Sound in ducts - Optimum damping and the Cremer impedance

Abstract: Mode merging and the formation of exceptional points can be used to achieve optimum damping in a lined duct, as originally demonstrated by Cremer (1953). The influence of mean flow has traditionally been analysed using the Ingard–Myer boundary condition at the wall. However, at low frequencies, the classical (no-flow) boundary condition provides a more accurate alternative. This choice resolves two key issues in low-frequency predictions: the occurrence of a negative real part in the Cremer impedance and the emergence of non-physical solutions for upstream propagation. The new modified version of Cremer's solution has been applied to the design of a multi-chamber micro-perforated panel (MPP) absorber, optimized for broadband low-frequency sound attenuation under grazing flow conditions. The total acoustic impedance of these complex, multi-degree-of-freedom (MDOF) absorbers is modelled and optimized using a graph-theory-based two-point impedance method. Liner samples, each 200 mm in length, were fabricated via 3D printing and tested in a grazing flow facility.