A Study of the Viscous Effects over an Acoustic Liner using the Linearised Navier-Stokes equations in the Frequency Domain

Abstract: New noise regulations for civil aviation restrict the sound level that engines can emit to a great extent. Acoustic liners are the most widespread solution in order to damp sound in aircraft engines. Usually the Linearised Euler equations (LEE) are used to calculate the sound propagation through the engine. In addition, the viscous effects close to the near wall region, where the acoustic liner is located, are considered by the Myers impedance boundary condition. However, this boundary condition has been proved to be ill-posed and to not fully capture the viscous acoustics. Hence, a different approach is taken by using the full Linearised Navier-Stokes equations. In order to assess the validity of this method a computational model is created to reproduce the experimental work done by Aurégan et.al. where the scattering matrix of a two source model is measured and time domain simulations are done using LEE and Myers boundary condition in order to compare them. An improvement, with respect to the inviscid time domain simulations, is achieved when the upstream educed impedance values are used. Therefore, the Myers impedance boundary condition can still be used in numerical impedance eduction codes and the obtained values render good results if a viscous solution is adopted. Also, considering a viscous solution implies that both the hydrodynamic and the acoustic boundary layer need to be resolved. Nonetheless, the latter is very small compared to the hydrodynamic one and its inclusion will result in a very fine mesh that might increase the computational time. Thus, a second study is done in order to assess the importance of the acoustic boundary layer in these calculations, and to determine if some assumption can be applied in order to reduce the computational effort. To that purpose, all the simulations are done in the frequency domain since it is a lighter computational method than the time domain. Results of this second test case show that the resolution of the acoustic boundary layer is not a crucial factor in order to achieve an accurate solution.