Acoustically Induced Periodic Vortex Shedding At Sharp Edged Open Channel Ends: Simple Vortex Models

Abstract

Simple flow models proposed by Howe [1975 Journal of Fluid Mechanics 71 , 625-673] and Disselhorst and van Wijngaarden [1980 Journal of Fluid Mechanics 99, 293-319] are used to describe the periodic vortex shedding induced at a two-dimensional channel end with infinitely thin, sharp edges by a harmonically varying acoustic flow with zero mean flow. For low Strouhal numbers a quasi-stationary theory can be used, while for high Strouhal numbers the problem can be simplified to that of vortex shedding at a semi-infinite plate. Our experiments show fair agreement with both limiting theories. A single vortex theory will be shown to be useful in the high Strouhal number limit, although a correction for the pressure force acting at a connecting line between the edge and the vortex is necessary when the vortex is increasing in strength. A correction in terms of a Magnus force applied to the single vortex does, however, influence the acoustic energy balance. A correction to the theoretical formula derived for a continuous distribution of vorticity due to the action of external forces is proposed. For intermediate Strouhal numbers, both the quasi-stationary and single vortex models fail to describe the flow at the channel end accurately. A single panel method proposed in this paper is a compromise between the single vortex description and the much more accurate but time-consuming panel method. The vortex shedding process described by the single panel method is compared with flow visualization experiments performed by Diselhorst and van Wijngaarden. Fair agreement between the single panel theory and experiments is obtained.