The main objective of this research was to better understand the flow physics of aircraft wings undergoing highly unsteady maneuvers. Reduced-order models play a central role in this study, both to elucidate the overall dynamical mechanisms behind various flow phenomena (such as dynamic stall and vortex shedding), and ultimately to guide flight control design for vehicles for which these unsteady phenomena are important.

Unsteady phenomena are of increasing interest to the Air Force, as lightweight unmanned air vehicles become more prevalent. With increasingly smaller and lighter vehicles envisioned in the future, understanding unsteady aerodynamics will become even more important, in order to design control systems that can respond to severe gusts, or perform highly agile maneuvers. The flight of small, highly maneuverable aircraft, whether biological or man-made, is greatly impacted by unsteady aerodynamic effects, which can be either beneficial or detrimental to flight. Accurate understanding of such effects can allow for the design of aircraft that are more efficient, responsive, and robust.

With advances in both experimental techniques and equipment, and computational power and storage capacity, researchers in fluid dynamics can now generate more high-fidelity data than ever before. The presence of increasingly large data sets calls for appropriate data analysis techniques, that are able to extract tractable and physically relevant information from the data. In particular, a much-desired goal in fluid mechanics, and indeed many other fields, is to obtain simple models that are capable of predicting the behavior of seemingly complex systems. Low-dimensional models can not only improve our fundamental understanding of such systems, but are often required for the purpose of efficient and accurate prediction, estimation and control.

Broadly speaking, one can obtain low-dimensional information about a system (whether it be in the form of a reduced-order model, or simply spatial modes corresponding to certain energetic or dynamic characteristics) in numerous ways, potentially using some combination of data collected from simulations and experiments, and theoretical knowledge of the system, such as the governing partial differential equations (PDEs).

Purely data-driven methods can include those developed particularly for fluids applications, such as the dynamic mode decomposition (DMD), or those which are appropriated from other communities, such as the eigensystem realization algorithm (ERA), which was first applied to study spacecraft structures, but has more recently been appropriated to model a wide range of fluids systems.

Dynamic mode decomposition allows for the identification and analysis of dynamical features of time-evolving fluid flows, using data obtained from either experiments or simulations. In contrast to other data-driven modal decompositions such as the proper orthogonal decomposition (POD), DMD allows for spatial modes to be identified that can be directly associated with characteristic frequencies and growth/decay rates. Following its conception, DMD was quickly shown to be useful in extracting dynamical features in both experimental and numerical data. It has subsequently been used to gain dynamic insight on a wide range of problems arising in fluid mechanics and other fields.

One of the major advantages of DMD over techniques such as global stability analysis is that it can be applied directly to data, without the need for the knowledge or construction of the system matrix, which is typically not available for experiments. For this reason, analysis of the sensitivity of DMD to the type of noise typically found in experimental results is of particular importance.

This work was done by Clarence W. Rowley and David R. Williams of Princeton University for the Air Force Research Laboratory. AFRL-0250

This Brief includes a Technical Support Package (TSP).
Identifying the ow physics and modeling transient forces on two-dimensional wings

(reference AFRL-0250) is currently available for download from the TSP library.

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