Conference_programme: 19.1 - Duct Acoustics

Lecture: The Cremer impedance at low frequencies

Author(s): Zhang Zhe , Åbom Mats

Summary:
The problem of optimal damping of a sound wave in a duct with locally reacting walls (“a lining”) was first treated by Cremer (Acustica 3(5), 1953). The result (“the Cremer impedance”) was later extended by Tester (JSV 28(2), 1973) to any type of cross-section and mode order including the effect of a uniform (“plug”) mean flow. One limitation in Tester’s work is that it simplified the analysis on the effect of flow by only considering the asymptotic or high frequency case with ‘well cut-on’ modes. This approximation is reasonable for large duct applications, e.g., aero-engines, but not for many other cases of interest such as vehicle exhaust systems. Kabral et al. (DOI: 10.3813/AAA.918999) recently removed this limitation and investigated the Cremer impedance at low frequencies, revealing an appreciable difference compared to Tester´s asymptotic solution. In addition, the exact solution is found to exhibit some special properties at low frequencies, e.g., a negative resistance. One can question if this negative resistance is physically correct or an artefact of the assumption of a plug flow profile and the use of the so-called Ingard-Myer boundary condition. To investigate this the Cremer solution is here extended to the case with a more general and realistic flow profile, using a modified version of the Ingard-Myer condition suggested by Brambley (DOI: 10.2514/1.J050723).

Corresponding author

Name: Prof Mats Åbom

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Country: Sweden