Construction of the linear reduced-order model based on PIV data of flow field around airfoil

In this study, a linear reduced-order model of flow fields around the NACA0015 for an observer of active flow control system is constructed based on the time-resolved particle image velocimetry (PIV) data, and its behavior and accuracy are investigated. The PIV data were obtained at the chord Reynolds number of 6.0 × 10⁴, and the angle of attack of from 11° to 20°. Proper orthogonal decomposition (POD) analysis is employed to the PIV data and degrees of freedom of data are reduced by truncating the POD modes. Then, the linear model of POD modes is constructed by the least squares method based on the obtained time history of POD modes. Although the estimated time advancement of POD modes by the model reproduces the time history of the original data at the beginning, it gradually attenuates and finally converges to zero. This behavior is also supported by the eigenvalue analysis results of coefficient matrices of the linear model. In addition, behavior of the low-order (more energetic) POD modes was reproduced better than high-order (less energetic) POD modes. The results imply that 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 POD modes were reproduced well in the case of high angle of attack.