Direct numerical simulations are carried out to investigate the flow features responsible for secondary tones arising in trailing-edge noise at moderate Reynolds numbers. Simulations are performed for a NACA 0012 airfoil at freestream Mach numbers 0.1, 0.2 and 0.3 for angle of incidence 0 deg. and for Mach number 0.3 at 3 deg. angle of incidence. The Reynolds number based on the airfoil chord is fixed at Re c = 10 5 . Flow configurations are investigated where noise generation arises from the scattering of boundary layer instabilities at the trailing edge. Results show that noise emission has a main tone with equidistant secondary tones, as discussed in literature. An interesting feature of the present flows at zero incidence is shown; despite the geometric symmetry, the flows become non-symmetric with a separation bubble only on one side of the airfoil. A separation bubble is also observed for the non-zero incidence flow. For both angles of incidence analyzed, it is shown that low-frequency motion of the separation bubbles induce a frequency modulation of the flow instabilities developed along the airfoil boundary layer. When the airfoil is at 0 deg. angle of attack an intense amplitude modulation is also observed in the flow quantities, resulting in a complex vortex interaction mechanism at the trailing edge. Both amplitude and frequency modulations directly affect the velocity and pressure fluctuations that are scattered at the trailing edge, what leads to secondary tones in the acoustic radiation.

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List of symbols c ∞Free-stream speed of sound cAirfoil chord E Total energy f FW-H surface F i Dipole source G Green's function g ij Covariant metric tensors g ij Contravariant metric tensors H Heaviside function H (2) 0

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