No description available.

Most of the concrete buttress dams in Sweden were built from the 1950s till the1980s based on the traditional method of analyses. Those structures are reinforced and heavy in structure. Their height to thickness ratio being large makes them prone to crack during their lifespan. The presence of these cracks make the reinforcements used in the buttress dam susceptible to corrosion due to the water entering through the cracked areas. Therefore, studying the effect of cracks and corrosion regarding the safety of dams is important and should be carried out before the dams fail to function. However, only limited researches have been conducted to address these issues. The main goal of this project is to evaluate if the traditional method of analysis were sufficient to capture the failure modes of the dam before and after the occurrence of cracks and corrosion of the reinforcement. In the traditional method, the analytical stability calculations for the factor of safety of sliding and overturning are computed separately. However, in reality, those two failure modes do not occur separately but in combined mode. Therefore, to study this matter, two case studies were considered. In these studies, both finite element analysis (FEA) and analytical calculations were performed to investigate the failure modes. Moreover, this project assesses the influence of cracks and corrosion of reinforcements in the factor of safety. And, the software that was used to carry out the FE analyses were COMSOL and Abaqus. And alongside to FE software, MATLAB was used to carry out the analytical calculations. The results from the analyses showed that the combined failure modes in FE-analyses were the mode of failure of the buttress dams in all cases. Therefore, the analytical calculations were not sufficient to capture the failure modes. Furthermore, the reinforcements that were incorporated in the dam were observed to have a significant effect on the factor of safety depending on the patterns of the cracks. Similarly, the corrosion of the reinforcement had severe effects on the factor of safety based on the crack patterns. Based on the findings from the project, the combined failure mode from FE analysis the governing failure mode, and therefore, traditional analytical methods should be carried out to help evaluate those FE analyses but not to capture the actual failure modes. Besides, the incorporated reinforcements and their corrosion had notable influences on the safety factor of dams which should be investigated carefully. / De flesta betonglamelldammar i Sverige byggdes under 1950 - 80-talet baserat påden traditionella analysmetoden. Dessa strukturer är armerade och tunga. Derashöjd-tjocklek förhållande är stor nog för att de ska vara benägna att spricka underderas livstid. Uppkomsten av dessa sprickor utsätter armeringen i lamelldammar förkorrosion på grund av att vattnet tränger in genom dessas sprickor. Därför är detytterst viktigt att studera effekter av sprickor och medföljande korrosion avseendedammsäkerhet och bör utföras innan dammarna är ur funktion. Trots vikten avdetta problem, har endast begränsade studier genmfört för att hantera dessa frågor.Huvudmålet med detta examensarbete är att utvärdera den traditionellaanalysmetodens kapacitet att fånga dammens brottillstånd före och efteruppkomsten av sprickor och armeringskorrosion. I den traditionella metoden utförsde analytiska stabilitetsberäkningar av säkerhetsfaktorn för glidning och stjälpningseparat. Men i verkligheten förekommer inte dessa två fenomen separat utan ikombinerat form. För att studera detta fenomen beaktades därför två fallstudier. Ibåda fallen utfördes finita element metod (FEM) och analytiska beräkningar föratt utvärdera brottillstånd. Dessutom utvärderas påverkan av sprickor ocharmeringskorrosion på säkerhetsfaktorn. Programvaran som användes för attutföra FE-analyserna var COMSOL och ABAQUS. Analytiska beräkningarutfördes i MATLAB.Resultaten från analyserna visade att ett kombinerat brottillstånd uppstod iFE-analyserna av lamelldammarna i samtliga studerade fall. Därmed är de utfördaanalytiska beräkningar inte tillräckliga för att fånga brottillståndet. Vidareobserverades att armeringar hade betydande inverkan på säkerhetsfaktornberoende på sprickmönstren. På liknande sätt hade armeringskorrosion signifikantinverkan på säkerhetsfaktorn beroende på sprickmönstren.Utifrån resultatet av FE-analyserna kan man konstatera att den kombineradebrottmoden var det avgörande brottillståndet, och därför bör traditionellaanalysmetoder utföras för att stödja utvärderingen av dessa FE-analyser men inteför att erhålla de faktiska brottillstånd. Dessutom, det kunde observeras attarmering och armeringskorrosion har betydande påverkan på säkerhetsfaktorn avdammar och bör undersökas noggrant.

Thesis regarding the application of the Kinematic Element Method to slope stability analysis in geotechnical engineering. / In this thesis, the effectiveness of the Kinematic Element Method (KEM), developed by Dr. Gussmann at the University of Stuttgart, was evaluated by comparing the solutions with the Limit Equilibrium Method (LEM), specifically the Morgenstern-Price method. The KEM was evaluated using a variety of problems, ranging from homogeneous slopes to retaining walls. The KEM was shown to predict similar potential failure mechanisms and values for the factor of safety (FS) as the Morgenstern-Price method. The FS were generally within the ±6% which is the range of variance for rigorous limit equilibrium methods. A simplified version of KEM (KEMv) was developed based on limit equilibrium formulations. In KEMv, an alternate iterative scheme to determine the FS is proposed, in which boundaries between elements are vertical. The KEMv provided similar values for the factor of safety and interelement forces as Gussmann’s KEM for vertical interelement boundaries given similar element locations. The KEM was assumed by Gussmann to be an upper bound solution. However, given the similarities in the solutions between KEM and KEMv, it may be a limit equilibrium method. The interelement forces from the KEM and KEMv were found to be sensitive to the location of the elements. Elements in the upper part of the slope often had small normal forces relative to shear forces, possibly being negative as well. Sensitivity analysis regarding the number of elements showed that a 5-element solution predicts the appropriate failure mechanism and provides a reasonably accurate FS. In a parametric study, slope geometry and soil properties were varied and comparisons were made between KEM and the Morgenstern-Price method. The KEMv displayed similar trends in factor of safety as the Morgenstern-Price method but predicted slightly larger values. The change in KEM critical slip surfaces with soil properties was consistent with trends predicted by Janbu’s dimensionless parameter. / Thesis / Master of Applied Science (MASc) / The stability of slopes is a challenging subject in geotechnical engineering. Geotechnical engineers are often interested in the factor of safety (FS), which is a quantitative measure of the stability of a slope. In this thesis, the effectiveness of the Kinematic Element Method (KEM) is evaluated by comparing its solutions to the Limit Equilibrium Method (LEM). The KEM was shown to predict similar potential failure mechanisms and values for the factor of safety. A simplified version of the KEM (KEMv) was developed based on LEM formulations. In KEMv, an alternate iterative scheme to determine the FS is proposed, in which the boundaries between elements are vertical. The KEMv provided similar values for the factor of safety and element forces as Gussmann’s KEM for vertical interelement boundaries. In a parametric study, KEM displayed similar trends in the change in FS and critical slip surface as the LEM.

This work utilizes the small-signal impedance-based stability analysis method to develop stability assessment criteria for a single-aisle turboelectric aircraft with aft boundary-layer propulsion (STARC-ABL) system. The impedance-based stability analysis method outperforms other stability analysis methods because it does not require detailed information of individual components for system integration, therefore, a system integrator can just require the vendors to make the individual components meet the impedance specifications to ensure whole system stability. This thesis presents models of a generator, motor, housekeeping loads, and battery all with power electronics interface which form an onboard electrical system and analyzes the relationship between the impedance shape of each component and their physical design and control loop design. Based on the developed small-signal model of the turbine-generator-rectifier subsystem and load subsystem, this thesis analyzes the impact of electromechanical dynamics of the turbofan passed through the generator on the dc distribution system, concluding that the rectifier can mitigate the impact. Finally, to ensure the studied system stable operation during the whole flying profile, the thesis provides impedance specifications of the dc distribution system and verifies the specifications with several cases in time-domain simulations. / M.S. / Electric aircraft propulsion (EAP) technologies have been a trend in the aviation industry for their potential to reduce environmental emissions, increase fuel efficiency and reduce noise for commercial airplanes. Achieving these benefits would be a vital step towards environmental sustainability. However, the development of all-electric aircraft is still limited by the current battery technologies and maintenance systems. The single-aisle turboelectric aircraft with aft boundary-layer (STARC-ABL) propulsion concept is therefore developed by NASA aiming to bridge the gap between the current jet fuel-powered aircraft and future all-electric vehicles. The plane uses electric motors powered by onboard gas turbines and transfers the generated power to other locations of the airplane like the tail fan motor to provide distributed propulsion. Power electronics-based converter converts electricity in one form of electricity to another form, for example, from ac voltage to dc voltage. This conversion of power is very important in the whole society, from small onboard chips to Mega Watts level electrical power system. In the aircraft electrical power system context, power electronics converter plays an important role in the power transfer process especially with the recent trend of using high voltage dc (HVDC) distribution instead of conventional ac distribution for the advantage of increased efficiency and better voltage regulation. The power generated by the electric motors is in ac form. Power electronics converter is used to convert the ac power into dc power and transfer it to the dc bus. Because the power to drive the electric motor to provide distributed propulsion is also in ac form, the dc power needs to be converted back into ac power still through a power electronics converter. With a high penetration of power electronics into the onboard electrical power system and the increase of electrical power level, potential stability issues resulted from the interactions of each subsystem need to be paid attention to. There are mainly two stability-related studies conducted in this work. One is the potential cross-domain dynamic interaction between the mechanical system and the electrical system. The other is a design-oriented study to provide sufficient stability margin in the design process to ensure the electrical system’s stable operation during the whole flying profile. The methodology used in this thesis is the impedance-based stability analysis. The main analyzing process is to find an interface of interest first, then grouped each subsystem into a source subsystem and load subsystem, then extract the source impedance and load impedance respectively, and eventually using the Nyquist Criterion (or in bode plot form) to assess the stability with the impedance modeling results. The two stability-related issues mentioned above are then studied by performing impedance analysis of the system. For the electromechanical dynamics interaction study, this thesis mainly studies the rotor dynamics’ impact on the output impedance of the turbine-generator-rectifier system to assess the mechanical dynamics’ impact on the stability condition of the electrical system. It is found that the rotor dynamics of the turbine is masked by the rectifier; therefore, it does not cause stability problem to the pre-tuned system. For the design-oriented study, this thesis mainly explores and provides the impedance shaping guidelines of each subsystem to ensure the whole system's stable operation. It is found that the stability boundary case is at rated power level, the generator voltage loop bandwidth is expected to be higher than 300Hz, 60˚ to achieve a 6dB, 45˚ stability margin, and load impedance mainly depends on the motor-converter impedance.

No / This paper presents a novel concept to describe the couplings among the outputs of the stochastic systems which are represented by NARMA models. Compared with the traditional coupling description, the presented concept can be considered as an extension using statistical independence theory. Based on this concept, the decoupling control in statistical sense is established with the necessary and sufficient conditions for complete decoupling. Since the complete decoupling is difficult to achieve, a control algorithm has been developed using the Cauchy-Schwarz mutual information criterion. Without modifying the existing control loop, this algorithm supplies a compensative controller to minimise the statistical couplings of the system outputs and the local stability has been analysed. In addition, a further discussion illustrates the combination of the presented control algorithm and data-based mutual information estimation. Finally, a numerical example is given to show the feasibility and efficiency of the proposed algorithm.

Dans les alliages multiphasés, la cohérence des interfaces entre des phases en désaccord paramétrique génère des champs élastiques internes à longue distance et généralement anisotropes. L'interaction de ces champs affecte fortement la cinétique des transformations de phase diffusives, et influence la forme et l'arrangement spatial des précipités. Dans la microstructure des superalliages monocristallins à base de nickel, obtenue par précipitation de la phase γ’ ordonnée L12 dans la matrice CFC γ, l'élasticité conduit à la formation d'alignements quasi-périodiques des précipités γ’ cuboïdaux. La microstructure γ/ γ’ possède cependant des défauts systématiques d'alignement des précipités: des branches, des macro-dislocations et des motifs en chevrons. Nous nous intéressons à l'origine de ces défauts d'alignement. Nous conduisons des analyses de stabilité de l'arrangement périodique de précipités en interactions élastiques. Contrairement à la stabilité attendue, les calculs semi-analytiques ont révélé l'instabilité de la distribution périodique de précipités γ’ cubiques, vis-à-vis de certains modes de perturbation. Les principales instabilités sont le mode longitudinal [100] et le mode transverse [110], et leur domaine d'instabilité est analysé vis-à-vis de l'anisotropie élastique. Le développement de ces modes instables est étudié par une méthode de champ de phase classique, en simulant l'évolution de microstructures périodiques soumises à des légères perturbations initiales. Nous montrons que l'expression des instabilités d'arrangement procède essentiellement par l'évolution de la forme des précipités, et conduit à la formation de motifs qui ont pu être reliés à des microstructures expérimentales. En particulier, le mode transverse [110] conduit à la formation de motifs en chevrons. Nous étudions l'influence du taux de phase γ’ et de l'inhomogénéité du module élastique C’, et nous montrons le rôle qu'ils jouent dans la stabilisation de l'arrangement périodique. Dans des simulations réalisées dans des études antérieures, la dynamique des défauts est analysée au moyen de paramètres topologiques issus de la phénoménologie des structures hors-équilibre. Au cours d'un recuit isotherme, nous observons que les branches et les macro-dislocations migrent dans la microstructure selon des mécanismes de montée et de glissement. Nous utilisons ensuite une nouvelle formulation des modèles de champ de phase, intrinsèquement discrète, dans laquelle les interfaces sont résolues essentiellement avec un pas de grille sans friction de réseau et avec une invariance par rotation précise. Cette approche, appelée Sharp Phase Field Method (S-PFM), est implémentée sur une grille CFC, et avec une description des quatre variants de translation des précipités γ’. Nous montrons que la S-PFM permet la modélisation de microstructures à grande échelle, avec plusieurs milliers de précipités à deux et trois dimensions, et donne ainsi accès à des informations statistiques sur l'évolution de la microstructure et sur la dynamique des défauts d'alignement. Nous discutons finalement la perspective de modéliser l'évolution de la microstructure γ/γ’ à une échelle supérieure par une description de la dynamique des défauts d'alignement des précipités. / In multiphase alloys, internal elastic fields often arise as a result of a coherently adjusted misfit between the lattices of coexisting phases. Given their long-range and usually anisotropic nature, the interaction of these fields is known to significantly alter the kinetics of diffusion-controlled phase transformations, as well as influence the shapes and spatial arrangement of the misfitting precipitates. In the microstructure of single-crystal nickel-base superalloys, obtained by precipitation of the L12-ordered γ’ phase in the FCC γ matrix, elasticity leads to the formation of nearly periodic alignments of the cuboidal γ’ precipitates. However, the γ/γ’ microstructure systematically displays defects in the precipitate alignment: branches, macro-dislocations and chevron patterns. We first address the question of the origin of these alignment defects. Stability analyses of the periodic arrangement of elastically interacting precipitates are carried out. Contrary to the expected stability, the semi-analytical calculations revealed the periodic distribution of cubic γ‘ precipitates to be unstable against specific perturbation modes. The main instabilities are the [100] longitudinal mode and the [110] transverse mode, and their instability range is analyzed with respect to the elastic anisotropy. The consequences of these unstable modes are investigated using a classic phase field method, by modeling the evolution of periodic microstructures undergoing small initial perturbations. We show the expression of the instabilities mainly proceeds by the evolution of the precipitate shapes, and leads to the formation of patterns which were related to experimental microstructures. Specifically, the [110] transverse instability is responsible for the formation of chevron patterns. The effects of the volume fraction and of an inhomogeneity on the C’ shear modulus on the stability of the arrangement are studied, and we show the role they play in the partial stabilization of the periodic distribution, though the [100] longitudinal mode always remains unstable. In phase field calculations carried out in previous studies, the dynamics of alignment defects are analyzed by means of topological parameters derived from pattern formation theory. During annealing, branches and macro-dislocations were observed to migrate in the microstructure according to climbing and gliding mechanisms. We then use a new formulation of phase field models, intrinsically discrete, in which the interfaces are resolved with essentially one grid point with no pinning on the grid and an accurate rotational invariance. This approach, known as the Sharp Phase Field Method (S-PFM), is implemented on a FCC grid and accounts for the four translational variants of the γ’ precipitates. We show that the S-PFM allows for the modeling of large-scale microstructures, with several thousand precipitates both in two and three dimensions, and provides access to statistical information on the microstructure evolution and on the the dynamics of alignment defects. We finally discuss the perspective of modeling the evolution of the γ/γ’ microstructure at the macroscale by means of a description of the defect dynamics in the precipitate alignments.

No description available.

L’étude présentée dans cette thèse se situe dans le domaine de l’acoustique modale des conduits avec des parois absorbantes et un écoulement moyen. Nous considérons une source de bruit en amont avec une fréquence fixe. Avec cela, nous étudions les modes propres acoustiques du conduit en terme de nombre d’onde qui sont présents.Avec cette étude, nous contribuons à la meilleure compréhension de la propagation du sondans ce type de configuration. Parmi les applications, il y a la réduction du bruit des moteurs des aéronefs.Une analyse numérique par la méthode pseudospectrale de collocation, sur la base de polynômes de Chebyshev, a été mise en ouvre pour obtenir le spectre des modes, dans un domaine transversal.Pour cela, deux programmes ont été utilisés : le programme FiEStA, qui a été développé dans le cadre de cette thèse, et qui résout les équations d’Euler linéarisées, en considérant un problème à une ou deux une ou deux dimensions. D’autre part, le programme MAMOUT, a été utilisé pour résoudre les équations de Navier-Stokes linéarisées, pour étudier plus spécifiquement les effets de la viscosité.Avec ces outils, on a constaté les effets de trois paramètres : lorsque le rapport d’aspect augmente, la densité des modes, en particulier des modes propagatifs, se développe également.Quand le nombre de Mach de l’écoulement moyen augmente, on observe les effets suivants sur les valeurs propres : un déplacement vers la partie réelle négative, une amplification de leur valeur absolue et un déplacement vers les modes d’indice inférieur. Le profil d’écoulement moyen induit aussi un déplacement dans les valeur propres, pas facilement prévisible. Il modifie également la forme des fonctions propres ; ce qui est notamment visible pour le mode d’onde plane. Les changements d’impédance induisent un échange cyclique de valeurs propres entre les valeurs de parois rigides des modes consécutifs. Avec certaines valeurs d’impédance, les modes acoustiques de paroi apparaissent. Ils sont caractérisés par la forme exponentielle de leurs fonctions propres.En plus des modes acoustiques, il existe des modes hydrodynamiques de surface qui se sont révélés avec quelques valeurs d’impédance et forme et nombre de Mach de l’écoulement moyen. Pour un ensemble de données de référence, ces modes ont été étudiés. L’impédance a été considérée avec un modèle basé sur des données de la littérature, tout comme le profil d’écoulement moyen.Un mode hydrodynamique a été trouvé. Avec certaines valeurs de la fréquence, l’ensemble des paramètres donne lieu à une instabilité. En utilisant le critère Briggs Bres pour la stabilité,l’instabilité a été jugée absolue.À partir du comportement des modes avec différentes valeurs de l’impédance, et conformément aux résultats publiés, nous avons défini la condition que le spectre doit remplir pour réduire autant que possible le bruit. C’est cela qu’on appelle l’impédance optimale. Nous avons calculé cette valeur pour différents fréquences et écoulements moyens. / The study presented in this thesis is within the domain of modal acoustics of lined ducts withgrazing flow. We consider an upstream source of noise with a fixed frequency, within a lined duct.From this, we study the eigenmodes in terms of wavenumber that are present in this system.With this study, we contribute to the better understanding of sound propagation in thedescribed configuration. Within its main applications, we can find the noise reduction fromaeroengines.A numerical analysis with the pseudospectral collocation method, based on Chebyshevpolynomials was used to obtain the spectrum of modes within the duct, in a domain transversalto the mean flow. For this, two programs were used: On one hand, within the frame of this thesis,the program FiEStA was developed. It solves the linearized Euler Equations, considering eitherone or two dimensions of the transversal plane. On the other hand, the already existing programMAMOUT was used for verification and to solve also the linearized Navier-Stokes Equations toobserve the effects of viscosity.With these tools, the first result was to notice the effects of three parameters: When theaspect ratio grows, the density of modes in the spectrum grows also. In particular, we havemore propagative modes. As the mean flow Mach number grows, we observe these effects on theeigenvalues: a displacement to the negative real part, a slight amplification of their absolute valueand a displacement towards the modes of lower index. The difference in mean flow profile inducesanother displacement in modes, not easily predictable. It changes also the shape of eigenfunctions,which is clearly seen for the planewave mode. The impedance changes induce a cyclic exchange ofeigenvalues from their hard wall value to the hard wall value of a consecutive mode. The changeof eigenfunction is gradually change in wavelength, to obtain the shape of the destination mode.With some impedance values, a pair of modes, called the acoustic surface modes arise. They arecharacterized by the exponential shape of their eigenfunctions.Besides these acoustic surface modes, there are also a pair of hydrodynamic surface modeswhich come to light with some values of impedance and shape and Mach number of the meanflow. With a benchmark data, these modes were studied. The impedance was considered from themodel of a measured liner while the mean flow profile was taken from experimental values. Withthis, the hydrodynamic mode was found. With specific values of frequency, the set of parametersgives rise to an instability. Using the Briggs-Bers criterion for stability, the instability was foundto be absolute for a given frequency.From the comportment of modes with different values of impedance, and in accordance withpublished results, we defined the condition that the spectrum has to fulfill to reduce as much aspossible the upstream noise. This is what we called the optimal impedance. We obtained it forseveral flow profiles and frequencies, in both 1D and 2D domains.

[pt] O processo de revestimento por rotação é caracterizado pelo uso de cilindros girantes para controlar a espessura e aplicar uma fina camada de líquido em um substrato em movimento. A não ser a baixas velocidades dos cilindros, o escoamento bi-dimensional na região de formação dos filmes sobre cada cilindro é instável e o padrão observado experimentalmente consiste em um escoamento tri-dimensional e periódico na direção transversal ao substrato. Esta instabilidade pode limitar a velocidade máxima do processo se a camada líquida depositada sobre o substrato tem que ser uniforme. Para líquidos Newtonianos, a estabilidade deste escoamento é determinada pela competição de forças viscosas e capilares: a instabilidade ocorre acima de um número de capilaridade máximo. Apesar da maioria dos líquidos utilizados em processos de revestimento serem não Newtonianos, as análises disponíveis deste escoamento se limitam a estudos de líquidos Newtonianos. O comportamento não Newtoniano do líquido pode alterar completamente a natureza do escoamento perto da superfície livre; quando pequenas quantidades de polímeros flexíveis de alto peso molecular estão presentes, a instabilidade na direção transversal ocorre a velocidades muito mais baixas, quando comparado ao caso Newtoniano. Os mecanismos responsáveis pela instabilidade a baixas velocidades ainda não são completamente compreendidos. Este escoamento viscoelástico com superfície livre é analisado neste trabalho através de duas equações constitutivas diferenciais, o modelo de Oldroyld-B e o modelo de FENE-P. As equações de conservação de massa, quantidade de movimentos acopladas com os modelos constitutivos, e as equações não-lineares de mapeamento que transformam o problema de superfície livre em um problema de valor de contorno foram resolvidas pelo método de elementos finitos DEVSS-G/SUPG. O sistema de equações algébricas não linear foi resolvido pelo método de Newton com continuação por pseudo-comprimento de arco. Os resultados mostram como o campo de tensão muda com o aumento do número de Weissenberg (elasticidade do líquido), levando a formação de uma camada limite de tensão elástica na superfície livre e tensões elásticas compressivas na direção transversal, que podem explicar o aparecimento da instabilidade a baixas velocidades. Este trabalho também apresenta a formulação de estabilidade linear para escoamentos viscoelásticos com superfícies livres. O modelo dá origem a um problema de auto-valor generalizado, que foi resolvido pelo método de GMRES (ARPACK). Os auto-valores dominantes da matriz Jacobiana indicam a estabilidade do escoamento. Esta formulação foi testada em três escoamentos distintos: escoamento em uma cavidade de tampa móvel, piscina de líquido estática e um escoamento de Couette (simples de cisalhamento). / [en] Roll coating is distinguished by the use of one or more gaps between rotating cylinders to meter and apply a liquid layer to a substrate. Except at low speed, the film splitting flow that occurs in forward roll coating is three-dimensional and results in more or less regular stripes in the machine direction. This instability can limit the speed of the process if a smooth film is required as a final product. For Newtonian liquids, the stability of the film-split flow is determined by the competition of capillary forces and viscous forces: the onset of meniscus nonuniformity is market by a critical value of the capillary number. Although most of the liquids coated industrially are polymeric solutions and dispersions, that are not Newtonian, most of previous theoretical analyses of film splitting flows dealt only with Newtonian liquids. Non-Newtonian behavior can drastically change the nature of the flow near the free surface; when minute amounts of flexible polymer are present, the onset of the three-dimensional instability occurs at much lower speeds than in the Newtonian case. the mechanisms responsible for the early onset of this flow instability is not well understood. This free surface coating flow is analyzed here with differential constitutive models, the Oldroyld-B and the FENE-P equations. The continuity, momentum equations coupled with the constitutive models, and the non-linear mapping equations that transform the free boundary problem into a fixed boundary problem are solved by Newton s method with pseudo-arc-length continuation. The results show how the stress field changes with Weisenberg number, leading to the formation of an elastic boundary layer near the free surface and compressive elastic stresses in the crss-flow direction that may explain the onset of the ribbing instability at the smaller Capillary numbers when viscoelastic liquids are used. This work also presents the formulation for linear stanility analysis of viscoelastic free surface flows. The model leads to a generalized eigenproblem that is solved here using the Arnoldi s method with the software (ARPACK). The leading eigenvalues of the Jacobian Matrix indicate the stability of the flow. The formulation is tested in three different flows: lid-driven cavity, static liquid pool and a couette flow.

Este trabalho aborda o escoamento incompressível ao redor de um cilindro circular. A tese que se quer defender, com base em experimentos numéricos, é: A equação de Landau pode ser obtida a partir das equações de Navier-Stokes por uma análise de estabilidade não-linear global. A teoria produz um procedimento bem-definido para determinação dos coeficientes da equação de Landau, permitindo assim a sua interpretação como um modelo simplificado (equações reduzidas de Navier-Stokes) para a predição das forças aplicadas pelo fluido ao cilindro, que podem ser comparados com resultados experimentais. O modelo não-linear se baseia em uma teoria assintótica que, como se sabe, tem sua faixa de validade no espaço de parâmetros determinada a posteriori, por meio da própria comparação com dados de laboratório. Resultados na faixa 46 <= Re <= 80 são apresentados. Descobriu-se, que a faixa de aplicabilidade da teoria como aqui exposta é restrita, não excedendo em muito o valor crítico do número de Reynolds. Argumentos são expostos para justificar esta afirmação e possíveis maneiras de modificar a teoria para estender esta faixa são apresentadas. São reportados, ainda, teoria e resultados sobre um novo tipo de condição de contorno,denominado impedância fluida, que permite reduzir o tamanho do domínio de cálculo necessário para simulação de escoamentos externos, comparativamente à comumente utilizada condição de outflow. Neste caso, abordou-se a faixa 20 <= Re <= 600. / This work adresses the incompressible flow around a circular cylinder. What we want to prove, based on numerical experiments, reads: The Landau equation can be derived from the Navier-Stokes equations by means of a global nonlinear stability analysis. The theory leads to a procedure for calculating numerically the coefficients of these equation, thus permitting their interpretation as a simplified model - reduced Navier-Stokes equation - for the prediction of the forces applied by the fluid on the cylindrical structure, which can be compared against experimental data. The nonlinear model is based on an asymptotic theory which, as is known, has its validity range in the parameter space determined a posteriori. The focus lies in the range 46 <= Re <= 80. It was found that the theorys applicability range as presented here is restricted to a small neighborhood of Rec. This affirmation in justified and possible means of modifying the theory in order to enlarge this range are proposed. Theory and results concerning a new type of boundary condition called fluid impedance are also reported, permitting the reduction of the domain size necessary for simulating external flows, comparatively to the commonly used outflow condition. In this case, the range 20 <= Re <= 600 was considered.