Elastic Blade-Vortex Interaction Noise

Abstract

An analysis is made of the sound produced when a rectilinear vortex is cut by a spring-restrained, rigid airfoil. The airfoil has rectangular planform of large aspect ratio, and can execute small amplitude translational oscillations in the lift direction under the influence of a linear, elastic restoring force. When the convection Mach number of the vortex is small the sound can be attributed to a dipole source whose strength equals the fluctuating lift, which is dependent on the airfoil motion induced by the vortex. For a fixed airfoil, most of the sound is generated when the vortex is first cut by the leading edge, provided that the vortex core radius R is much smaller than the chord. For an airfoil, the added mass of which exceeds the mass of the airfoil, the influence of airfoil motion on the radiation is governed by the value of ω0R/U, where U is the convection velocity of the vortex relative to the airfoil and ω0 is the resonance frequency of the airfoil. When ω0R/U is small, the airfoil motion tends to suppress the generation of sound at the leading edge; when ω0R/U ⪢ 1, the amplitude of the leading edge radiation is increased and the pressure signature is dominated by oscillations at the resonance frequency ω0.