Comparison of time-domain impedance boundary conditions for lined duct flows

Two time-domain impedance models developed recently have been examined and tested numerically. One is based on the three-parameter model of Tam and Auriault augmented by a method to evaluate the effective impedance under flow conditions for a harmonic source. The other is Rienstra's extended Helmholtz resonator model. Its time-domain representation is fully based on the idea of Ozyoruk and Long to use a z transformation for an impedance function with periodic frequency response. The implementation of the models in a numerical simulation tool with the dispersion relation preserving scheme is discussed in detail. A filtering approach guarantees the stability of the Myers boundary condition. The results from both of the two models agree notably well with each other. The validation and verification of both models are carried out for the latest NASA impedance tube experiment. The adaptability to realistic inlet configurations is shown using a generic aeroengine geometry with available numerical results. Overall, both models give a similar physical behavior if limitations are carefully considered. The extended Helmholtz resonator is used as termination impedance. A broadband impedance eduction is successfully carried out, resulting in an extended Helmholtz resonator representation for a ceramic tubular liner.