Dynamical Modeling of the Unsteady Flow Over a Flapping Wing by Applying Proper Orthogonal Decomposition and System Identification To Particle Image Velocimetry Data

Abstract

In this work a novel approach for the dynamical modeling of the unsteady flow over a pitching airfoil is considered. The technique is based on collecting instantaneous velocity field data of the flow using particle image velocimetry (PIV), applying image processing to these snapshots to locate the airfoil, filling the airfoil and its surface with proper velocity data, applying proper orthogonal decomposition (POD) to these post-processed images to compute the POD modes and time coefficients, and finally fitting a discrete time state space dynamical model to the trajectories of the time coefficients using subspace system identification (N4SID). The procedure is implemented using MATLAB for the data obtained from a NACA0012 airfoil, and the results show that the dynamical model obtained can represent the flow dynamics with acceptable accuracy.