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A large eddy simulation is performed to study secondary tones generated by aNACA0012 airfoil at angle of attack of $\alpha = 3^{\circ}$ with freestreamMach number of $M_{\infty} = 0.3$ and Reynolds number of $Re = 5 \times 10^4$.Laminar separation bubbles are observed over the suction side and near thetrailing edge, on the pressure side. Flow visualization and spectral analysisare employed to investigate vortex shedding aft of the suction side separationbubble. Vortex interaction results in merging or bursting such that coherentstructures or turbulent packets are advected towards the trailing edge leadingto different levels of noise emission. Despite the intermittent occurrence oflaminar-turbulent transition, the noise spectrum depicts a main tone withmultiple equidistant secondary tones. To understand the role of flowinstabilities on the tones, the linearized Navier-Stokes equations are examinedin its operator form through bi-global stability and resolvent analyses, and bytime evolution of disturbances using a matrix-free method. These linear globalanalyses reveal amplification of disturbances over the suction side separationbubble. Non-normality of the linear operator leads to further transientamplification due to modal interaction among eigenvectors. Two-point, one timeautocovariance calculations of pressure along the spanwise direction elucidateaspects of the acoustic feedback loop mechanism in the non-linear solutions.This feedback process is self-sustained by acoustic waves radiated from thetrailing edge, which reach the most sensitive flow location between the leadingedge and the separation bubble, as identified by the resolvent analysis.Leading edge disturbances arising from secondary diffraction and phaseinterference among the most unstable frequencies computed in the eigenspectrumare also shown to have an important role in the feedback loop.

Transition, intermittency and phase interference effects in airfoil secondary tones and acoustic feedback loop