Helmholtz-Like Resonator Self-Sustained Oscillations, Part 1: Acoustical Measurements and Analytical Models

Abstract

We consider self-sustained oscillations of the grazing e ow along the neck of a Helmholtz-like resonator. Such oscillations are driven by a coupling between the intrinsic instability of the shear layer, separating the main e ow from the cavity, and the resonant acoustical e eld in the cavity. Depending on details of the shape of the neck, acoustical velocities through the neck of the resonator of the same order of magnitude as the main e ow velocity can be reached. For particular neck geometries, whistling is suppressed. A nonlinear model, which assumes that the vorticity of the shear layer is concentrated in line vortices traveling at constant velocity, provides insight into the phenomenon. For rounded edges, the model predicts the pulsation amplitude of the e rst hydrodynamic mode surprisingly well but severely overestimates the amplitude of higher hydrodynamic modes. For sharp edges, a modie cation of the original model is proposed, which yields a reasonable prediction of the pulsation amplitude (within a factor of two ) of the e rst hydrodynamic mode and does not overestimate higher hydrodynamic modes.