The acoustic properties of a liner in the presence of a flow are studied using the linearized Navier-Stokes equations. The method is based on a stabilized finite element formulation of the governing equations using the Galerkin least squares (GLS) stabilization technique. The equations are implemented and solved in COMSOL Multiphysics version 5.4. The solution procedure consists of three steps. First, the steady state grazing background flow across the liners is solved with an SST turbulence model from the CFD Module of COMSOL Multiphysics. The background flow data is then mapped to the acoustic computational mesh. Finally, the perturbations to the steady state flow, including acoustics, are solved with the linearized Navier-Stokes equations formulated in the frequency domain from the Acoustics Module of COMSOL Multiphysics. The linearized Navier-Stokes equations include the propagating pressure waves, vorticity waves, and entropy waves. When pressure waves propagate, energy can be transferred to and from the acoustic component to both the vorticity and entropy components. This results in apparent damping or amplification. The model also includes the effect of waves being damped when propagation through flow turbulence. The equations are solved in the frequency domains which reduces the Kelvin-Helmholtz-like instabilities associated with the reactive terms in the model. This procedure is fast and gives good results when compared to published experimental data of a liner system. The method is further used to analyze the case when acoustics waves are moving downstream and upstream of a grazing flow across the liner. The effective surface impedance of the liner is deduced for the two propagation configurations and the results compared.
