Identification of coherent structures in the flow past a NACA0012 airfoil via proper orthogonal decomposition

Abstract

Proper orthogonal decomposition, POD, is employed to identify coherent structures in the turbulent flow past a NACA0012 airfoil. An analysis of different POD techniques is presented including the standard snapshot method, the spectral POD (SPOD) method, and a Fourier-POD implementation combined with the SPOD. The latter technique is viable once the present turbulent flow has a homogeneous direction along the airfoil span. An assessment of different vector norms and filter functions employed in the POD reconstruction is presented. The evaluation of the several POD techniques allows the investigation of the physics of the current turbulent flow including the observation of coherent structures and their relation to the airfoil noise generation mechanisms. The SPOD technique is applied assuming periodic and non-periodic temporal signals in the construction of the covariance matrix. Although it slightly alters the spectrum of the POD singular values, the periodic SPOD considerably reduces the noise observed in the singular vectors. The application of the Gaussian filtering allows an enhanced control in the response of the SPOD when compared with a square-box filter. The present POD reconstructions employ norms based on kinetic energy and pressure. For both norms, twodimensional coherent structures are observed along the turbulent boundary layer and wake regions for the first pair of modes. These structures have a spectral content at the same frequency of the tonal noise radiation by the airfoil. The POD analysis also allows the identification of further coherent structures in the present flow. The kinetic energy norm is able to reconstruct low-frequency structures in the flow field for higher POD modes, while the pressure norm reconstructs high-frequency structures. This behavior is related to the physics captured by each POD norm in the present turbulent flow