Ambient wind causes trees to oscillate. Wind-induced oscillations of trees constitute a fluid-structure interaction problem, which has been studied by many researchers from various points of view. However, there is yet a lot to be done. From an engineering point of view, the complex structure of trees, which are very different from man-made structures, as well as the highly nonlinear interaction between wind and tree, makes it a challenging task to predict the amplitude and frequency of the resulting oscillations. From a biological point of view, the influence of wind on photosynthesis as well as the growth and death of plants is crucial. A nonlinear model is derived for wind-induced oscillations of trees to investigate the effect of structural nonlinearities. It is shown that the structural nonlinearities in the system can result in a hardening behavior of the tree, indicating the importance of taking such nonlinearities into account. The influence of various system parameters such as tree’s age, taper and slenderness ratio on the tree oscillations is studied using this nonlinear model.

A coupled fluid-structure interaction solver capability is developed and validated. A high fidelity fluids solver, Loci-Chem, is coupled with a finite-element structural dynamics toolkit, MAST. The coupled solver is validated for the prediction of several panel instability cases in uniform flows and in the presence of an impinging shock for a range of subsonic and supersonic Mach numbers, dynamic pressures, and pressure ratios. The panel deflections and limit-cycle oscillation amplitudes, frequencies, and bifurcation point predictions compare very well with benchmark results for 2D simulations. The same procedures outlined in the validation study have been applied to simulations of varying dynamic pressures at M = 2 for an impinging oblique shockwave. The influence of inviscid, laminar and turbulent boundary layer profiles on the development of flow field characteristics has been analyzed, and laminar predictions characterized by a large flow separation results in vastly different behavior than that of traditional flutter.

The thesis develops singly-periodic mathematical models for complex laminar wakes which are formed behind vortex-shedding bluff bodies. These wake structures exhibit a variety of patterns as the bodies oscillate or are in close proximity of one another. The most well-known formation comprises two counter-rotating vortices in each shedding cycle and is popularly known as the vk vortex street. Of the more complex configurations, as a specific example, this thesis investigates one of the most commonly occurring wake arrangements, which consists of two pairs of vortices in each shedding period. The paired vortices are, in general, counter-rotating and belong to a more general definition of the 2P mode, which involves periodic release of four vortices into the flow. The 2P arrangement can, primarily, be sub-classed into two types: one with a symmetric orientation of the two vortex pairs about the streamwise direction in a periodic domain and the other in which the two vortex pairs per period are placed in a staggered geometry about the wake centerline. The thesis explores the governing dynamics of such wakes and characterizes the corresponding relative vortex motion. In general, for both the symmetric as well as the staggered four vortex periodic arrangements, the thesis develops two-dimensional potential flow models (consisting of an integrable Hamiltonian system of point vortices) that consider spatially periodic arrays of four vortices with their strengths being +/-1 and +/-2. Vortex formations observed in the experiments inspire the assumed spatial symmetry. The models demonstrate a number of dynamic modes that are classified using a bifurcation analysis of the phase space topology, consisting of level curves of the Hamiltonian. Despite the vortex strengths in each pair being unequal in magnitude, some initial conditions lead to relative equilibrium when the vortex configuration moves with invariant size and shape. The scaled comparisons of the model results with experiments conducted in a flowing soap film with an airfoil, which was imparted with forced oscillations, are satisfactory and validate the reduced order modeling framework. The experiments have been performed by a collaborator group at the Department of Physics and Fluid Dynamics at the Technical University of Denmark (DTU), led by Dr. Anders Andersen. Similar experiments have also been run at Virginia Tech as part of this dissertation and the preliminary results are included in this treatise. The thesis also employs the same dynamical systems techniques, which have been applied to study the 2P regime dynamics, to develop a mathematical model for the P+S mode vortex wakes, with three vortices present in each shedding cycle. The model results have also been compared favorably with an experiment and the predictions regarding the vortex circulation data match well with the previous results from literature. Finally, the thesis introduces a novel concept of clean and renewable energy extraction from vortex-induced vibrations of bluff bodies. The slow-moving currents in the off-shore marine environments and riverine flows are beyond the operational capabilities of the more established hydrokinetic energy converters and the discussed technology promises to be a significant tool to generate useful power from these copiously available but previously untapped sources. / Ph. D.

A high fidelity approach coupling the computational fluid dynamics method (CFD) and multi-body dynamics method (MBD) is presented for aero-servo-elastic wind turbine simulations. The approach uses the incompressible CFD dynamic overset code CFDShip-Iowa v4.5 to compute the aerodynamics, coupled with the MBD code Virtual.Lab Motion to predict the motion responses to the aerodynamic loads. The IEC 61400-1 ed. 3 recommended Mann wind turbulence model was implemented in this thesis into the code CFDShip-Iowa v4.5 as boundary and initial conditions, and used as the explicit wind turbulence for CFD simulations. A drivetrain model with control systems was implemented in the CFD/MBD framework for investigation of drivetrain dynamics. The tool and methodology developed in this thesis are unique, being the first time with complete wind turbine simulations including CFD of the rotor/tower aerodynamics, elastic blades, gearbox dynamics and feedback control systems in turbulent winds. Dynamic overset CFD simulations were performed with the benchmark experiment UAE phase VI to demonstrate capabilities of the code for wind turbine aerodynamics. The complete turbine geometry was modeled, including blades and approximate geometries for hub, nacelle and tower. Unsteady Reynolds-Averaged Navier-Stokes (URANS) and Detached Eddy Simulation (DES) turbulence models were used in the simulations. Results for both variable wind speed at constant blade pitch angle and variable blade pitch angle at fixed wind speed show that the CFD predictions match the experimental data consistently well, including the general trends for power and thrust, sectional normal force coefficients and pressure coefficients at different sections along the blade. The implemented Mann wind turbulence model was validated both theoretically and statistically by comparing the generated stationary wind turbulent field with the theoretical one-point spectrum for the three components of the velocity fluctuations, and by comparing the expected statistics from the simulated turbulent field by CFD with the explicit wind turbulence inlet boundary from the Mann model. The proposed coupled CFD/MBD approach was applied to the conceptual NREL 5MW offshore wind turbine. Extensive simulations were performed in an increasing level of complexity to investigate the aerodynamic predictions, turbine performance, elastic blades, wind shear and atmospheric wind turbulence. Comparisons against the publicly available OC3 simulation results show good agreements between the CFD/MBD approach and the OC3 participants in time and frequency domains. Wind turbulence/turbine interaction was examined for the wake flow to analyze the influence of turbulent wind on wake diffusion. The Gearbox Reliability Collaborative project gearbox was up-scaled in size and added to the NREL 5MW turbine with the purpose of demonstrating drivetrain dynamics. Generator torque and blade pitch controllers were implemented to simulate realistic operational conditions of commercial wind turbines. Interactions between wind turbulence, rotor aerodynamics, elastic blades, drivetrain dynamics at the gear-level and servo-control dynamics were studied, showing the potential of the methodology to study complex aerodynamic/mechanic systems.

Cette thèse vise à analyser expérimentalement une structure flexible et légère dans différents régimes d’écoulement, dont le régime cavitant. Un protocole expérimental a donc été mis en place afin de caractériser le comportement hydroélastique d’un profil NACA 0015 en polyoxyméthylène (POM) et de le comparer à un profil en acier inoxydable considéré comme « rigide ». Des mesures en écoulement subcavitant ont été réalisées : chargement hydrodynamique, contraintes, déformées statiques, réponse vibratoire et champ de vitesse ont été mesurés pour les deux matériaux. Enfin, une analyse vibratoire a été menée en écoulement cavitant. Ces mesures nous ont permis de constater que les déformées statiques du profil flexible sont similaires aux déformations observées sur une poutre encastrée : la flexion est la déformation principale et la torsion est faible. Toutefois les performances du profil flexible sont moins bonnes que pour un profil rigide : la portance diminue tandis que la traînée augmente. D’autre part, il apparaît que la dynamique du profil est contrôlée par l’écoulement. En effet, lorsque l’incidence du profil est proche de l’angle de décrochage, une fréquence liée au détachement tourbillonnaire apparaît sur les spectres de vibration des profils. Elle conduit à une réduction des fréquences propres liées à la flexion : si l’influence de cette fréquence sur le profil rigide reste faible à basse vitesse, sa proximité avec la fréquence propre du profil flexible conduit à un lock-in. Celui-ci se produit également en écoulement cavitant : lorsque la poche de cavitation devient instable, sa fréquence d’oscillation devient très énergétique et prend le contrôle de la dynamique du profil flexible. Le lock-in prend fin quand une supercavitation se développe autour du profil. Il conduit à une augmentation de la masse ajoutée au profil alors qu’elle devrait diminuer en présence de vapeur d’eau. / This work deals with an experimental analysis of a flexible and light lifting profile for various flow conditions, including cavitation. An experimental protocol was set up to study a flexible NACA 0015 made of polyoxymethylene (POM) and compare its behaviour with a foil made of steel, which is considered as rigid. The forces, strains, stresses and vibrations of the foils were measured, as well as the velocity field. Moreover, a vibratory analysis was performed in cavitating flow. The flexible foil behaves like a built-in beam : the deformations corresponds to predictions from the beam theory, with high bending and low twisting. These deformations imply lower lift and higher drag compared to the rigid foil. The vortex shedding frequency appears on the vibration spectra near stall. It increases with flow velocity and leads to a decrease of the natural bending frequency. But flexibility involves lower natural frequencies : the first bending frequency of the flexible foil is 3.5 times lower than the rigid one. This allows lock-in between the first bending frequency of the flexible foil and the vortex shedding frequency. Lock-in occurs in cavitating flows too : when cavitation becomes unstable, it oscillates with a frequency close to the bending natural frequency of the flexible foil. This lock-in ends when the cavitation number is low enough, what leads to a decrease of the cavitation oscillation frequency. In those conditions, the added mass of the flexible foil does not decrease with the cavitation number as the added mass of the rigid foil.

It is well known that when a flexible or flexibly-mounted structure is placed perpendicular to the flow of a Newtonian fluid, it can oscillate due to the shedding of separated vortices at high Reynolds numbers. If the same flexible object is placed in non-Newtonian flows, however, the structure's response is still unknown. The main objective of this thesis is to introduce a new field of viscoelastic fluid-structure interactions by showing that the elastic instabilities that occur in the flow of viscoelastic fluids can drive the motion of a flexible structure placed in its path. Unlike Newtonian fluids, the flow of viscoelastic fluids can become unstable at infinitesimal Reynolds numbers due to the onset of a purely elastic flow instability. This instability occurs in the absence of nonlinear effects of fluid inertia and the Reynolds number of the flows studied here are in the order of 10-4. When such an elastic flow instability occurs in the vicinity of a flexible structure, the fluctuating fluid forces exerted on the structure grow large enough to cause a structural instability which in turn feeds back into the fluid resulting in a flow instability. Nonlinear periodic oscillations of the flexible structure are observed which have been found to be coupled to the time-dependent growth and decay of viscoelastic stresses in the wake of the structure. Presented in this thesis are the results of an investigation of the interaction occurring in the flow of a viscoelastic wormlike micelle solution past a flexible rectangular sheet. The structural geometries studied include: flexible sheet inclinations at 20°, 45° and 90° and flexible sheet widths of 5mm and 2.5mm. By varying the flow velocity, the response of the flexible sheet has been characterized in terms of amplitude and frequency of oscillations. Steady and dynamic shear rheology and filament stretching extensional rheology measurements are conducted in order to characterize the viscoelastic wormlike micelle solution. Bright field images show the deformation of the flexible sheet during an unstable oscillation while flow-induced birefringence images highlight the viscoleastic fluid stresses produced in the wake of the flexible sheet.

Une capsule est une goutte de liquide enveloppée par une membrane fine et déformable. Les propriétés mécaniques de la membrane sont essentielles pour le mouvement de la capsule. L’analyse de l’écoulement d’une suspension de capsules dans un canal microfluidique au moyen d’un modèle mécanique est une technique permettant de déterminer les propriétés élastiques de la membrane. Un modèle numérique tridimensionnel a été développé pour résoudre ce problème d’interaction fluide-structure en écoulement confiné. Il couple une méthode des intégrales de frontières pour les écoulements des fluides et une méthode éléments finis pour la déformation de la membrane. Le modèle est utilisé pour étudier l’écoulement d’une capsule initialement sphérique dans des canaux de différentes sections. Dans un canal cylindrique, on montre que l’effet de confinement du canal conduit à la compression de la capsule. Cela engendre la formation de plis sur la membrane autour de l’axe de l’écoulement, phénomène également observé expérimentalement. Dans un canal de section carrée, les effets de la loi constitutive de la membrane, du rapport de taille et du débit d’écoulement sur la déformation de la capsule sont systématiquement étudiés. La comparaison entre les résultats expérimentaux et numériques nous permet de déduire les propriétés mécaniques de la membrane d’une population de capsules artificielles. Ce travail démontre la faisabilité de la mesure de propriétés mécaniques d’une membrane en utilisant une technique microfluidique en canal carré. Il pourrait être étendu par l’étude d’écoulements instationnaires dans un canal de section variable ou avec bifurcations. / A capsule is a liquid droplet enclosed by a thin and deformable membrane. The membrane mechanical properties are critical for the deformation and motion of capsules. The flow of a capsule suspension through a microfluidic channel with dimensions comparable to those of the suspended particles can be used to infer the membrane elastic properties. However a mechanical model of the process is necessary. We present a three-dimensional numerical model to simulate such fluid-structure interaction problem. We use a novel numerical model that couples a boundary integral method for the internal and external fluid flows and a finite element method for the membrane deformation. The model is applied to study the flow of an initially spherical capsule in channels with different cross-sections. In a cylindrical channel with circular cross-section, we show that the confinement effect leads to the compression of the capsule in the hoop direction. The membrane tends to buckle and to fold as observed experimentally. In a microfluidic channel with a square cross-section, the effects of the membrane constitutive law, size ratio and flow strength on the capsule deformation are systematically studied. The comparison between experimental and numerical results allows us to deduce the membrane mechanical properties of a population of artificial capsules. The present work shows that it is possible to measure the membrane mechanical properties by using a microfluidic channel with a square cross-section. It can be extended to unsteady capsule flows in a channel with variable cross-sections or bifurcations.

The highly optimized performance of nature’s creations and biological assemblies has inspired the development of their engineered counter parts that can potentially outperform conventional systems. In particular, bat wings are populated with air flow hair receptors which feedback the information about airflow over their surfaces for enhanced stability and maneuverability during their flight. The hairs in the bat wing membrane play a role in the maneuverability tasks, especially during low-speed flight. The developments of artificial hair sensors (AHS) are inspired by biological hair cells in aerodynamic feedback control designs. Current mathematical models for hair receptors are limited by strict simplifying assumptions of creeping flow hair Reynolds number on AHS fluid-structure interaction (FSI), which may be violated for hair structures integrated on small-scaled Unmanned Aerial Vehicles (UAVs). This study motivates by an outstanding need to understand the dynamic response of hair receptors in flow regimes relevant to bat-scaled UAVs. The dynamic response of the hair receptor within the creeping flow environment is investigated at distinct freestream velocities to extend the applicability of AHS to a wider range of low Reynolds number platforms. Therefore, a threedimensional FSI model coupled with a finite element model using the computational fluid dynamics (CFD) is developed for a hair-structure and multiple hair-structures in the airflow. The Navier-Stokes equations including continuity equation are solved numerically for the CFD model. The grid independence of the FSI solution is studied from the simulations of the hairstructure mesh and flow mesh around the hair sensor. To describe the dynamic response of the hair receptors, the natural frequencies and mode shapes of the hair receptors, computed from the finite element model, are compared with the excitation frequencies in vacuum. This model is described with both the boundary layer effects and effects of inertial forces due to fluid-structure xiv interaction of the hair receptors. For supporting the FSI model, the dynamic response of the hair receptor is also validated considering the Euler-Bernoulli beam theory including the steady and unsteady airflow.

Cette thèse est motivée par un problème aéronautique: le ballottement du carburantdans des réservoirs d’ailes d’avion très flexibles. Les vibrations induites par le couplagedu fluide avec la structure peuvent conduire à des problèmes tels que l’inconfort des passagers,une manoeuvrabilité réduite, voire même provoquer un comportement instable. Cette thèse apour objectif de développer de nouveaux modèles d’interaction fluide-structure, en mettant enoeuvre la théorie des systèmes Hamiltoniens à ports d’interaction (pHs). Le formalisme pHsfournit d’une part un cadre unifié pour la description des systèmes multi-physiques complexeset d’autre part une approche modulaire pour l’interconnexion des sous-systèmes grâce auxports d’interaction. Cette thèse s’intéresse aussi à la conception de contrôleurs à partir desmodèles pHs. Des modèles pHs sont proposés pour les équations de ballottement du liquide en partantdes équations de Saint Venant en 1D et 2D. L’originalité du travail est de donner des modèlespHs pour le ballottement dans des réservoirs en mouvement. Les ports d’interaction sont utiliséspour coupler la dynamique du ballottement à la dynamique d’une poutre contrôlée par desactionneurs piézo-électriques, celle-ci étant préalablement modélisée sous forme pHs. Aprèsl’écriture des équations aux dérivées partielles dans le formalisme pHs, une approximation endimension finie est obtenue en utilisant une méthode pseudo-spectrale géométrique qui conservela structure pHs du modèle continu au niveau discret. La thèse propose plusieurs extensionsde la méthode pseudo-spectrale géométrique, permettant la discrétisation des systèmesavec des opérateurs différentiels du second ordre d’une part et avec un opérateur d’entrée nonborné d’autre part. Des essais expérimentaux ont été effectués sur une structure constituéed’une poutre liée à un réservoir afin d’assurer la validité du modèle pHs du ballottementdu liquide couplé à la poutre flexible, et de valider la méthode pseudo-spectrale de semi-discrétisation.Le modèle pHs a finalement été utilisé pour concevoir un contrôleur basé surla passivité pour réduire les vibrations du système couplé. / This thesis is motivated by an aeronautical issue: the fuel sloshing in tanksof very flexible wings. The vibrations due to these coupled phenomena can lead to problemslike reduced passenger comfort and maneuverability, and even unstable behavior. Thisthesis aims at developing new models of fluid-structure interaction based on the theory ofport-Hamiltonian systems (pHs). The pHs formalism provides a unified framework for thedescription of complex multi-physics systems and a modular approach for the coupling ofsubsystems thanks to interconnection ports. Furthermore, the design of controllers using pHsmodels is also addressed. PHs models are proposed for the equations of liquid sloshing based on 1D and 2D SaintVenant equations and for the equations of structural dynamics. The originality of the workis to give pHs models of sloshing in moving containers. The interconnection ports are used tocouple the sloshing dynamics to the structural dynamics of a beam controlled by piezoelectricactuators. After writing the partial differential equations of the coupled system using thepHs formalism, a finite-dimensional approximation is obtained by using a geometric pseudospectralmethod that preserves the pHs structure of the infinite-dimensional model at thediscrete level. The thesis proposes several extensions of the geometric pseudo-spectral method,allowing the discretization of systems with second-order differential operators and with anunbounded input operator. Experimental tests on a structure made of a beam connected to atank were carried out to validate both the pHs model of liquid sloshing in moving containersand the pseudo-spectral semi-discretization method. The pHs model was finally used to designa passivity-based controller for reducing the vibrations of the coupled system.

Avec la hausse des niveaux de dimensionnement sismique il est devenu nécessaire de limiter les chargements internes dans les structures, notamment en utilisant des dispositifs glissants. Ces dispositifs plafonnent les efforts internes en déclenchant un glissement de la structure. Il devient cependant nécessaire d'estimer l'amplitude des déplacements de corps rigide, notamment pour les structures stockées dans des réservoirs. Dans ce cas, il est nécessaire de prévenir les impacts entre la structure glissante et les bords du réservoir pour contrôler les risques de fuite. Parmi les structures glissantes immergées, on citera les ponts, les structures côtières en maçonnerie, les râteliers de stockage de combustible nucléaire, etc...Les équations de dynamique associées au comportement de ces structures sont non-linéaires et nécessitent l'utilisation de simulations numériques coûteuses en temps de calcul et ne permettant pas de faire des études de sensibilité rapides. On propose donc une méthode de résolution quasi-analytique de ces équations en traitant dans un premier temps, l'évaluation analytique des matrices de masses ajoutées du couplage fluide-structure, dans un second temps, une méthode de résolution quasi-analytique du glissement d'une structure quelconque immergée dans un fluide avec une actualisation de la géométrie de lames d'eau. Les résultats obtenus présentent une bonne adéquation avec des simulations numériques et offrent un temps de calcul quasiment instantané compatible avec une étude paramétrique ou stochastique de ces structures / As the seismic loadings are increasing in accordance to the recent regulations regarding Earthquake design, the use of sliding devices in structures is becoming more common. These devices limitate the internal forces by creating a rigid body sliding. It is then necessary to estimate the global displacement of the structure, especially concerning structures that are immersed in a reservoir. In this case, the displacement must be well estimated in order to prevent impacts between the sliding structure and the boundaries of the reservoir. We can find such structures in : bridges, costal structures in brick and masonry, or in the nuclear industry with the underwater fuel storage racks, ...The governing equations for the behaviour of these structures are non linear and must be solved using time-consuming computer simulations which are not fit for a stochastic study. Our method consists in, firstly, evaluating analytically the added masses of the fluid-structure interaction, secondly, a semi-analytical solving of the governing equations including the updating of the dimensions of the fluid layers surrounding the sliding structure. The results of this new method are in accordance with the numerical simulations and can be obtained in a short time (1 or 2 seconds) which offers the possibility to make a stochastic analysis of the non linear behaviour