Nonlinear broadband time-domain admittance boundary condition for duct acoustics. Application to perforated plate liners

The behavior of perforated plates at high excitation level is generally modeled by a surface impedance that depends on the rms velocity in the perforations. A time-domain admittance boundary condition (TDABC) is developed to account for this variation using a multipole model. Two formulations are considered, based on the interpolation either of the admittance or of the multipole coefficients from a data set of reference values. These TDABC are implemented in a finite-difference time-domain solver of the linearized Euler equations and are validated by comparison with experimental results on an impedance tube. Application to a two-dimensional lined duct corresponding to the reference geometry of the NASA Grazing Incidence Tube is then performed. The spatial variation of the perforated plate liner impedance is highlighted and it is shown that assuming a uniform impedance can lead to an unacceptable prediction of the liner attenuation. These results are confirmed both for a harmonic or broadband excitation.