Scattering of sound waves at an area expansion in a cylindrical flow duct

Sound propagation in pipes and ducts with flow, like ventilation ducts and exhaust pipes, is influenced by flow separation and vortex production at sharp edges along the ducts, such as at bends and area expansions. Shear layers form at the separation points, and such layers are unstable to low frequency acoustic disturbances. An analytical model, aiming at physical insight into this interaction, is presented. Results in the plane wave region for the so called scattering matrix for a sudden area expansion with flow in cylindrical pipes are compared with experimental values. Both the magnitude and the phase, in the form of an end correction, is presented. The model is also compared to a 2 dimensional model, in order to evaluate the anticipated increased accuracy of the 3 dimensional modeling. The scattering coefficients are strongly dependent on the flow speed, which is up to a Mach number of 0.5. It is observed that for low frequencies, the interaction is dominated by the dynamics of an unstable shear layer downstream of the edges. For higher frequencies, the wave propagation is mainly affected by convective effects. Differences in properties for the 2D and the 3D cases are also explored.