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.
Highlights
The Cremer impedance is a well known solution for optimizing propagational damping of a mode in a duct.1–3 It is based on the creation of an exceptional point where two modes merge
The main result is that the classical B.C. (“classical solution”) will remove the negative real part of the Cremer impedance at low Helmholtz number (He)
The classical solution unlike the solution with the IM B.C. remains valid in the upstream case, i.e., it preserves the merging of modes 0 and 1 for all cases
Summary
The Cremer impedance is a well known solution for optimizing propagational damping of a mode in a duct. It is based on the creation of an exceptional point where two modes merge. The solution is derived based on the Ingard–Myer boundary condition (IM B.C.), i.e., continuity of pressure and normal displacement. This leads to the occurrence of a negative real part of the impedance in the low-frequency limit.. The proposed models and the experimental data affirm that at sufficiently low frequencies, the classical boundary condition (classical B.C.), i.e., continuity of pressure and normal velocity, should be used. This assumption will be used here to revisit the low-frequency behavior of the Cremer impedance
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