Absorption of sound near abrupt area expansions

Sound incident onto an abrupt area expansion in a channel is investigated b oth numerically and analytically. In the presence of a mean flow, the incid ent sound leads to unsteady vortex shedding from the lip of the expansion, thereby converting acoustic into vortical energy. We use an acoustic analog y and Green's functions to determine the sound reflected and transmitted ac ross the area change. We compare predictions obtained from three different Green's functions with source terms derived either using a simple analytica l model or from a numerical calculation. The compact Green's function, with zero normal derivative on the duct walls, gives the best results for a low -Mach-number flow. This Green's function contains a singularity at the lip of the expansion (and hence acoustic sources near the lip have the greatest effect). This means that our estimate of the overall vorticity held can be relatively crude, when using the compact Green's function, provided it is accurate near the lip. Therefore, although predictions for the radiated sou nd field made using all three Green's functions are formally correct, the s olution made using the compact Green's function is less susceptible to erro rs in the source terms and gives more accurate results. In addition, we fin d that there is a Strouhal number at which sound absorption is maximized an d that this absorption can be enhanced by multiple reflections from the duc t ends. Our predictions are compared with an experiment.