Effects of Non-Linear Eddy-Airfoil Interaction on the Acoustic Radiation of a Thin Wing

Abstract

We study the combined effect of boundary animation (small-amplitude heaving) and incoming flow unsteadiness (incident vorticity) on the vibroacoustic signature of a thin rigid airfoil in low-Mach high-Reynolds number flow. The nonlinear dynamical problem for the vortex trajectory is studied using potential flow theory. The dynamical description then serves as an effective source term to evaluate the far-field sound using Powell-Howe’s analogy. The results identify the fluid-airfoil system as a dipole-type source, and demonstrate the significance of non-linear eddy-airfoil interaction on the acoustic radiation. At low heaving frequencies (ωa/U < 1, where ω denotes the heaving frequency, 2a the airfoil chord, and U the mean stream speed), the effect of heaving is minor, and the acoustic field can be approximated by neglecting airfoil motion. However, at ωa/U > 1, heaving becomes dominant, radiating sound through an “airfoil motion” dipole (oriented along the direction of heaving) and airfoil-induced oscillations in the vortex trajectory. In contrast with the periodic “airfoil motion” signal, the non-periodic incident vortex sound has a component along the airfoil chord, which becomes significant when the vortex passes close to the airfoil. The work is suggested as a preliminary tool to examine the acoustic radiation during flapping flight at unsteady flow conditions.