Unsteady Nonlinear Aerodynamic Modeling and Applications

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Virginia Tech


Unsteady aerodynamic modeling is indispensable in the design process of rotary air vehicles, flapping flight and agile unmanned aerial vehicles. Undesirable vibrations can cause high-frequency variations in motion variables whose effects cannot be well predicted using quasi-steady aerodynamics. Furthermore, one may exploit the lift enhancement that can be generated through an unsteady motion for optimum design of flapping vehicles. Additionally, undesirable phenomena like the flutter of fixed wings and ensuing limit cycle oscillations can be exploited for harvesting energy. In this dissertation, we focus on modeling the unsteady nonlinear aerodynamic response and present various applications where unsteady aerodynamics are very relevant.

The dissertation starts with experiments for measuring unsteady loads on an NACA-0012 airfoil undergoing a plunging motion under various operating conditions. We supplement these measurements with flow visualization to obtain better insight into phenomena causing enhanced lift. For the model, we present the frequency response function for the airfoil at various angles of attack. Experiments were performed at reduced frequencies between 0.1 and 0.95 and angles of attack up to 65 degrees. Then, we formulate an optimization problem to unify the transfer function coefficients for each regime independently to obtain one model that represents the global dynamics. An optimization-based finite-dimensional (fourth-order) approximation for the frequency responses is developed. Converting these models to state-space form and writing the entries of the matrices as polynomials in the mean angle of attack, a unified unsteady model was developed. In the second set of experiments, we measured the unsteady plunging forces on the same airfoil at zero forward velocity. The aim is to investigate variations of the added forces associated with the oscillation frequency of the wing section for various angles of attack. Data of the measured forces are presented and compared with predicted forces from potential flow approximations. The results show a significant departure from those estimates, especially at high frequencies indicating that viscous effects play a major role in determining these forces.

In the second part of this dissertation, we consider different applications where unsteady loads and nonlinear effects play an important role. We perform a multi-objective aerodynamic optimization problem of the wing kinematics and planform shape of a Pterosaur replica ornithopter. The objective functions included minimization of the required cycle-averaged aerodynamic power and maximization of the propulsive efficiency. The results show that there is an optimum kinematic parameter as well as planform shape to fulfill the two objectives. Furthermore, the effects of preset angle of attack, wind speed and load resistance on the levels of harvested power from a composite beam bonded with the piezoelectric patch are determined experimentally. The results point to a complex relation between the aerodynamic loading and its impact on the static deflection and amplitudes of the limit cycle oscillations as well as the level of power harvested. This is followed by testing of a centimeter scale micro wind turbine that has been proposed to power small devices and to work as a micro energy harvester. The experimental measurements are compared to predicted values from a numerical model.

The methods developed in this dissertation provide a systematic approach to identifying unsteady aerodynamic models from numerical or experimental data that may work within different regimes. The resulting reduced-order models are expressed in a state-space form, and they are, therefore, both simple and efficient. These models are low-dimensional linear systems of ordinary differential equations so that they are compatible with modern flight dynamic models. The specific form of the obtained added force model, which defines the added forces as a function of plunging velocity and drag forces, guarantees that the resulting model is accurate over a range of high frequencies. Moreover, presented applications give a sense of the broad range of application of unsteady aerodynamics.



Unsteady nonlinear aerodynamics, Wind tunnel testing, Flow Visualization, High angles of attack, Energy harvesting