Identification of the empirical Wagner model of a pitching airfoil used as a blade apparatus for harvesting systems

This study aims to identify the aeroelasticity of a pitching airfoil, used as a “blade-airfoil” apparatus for a torsional flutter harvester, by two-dimensional (2-D) Navier-Stokes simulations. An empirical Wagner model, capable of accounting for viscosity and thick, non-flat geometry of the blade-airfoil, is proposed to accurately predict the unsteady lift coefficient at the Reynolds number of 1E6. Two separate identification algorithms, based on the concept of deconvolution, are developed: one in the frequency domain utilizing rational function approximation, and the other in the time domain utilizing Observer/Kalman filter identification. Specific models and numerical methods are proposed for each approach to enhance the robustness and accuracy of the identification. The results suggest that both approaches can effectively identify the empirical Wagner function of the pitching blade-airfoil. However, the identification quality is reduced, although still better than the theoretical Wagner function, when the identification is based on lift coefficients generated by sufficiently rapid maneuvers, due to the presence of trailing-edge vortices. In addition, efforts are made to numerically compute the exact Wagner function using a truncation strategy and the Filon-Clenshaw-Curtis quadrature rule, with the associated numerical errors carefully examined.