Time-domain impedance boundary conditions for surfaces with subsonic mean flows

The time-domain impedance boundary conditions of Tam and Auriault are extended for impedance boundaries with subsonic mean flows. This extension requires an effective impedance. A model for the effective impedance is proposed, which guarantees the continuity of particle displacement over an infinitely thin shear layer connecting the fluid to the impedance boundary as described by Myers. Together with the effective impedance model, the time domain impedance boundary condition renders the requirement of measuring the effective impedance under flow conditions unnecessary. To demonstrate the feasibility of the extended boundary conditions, a numerical validation using the NASA Grazing Incidence Tube measurements of Jones is carried out. The assumed velocity on the infinitely thin shear layer connecting the flow over the surface to the locally reacting wall is shown to have a strong influence on the performance of the liner. Another important parameter identified is the shape of the mean flow profile, which not only causes convective effects but also may excite possible flow instabilities. It is demonstrated that satisfactory results can be obtained using the extended time domain impedance boundary condition based on the correct effective impedances and mean flow profiles.