chambres de combustion annulaires sont abordés avec plusieurs approches: un modèle analytique 1D, un solveur acoustique de Helmholtz 3D et enfin des Simulations aux Grandes Echelles. Combiner ces méthodes permet une meilleure compréhension de la structure de ces modes et peut amener à considérer des solutions innovantes pour concevoir des chambres inconditionnellement stables. / Increasingly stringent regulations and the need to tackle rising fuel prices have placed great emphasis on the design of aeronautical gas turbines. This drive towards innovation has resulted sometimes in new concepts being prone to combustion instabilities. Combustion instabilities arise from the coupling of acoustics and combustion. In the particular field of annular combustion chambers, these instabilities often take the form of azimuthal modes. To predict these modes, one must consider the full combustion chamber, which, in the numerical simulation domain, remained out of reach until very recently and the development of massively parallel computers. In this work, azimuthal modes that may develop in annular combustors are studied with different numerical approaches: a low order model, a 3D Helmholtz solver and Large Eddy Simulations. Combining these methods allows a better understanding of the structure of the instabilities and may provide guidelines to build intrinsically stable combustion chambers.

Les besoins énergétiques de la population mondiale ne cessent d’augmenter. Les prévisions indiquent par exemple une forte croissance de la demande du secteur du transport aéronautique. La recherche de systèmes toujours plus performants et moins polluants est nécessaire. Des nouveaux concepts pour la combustion ont été mis au point et appliqués aux turbines à gaz. Parmi eux il existe ceux basés sur la combustion en prémélange pauvre ou en prémélange pauvre pré-vaporisé dans le cas où le carburant utilisé est liquide. Les nouveaux systèmes énergétiques basés sur la combustion en régime pauvre sont prometteurs pour satisfaire les futures normes d’émissions polluantes, mais ils sont plus sensibles aux instabilités de combustion qui limitent leur plage de fonctionnement et peuvent détériorer irréversiblement ces systèmes. Dans ce domaine il reste des questions à aborder. En particulier celle du comportement des flammes tourbillonnaires en combustion diphasique soumises à des perturbations acoustiques. La plupart des moteurs aéronautiques utilisent des flammes de ce type, cependant leur dynamique et leurs interactions mutuelles, quand elles subissent les effets d’une perturbation acoustique, sont loin d’être bien comprises. Ce travail aborde ces questions et apporte des éléments de compréhension sur les mécanismes pilotant la réponse de l’écoulement diphasique et de la flamme, ainsi que des éléments de validation des modèles de prédiction des points de fonctionnement instables. TACC-Spray est le banc expérimental utilisé pour ce travail. Il a été conçu et développé au sein du laboratoire CORIA lors de ce doctorat qui s’inscrit dans le cadre du projet ANR FASMIC. Le système d’injection qui équipe ce banc expérimental reçoit trois injecteurs tourbillonnaires alimentés en combustible liquide (ici n-heptane), développés par le laboratoire EM2C. Ils sont montés en lignes dans le banc, celui-ci représentant ainsi un secteur d’une chambre annulaire. Le montage étant complexe et nouveau, un travail de développement de solutions techniques a été fait pour rendre possible l’équipement du TACC-Spray avec des capteurs de pression, température, photomultiplicateur ainsi que des diagnostiques optiques performants (e.g. LDA, PDA, imagerie à haute cadence). Pour cette étude, le système énergétique, composé par l’écoulement diphasique et la flamme, a été soumis à l’impact d’un mode acoustique transverse excité dans la cavité acoustique. La réponse du système a été étudiée en fonction de son positionnement dans le champ acoustique. Trois bassins d’influence du champ acoustique sur le système énergétique ont été choisis, à savoir: (i) le ventre de pression acoustique caractérisé principalement par des fortes fluctuations de pression, (ii) le ventre d’intensité acoustique présentant de forts gradients de pression et vitesse acoustique, (iii) le ventre de vitesse acoustique avec de fortes fluctuations de vitesse où la fluctuation de pression est résiduelle. L’approche de cette étude a consisté à étudier en premier lieu le système de référence en absence de forçage acoustique, les résultats sont recueillis dans la Partie I de ce manuscrit. En deuxième lieu le système énergétique est placé à chacune des positions d’intérêt dans le champ acoustique et la réponse de l’écoulement d’air sans combustion, la réponse de l’écoulement diphasique avec combustion et finalement celle des flammes, sont étudiées systématiquement. Les résultats de l’étude avec forçage acoustique sont rassemblés dans la Partie II du manuscrit. / The energy needs of population around the word are continuously increasing. For instance, forecasts indicates an important grow of the request of the aeronautic transportation sector. It is necessary to continue the research efforts to get more performants and less contaminating systems. New concepts for combustion have been developed and introduced to the gas turbine industry. Among these concepts it is found technologies based on lean-premixed combustion or lean-premixed prevaporized combustion when liquid fuels are employed. These novel energetic systems, making use of lean combustion, are promising to meet the future norms about pollutant emissions, but this make them more sensitive to combustion instabilities that limit their operating range and can lead to irreversible damage. In this domain, many questions still need to be considered. In particular that of the behavior of two-phase flow swirling flames subjected to acoustic perturbations. Indeed most of aero-engines operate with this type of flames, but the dynamics and mutual interaction of these flames, as they are submitted to acoustic perturbation, are not yet well understood. This work addresses these issues and gives some understanding elements for the mechanisms driving the response of the flow and of the flame to acoustic perturbations and delivers data to validate models predicting unstable operating points.The experimental bench employed for this work is TACC-Spray. It has been designed and developed in the CORIA laboratory during this PhD thesis which is inscribed in the framework of the ANR FASMIC project. The injections system that equips this bench is composed by three swirled injectors fed with a liquid fuel (here n-heptane), developed by the EM2C laboratory. They are linearly arranged in the bench such that this represents an unwrapped sector of an annular chamber. The setup, being new and complex, needed technical solutions developed during this work and applied then in order to equip TACC-Spray with pressure and temperature sensors, a photomultiplier as well as adequate optic diagnostics (LDA, PDA, high speed imaging systems). In this study, the energetic system, composed by the two-phase swirling flow and the spray flame, has been submitted to the impact of a transverse acoustic mode excited within the acoustic cavity. The system response has been studied as a function of its location in the acoustic field. Three basins of influence of the acoustic field on the energetic system have been chosen, namely: (i) the pressure antinode characterized mainly by strong pressure fluctuations, (ii) the intensity antinode where important acoustic pressure and velocity gradients are present, (iii) the velocity antinode with strong velocity fluctuations where the acoustic pressure is residual. The approach of the study presented here is to investigate in first place the energetic system free of acoustic forcing. The results concerning this first study are presented in the Part I of this manuscript. In second place, the energetic system is placed in each of the location of interest within the acoustic field and the response of the air flow without combustion, that of the two-phase flow with combustion and finally that of the spray flames, are systematically investigated. The results of the study under acoustic forcing are shown in Part II of the manuscript.