Analysis and design of conical concentric tube resonators

Abstract

The concept of perforate impedance and its exploitation for acoustic attenuation through several elements including concentric tube resonators, is common in practice. Variable cross-sectional area ducts are often used for better performance at lower frequencies (like in horns), whereas concentric tube resonators are often used to provide attenuation at relatively higher frequencies. A combination of the two leads to conical concentric-tube resonators. Using a one-dimensional control volume approach, a mathematical model is presented that accounts for waves in an incompressible mean flow in the center tube, wave propagation in the cavity, and an acoustic coupling between the two due to the impedance of the perforate. The matrizant model results have been validated for self consistency. In the sections dealing with discussion and parametric study, the effect of the moving medium has been neglected so as to bring out clearly the physical effect of the variable area ducts. A few notable effects have been found that include an effective length shorter than the geometric length for an inhomogeneous duct. Some useful features like the absence of pass bands are noticed in the transmission loss spectrum. Finally, results of a parametric study are presented for use by the noise control engineers.