Industrial-scale time domain modelling of acoustic surface treatments for aero-engines using discontinuous Galerkin method

Acoustic surface treatments commonly referred to as liners are broadly employed in the aircraft industry for noise reduction. Depending on the materials used, internal geometry and configuration, these noise-reduction techniques can be effective and behave differently over a wide band of frequencies. Indeed, acoustic characterization of liners via their impedance or admittance is normally done in frequency domain. However, working in the time domain for acoustic liner optimization offers noticeable advantages such as: (i) addressing broadband problems; (ii) allowing the usage of sheared complex mean flow; and (iii) the explicitness of the numerical solver allows efficient parallelization techniques and a straightforward way to account for non-linearity. Therefore, such time dependent solvers need to consider a time domain equivalent of the impedance boundary condition originally defined in frequency domain. In the present work, an implementation of the extended multi-pole broadband impedance boundary condition is presented. This model combines mass-spring-damper model with a series of pairs of complex-conjugated poles for representing the impedance function in frequency domain. Such a representation guarantees to be causal, real, and passive by construction, leading to numerically stable calculations and translates in time domain as a series of efficient recursive convolutions. The impedance model is implemented in the context of a high-order discontinuous Galerkin solver to obtain the solutions of the linearized Euler equations in time domain. The time domain impedance model is first successfully validated and compared with experimental data from the well-known NASA Grazing Incidence Tube (GIT) benchmark and confirmed with an Airbus’s CANNELLE acoustic test bench. Finally, an industrial-size demonstration is performed with an aircraft nacelle configuration under realistic flow conditions. The numerical results obtained are also compared to single-frequency time domain impedance models on the same industrial configuration.