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
