Numerical Computation of Sound Propagation in Lined Ducts by Time-Domain Impedance Boundary Conditions

Abstract

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