Analysis of concentric-tube resonators having unpartitioned cavities

Abstract

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.

Muffler modeling by transfer matrix method and experimental verification

“…When using perforate tube elements, the transfer matrices depend on the porosity (number of perforations per unit length of pipe axis) and particularly on the normalized partition impedance of the perforate. This impedance can be evaluated by means of empirical expressions given for different flow conditions, such as stationary medium (Sullivan and Crocker, 1978), perforates with cross-flow (Sullivan, 1979), and perforates with grazing flow (Rao and Munjal, 1986).…”

“…In the late fifties and sixties, equivalent electrical circuits based on the four-pole transmission matrices were widely used to predict the muffler performance through the use of analogue computers (Igarashi and Toyama, 1958;Davies, 1964). In the seventies and eighties Alfredson (1970), Munjal (1970 and1987), Thawani and Noreen (1988), Sullivan and Crocker (1978) and Jayaraman and Yam (1981) presented approaches to the partial and full modeling of mufflers. In addition, Craggs (1989) reported a technique that combines the use of transfer matrix approach and finite elements in the study of duct acoustics.…”

Acoustic Performance of Exhaust Muffler Based Genetic Algorithms and Artificial Neural Network

“…In the past decade, intent on increasing acoustical performance, the assessment of a new acoustical element was introduced and discussed by Sullivan and Crocker in 1978 [1]. Based on the couple equations derived by Sullivan and Crocker, a series of theories and numerical techniques in decoupling the acoustical problems were proposed [2]- [5].The shape optimization of a one-chamber muffler equipped with a perforated tube and plug/non-plug tubes has been discussed with neural network.…”

Optimization Design of Hybrid Mufflers on Broadband Frequencies Using the Genetic Algorithm

“…In 1978, an assessment of a perforated acoustical element used to depress low frequency sound energy was introduced and discussed by Sullivan, Crocker (1978). On the basis of coupled differential equations, a series of theoretical and numerical techniques in decoupling the acoustical problems have been proposed (Sullivan, 1979a(Sullivan, , 1979bThawani, Jayaraman, 1983;Rao, Munjal, 1984;Jayaraman, Yam, 1981;Munjal et al, 1987).…”