Sources of flow noise due to time‐varying tip relief

Abstract

This paper begins with a brief review of the conventional cause of shed vorticity in two‐dimensional unsteady lifting flows around airfoils. It then poses the following three‐dimensional theoretical problem in support of experimental work recently conducted at Penn State/ARL: Take a wing tip of arbitrary three‐dimensional shape and place a wall near it such that its plane is normal to that of flight. Let the wall be sinusoidally corrugated in the direction of the flow and be convected by it, so that an observer stationed on the wing’s tip experiences time‐varying influences determined by the wall’s passing serpentine pattern. Our presentation will describe a linearizing perturbation analysis whereby the ratio of the wall’s sinusoidal amplitude to its wavelength becomes a small parameter. The zeroth‐order problem becomes then one of steady three‐dimensional aerodynamics barring the presence of external fluctuations. The first‐order problem is fundamentally unsteady and driven, as usual, by the zeroth‐order one. An unconventional source of flow noise emerges: the ultimately unacceptable axial changes in the strength of trailing vortices, as brought about by their irregular images behind the corrugated wall, lead to new neutralizing shed vortices and harmonic lift.