Optimum sound attenuation in flow ducts based on the "exact" Cremer impedance

The Cremer impedance (Acustica 3, 1953) [1] is the locally reacting boundary condition that maximizes the attenuation of a certain mode in a uniform wave guide taken as the lowest order mode or "plane" wave. This paper presents the analysis of the "exact" Cremer impedance model, i.e., the high frequency asymptotic results proposed by Tester for uniform mean flow (JSV 28(2), 1973) [2] are extended to lower frequencies. It is shown that significantly larger attenuation per unit length can be obtained using the exact instead of the asymptotic solution. However, for sufficiently low frequencies the "exact" Cremer solution and optimum attenuation is requiring a wall impedance with a negative real part, i.e. an active boundary. In addition, the effect of a finite length on the resulting attenuation is studied using a finite element method for solving the convected wave equation. Finally, it is demonstrated how a silencer can be built that realize the optimum Cremer impedance at a given frequency by using a micro-perforated panel and locally reacting cavities. The performance of the optimized silencer is determined experimentally and the results are compared to the prediction of the finite element model.