On the acoustic radiation of a pitching airfoil

We examine the acoustic far field of a thin elastic airfoil, immersed in low-Mach non-uniform stream flow, and actuated by small-amplitude sinusoidal pitching motion. The near-field fluid-structure interaction problem is analyzed using potential thin-airfoil theory, combined with a discrete vortex model to describe the evolution of airfoil trailing edge wake. The leading order dipole-sound signature of the system is investigated using Powell-Howe acoustic analogy. Compared with a pitching rigid airfoil, the results demonstrate a two-fold effect of structure elasticity on airfoil acoustic field: at actuation frequencies close to the system least stable eigenfrequency, elasticity amplifies airfoil motion amplitude and associated sound levels; however, at frequencies distant from this eigenfrequency, structure elasticity acts to absorb system kinetic energy and reduce acoustic radiation. In the latter case, and with increasing pitching frequency ωp, a rigid-airfoil setup becomes significantly noisier than an elastic airfoil, owing to an ω_p^5/2 increase of its direct motion noise component. Unlike rigid airfoil signature, it is shown that wake sound contribution to elastic airfoil radiation is significant for all ωp. Remarkably, this contribution contains, in addition to the fundamental pitching frequency, its odd multiple harmonics, which result from nonlinear interactions between the airfoil and the wake. The results suggest that structure elasticity may serve as a viable means for design of flapping flight noise control methodologies.