Revisiting the Cremer impedance

In a classical paper (Acustica 3, 1953) Cremer demonstrated that in a rectangular duct, with locally reacting walls, there exits an impedance (“the Cremer impedance”) that maximizes the propagational damping for the lowest mode. Later (JSV 28, 1973) Tester extended the analysis to include a plug flow and ducts of both circular and rectangular cross-section. One limitation in the work of Tester is that it simplified the analysis of the effect of flow only considering high frequencies or well cut-on modes. This approximation is reasonable for large duct applications, e.g., aero-engines, but not for many other cases of interest. Kabral et al. (Acta Acustica united with Acustica 102, 2016) removed this limitation and investigated the ‘exact’ Cremer impedance for circular ducts including flow effects. As demonstrated in that paper the exact solution exhibits some special properties at low frequencies, e.g., a negative real part of the wall impedance. In this paper the exact Cremer impedance is further analyzed and discussed. Also, the exact solution for rectangular ducts is presented.