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.

This study seeks to understand the interplay of vorticity and elasto-dynamics that forms the basis for a fluttering flag and flapping wing propulsion, and factors that distinguish one from the other. The fluid dynamics is assumed two dimensional and incompressible, and comprises potential and viscous flow simulations. The elastic solid is one dimensional and governed by the Bernoulli-Euler flexure model. The fluid and elastic solid models are coupled using a predictor-corrector algorithm. Flutter of a flag or foil is associated with drag and we show that the pressure on the foil is predominantly circulatory in origin. The circulatory pressure generated on the foil depends primarily on the slope and curvature. The wake vorticity exhibits a wide range of behavior starting from a Kelvin-Helmholtz type instability to a von Kármán wake. Potential flow simulations do not capture the wake accurately both at high and low mass ratios. This is reflected in the flutter boundary and pressure over the foil when compared with viscous flow simulations. Thrust due to heaving of a flexible foil shows maxima at a set of discrete frequencies that coincide with the frequencies at which the flapping velocity of the foil tip is a maximum. The propulsive efficiency shows maxima at a set of discrete frequencies that are close but distinct from the thrust maxima set of frequencies. These discrete frequencies are close to the natural frequencies of vibration of a cantilevered foil vibrating in vacuum. At low frequencies thrust is a consequence of a strong leading edge vortex developed over the foil and it remains attached to the foil as it is convected due to the favorable pressure gradient presented by the time and spatially varying shape of the foil. At moderate and high frequencies of oscillation the pressure, and consequently the thrust, generated by the foil is non-circulatory in origin and they are high where the accelerations of the foil are high. At high frequencies the leading edge vortex is weak. Except in the low frequency range, potential flow simulations qualitatively compares well with viscous flow predictions. We show that thrust and drag on a flexible foil oscillating in a flow is caused by the phase difference between the slope of the foil and the fluid pressure on it. Propulsive efficiency though is governed by the phase difference between foil velocity and fluid pressure and inertia forces. Thus, the interplay of vorticity and elasto-dynamics determine the behavior of a flutter and propulsion of a flexible foil in a fluid flow.

In nature, many of the flapping wings and fins in swimming and flying animals have various degrees of flexibility with strong and coupled solid-fluid interactions between the structure and the fluid. In most cases, the wing structure, the flow and their interactions are complex. This thesis experimentally investigates a ‘simple’ fluid-flexible foil interaction problem: flow generated by a pitching foil with chordwise flexibility. To explore the effect of flexibility on the flow, we study the flow generated in quiescent water (the limiting case of infinite Strouhal number) by a sinusoidally pitching rigid symmetrical NACA0015 foil to which is attached a 0.05 mm thick chordwise flexible polythene flap at the trailing edge. The chordwise length of flap is 0.79 c, where c = 38 mm is the chord length of the rigid foil; span of the foil and flap is 100 mm. Detailed particle image velocimetry (PIV) and flow visualization measurements have been made for twelve cases, corresponding to three pitching amplitudes, ±10◦,± 15◦, ±20◦, and four frequencies, 1, 2, 3 and 4 Hz for each amplitude. For most of these cases, a narrow coherent jet aligned along the center-line, containing a reverse B’enard–K´arm´an vortex street, and a corresponding unidirectional thrust are generated. This thrust is similar to the upward force generated during hovering, but motion of our foil is much simpler than the complex wing kinematics found in birds and insects; also the thrust generation mechanism seems to be different. In our case, the thrust is from a coordinated pushing action of the rigid foil and the flexible flap. Control volume analysis reveals the unsteady nature of thrust generation. In this intricately coupled flow generation problem, chordwise flexibility is found to be crucial in producing the coherent jet. In this thesis, we explore in detail the physics of jet flow produced by the foil with a flexible flap, and identify the importance of flexibility in flow generation. Flap motion ensures appropriate spatial and temporal release of vortices, and also imparts them convective motion, to obtain the staggered pattern that produces the jet. To describe the fluid-flap interaction, we conveniently characterize the flap through a non-dimensional stiffness, ‘effective stiffness’ (EI)∗ of the flap, that captures the effects of both the flap properties as well as the external forcing. With the same flap by changing the pitching parameters, we cover a fairly large (EI)∗ range varying over nearly two orders of magnitude. However, we observed that only moderate (EI)∗ (~0.1 - 1) generates sustained narrow, orderly jet. We provide thrust estimates useful for the design of flapping foil thrusters/propulsors. Although this study has only indirect connections with the hovering in nature, it may be useful in understanding the role of flexibility of bird and insect wings during hovering. In contrast, a foil with a rigid trailing edge produces a weak jet whose inclination changes continually with time. This meandering is observed to be random and independent of the initial conditions over a wide range of pitching parameters.