Direct simulations of trailing-edge noise generation from two-dimensional airfoils at low Reynolds numbers

The aeroacoustic sound generated from the flow around two NACA four-digit airfoils is investigated numerically, at relatively low Reynolds numbers that do not prompt boundary-layer transition. By using high-order finite-difference schemes to discretize compressible Navier–Stokes equations, the sound scattered on airfoil surface is directly resolved as an unsteady pressure fluctuation. As the wavelength of an emitted noise is shortened compared to the airfoil chord, the diffraction effect on non-compact chord length appears more noticeable, developing multiple lobes in directivity. The instability mechanism that produces sound sources, or unsteady vortical motions, is quantitatively examined, also by using a linear stability theory. While the evidence of boundary-layer instability waves is captured in the present result, the most amplified frequency in the boundary shear layer does not necessarily agree with the primary frequency of a trailing-edge noise, when wake instability is dominant in laminar flow. This contradicts the observation of other trailing-edge noise studies at higher Reynolds numbers. However, via acoustic disturbances, the boundary-layer instability may become more significant, through the resonance with the wake instability, excited by increasing a base-flow Mach number. Evidence suggests that this would correspond to the onset of an acoustic feedback loop. The wake-flow frequencies derived by an absolute-instability analysis are compared with the frequencies realized in flow simulations, to clarify the effect of an acoustic feedback mechanism, at a low Reynolds number.