INFLUENCE OF SEPARATION ON SOUND GENERATED BY VORTEX-STEP INTERACTION

Abstract

An analysis of the sound produced when a line vortex interacts at low Mach number with forward or backward facing steps is made. The radiation is dominated by an aeroacoustic dipole whose strength is equal to the unsteady drag on the step. The drag is determined by the vorticity distribution, and a correct estimate of the sound must therefore include contributions from vorticity in the separated flow induced by the vortex. The separation is modelled by assuming that the shed vorticity rolls up into a concentrated core, fed by a connecting sheet from the edge of the step of negligible circulation. The motion everywhere is irrotational except at the impinging vortex and the separation core, and the trajectory of the core is governed by an emended Brown & Michael equation. For large steps it is found that estimates of the generated sound that neglect separation are typically an order of magnitude too large. The sound levels predicted for small steps with and without separation are of comparable magnitudes, although the respectivephasesare different.Turbulentflow over a step frequently involves separation and large surface pressure fluctuations at reattachment zones. The results of this paper suggest that numerical schemes for determining the noise generated by turbulent flow over a step must take proper account of “forcing” of the separation region by the impinging turbulence and of vorticity production via the no-slip condition.