Self-excitation of an acoustic resonance by vortex shedding

The vortex excited β mode has been studied by using a low speed wind tunnel with two loudspeakers attached by horns to opposite sides of the test section. The independent generation of the resonance enabled the separation of the effect of sound on the vortex shedding from the effect of vortex shedding on the resonance. By using the applied sound field it was possible to lock the vortex shedding from a bluff flat plate and shift the Strouhal number by ±20%. The shift in Strouhal number caused the vortex shedding pressure on the flat plate surface near the trailing edge to vary in magnitude and phase with the reference acoustic field. At constant Strouhal number, the magnitude of the vector shedding was shown to depend upon the acoustic magnitude and trailing edge geometry. The phase did not change with acoustic mode magnitude, but the phase at any selected Strouhal number increased as the geometry was varied from convex to concave. Flow visualization pictures of the wake formation region are presented which show this phase variation and also the distinct large and fine scale wake structure at these high Reynolds numbers. A linear feedback model is developed which accounts for many of the properties of this self-exciting system. This is an extension of the work of Cumpsty and Whitehead whose theory for the excitation of the acoustic mode by the vortex shedding is shown to describe the forward portion of the loop. The feedback portion of the loop is constructed from the experimental results. The different frequency and velocity behavior during self-excitation, as reported in the literature, is explained by this theory and is traced to the difference in trailing edge geometry. The region of significant in-phase unsteady vortex shedding pressure extended about one wake perturbation wavelength upstream from the trailing edge. The unsteady pressure distribution in this region increased almost linearly from zero to a maximum at the trailing edge, indicating that the unsteady Kutta condition, stated as zero trailing edge loading, is not satisfied for vortex shedding.