Sound generated by convected turbulence past an elastic airfoil

We study the motion and sound generated when a line vortex is convected in a uniform low-Mach flow parallel to a thin elastic plate. The linearized plate motion is analyzed under conditions where the unforced plate (in absence of the line vortex) is stationary. The vortex passage above the plate excites a resonance mode of motion, where the airfoil oscillates at its least stable eigenmode. The sources of sound in the acoustic problem include the plate velocity and fluid vorticity. It is shown that the release of trailing-edge vortices, resulting from the satisfaction of the Kutta condition, has two opposite effects on sound radiation: while trailing-edge vortices act to reduce the pressure fluctuations occurring owing to the direct interaction of the line vortex with the unperturbed plate, they extend and amplify the acoustic signal produced by the motion of the airfoil. The plate motion radiates higher sound levels as the system approaches its critical conditions for instability, where the effect of resonance becomes more pronounced. It is argued that the present theory describes the essential mechanism by which sound is generated as a turbulent eddy is convected in a mean flow past a thin elastic airfoil.