No description available.

Studies of resonant magnetic perturbations (RMP) have been an active topic in the tokamak research. The RMP technique involves the use of magnetic perturbations generated by external coils installed on a tokamak device. The resonant interaction between the plasma and RMP has favorable effects on magnetohydrodynamic (MHD) stability and other plasma parameters in tokamaks. The RMP experiments are carried out in the Saskatchewan Torus-Modified (STOR-M) tokamak using (l = 2, n = 1) helical coils carrying a static current pulse. The effect of RMP on the (m = 2, n = 1) magnetic islands is examined during ohmic discharges with high MHD activities. The amplitude and frequency of (2, 1) Mirnov fluctuations are significantly reduced after application of RMP. A phase of improved plasma confinement, characterized by a reduction in the H_alpha emission level and an increase in the soft x-ray (SXR) emission, is induced after application of RMP. It is also observed using the ion Doppler spectroscopy (IDS) that RMP can strongly affect the plasma rotation in STOR-M. It is found that during the RMP pulse, the toroidal velocity of C_III impurities (located at the plasma edge) increases in the co-current direction. However, the toroidal velocities of O_V and C_VI impurities (located near the plasma core) change direction from counter-current to co-current. The reduction of the toroidal flow velocity is accompanied by a reduction of the MHD frequency. It is also found that radial profiles of ion saturation current and floating potential in the edge region can be modified by RMP. An increase in the pedestal plasma density and a more negative electric field are observed at the plasma edge region during the RMP pulse. An internal probe array is assembled and installed in STOR-M to study the RMP penetration and the plasma response to RMP.

Doctor of Philosophy(PhD) / Complex (dusty) plasmas are a subject of growing interest. They areionized gases containing charged dust particles. In capacitively-coupled RF discharges, dust growth can occur naturally and two methods can be used to grow dust particles: chemically active plasmas or sputtering. The growth of dust particles in argon discharges by RF sputtering and the effect of dust particles on theplasma have been investigated from the plasma ignition to the afterglow. It was shown that plasma and discharge parameters are greatly affected by the dust particles. Furthermore, plasma instabilities can be triggered by the presence of the dust particles. These instabilities can be due to dust particle growth or they can be instabilities of a well established dust cloud filling the interelectrode space. When the discharge is switched off, the dust particles act like a sink for the charge carrier and consequently affect the plasma losses. It was shown that the dust particles do keep residual chargeswhich values are greatly affected by the diffusion of the charge carriers and especially the transition from ambipolar to free diffusion.

This dissertation is concerned with identification of nonlinear instabilities in rotating multibody systems and subsequent control to eliminate the vibrations. Three nonlinear mechanical systems of this type are investigated and instabilities arising from their inherent nonlinearities are shown to exist for a range of system parameters and conditions. Subsequently, various nonlinear methods of vibration control have been employed to eliminate or suppress the instabilities. Analytical and numerical models have been designed to demonstrate various unstable dynamical behaviour with consistent results. The motion is studied by means of time history, phase space, frequency spectrum, Poincare map, Lyapunov characteristic exponents and Correlation Dimension. Numerical simulations have also shown the effectiveness and robustness of the control techniques over a range of instability conditions for each model. The dynamics of a rotating body with internal energy dissipation is first investigated. Such a model may be considered to be representative of a simplified spinning spacecraft. A comprehensive stability analysis is performed and regions of highly nonlinear behaviour are identified for more rigorous investigation. Numerical simulations using typical satellite parameter values are performed and the system is found to exhibit chaotic motion when a sinusoidally varying torque is applied to the spacecraft for a range of forcing amplitude and frequency. Analysis of this model using Melnikov’s method is performed and a sufficient criterion for chaotic instabilities is obtained in terms of system parameters. Evidence is also presented, indicating that the onset of chaotic motion is characterised by period doubling as well as intermittency. Subsequently, Control of chaotic vibrations in this model is achieved using three techniques. The control methods are implemented on the model under instability conditions. The first two control techniques, recursive proportional feedback (RPF) and continuous delayed feedback are recently developed model independent methods for control of chaotic motion in dynamical systems. As such these methods are employed on all three rotating multibody systems in this dissertation. Control of chaotic instability in this model is also achieved using an algorithm derived using Lyapunov’s second method. Each technique is outlined and the effectiveness of the three strategies in controlling chaotic motion exhibited by the present system is compared and contrasted. The dynamics of a dual-spin spacecraft with internal energy dissipation in the form of an axial nutational damper is also investigated for non-linear phenomena. The problem involves the study of a body with internal moving parts that is characterised by a coupling of the motions of the damper mass and the angular rotations of the platform and rotor of the spacecraft. Two realistic spacecraft parameter configurations are investigated and each is found to exhibit chaotic motion when a sinusoidally varying torque is applied to the spacecraft rotor for a range of forcing amplitude and frequency. Onset of chaotic motion was shown to be characterised by period doubling and Hopf bifurcations. An investigation of the effects of damping upon the configuration is also performed. Predicted instabilities indicate the range of rotor speeds, perturbation amplitudes and damping coefficients to be avoided in the design of dual-spin spacecraft. Control of chaotic vibrations in this model is also achieved using recursive proportional feedback (RPF) and continuous delayed feedback. Subsequently a more effective model dependent method based on energy considerations is derived and implemented. The effectiveness and robustness of each technique is shown using numerical simulations. Another rotating multibody system that is physically distinct from the previously described models is also investigated for nonlinear instabilities and control. The model is in the form of a driveline which incorporates a commonly used coupling called a Hooke’s joint. In particular, torsional instabilities due to fluctuating angular velocity ratio across the joint are examined. Linearised equations are used for the prediction of critical speed ranges where parametric instabilities characterised by exponential build up of torsional response amplitudes occur. Predicted instabilities indicate the range of driveshaft speeds to be avoided during the design of a driveline which employs a Hooke's joint. Numerical simulations further demonstrate the existence of parametric, quasi-periodic and chaotic instabilities. Subsequently, suppression of these vibrations is achieved using the previously described model independent techniques. Chaotic vibrations have also been observed in a range of simple mechanical systems such as a periodically kicked rotor, forced pendulum, synchronous rotor, aeroelastic panel flutter and impact print hammer to name but a few. It is thus becoming of increasing importance to engineers to be aware of chaotic phenomena and be able to recognise, quantify and eliminate these undesirable vibrations. The analytical and numerical methods described in this dissertation may be usefully employed by engineers for detecting as well as controlling chaotic vibrations in an extensive range of physical systems.

No description available.

The speed and efficiency of stratified turbulent mixing in homogenising temperatures, chemical composition and flow speeds makes it one of farthest reaching fluid mechanical phenomenon for life on earth. It is an aesthetically beautiful phenomenon, rich in complex physical behaviours and extremely challenging to model mathematically. Laboratory experiments have a valuable role to play to guide theoretical and numerical work towards a better understanding of this phenomenon by providing insight into real flows under controlled conditions. This dissertation addresses some aspects of the laboratory buoyancy-driven exchange flows through an inclined duct connecting two reservoirs containing fluids of different densities. We employ a novel experimental technique to perform near-instantaneous, volumetric measurements of the three-component velocity field and density field simultaneously, providing an unprecedented quantitative picture of these sustained stratified shear flows. We start by characterising the variety of observed behaviours, or flow regimes, as we vary the density difference between the two reservoirs, the angle of inclination of the duct with respect to the horizontal, the way the density difference is achieved (solutions of salt/fresh water or cold/warm water) and the geometry of the duct. These empirical observations allow us to formulate a number of specific research questions, guiding the work of the next chapters. We then focus on the regime in which Holmboe waves are observed, and demonstrate that these well-known interfacial travelling disturbances have a distinct structure when confined by solid boundaries. We characterise this structure and identify the physical mechanisms at its origin by means of linear stability theory. Since Holmboe waves are found in the intermediate, transitional regime between laminar and turbulent flows, we conjecture that their structure may be relevant to more turbulent flows, where resembling structures are indeed observed. Next, we tackle the quantitative analysis of universal transition curves separating the observed flow regimes (laminar, waves, intermittently turbulent or fully turbulent) as well and the net mass flow rate exchanged by the reservoirs. We show that these long-lasting questions in the study of exchange flows can be addressed in the framework of frictional hydraulic theory, and we derive detailed scaling laws involving only a few nondimensional parameters. Finally, we overcome some of the limitations of hydraulic theory by performing a more detailed, time-resolved, three-dimensional analysis of the energetics of the wave, intermittent and turbulent regimes. We identify and quantify the sources and sinks of energy in each regime, and identify some of the structures responsible for viscous energy dissipation and mixing. We also suggest possible future directions for the present work given recent progress in the literature.

abstract: In this thesis I model the thermal and structural evolution of Kuiper Belt Objects (KBOs) and explore their ability to retain undifferentiated crusts of rock and ice over geologic timescales. Previous calculations by Desch et al. (2009) predicted that initially homogenous KBOs comparable in size to Charon (R ~ 600 km) have surfaces too cold to permit the separation of rock and ice, and should always retain thick (~ 85 km) crusts, despite the partial differentiation of rock and ice inside the body. The retention of a thermally insulating, undifferentiated crust is favorable to the maintenance of subsurface liquid and potentially cryovolcanism on the KBO surface. A potential objection to these models is that the dense crust of rock and ice overlying an ice mantle represents a gravitationally unstable configuration that should overturn by Rayleigh-Taylor (RT) instabilities. I have calculated the growth rate of RT instabilities at the ice-crust interface, including the effect of rock on the viscosity. I have identified a critical ice viscosity for the instability to grow significantly over the age of the solar system. I have calculated the viscosity as a function of temperature for conditions relevant to marginal instability. I find that RT instabilities on a Charon-sized KBO require temperatures T > 143 K. Including this effect in thermal evolution models of KBOs, I find that the undifferentiated crust on KBOs is thinner than previously calculated, only ~ 50 km. While thinner, this crustal thickness is still significant, representing ~ 25% of the KBO mass, and helps to maintain subsurface liquid throughout most of the KBO's history. / Dissertation/Thesis / M.S. Astrophysics 2013

La réduction des émissions de polluants et l’augmentation du rendement des moteurs ont conduit à une large utilisation de régimes de combustion pauvres en carburant dans les foyers de type moteurs aéronautiques et turbines à gaz. Des phénomènes de bruit et d’instabilités de combustion peuvent alors apparaître. Des fluctuations cycliques auto-entretenues de la pression au sein d’un foyer peuvent conduire à une limitation des régimes de fonctionnement ou une usure rapide et indésirable des installations et dans certains cas une destruction du système. L’objectif de ce travail de thèse est d’étudier les mécanismes responsables du bruit de combustion et des instabilités dans un foyer turbulent prémélangé swirlé. L’étude repose sur une analyse du champ de pression au sein du foyer, de la dynamique de la combustion et une caractérisation détaillée des conditions limites en amont, aval et dans les lignes d’alimentation en combustible et en comburant. Le banc expérimental CESAM ("Combustion Étagée Swirlée Acoustiquement Maîtrisée") est utilisé au cours de ce travail. Basée sur des observations expérimentales, une étude théorique de l’acoustique du foyer est tout d’abord réalisée grâce à un modèle à deux cavités couplées qui modélisent le tube de prémélange et la chambre de combustion de ce banc. Les fréquences et les structures spatiales des modes propres du foyer sont examinées, et des comparaisons sont menées avec les résultats expérimentaux. La condition limite au fond du tube de prémélange est mesurée, et utilisée comme entrée dans le modèle. L’effet de cette condition sur la prévision des fréquences des modes propres est examiné. Par la suite, le code de calcul AVSP est utilisé pour valider les résultats obtenus avec le modèle couplé. L’interaction entre ces modes acoustiques et la flamme est mise en évidence en caractérisant la dynamique de l’écoulement réactif. La vélocimétrie par images de particules (PIV) à haute cadence est utilisée. Une première étude est menée sur les champs de vitesse moyens et fluctuants puis on s’intéresse à l’analyse spectrale des champs de vitesse instantanés, rendue possible par la haute cadence du diagnostic. Un post-traitement faisant intervenir une méthode de détection des tourbillons est ensuite mis en oeuvre en utilisant le critère _2. Des structures cohérentes sont convectées le long du front de flamme à la fréquence du second mode instable du foyer. Le chapitre précédent ayant permis de montrer que ce mode acoustique était essentiellement associé au tube de prémélange, le mécanisme de couplage est clairement identifié. Par la suite, un traitement en moyenne de phase est appliqué aux champs de vitesse axiale. Des mouvements de battements des bras de la flamme dans les directions longitudinale et transverse sont mis en évidence aux fréquences des modes instables. L’émission naturelle de la flamme est également mesurée avec une caméra rapide. Une analyse spectrale et un traitement en moyenne phase avec transformée d’Abel sont appliqués aux images pour caractériser les régions de la flamme présentant une forte réponse aux fréquences des modes acoustiques du foyer. Les mécanismes à l’origine du bruit sont analysés en corrélant les mesures optiques et acoustiques. Au cours de cette étude, des fonctions de transfert de flamme FTF sont également caractérisées aux fréquences des modes propres du foyer, liant perturbations amont et réponse de flamme. La vitesse acoustique est reconstruite dans le tube de prémélange à partir des mesures des microphones. La FTF est calculée grâce aux mesures de vitesse par PIV, à l’émission des radicaux OH* et CH* et à l’émission naturelle de la flamme obtenue par caméra rapide. La caractérisation et la modélisation du système composé du tube de prémélange et de la chambre de combustion montrent qu’il est nécessaire de s’intéresser à l’influence des conditions aux limites sur les propriétés de la flamme et la stabilité du brûleur. / Lean premixed combustion is widely used to limit pollutant emissions and improve efficiency. However in this situation combustion instabilities and associated noise may occur. The growth of self-sustained pressure fluctuations within the combustor may limit the operating conditions and eventually damage the installation. The objective of this work is to study the mechanisms induced in combustion noise and instabilities in a turbulent premixed swirled burner. The study is based on a detailed analysis of the pressure field of the combustor, the flame dynamics and a characterization of the upstream and downstream acoustic boundary conditions and in the air and fuel feeding lines. Based upon experimental investigations, a theoretical study of the burner acoustics is carried out using a low-order model with two coupled cavities. The eigenfrequencies and spatial distribution of the pressure field are obtained, allowing comparisons with experimental results. The impact of the inlet acoustic impedance on the prediction of the eigenmodes is examined through the use of the measured impedance in the model. Thereafter calculations with the AVSP Helmholtz code are carried out to confirm the results obtained with the loworder model. The interactions between the burner acoustic modes and the flame are investigated and the reacting flow dynamics is characterized, using High Speed Particle Image Velocimetry HSPIV at 15 kHz. A first analysis concerns the mean and fluctuating velocity fields and a spectral analysis of the collection of instantaneous velocity fields is carried out. Then a method based on the _2 criterion is used to detect vortices, showing that coherent structures are convected through the flame front at the frequency of the second unstable combustor mode. It is shown in the previous chapter that this mode is essentially associated with the premixer acoustics, allowing a clear coupling scenario between the acoustics and the flame. A phase locked averaging method is applied to the axial velocity fields. Flapping motions of the flame branches are highlighted in longitudinal and transverse directions at the unstable modes frequencies. The natural light emission from the flame is also measured using a fast camera. Spectral analysis and phase locked averaging with Abel transform are applied to images in order to determine the flame regions where a strong response is visible at the acoustic modes. Mechanisms underlying combustion noise are analyzed by correlating the optical and acoustic measurements. Flame transfer functions FTF are also characterized between upstream disturbances and the flame response at the combustor eigenfrequencies. Acoustic velocity is reconstructed in the premixer using microphones measurements. The FTF is calculated using PIV velocity fields, OH* or CH* intensities and flame natural light emissions measurements. Measurements and modeling show that boundary conditions play a crucial role in the burner stability. The acoustic impedance at the premixer inlet can be modified using an impedance control system (ICS). Thus, the pressure field and flame dynamics are characterized for different boundary conditions imposed by the ICS. The acoustic boundary conditions in the feeding lines are characterized using an Impedance Measurement Device (IMD) equipped with microphones and mounted within the supplies.

Cette thèse présente une étude des instabilités haute-fréquence dans les moteurs-fusées. Ce phénomène, qui a posé de nombreux problèmes dans les programmes de développement de moteur, est abordé de trois façons complémentaires : expérimentalement, théoriquement et numériquement. Premièrement, des expériences sont menées afin d’identifier les principaux processus et d’apporter les mécanismes ayant lieu lorsque le moteur devient instable. Pour parvenir à ce stade, un nouveau modulateur (VHAM), capable de créer des ondes acoustiques représentatives de ce qui se produit dans un moteur réel, est conçu et caractérisé. La deuxième partie concerne l’analyse théorique. Deux modèles (FAME, SDM) sont développés en suivant les principales conclusions de la campagne expérimentale : les oscillations de dégagement de chaleur sont dues au mouvement transverse des flammes, et le phénomène est déclenché lorsque des gouttelettes deviennent suffisamment petites pour être convectées par le champ acoustique. En utilisant ces modèles comme base de référence, un code numérique (STAHF) est présenté. Son but est de rendre compte des mécanismes déjà identifiés pour un coût de calcul faible. Il est ensuite montré qu’il peut être utilisé pour étudier des moteurs-fusées grandeur nature. La LES compressible est choisie pour étudier l’interaction entre l’acoustique et la combustion numériquement. Un nouveau modèle de combustion pour flammes non-prémélangées basé sur une hypothèse de chimie infiniment rapide est présenté et validé sur une flamme bien documentée (H3). Il est ensuite utilisé pour étudier l’interaction entre une onde acoustique transverse et la flamme H3. Une comparaison entre le terme source de Rayleigh calculé à partir de la simulation et celui prédit par le modèle théorique FAME est finalement menée. / This thesis presents a study of high frequency instabilities in rocket engines. This issue, which has plagued many engine development programs, is approached by three complementary viewpoints: experimental, theoretical, and numerical. First, experiments are carried out to identify the main processes involved and bring forth mechanisms taking place when an engine becomes unstable. To achieve this stage, a new modulator (the VHAM), capable of creating acoustic waves representative of what occurs in an actual engine, is designed and characterized. The second part of this thesis concern theoretical analysis. Two models are developed following the main conclusions of the experimental campaign: heat release oscillations are due to the transverse flames’ motion, and the phenomenon is triggered when droplets become small enough to be convected by the acoustic field. Using these models as a baseline, a numerical code (STAHF) is presented. Its purpose is to account for mechanisms identified previously for little computational cost. This code is validated on particularly responding situations observed during experiments. It is then shown that it can be used to study real scale rocket engines. The third point of view adopted to address the problem is numerical simulation. Full compressible LES is chosen to study the interaction between acoustics and combustion. A new combustion model for non-premixed flames with infinitely fast chemistry is presented and validated on a well documented flame (H3). It is then used to study the interaction between a transverse acoustic wave and the H3 flame. A comparison between the Rayleigh source term computed from the simulation and the one predicted by the theoretical model FAME is conducted eventually.

Des crises vibratoires ont été constatées dans plusieurs centrales thermiques d’EDF opérant avec du fioul lourd, certaines ayant entraîné l’arrêt du foyer. Ce travail traite des instabilités de combustion pouvant se déclencher dans ce type de système où le combustible liquide est injecté avec de la vapeur d’eau et où l’écoulement d’air est mis en rotation. Ces phénomènes vibratoires résultent d’un couplage résonant entre la dynamique de la combustion et l’acoustique du foyer. La réponse acoustique des flammes diphasiques non-prémélangées swirlées reste largement méconnue et est difficilement analysable sur le foyer réel. L’objectif de ce travail est donc d’étudier la stabilité des chaudières EDF à partir de l’analyse de la réponse d’une flamme diphasique non-prémélangée swirlée issue d’un injecteur générique et soumise à des perturbations de la vitesse acoustique. Cette réponse est déterminée sur un dispositif original (DIFAV) équipé d’un swirler et d’un injecteur bi-fluides fonctionnant à la vapeur d’eau et au dodécane. Ce système est constitué des principaux éléments des brûleurs utilisés sur les centrales thermiques EDF à une échelle 1/7000. Le dispositif est conçu pour facilement modifier la géométrie de la tête d’injection, les conditions d’injection de combustible et de vapeur et ainsi contrôler le spray généré. Des visualisations à la sortie d’une buse d’injection montrent l’influence de la topologie de l’écoulement diphasique dans l’injecteur sur la taille des gouttes mesurées dans le spray. Des mesures de taille et de vitesse des gouttes lorsque le rapport des débits de vapeur et de combustible (GLR) est modifié sont réalisées. Ces données comparées à des modèles ont permis d’estimer l’évolution de la taille des gouttes générées par l’injecteur qui équipe les centrales thermiques lorsque le GLR varie. Une analyse modale du foyer DIFAV et d’un modèle simplifié de la chaudière réelle est ensuite menée. Les fréquences propres et les taux d’amortissement du foyer DIFAV sont déterminés expérimentalement en soumettant le système à une modulation acoustique externe. Un modèle acoustique simplifié composé de trois cavités couplées représentatif du brûleur DIFAV est également développé. Des simulations acoustiques réalisées avec COMSOL Multiphysics sur une coupe transverse d’une chaudière générique représentative de la chaudière industrielle permettent d’identifier trois modes à basses fréquences établis entre les plenums et la chambre de combustion qui sont susceptibles d’être instables. La sensibilité de ces modes à la géométrie du foyer et aux conditions limites est étudiée. La réponse de la flamme générique lorsqu’elle est soumise à des modulations acoustiques de l’écoulement d’air en amont du brûleur est ensuite mesurée sur le banc DIFAV pour différents niveaux d’excitation et deux topologies de flamme lorsque les conditions d’injection sont modifiées. Les mécanismes qui pilotent l’évolution du gain de l’une des fonctions de transfert généralisées (FDF) de la flamme sont étudiés à l’aide de visualisations en moyenne de phase de l’écoulement et de mesures des vitesses axiale et azimutale de l’écoulement d’air au cours d’un cycle de modulation. Une forte sensibilité de la phase de la FDF à l’amplitude des perturbations acoustiques est observée. Un adimensionnement par le nombre de Strouhal basé sur la vitesse débitante et la longueur efficace de la flamme est proposé pour transposer ces FDFs sur le brûleur réel. Une analyse de stabilité du foyer DIFAV est réalisée en intégrant les FDF au modèle acoustique afin de déterminer les cycles limites des oscillations lorsque la longueur de la chambre de combustion varie. Ces calculs sont comparés aux fréquences des instabilités auto-entretenues mesurées aux cycles limites dans le foyer DIFAV. [...] / Vibratory crises have been observed in EDF thermal power plants operating with heavy fuel oil. Such instabilities may lead to shutdown and damage the boiler. This work deals with combustion instabilities that can take place in boilers equipped with steam-assisted atomizers and where the airflow is swirled. These vibratory phenomena result from a resonant coupling between the combustion dynamics and the boiler acoustics. Analyses of combustion dynamics of non-premixed swirling spray flames remain rare and are difficult to realize on the real system. The objective of this work is to analyze the stability of EDF boilers using the response of generic non-premixed swirling spray flames submitted to acoustic velocity disturbances. This response is determined on an original device (DIFAV) equipped with a swirling vane and a twin-fluid atomizer operated with steam and dodecane. This burner is equipped with the main elements of those used in the thermal power plant, but has a reduced scale of 1/7000. The influence of the injector geometry and of the operating conditions on the spray generated by the injector can be studied. Spray visualizations at the outlet of the injector reveal the relationship between the topology of the two-phase flow in the injector and the measured droplet size. Measurements of the droplet diameter and velocity as a function of the gas-to-liquid ratio (GLR) have been performed at the outlet of the injector. These data have been compared to models and were used to estimate the evolution of the droplets diameter as a function of the GLR generated by the industrial injector. A modal analysis of the DIFAV combustor is then carried out and a simplified acoustic model made of three coupled cavities is developed. The natural frequencies and damping rates of the DIFAV combustor are determined experimentally when it is submitted to acoustic modulation. Acoustic simulations are performed with COMSOL Multiphysics on a simplified geometrical model of the industrial boiler. Three low frequency modes established between the plenums and the combustion chamber have been identified and may be unstable. Their sensitivity to modifications of the boiler geometry and boundary conditions are studied. Flame responses subjected to acoustic modulations of the airflow rate are then measured on the DIFAV combustor for several amplitudes and two flames topologies obtained at globally lean condition. Phase-conditioned flame visualizations and measurements of swirl number fluctuations during an acoustic forcing cycle are conducted to explain the mechanisms that control the evolution of gain of the Flame Describing Function (FDF). A high sensitivity of the phase of the FDF to the amplitude of the acoustic disturbance is observed. The Strouhal number based on the airflow velocity and the effective length of the flame is used to transpose these FDF on the industrial burner. FDF are integrated in the acoustic model of the DIFAV setup to carry out a stability analysis and predict the limit cycle oscillations as a function of the combustion chamber length. These calculations are compared to frequencies of self-sustained instability measured at the limit cycles in the DIFAV combustor. A reasonable agreement is obtained showing the validity of the stability analysis for the non-premixed two-phase flames investigated based on the knowledge of their FDF. Finally, a stability analysis of the EDF boiler is conducted with the COMSOL Multiphysics model by including the acoustic flame response of the industrial burner in the simulation. This FDF is deducted from the dimensionless FDF measured on the generic burner. The Rayleigh criterion is used to analyze the stability of the combustor as a function of the flame length for different boundary conditions. Indications are given to improve the stability of the EDF boiler.