Unsteady aerodynamic models for agile flight at low Reynolds numbers

Abstract

This work develops low-order models for the unsteady aerodynamic forces on a wing in response to agile maneuvers at low Reynolds number. Model performance is assessed on the basis of accuracy across a range of parameters and frequencies as well as of computational efficiency and compatibility with existing control techniques and flight dynamic models. The result is a flexible modeling procedure that yields accurate, low-dimensional, state-space models. The modeling procedures are developed and tested on direct numerical simulations of a two-dimensional flat plate airfoil in motion at low Reynolds number, Re=100, and in a wind tunnel experiment at the Illinois Institute of Technology involving a NACA 0006 airfoil pitching and plunging at Reynolds number Re=65,000. In both instances, low-order models are obtained that accurately capture the unsteady aerodynamic forces at all frequencies. These cases demonstrate the utility of the modeling procedure developed in this thesis for obtaining accurate models for different geometries and Reynolds numbers.

Linear reduced-order models are constructed from either the indicial response (step response) or realistic input/output maneuvers using a flexible modeling procedure. The method is based on identifying stability derivatives and modeling the remaining dynamics with the eigensystem realization algorithm. A hierarchy of models is developed, based on linearizing the flow at various operating conditions. These models are shown to be accurate and efficient for plunging, pitching about various points, and combined pitch and plunge maneuvers, at various angle of attack and Reynolds number. Models are compared against the classical unsteady aerodynamic models of Wagner and Theodorsen over a large range of Strouhal number and reduced frequency for a baseline comparison. Additionally, state-space representations are developed for Wagner's and Theodorsen's models, making them compatible with modern control-system analysis.

A number of computational tools are developed throughout this work. Highly unsteady maneuvers are visualized using finite-time Lyapunov exponent fields, which highlight separated flows and wake structures. A new fast method of computing these fields is presented. In addition, we generalize the immersed boundary projection method computations to use a moving base flow, which allows for the simulation of complex geometries undergoing large motions with up to an order of magnitude speed-up.

The methods developed in this thesis provide a systematic approach to identify unsteady aerodynamic models from analytical, numerical, or experimental data. The resulting models are shown to be reduced-order models of the linearized Navier-Stokes equations that are expressed in state-space form, and they are, therefore, both efficient and accurate. The specific form of the model, which separates added-mass forces, quasi-steady lift, and transient forces, guarantees that the resulting models are accurate over the entire range of frequencies. Finally, the models are low-dimensional linear systems of ordinary differential equations, so that they are compatible with existing flight dynamic models as well as a wealth of modern control techniques.