3. A WEM-based methodology for computing the propagation in a lined flow duct
In order to compute the linear acoustic propagation in a lined duct, it is necessary to decide how the lined wall or impedance boundary is to be introduced into the computation and what assumption can be made about the background flow. In the absence of a mean flow, the impedance relates the Fourier transformed acoustic pressure and normal acoustic particle velocity at the surface. This is also the case when mean flow is present where the velocity goes to zero at the wall (no-slip condition). However, in this case, the effect of the viscous boundary layer over the liner must be included in the propagation. This may be done by solving the linearised Navier–Stokes equations. The linearised Navier–Stokes equations may also support vorticity and entropy waves but these are not of primary interest here. A pragmatic alternative frequently employed has been to include the boundary layer in the impedance model and to assume that the flow is potential [2]. This is computational much lighter and is attractive particularly for inverse searches of liner impedance values from experimental data or large-scale design optimisations