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

Abstract

A large eddy simulation is performed to study secondary tones generated by a NACA0012 airfoil at angle of attack of $\alpha = 3^{\circ}$ with freestream Mach 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 the trailing edge, on the pressure side. Vortex shedding occurs aft of the suction side separation bubble, and vortex interaction results in merging or bursting such that coherent structures or turbulent packets are advected towards the trailing edge. This mechanism modulates the amplitude of the incident pressure signal, leading to different levels of noise emission. Despite the intermittent occurrence of laminar–turbulent transition, the noise spectrum depicts a main tone with multiple equidistant secondary tones. To understand the role of flow instabilities on the tones, the linearised Navier–Stokes equations are examined in their operator form through biglobal stability and resolvent analyses, and by time evolution of disturbances using a matrix-free method. These linear global analyses reveal amplification of disturbances over the suction side separation bubble. Spanwise-averaged pressure fluctuations elucidate aspects of the acoustic feedback loop mechanism in the nonlinear solutions. This feedback process is self-sustained by acoustic waves radiated from the trailing edge, which reach the most sensitive flow location near the leading edge, as identified by the resolvent analysis. Flow disturbances arising from secondary diffraction and phase interference among the most unstable frequencies computed in the eigenspectrum are shown to have an important role in the feedback loop.

Switch of tonal noise generation mechanisms in airfoil transitional flows

“…The flow transients are discarded after they achieve a statistically stationary condition. After that, the simulations were conducted for long time periods in order to capture different intermittent flow patterns and their impact on the instantaneous noise generation [10,12,28].…”

“…For the lowest Reynolds number, Re = 0.5 × 10 5 , the overall dynamics is dictated by vortex pairing on the suction side [10]. The flow instabilities that originate near mid-chord are purely 2D but, as they are advected, interaction among vortices may introduce threedimensionality to the structures that eventually leads to vortex breakdown.…”

“…For the flows investigated, it was argued that the acoustic waves would propagate upstream, exciting new hydrodynamic disturbances that convect downstream, sustaining a self-excited acoustic feedback loop [2][3][4]. This flow dynamics has been corroborated by means of linear stability analyses that provide further insights on the sensitivity and response to acoustic perturbations at the frequencies of the tonal noise components [5][6][7][8][9][10].…”

“…These simulations provided valuable insights on the noise sources but could not account for intrinsic threedimensional (3D) effects, such as vortex stretching and transition to turbulence. To over-come this limitation, 3D simulations have been recently employed to investigate such effects in the context of airfoil secondary tones and the feedback loop mechanisms [9,10,[12][13][14].…”

“…When combined, these parameters will dictate the physical mechanisms responsible for airfoil tonal noise generation including the detachment and reattachment dynamics of separation bubbles, and the subsequent shedding of coherent structures. For instance, it has been reported that vortex merging [10,22], bursting [12,[23][24][25][26][27], and intermittency [6,10,12,20] take place downstream of suction side separation bubbles. Thus, it is clear that the investigation of the flow dynamics driven by the separation bubbles is important to understand the noise sources.…”