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This dissertation presents shape and structural optimization studies on flapping wings for micro air vehicles. The design space of the optimization includes the wing planform and the structural properties that are relevant to the wing model being analyzed. The planform design is parameterized using a novel technique called modified Zimmerman, which extends the concept of Zimmerman planforms to include four ellipses rather than two. Three wing types are considered: rigid, plate-like deformable, and membrane. The rigid wing requires no structural design variables. The structural design variables for the plate-like wing are the thickness distribution polynomial coefficients. The structural variables for the membrane wing control the in-plane distributed forces which modulate the structural deformation of the wing. The rigid wing optimization is performed using the modified Zimmerman method to describe the wing. A quasi-steady aerodynamics model is used to calculate the thrust and input power required during the flapping cycle. An assumed inflow model is derived based on lifting-line theory and is used to better approximate the effects of the induced drag on the wing. A multi-objective optimization approach is used since more than one aspect is considered in flapping wing design. The the epsilon-constraint approach is used to calculate the Pareto optimal solutions that maximize the cycle-average thrust while minimizing the peak input power and the wing mass. An aeroelastic model is derived to calculate the aerodynamic performance and the structural response of the deformable wings. A linearized unsteady vortex lattice method is tightly coupled to a linear finite element model. The model is cost effective and the steady-state solution is solved by inverting a matrix. The aeroelastic model is used to maximize the thrust produced over one flapping cycle while minimizing the input power. / Ph. D.

This dissertation broadly seeks to understand the effect different kinematic parameters, external forces, and dynamic wing conformation have on the fluid dynamics of flapping flight. The primary motivation is to better grasp the fundamental fluid phenomena driving efficient flapping flight in the Reynolds number regime of birds, bats, and man made fliers of similar scale. The CFD solver (GenIDLEST) used is a Navier-Stokes solver in a finite volume formulation on non-staggered structured multiblock meshes. It has the capability for both body-fitted moving grid simulations and Immersed Boundary Method (IBM) for simulating complex bodies moving within a fluid. To that purpose we investigate the response of a rigid flapping thin surface planar wing in forward flight, at Re=10,000, subjected to frontal gusts. Gusts are a common ecological hazard for flapping fliers, especially in crowded environments. Among the various temporal and spatial scales of gust possible, we look at the phasing and duration of very large spatial scale gusts and their impact on the unsteady fluid dynamics of flapping within a single flapping cycle. The gust is characterized by a step function with time scale much smaller than the flapping time period. Having the advantage of prescribing the motion, as well as the timing and duration of the gust, this allowed the observation of the effect of angle of attack (AOA) and wing rotation on the evolution of the Leading Edge Vortex (LEV) and, hence the instantaneous lift and thrust profiles, by varying the parameters. During the downstroke, frontal gusts accelerated the flow development resulting in early separation of existing LEVs and formation of new ones on the wing surface which influenced the force generation by increasing the lift and thrust. These phenomena underscored the importance of the unsteady vortex structures as the primary force generators in flapping flight.The effect of the gust is observed to be diminished when it occurs during rapid supination of the wing. Unlike the influence of the vortices during the downstroke, the upstroke primarily reacted to effective AOA changes. A key characteristic of the kinematics of fliers in nature is stroke deviation. We investigate this phenomenon using a similar framework as above on a rigid thin surface flat-plate flapping wing in forward flight. Stroke deviation happens due to a variety of factors including wing flexion, wing lateral translation, and wing area change and here we investigate the different stroke deviation trajectories. Various trajectories were analyzed to assess the different capabilities that such kinematics might offer. The instantaneous lift and thrust profiles were observed to be influenced by a combination of the Leading Edge Vortex (LEV) and the Trailing Edge Vortex (TEV) structures existing in the flow at any given time. As an index of the cost of performance across all cases, the power requirements for the different cases, based on the fluid torques, are analyzed. Anti-clockwise figure-of-eight-cycle deviation is shown to be very complex with high power costs while having better performance. The clockwise elliptic-cycle held promise in being utilized as a viable stroke deviation trajectory for forward flight over the base non stroke deviation case. Armed with insight gained from these simple flapping structures, we are able to conduct the analysis of the flapping flight data obtained on a fruit bat. Understanding the full complexity of bat flight and the ways in which bat flight differs from that of other vertebrate flight requires attention to the intricate functional mechanics and architecture of the wings and the resulting unsteady transient mechanisms of the flow around the wings. We extract the detailed kinematic motion of the bat wing from the recorded data and then simulate the bat wing motion in the CFD framework for a range of Reynolds numbers. The Strouhal number calculated from the data is high indicating that the flow physics is dominated by the oscillatory motion. From the data the bat exhibits fine control of its mechanics by actively varying wing camber, wing area, torsional rotation of the wing, forward and backward translational sweep of the wing, and wing conformation to dictate the fluid dynamics. As is common in flapping flight, the primary force generation is through the attached unsteady vortices on the wing surface. This force output is modulated by the bat through varying wing camber and the wing area. Proper orthogonal decomposition of the wing kinematics is undertaken to compile a simpler set of kinematic modes that can approximate the original motion used by the fruit bat. These modes are then analyzed based on aerodynamic performance and power cost for more efficient flight. Understanding the physics of these modes will help us use them as prescribed kinematics for mechanical flappers as well as improve upon them from nature. / Ph. D.

Au cours des dernières décennies, la possibilité d’exploiter les capacités de vol exceptionnelles des insectes a été à l’origine de nombreuses recherches sur l’élaboration de nano-véhicules aériens (NAVs) à ailes battantes. Cependant, lors de la conception de tels prototypes, les chercheurs doivent analyser une vaste gamme de solutions liées à la grande diversité des insectes volants pour identifier les fonctionnalités et les paramètres adaptés à leurs besoins. Afin d’alléger cette tâche, le but de ce travail est de développer un outil permettant à la fois d’examiner le comportement cinématique et énergétique d’un nano-véhicule aérien à ailes flexibles résonantes, et donc d'évaluer son efficacité. Cet objectif reste néanmoins extrêmement difficile à atteindre car il concerne des objets de très petites tailles. Aussi, nous avons choisi tout d’abord de travailler sur un micro-véhicule aérien (MAV) à ailes battantes. Il s’agit avant tout de valider l’outil de modélisation à travers une comparaison systématique des simulations avec des résultats expérimentaux effectués lors de l’actionnement des ailes, puis au cours du décollage et du vol stationnaire du prototype. Une partie des connaissances et expériences acquises pourra ensuite être utilisée afin de mieux comprendre le fonctionnement et identifier la distribution d'énergie au sein du NAV. Bien que les deux véhicules s’inspirent directement de la cinématique des ailes d'insectes, les mécanismes d'actionnement des ailes artificielles des deux prototypes ne sont pas les mêmes en raison de la différence de taille. Comme le NAV est plus petit, ces ailes ont un mouvement de battement à une fréquence plus élevée que celles du MAV, à l’instar de ce qui existe dans la nature. En conséquence, lorsque l’on passe du MAV au NAV, le mécanisme d’actionnement des ailes doit être adapté et cette différence nécessite d’une part, de revoir la conception, l'approche de modélisation et le processus d'optimisation, et d’autre part, de modifier le procédé de fabrication. Une fois ces améliorations apportées, nous avons obtenu des résultats de simulations en accord avec les tests expérimentaux. Le principal résultat de ce travail concerne l’obtention pour les deux prototypes, le MAV et le NAV, d’une cinématique appropriée des ailes, qui conduit à une force de portance équivalente au poids. Nous avons d’ailleurs démontré que le MAV était capable de décoller et d’avoir un vol stationnaire stable selon l’axe vertical. En tirant parti des modèles basés sur le langage Bond Graph, il est également possible d'évaluer les performances énergétiques de ces prototypes en fonction de la dynamique de l'aile. En conclusion, cette étude contribue à la définition des paramètres essentiels à prendre en compte lors de la conception et l'optimisation énergétique de micro et nano-véhicules à ailes battantes. / In recent decades, the prospect of exploiting the exceptional flying capacities of insects has prompted much research on the elaboration of flapping-wing nano air vehicles (FWNAV). However, when designing such a prototype, designers have to wade through a vast array of design solutions that reflects the wide variety of flying insects to identify the correct combination of parameters to meet their requirements. To alleviate this burden, the purpose of this work is to develop a suitable tool to analyze the kinematic and power behavior of a resonant flexible-wing nano air vehicle. The key issue is evaluating its efficiency. However, this ultimate objective is extremely challenging as it is applied to the smallest flexible FWNAV. However, in this work, we worked first with a flapping-wing micro air vehicle (FWMAV) in order to have a tool for the simulation and experimentation of wing actuation, take-off and hovering. Some of the knowledge and experience acquired will then be transferred to better understand how our FWNAV works and identify the energy, power distribution. Although both of the vehicles employ the insect wing kinematics, their wings actuation mechanisms are not the same due to their sizes difference. Since the FWNAV is smaller, their wings flap at a higher frequency than the FWMAV as inspired by nature. As a consequence, from MAV to NAV, the wing actuation mechanism must be changed. Throughout this work, it can be seen clearly that this difference affects the whole vehicles development including the design, the manufacturing method, the modeling approach and the optimizing process. It has been demonstrated that the simulations are in good correlation with the experimental tests. The main result of this work is the proper wing kinematics of both FWMAV and FWNAV which leads to a lift to the weight ratio bigger and equal to one respectively. The FWMAV is even success to take-off and vertically stable hover. Moreover, taking advantage of the Bond Graph-based models, the evolution power according to the wing dynamic and the efficiency of the subsystem can be evaluated. In conclusion, this study shows the key parameters for designing and optimizing efficiency and the lift generated for two flapping wing vehicles in different size regimes.

In this study the dynamical modeling of the unsteady flow over a flapping wing is considered. The technique is based on collecting instantaneous velocity field data of the flow using Particle Image Velocimetry (PIV), applying image processing to these snapshots to locate the airfoil, filling the airfoil and its surface with proper velocity data, applying Proper Orthogonal Decomposition (POD) to these post-processed images to compute the POD modes and time coefficients, and finally fitting a discrete time state space dynamical model to the trajectories of the time coefficients using subspace system identification (N4SID). The procedure is applied using MATLAB for the data obtained from NACA 0012, SD 7003, elliptic airfoil and flat plate, and the results show that the dynamical model obtained can represent the flow dynamics with acceptable accuracy.

Ce travail de thèse s'inscrit dans le contexte des drones vise à réaliser à terme un Nano-dispositif volant (Nano Aerial Vehicle) capable d'imiter le vol des insectes. Ce mode de locomotion est privilégié car il présente des caractéristiques très adaptées au vol en milieu confiné. La solution proposée consiste à développer un drone de la taille d'un insecte s'appuyant sur des ailes vibrantes pour se mouvoir et à utiliser les technologies MEMS pour répondre aux problématiques de fabrication et de réduction d'échelle. La réussite d'un tel projet soulève néanmoins de nombreux défis scientifiques et technologiques, en particulier, les aspects aéro-élastiques des ailes et l'autonomie du drone. Pour répondre à ces défis, nous proposons dans un premier temps de mettre en œuvre des concepts comme la résonance et la torsion passive sur des prototypes en polymère (SU-8) réalisés par photolithographie. Dans un second temps, les différents composants de la chaîne de puissance sont optimisés, notamment l'actionneur électromagnétique, la liaison et les ailes de manière à maximiser la force de portance générée. Suite à ces améliorations, nous démontrons de façon expérimentale que le prototype était capable non seulement de reproduire une cinématique complexe mais également de compenser 75% de son poids. / This manuscript reports a work which aims to develop a tiny flying robots inspired by natural flyers. Our main objective is to devise a flying robot mimicking insects in terms of kinematics and scale using MEMS technologies in order to answer the scale challenges: the large-scale manufacturing and the system's small scale. The success this project faces different challenges such as aeroelastic aspects of wings and drone autonomy.In this work we propose the use of original concepts like resonance and passive torsion of the wings which are implemented on all-polymer prototypes obtained using a micromachining SU-8 photoresist process. In order to achieve a better efficiency of the prototype, each element of the energy transduction has been carefully examined and optimized. Especially, the actuation, the transmission and the wings in order to increase the lift. These improvements demonstrate experimentally that the prototype is able to produce a complex kinematic and compensate 75 % of its weight.

As the understanding of the workings of the biological world expands, biomimetic designs increasingly move into the focus of engineering research studies. For this thesis, two studiesinvolving leading edge vortex generation for lift production as observed in nature were explored intheir respective flow regimes. The first study focused on the steady state analysis of streamwise vortices generated byleading edge tubercles of an adult humpback whale flipper. A realistic scaled model of a humpbackflipper was fabricated based on the 3D reconstruction from a sequence of 18 images taken whilecircumscribing an excised flipper of a beached humpback whale. Two complementary modelswith smooth leading edges were transformed from this original digitized model and fabricatedfor testing to further understand the effect of the leading edge tubercles. Experimentally-obtainedforce and qualitative flow measurements were used to study the influence of the leading edgetubercles. The presence of leading edge tubercles are shown to decrease maximum lift coefficient(Cl ), but increase Cl production in the post-stall region. By evaluating a measure of hydrodynamicefficiency, humpback whale flipper geometry is shown to be more efficient in the pre-stall regionand less efficient in the post-stall region as compared to a comparable model with a smooth leadingedge. With respect to a humpback whale, if the decrease in efficiency during post-stall angles ofattack was only required during short periods of time (turning), then this decrease in efficiencymay not have a significant impact on the lift production and energy needs. For the pursuit ofbiomimetic designs, this decrease in efficiency could have potential significance and should beinvestigated further. Qualitative flow measurements further demonstrate that these force results aredue to a delay of separation resulting from the presence of tubercles.The second study investigated explored the effects of flapping frequency on the passive flowcontrol of a flapping wing with a sinusoidal leading edge profile. At a flapping frequency of f =0.05 Hz, an alternating streamwise vortical formation was observed for the sinusoidal leading edge,while a single pair of vortices were present for the straight leading edge. A sinusoidal leading edgecan be used to minimize spanwise flow by the generation of the observed alternating streamwisevortices. An increase in flapping frequency results in these streamwise vortices becoming stretchedin the path of the wing. The streamwise vortices are shown to minimize spanwise flow even afterbeing stretched. Once instabilities are formed at f ≥ 0:1 Hz due to velocity shearing generatedby the increase in cross-radial velocity, the alternating streamwise vortices begin to break downresulting in a increase of spanwise flow.

A flapping-wing micro-air-vehicle (FWMAV) represents a complex multi-disciplinary system whose analysis invokes the frontiers of the aerospace engineering disciplines. From the aerodynamic point of view, a nonlinear, unsteady flow is created by the flapping motion. In addition, non-conventional contributors, such as the leading edge vortex, to the aerodynamic loads become dominant in flight. On the other hand, the flight dynamics of a FWMAV constitutes a nonlinear, non-autonomous dynamical system. Furthermore, the stringent weight and size constraints that are always imposed on FWMAVs invoke design with minimal actuation. In addition to the numerous motivating applications, all these features of FWMAVs make it an interesting research point for engineers. In this Dissertation, some challenging points related to FWMAVs are considered. First, an analytical unsteady aerodynamic model that accounts for the leading edge vortex contribution by a feasible computational burden is developed to enable sensitivity and optimization analyses, flight dynamics analysis, and control synthesis. Second, wing kinematics optimization is considered for both aerodynamic performance and maneuverability. For each case, an infinite-dimensional optimization problem is formulated using the calculus of variations to relax any unnecessary constraints induced by approximating the problem as a finite-dimensional one. As such, theoretical upper bounds for the aerodynamic performance and maneuverability are obtained. Third, a design methodology for the actuation mechanism is developed. The proposed actuation mechanism is able to provide the required kinematics for both of hovering and forward flight using only one actuator. This is achieved by exploiting the nonlinearities of the wing dynamics to induce the saturation phenomenon to transfer energy from one mode to another. Fourth, the nonlinear, time-periodic flight dynamics of FWMAVs is analyzed using direct and higher-order averaging. The region of applicability of direct averaging is determined and the effects of the aerodynamic-induced parametric excitation are assessed. Finally, tools combining geometric control theory and averaging are used to derive analytic expressions for the textit{Symmetric Products}, which are vector fields that directly affect the acceleration of the averaged dynamics. A design optimization problem is then formulated to bring the maneuverability index/criterion early in the design process to maximize the FWMAV maneuverability near hover. / Ph. D.

There is currently a great deal of interest within the aviation community in the design of small, slow-flying but manoeuvrable uninhabited vehicles for reconnaissance, surveillance, and search and rescue operations in urban environments. Inspired by observation of birds, insects, fish and cetaceans, flapping wings are being actively studied in the hope that they may provide greater propulsive efficiencies than propellers and rotors at low Reynolds numbers for such Micro-Air Vehicles (MAVs). Researchers have posited the Strouhal number (combining flapping frequency, amplitude and forward speed) as the parameter controlling flapping wing aerodynamics in cruising flight, although there is conflicting evidence. This thesis explores the effect of flapping frequency and amplitude on forces and wake structures, as well as physical mechanisms leading to optimum propulsive efficiency. Two-dimensional rigid airfoils are considered at Reynolds number 2,000 ??? 40,000. A compressible Navier-Stokes simulation is combined with numerical and analytical potential flow techniques to isolate and evaluate the effect of viscosity, leading and trailing edge vortex separation, and wake vortex dynamics. The wake structures of a plunging airfoil are shown to be sensitive to the flapping frequency independent of the Strouhal number. For a given frequency, the wake of the airfoil exhibits ???vortex lock-in??? as the amplitude of motion is increased, in a manner analogous to an oscillating circular cylinder. This is caused by interaction between the flapping frequency and the ???bluff-body??? vortex shedding frequency apparent even for streamlined airfoils at low Reynolds number. The thrust and propulsive efficiency of a plunging airfoil are also shown to be sensitive to the flapping frequency independent of Strouhal number. This dependence is the result of vortex shedding from the leading edge, and an interaction between the flapping frequency and the time for vortex formation, separation and convection over the airfoil surface. The observed propulsive efficiency peak for a pitching and plunging airfoil is shown to be the result of leading edge vortex shedding at low flapping frequencies (low Strouhal numbers), and high power requirements at large flapping amplitudes (high Strouhal numbers). The efficiency peak is governed by flapping frequency and amplitude separately, rather than the Strouhal number directly.