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Unsteady aerodynamic theories are essential in the analysis of bird and insect flight. The study of these types of locomotion is vital in the development of flapping wing aircraft. This paper uses potential flow aerodynamics to extend the unsteady aerodynamic theory of Theodorsen and Garrick (which is restricted to rigid airfoil motion) to deformable thin airfoils. Frequency-domain lift, pitching moment and thrust expressions are derived for an airfoil undergoing harmonic oscillations and deformation in the form of Chebychev polynomials. The results are validated against the time-domain unsteady aerodynamic theory of Peters. A case study is presented which analyzes several combinations of airfoil motion at different phases and identifies various possibilities for thrust generation using a deformable airfoil. / Master of Science

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This dissertation presents both analytical and numerical approaches to optimizing thrust and thrust efficiency of harmonically deforming thin airfoils and membrane wings. A frequency domain unsteady aerodynamic theory for deformable thin airfoils, with Chebychev polynomials as the basis functions is presented. Stroke-averaged thrust and thrust efficiency expressions are presented in a quadratic matrix form. The motion and deformation of the airfoil is optimized for maximum thrust and efficiency. Pareto fronts are generated showing optimum deformation conditions (magnitude and phase) for various reduced frequencies and constraints. It is shown that prescribing the airfoil to deform in a linear combination of basis functions with optimal magnitude and phase results in a larger thrust as compared to rigid plunging, especially at low reduced frequencies. It is further shown that the problem can be constrained significantly such that thrust is due entirely to pressure with no leading edge suction, and associated leading edge separation. The complete aeroelastic system for a membrane wing is also optimized. The aerodynamic theory for deformable thin airfoils is used as the forcing in a membrane vibration problem. Due to the nature of the two dimensional theory, the membrane vibration problem is reduced to two dimensions via the Galerkin method and nondimensionalized such that the only terms are nondimesional tension, mass ratio and reduced frequency. The maximum thrust for the membrane wing is calculated by optimizing the tension in the membrane so that the the aeroelastic deformation due to wing motion leads to optimal thrust and/or efficiency. A function which describes the optimal variation of spanwise tension along the chord is calculated. It is shown that one can always find a range of membrane tension for which the flexible membrane wings performs better than the rigid wing. These results can be used in preliminary flapping wing MAV design. / Ph. D.

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.

Boundary-layer flows near leading edges of generally curved obstacles have been studied for a long time. Apart from having many practical applications, the theory and approaches prevailing in this area stimulate development of a variety of computational tools and form a ground for testing them. The specific aim of this work is to study two-dimensional laminar boundary layer flows near the leading edges of airfoils and other elongated bodies, and to explore geometries for which boundary layer separation can be avoided. This class of problems is relevant to optimal design of wings, aircraft and projectile noses, laminar flow control methods and adaptive wing technology. One of the findings of this work suggests that local modifications to parabolic wing noses can yield up to 11% increase in the unseparated angle of attack. Another result obtained here is the set of shortest possible generalised elliptic noses of long symmetric bodies which allow unseparated flow. Methods adopted in this work are based on the combined use of numerically solved Prandtl equations written in Gortler variables, and inviscid solutions obtained semi-analytically by the conformal mapping method. The resulting technique being reliable, fast and computationally inexpensive, can complement or test the results obtained using a comprehensive CFD approach. / Thesis (Ph.D.)--School of Mathematical Sciences, 2002.

Limit Cycle Oscillation is a type of aircraft wing structural vibration caused by the non-linearity of the system. The objective of this thesis is to provide a numerical study of this aeroelastic behavior. A CFD solver is used to simulate airfoils displaying such an aeroelastic behavior under certain airflow conditions. Two types of airfoils are used for this numerical study, including the NACA64a010 airfoil, and the supercritical NLR 7301 airfoil. The CFD simulation of limit cycle oscillation (LCO) can be obtained by using published flow and structural parameters. Final results from the CFD solver capture LCO, as well as flutter, behaviors for both wings. These CFD results can be obtained by using two different solution schemes, including the Roe and Zha scheme. The pressure coefficient and skin friction coefficient distributions are computed using the CFD results for LCO and flutter simulations of these two airfoils, and they provide a physical understanding of these aeroelastic behaviors.

The scope of the thesis is to numerically investigate the aerodynamics of flapping airfoils in hover and forward flight. The flowfields around flapping airfoils are computed by solving the governing equations on moving and/or deforming grids. The effects of Reynolds number, reduced frequency and airfoil geometry on unsteady aerodynamics of flapping airfoils undergoing pure plunge and combined pitch-plunge motions in forward flight are investigated. It is observed that dynamic stall of the airfoil is the main mechanism of lift augmentation for both motions at all Reynolds numbers ranging from 10000 to 60000. However, the strength and duration of the leading edge vortex vary with airfoil geometry and reduced frequency. It is also observed that more favorable force characteristics are achieved at higher reduced frequencies and low plunging amplitudes while keeping the Strouhal number constant. The computed flowfields are compared with the wide range of experimental studies and high fidelity simulations thus it is concluded that the present approach is applicable for investigating the flapping wing aerodynamics in forward flight. The effects of vertical translation amplitude and Reynolds number on flapping airfoils in hover are also studied. As the vertical translation amplitude increases, the vortices become stronger and the formation of leading edge vortex is pushed towards the midstroke of the motion. The instantaneous aerodynamic forces for a given figure-of-eight motion do not alter significantly for Reynolds numbers ranging from 500 to 5500.

Two active flow control methods are investigated numerically to understand the mechanism by which they control aerodynamics in the presence of severe flow separation on an airfoil. In particular, synthetic jets are applied to separated flows generated by additional surface feature (the actuators) near the trailing edge to obtain Coanda-like effects, and an impulse jet is used to control a stalled flow over an airfoil. A moving-grid scheme is developed, verified and validated to support simulations of external flow over moving bodies. Turbulent flow is modeled using detached eddy simulation (DES) turbulence models in the CFD code CDP (34) developed by Lopez (54). Synthetic jet actuation enhances turbulent mixing in flow separation regions, reduces the size of the separation, deflects stream lines closer to the surface and changes pressure distributions on the surface, all of which lead to bi-directional changes in the aerodynamic lift and moment. The external flow responds to actuation within about one convective time, which is significantly faster than for conventional control surfaces. Simulation of pitching airfoils shows that high-frequency synthetic jet affects the flow independently of the baseline frequencies associated with vortex shedding and airfoil dynamics. These unique features of synthetic jets are studied on a dynamically maneuvering airfoil with a closed-loop control system, which represents the response of the airfoil in wind-tunnel experiments and examines the controller for a rapidly maneuvering free-flight airfoil. An impulse jet, which is applied upstream of a nominal flow separation point, generates vortices that convect downstream, interact with the separating shear layer, dismantle the layer and allow following vortices to propagate along the surface in the separation region. These following vortices delay the separation point reattaching the boundary layer, which returns slowly to its initial stall condition, as observed in wind-tunnel experiments. A simple model of the impulse jet actuator used herein is found to be sufficient to represent the global effects of the jet on the stalled flow because it correctly represents the momentum injected into the flow. / text

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