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

A large eddy simulation is performed to study secondary tones generated by a NACA0012 airfoil at angle of attack $\alpha = 3^{\circ}$ with freestream Mach number $M_{\infty} 0.3$ and Reynolds $Re 5 \times 10^4$. Laminar separation bubbles are observed over the suction side near trailing edge, on pressure side. Flow visualization spectral analysis employed investigate vortex shedding aft bubble. Vortex interaction results in merging or bursting such that coherent structures turbulent packets advected towards edge leading different levels noise emission. Despite intermittent occurrence laminar-turbulent transition, spectrum depicts main tone multiple equidistant tones. To understand role flow instabilities tones, linearized Navier-Stokes equations examined its operator form through bi-global stability resolvent analyses, time evolution disturbances using matrix-free method. These linear global analyses reveal amplification Non-normality leads further transient due modal among eigenvectors. Two-point, one autocovariance calculations along spanwise direction elucidate aspects acoustic feedback loop mechanism non-linear solutions. This process self-sustained waves radiated from which reach most sensitive location between bubble, as identified analysis. Leading arising diffraction phase interference unstable frequencies computed eigenspectrum also shown have an important loop.