Quasi-steady model of the acoustic scattering properties of a T-junction

T-junctions are common elements in flow duct networks. It is shown that for low Strouhal numbers, based on the duct diameter, their acoustic scattering properties can be described using an incompressible quasi-steady model. Models are derived for systems subjected to combinations of grazing and bias mean flow, and are shown to work in both the limiting cases—that is, grazing or bias flow alone—as well as for the joining or dividing flow configurations. The upper Strouhal number for which the quasi-steady models are applicable is limited by flow–acoustic interaction effects, which differ significantly between the different flow configurations. Generally the models are applicable up to Strouhal numbers of approximately 0.1–0.2, which is comparable with previous published models for other configurations such as bends and orifices. This range is sufficient to make the model useful in many important engineering applications.