Study on the multi-freedom broadband impedance model for time-domain simulations

The purpose of this paper is to construct a general broadband impedance model which is suited for predicting acoustic propagation problems in time domain. A multi-freedom broadband impedance model for sound propagation over impedance surfaces is proposed and the corresponding time domain impedance boundary condition is presented. Basing on the Extended Helmholtz resonator, the multi-freedom impedance model is constructed through combing with a sum of rational functions with general complex-conjugate pole-residue pairs and it is proved that the impedance model is well-posed. The impedance boundary condition can be implemented into a computational aeroacoustics solver by a recursive convolution technique which results in a fast and computationally efficient algorithm. The two dimensional and three dimensional benchmark problems are selected to validate the accuracy of the current impedance model and time domain simulations. The numerical results are in good agreement with the reference solutions. It is demonstrated that the proposed impedance model can be used to describe the broadband characteristics of acoustic liners. And the corresponding time domain impedance boundary condition is viable and accurate for the prediction of sound propagation over broadband impedance surfaces.