Simulations of the scattering of sound waves at a sudden area expansion

Abstract

The scattering of acoustic plane waves at a sudden area expansion in a flow duct is simulated using the linearized Navier–Stokes equations. The aim is to validate the numerical methodology for the flow duct area expansion, and to investigate the influence of the downstream mean flow on the acoustic scattering properties. A comparison of results from numerical simulations, analytical theory and experiments is presented. It is shown that the results for the acoustic scattering obtained by the different methods gives excellent agreement. For the end correction, the numerical approach is found superior to the analytical model at frequencies where coupling of acoustic and hydrodynamic waves is significant. A study with two additional flow profiles, representing a non-expanding jet with an infinitely thin shear layer, and an immediate expansion, shows that a realistic jet is needed to accurately capture the acoustic–hydrodynamic interaction. A study with several different artificial jet expansions concluded that the acoustic scattering is not significantly dependent on the mean flow profile below the area expansion. The constructed flow profiles give reasonable results although the reflection and transmission coefficients are underestimated, and this deviation seems to be rather independent of frequency for the parameter regime studied. The prediction of the end correction for the constructed mean flow profiles deviates significantly from that for the realistic profile in a Strouhal number regime representing strong coupling between acoustic and hydrodynamic waves. It is concluded that the constructed flow profiles lack the ability to predict the loss of energy to hydrodynamic waves, and that this effect increases with increasing Mach number.