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Abstract
A systematic approach for the dynamical modelling of the unsteady flow over a flapping wing is developed, which is based on instantaneous velocity field data of the flow collected using particle image velocimetry (PIV) and computational fluid dynamics (CFD) simulations. The location and orientation of the airfoil is obtained by image processing and the airfoil is filled with proper velocity data. Proper orthogonal decomposition (POD) is applied to these post-processed images to compute POD modes and time coefficients, and a discrete-time state-space dynamical model is fit to the trajectories of the time coefficients using subspace system identification (N4SID). The procedure is verified using PIV and CFD data obtained from a pitching NACA0012 airfoil. The simulation results confirm that the dynamical model obtained from the method proposed can represent the flow dynamics with acceptable accuracy.
Acknowledgements
The authors thank the Scientific and Technological Research Council of Turkey (TUBITAK) and the European Commission (EC) for supporting this work through projects 109E233 and PIRG-2008-GA-239536, respectively.
Notes
1. Note that this will result in different flow dynamics than that of Section 2.1, but this is not an issue for our purposes as we are not attempting in any way to study the consistency of PIV and CFD results. These methods are just tools to generate data for the modelling process, and the data collected from PIV and CFD will be used separately to generate two separate models; the former for the unforced slow-pitching airfoil and the latter for an actuated fast-pitching airfoil. Ideally, we would have preferred to generate PIV data for both; unfortunately, our experimental hardware is limited and cannot generate pitching velocities beyond a certain value. In addition, we currently do not have actuators installed on our set-up.