A comment on the correct boundary conditions for the Cremer impedance
1Department of Mechanics, Linne FLOW Centre, Marcus Wallenberg Laboratory for Sound and Vibration Research, KTH Royal Institute of Technology, 100 44 Stockholm, Sweden matsabom@kth.se, ssack@kth.se.
Abstract:
Mode merging and the creation of exceptional points can be used to create optimum damping in a lined duct, as pointed out by Cremer [Acustica 3, 249-263 (1953)]. The effect of a mean flow has traditionally been analyzed by assuming the Ingard-Myer boundary condition at the wall. For low frequencies, however, the classical boundary condition is a better alternative. This paper shows that this choice removes two problems with the low-frequency solution: the negative real part of the optimum wall impedance and the non-valid solution for the upstream case. Theoretical derivations are complemented by numerical results to support these conclusions.
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