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Submitted by Fabiano Dias da Silva (fabiano.engenharia@yahoo.com.br) on 2018-12-21T16:25:47Z No. of bitstreams: 1 Dissertação Fabiano Dias.pdf: 8518992 bytes, checksum: cafcf3bc3c4805d54790f43c6fdffe37 (MD5) Approved for entry into archive by Pamella Benevides Gonçalves null (pamella@feg.unesp.br) on 2019-01-03T13:28:37Z (GMT) No. of bitstreams: 1 silva_fd_me_guara.pdf: 8518992 bytes, checksum: cafcf3bc3c4805d54790f43c6fdffe37 (MD5) Made available in DSpace on 2019-01-03T13:28:37Z (GMT). No. of bitstreams: 1 silva_fd_me_guara.pdf: 8518992 bytes, checksum: cafcf3bc3c4805d54790f43c6fdffe37 (MD5) Previous issue date: 2018-12-03 O objetivo geral deste trabalho é a análise de estabilidade global de torres metálicas treliçadas de transmissão de energia utilizando o Método dos Elementos Finitos (MEF). Todo estudo foi baseado nas normativas da NBR-8800/2007 em que sugere-se uma análise de deslocabilidade da estrutura por meio dos parâmetros B2 e consequentemente a aplicação do MAES (método de amplificação de esforços), processo simplificado para análise dos efeitos globais de segunda ordem. Abordou-se o sistema elétrico brasileiro, descrição bem detalhada sobre tipos e modelos de torres, acidentes envolvendo torres de transmissão, treliças espaciais, método de análise estrutural, MEF, análise de estabilidade de estruturas, MAES e abordagem atualizada sobre o estado da arte em diversas universidades do mundo, em especial da China e Canadá, em que a grande preocupação é como simular nos projetos de torres de transmissão sobre efeitos climáticos como terremotos, tornados e furações por meio de modelos reduzidos em laboratório. Visando oferecer uma contribuição científica para o setor, desenvolveu-se uma planilha eletrônica no software Excel, devido a sua facilidade de utilização, acesso e capacidade de resolver cálculos matriciais facilitando a aplicação do MEF. A mesma foi validada com um software específico e consagrado na área de MEF, o SAP2000 e um software comercial de dimensionamento de estruturas metálicas usado em vários escritórios de projeto e consultoria estrutural, o METÁLICA 3D. A planilha contempla pré-dimensionamentos de cabos condutores e para-raios, visualização do modelo 3D, concepção estrutural, análise estrutural por meio de cálculo matricial, análise de deslocabilidade, aplicação dos efeitos de segunda ordem utilizando o MAES e pré dimensionamento das barras segundo NBR8800/2007. A verdadeira contribuição se dá pelo fato de vários softwares educacionais freeware não analisarem a estabilidade da estrutura e nem fazerem simulações de modo a obter uma estrutura economicamente estável, além de poder simular a torre em qualquer região do país, com diferentes tipos de materiais e simular o efeito de cabos rompendo The main objective of this project is the analysis of the global stability of the lattice towers of energy transmission using the FEM (finite element method). The whole study was based on NBR-8800/2007, normative where suggest a displaceability’s analysis of the structures thought the B2 parameters and consequently the application of MAES’ method, a simplified procedure for the analysis of second-order’s global effects. In this project was approached the Brazilian electric system, a detail description of types and model of towers, accident involving transmission towers, space trusses, structural analysis’ method, FEM, structure stability analysis, MAES’ method. Also in this project, an updated approach the increase knowledge at this area in several universities all around the world, in special China and Canada, where the major concern is how to simulate at The transmission tower’s project some climate effects such as earthquakes, tornadoes and hurricanes through reduced laboratory models. In order to offer a scientific contribution to this sector, a spreadsheet was developed in Excel software due to it facility of use, access and ability to solve matrix calculations, which facilitates the use of FEM. The same one was valid with a specific and consecrated software in the FEM area: The SAP2000; and commercial metal structural design software used in various design and structural consulting offices: the METÁLICA 3D. The spreadsheet contemplates pre-dimensioning of conductor cables and lightning rods, visualization of the 3D model, structural design, structural analysis through matrix calculations, displacement analysis, application of second order effects using MAES and dimensioning of towers according to NBR8800/2007. The real contribution was made by the fact that several freeware educational software do not analyze the stability of the structure nor make simulations in order to obtain an economically stable structure, besides being able to simulate the tower in any region of the country with different types of materials and to simulate the effect of breaking cables

The transonic buffet is a complex aerodynamic instability which appears on wings and aerofoils in high subsonic regime for certain values of Mach number and angle of attack. The aim of the present study is to improve the understanding of the flow physics behind the instability and, in particular, to explain the evolution of the transonic buffet phenomenon from two-dimensional aerofoils to three-dimensional swept wings.First the work by Crouch et al. (2007, 2009) has been reproduced. Then, the two-dimensional transonic buffet is analysed to highlight the zones of the flow necessary for the persistence of the instability. The study has been conducted numerically through the coupling between two techniques based on different approaches: linear stability analysis and numerical simulations. The two different approaches give the same results: the shock foot is identified as the core of the instability, the shock and the detached boundary layer are also necessary zones. In order to outline the differences between two-dimensional and three-dimensional buffet, the analysis and comparison of four different experimental databases of three-dimensional wings is performed. The experimental analysis identifies the characteristic values of the buffet phenomenon such as Strouhal numbers, convection velocities, buffet onset etc. Three-dimensional buffet exhibits different characteristics in comparison with the two-dimensional one: higher Strouhal number, bump instead of peak in the power spectral density, lower shock amplitude oscillation and three-dimensional patterns in the detached boundary layer which are convected outboard. These differences suggest different physical mechanisms.Finally a three-dimensional global stability analysis of a wing is performed. The two and three-dimensional buffet phenomena appear as two different unstable modes in the spectrum. The phenomenon called in the literature three-dimensional transonic buffet corresponds to a "detached boundary" cells convection phenomenon with a zero-frequency unstable global mode, which becomes unsteady with the addition of sweep.; Le tremblement transsonique est une instabilité aérodynamique complexe qui apparaît sur les ailes et les profils en régime haut-subsonique pour certaines valeurs du nombre de Mach et de l’angle d’attaque. L'objectif de cette thèse est d'améliorer la compréhension de la physique de ce phénomène et, en particulier, d'expliquer l'évolution de ces caractéristiques (fréquence, amplitude d’oscillation) des profils bidimensionnels aux ailes tridimensionnelles en flèche. L’étude commence par la reproduction du travail de Crouch et al. (2007, 2009). Ensuite, le tremblement transsonique bidimensionnel est analysé pour mettre en évidence les zones de l’écoulement nécessaires à l’existence de l’instabilité. Cette étude a été menée numériquement en couplant deux techniques basées sur des approches différentes : l’analyse de stabilité linéaire et la simulation numérique. Ces deux approches aboutissent aux mêmes résultats : le pied du choc est identifié comme le cœur de l'instabilité, le choc et la couche limite détachée sont également des zones nécessaires à l’existence de l’instabilité. Afin de souligner les différences entre le tremblement bidimensionnel et tridimensionnel, une analyse de quatre bases des données expérimentales d’ailes tridimensionnelles est accomplie. L'analyse expérimentale identifie les valeurs caractéristiques du phénomène, telles que les nombres de Strouhal, les vitesses de convection, le seuil d’apparition du tremblement etc. Le tremblement tridimensionnel possède des caractéristiques différentes du tremblement bidimensionnel : nombre de Strouhal supérieur, bosses au lieu de pics sur la densité de puissance spectrale, amplitude d’oscillation du choc plus faible et motifs tridimensionnels dans la couche limite détachée qui sont convectés en envergure. Ces différences suggèrent des mécanismes physiques distincts. Enfin, une analyse de la stabilité globale en trois dimensions d'une aile est effectuée. Le tremblement bi et tridimensionnel apparai comme deux modes instables différents dans le spectre. Le phénomène appelé dans la littérature tremblement transsonique tridimensionnel correspond en fait à un phénomène de convection de cellules de "couche limite détachée" avec un mode global instable à fréquence nulle devenant instationnaire avec l’augmentation de l’angle de flèche.

The transonic buffet is a complex aerodynamic instability which appears on wings and aerofoils in high subsonic regime for certain values of Mach number and angle of attack. The aim of the present study is to improve the understanding of the flow physics behind the instability and, in particular, to explain the evolution of the transonic buffet phenomenon from two-dimensional aerofoils to three-dimensional swept wings.First the work by Crouch et al. (2007, 2009) has been reproduced. Then, the two-dimensional transonic buffet is analysed to highlight the zones of the flow necessary for the persistence of the instability. The study has been conducted numerically through the coupling between two techniques based on different approaches: linear stability analysis and numerical simulations. The two different approaches give the same results: the shock foot is identified as the core of the instability, the shock and the detached boundary layer are also necessary zones. In order to outline the differences between two-dimensional and three-dimensional buffet, the analysis and comparison of four different experimental databases of three-dimensional wings is performed. The experimental analysis identifies the characteristic values of the buffet phenomenon such as Strouhal numbers, convection velocities, buffet onset etc. Three-dimensional buffet exhibits different characteristics in comparison with the two-dimensional one: higher Strouhal number, bump instead of peak in the power spectral density, lower shock amplitude oscillation and three-dimensional patterns in the detached boundary layer which are convected outboard. These differences suggest different physical mechanisms.Finally a three-dimensional global stability analysis of a wing is performed. The two and three-dimensional buffet phenomena appear as two different unstable modes in the spectrum. The phenomenon called in the literature three-dimensional transonic buffet corresponds to a "detached boundary" cells convection phenomenon with a zero-frequency unstable global mode, which becomes unsteady with the addition of sweep.; Le tremblement transsonique est une instabilité aérodynamique complexe qui apparaît sur les ailes et les profils en régime haut-subsonique pour certaines valeurs du nombre de Mach et de l’angle d’attaque. L'objectif de cette thèse est d'améliorer la compréhension de la physique de ce phénomène et, en particulier, d'expliquer l'évolution de ces caractéristiques (fréquence, amplitude d’oscillation) des profils bidimensionnels aux ailes tridimensionnelles en flèche. L’étude commence par la reproduction du travail de Crouch et al. (2007, 2009). Ensuite, le tremblement transsonique bidimensionnel est analysé pour mettre en évidence les zones de l’écoulement nécessaires à l’existence de l’instabilité. Cette étude a été menée numériquement en couplant deux techniques basées sur des approches différentes : l’analyse de stabilité linéaire et la simulation numérique. Ces deux approches aboutissent aux mêmes résultats : le pied du choc est identifié comme le cœur de l'instabilité, le choc et la couche limite détachée sont également des zones nécessaires à l’existence de l’instabilité. Afin de souligner les différences entre le tremblement bidimensionnel et tridimensionnel, une analyse de quatre bases des données expérimentales d’ailes tridimensionnelles est accomplie. L'analyse expérimentale identifie les valeurs caractéristiques du phénomène, telles que les nombres de Strouhal, les vitesses de convection, le seuil d’apparition du tremblement etc. Le tremblement tridimensionnel possède des caractéristiques différentes du tremblement bidimensionnel : nombre de Strouhal supérieur, bosses au lieu de pics sur la densité de puissance spectrale, amplitude d’oscillation du choc plus faible et motifs tridimensionnels dans la couche limite détachée qui sont convectés en envergure. Ces différences suggèrent des mécanismes physiques distincts. Enfin, une analyse de la stabilité globale en trois dimensions d'une aile est effectuée. Le tremblement bi et tridimensionnel apparai comme deux modes instables différents dans le spectre. Le phénomène appelé dans la littérature tremblement transsonique tridimensionnel correspond en fait à un phénomène de convection de cellules de "couche limite détachée" avec un mode global instable à fréquence nulle devenant instationnaire avec l’augmentation de l’angle de flèche.

The stability properties of basic states are often elucidated by examining the evolution of small disturbances. Such studies have recently been successfully applied to mean turbulent states, obtained through averaging of experimental measurements or Large-Eddy Simulations (LES), for both wall-bounded as well as free shear flows. Typically, the equations are employed using the disturbance form of the equations. To circumvent the necessity to linearize the governing equations, an especially tedious task for viscous and turbulent closure terms, Touber and Sandham (2009) [21], proposed an approach that achieves the same purpose by solving the full Navier-Stokes (NS) equations, with a forcing term to maintain mean flow invariance. The method places no restrictions, such as slow streamwise variations, on the underlying basic state. The goals of the current work are to first verify this mean flow perturbation (NS-MFP) technique and then apply it to the problem of jet noise. For the first thrust, we show that when the basic state is appropriately constrained, the technique reverts to Linear, Parabolized and Global stability methods. The method is then verified by reproducing the growth of unstable modes in an inviscid Mach 6 entropy layer. The application to jet noise considers subsonic Mach 0.9 and perfectly expanded supersonic Mach 1.3 round jets. The results are compared with those from Parabolized Stability Equations (PSE) and LES solutions, respectively, considering monochromatic and multi-frequency perturbations. The NS-MFP method successfully reproduces key features of the modal response, including Strouhal number dependent directivity of noise radiation. Aspects related to the manner in which the mean basic state is obtained, whether from LES or Reynolds-averaged Navier-Stokes (RANS) equation are also explored. In particular, the sensitivity of the perturbation to whether the eddy viscosity is included or not, is examined in reference to maximum intensity of pressure fluctuation, directivity of noise radiation and the rate of fall-off of the spectra at higher Strouhal numbers. The results indicate that a closer match on the noise-radiation characteristics is obtained when effects of eddy-viscosity on the disturbances are neglected. (C) 2018 Elsevier Masson SAS. All rights reserved.

The structural instabilities of base flow in hypersonic wake flow over sphere are investigated by numerical simulation in this paper. Numerical simulation method is second-order accuracy NND scheme in spatial direction and Second-order Runge-Kutta scheme in temporal direction. Wakes flow of sphere at M∞ =2, Re =1.71E+6(based on the sphere radius) and at M ∞ =6, Re =1.71E+6 are simulated. Stable solutions are obtained and there are a primary separation and a secondary separation zone in flow over sphere at M∞ =2 and M∞ =6. Later, without any arbitrary disturbance imposed, the structural instability still occurs after a certain critical time. The evolving process of the structure of flow over sphere is a periodic behavior in the forepart, but it evolves into a non-periodic behavior after a critical time at M∞ =2. In the period time, the topological structures of the flow field over sphere and their evolving process at M∞ =6 are similar to that of M∞ =2, but there is non-periodic behavior observed at M∞ =6 in spite of long calculation time. In the case of sphere, the results by global stability theory, numerical results and results of power spectrum are compared each other. The global stability analysis method can give a good prediction result. This study result indicates that the present numerical simulation method and global stability analysis method can be used for the study of the stability of base flow and confirms that hypersonic flow at the base is also instability.

In this paper, we propose and analyze a mathematical model for the dynamics of visceral leishmaniasis with seasonality. Our results show that the disease-free equilibrium is globally asymptotically stable under certain conditions when R 0 , the basic reproduction number, is less than unity. When R 0 > 1 and under some conditions, then our system has a unique positive ω -periodic solution that is globally asymptotically stable. Applying two controls, vaccination and treatment, to our model forces the system to be non-periodic, and all fractions of infected populations settle on a very low level.

平成28年度衝撃波シンポジウム (2017年3月8日-10日. ヴェルクよこすか 横須賀市立勤労福祉会館）横須賀市, 神奈川県, Symposium on Shock Waves in Japan, FY2016 (March 8-10, 2017. Werk Yokosuka), Kanagawa, Japan, 資料番号: SA6000084061, レポート番号: 2A2-1

The dynamics of oblique shock wave/turbulent boundary layer interactions is analyzed by mining a large-eddy simulation (LES) database for various strengths of the incoming shock. The flow dynamics is first analyzed by means of dynamic mode decomposition (DMD), which highlights the simultaneous occurrence of two types of flow modes, namely a low-frequency type associated with breathing motion of the separation bubble, accompanied by flapping motion of the reflected shock, and a high-frequency type associated with the propagation of instability waves past the interaction zone. Global linear stability analysis performed on the mean LES flow fields yields a single unstable zero-frequency mode, plus a variety of marginally stable low-frequency modes whose stability margin decreases with the strength of the interaction. The least stable linear modes are grouped into two classes, one of which bears striking resemblance to the breathing mode recovered from DMD and another class associated with revolving motion within the separation bubble. The results of the modal and linear stability analysis support the notion that low-frequency dynamics is intrinsic to the interaction zone, but some continuous forcing from the upstream boundary layer may be required to keep the system near a limit cycle. This can be modeled as a weakly damped oscillator with forcing, as in the early empirical model by Plotkin (AIAA J 13:1036–1040, 1975).

We present a global stability analysis of a Curzon–Ahlborn heat engine considering different regimes of performance. The stability theory is used to construct the Lyapunov functions to prove the asymptotic stability behavior around the steady state of internal temperatures. We provide a general analytic procedure for the description of the global stability by considering internal irreversibilities and a linear heat transfer law at the thermal couplings. The conditions of the global stability are explored for three regimes of performance: maximum power (MP), efficient power (EP) and the so-called ecological function (EF). Moreover, the analytical results were corroborated by means of numerical integrations, which fully validate the properties of the global asymptotic stability.

The onset of two-dimensional instabilities in the flow past two side-by-side circular cylinders is numerically investigated in the ranges $0.1\leq g\leq 3$ and $\mathit{Re}, with $g$ being the non-dimensional gap spacing between the surfaces of the two cylinders and $\mathit{Re}$ the Reynolds number. A comprehensive, global stability analysis of the symmetric base flow is carried out, indicating that three harmonic modes and one steady antisymmetric mode become unstable at different values of $g$ and $\mathit{Re}$. These modes are known to promote distinct flow regimes at increasing values of $g$: single bluff-body, asymmetric, in-phase and antiphase synchronized vortex shedding. For each mode, the inherent structural sensitivity is examined in order to identify the core region of the related instability mechanism. In addition, by exploiting the structural sensitivity analysis to base flow modifications, a passive control strategy is proposed for the simultaneous suppression of the two synchronized shedding modes using two small secondary cylinders. Its effectiveness is then validated a posteriori by means of direct numerical simulations.

This work is concerned with stability and receptivity analysis as well as studies on control of the laminar-turbulent transition in boundary-layer flows through direct numerical simulations. Various flow configurations are considered to address flow around straight and swept wings. The aim of this study is to contribute to a better understanding of stability characteristics and different means of transition control of such flows which are of great interest in aeronautical applications. Acoustic receptivity of flow over a finite-thickness flat plate with elliptic leading edge is considered. The objective is to compute receptivity coefficient defined as the relative amplitude of acoustic disturbances and TS wave. The existing results in the literature for this flow case plot a scattered image and are inconclusive. We have approached this problem in both compressible and incompressible frameworks and used high-order numerical methods. Our results have shown that the generally-accepted level of acoustic receptivity coefficient for this flow case is one order of magnitude too high. The continuous increase of computational power has enabled us to perform global stability analysis of three-dimensional boundary layers. A swept flat plate of FSC type boundary layer with surface roughness is considered. The aim is to determine the critical roughness height for which the flow becomes turbulent. Global stability characteristics of this flow have been addressed and sensitivity of such analysis to domain size and numerical parameters have been discussed. The last flow configuration studied here is infinite swept-wing flow. Two numerical set ups are considered which conform to wind-tunnel experiments where passive control of crossflow instabilities is investigated. Robustness of distributed roughness elements in the presence of acoustic waves have been studied. Moreover, ring-type plasma actuators are employed as virtual roughness elements to delay laminar-turbulent transition. QC 20161124

In this work we rst study the non-Newtonian effects on the inertial instabilities in shear flows and second the inertial suspensions of finite size rigid particles by means of numerical simulations. In the first part, both inelastic (Carreau) and elastic models (Oldroyd-B and FENE-P) have been employed to examine the main features of the non-Newtonian fluids in several congurations; flow past a circular cylinder, in a lid-driven cavity and in a channel. In the framework of the linear stability analysis, modal, non-modal, energy and sensitivity analysis are used to determine the instability mechanisms of the non-Newtonian flows. Signicant modifications/alterations in the instability of the different flows have been observed under the action of the non-Newtonian effects. In general, shear-thinning/shear-thickening effects destabilize/stabilize the flow around the cylinder and in a lid driven cavity. Viscoelastic effects both stabilize and destabilize the channel flow depending on the ratio between the viscoelastic and flow time scales. The instability mechanism is just slightly modied in the cylinder flow whereas new instability mechanisms arise in the lid-driven cavity flow. In the second part, we employ Direct Numerical Simulation together with an Immersed Boundary Method to simulate the inertial suspensions of rigid spherical neutrally buoyant particles in a channel. A wide range of the bulk Reynolds numbers, 500QC 20151127

International audience; This work is dedicated to the presentation of a matrix-free method for global linear stability analysis in geometries composed of multi-connected rectangular subdomains. An Arnoldi technique using snapshots in subdomains of the entire geometry combined with a multidomain linearized Direct Numerical Finite difference simulations based on an influence matrix for partitioning are adopted. The method is illustrated by three benchmark problems: the lid-driven cavity, the square cylinder and the open cavity flow. The efficiency of the method to extract large-scale structures in a multidomain framework is emphasized. The possibility to use subset of the full domain to recover the perturbation associated with the entire flow field is also highlighted. Such a method appears thus a promising tool to deal with large computational domains and three-dimensionality within a parallel architecture.

A global stability study of a divergent channel flow reveals features not obtained hitherto by making either the parallel or the weakly non-parallel (WNP) flow assumption. A divergent channel flow is chosen for this study since it is the simplest spatially developing flow: the Reynolds number is constant downstream, and for a theoretical Jeffery-Hamel flow, the velocity profile obeys similarity. Even in this simple flow, the global modes are shown to be qualitatively different from the parallel or WNP. In particular, the disturbance modes are often not wave-like, and the local scale, estimated from a wavelet analysis, can be a function of both streamwise and normal coordinates. The streamwise variation of the scales is often very different from the expected linear variation. Given recent global stability studies on boundary layers, such spatially extended modes which are not wave-like are unexpected. A scaling argument for why the critical Reynolds number is so sensitive to divergence is offered. � 2010 Springer-Verlag.

Experiments on transonic flow over an airfoil have revealed a characteristic oscillatory motion of the transonic shock location. This shock buffeting causes oscillatory wing loads that are detrimental to both lift generation and material fatigue. The description of this low-frequency shock oscillation shall be the subject of this thesis where special emphasis shall be directed at explaining the physical mechanisms underlying this phenomenon as well as efficient means in manipulating it. Iterative techniques, applied to direct numerical simulations and resulting in global modes, are expected to shed light on the dominant features that cause shock buffeting. So this memory will include a variety of techniques ranging from global stability analysis to direct numerical simulations of transonic flow subjected shock buffeting. In particular, the approach of this thesis will take as a starting point the work carried out by the team of Crouch. In this context, the objective of this thesis is the development of a digital tool making it possible to study the global stability of transonic flow for unspecified geometries. In this work, we will implement in the software elsA of ONERA, to obtain the basic flow and the achievement of the extraction of the Jacobin matrix of the RANS equations linearized. The purpose of this objective is to prove that we are able to find the actors responsible for the phenomenon of buffeting that appears on the upper surface of a bi-dimensional wing., En configuration croisière d'un avion de transport civil, où les conditions de l'écoulement sont transsoniques, une augmentation de la vitesse ou de l'incidence, nécessaire par exemple lors d'un virage ou d'un changement d'altitude, peut générer des décollements sur l'extrados de l'aile par la recompression de l'écoulement ou par l'interaction onde de choc/couche limite plus forte. Ces décollements modifient la répartition de charge sur la voilure, donc la portance, et deviennent instables par les échappées tourbillonnaires dans le sillage lorsqu'ils sont étendus jusqu'au bord de fuite. Ces instabilités aérodynamiques, correspondent à la répartition spatiale et temporelle des décollements et de la position du choc. Elles modifient la charge de la voilure et par couplage excitent la structure sur ces modes propres, tremblement. Par conséquent, il apparaît intéressant d'approfondir l'étude des instabilités qu'on vient d'identifier à travers d'une nouvelle approche. De ce fait, ce mémoire s'orientera vers une analyse de stabilité linéaire globale d'un écoulement compressible turbulent soumis au phénomène de tremblement. En particulier, la démarche de cette thèse s'inspirera des travaux effectués par l'équipe de Crouch. Dans ce contexte, l'objectif de cette thèse est le développement d'un outil numérique permettant d'étudier la stabilité globale d'un écoulement compressible turbulent pour des géométries quelconques. Ce travail est essentiellement numérique, il mettra en oeuvre l'implémentation du code dans le logiciel elsA de l'ONERA, pour calculer le champ de base et réaliser l'extraction explicite de la jacobienne des équations RANS linéarisées. Cet objectif, a pour but de prouver qu'on est capable de retrouver les acteurs responsables du phénomène de tremblement qui apparaît à l'extrados d'une voilure bidimensionnelle. En vue de l'étude de la stabilité de l'écoulement, l'implémentation des méthodes numériques ainsi que leurs validations au sein du logiciel elsA, ont été réalisé avec succès. Une fois ce résultat est acquis, on s'intéressera, en particulier, à déterminer le spectre des modes propres, grâce aux techniques spécifiques fournies par la théorie de stabilité.