Numerical computation of sound propagation in lined ducts by time-domain impedance boundary conditions

The single-frequency and broadband time-domain impedance boundary conditions by Tam &: Auriault assume a zero mean flow on the impedance wall. To be suitable for arbitrary mean flow profiles, mean flow convection effects are incorporated into the two boundary conditions. The modification requires the impedance to be measured under mean flow conditions or to be simulated including mean flow effects. It is proved that both the single-frequency and broadband effective impedance time-domain boundary conditions lead to well-posed initial boundary value problems. The NASA flow impedance tube configuration is selected for benchmarking the modified boundary conditions. The effective plane-wave impedance model is utilized to estimate the impedances in the presence of mean flows. Uniform and sheared mean flow profiles are assumed to check the validity, accuracy and stability of the modified time-domain impedance boundary conditions. It is shown that numerical computations can be carried out for both the slip and sheared mean flow profiles without stability problems, and that satisfactory results can be obtained providing that the impedance and mean flow profiles are estimated or measured correctly.