Resolvent-based reconstruction of trailing-edge noise of the transitional flow over a NACA0012 airfoil*

This numerical work investigates the relation between trailing-edge noise generated by a NACA0012 profile at 3° angle of attack and spanwise-coherent structures developing in the naturally transitional boundary layer over the airfoil. The aim of this work is to propose a low-order model of the radiated sound, based on surface pressure fluctuations obtained from resolvent analysis combined with acoustic analogies. The analysis is based on a numerical dataset obtained from a compressible large eddy simulation (LES) at a chord Reynolds number of 5e4 and a Mach number of 0.3.

Coherent structures are obtained from a spectral proper orthogonal decomposition (SPOD) of the LES snapshots, and from incompressible global resolvent modes of the mean fields. Preliminary results show a very good agreement between the most energetic structures captured by the SPOD and the leading resolvent mode, both in terms of the most frequency and mode shape. The mode shapes reveal that disturbances start to grow in the detached boundary layer on the suction side due to the Kelvin-Helmholtz mechanism and extend into the wake. Furthermore, surface pressure fluctuations obtained from the resolvent modes compare well with Fourier modes of the LES snapshots. These fluctuations are then used to rebuild the noise radiated based on acoustic analogy.