Application of a high-order FEM solver to realistic aeroengine exhaust noise radiation

For many industries the propagation of sound in complex flows is a critical issue. Most Computational Aero Acoustics propagation methods currently in use in industry are based on the full potential theory which cannot properly describe sound propagation through complex sheared flows. When dealing with turbomachinery noise radiated from the engine exhaust, a strong refraction occurs through the jet shear layer. To better represent the physics at hand one can solve instead the Linearised Euler Equations (LEE). However, time-domain LEE models have shortcomings for industrial applications, such as the presence of linear instabilities and the stability of impedance models. Most of these issues can be avoided by solving the LEE in the frequency domain. Nevertheless, this can be very demanding because of the high memory requirements associated with solving large sparse linear systems. For high frequency, the standard finite element method (FEM) is known to suffer from large dispersion errors. Its straightforward application to the LEE, which involve up to five unknowns in 3D, would be computationally costly. To address these issues, an alternative approach based on high-order FEM is presented in this paper. A discretised axisymmetric form of the LEE is described in conjunction with Perfectly Matched Layers. In addition, a numerical stabilisation scheme of type Galerkin/Least-Squares is included in the numerical model. The proposed method is applied to the propagation of duct modes inside a turbofan engine exhaust, with complex geometry and non-uniform mean flow. The sound propagation and radiation are accurately described, as well as the interaction between the acoustic waves and the hydrodynamic field resulting in the vorticity shedding from the duct lips