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.

Narrow sidebranch arrays for low frequency duct noise control

“…There are many derivatives proposed as well. Examples include the resonators with extended necks, 9 coupled resonators, [10][11][12] the conical tube resonator, 13 and the Herschel-Quincke tubes, 14 and this list is far from exhaustive. However, these devices can give very good sound reduction performance only at the resonance frequencies or within a relatively narrow frequency range around those frequencies.…”

Plane wave analysis of acoustic wedges using the boundary-condition-transfer algorithm

“…Error associated with the approximation depends upon both, the number of segments and the characteristics of the functions [f] ik . Thus, for any such interval that spans (z, z + L s ), the state vectors at the boundaries are related as [9] fVg z ¼ e ½C fVg zþLs ; ½C ik ¼ À…”

“…As shown in Fig. 1, the tapered part (computational domain N 1 ) of length L 1 will be regarded as a perforated element with two interacting ducts [8] of variable cross-sectional area [9]. A metonymic comparison for this domain may be drawn with the cross-flow contraction element [10].…”

On the length scale and Strouhal numbers for sound transmission across coupled duct cavities at low Mach number

“…Typical examples include the Helmholtz resonators, 8 the expansion chambers/plenum chambers, 9 the Herschel-Quincke tubes 10 and conical tube resonators. 11 One major drawback of this silencer type is that it can only give satisfactory performance at or close to its resonance frequency. Coupled resonators, such as those of Seo and Kim 12 and Howard et al, 13 can give wider working bandwidths.…”