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 chromosphere and transition region of the solar atmosphere provide an interface between the cool photosphere (6000 K) and the hot corona (1 million K). Both layers exhibit dramatic deviations from thermal and hydrostatic equilibrium in the form of intense plasma heating and mass transfer. The exact mechanisms responsible for transporting energy to the upper atmosphere remain unknown, but these must include a variety of energetic processes operating across many spatial and temporal scales. This dissertation comprises three studies of possible mechanisms for plasma heating and energy transport in the solar chromosphere and transition region. The first study establishes the theoretical framework for a collisional, two-stream plasma instability in the quiet-Sun chromosphere similar to the Farley-Buneman instability which actively heats the E-region of Earth's ionosphere. After deriving a linear dispersion relationship and employing a semi-empirical model of the chromosphere along with carefully computed collision frequencies, this analysis shows that the threshold electron drift velocity for triggering the instability is remarkably low near the temperature minimum where convective overshoots could continuously trigger the instability. The second study investigates simultaneous Interface Region Imaging Spectrograph (IRIS) observations of magnetohydrodynamic (MHD) waves in the chromospheres and transition regions of sunspots. By measuring the dominant wave periods, apparent phase velocities, and spatial and temporal separations between appearances of two observationally distinct oscillatory phenomena, the data show that these are consistent with upward-propagating slow magnetoacoustic modes tied to inclined magnetic field lines in the sunspot, providing a conduit for photospheric seismic energy to transfer upward. The third and final study focuses on intense, small-scale (1 arcsec) active region brightenings known as IRIS UV bursts. These exhibit dramatic FUV/NUV emission line splitting and deep absorption features, suggesting that they result from reconnection events embedded deep in the cool lower chromosphere. IRIS FUV spectral observations and Solar Dynamics Obser- vatory/Helioseismic and Magnetic Imager (SDO/HMI) magnetograms of a single evolving active region reveal that bursts prefer to form during the active region's emerging phase. These bursts tend to be spatially coincident with small-scale, photospheric, bipolar regions of upward and downward magnetic flux that dissipate as the active region matures.

Dans cette thèse, les instabilités de combustion sont étudiées sur deux types de configuration. Tout d’abord, un cas académique stabilisé par un dièdre (Volvo) est étudié. Les simulations sont validées par comparaison avec les données expérimentales. En faisant varier le point de fonctionnement, des modes transverses et longitudinaux sont observés, en bon accord avec les données expérimentales en termes de fréquence des fluctuations de pression et de la dynamique de l’écoulement. Dans un second temps, une configuration proche des cas industriels a été étudiée dans le cadre du projet européen KIAI (Lotar). Les données expérimentales ont été obtenues lors d’une campagne d’essais à l’ONERA. Plusieurs simulations aux grandes échelles sont conduites sur cette configuration. Les instabilités transverses de combustion sont analysées et les mécanismes essentiels qui les pilotent sont identifiés. Sur la base de ces observations, la forme du modèle à Fonction de Transfert de Flamme est modifiée et associée à un solveur de Helmholtz pour prédire la stabilité des modes transverses. Les résultats obtenus par le solveur acoustique sont en bon accord avec la carte de stabilité obtenue par la simulation aux grandes échelles. / In this work longitudinal and transverse combustion instabilities are studied in two types of configurations. While longitudinal modes have been observed in many previous studies at low frequencies, the present work also focusses on high-frequency transverse modes. First, a premixed flame stabilized on a V-fame holder is investigated where experimental results obtained by Volvo are used to validate the simulations. For different operating conditions, longitudinal and transverse modes are observed in Large Eddy Simulations (LES) and show good agreement with the experimental data in terms of pressure frequency and flow dynamics. In a second step, a semi-industrial case is examined within the European project KIAI. Experiments are conducted by ONERA and LES of this two-phase flow configuration (called Lotar) are carried out. Transverse combustion instabilities are analyzed and key elements which drive instabilities are identied. These observations are used to reformulate the classic Flame Transfer Function (FTF) in order to predict the stability of transverse modes by use of an Helmholtz solver. The results reproduce fairly well the stability map generated by LES.

On calcule les amplifications d’énergie optimales de structures quasi longitudinales dans le sillage d’un corps épais axisymétrique à culot droit et dans une couche de mélange parallèle. Les amplifications d'énergie sont seulement modérées dans le sillage du corps axisymétrique tandis qu'elles sont grandes dans la couche de mélange. Les amplifications maximales augmentent avec le nombre de Reynolds et lorsque le nombre d’onde transverse (azimutal) décroît. Les structures amplifiées optimalement sont des stries longitudinales. Lorsqu’elles sont forcées à amplitudes finies, les stries optimales réduisent considérablement l’instationnarité du sillage du corps épais axisymétrique. Pour des nombres de Reynolds modérés, l’instationnarité du sillage peut être complètement supprimée si le forçage optimal est combiné avec un soufflage au culot uniforme. Dans le cas de la couche de mélange 2D, le taux de croissance maximal de l'instabilité de KelvinHelmholtz et le ratio de vitesse critique d'apparition de l'instabilité absolue peuvent être soit réduits soit augmentés en fonction des symétries des stries forcées. Dans ce cas, on montre que la déformation non linéaire moyenne doit être incluse dans l'analyse de sensibilité de l'instabilité et que cela n'influe pas sur la dépendance quadratique par rapport à l'amplitude des stries. / Optimal energy amplifications of quasi-streamwise structures are computed in the wake of a bluntbased axisymmetric bluff body and in a parallel mixing layer. Only moderate energy amplifications are observed in the wake of the axisymmetric body while they are large in the mixing layer. The maximum amplifications increase with the Reynolds number and with decreasing spanwise (azimuthal) wavenumbers. The optimally amplified structures are streamwise streaks. When forced with finite amplitudes, optimal streaks greatly reduce the unsteadiness in the wake of the axisymmetric bluff body. At moderate Reynolds numbers the wake unsteadiness can be completely suppressed if the optimal forcing is combined with uniform base bleed. In the case of the 2D mixing layer, the maximum growth rate of the Kelvin-Helmholtz instability and the critical velocity ratio for the onset of the absolute instability can be either reduced or increased depending on the symmetries of the forced streaks. It is shown that in this case the nonlinear mean flow distortion must be included in the sensitivity analysis of the instability and that this inclusion preserves the quadratic dependence on the streaks amplitude.

Combustion devices are prone to combustion instabilities. They arise from a constructive coupling between the unsteady heat release rate of the flame and the resonant acoustic modes of the entire system. The occurence of such instabilities can pose a threat to both performance and integrity of combustion systems. Although these phenomena have been known for more than a century, avoiding their appearance in industrial engines is still challenging. The objective of this thesis is threefold: (1) study the dynamics of the resonant acoustic modes, (2) investigate the flame response of a liquid rocket engine under unstable conditions using Large Eddy Simulation(LES) and (3) derive, use and study Time Domain Impedance Boundary Conditions (TDIBCs), i.e. boundary conditions modeling complex acoustic impedances.

Context. Whether or not a self-gravitating accretion disk fragments is still an open issue. There are many different physical and numerical explanations for fragmentation, but simulations often show a non-convergent behavior for ever better resolution. Aims. We aim to investigate the influence of different numerical limiters in Godunov type schemes on the fragmentation boundary in self-gravitating disks. Methods. We have compared the linear and non-linear outcomes in two-dimensional shearingsheet simulations using the VANLE ER and the SUPERBEE limiter. Results. We show that choosing inappropriate limiting functions to handle shock-capturing in Godunov type schemes can lead to an overestimation of the surface density in regions with shallow density gradients. The effect amplifies itself on timescales comparable to the dynamical timescale even at high resolutions. This is exactly the environment in which clumps are expected to form. The effect is present without, but scaled up by, self-gravity and also does not depend on cooling. Moreover it can be backtracked to a well known effect called oversteepening. If the effect is also observed in the linear case, the fragmentation limit is shifted to larger values of the critical cooling timescale.

Cette thèse est consacrée à l’étude en microfluidique de la fabrication de fibres. Les deux étapes critiques sont : - la mise en forme du matériau : nous avons étudié des instabilités qui peuvent se déclencher dans des coécoulements coeur/écorce faisant intervenir des fluides complexes (polymères, suspensions concentrées), celles-ci peuvent empêcher un contrôle de cette étape ; - le figeage de cette forme : nous avons étudié la gélification de l’alginate (un biopolymère formant un gel par l’ajout d’ions calcium) sous écoulement. Nous avons étudié des phénomènes de diffusion-réaction sous écoulement pour comprendre les points de fonctionnement de nos dispositifs. Une fois ces étapes contrôlées, nous nous sommes intéressés à la fabrication des fibres d’alginates fortement chargées en cellules pour l’ingénierie tissulaire. / Abstract

The million-degree temperature of the solar corona might be due to the combined effect of barely distinguishable energy releases, called nanoflares, that occur throughout the solar atmosphere. Unfortunately, the high density of nanoflares, implied by this hypothesis, means that conclusive verification is beyond present observational capabilities. Nevertheless, it might be possible to investigate the plausibility of nanoflare heating by constructing a magnetohydrodynamic (MHD) model; one that can derive the energy of nanoflares, based on the assumption that the ideal kink instability of a twisted coronal loop triggers a relaxation to a minimum energy state. The energy release depends on the current profile at the time when the ideal kink instability threshold is crossed. Subsequent to instability onset, fast magnetic reconnection ensues in the non-linear phase. As the flare erupts and declines, the field transitions to a lower energy level, which can be modelled as a helicity-conserving relaxation to a linear force-free state. The aim of this thesis is to determine the implications of such a scheme with respect to coronal heating. Initially, the results of a linear stability analysis for loops that have net current are presented. There exists substantial variation in the radial magnetic twist profiles for the loop states along the instability threshold. These results suggest that instability cannot be predicted by any simple twist-derived property reaching a critical value. The model is applied such that the loop undergoes repeated episodes of instability followed by energy-releasing relaxation. Photospheric driving is simulated as an entirely random process. Hence, an energy distribution of the nanoflares produced is collated. These results are discussed and unrealistic features of the model are highlighted.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第22248号 / 理博第4562号 / 新制||理||1655(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 野上 大作, 教授 嶺重 慎, 教授 長田 哲也 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

The first experimental demonstration of feedback suppression of rotating external kink modes near the ideal wall limit in a tokamak using Kalman filtering to discriminate the n = 1 kink mode from background noise is reported. In order to achieve the highest plasma pressure limits in tokamak fusion experiments, feedback stabilization of long-wavelength, external instabilities will be required, and feedback algorithms will need to distinguish the unstable mode from noise due to other magnetohydrodynamic activity. When noise is present in measurements of a system, a Kalman filter can be used to compare the measurements with an internal model, producing a realtime, optimal estimate for the system's state. For the work described here, the Kalman filter contains an internal model that captures the dynamics of a rotating, growing instability and produces an estimate for the instability's amplitude and spatial phase. On the High Beta Tokamak-Extended Pulse (HBT-EP) experiment, the Kalman filter algorithm is implemented using a set of digital, field-programmable gate array controllers with 10 microsecond latencies. The feedback system with the Kalman filter is able to suppress the external kink mode over a broad range of spatial phase angles between the sensed mode and applied control field, and performance is robust at noise levels that render feedback with a classical, proportional gain algorithm ineffective. Scans of filter parameters show good agreement between simulation and experiment, and feedback suppression and excitation of the kink mode are enhanced in experiments when a filter made using optimal parameters from the experimental scans is used.