<p dir="ltr">Thermo-acoustic interactions, characterized by the coupling between heat release and acoustic waves, are a phenomenon that can lead to combustion instability in high-speed propulsion devices. These interactions are highly undesirable as they can damage engine components and, in severe cases, cause catastrophic failure of the entire propulsion system. Mitigating these instabilities is crucial for ensuring reliable combustor operation. This work presents a computational investigation of combustion instability in Purdue's Continuously Variable Resonance Combustor (CVRC), focusing on the prediction of instability trend over the entire oxidizer-post length range. Computational fluid dynamics (CFD) studies in the past mainly focused on individual CVRC cases with specific oxidizer-post lengths. Those studies help understand the instability mechanism for individual CVRC cases but are limited in examining the applicability of model predictions over a wide range of instability conditions. No studies have been reported to assess the model predictivity over the entire oxidizer-post range in CVRC. </p><p dir="ltr">In this work, we first conduct a series of CFD simulations that cover the entire oxidizer-post length in CVRC to assess the models for a wide range of instability conditions. It is found that the CFD models generally fail to capture the instability trend over the entire oxidizer-post length although they can capture some individual cases. To understand the model failure, parametric studies are often deemed the first step of investigation. Such parameter studies, however, are expensive for CVRC since more than ten simulation cases to cover the entire oxidizer-post range are needed for each parametric study. Multiple parametric studies are typically needed to cover various uncertainties from numerics and physical models and those involved in the experimental conditions, making parametric studies for CVRC a computationally expensive task. Therefore, our focus next is on developing faster approaches.</p><p dir="ltr">The second part of this work is to develop a reduced-order model to quickly conduct the needed parametric studies. The developed reduced-order model leverages the instability mechanisms observed from the CFD simulations conducted in the first part. Monte Carlo approaches are employed to replace expensive CFD simulations by replicating the randomness in the combustor through statistical sampling. The developed reduced-order model is first validated by comparing its predictions with the CFD simulation results in a number of cases. The reduced-order model, despite its simplicity, reasonably reproduced the overall trend of instability from CFD simulations, making it an attractive alternative to the detailed model simulations for parametric studies. </p><p dir="ltr">The validated reduced-order model is then applied to parametric studies of CVRC to help identify the uncertainties of CFD predictions of CVRC. Four sets of parametric studies are conducted to provide a rapid examination of the effect of heat loss, the effect of oxidizer temperature, the effect of equivalence ratio, and the effect of turbulence on the instability predictions in CVRC. From the rapid reduced-order parametric studies, we found that the heat losses in upstream of the oxidizer inlet and the combustor wall are the two most contributing factors to the uncertainties of CFD model predictions. The turbulence level and the error involved in the equivalence ratio due to experimental uncertainties play an insignificant role in contributing to the CFD prediction uncertainties. </p><p dir="ltr">This work is a significant contribution to the combustion instability community by enabling an alternative rapid assessment of CFD model predictions. This capability facilitates the identification of major contributing factors of CFD modeling uncertainties with much less computational cost, thereby allowing for a more focused approach to CFD analysis and ultimately accelerating the improvement of CFD models for combustion instability studies. </p>

La réfrigération solaire est une alternative à la production de froid à partir de machines à compression mécanique de vapeur dont l’alimentation est électrique. Parmi les technologies envisageables, le couplage d’une machine de réfrigération thermoacoustique avec un concentrateur solaire et un stockage frigorifique par chaleur latente apparait comme une option intéressante. Cette thèse introduit la problématique du sujet et présente les différentes technologies envisageables pour la conception d’un réfrigérateur thermoacoustique solaire. Ensuite, pour répondre au problème, le prototype expérimental qui a été conçu et fabriqué est présenté. Une méthode de modélisation transitoire au niveau système du prototype est proposée. Enfin les résultats obtenus par les simulations dynamiques sont discutés à travers l’analyse du comportement transitoire de l’ensemble du procédé et des performances associées. / Solar refrigeration is an alternative to electrically driven vapor compression cycle for refrigeration. Among the solar refrigeration technologies, the coupling of a heat driven thermoacoustic refrigerator with a solar concentrator and a cold latent energy storage system seems to be a promising technology. This thesis introduces the issue of the subject and analyzes the different available technologies to design a solar driven thermoacoustic refrigerator. Then, to address the problem, the prototype that has been designed and built, is presented. A lumped model is introduced to describe the transient behavior of the prototype. Finally, simulation results are presented and discussed in terms of dynamic behavior and performance analysis.

Reduction of the pollutant emissions is a challenge for the gas turbine industry. A solution to this problem is to employ the low swirl burner which can operate at lower equivalence ratios than a conventional swirl burner. However, flames in the lean regime of combustion are susceptible to flow perturbations and combustion instability. Combustion instability is the coupling between unsteady heat release and combustor acoustic modes where one amplifies the other in a feedback loop. The other method for significantly reducing NOx and CO2 is increasing fuel reactivity, typically done through the addition of hydrogen. This helps to improve the flammability limit and also reduces the pollutants in products by decreasing thermal NOx and reducing CO2 by displacing carbon. In this work, the flammability limits of a low swirl burner at various operating conditions, is studied and the effect of pressure, bulk velocity, burner shape and percent of hydrogen (added to the fuel) is investigated. Also, the flame structure for these test conditions is measured using OH planar laser induced fluorescence and assessed. Also, the OH PLIF data is used to calculate Rayleigh index maps and to construct averaged OH PLIF intensity fields at different acoustic excitation frequencies (45-155, and 195Hz). Based on the Rayleigh index maps, two different modes of coupling between the heat release and the pressure fluctuation were observed: the first mode, which occurs at 44Hz and 55Hz, shows coupling to the flame base (due to the bulk velocity) while the second mode shows coupling to the sides of the flame. In the first mode, the flame becomes wider and the flame base moves with the acoustic frequency. In the second mode, imposed pressure oscillations induce vortex shedding in the flame shear layer. These vortices distort the flame front and generate locally compact and sparse flame areas. The local flame structure resulting from these two distinct modes was markedly different.

Le transport aérien est devenu un mode de déplacement primordial, et le nombre de passagers transportés chaque année est en rapide augmentation à travers le monde. La International Civil Aviation Organization estime que ce nombre est passé de 2.2 milliards en 2009 à 3.0 milliards en 2013, dû en partie à la croissance rapide de pays émergents comme la Chine. Les réglementations concernant les émissions polluantes et sonores s’adaptent et se durcissent, entraînant de nouveaux défis pour les constructeurs aéronautiques. Les chambres de combustion évoluent vers des technologies de combustion pauvre prémélangée prévaporisée pour améliorer l’efficacité et réduire la production de gaz néfastes. Malheureusement, cette technologie tend à réduire la robustesse des moteurs, en diminuant les marges de stabilité et de stabilisation de flamme. Des études récentes indiquent que cela pourrait aussi augmenter le bruit de combustion. Afin de poursuivre le design et l’optimisation des futurs moteurs, de nouvelles méthodes sont nécessaires pour décrire et comprendre les mécanismes en jeu, et d’opérer ces moteurs en toute sécurité tout en atteignant les objectifs de la réglementation. La Simulation aux Grandes Échelles (SGE) est une approche numérique de ces problèmes, qui a montré d’excellents résultats par le passé et qui est très prometteuse pour les designs futurs. La comprehension de ces systèmes énergétiquement denses, confinés et instationnaires passe par la description des interactions flamme-turbulence, de l’acoustique et des couplages multi-physiques. À mesure que la puissance de calcul augmente, la quantité de physique qui peut être modélisée croît également, tout comme la taille des domaines de calcul. Autrefois limités à la zone de fluide réactif, la zone de mélange entre l’air et le carburant a pu être incluse, puis des parois de la chambre et des contournement de flux secondaire, jusqu’à finalement les éléments en amont et en aval de la chambre de combustion. Dans cette thèse, un solveur SGE compressible nommé AVBP est utilisé pour décrire CESAM-HP, un banc d’essai académique situé au laboratoire EM2C: une chambre de combustion pressurisée, siège d’une flamme partiellement prémélangée stabilisée par un tourbillonneur, alimente une tuyère amorcée en fin de chambre. Ces calculs décrivent simultanément la chambre et la tuyère, tout en résolvant l’acoustique, ouvrant la voie à l’étude de la dynamique du système complet, et par là aux instabilités et au bruit de combustion. Cette étude montre enfin que la stabilisation de flamme est impactée par ce comportement dynamique, qui peut parfois entraîner des retours de flamme dans l’injecteur. Ce manuscrit est organisé de la manière suivante : dans une première partie, le contexte pour la chimie, le mouvement et l’acoustique dans un écoulement réactif multi-espèces est donné. L’état de l’art en matière de thermodynamique, de thermoacoustique, de bruit de combustion et de stabilisation de flamme dans les brûleurs tourbillonnaires est présenté. Des modèles simples et des cas test sont exposés pour valider la comprehension des phénomènes en jeu de manière isolée, et des confirmations numériques sont apportées. Dans une seconde partie, les détails pratiques de la mise en œuvre de tels calculs sont donnés. Enfin, la troisième partie décrit l’application de ces outils et méthodes au banc CESAM-HP. L’inclusion de la tuyère compressible dans le domaine fournit des résultats concernant trois sujets majeurs pour le brûleur: (1) la stabilité de la flamme, en lien avec les instabilités de combustion; (2) la stabilisation de la flamme, et l’apparition de retour de flamme dans l’injecteur; (3) le bruit de combustion produit par le brûleur, ainsi que l’identification de ses diverses contributions. / Air transportation is an essential part of modern business and leisure needs, and the number of passengers carried per year is rapidly increasing worldwide. The International Civil Aviation Organization estimates that this number went from 2.2 billion in 2009 to 3.0 billion in 2013, due in part to rapid growth in emerging countries such as China. Many challenges for aircraft designers arise from this increase in air traffic, such as meeting pollutant and noise emission regulations. The engines play a major part in these emissions, and combustor technology has evolved towards high-pressure Lean Prevaporized Premixed (LPP) combustion to increase efficiency and decrease pollutant emissions. Unfortunately, this technology tends to reduce engine robustness, with a decrease in flame stability and stabilization margins. Recent studies suggest that combustion noise could also be increased in these systems. New methods are needed to describe and understand the mechanisms at hand for future design and optimization in order to operate these engines safely while still achieving emission targets. Large Eddy Simulation (LES) is a numerical approach to these problems which has shown excellent results in the past and is very promising for future design. The description of unsteady phenomena in these power-dense, confined and unsteady systems is essential to describe flame-turbulence interactions, acoustics and multiphysic couplings. As computing power grows, so does the amount of physics which can be modeled. Computational domains can be increased, and have gone from including only the reacting zone, to adding the fuel-air mixing areas, the heat liners and secondary flows, and the upstream and downstream elements. In this Ph.D., a compressible LES solver named AVBP is used to describe an academic test rig operated at the EM2C laboratory named CESAM-HP, a pressurized combustion chamber containing a swirl-stabilized partially-premixed flame and ended by a choked nozzle with high-speed flow. This leads to an accurate description of the chamber outlet acoustic behavior, and offers the possibility to investigate the dynamic behavior of the full system, and the occurrence of flame-acoustic coupling leading to combustion instabilities. It also gives insight into the combustion noise mechanisms, which are known to occur both in the reacting zone and in the nozzle. As shown in this study, this behavior also has an impact on flame stabilization in this system. This manuscript is organized as follows. In a first part, the context for chemistry, motion and acoustics of reacting multi-species flow is given. State of the art theories on reacting multi-species flow thermodynamics, thermoacoustics, combustion noise and flame stabilization in swirled burners are presented. Basic toy models and test cases are derived to validate the understanding of direct and indirect combustion noise, and numerical validations are performed. In a second part, the practical details about numerical investigation of such systems are reported. Finally, the third part describes the application of these tools and methods to the CESAM-HP4 test rig. The inclusion of the compressible nozzle in the LES computation yields results concerning three major issues for the burner: (1) flame stability, related to thermoacoustic instabilities; (2) flame stabilization, and the occurrence of flame flashback into the system’s injection duct; (3) combustion noise produced by the system, and identification of its separate contributions.

Les travaux présentés dans cette thèse concernent la simulation numérique du démarrage et de la saturation d'un moteur thermoacoustique à ondes stationnaires couplé à une charge résistive placée à une de ses extrémités. Le modèle utilisé est hybride : l'écoulement dans la cellule est décrit dans le cadre bidimensionnel et non linéaire ; il est couplé à un modèle monodimensionnel d'acoustique linéaire du résonateur, par raccordement dans la limite asymptotique de faible nombre de Mach. Le système sélectionne naturellement les modes acoustiques instables. L'analyse du signal temporel de pression issu de la simulation numérique permet de calculer les taux de croissance des modes dominants. On peut ainsi déterminer la température critique de l'échangeur chaud permettant au moteur de démarrer ainsi que la fréquence du mode associé. Les variations de la température critique et de la fréquence d'oscillation sont caractérisées pour toutes les valeurs possibles de la charge résistive. L'influence de paramètres physiques tels que la pression moyenne, ou de divers paramètres géométriques de la cellule active est également examinée. Les résultats sont confrontés avec succès à la théorie linéaire et avec des résultats expérimentaux de la littérature. Le modèle hybride a permis, dans certains cas, de mener les simulations jusqu'à l'obtention du régime périodique, ce qui représente plusieurs dizaines de milliers de périodes acoustiques. Enfin, deux simulations en régime périodique sont détaillées pour analyser la dynamique de l'écoulement (formation de tourbillons) au voisinage des extrémités des plaques du stack et des échangeurs, pour des ondes de faible ou de forte intensité. / The work presented in this thesis concerns the numerical simulation of the starting phase and saturation regime of a thermoacoustic engine equipped with a resistive load. A hybrid model is used: the flow in the active cell, described by two-dimensional nonlinear equations, is coupled to a one-dimensional linear acoustics model in the resonator, using matched asymptotic expansions in the low Mach number limit. Unstable acoustic modes develop spontaneously in the system. The computed acoustic pressure signal in the active cell is analyzed in order to extract the growth rate and frequency of the dominant modes. Therefore the critical hot exchanger temperature and frequency of the associated mode allowing the engine to start can be determined. Those critical parameters are characterized for all possible values of the resistive load. The effects of physical parameters such as mean pressure or of geometrical parameters of the active cell are also investigated. Results are found in agreement with linear theory and with experimental results from the literature. In some instances, the hybrid model enables to carry the simulations up to the periodic regime, which represents tens of thousands of acoustic periods. Finally, two simulations of the periodic regime are detailed in order to analyze flow dynamics (vortex formation) in the vicinity of the stack plate/heat exchanger extremities, for small and large drive ratio.

This thesis is a collection of the three projects I have worked on at Purdue. The first is a paper on thermoacoustic tomography involving circular integrating detectors that was published in Inverse Problems and Imaging. Results from this paper include demonstrating that the measurement operators involved are Fourier integral operators, as well as proving microlocal uniqueness in certain cases, and also stability. The second paper, submitted to the Journal of Inverse and Ill-Posed Problems, is much more of an application of sampling theory in to the specific case of thermoacoustic tomography. Results from this paper include demonstrating resolution limits imposed by sampling rates, and showing that aliasing artifacts appear in predictable locations in an image when the measurement operator is under sampled in either the time variable or space variables. We also show an application of a basic anti aliasing scheme based on averaging of data. The last project moves slightly away from microlocal analysis and considers the uniqueness in medical imaging of the restricted Radon transform in even dimensions. This is the classical interior problem, and we show a characterization of the range of the Radon transform, and from this are able to obtain a characterization of the kernel of the restricted Radon transform. We include figures throughout to illustrate results.

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

Diese Arbeit zielt darauf ab, die raumzeitlichen Regelmäßigkeiten an Übergängen aufzudecken, die in saisonalen Klima- und Ingenieursystemen beobachtet werden, indem moderne Methoden der komplexen Systemwissenschaft verwendet werden. Das erste System ist der indische Sommermonsun - eine Regenzeit, deren jährliche Schwankungen das Leben und den Wohlstand von mehr als einer Milliarde Menschen auf dem indischen Subkontinent beeinflussen und die Wirtschaft des von der Landwirtschaft abhängigen Landes stark beeinträchtigen. Insbesondere die Kenntnis des zeitlichen Ablaufs des Übergangs vom Vormonsun zum Monsun ist für die Planung landwirtschaftlicher Aktivitäten dringend erforderlich. Die Vorhersage des Monsunzeitpunkts über dem indischen Kontinent bleibt jedoch eine große wissenschaftliche Herausforderung. Das zweite ist ein Verbrennungssystem, das anfällig für ein katastrophales Phänomen namens thermoakustische Instabilität ist, das verhindert, dass das Verbrennungssystem unter klimafreundlichen Bedingungen betrieben wird. Eine solche Brennkammer ist typisch für Energie- und Antriebssysteme wie Gasturbinentriebwerke, Boiler und Raketen. Zu verstehen, wann der Übergang zur thermoakustischen Instabilität auftritt und wie dieser Übergang unterdrückt werden kann, sind Schlüsselfragen für die Entwicklung klimafreundlicher Motoren. Diese Dissertation liefert ein neues Verständnis des indischen Sommermonsuns und der thermoakustischen Instabilität durch auf statistischer Physik basierende Ansätze, die verborgene Merkmale in diesen Systemen nahe ihren jeweiligen Übergängen aufdecken. / This thesis aims to reveal the spatiotemporal regularities at transitions observed in seasonal climate and engineering systems by utilizing modern methods of complex systems science. The first system is the Indian Summer Monsoon - a rainy season whose yearly variability affects the life and prosperity of more than a billion people in the Indian subcontinent and strongly impacts the economy of the agriculture-dependent country. In particular, knowledge of the timing of the transition from pre-monsoon to monsoon is greatly needed for the planning of agriculture activities. However, the prediction of monsoon timing over the Indian continent remains a significant scientific challenge. The second is a combustion system prone to a catastrophic phenomenon called thermoacoustic instability, which prevents the combustion system from being operated in climate-friendly conditions. Such a combustor is typical in power and propulsion systems such as gas turbine engines, boilers, and rockets. Understanding when the transition to thermoacoustic instability occurs and how to suppress this transition are key questions for developing climate-friendly engines. This thesis provides a new understanding of the Indian Summer Monsoon and thermoacoustic instability through statistical physics-based approaches that reveal hidden features in these systems near their respective transitions.

Thermoacoustic instabilities in modern high-performance, low-emission gas turbine engines are often observable as large amplitude pressure oscillations and can result in serious performance and structural degradations. These acoustic oscillations can cause oscillations in combustor through-flows and given the right phase conditions, can also drive unsteady heat release. This coupling has the potential to enhance the amplitude of pressure oscillations. To curb the potential harms caused by the existence of thermoacoustic instabilities, recent efforts have focused on the active suppression and even complete control of these instabilities. Intuitively, development of effective active combustion control methodologies is strongly dependent on the knowledge of the onset and sustenance of thermoacoustic instabilities. Specially, non-premixed spray combustion environment pose additional challenges due to the inherent unstable dynamics of sprays. The understanding of the manner in which the combustor acoustics affect the spray characteristics, which in turn result in heat release oscillation, is therefore, of paramount importance. The experimental investigations and the modeling studies conducted towards achieving this knowledge have been presented in this dissertation. Experimental efforts comprise both reacting and non-reacting flow studies. Reacting flow experiments were conducted on a overall lean direct injection, swirl-stabilized combustor rig. The investigations spanned combustor characterization and stability mapping over the operating regime. All experiments were performed under atmospheric pressure condition, which is considered as an obvious first step towards providing valuable insights into more intense processes in actual gas turbine combustors. The onset of thermoacoustic instability and the transition of the combustor to two unstable regimes were investigated via phase-locked chemiluminescence imaging and measurement and phase-locked acoustic characterization. It was found that the onset of the thermoacoustic instability is a function of the energy gain of the system, while the sustenance of instability is due to the in-phase relationship between combustor acoustics and unsteady heat release driven by acoustic oscillations. The presence of non-linearities in the system between combustor acoustic and heat release and also between combustor acoustics and air through-flow were found to exist. The impact of high amplitude limit-cycle pressure on droplet breakdown under very low mean airflow and the localized effects of forced primary fuel modulations on heat release were also investigated. The non-reacting flow experiments were conducted to study the spray behavior under the presence of an acoustic field. An isothermal acoustic rig was specially fabricated, where the pressure oscillations were generated using an acoustic driver. Phase Doppler Anemometry was used to measure the droplet velocities and sizes under varying acoustic forcing conditions and spray feed pressures. Measurements made at different locations in the spray were related to these variations in mean and unsteady inputs. The droplet velocities were found to show a second order response to acoustic forcing with the cut-off frequency equal to the relaxation time corresponding to mean droplet size. It was also found that under acoustic forcing the droplets migrate radially away from the spray centerline and show oscillatory excursions in their movement. Non-reacting flow experiments were also performed using Time-Resolved Digital Particle Image Velocimetry to characterize modulated sprays. Frequency response of droplet diameters were analyzed in the pulsed spray. These pilot experiments were conducted to assess the capability of the system to measure dynamic data. Modeling efforts were undertaken to gain physical insights of spray dynamics under the influence of acoustic forcing and to explain the experimental findings. The radial migration of droplets and their oscillatory movement were validated. The flame characteristics in the two unstable regimes and the transition between them were explained. It was found that under certain acoustic and mean air-flow condition, bands of high droplet densities were formed which resulted in diffusion type group burning of droplets. It was also shown that very high acoustic amplitudes cause secondary breakup of droplets. / Ph. D.

Controlling unsteady combustion induced gas flow fluctuations and the resultant motor vibrations is a very significant step in rocket motor design. It occurs when the unsteady heat release due to combustion happens to feed the acoustic oscillations of the closed duct forming a feed-back system. The resultant vibrations concerned may even lead to total failure of the rocket system unless analysed and tested thoroughly. This thesis aims developing a linear numerical analysis method for the growth rate of instabilities and possible mode shape of a liquid-propelled chamber geometry. In particular, A 3-D Helmholtz code, utilizing Culicks spatial averaging linear iterative method, is developed to find the form of deformed mode shapes iteratively to obtain possible effects of heat source and impedance boundary conditions. The natural mode shape phase is solved through finite volume discretization and the open-source eigenvalue extractor, ARPACK, and its parallel implementation PARPACK. The iterative method is particularly used for analyzing the geometries with complex shapes and essentially for disturbances of small magnitudes to natural mode shapes. The developed tools are tested via two simple cases, a duct with inactive flame and a Rijke tube, used as validation cases for the code particularly with only boundary contribution and heat contribution respectively. A sample 2-D and 3-D liquid-propelled combustion chamber is also analysed with heat sources. After comparing with the expected values, it is eventually proved that the method should be only used for determining the modes instability analysis, as to whether it keeps vibrating or decays. The methodology described can be used as a preliminary design tool for the design of liquid-propellant rocket engine combustors, rapidly revealing only the onset of instabilities.