Linear Reduced-order Model Based on PIV Data of Flow Field around Airfoil

Abstract

In this study, a linear reduced-order model of flow fields around a NACA0015 is constructed based on time-resolved particle image velocimetry (PIV) data. The PIV data were obtained at the chord Reynolds number of 6.4 × 10⁴, and angles of attack from 11° to 20°. Proper orthogonal decomposition (POD) analysis is employed for the PIV data and the degrees of freedom are reduced by truncating the POD modes. Next, a linear model of the POD modes is constructed using the least-squares method based on the POD-mode time histories. Although the estimated POD modes initially reproduce original data, they gradually attenuate and converge to zero. This behavior is also supported by the eigenvalue analysis results of the model's coefficient matrices. In addition, the behavior of the low-order (more energetic) POD modes was reproduced better than that of the high-order (less energetic) POD modes. These results imply that the temporal fluctuation of large vortex structures has strong linearity and is not significantly affected by noise included in data. The former insight is also supported by the fact that the behaviors of POD modes were reproduced well in the case of high angle of attack.