Analysis of concentric‐tube resonators having unpartitioned cavities

In muffler design, concentric‐tube resonators are often used to provide high‐frequency attentuation. These resonators are constructed by shaping a rigid shell around a length of perforated tube, forming an unpartitioned cavity. Often the entire length of tube is perforated. Because of the length of the assembly, it is not possible to use the simple Helmholtz resonator theory to predict the attentuation. Beginning with a one‐dimensional control volume, a mathematical model was derived which accounted for mean flow in the tube and for the wave motion in the cavity and the coupling between cavity and tube via the impedance boundary of the perforate. For impedance in the linear regime, a closed‐form solution for the resonator transmission loss was obtained. With this restriction and for the case of zero mean flow, excellent agreement was obtained with experimental results. Limited parametric studies suggest that the performance of this type resonator is quite sensitive to the porosity of the perforate, and that unusually large bandwidths of attenuation may be obtained for select geometries at zero or near‐zero mean flow conditions. As mean flow is increased, however, the model suggest that such large bandwidths may not be attainable in practice.