Dissertations / Theses on the topic 'Turing instability'

Questa tesi riguarda modelli differenziali preda-predatore, trattati inizialmente nel caso spazialmente omogeneo e successivamente considerando la diffusione spaziale. Dal punto di vista matematico pertanto vengono considerati sistemi di equazioni differenziali ordinarie e di equazioni differenziali alle derivate parziali di tipo parabolico. In particolare, nella prima parte viene studiato un modello preda-predatore spazialmente omogeneo, retto da due equazioni differenziali ordinarie, in cui sono presi in considerazione un effetto Allee forte nella crescita delle prede e una risposta funzionale predatore dipendente. Il punto di forza dello studio risiede nel fatto che le funzioni che descrivono questi processi non hanno un'espressione esplicita, ma sono caratterizzate solo da alcune proprietà comuni a funzioni specifiche utilizzate in letteratura. Tali proprietà sono sufficienti per effettuare l'analisi qualitativa del sistema, con riguardo all'esistenza degli equilibri e alle loro proprietà di stabilità mediante i criteri di Lyapunov, utilizzando due parametri di biforcazione che caratterizzano il processo di predazione. Il modello presenta dei punti di biforcazione di codimensione 2 quali una biforcazione Bogdanov-Takens e una di tipo cuspide, non legati alla particolare realizzazione scelta per le funzioni del modello. Lo studio è stato proseguito numericamente fissando un'espressione per la funzione di crescita delle prede e per la funzione trofica che soddisfano le proprietà considerate e utilizzando il software di continuazione Matcont per Matlab. Tale studio ha mostrato l'ulteriore presenza di biforcazioni globali che determinano la sparizione dei cicli limite, mediante la formazione di orbite omocline ed eterocline. Inoltre è stato individuato una biforcazione di Hopf generalizzata, un altro punto di biforcazione di codimensione 2. Le biforcazioni di codimensione 2 individuate sono tutte e sole quelle ammesse da un sistema a due equazioni differenziali. La seconda parte della tesi verte invece sullo studio di due sistemi preda-predatore con diffusione in cui vengono dedotte in un opportuno limite due tipi di risposte funzionali classiche come termine reattivo e un termine diffusivo non lineare. In dettaglio, vengono considerati due livelli trofici, le prede e i predatori. Questi ultimi sono suddivisi in due classi, searching predators e handling predators: i primi sono i predatori effettivamente impegnati nella predazione, mentre i secondi non sono attivi in tale processo. Ne deriva un sistema composto da tre equazioni differenziali alle derivate parziali, in cui la diffusione è modellizzata in modo classico, mediante un termine lineare in forma di Laplaciano e l'interazione tra prede e predatori è inizialmente del tipo Lotka-Volterra. Mediante una approssimazione quasi steady-state è possibile ridurre il sistema di partenza, ottenendo un sistema di due PDE, una per le prede e una per la totalità dei predatori, in cui la risposta funzionale è del tipo Holling-II, in particolare preda-dipendente, e che presenta una non-linearità nel termine di diffusione. Questa classe di modelli non dà luogo a instabilità di Turing. Viene quindi considerata nel modello a tre equazioni una competizione tra i predatori che permette di ricavare, mediante un'approssimazione quasi steady-state, un sistema preda-predatore con risposta funzionale del tipo Beddington-DeAngelis nel termine di reazione e ancora una non-linearità nel termine di diffusione. Vengono quindi ricavate condizioni sui parametri che permettono di avere instabilità di Turing e confrontati i risultati sia nel caso di diffusione lineare che in quello non-lineare.
Predator-prey models, homogeneous in space or with spatial diffusion, play a central role in this thesis. Indeed, from a mathematical view point, we investigate stability in systems of ordinary differential equations and of partial differential equations of parabolic type. First, we deal with a predator-prey model, described by a system of two ODEs, in which a strong Allee effect on the prey growth and a predator-dependent trophic function are taken into account. The main strength of this part is that these functions are not specified by analytical expressions, but only characterized by some biologically meaningful properties determining their shapes. On the basis of these properties we are able to perform the stability analysis of the system, using the predation efficiency and a measure of the predator interference as bifurcation parameters. The system admits codimension-two bifurcations points, such as a Bogdanov-Takens and a cusp point; it is worthwhile to notice that they are independent of the particular expression of the model functions. The numerical investigation is further carried on choosing for the model equations some analytical expressions well known in literature, which satisfied the assumed properties, and using Matcont, a continuation Matlab toolbox. This investigation, in addition, has shown the presence of global bifurcations that determine the disappearance of limit cycles through the formation of homoclinic and heteroclinic orbits involving some equilibrium points. Moreover, we have detected a further codimension-two bifurcation point, a Generalized-Hopf. Together with the cusp and the Bogdanov-Takens bifurcation points, these three types of codimension-two bifurcations are the only admissible by a planar system of ordinary differential equations. The second part of this thesis focuses on the study of two predator-prey models with diffusion that justify, in a suitable limit, two classical types of functional responses in the reaction part and present a cross-diffusion term. In detail, two trophic levels are considered, preys and predators which are further divided into searching predators and handling predators. The former are predators active in the predation process, the latter are resting individuals. Then, we start from a system of three partial differential equations, with a standard linear diffusion in terms of Laplacian, and with a Lotka-Volterra reaction term. Through a quasi steady-state approximation we end up with a system of two PDEs with prey and total predator densities as unknowns, in which an Holling-type II functional response appears together with a cross-diffusion term in the predator equation. It is proved that this class of predator-prey models can not give rise to Turing instability. Then we modify the starting model inserting a competition among predators. With this change we end up after a quasi steady-state approximation with a system of two PDEs for prey and total predator densities, characterized by a Beddington-DeAngelis-type functional response and a cross-diffusion term in the predator equation. We look for conditions on the parameters values which lead to Turing instability and we compare these Turing instability regions with the ones obtained when the cross-diffusion term is substituted by a linear diffusion.

Inflammation is the body's immune response to outside threats and traumas, aiming to prevent the insurgence of diseases. Although it is a protective mechanism, a derangement of the inflammatory response can lead to severe and debilitating diseases, such as Multiple Sclerosis. For this reason, understanding the mechanisms driving an inflammatory response has become one of the biggest challenge in immunology. The subject of this Thesis is the study of mathematical models aiming to explore the mechanisms of the inflammatory response and the resulting clinical patterns. Our aim to prove that the proposed models, within biologically relevant ranges of the parameter values, are able to reproduce different pathological scenarios observed in patients.

Cette thèse est consacrée à l'étude des systèmes d'équations différentielles ordinaires, et ceux aux dérivées partielles paraboliques issus de modèles de dynamique des populations et de la biologie. L'objectif principal est de faire l'analyse mathématique, la simulation numérique ainsi que l'identification des diffusions croisées dans les modèles construits. Nous présentons d'abord un système de réaction-diffusion modélisant la croissance de plantes en compétition spatiale dans un milieu saturé. Nous effectuons par la suite l'étude théorique et numérique de tels systèmes, ainsi que l'étude des problèmes d'identification des termes de diffusions croisées. Ensuite, nous proposons un modèle proie-prédateur de type Leslie-Gower modifié avec une fonction de réponse de type Crowley-Martin. Nous étudions dans un premier temps la dynamique temporelle globale du modèle considéré, et nous présentons des simulations numériques pour illustrer les résultats théoriques. En outre, nous introduisons la dimension spatiale dans le modèle dynamique considéré, et nous effectuons une analyse théorique complète de la dynamique spatio-temporelle du modèle.

Mathematical models for the collective dynamics of interacting and spatially distributed populations find applications in several contexts (biology, ecology, social sciences). Their formulation depends primarily on the (continuous or discrete) description of the space. Reaction-diffusion equations have been widely used in bioecology (morphogenesis, migration of biological species, tumor growth, neuro-degenerative diseases) and in the social sciences (diffusion of opinions or decisionmaking processes), and exhibit complex behaviors (propagation of oscillatory phenomena, pattern formation caused by instability). A reaction–diffusion system exhibits diffusion-driven instability, sometimes called Turing instability, if the homogeneous steady state is stable to small perturbations in the absence of diffusion but unstable to small spatial perturbations when diffusion is present. In this thesis, we move from this classical approach, considering a so called crimo-taxis model (Epstein, 1997), and proposing two variants (Inferrera et al., 2022) enabling us to study the formation of some patterns due to instability driven by self- and cross-diffusion terms, to operatorial models built by means of some techniques typical of quantum mechanics (see Bagarello, 2012; Bagarello, 2019). The leading idea in this approach relies on the evidence, shown in the last fifteen years in several applications, that the operatorial framework provides useful tools for describing the interactions occurring within macroscopic systems. Therefore, three applications of the operatorial formalism are discussed: 1)an operatorial version of crimo-taxis model; 2)a model where two populations spatially distributed in a one–dimensional domain compete both locally and nonlocally and are able to migrate (Inferrera and Oliveri, 2022); 3) a model of a finite number of agents subjected both to cooperative and competitive interactions (Gorgone, Inferrera, and Oliveri, 2022).

Many biological populations reside in increasingly fragmented landscapes, which arise from human activities and natural causes. Landscape characteristics may change abruptly in space and create sharp transitions (interfaces) in landscape quality. How patchy landscape affects ecosystem diversity and stability depends, among other things, on how individuals move through the landscape. Individuals adjust their movement behaviour to local habitat quality and show preferences for some habitat types over others. In this dissertation, we focus on how landscape composition and the movement behaviour at an interface between habitat patches of different quality affects the steady states of a single species and a predator-prey system. First, we consider a model for population dynamics in a habitat consisting of two homogeneous one-dimensional patches in a coupled ecological reaction-diffusion equation. Several recent publications by other authors explored how individual movement behaviour affects population-level dynamics in a framework of reaction-diffusion systems that are coupled through discontinuous boundary conditions. The movement between patches is incorporated into the interface conditions. While most of those works are based on linear analysis, we study positive steady states of the nonlinear equations. We establish the existence, uniqueness and global asymptotic stability of the steady state, and we classify their qualitative shape depending on movement behaviour. We clarify the role of nonrandom movement in this context, and we apply our analysis to a previous result where it was shown that a randomly diffusing population in a continuously varying habitat can exceed the carrying capacity at steady state. In particular, we apply our results to study the question of why and under which conditions the total population abundance at steady state may exceed the total carrying capacity of the landscape. Secondly, we model population dynamics with a predator-prey system in a coupled ecological reaction-diffusion equation in a heterogeneous landscape to study Turing patterns that emerge from diffusion-driven instability (DDI). We derive the DDI conditions, which consist of necessary and sufficient conditions for initiation of spatial patterns in a one-dimensional homogeneous landscape. We use a finite difference scheme method to numerically explore the general conditions using the May model, and we present numerical simulations to illustrate our results. Then we extend our studies on Turing-pattern formation by considering a predator-prey system on an infinite patchy periodic landscape. The movement between patches is incorporated into the interface conditions that link the reaction-diffusion equations between patches. We use a homogenization technique to obtain an analytically tractable approximate model and determine Turing-pattern formation conditions. We use numerical simulations to present our results from this approximation method for this model. With this tool, we then explore how differential movement and habitat preference of both species in this model (prey and predator) affect DDI.

Spontaneous travelling waves of neuronal activity are a prominent feature throughout the developing brain and have been shown to be essential for achieving normal function, but the mechanism of their action on post-synaptic connections remains unknown. A well-known and widespread mechanism for altering synaptic strengths is spike-timing dependent plasticity (STDP), whereby the temporal relationship between the pre- and post-synaptic spikes determines whether a synapse is strengthened or weakened. Here, I answer the theoretical question of how these two phenomenon interact: what types of connectivity patterns can emerge when travelling waves drive a downstream area that implements STDP, and what are the critical features of the waves and the plasticity rules that shape these patterns? I then demonstrate how the theory can be applied to the development of the visual system, where retinal waves are hypothesised to play a role in the refinement of downstream connections. My major findings are as follows. (1) Mathematically, STDP translates the correlated activity of travelling waves into coherent patterns of synaptic connectivity; it maps the spatiotemporal structure in waves into a spatial pattern of synaptic strengths, building periodic structures into feedforward circuits. This is analogous to pattern formation in reaction diffusion systems. The theory reveals a role for the wave speed and time scale of the STDP rule in determining the spatial frequency of the connectivity pattern. (2) Simulations verify the theory and extend it from one-dimensional to two-dimensional cases, and from simplified linear wavefronts to more complex realistic and noisy wave patterns. (3) With appropriate constraints, these pattern formation abilities can be harnessed to explain a wide range of developmental phenomena, including how receptive fields (RFs) in the visual system are refined in size and topography and how simple-cell and direction selective RFs can develop. The theory is applied to the visual system here but generalises across different brain areas and STDP rules. The theory makes several predictions that are testable using existing experimental paradigms.

The aim of this thesis is to investigate the dynamical behaviors of spatially extended systems with fluctuating time delays. In recent years, the study of spatially extended systems and systems with fluctuating delays has experienced a fast growth. In ubiquitous natural and laboratory situations, understanding the action of time-delayed signals is a crucial for understanding the dynamical behavior of these systems. Frequently, the length of the delay is found to change with time. Spatially extended systems are widely studied in many fields, such as chemistry, ecology, and biology. Self-organization, turbulence, and related nonlinear dynamic phenomena in spatially extended systems have developed into one of the most exciting topics in modern science. The first part of this thesis considers the discrete system. Diffusively coupled map lattices with a fluctuating delay are used in the study. The uncoupled local dynamics of the considered system are represented by the delayed logistic map. In particular, the influences of diffusive coupling and fluctuating delay are studied. To observe and understand the influences, the results for the considered system are compared with coupled map lattices without delay and with a constant delay as well as with the uncoupled logistic map with fluctuating delays. Identifying different patterns, determining the existence of traveling wave solutions, and specifying the fully synchronized stable state are the focus of this part of the study. The Lyapunov exponent, the master stability function, spectrum analysis, and the structure factor are used to characterize the different states and the transitions between them. The second part examines the continuous system. The delay is introduced into the reactionterm of the Fisher-KPP equation. The focus of this part of study is the time-delay-induced Turing instability in one-component reaction-diffusion systems. Turing instability has previously only been found in multiple-component reaction-diffusion systems. However, this work demonstrates with the help of the stability exponent that fluctuating delay can result in Turing instability in one-component reaction-diffusion systems as well
Ziel der vorliegenden Arbeit ist die Untersuchung der Einflüsse der zeitlich fluktuierenden Verzögerungen in räumlich ausgedehnten diffusiven Systemen. Durch den Vergleich von Systemen mit konstanter Verzögerung bzw. Systemen ohne räumliche Kopplung erhält man ein tieferes Verständnis und eine bessere Beschreibungsweise der Dynamik des räumlich ausgedehnten diffusiven Systems mit fluktuierenden Verzögerungen. Im ersten Teil werden diskrete Systeme in Form von diffusiven Coupled Map Lattices untersucht. Als die lokale iterierte Abbildung des betrachteten Systems wird die logistische Abbildung mit Verzögerung gewählt. In diesem Teil liegt der Fokus auf Musterbildung, Existenz von Multiattraktoren und laufenden Wellen sowie der Möglichkeit der vollen Synchronisation. Masterstabilitätsfunktion, Lyapunov Exponent und Spektrumsanalyse werden benutzt, um das dynamische Verhalten zu verstehen. Im zweiten Teil betrachten wir kontinuierliche Systeme. Hier wird die Fisher-KPP Gleichung mit Verzögerungen im Reaktionsteil untersucht. In diesem Teil liegt der Fokus auf der Existenz der Turing Instabilität. Mit Hilfe von analytischen und numerischen Berechnungen wird gezeigt, dass bei fluktuierenden Verzögerungen eine Turing Instabilität auch in 1-Komponenten-Reaktions-Diffusionsgleichungen gefunden werden kann

The aim of this thesis is to investigate the dynamical behaviors of spatially extended systems with fluctuating time delays. In recent years, the study of spatially extended systems and systems with fluctuating delays has experienced a fast growth. In ubiquitous natural and laboratory situations, understanding the action of time-delayed signals is a crucial for understanding the dynamical behavior of these systems. Frequently, the length of the delay is found to change with time. Spatially extended systems are widely studied in many fields, such as chemistry, ecology, and biology. Self-organization, turbulence, and related nonlinear dynamic phenomena in spatially extended systems have developed into one of the most exciting topics in modern science. The first part of this thesis considers the discrete system. Diffusively coupled map lattices with a fluctuating delay are used in the study. The uncoupled local dynamics of the considered system are represented by the delayed logistic map. In particular, the influences of diffusive coupling and fluctuating delay are studied. To observe and understand the influences, the results for the considered system are compared with coupled map lattices without delay and with a constant delay as well as with the uncoupled logistic map with fluctuating delays. Identifying different patterns, determining the existence of traveling wave solutions, and specifying the fully synchronized stable state are the focus of this part of the study. The Lyapunov exponent, the master stability function, spectrum analysis, and the structure factor are used to characterize the different states and the transitions between them. The second part examines the continuous system. The delay is introduced into the reactionterm of the Fisher-KPP equation. The focus of this part of study is the time-delay-induced Turing instability in one-component reaction-diffusion systems. Turing instability has previously only been found in multiple-component reaction-diffusion systems. However, this work demonstrates with the help of the stability exponent that fluctuating delay can result in Turing instability in one-component reaction-diffusion systems as well.
Ziel der vorliegenden Arbeit ist die Untersuchung der Einflüsse der zeitlich fluktuierenden Verzögerungen in räumlich ausgedehnten diffusiven Systemen. Durch den Vergleich von Systemen mit konstanter Verzögerung bzw. Systemen ohne räumliche Kopplung erhält man ein tieferes Verständnis und eine bessere Beschreibungsweise der Dynamik des räumlich ausgedehnten diffusiven Systems mit fluktuierenden Verzögerungen. Im ersten Teil werden diskrete Systeme in Form von diffusiven Coupled Map Lattices untersucht. Als die lokale iterierte Abbildung des betrachteten Systems wird die logistische Abbildung mit Verzögerung gewählt. In diesem Teil liegt der Fokus auf Musterbildung, Existenz von Multiattraktoren und laufenden Wellen sowie der Möglichkeit der vollen Synchronisation. Masterstabilitätsfunktion, Lyapunov Exponent und Spektrumsanalyse werden benutzt, um das dynamische Verhalten zu verstehen. Im zweiten Teil betrachten wir kontinuierliche Systeme. Hier wird die Fisher-KPP Gleichung mit Verzögerungen im Reaktionsteil untersucht. In diesem Teil liegt der Fokus auf der Existenz der Turing Instabilität. Mit Hilfe von analytischen und numerischen Berechnungen wird gezeigt, dass bei fluktuierenden Verzögerungen eine Turing Instabilität auch in 1-Komponenten-Reaktions-Diffusionsgleichungen gefunden werden kann

Cette thèse est consacrée à l'étude des instabilités du sillage tourbillonnaire des rotors, largement utilisés dans l'industrie pour la conversion d'énergie mécanique. Leur sillage peut être modélisé par un ensemble de vortex hélicoïdaux entrelacés, au sein duquel de nombreuses instabilités peuvent émerger. Ces mécanismes ont un impact significatif sur l'évolution intermédiaire du sillage et peuvent influencer les performances du rotor. Ce travail, plus particulièrement dédié aux hélicoptères, s'est tout d'abord attaché à caractériser expérimentalement l'écoulement derrière trois rotors conçus pour des régimes de vols différents. Ces conditions de bases ont ensuite servi à étudier les différents modes instables de grande longueur d'onde pouvant apparaître dans le sillage. Une bonne correspondance est trouvée entre les prédictions théoriques et les mesures expérimentales des taux de croissance associés. Une rapide analyse de l'évolution spatio-temporelle de ces perturbations a permis d'étudier la propagation d'une perturbation localisée dans le plan rotor. Il est en effet envisagé que dans certaines configurations de vol de descente, les instabilités provoquent la transition du sillage vers un état spécifique connu sous le nom d'état d'anneau tourbillonnaire, potentiellement dangereux pour l'appareil. Il se caractérise par une stagnation du sillage au voisinage du plan rotor qui en dégrade les performances
This work studies the instabilities associated with the wake of a rotor. These devices are used in many applications such as energy harvesting or propulsion,and their optimisation is crucial for both industry and the environment. The wakebehind a rotor is broadly defined as a system of interlaced helical vortices, whose dynamics governs the transition from the near-wake to the far-wake regime. In our first study, we investigate the wake behind different small-scale rotors in their design operating condition. We use the resulting flows in a subsequent linear stability analysis, aiming at predicting long-wavelength instability modes in the helical vortex. We find that the theoretical prediction of the modes growth-rates matches our experimental measurements. We also show that the dynamics of helical vortex filaments can be predicted from simple two-dimensional theory. In more critical flow configurations, instabilities are suspected to promote the transition to hazardous regimes such as the so called Vortex-Ring State, characterised by large-scale recirculating structures.The second part of this work is thus dedicated to the spatio-temporal evolution of localised perturbations in the rotor plane, and their potential tendency to propagate upstream in the flow

The goal of this thesis is to evaluate if flutter is a challenge to a 10 MW wind turbine. Flutter is an aeroelastic instability which occurs due to the interaction between the aerodynamic forces and the elasticity of the blade. Torsional motions of the blade lead to variations in the aerodynamic forces due to changes in the angle of attack of the airfoil. The variation in aerodynamic forces creates flapwise vibration of the blade. When the vibrations of the blades are in an unfavourable phase with the aerodynamic forces, flutter occurs. Flutter may lead to rapidly increasing vibrations of the blade and failure of the blade. The 10 MW reference turbine from NOWITECH, Norwegian Research Centre for Offshore Wind Technology, was studied. An aeroelastic stability analysis was performed using the aeroelastic stability tool HAWCStab2. It was found that this wind turbine becomes unstable at approximately twice the operational speed of the turbine. The turbine does not experience flutter in normal power producing operation. A simulation in the time domain was also performed, using the aeroelastic tool HAWC2. In a run-away situation, the turbine was found to become unstable with flutter before it reached the run-away speed. The turbine was then analysed with other blades. A softer blade and a stiffer blade were studied. The soft blade was found to become unstable at 1.8 times the operational speed of the turbine. The stiff blade was found to become unstable at around 2.5 times the operational speed. The stiff blade was the only blade where the turbine was able to reach the run-away speed without experiencing instabilities.

Numerical simulations of the Navier-Stokes equations are conducted to achieve a better understanding of the behavior of wakes generated by the wind turbines. The simulations are performed by combining the in-house developed code EllipSys3D with the actuator line technique. In step one of the project, a numerical study is carried out focusing on the instability onset of the trailing tip vortices shed from a 3-bladed wind turbine. To determine the critical frequency, the wake is perturbed using low-amplitude excitations located near the tip spirals. Two basic flow cases are studied; symmetric and asymmetric setups. In the symmetric setup a 120 degree flow symmetry condition is dictated due to the confining the polar computational grid to 120 degree or introducing identical excitations. In the asymmetric setup, uncorrelated excitations are imposed near the tip of the blades. Both setups are analyzed using proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD). By analysing the dominant modes, it was found that in the symmetric setup the amplification of specific waves (traveling structures) traveling along the tip vortex spirals is responsible for triggering the instability leading to wake breakdown, while by breaking the symmetry almost all the modes are involved in the tip vortex destabilization. The presence of unstable modes in the wake is related to the mutual inductance (vortex pairing) instability where there is an out-of-phase displacement of successive helix turns. Furthermore, using the non-dimensional growth rate, it is found that the mutual inductance instability has a universal growth rate equal to Π/2. Using this relationship, and the assumption that breakdown to turbulence occurs once a vortex has experienced sufficient growth, an analytical relationship is provided for determining the length of the stable wake. This expression shows that the stable wake length is inversely proportional to thrust, tip speed ratio and the logarithmic of the turbulence intensity. In second study, large eddy simulations of the Navier-Stokes equations are also performed to investigate the wake interaction. Previous actuator line simulations on the single model wind turbine show that the accuracy of the results is directly related to the quality of the input airfoil characteristics. Therefore, a series of experiments on a 2D wing are conducted to obtain high quality airfoil characteristics for the NREL S826 at low Reynolds numbers. The new measured data are used to compute the rotor performance. The results show that the power performance as well as the wake development behind the rotor are well-captured. There are, however, some difficulties in prediction of the thrust coefficients. The continuation of this work considers the wake interaction investigations of two turbines inline (full-wake interaction) and two turbines with spanwise offset (half wake interaction). It is demonstrated that the numerical computations are able to predict the rotor performances as well as the flow field around the model rotors, and it can be a suitable tool for investigation of the wind turbine wakes. In the last study, an evaluation of the performance and near-wake structure of an analytical vortex model is presented. The vortex model is based on the constant circulation along the blades (Joukowsky rotor) and it is able to determine the geometry of the tip vortex filament in the rotor wake, allowing the free wake expansion and changing the local tip vortex pitch. Two different wind turbines have been simulated: a wind turbine with constant circulation along the blade and the other setup with a realistic circulation distribution, to compare the outcomes of the vortex model with real operative wind turbine conditions. The vortex model is compared with the actuator line approach and the presented comparisons show that the vortex method is able to approximate the single rotor performance and qualitatively describe the flow field around the wind turbine but with a negligible computational effort. This suggests that the vortex model can be a substitute of more computationally-demanding methods like actuator line technique to study the near-wake behavior.

QC 20141010

A computational study aimed at improving the understanding of rotating instability in the LP steam turbine last stage working under low flow rate conditions is described in this thesis. A numerical simulation framework has been developed to investigate into the instability flow field. Two LP model turbine stages are studied under various flow rate conditions. By using the 2D simulations as reference and comparing the results to those of the 3D simulations, the basic physical mechanism of rotating instability is analysed. The pressure ratio characteristics across the rotor row tip are found to be crucial to the inception of rotating instability. The captured instability demonstrates a 2D mechanism based on the circumferential variation of unsteady separation flow in the rotor row. The 3D tip clearance flow is found not a necessary cause of the instability onset. Several influential parameters on the instability flow are also investigated by a set of detailed studies on different turbine configurations. The results show that the instability flow pattern and characteristics can be altered by the gap distance between the stator and rotor row, the rotor blading and the stator row stagger angle. Some flow control approaches are proposed based on the observations, which may also serve as design reference. The tip region 3D vortex flow upstream to the rotor row is also captured by the simulations under low flow rate conditions. Its appearance is found to be able to suppress the inception of rotating instability by disrupting the interaction between the rotor separation flow and the incoming flow. Finally, some recommendations for further work are proposed.

Combustion instabilities are a major technical problem in most of industrial applications since they cause a performance deterioration of the combustion process. Under unstable operation the large amplitude oscillations of the flow induce many dangerous effects such as large mechanical vibrations, noise, augmented heat transfer rates at the combustor walls and increased pollutant emissions. In the gas turbines, an unstable heat release inside the combustion chamber can damage the hottest components of the combustor and reduce the life of the turbine blades. This study presents an investigation of the thermoacoustic behaviour of a single can gas turbine combustor. The combustor, originally conceived for operation with liquid and gaseous fossil fuels, was modified by the manufacturer to burn pure hydrogen or hydrogen/natural gas mixtures. Combustor design development was supported by experimental activities performed on a full-scale full-pressure test rig. A detailed procedure is proposed in this work to study the thermoacoustic instabilities in the combustor. Both hydrogen and natural gas operation are simulated by means of CFD RANS simulations carried out on a finite volume commercial code. The three-dimensional CFD analyses are performed on a coarse grid and take advantage of simplified numerical models to reduce the computation time. Due to this approach, the CFD analyses can simulate the time dependent thermoacoustic reactive flow field for a period of time large enough to capture unstable oscillation regimes, if present. Experimental measurements are used to impose the model boundary conditions and to validate the numerical results. The pressure signals recorded during the simulated period show a constant low-amplitude oscillation (a limit cycle) which does not affect the combustor performance. This behaviour agrees with the experimental data acquired during the combustion tests. The final part of this study compares the computed frequency spectra with the measured ones. The good agreement between the numerical results and the experimental values validate the potential of the low computational cost CFD approach to describe the thermoacoustic behaviour of the considered combustor.
L'instabilità di combustione peggiora le prestazioni di un combustore a flusso continuo e pertanto deve essere considerata un fenomeno indesiderato. Fluttuazioni della pressione e del rilascio termico possono infatti causare vibrazioni meccaniche, rumore, formazione di punti caldi sulle pareti della camera di combustione e incremento delle emissioni inquinanti. La combustione instabile è particolarmente dannosa nei combustori per turbina a gas nei quali ampie oscillazioni di portata e di rilascio termico possono danneggiare irreparabilmente le parti fisse e rotanti della turbina. Nel lavoro che si presenta viene studiato il comportamento termoacustico di un combustore di turbina a gas. Il combustore esaminato è del tipo tubolare, con singolo bruciatore a fiamma diffusiva ed è stato modificato dal costruttore per essere alimentato non solo a gas naturale ma anche a idrogeno. Il processo di sviluppo è stato supportato da prove di combustione su scala reale eseguite su un banco prova in grado di riprodurre le condizioni di pieno carico. L’analisi termoacustica viene condotta seguendo una procedura di indagine basata sulla simulazione numerica del fenomeno mediante un codice numerico commerciale con modelli di turbolenza di tipo RANS. Nelle analisi numeriche i modelli numerici e le griglie di calcolo sono scelti in modo da minimizzare tempi e risorse di calcolo. In questo modo è possibile simulare un intervallo temporale sufficientemente ampio da consentire al sistema di evolvere liberamente fino alle condizioni di regime per poter così valutare l’eventuale presenza di instabilità termoacustiche. Le misure raccolte durante le prove sperimentali sono impiegate nei calcoli sia per l’imposizione delle condizioni al contorno sia per la valutazione dei risultati. I segnali di pressione registrati durante le simulazioni mostrano la permanenza di oscillazioni di pressione nel combustore caratterizzate da un’ampiezza piuttosto ridotta. Queste oscillazioni sono dunque ampiamente tollerabili dal sistema (la combustione è ovunque completa e non vi sono fenomeni di estinzione di fiamma e di surriscaldamento delle pareti del combustore), in accordo con quanto osservato durante le prove sperimentali. Gli spettri calcolati al termine delle simulazioni sono comparati con gli spettri acquisiti durante le prove di combustione. Dal confronto emerge una sostanziale corrispondenza tra i modi di vibrare calcolati e quelli misurati al banco prova.

This thesis describes the coincident prediction and observation of thermo-acoustic instabilities in a turbulent, swirl-stabilized research combustor using a stability model constructed from validated reduced-order component models. The component models included the acoustic response to flame heat release rate at various locations in the combustor, the turbulent diffusion of uneven fuel-air mixing, and the flame's response to perturbations in both inlet velocity and equivalence ratio. These elements are closed in a system-level model to reflect their natural dynamic coupling and assessed with linear stability criteria. The results include the empirical validation of each of the component models and limited validation of the total closed-loop model with a lean premixed gaseous fuel combustor not dissimilar to an industrial burner. The degree of agreement between the predictions and the measurements encourages the conclusion that the reduced-order technique described herein not only includes the relevant physics, but has characterized them with sufficient acuracy to be the basis for design techniques for the passive avoidance of thermo-acoustic instabilities.
Master of Science

Lo studio delle miscele di gas è un tema che oggigiorno risponde alle necessità di vari campi di ricerca, come l'ingegneria aerospaziale, gli studi climatici, le industrie energetiche, ecc. Per questo motivo la costruzione di modelli matematici che simulino il comportamento di gas reali si rivela estremamente utile. Tra tutti gli approcci possibili, quello cinetico, che si basa sulle equazioni di Boltzmann per le funzioni di distribuzione dei gas, rappresenta uno degli strumenti più validi. Esso permette, infatti, di descrivere miscele a partire dall'interazione tra particelle, per poi derivare modelli per le quantità osservabili. Il lavoro contenuto in questa tesi è volto a riprendere i risultati presenti in letteratura per miscele di gas e a estenderli considerando casi più realistici, come miscele di specie monoatomiche e poliatomiche, che interagiscono in modo inelastico o chimico. Per prima cosa, nell'introduzione vengono presentati i concetti basilari e i risultati più rilevanti per lo studio cinetico dei gas, insieme a una sintesi più dettagliata dei contenuti della tesi. Nel Capitolo 1 proponiamo lo studio di una miscela reattiva costituita da quattro gas utilizzando la classica teoria cinetica di Boltzmann. Questo problema è già stato analizzato nell’ipotesi in cui i gas hanno lo stesso numero di livelli di energia interna, lo affrontiamo nel caso più generale supponendo che ciascuna delle specie coinvolte abbia un diverso numero di livelli energetici. Nei due capitoli successivi vengono studiate miscele di gas utilizzando un approccio cinetico di tipo BGK. In particolare, nel Capitolo 2 forniamo un modello BGK per una miscela inerte di gas monoatomici e poliatomici. Dimostriamo la consistenza del modello e analizziamo la stabilità degli equilibri; deriviamo poi opportune equazioni macroscopiche ed eseguiamo alcune simulazioni numeriche ispirandoci ai gas reali. Nel Capitolo 3, invece, proponiamo due modelli BGK per miscele di gas reagenti. Nel primo consideriamo quattro specie di gas coinvolte in una reazione chimica reversibile, nel secondo otto gas che partecipano a due reazioni disgiunte. La procedura precedente viene applicata in entrambi i casi, la principale differenza risiede nel dimostrare la consistenza del modello, poiché si ottengono equazioni trascendenti più complicate per la determinazione di tutti i parametri. Anche in questo contesto vengono eseguite simulazioni numeriche che modellino il comportamento di miscele reattive reali. Nella parte restante della tesi, studiamo miscele di gas mediante tecniche ulteriori. Nel Capitolo 4 consideriamo una miscela di cinque specie di gas, di cui tre costituiscono il mezzo ospite in cui interagiscono le altre due. Gli urti tra le particelle possono essere di tipo elastico, inelastico o chimico e ipotizziamo che questi avvengano su scale temporali diverse. Successivamente, scriviamo le equazioni di Boltzmann classiche per le funzioni di distribuzione delle varie componenti. Dopo opportune integrazioni delle equazioni e tramite un passaggio al limite otteniamo equazioni di reazione-diffusione per le densità di specie. Nello specifico, applichiamo questo procedimento in tre diversi regimi idrodinamici, ottenendo per ciascuno di essi un diverso sistema di reazione-diffusione. Le proprietà di stabilità di tali sistemi vengono discusse nel Capitolo 5. Ci concentriamo in particolare sul verificarsi del fenomeno dell’instabilità di Turing per scelte opportune dei valori energetici e delle frequenze di collisione. Attraverso simulazioni numeriche, verifichiamo poi la formazione di pattern nell’evoluzione delle densità, come previsto dall'analisi di Turing. Concludiamo con alcune ulteriori osservazioni e prospettive per futuri sviluppi del presente lavoro di ricerca.
The study of gas flows is an issue that nowadays responds to the necessities of various fields of research, as aerospace engineering, climate studies, energy industries, etc. For this reason, the construction of mathematical models simulating the behavior of real gas mixtures is extremely useful. Among all possible approaches, the kinetic one, based on Boltzmann equations for species distribution functions, seems to be a very powerful tool. It allows, in fact, to describe mixtures starting from interaction among particles, with the possibility of deriving models for the behavior of the global system at observable level. The work of this thesis is devoted to considering results obtained so far for mixtures of gases and extending them considering more real-like cases, such as mixtures of monoatomic and polyatomic gas species, that may also interact inelastically or chemically. As first, we provide an introduction in which the basic concepts and the most relevant results for kinetic description of gases are presented, along with a more detailed summary of the work carried out in the thesis. In Chapter 1, we propose the study of a reacting mixture of four gases using the classical Boltzmann kinetic theory. This case was already analyzed when the four gases are considered to have the same number of internal energy levels. We generalize it allowing each of the gas species to have a different number of energetic levels. Chapter 2 and Chapter 3 are devoted to the study of gas mixtures using a kinetic approach of BGK type. In particular, in Chapter 2 we provide a BGK model for an inert mixture of monatomic and polyatomic gases. We prove the consistency of the model and analyze the stability of equilibria, then we derive macroscopic equations and perform some numerical simulations being inspired by real gases. In Chapter 3, instead, we propose two BGK models for mixtures of reacting gases. In the first one we have four gas species involved in a reversible chemical reaction, in the second case eight gases react through two disjoint reactions. The previous strategy is applied to both cases, the main differences are in proving the consistency of the model, since we face more complicate transcendental equations to determine all the parameters. Also in these cases, numerical simulations are performed to reproduce the behavior of real reacting mixtures. In the remaining part of the thesis, we study gas mixtures using different techniques. In Chapter 4 we consider a mixture of five gas species, three of them constituting a background medium in which the other two interact. Encounters among particles can be elastic, inelastic, or chemical and we suppose that they occur at different time scales. We write classical Boltzmann equations for the interacting components, we pass to the asymptotic diffusive limit and, by means of suitable integrations of the kinetic equations, we obtain reaction-diffusion equations for densities of the species. Specifically, we apply this procedure in three different hydrodynamic regimes, obtaining in each case a proper reaction-diffusion system. The stability properties of these systems are then studied in Chapter 5. We consider the possibility of having Turing instability for a suitable choice of internal energy amounts and of collision frequencies. Through numerical simulations, we verify the formation of spatial patterns in the evolution of the number densities of reactants, as predicted by Turing analysis. We conclude with some further observations and perspectives for a future development of the present research work.

It has been recognized that the evaporation process is one of the pivotal mechanisms driving thermo-acoustic instability in gas turbines and rockets in particular. In this regard, this study is principally focused on studying the evaporation process relevant to thermo-acoustic instability from three complementary viewpoints in an effort to contribute to an overall instability model driven primarily by evaporation in gas turbine combustors. Firstly, a state of the art LES algorithm is employed to validate an evaporation model to be employed in predictive modelling regarding combustion instabilities. Good agreement between the numerical predictions and experimental data is achieved. Additionally, transient sub-critical droplet evaporation is investigated numerically. In particular, a numerical method is proposed to capture the extremely important pressure-velocity-density coupling. Furthermore, the dynamic system nonlinear behaviour encountered in classical thermo-acoustic instability is investigated. The Poincaré map is adopted to analyse the stability of a simple non-autonomous system considering a harmonic oscillation behaviour for the combustion environment. The bifurcation diagram of a one-mode model is obtained where the analysis reveals a variety of chaotic behaviours for some select ranges of the bifurcation parameter. The bifurcation parameter and the corresponding period of a two-mode dynamic model are calculated using both analytical and numerical methods. The results computed by different methods are in good agreement. In addition, the dependence of the bifurcation parameter and the period on all the relevant coefficients in the model is investigated in depth. Moreover, a discrete dynamic model accounting for both combustion and vaporization processes is developed. In terms of different bifurcation parameters relevant to either combustion or evaporation, various bifurcation diagrams are presented. As part of the nonlinear characterization, the governing process Lyapunov exponent is calculated and employed to analyze the stability of the particular dynamic system. The study has shown conclusively that the evaporation process has a significant impact on the intensity and nonlinear behaviour of the system of interest, vis-à-vis a model accounting for only the gaseous combustion process. Furthermore, two particular nonlinear control methodologies are adopted to control the chaotic behaviour displayed by the particular aperiodic motions observed. These algorithms are intended to be implemented for control of combustion instability numerically and experimentally to provide a rational basis for some of the control methodologies employed in the literature. Finally, a state of the art neural network is employed to identify and predict the nonlinear behaviour inherent in combustion instability, and control the ensuing pressure oscillations. Essentially, the NARMAX model is implemented to capture nonlinear dynamics relating the input and output of the system of interest. The simulated results accord with the results reported. Moreover, a control system using the NARMA-L2 algorithm is developed. The simulation conclusively points to the fact that the amplitude of pressure oscillations can be attenuated to an acceptable level and the controller proposed may be implemented in a practical manner.

This thesis describes the development, verification, and validation of a three dimensional time domain thermoacoustic solver. The purpose of the solver is to predict the frequencies, modeshapes, linear growth rates, and limit cycle amplitudes for combustion instability modes in gas turbine combustion chambers. The linearized Euler equations with nonlinear heat release source terms are solved using the finite volume method. The treatment of mean density gradients was found to be vital to the success of frequency and modeshape predictions due to the sharp density gradients that occur across deflagration waves. In order to treat mean density gradients with physical fidelity, a non-conservative finite volume method based on the wave propagation approach to the Riemann problem is applied. For modelling unsteady heat release, user input flexibility is maximized using a virtual class hierarchy within the OpenFOAM C++ library. Unsteady heat release based on time lag models are demonstrated. The solver gives accurate solutions compared with analytical methods for one-dimensional cases involving mean density gradients, cross-sectional area changes, uniform mean flow, arbitrary impedance boundary conditions, and unsteady heat release in a one-dimensional Rijke tube. The solver predicted resonant frequencies within 1% of the analytical solution for these verification cases, with the dominant component of the error coming from the finite time interval over which the simulation is performed. The linear growth rates predicted by the solver for the Rijke tube verification were within 5% of the theoretical values, provided that numerical dissipation effects were controlled. Finally, the solver is then used to predict the frequencies and limit cycle amplitudes for two lab scale experiments in which detailed acoustics data are available for comparison. For experiments at the University of Melbourne, an empirical flame describing function was provided. The present simulation code predicted a limit cycle of 0.21 times the mean pressure, which was in close agreement with the estimate of 0.25 from the experimental data. The experiments at Purdue University do not yet have an empirical flame model, so a general vortex-shedding model is proposed on physical grounds. It is shown that the coefficients of the model can be tuned to match the limit cycle amplitude of the 2L mode from the experiment with the same accuracy as the Melbourne case. The code did not predict the excitation of the 4L mode, therefore it is concluded that the vortex-shedding model is not sufficient and must be supplemented with additional heat release models to capture the entirety of the physics for this experiment.
M.S.M.E.
Masters
Mechanical and Aerospace Engineering
Engineering and Computer Science
Mechanical Engineering; Thermo-Fluids

Acoustic Transfer Functions Derived from Finite Element Modeling for Thermoacoustic Stability Predictions of Gas Turbine Engines

Design and prediction of thermoacoustic instabilities is a major challenge in aerospace propulsion and the operation of power generating gas turbine engines. This is a complex problem in which multiple physical systems couple together. Traditionally, thermoacoustic models can be reduced to dominant physics which depend only on flame dynamics and acoustics. This is the general approach adopted in this research. The primary objective of this thesis is to describe how to obtain acoustic transfer functions using finite element modeling. These acoustic transfer functions can be coupled with flame transfer functions and other dynamics to predict the thermoacoustic stability of gas turbine engines. Results of this research effort can go beyond the prediction of instability and potentially can be used as a tool in the design stage. Consequently, through the use of these modeling tools, better gas turbine engine designs can be developed, enabling expanded operating conditions and efficiencies.

This thesis presents the finite element (FE) methodology used to develop the acoustic transfer functions of the Combustion System Dynamics Laboratory (CSDL) gaseous combustor to support modeling and prediction of thermoacoustic instabilities. In this research, several different areas of the acoustic modeling were addressed to develop a representative acoustics model of the hot CSDL gaseous combustor. The first area was the development and validation of the cold acoustic finite element model. A large part of this development entailed finding simple but accurate means for representing complex geometries and boundary conditions. The cold-acoustic model of the laboratory combustor was refined and validated with the experimental data taken on the combustion rig.

The second stage of the research involved incorporating the flame into the FE model and has been referred to in this thesis as hot-acoustic modeling. The hot-acoustic model also required the investigation and characterization of the flame as an acoustic source. The detailed mathematical development for the full reacting acoustic wave equation was investigated and simplified sufficiently to identify the appropriate source term for the flame. It was determined that the flame could be represented in the finite element formulation as a volumetric acceleration, provided that the flame region is small compared to acoustic wavelengths. For premixed gas turbine combustor flames, this approximation of a small flame region is generally a reasonable assumption.

Both the high temperature effects and the flame as an acoustic source were implemented to obtain a final hot-acoustic FE model. This model was compared to experimental data where the heat release of the flame was measured along with the acoustic quantities of pressure and velocity. Using these measurements, the hot-acoustic FE model was validated and found to correlate with the experimental data very well.

The thesis concludes with a discussion of how these techniques can be utilized in large industrial-size combustors. Insights into stability are also discussed. A conclusion is then presented with the key results from this research and some suggestions for future work.
Master of Science

Combustion instability represents a significant problem in the application of low emission lean premixed combustion for gas turbines and has become one of the primary concerns in modern gas turbine industry. Effusion cooling has become common practice in gas turbine combustors and when calibrated, perforated combustor liners are able to attenuate combustion instability within a wide frequency range. However, the acoustic attenuation effect of perforated liner absorbers varies with a considerable number of flow and geometry influencing factors. The traditional approach of designing perforated combustor liners relies heavily on expensive and lengthy trial-and-error experimental practice. Computational fluid dynamics (CFD), especially large eddy simulation (LES) method has gained recognition as a viable tool for the simulation of unsteady flows and the phenomenon of combustion instability in gas turbine combustors. However, detailed resolution of the many small scale features, such as effusion cooling holes, is computationally very expensive and restricts the routine simulation of detailed engine geometries. In this thesis, a novel homogenous porous media model is proposed for the simulation of acoustic attenuation effect of gas turbine perforated liners. The model is validated against a number of well-acknowledged experiments and is shown to be able to predict acoustic attenuation properties of gas turbine liners both in the linear and non-linear absorption regimes and also the effect of bias flow, grazing flow and the temperature of flow on the acoustic properties of the liners. The model is applied to a large eddy simulation of a lab-scale premixed combustor "PRECCINSTA" and is demonstrated to successfully represent noise attenuation effects of perforated liner absorbers in both cold flow and reacting flow conditions. This model is able to provide a significant reduction in the overall computational time in comparison to directly resolved geometries, and can be applied as such a viable option for routine engineering simulation of perforated combustor liners.

Ce travail de thèse porte sur les propriétés de stabilité des tourbillons hélicoïdaux, structures que l'on retrouve notamment dans le sillage des rotors d'hélicoptères et d'éoliennes.Dans une première partie, le développement spatio-temporel de l'instabilité d'appariement est caractérisé à l'aide d'un code numérique pseudo-spectral pour une allée infinie d'anneaux tourbillonnaires. On montre que ce modèle axisymétrique d'écoulement est en effet une bonne approximation du système hélicoïdal dans la limite des grands rayons et petits pas d’hélice. Dans ces conditions, et en utilisant un adimensionnement judicieux, on obtient également que le résultat théorique pour le taux de croissance spatio-temporel obtenu pour une double allée de tourbillons ponctuels s’avère être une bonne prédiction pour le cas hélicoïdal.Dans une seconde partie, on décrit comment un ou plusieurs tourbillons hélicoïdaux ont pu être générés de façon très peu perturbée à l’aide de modèles réduits de rotors dans le canal hydrodynamique du laboratoire. Grâce à l’introduction de perturbations d’amplitudes et de fréquences soigneusement contrôlées, le taux de croissance de l’instabilité d’appariement a pu être mesuré et comparé aux résultats théoriques. L’évolution non linéaire de ces perturbations ainsi que d’autres modes instables, à plus petites longueurs d’onde, ont également pu être observés expérimentalement pour la première fois.Enfin, ces résultats ont été appliqués au cas des rotors d’hélicoptères pour la prédiction du régime de Vortex Ring State (VRS) et à la transition vers la turbulence du sillage des éoliennes
This thesis is devoted to the stability properties of helical vortices, which are of interest for applications such as helicopter and wind turbine wakes.In a first part, the spatio-temporal development of the pairing instability is characterised for an infinite array of vortex rings, using a pseudo-spectral numerical code. We show that this axisymmetric flow model is indeed a good approximation of the helical system in the limit of large helix radius and small pitch. Under these assumptions, and by using appropriate dimensionless variables, we also show that the theoretical result concerning the spatio-temporal growth rate for a double row of point vortices represents a good prediction for the helical case.In a second part, we describe how one or several helical vortices were generated in a carefully controlled way using small-scale rotor models in the water channel of the laboratory. Introducing perturbations with well-defined amplitudes and frequencies, the growth rate of the pairing instability could be measured experimentally and compared to theoretical predictions. The non-linear evolution of these perturbations, as well as other unstable modes of smaller wavelengths, were also observed experimentally for the first time.Finally, these results were applied to helicopter wakes for the prediction of the Vortex Ring State (VRS) regime and to the transition to turbulence in wind turbine wakes

Cette thèse est consacrée à l’étude de la dynamique de quelques problèmes de proie-prédateur de type Leslie-Gower avec des systèmes d’équations différentielles ordinaires et des équations de réaction-diffusion. L’objectif principal est de faire l’analyse mathématique, la simulation numérique des modèles construits. La thèse est divisée en trois parties : La première partie est consacrée à un système proie-prédateur avec récolte de proie, le modèle est donné par un système d’équation différentielle ordinaire. Le but de cette partie est d’étudier l’impact de la récolte sur le comportement du système. Dans la deuxième partie, nous introduisons la dimension spatiale dans le modèle dynamique considéré sans récolte, modélisant une chaîne alimentaire de deux espèces avec diffusion sur un domaine circulaire et une fonction de réponse de Holling type II. Nous effectuons une analyse théorique complète de la dynamique spatio-temporelle du modèle construit ainsi que l’étude du système sur le domaine circulaire. Une étude mathématique similaire est menée dans le cadre de la réponse fonctionnelle de Benddington-DeAngelis. Nous étudions, aussi le comportement qualitatif d’une chaîne alimentaire de trois espèces avec une réponse fonctionnelle de Holling type II. Dans la dernière partie, nous introduisons des termes de diffusions croisées dans le modèle dynamique considéré dans le but d’avoir l’effet de ce dernier sur le comportement du système
This thesis is devoted to the study of the dynamics of some problems Leslie Gower-type predator-prey with ordinary differential equations and reaction-diffusion equations. The main objective is to make mathematical analysis, numerical simulation of constructed models. The thesis is divided in three parts : The first part is devoted to a predator-prey system with prey harvesting, the model is given by an ordinary differential equation system. The aim of this part is to study the impact of harvesting on the system behavior. In the second part, we introduce the spatial dimension in the dynamic model considered without harvesting, modeling a food chain of two species with diffusion on the circular area and Holling Type II response function. We perform a complete theoretical analysis of the spatiotemporal dynamics model built and the system study on the circular area. A similar mathematical study is conducted as part of the functional response of Benddington-DeAngelis.We study, also the qualitative behavior of a food chain of three species with a Holling type II response function. In the last party, we introduce of cross-diffusion terms in the considered dynamic model in order to have the effect of the latter on the system behavior

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 <> 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

Cette thèse est consacré à l'analyse de modèles de croissance et de mouvement intervenant en biologie et en écologie. Nous regardons en particulier deux types de modèles: des équations de dynamique de populations structurées et des modèles de diffusion croisée. Dans une première partie consacrée au travail sur les populations structurées, nous étudions d'abord des modèles linéaires de croissance en environnement périodique en temps. Ces modèles sont caractérisés par l'existence d'un exposant de croissance, appelé valeur propre de Floquet, dont nous comparons les propriétés avec celui qui apparaît en environnement stationnaire. Nous mettons en évidence grâce à un contre exemple le fait qu'il n'y a pas de comparaison générale possible entre l'exposant de croissance en milieu périodique et celui associé à un milieu moyenné. Les résultats de convexité de Kingman sur le rayon spectral des matrices positives sont étendus à la valeur propre de Floquet. Nous étudions également le comportement de cette valeur propre dans des cas dégénérés, où certains paramètres peuvent s'annuler ou exploser. Dans cette partie est également exposé une justification de la dérivation d'un modèle d'équations aux dérivées partielles pour la réplication du prion. Ce modèle est vu comme approximation d'un système infini d'équation différentielles ordinaires. Ceci se fait grâce à des résultats de compacité faible et la preuve permet de proposer des pistes pour un modèle plus complet. La deuxième partie est consacrée à l'étude de modèles de diffusion croisée. Nous nous plaçons dans le cas d'un domaine bornée et en absence de termes de réactions. Le but est de questionner la stabilité de l'équilibre homogène. L'application de techniques de dualité utilisées pour les système de réaction-diffusion permettent d'obtenir des bornes qui servent elles-même ensuite, combinées à la régularité elliptique à obtenir l'existence globale pour une version régularisée du système. Ladite régularisation est dépendante d'un paramètre dont les valeurs déterminent la stabilité ou l'instabilité linéaire de l'équilibre homogène. La valeur critique du paramètre de régularisation est d'ailleurs une valeur de bifurcation pour les équilibres.

The continuous trend in gas turbine design towards lighter, more powerful and more reliable engines on one side and use of alternative fuels on the other side renders flutter problems as one of the paramount challenges in engine design. Flutter denotes a self-excited and self-sustained aeroelastic instability phenomenon that can lead to material fatigue and eventually damage of structure in a short period of time unless properly damped. The design for flutter safety involves the prediction of unsteady aerodynamics as well as structural dynamics that is mostly based on in-house developed numerical tools. While high confidence has been gained on the structural side unanticipated flutter occurrences during engine design, testing and operation evidence a need for enhanced validation of aerodynamic models despite the degree of sophistication attained. The continuous development of these models can only be based on the deepened understanding of underlying physical mechanisms from test data.

As a matter of fact most flutter test cases treat the turbomachine flow in two-dimensional manner indicating that the problem is solved as plane representation at a certain radius rather than representing the complex annular geometry of a real engine. Such considerations do consequently not capture effects that are due to variations in the third dimension, i.e. in radial direction. In this light the present thesis has been formulated to study three-dimensional effects during flutter in the annular environment of a low-pressure turbine blade row and to describe the importance on prediction of flutter stability. The work has been conceived as compound experimental and computational work employing a new annular sector cascade test facility. The aeroelastic response phenomenon is studied in the influence coefficient domain having one blade oscillating in various three-dimensional rigid-body modes and measuring the unsteady response on several blades and at various radial positions. On the computational side a state-of-the-art industrial numerical prediction tool has been used that allowed for two-dimensional and three-dimensional linearized unsteady Euler analyses.

The results suggest that considerable three-dimensional effects are present, which are harming prediction accuracy for flutter stability when employing a two-dimensional plane model. These effects are mainly apparent as radial gradient in unsteady response magnitude from tip to hub indicating that the sections closer to the hub experience higher aeroelastic response than their equivalent plane representatives. Other effects are due to turbomachinery-typical three-dimensional flow features such as hub endwall and tip leakage vortices, which considerably affect aeroelastic prediction accuracy. Both effects are of the same order of magnitude as effects of design parameters such as reduced frequency, flow velocity level and incidence. Although the overall behavior is captured fairly well when using two-dimensional simulations notable improvement has been demonstrated when modeling fully three-dimensional and including tip clearance.

Combustion instabilities (thermo-acoustic pressure oscillations) have been recognised for some time as a problem limiting the development of low emissions (e.g., lean burn) gas turbine combustion systems, particularly for aviation propulsion applications. Recently, significant research efforts have been focused on acoustic damping for suppression of combustion instability. Most of this work has either been experimental or based on linear acoustic theory. The last 3-5 years has seen application of density based CFD methods to this problem, but no attempts to use pressure-based CFD methods which are much more commonly used in combustion predictions. The goal of the present work is therefore to develop a pressure-based CFD algorithm in order to predict accurately acoustic propagation and acoustic damping processes, as relevant to gas turbine combustors. The developed computational algorithm described in this thesis is based on the classical pressure-correction approach, which was modified to allow fluid density variation as a function of pressure in order to simulate acoustic phenomena, which are fundamentally compressible in nature. The fact that the overall flow Mach number of relevance was likely to be low ( mildly compressible flow) also influenced the chosen methodology. For accurate capture of acoustic wave propagation at minimum grid resolution and avoiding excessive numerical smearing/dispersion, a fifth order accurate Weighted Essentially Non-Oscillatory scheme (WENO) was introduced. Characteristic-based boundary conditions were incorporated to enable accurate representation of acoustic excitation (e.g. via a loudspeaker or siren) as well as enable precise evaluation of acoustic reflection and transmission coefficients. The new methodology was first validated against simple (1D and 2D) but well proven test cases for wave propagation and demonstrated low numerical diffusion/dispersion. The proper incorporation of Characteristic-based boundary conditions was validated by comparison against classical linear acoustic analysis of acoustic and entropy waves in quasi-1D variable area duct flows. The developed method was then applied to the prediction of experimental measurements of the acoustic absorption coefficient for a single round orifice flow. Excellent agreement with experimental data was obtained in both linear and non-linear regimes. Analysis of predicted flow fields both with and without bias flow showed that non-linear acoustic behavior occurred when flow reversal begins inside the orifice. Finally, the method was applied to study acoustic excitation of combustor external aerodynamics using a pre-diffuser/dump diffuser geometry previously studied experimentally at Loughborough University and showed the significance of boundary conditions and shear layer instability to produce a sustained pressure fluctuation in the external aerodynamics.

Ce travail de thèse se compose en deux parties :Partie 1Nous nous intéressons à la propagation lumineuse non-linéaire dans des cellules planaires de cristal liquide nématique mélangé avec un colorant, l’effet non-linéaire considéré étant l'effet thermique. Puis, nous nous intéressons à l'amélioration de la fluorescence émise par le colorant.Nous concluons que pour améliorer le spectre de la fluorescence, il faut utiliser une source se propageant en mode soliton, optimiser la distance entre la fibre optique d’excitation de celle de collecte et l’ajout des nanoparticules d'or au cristal liquide. Cette amélioration de la fluorescence ouvrira la voie à la création du laser à colorant assisté par propagation de soliton.Partie 2Nous étudions la dynamique spatiotemporelle d'une cavité en anneau remplie d'un milieu de type Kerr non-instantané et pompée par un faisceau cohérent. Nous effectuons d’abord une étude analytique afin de déterminer les types d’instabilités possibles et leurs seuils. Puis, une étude numérique est menée pour observer l’évolution du champ dans la cavité. Nous montrons l’existence des structures périodiques et localisées
The work of this thesis consists of two parts:Part 1We are interested in non-linear light propagation in planar cells of nematic liquid crystal mixed with a dye. The non-linear effect is considered to be a thermal effect. Then, we are interested in improving the fluorescence emitted by the dye.We conclude that to improve the fluorescence spectrum, we need to use a source propagating in soliton mode, to optimize the distance between the excitation optical fiber and the collecting one and to add the gold nanoparticles to the liquid crystal. This improvement of fluorescence spectrum will pave the way for the creation of a dye laser assisted with soliton propagation.Part 2We study the spatiotemporal dynamics of a ring cavity filled with a non-instantaneous Kerr-type medium and pumped by a coherent beam. We first carried out an analytical study to determine the types of instabilities and their thresholds. Then, a numerical study is carried out to observe the evolution of the field in the cavity. We show the existence of periodic and localized structures

This thesis provides a numerical and theoretical investigation of transitional and turbulent enclosed rotating flows, with a focus on the formation of macroscopic coherent flow structures. The underlying processes are strongly threedimensional due to the presence of boundary layers on the discs and on the walls of the outer (resp. inner) cylindrical shroud (resp. shaft). The complexity of these flows poses a great challenge in fundamental research however the present work is also of importance for industrial rotating machinery, from hard-drives to space engines turbopumps - the design issues of the latter being behind the motivation for this thesis. The present work consists of two major investigations. First, industrial cavities are modeled by smooth rotor/stator cavities and therein the dominant flow dynamics is investigated. For the experimental campaigns on industrial machinery revealed dangerous unsteady phenomena within the cavities, the emphasis is put on the reproduction and monitoring of unsteady pressure fluctuations within the smooth cavities. Then, the LES of three configurations of real industrial turbines are conducted to study in situ the pressure fluctuations and apply the diagnostics already vetted on academic problems.

This work is concerned with the fluid dynamic processes and the associated loss of acoustic energy produced by circular apertures within noise absorbing perforated walls. Although applicable to a wide range of engineering applications particular emphasis in this work is placed on the use of such features within a gas turbine combustion system. The primary aim for noise absorbers in gas turbine combustion systems is the elimination of thermo-acoustic instabilities, which are characterised by rapidly rising pressure amplitudes which are potentially damaging to the combustion system components. By increasing the amount of acoustic energy being absorbed the occurrence of thermo-acoustic instabilities can be avoided. The fundamental acoustic characteristics relating to linear acoustic absorption are presented. It is shown that changes in orifice geometry, in terms of gas turbine combustion system representative length-to-diameter ratios, result in changes in the measured Rayleigh Conductivity. Furthermore in the linear regime the maximum possible acoustic energy absorption for a given cooling mass flow budget of a conventional combustor wall will be identified. An investigation into current Rayleigh Conductivity and aperture impedance (1D) modelling techniques are assessed and the ranges of validity for these modelling techniques will be identified. Moreover possible improvements to the modelling techniques are discussed. Within a gas turbine system absorption can also occur in the non-linear operating regime. Hence the influence of the orifice geometry upon the optimum non-linear acoustic absorption is also investigated. Furthermore the performance of non-linear acoustic absorption modelling techniques is evaluated against the conducted measurements. As the amplitudes within the combustion system increase the acoustic absorption will transition from the linear to the non-linear regime. This is important for the design of absorbers or cooling geometries for gas turbine combustion systems as the propensity for hot gas ingestion increases. Hence the relevant parameters and phenomena are investigated during the transition process from linear to non-linear acoustic absorption. The unsteady velocity field during linear and non-linear acoustic absorption is captured using particle image velocimetry. A novel analysis technique is developed which enables the identification of the unsteady flow field associated with the acoustic absorption. In this way an investigation into the relevant mechanisms within the unsteady flow fields to describe the acoustic absorption behaviour of the investigated orifice plates is conducted. This methodology will also help in the development and optimisation of future damping systems and provide validation for more sophisticated 3D numerical modelling methods. Finally a set of design tools developed during this work will be discussed which enable a comprehensive preliminary design of non-resonant and resonant acoustic absorbers with multiple perforated liners within a gas turbine combustion system. The tool set is applied to assess the impact of the gas turbine combustion system space envelope, complex swirling flow fields and the propensity to hot gas ingestion in the preliminary design stages.

The purpose of this thesis was to get an idea of how tourism in Ukraine and specifically in the capital, Kiev, changed since the major events in recent years. In 2012 Ukraine and Poland welcomed the big football event Euro 2012 where Kiev was one of the hosting cities. After that the tourist flow increased until the terrible riot that took place at the end of 2013. Among other consequences, it led to Kiev receiving a bad image internationally via mass media, which in turn led to the reduction of the tourist flow. This thesis is a qualitative study, based on interviews with two government officials who had given us an overview of how tourism is today and what government does to improve the city’s image of having poor security and threats to potential tourists in Kiev today. Interviews with both representatives took place on location in Kiev. In addition to that, we conducted an email-survey with 13 Swedish tourists who had not previously visited Kiev to get a picture of their knowledge of Ukraine’s capital. Based on the answers from our respondents, we had worked to obtain the relevant theories and previous research for further analysis. The results of this thesis show that nowadays tourism in Kiev is not a profitable industry and there is too little focus dedicated to this topic as well as the city's marketing, because of the ongoing war in parts of the country. Furthermore, there is no ministry responsible for tourism in Kiev, but only departments that are being constantly moved between different ministries.
Syftet med denna uppsats var att få en uppfattning över hur turism i Ukraina och specifikt i huvudstaden Kiev ser ut, då den ändrades i och med stora händelser under de senaste åren. År 2012 hade Ukraina och Polen välkomnat det stora fotbollsevenemanget EM 2012 och Kiev var en av städerna som evenemanget arrangerades i. Efter detta hade turistflödet ökat tills det förfärliga upploppet som skedde i slutet av år 2013. Det ledde till att Kiev fick en dålig image internationellt via massmedia som i sin tur ledde till turismflödets minskning. Uppsatsen är en kvalitativ studie, byggt på intervjuer med två myndighetsrepresentanter som har gett oss en överblick om hur turismen ser ut idag och vad staten gör för att avlägsna denna image om dålig säkerhet och hot mot potentiella turister som Kiev har idag. Med potentiell turist menas en person som hittar något intresse för att besöka ett turistställe. Intervju med både representanter skedde på plats i Kiev. Samtidigt hade vi genomfört en undersökning då vi via e-post intervjuade 13 svenska turister som inte tidigare hade besökt Kiev. Syftet med e-post intervjuerna var att få deltagarnas bild av vad de har för kunskap om Kiev. Utifrån svar från våra respondenter hade vi arbetat för att få fram de relevanta teorier samt tidigare forskning för vidare analys. Resultatet av denna uppsats visar att dagens turism i Kiev inte är den lönsamma näringen och det fokus som läggs på detta område samt stadens marknadsföring är obetydlig, då det pågår krig i delar av landet. Samtidigt som förvärvsarbetet av turismen brister på grund av saknad av ett departement som ska vara ansvarig för turismen i Kiev. Det finns endast inaktiva avdelningar som ständigt flyttas till olika departement.

L'un des objectifs actuellement poursuivis par les motoristes aéronautiques est de concevoir des injecteurs qui associent un niveau de performance élevé à un faible taux d'émissions polluantes. Cela a conduit au dévelopement de systèmes fonctionnant en régime de combustion pauvre et pré-mélangé qui permet de réduire les températures de flamme et donc de limiter la formation d'espèces polluantes (oxydes d'azote ou monoxide de carbone). Cependant, ces systèmes sont souvent le siège de phénomènes indésirables comme les remontées de flamme, l'auto-allumage ou les instabilités de combustion. Afin de pallier ces problèmes, SAFRAN/SNECMA souhaite actuellement développer de nouvelles technologies d'injecteurs pauvres et pré-mélangés : des systèmes multipoints. Afin d'améliorer la compréhension de ces injecteurs, un prototype expérimental a été développé au laboratoire EM2C. Les effets de la multi-injection de combustible sur la dynamique de combustion ont été particulièrement étudiés. Pour ce faire, plusieurs diagnostics sont mis en œuvre : un ensemble de microphones pour mesurer les fluctuations de pression dans le banc expérimental, un dispositif de mesure de vitesse à haute cadence et un dispositif de fluorescence induite par laser sur le radical OH pour visualiser la position du front de flamme. L'ensemble de ces mesures a permis de dégager des scénarii de stabilisation de la flamme et de couplages acoustique-combustion, ainsi que le développement d'un premier système de contrôle du banc de combustion expérimental
One of the objectives pursued by aircraft engine designers is to develop injectors that associate high performance level with low pollutant emissions. This leads to the design of combustors operating under lean premixed combustion regimes, since they permit to decrease flame temperature and then the emission of pollutant species such as oxides of nitrogen and carbon monoxide. However, these devices often exhibit undesirable phenomena such as flashback, self-ignition, strong combustion instabilities. In order to reduce these phenomena, SAFRAN/SNECMA wants to develop new technologies of lean premixed injectors: staged multipoint devices. To improve their understanding, an experimental prototype has been developped and analyzed in the laboratory EM2C. The effects of multi fuel-injection on the experimental burner combustion dynamics are particularly studind using several diagnostics including a set of microphones to measure pressure fluctuations in the combustion chamber, a High Speed Particle Image Velocimetry system to analyze flow fields and a Planar Induced Fluorescence system to visualize the flame front position in the combustion chamber. These measurement have permitted to identify several flame stabilization and a combustion-acoustic coupling scenarii, as well as the development of a first control system of the experimental burner

Cette thèse s'inscrit dans le cadre de la modélisation des interactions entre hôtes et auxiliaires de lutte biologique. L'objectif principal est de faire l'analyse mathématique et la simulation numérique des modèles spatiotemporels construits. Il s'agit de déterminer la typologie et la catégorisation des structures spatiales émergentes en fonction des paramètres de contrôle. Nous considérons dans la première partie de la thèse, une chaîne alimentaire de deux espèces, c'est à dire une population de proies et une population de prédateurs modélisées par un système de réaction-diffusion. Nous étudions l'analyse qualitatives des solutions, les bifurcations globales et locales, et déterminons les conditions de variation spatiales et temporales des motifs. Nous démontrons l'existence de "Travelling waves" par les outils d'analyse fonctionnelle en généralisant la méthode développée par S. Ahmad. Une étude mathématique similaire est menée dans le cadre d'une chaîne alimentaire de trois espèces constituée d'une proie, d'un prédateur et d'un super-prédateur. Le dernier chapitre de cette thèse est consacré à la construction et l'étude d'un modèle mathématique de type réaction-diffusion de la thérapie génétique du cancer. Le modèle prend en considération à la fois la dynamique de la population des cellules cancéreuses, des virus réplicatifs et de la réponse immunitaire qui reconnait les antigènes viraux dans les cellules cancéreuses. Nous établissons les conditions de stabilité de l'état d'équilibre endémique et celui correspondant à l'élimination de la tumeur. Si la tumeur ne peut pas être complétement guérie, nous déterminons les conditions d'une thérapie optimale et estimons par simulation le temps de survie du patient.

L’influence de certains effets technologiques sur les performances d’une turbine n’est pas encore bien comprise. En particulier, des essais ont été réalisés par Safran Helicopter Engines sur un étage de turbine haute pression dont l’anneau de roue forme une cavité reliée à la veine au niveau de l’espace inter-grilles, dans laquelle est injecté de l’air de refroidissement. Ils ont montré une sensibilité inattendue des performances à certains paramètres géométriques. Cette thèse a pour but d’expliquer ce comportement, et d’améliorer la compréhension et la prédiction par simulation numérique de l’effet d’une telle cavité sur l’aérodynamique et l’aérothermique de la turbine. Cette problématique a été traitée à l’aide de simulations numériques RANS instationnaires, réalisées avec le code elsA. Dans un premier temps, seule une partie de la cavité a été simulée, ce qui la ramène à une simple injection d’air de refroidissement dans la veine par une fente axisymétrique. Ces calculs ont montré que l’écoulement dans la veine est profondément modifié par l’air de refroidissement. Entre autres, le tourbillon de passage au carter et l’écoulement de jeu dans le rotor sont impactés, et deviennent fortement instationnaires. Les mécanismes d’interaction entrant en jeu sont détaillés, et l’effet sur les pertes est discuté. Des calculs prenant en compte la cavité entière ont ensuite été mis en place, d’abord avec un écoulement dans la veine simplifié, puis avec l’étage de turbine complet. Ils ont permis d’identifier une structure composée de poches de gaz de veine ingéré dans la cavité et de zones d’éjection d’air de refroidissement, tournant à une vitesse inférieure à celle du rotor, et manifestement générée par une instabilité. Des structures semblables avaient déjà été identifiées dans des turbines par de nombreuses études concernant des cavités inter-disques au moyeu, mais c’est ici la première fois qu’un tel comportement est obtenu dans une cavité composée de parois fixes et débouchant au carter. L’effet de cette structure sur l’écoulement dans la veine est qualitativement identique à celui obtenu par les simulations avec seulement une partie de la cavité, mais l’intensité et la fréquence des phénomènes d’interaction entre l’air de refroidissement injecté et l’écoulement principal sont modifiés par la rotation de la structure dans la cavité. Finalement, bien que les résultats d’essai n’ont pas pu être entièrement expliqués, ces travaux ont permis d’améliorer la compréhension des phénomènes se produisant dans une telle configuration, d’identifier les défis qu’ils posent aux simulations numériques, et d’ouvrir de nouvelles pistes de recherche
The impact of some technological effects on the performances of a turbine are not yet well understood. More specifically, tests were performed by Safran Helicopter Engines on a high pressure turbine stage featuring a cavity over the rotor shroud, connected to the main gas path in the inter-rows space. Cooling air is injected in this cavity. This experimental campaign has shown an unexpected sensitivity of the turbine performances to some geometric parameters. This thesis aims at explaining this behaviour, and at improving the understanding and the prediction through numerical simulations of the effect of such a cavity on the aerodynamic and aerothermic behaviour of the turbine. Unsteady RANS numerical simulations have been performed with the elsA code. First, simulations were set up with a small part of the cavity, which forms a simple axisymmetric slot injecting cooling air into the main gas path. These computations have shown that the flow through the stage is deeply modified by the injected cooling air. The rotor shroud passage vortex and the tip leakage flow are affected and undergo large fluctuations. The interaction mechanisms are detailed and the effect on loss generation is discussed. Then, computations modeling the full cavity were performed, beginning with a simplified annulus flow and next with the full turbine stage. They identified a flow structure made of hot annulus gas pockets ingested in the cavity and cooling air ejection zones. This structure rotates at a lower speed than the rotor, and is clearly generated by an aerodynamic instability. Similar structures had already been found in turbines by numerous studies on inter-disks cavities at the hub, but it is the first time that such a behaviour is reported in a cavity with fixed walls and located at the shroud. The effect of this structure on the flow through the annulus is qualitatively identical to that simulated with only a small part of the cavity, but the intensity and the frequency of the interaction phenomena between the cooling air and the main flow are modified because of the rotation of the cavity flow structure. Finally, even if the simulations did not manage to fully explain the experimental results, this work contributed to the improvement of the understanding of the phenomena occuring in such a configuraiton. It also identified some challenges for the modelling of these flows by numerical simulations, as well as some topics for future research

Syftet med uppsatsen har varit att undersöka om Turkiets nuvarande politiska situation påverkar svensk-turkars vilja att åka till sitt ursprungsland. Den metod som har använts i denna undersökning är både en kvalitativ och en kvantitativ metod. De teorier som författarna har använt inkluderar bland annat Maslows behovspyramid, Hsu et al.s Hierarchy of destination selection model och Simpson och Siguaws teorier om turism och risk.   En enkätundersökning har genomförts med trettio svensk-turkar samt med representanter från Ving och TUI. Frågorna som ställdes till svensk-turkarna handlade om varför de valde eller inte valde att resa till Turkiet med tanke på landets politiska instabilitet. Vi frågade också om bristen på säkerhet i Turkiet är något som oroar dem eller betyder något när de väljer resmål. Författarna undrade också om informanternas etniska bakgrund påverkat valet att resa till Turkiet. Den analys som utförts är byggd på fem teman som hittats i den empiriska studien. De har kopplats till de teoretiska utgångspunkterna med syfte att undersöka hur det senaste politiska kaoset i Turkiet har påverkat svensk-turkars resvanor till landet.   Vi har kunnat konstatera att våra svensk-turkiska respondenters resvanor till Turkiet inte har påverkats så mycket av den politiska instabiliteten. De flesta har i någon mån, på grund av den politiska instabiliteten, börjat tänka mer på vilka delar av Turkiet de reser till men har inte minskat frekvensen på sina resor i någon större utsträckning. Det var endast nio av trettio respondenter som helt slutat åka till Turkiet på grund av den politiska instabiliteten i landet. En av respondenterna skrev att anledningen till att han slutat åka till Turkiet beror på att han inte vill bidra ekonomiskt till landet eftersom han är emot dess regerings politik. Åtta av trettio svenskturkar i vår undersökning tycker att media på ett alltför negativt sätt skildrat den politiska instabiliteten i Turkiet och att de därför inte låtit det påverka sina resvanor.
The purpose of this thesis has been to investigate whether Turkey's current political situation affects swedish-turks willingness to travel to their country of origin. A qualitative and a quantitative method have been used in this study. The theories used include, among others, B. Maslow's hierarchy of needs pyramid, Hsu et al.s Hierarchy of destination selection model and Simpson and Siguaw's theories about tourism and risk.  Surveys sent by e-mail have been carried out with thirty swedish-turks and representatives from Ving and TUI. Some of the questions that were asked to the swedish-turks regarded if they still chose to travel to Turkey even though they are aware of the country's political instability. We also asked if the lack of security in Turkey is something that concerns them or matters when choosing a destination. The authors also wondered if their ethnic background influenced the choice to travel to Turkey. The analytical part of the thesis is based on five themes found in the empirical study linked to the theoretical starting points with the purpose of investigating how the latest political chaos in Turkey has affected the swedish-turks travel habits.  We have found that the swedish-turks travel habits to Turkey have not been affected in a greater scale by the political instability. Although because of the political instability, some of them have begun to be more careful about which parts of Turkey they visit but they have not reduced the frequency of their travels to any significant extent. Only nine out of thirty swedish-turks have completely ceased to travel to Turkey and one of the survey respondents mentioned that the reason he stopped traveling there is because he does not want to contribute financially to the Turkish government as he is against their policies. Eight out of thirty of the swedish-turks found that the media portrayed the political instability in Turkey in an excessively negative way and therefore they have not let this affect their travel habits.

Des réglementations de plus en plus strictes et un intérêt environnemental grandissant ont poussé les constructeurs de moteurs aéronautiques à développer la génération actuelle de chambres de combustion, affichant des consommations et émissions de polluants plus basses que jamais. Cependant, les phases de conception de chambres modernes ont clairement mis en évidence que celles-ci sont plus susceptibles de développer des instabilités de combustion, où le couplage entre l'acoustique de la chambre et la flamme suscite de larges oscillations de pression ainsi que des vibrations de la structure. Ces instabilités peuvent endommager le moteur, et potentiellement entraîner sa destruction. Dans le même temps, de considérables avancées ont eu lieu dans le domaine de la simulation numérique, et la Mécanique des Fluides Numérique (MFN) a démontré sa capacité à reproduire la dynamique de flammes instationnaires et les instabilités de combustion observées dans les moteurs. Pourtant, même avec le matériel informatique moderne, le temps de calcul reste la contrainte clé de ces simulations haute-fidélité, qui demeurent très coûteuses. Typiquement, couvrir la totalité du domaine de fonctionnement pour un moteur industriel est encore hors de portée. Des modèles dits bas-ordre existent également, et prédire efficacement les instabilités de combustion par leur intermédiaire est envisageable à la condition d'une modélisation appropriée de l'interaction entre l'acoustique et la flamme. La méthode de modélisation la plus commune de cet élément critique est la fonction de transfert de flamme (FTF) qui lie les fluctuations de taux de dégagement de chaleur aux fluctuations de vitesse en un point donné. Cette fonction de transfert peut être obtenue à partir de modèles analytiques, mais très peu existent pour des flammes swirlées turbulentes. Une autre approche consiste à réaliser des mesures expérimentales ou des simulations haute fidélité coûteuses, réduisant à néant la capacité de prédiction rapide recherchée avec les méthodes bas-ordre. Cette thèse vise donc à développer des outils bas ordre à la fois rapides et fiables pour la modélisation des instabilités de combustion, ainsi qu'à améliorer la compréhension des mécanismes inhérents à la réponse acoustique d'une flamme swirlée. A cet effet, une approche hybride nouvelle est proposée, où un nombre réduit de simulations haute fidélité peut être utilisé pour déterminer les paramètres d'entrée d'un modèle analytique représentatif de la fonction de transfert d'une flamme swirlée prémélangée. Le modèle analytique s'appuie sur des travaux antérieurs traitant la flamme comme une interface perturbée, et prend en compte la conversion acoustique-vorticité à travers un swirler. La validité du modèle est mise à l'épreuve en déterminant les divers paramètres nécessaires associés à partir de simulations numériques réactives stationnaires et pulsées d'une flamme prémélangée swirlée académique. Il est également démontré que le modèle peut prendre en compte diverses amplitudes de perturbation. Enfin, des simulations haute-fidélité 3D d'une turbine à gaz industrielle alimentée par un combustible liquide sont réalisées afin de déterminer s'il est possible de prédire numériquement un mode d'instabilité de combustion observé lors des essais. Pour cela, un ensemble de simulations forcées est mené à bien afin de souligner l'importance de l'acquisition de la réponse de la flamme diphasique, en comparant les positions de référence utilisées pour mesurer les vitesses fluctuantes ainsi que l'amplitude et l'origine de la perturbation acoustique. L'applicabilité du modèle analytique à ce cas complexe est aussi étudiée. Les résultats montrent que l'analyse acoustique proposée prédit bien la présence d'un mode instable, mais que le modèle bas ordre nécessite davantage de développements pour étendre son domaine de validité présumé
Increasingly stringent regulations as well as environmental concerns have lead gas turbine powered engine manufacturers to develop the current generation of combustors, which feature lower than ever fuel consumption and pollutant emissions. However, modern combustor designs have been shown to be prone to combustion instabilities, where the coupling between acoustics of the combustor and the flame results in large pressure oscillations and vibrations within the combustion chamber. These instabilities can cause structural damages to the engine or even lead to its destruction. At the same time, considerable developments have been achieved in the numerical simulation domain, and Computational Fluid Dynamics (CFD) has proven capable of capturing unsteady flame dynamics and combustion instabilities for aforementioned engines. Still, even with the current large and fast increasing computing capabilities, time remains the key constraint for these high fidelity yet computationally intensive calculations. Typically, covering the entire range of operating conditions for an industrial engine is still out of reach. In that respect, low order models exist and can be efficient at predicting the occurrence of combustion instabilities, provided an adequate modeling of the flame/acoustics interaction as appearing in the system is available. This essential piece of information is usually recast as the so called Flame Transfer Function (FTF) relating heat release rate fluctuations to velocity fluctuations at a given point. One way to obtain this transfer function is to rely on analytical models, but few exist for turbulent swirling flames. Another way consists in performing costly experiments or numerical simulations, negating the requested fast prediction capabilities. This thesis therefore aims at providing fast, yet reliable methods to allow for low order combustion instabilities modeling. In that context, understanding the underlying mechanisms of swirling flame acoustic response is also targeted. To address this issue, a novel hybrid approach is first proposed based on a reduced set of high fidelity simulations that can be used to determine input parameters of an analytical model used to express the FTF of premixed swirling flames. The analytical model builds on previous works starting with a level-set description of the flame front dynamics while also accounting for the acoustic-vorticity conversion through a swirler. For such a model, validation is obtained using reacting stationary and pulsed numerical simulations of a laboratory scale premixed swirl stabilized flame. The model is also shown to be able to handle various perturbation amplitudes. At last, 3D high fidelity simulations of an industrial gas turbine powered by a swirled spray flame are performed to determine whether a combustion instability observed in experiments can be predicted using numerical analysis. To do so, a series of forced simulations is carried out in en effort to highlight the importance of the two-phase flow flame response evaluation. In that case, sensitivity to reference velocity perturbation probing positions as well as the amplitude and location of the acoustic perturbation source are investigated. The analytical FTF model derived in the context of a laboratory premixed swirled burner is furthermore gauged in this complex case. Results show that the unstable mode is predicted by the acoustic analysis, but that the flame model proposed needs further improvements to extend its applicability range and thus provide data relevant to actual aero-engines

Turism har länge varit ett svårdefinierat begrepp med sin direkta och indirekta påverkan på det ekonomiska och sociala livet. Även politik har direkta och indirekta konsekvenser, inte minst på servicesektorn som till stor del består av turister och aktörer inom turism. Storbritanniens uttåg ur EU kommer ha en stor inverkan på inhemsk,utgående och inkommande turism men också på aktörer inom och utanförturismsektorn. Det återstår att se vilken inverkan som Brexit kommer ha, både ekonomiskt, socialt och kulturellt inför framtiden där flera forskare och experter försöker förutspå olika utfall. Samarbetet mellan EU och Storbritannien har en lång historia bakom sig med över 40 år av delade åsikter och värderingar som skapat möjligheter för människor och företag att röra sig och handla fritt inom Europa. Samarbetet har medfört både positiva och negativa konsekvenser i mål om att underlätta och främja människors sätt att leva och utveckla en ekonomisk tillväxt. Denna studie kommer att undersöka vilken inverkan Brexit har på svenska besökare utifrån ett scenariobyggande perspektiv. Förståelsen förresenärers resemotiv kan vara viktigt för reseföretag som vill tillfredsställa sina kunder men även för myndigheter som vill utveckla turismnäringen. Både en kvalitativ och kvantitativ metod har använtsi denna studie. Den kvalitativa metoden består avintervjuermedett brittiskt företag,tvåsvenska företag och sex svenska resenärer.Den kvantitativa metoden består avenkätundersökning med160svenska konsumenter.Resultatet visar att Brexits påverkan kan vara annorlunda på privatresenärer och affärsresenärer samt att olika faktorer kan ha en påverkanpå svenska resenärer vid val av resa, till exempel visum,sjukförsäkring, reseförsäkring samt pris på varor och tjänster.

In questa tesi presentiamo diversi modelli matematici che interpretano i movimenti di aggregazione cellulare dovuti al fenomeno della chemiotassi, in ambito biomedico. Prendiamo in esame innanzitutto il modello pionieristico parabolico-parabolico di Keller-Segel, ne analizziamo la stabilità lineare, utilizzando il Metodo delle Onde Dispersive, e consideriamo alcuni risultati di decadimento e di blow-up delle soluzioni. Operando una correzione alla Cattaneo sulla prima equazione del modello, introduciamo il modello di Dolak-Hillen e analizziamo il ruolo del tempo di rilassamento sull’insorgenza del collasso chemiotattico, ovvero dell’aggregazione cellulare. Con l’introduzione di una correzione dello stesso tipo anche sulla seconda equazione del modello classico di Keller-Segel, giungiamo alla formulazione del modello iperbolico-iperbolico di Barbera e Valenti. Oltre allo studio delle onde di discontinuità iperboliche tipiche del modello, analizziamo la stabilità lineare degli stati di equilibrio, stazionari e omogenei, che andiamo poi a collegare con soluzioni del tipo Travelling Waves, che fra l’altro giustificano le proprietà di propagazione ondosa dei fenomeni di aggregazione cellulare. Consideriamo l’effetto di una reazione di tipo logistico prendendo spunto da un modello parabolico-ellittico recentemente proposto in letteratura. Sottolineiamo infine l’importanza degli effetti di tipo cross-diffusion nei modelli di diffusione e reazione a più specie interagenti, mettendo in risalto l’importanza dell’analisi delle instabilità di Turing nella ricerca attuale. Infine, tenendo conto anche degli effetti dell’aptotassi, presentiamo dei modelli matematici a tre specie per lo studio dell’invasione di cellule cancerogene del tessuto extracellulare.

Les réglementations toujours plus drastiques sur les émissions de polluants ont conduit au développement de systèmes de combustion opérant en régimes pauvres qui sont malheureusement sujet aux instabilités thermo acoustiques. La capacité de la Simulation aux Grandes Echelles (SGE) à simuler des turbines à gaz industrielles complexes de grande puissance est mise en évidence au cours de ce travail de thèse. Tout d’abord, la SGE est appliquée à un brûleur académique et validée par comparaison à des mesures effectuées à l’Université de Berlin ainsi qu’à des simulations SGE effectuées avec OpenFOAM chez Siemens. Afin de déterminer la stabilité de ce bruleur le couplage entre l’acoustique et la combustion est modélisé par l’approche de type fonction de transfert de flamme (FTF). Suite à ces calcules et l’évaluation de la FTF les fluctuations du nombre de swirl sont identifiées comme un paramètre à même de modifier cette réponse de flamme. Après cette première étape de validation, une turbine à gaz industrielle est simulée en SGE pour deux géométries différentes du brûleur et pour deux points de fonctionnement. La FTF issue de ces calculs est peu influencée par les deux points de fonctionnement. A l’inverse, des légères modifications de la géométrie du swirler modifient les caractéristiques de la FTF montrant que plusieurs mécanismes sont en jeu. Ces mécanismes sont identifiés comme étant la vitesse d’entrée, les fluctuations de swirl et les fluctuations de fraction de mélange. Cette dernière est causée par: 1) la pulsation du débit de carburant injecté et 2) la trajectoire fluctuante des jets de carburant. Bien que le swirler soit conçu pour fournir un mélange le plus homogène possible, d’importantes hétérogénéités de mélange à l’entrée de la chambre de combustion sont présentes. Les perturbations de mélange se combinent avec les fluctuations de vitesse (et donc avec les fluctuations de swirl) aboutissant à des résultats de FTF différents. Un modèle étendu pour la FTF reliant le dégagement de chaleur à la vitesse d’entrée et à la fluctuation de fraction de mélange (modèle MISO) se révèle être une bonne solution pour ces systèmes complexes. Une analyse non linéaire montre en outre que l’amplitude de forçage conduit non seulement à une saturation de la flamme, mais aussi à un changement de la réponse de flamme. La saturation de la flamme n’est vérifiée que pour la FTF globale et le gain augmente localement avec une amplitude croissante. Pour ce système on notera enfin que la flamme linéaire, comme la flamme non linéaire, ne sont pas compactes: certaines zones pourtant situées l’une à coté de l’autre, ont des différences significatives de délai de FTF, montrant que certaines parties de la flamme amortissent l’excitation alors que d’autres l’amplifient
Modern pollutant regulation have led to a trend towards lean combustion systems which are prone to thermo-acoustic instabilities. The ability of Large Eddy Simulation (LES) to handle complex industrial heavy-duty gas turbines is evidenced during this thesis work. First, LES is applied to an academic single burner in order to validate the modeling against measurements performed at TU Berlin and against OpenFoam LES simulations done at Siemens. The coupling between acoustic and combustion is modeled with the Flame Transfer Function (FTF) approach and swirl number fluctuations are identified changing the FTF amplitude response of the flame. Then, an industrial gas turbine is analyzed for two different burner geometries and operating conditions. The FTF is only slightly influenced for the two operating points but slight modifications of the swirler geometry do modify the characteristics of the FTF showing that a simple model taking only into account the flight time is not appropriate and additional mechanisms are at play. Those mechanisms are identified being the inlet velocity, the swirl and the inlet mixture fraction fluctuations. The latter is caused by two mechanisms: 1) the pulsating injected fuel flow rate and 2) the fluctuating trajectory of the fuel jets. Although the diagonal swirler is designed to provide good mixing, effects of mixing heterogeneities at the combustion chamber inlet occur. Mixture perturbations phase with velocity (and hence with swirl) fluctuations and combine with them to lead to different FTF results. Another FTF approach linking heat release to inlet velocity and mixture fraction fluctuation (MISO model) shows further to be a good solution for complex systems. A nonlinear analysis shows that the forcing amplitude not only leads to a saturation of the flame but also to changes of the delay response. Flame saturation is only true for the global FTF and the gain increases locally with increasing forcing amplitude. Both, the linear and the nonlinear flames, are not compact: flame regions located right next to each other exhibited significant differences in delay meaning that at the same instant certain parts of the flame damp the excitation while others feed it

La combustion en mode pauvre prémélangé permet de réduire les émissions polluantes, mais elle est limitée par l'apparition de fortes instabilités. Afin d'étudier ces instabilités, nous avons conçu une chambre de combustion proche d'une configuration industrielle fonctionnant au gaz naturel. La chambre, pressurisée à 5 bar, est munie de deux dispositifs d'injection d'air: air secondaire et air de dilution. Le prémélange est créé par un injecteur constitué d'un swirl axial et d'un bluff body.
L'étude de l'instabilité a été effectuée en fonction de plusieurs paramètres: température d'entrée d'air, débit, richesse de combustion, angle du swirl, présence d'une flamme pilote, position des orifices d'injection d'air secondaire et géométrie du fond de chambre. Pour chaque configuration nous avons mesuré le champ de vitesse, les émissions polluantes, l'émission spontanée du radical CH* et l'évolution temporelle de la pression dans la chambre de combustion. Le résultat principal montre que les injections d'air secondaire jouent un rôle important et complexe dans les chambres de combustion notamment sur la structure et la dynamique de la flamme.
Les spectres temporels de pression et de CH* ont montré plusieurs fluctuations temporelles de la combustion que nous avons classées en trois categories:
- Les fluctuations basses fréquences dues aux instabilités de combustion
- Les fluctuations convectives dont les fréquences ne dépendent que de la vitesse de l'écoulement
- Les fluctuations acoustiques dont les fréquences ne dépendent que de la température de l'écoulement
L'étude locale des émissions de CH* montre que les positions des maximums de fluctuations se situent à des emplacements différents dans la zone de réaction suivant le régime de combustion. Nous avons adapté localement le modèle du temps de retard (time lag) qui permet de connaître les conditions favorables d'amplification d'une perturbation convective. Les résultats montrent que nous pouvons prédire la position et l'intensité des fluctuations convectives dans la zone réactive en fonction de la température d'entré ou de la puissance de l'installation. Toutefois, ce modèle trouve ses limites lorsque l'interaction de l'air de dilution secondaire devient trop importante avec la zone de réaction.

Le bon fonctionnement et les performances des turbines à vapeur sont liés à l'état de la vapeur et notamment au taux d'humidité qu'elle contient. EDF souhaite pouvoir maîtriser les phénomènes spécifiques à ces problématiques afin d'améliorer l'utilisation et l'évolution de ses turbines. Le sujet de recherche concerne la modélisation de la formation de l'humidité dans un corps de turbine et l'étude des couplages entre la phase liquide et les instationnarités. Dans ce contexte, la démarche adoptée est la suivante : la présence d'humidité est prise en compte à l'aide d'un modèle homogène, couplé à des modèles de condensation permettant de prendre en compte les phénomènes hors-équilibre thermodynamique : le grossissement et la nucléation des gouttes d'eau dans la vapeur. Pour mener à bien les calculs, des méthodes numériques adaptées aux gaz réels ont été utilisées et testées à l'aide d'un code monodimensionnel avant d'être intégrées dans le code 3D elsA. Deux types de modèles de condensation ont été mis en œuvre, considérant ou non la polydispersion des gouttes dans la vapeur. Les couplages instationnaires entre la condensation et l'écoulement principal ont été étudiés à différents niveaux d'observations (1D, 1D − 3D, 3D). Il a été montré que la méthode des moments apporte une richesse supplémentaire par rapport à un modèle mono-dispersé, et permet de mieux capter les couplages instationnaires entre l'humidité et le champ principal.

[ES] El principal desafío en los motores turbina de gas empleados en aviación reside en aumentar la eficiencia del ciclo termodinámico manteniendo las emisiones contaminantes por debajo de las rigurosas restricciones. Ésto ha conllevado la necesidad de diseñar nuevas estrategias de inyección/combustión que operan en puntos de operación peligrosos por su cercanía al límite inferior de apagado de llama. En este contexto, el concepto Lean Direct Injection (LDI) ha emergido como una tecnología prometedora a la hora de reducir los óxidos de nitrógeno (NOx) emitidos por las plantas propulsoras de los aviones de nueva generación. En este contexto, la presente tesis tiene como objetivos contribuir al conocimiento de los mecanismos físicos que rigen el comportamiento de un quemador LDI y proporcionar herramientas de análisis para una profunda caracterización de las complejas estructuras de flujo de turbulento generadas en el interior de la cámara de combustión. Para ello, se ha desarrollado una metodología numérica basada en CFD capaz de modelar el flujo bifásico no reactivo en el interior de un quemador LDI académico mediante enfoques de turbulencia U-RANS y LES en un marco Euleriano-Lagrangiano. La resolución numérica de este problema multi-escala se aborda mediante la descripción completa del flujo a lo largo de todos los elementos que constituyen la maqueta experimental, incluyendo su paso por el swirler y entrada a la cámara de combustión. Ésto se lleva a cabo través de dos códigos CFD que involucran dos estrategias de mallado diferentes: una basada en algoritmos de generación y refinamiento automático de la malla (AMR) a través de CONVERGE y otra técnica de mallado estático más tradicional mediante OpenFOAM. Por un lado, se ha definido una metodología para obtener una estrategia de mallado óptima mediante el uso del AMR y se han explotado sus beneficios frente a los enfoques tradicionales de malla estática. De esta forma, se ha demostrado que la aplicabilidad de las herramientas de control de malla disponibles en CONVERGE como el refinamiento fijo (fixed embedding) y el AMR son una opción muy interesante para afrontar este tipo de problemas multi-escala. Los resultados destacan una optimización del uso de los recursos computacionales y una mayor precisión en las simulaciones realizadas con la metodología presentada. Por otro lado, el uso de herramientas CFD se ha combinado con la aplicación de técnicas de descomposición modal avanzadas (Proper Orthogonal Decomposition and Dynamic Mode Decomposition). La identificación numérica de los principales modos acústicos en la cámara de combustión ha demostrado el potencial de estas herramientas al permitir caracterizar las estructuras de flujo coherentes generadas como consecuencia de la rotura de los vórtices (VBB) y de los chorros fuertemente torbellinados presentes en el quemador LDI. Además, la implementación de estos procedimientos matemáticos ha permitido tanto recuperar información sobre las características de la dinámica de flujo como proporcionar un enfoque sistemático para identificar los principales mecanismos que sustentan las inestabilidades en la cámara de combustión. Finalmente, la metodología validada ha sido explotada a través de un Diseño de Experimentos (DoE) para cuantificar la influencia de los factores críticos de diseño en el flujo no reactivo. De esta manera, se ha evaluado la contribución individual de algunos parámetros funcionales (el número de palas del swirler, el ángulo de dichas palas, el ancho de la cámara de combustión y la posición axial del orificio del inyector) en los patrones del campo fluido, la distribución del tamaño de gotas del combustible líquido y la aparición de inestabilidades en la cámara de combustión a través de una matriz ortogonal L9 de Taguchi. Este estudio estadístico supone un punto de partida para posteriores estudios de inyección, atomización y combus
[CA] El principal desafiament als motors turbina de gas utilitzats a la aviació resideix en augmentar l'eficiència del cicle termodinàmic mantenint les emissions contaminants per davall de les rigoroses restriccions. Aquest fet comporta la necessitat de dissenyar noves estratègies d'injecció/combustió que radiquen en punts d'operació perillosos per la seva aproximació al límit inferior d'apagat de flama. En aquest context, el concepte Lean Direct Injection (LDI) sorgeix com a eina innovadora a l'hora de reduir els òxids de nitrogen (NOx) emesos per les plantes propulsores dels avions de nova generació. Sota aquest context, aquesta tesis té com a objectius contribuir al coneixement dels mecanismes físics que regeixen el comportament d'un cremador LDI i proporcionar ferramentes d'anàlisi per a una profunda caracterització de les complexes estructures de flux turbulent generades a l'interior de la càmera de combustió. Per tal de dur-ho a terme s'ha desenvolupat una metodología numèrica basada en CFD capaç de modelar el flux bifàsic no reactiu a l'interior d'un cremador LDI acadèmic mitjançant els enfocaments de turbulència U-RANS i LES en un marc Eulerià-Lagrangià. La resolució numèrica d'aquest problema multiescala s'aborda mitjançant la resolució completa del flux al llarg de tots els elements que constitueixen la maqueta experimental, incloent el seu pas pel swirler i l'entrada a la càmera de combustió. Açò es duu a terme a través de dos codis CFD que involucren estratègies de mallat diferents: una basada en la generación automàtica de la malla i en l'algoritme de refinament adaptatiu (AMR) amb CONVERGE i l'altra que es basa en una tècnica de mallat estàtic més tradicional amb OpenFOAM. D'una banda, s'ha definit una metodologia per tal d'obtindre una estrategia de mallat òptima mitjançant l'ús de l'AMR i s'han explotat els seus beneficis front als enfocaments tradicionals de malla estàtica. D'aquesta forma, s'ha demostrat que l'aplicabilitat de les ferramente de control de malla disponibles en CONVERGE com el refinament fixe (fixed embedding) i l'AMR són una opció molt interessant per tal d'afrontar aquest tipus de problemes multiescala. Els resultats destaquen una optimització de l'ús dels recursos computacionals i una major precisió en les simulacions realitzades amb la metodologia presentada. D'altra banda, l'ús d'eines CFD s'ha combinat amb l'aplicació de tècniques de descomposició modal avançades (Proper Orthogonal Decomposition and Dynamic Mode Decomposition). La identificació numèrica dels principals modes acústics a la càmera de combustió ha demostrat el potencial d'aquestes ferramentes al permetre caracteritzar les estructures de flux coherents generades com a conseqüència del trencament dels vòrtex (VBB) i dels raigs fortament arremolinats presents al cremador LDI. A més, la implantació d'estos procediments matemàtics ha permès recuperar informació sobre les característiques de la dinàmica del flux i proporcionar un enfocament sistemàtic per tal d'identificar els principals mecanismes que sustenten les inestabilitats a la càmera de combustió. Finalment, la metodologia validada ha sigut explotada a traves d'un Diseny d'Experiments (DoE) per tal de quantificar la influència dels factors crítics de disseny en el flux no reactiu. D'aquesta manera, s'ha avaluat la contribución individual d'alguns paràmetres funcionals (el nombre de pales del swirler, l'angle de les pales, l'amplada de la càmera de combustió i la posició axial de l'orifici de l'injector) en els patrons del camp fluid, la distribució de la mida de gotes del combustible líquid i l'aparició d'inestabilitats en la càmera de combustió mitjançant una matriu ortogonal L9 de Taguchi. Aquest estudi estadístic és un bon punt de partida per a futurs estudis de injecció, atomització i combustió en cremadors LDI.
[EN] Aeronautical gas turbine engines present the main challenge of increasing the efficiency of the cycle while keeping the pollutant emissions below stringent restrictions. This has led to the design of new injection-combustion strategies working on more risky and problematic operating points such as those close to the lean extinction limit. In this context, the Lean Direct Injection (LDI) concept has emerged as a promising technology to reduce oxides of nitrogen (NOx) for next-generation aircraft power plants In this context, this thesis aims at contributing to the knowledge of the governing physical mechanisms within an LDI burner and to provide analysis tools for a deep characterisation of such complex flows. In order to do so, a numerical CFD methodology capable of reliably modelling the 2-phase nonreacting flow in an academic LDI burner has been developed in an Eulerian-Lagrangian framework, using the U-RANS and LES turbulence approaches. The LDI combustor taken as a reference to carry out the investigation is the laboratory-scale swirled-stabilised CORIA Spray Burner. The multi-scale problem is addressed by solving the complete inlet flow path through the swirl vanes and the combustor through two different CFD codes involving two different meshing strategies: an automatic mesh generation with adaptive mesh refinement (AMR) algorithm through CONVERGE and a more traditional static meshing technique in OpenFOAM. On the one hand, a methodology to obtain an optimal mesh strategy using AMR has been defined, and its benefits against traditional fixed mesh approaches have been exploited. In this way, the applicability of grid control tools available in CONVERGE such as fixed embedding and AMR has been demonstrated to be an interesting option to face this type of multi-scale problem. The results highlight an optimisation of the use of the computational resources and better accuracy in the simulations carried out with the presented methodology. On the other hand, the use of CFD tools has been combined with the application of systematic advanced modal decomposition techniques (i.e., Proper Orthogonal Decomposition and Dynamic Mode Decomposition). The numerical identification of the main acoustic modes in the chamber have proved their potential when studying the characteristics of the most powerful coherent flow structures of strongly swirled jets in a LDI burner undergoing vortex breakdown (VBB). Besides, the implementation of these mathematical procedures has allowed both retrieving information about the flow dynamics features and providing a systematic approach to identify the main mechanisms that sustain instabilities in the combustor. Last, this analysis has also allowed identifying some key features of swirl spray systems such as the complex pulsating, intermittent and cyclical spatial patterns related to the Precessing Vortex Core (PVC). Finally, the validated methodology is exploited through a Design of Experiments (DoE) to quantify the influence of critical design factors on the non-reacting flow. In this way, the individual contribution of some functional parameters (namely the number of swirler vanes, the swirler vane angle, the combustion chamber width and the axial position of the nozzle tip) into both the flow field pattern, the spray size distribution and the occurrence of instabilities in the combustion chamber are evaluated throughout a Taguchi's orthogonal array L9. Such a statistical study has supposed a good starting point for subsequent studies of injection, atomisation and combustion on LDI burners.
Belmar Gil, M. (2020). Computational study on the non-reacting flow in Lean Direct Injection gas turbine combustors through Eulerian-Lagrangian Large-Eddy Simulations [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/159882
TESIS

Au cours des dernières décennies, les instabilités de combustion ont constitué un important défi pour de nombreux projets industriels, en particulier dans la conception de moteurs-fusées à ergols liquide et de turbines à gaz. L'atténuation de leurs effets nécessite une solide compréhension scientifique de l'interaction complexe entre la dynamique de flamme et les ondes acoustiques qu'elles impliquent. Au cours de cette thèse, plusieurs directions ont été explorées pour fournir une meilleure compréhension de la dynamique des flammes dans les moteurs-fusées cryogéniques, ainsi que des méthodes numériques plus efficaces et robustes pour la prédiction des instabilités thermoacoustiques dans les chambres de combustion à géométries complexes. La première facette de ce travail a consisté en la résolution de modes thermoacoustiques dans les chambres de combustion complexes comportant à injecteurs multiples, une tâche qui nécessite souvent des simplifications pour être abordable en termes de coût de calcul. Ces hypothèses physiques nécessaires ont conduit à la popularité croissante des modèles bas-ordre acoustiques, parmi lesquels ceux utilisant l'expansion de Galerkin ont démontré une efficacité prometteuse tout en conservant une précision satisfaisante. Ceux-ci sont cependant limités à des géométries simples qui n'intègrent pas les caractéristiques complexes des systèmes industriels. Une grande partie de ce travail a donc consisté tout d'abord à identifier clairement les limitations mathématiques de l'expansion classique de Galerkin, puis à concevoir un nouveau type d'expansion modale, appelé expansion sur frame, qui ne souffre pas des mêmes restrictions. En particulier, l'expansion sur frame est capable de représenter avec précision le champ de vitesse acoustique près des parois de la chambre de combustion autres que des murs rigides, une capacité cruciale qui manque à la méthode Galerkin. Dans ce travail, le concept d'expansion modale de surface a également été introduit pour modéliser des frontières topologiquement complexes, comme les plaques multi-perforées rencontrées dans les turbines à gaz. Ces nouvelles méthodes numériques ont été combinées avec le formalisme state-space pour construire des réseaux acoustiques de systèmes complexes. Le modèle obtenu a été implémenté dans le code STORM (State-space Thermoacoustic low-ORder Model), qui permet la modélisation bas-ordre des instabilités thermoacoustiques dans des géométries arbitrairement complexes. Le deuxième ingrédient de la prédiction des instabilités thermoacoustiques est la modélisation de la dynamique de flamme. Ce travail a traité de ce point, dans le cas spécifique d'une flamme-jet cryogénique caractéristique d'un moteur-fusée à ergols liquides. Les phénomènes contrôlant la dynamique de flamme ont été identifiés grâce à des Simulations aux Grandes Échelles (SGE) du banc d'essai expérimental Mascotte, où les deux réactifs (CH4 et O2) sont injectés dans des conditions transcritiques. Une première simulation donne un aperçu détaillé de la dynamique intrinsèque de la flamme. Plusieurs SGE avec modulation harmonique de l'injection de carburant, à différentes fréquences et amplitudes, ont été effectués afin d'évaluer la réponse de la flamme aux oscillations acoustiques et de calculer une Fonction de Transfert de Flamme (FTF). La réponse non-linéaire de la flamme, notamment les interactions entre les oscillations intrinsèques et forcées, a également été étudiée. Enfin, la stabilisation de cette flamme dans la région proche de l'injecteur, qui est d'une importance primordiale sur la dynamique globale de la flamme, a été étudiée grâce à une simulation directe multi-physique, où un problème couplé de transfert de chaleur est résolu au niveau de la lèvre de l'injecteur
Over the last decades, combustion instabilities have been a major concern for a number of industrial projects, especially in the design of Liquid Rocket Engines (LREs) and gas turbines. Mitigating their effects requires a solid scientific understanding of the intricate interplay between flame dynamics and acoustic waves that they involve. During this PhD work, several directions were explored to provide a better comprehension of flame dynamics in cryogenic rocket engines, as well as more efficient and robust numerical methods for the prediction of thermoacoustic instabilities in complex combustors. The first facet of this work consisted in the resolution of unstable thermoacoustic modes in complex multi-injectors combustors, a task that often requires a number of simplifications to be computationally affordable. These necessary physics-based assumptions led to the growing popularity of acoustic Low-Order Models (LOMs), among which Galerkin expansion LOMs have displayed a promising efficiency while retaining a satisfactory accuracy. Those are however limited to simple geometries that do not incorporate the complex features of industrial systems. A major part of this work therefore consisted first in clearly identifying the mathematical limitations of the classical Galerkin expansion, and then in designing a novel type of modal expansion, named a frame expansion, that does not suffer from the same restrictions. In particular, the frame expansion is able to accurately represent the acoustic velocity field, near non-rigid-wall boundaries of the combustor, a crucial ability that the Galerkin method lacks. In this work, the concept of surface modal expansion is also introduced to model topologically complex boundaries, such as multi-perforated liners encountered in gas turbines. These novel numerical methods were combined with the state-space formalism to build acoustic networks of complex systems. The resulting LOM framework was implemented in the code STORM (State-space Thermoacoustic low-ORder Model), which enables the low-order modeling of thermoacoustic instabilities in arbitrarily complex geometries. The second ingredient in the prediction of thermoacoustic instabilities is the flame dynamics modeling. This work dealt with this problem, in the specific case of a cryogenic coaxial jet-flame characteristic of a LRE. Flame dynamics driving phenomena were identified thanks to three-dimensional Large Eddy Simulations (LES) of the Mascotte experimental test rig where both reactants (CH4 and O2) are injected in transcritical conditions. A first simulation provides a detailed insight into the flame intrinsic dynamics. Several LES with harmonic modulation of the fuel inflow at various frequencies and amplitudes were performed in order to evaluate the flame response to acoustic oscillations and compute a Flame Transfer Function (FTF). The flame nonlinear response, including interactions between intrinsic and forced oscillations, were also investigated. Finally, the stabilization of this flame in the near-injector region, which is of primary importance on the overall flame dynamics, was investigated thanks to muulti-physics two-dimensional Direct Numerical Simulations (DNS), where a conjugate heat transfer problem is resolved at the injector lip