Effect of turbulent eddy viscosity on the unstable surface mode above an acoustic liner

Lined ducts are used to reduce noise radiation from ducts in turbofan engines. In certain conditions they may sustain hydrodynamic instabilities. A local linear stability analysis of the flow in a 2D lined channel is performed using a numerical integration of the governing equations. Several model equations are used, one of them taking into account turbulent eddy viscosity, and a realistic turbulent mean flow profile is used that vanishes at the wall. The stability analysis results are compared to published experimental results. Both the model and the experiments show the existence of an unstable mode, and the importance of taking into account eddy viscosity in the model is shown. When this is done, quantities such as the growth rate and the velocity eigenfunctions are shown to agree correctly.