Adaptation of the experimental "Two microphone transfer function" method to compute the radiation impedance of ducts from numerical simulations

An adaptation is made of the experimental "two microphone transfer function" procedure so as to compute the radiation impedance of ducts using numerical methods. This transfer function approach, which is standardized in the ISO-10534-2, was originally devised to measure the impedance of material samples. When applied in the numerical context, it allows computing the radiation impedance of ducts without having to solve the wave equation in mixed form, thus avoiding dealing with the acoustic velocity. A wideband pulse is imposed at the tube entrance, and the radiation impedance is computed from the transfer function between two virtual microphones near the tube exit. However, the computational time of such an approach can be notorious given that the duct first eigenmode becomes hard to dissipate. This problem can be mitigated by appropriate imposition of extra damping at the duct walls of the numerical model. From an experimental point of view, dealing with damped walls usually involves a calibration process so as to quantify the waveguide attenuation. In contrast, in numerical simulations the latter can be analytically accounted for. Some benchmark cases are presented, and computed radiation impedances are compared to theoretical values. A time domain finite element method has been used in all simulations to solve the wave equation, together with a perfectly matched layer to account for free wave radiation towards infinity.