Acoustic performance of a concentric circular Helmholtz resonator with an extended neck is investigated theoretically, numerically, and experimentally. The effect of length and shape of, and the perforations on the neck extension is examined on the resonance frequency and the transmission loss. A two-dimensional analytical method is developed for an extended neck with constant cross-sectional area, while a three-dimensional boundary element method is applied for the variable area and perforated extension. Lumped and one-dimensional approaches are also included to illustrate the effect of the higher order modes. For a piston-driven model, predicted resonance frequencies using lumped, one-dimensional, and two-dimensional analytical methods are compared with those from multidimensional boundary element method. Analytical and computational transmission loss predictions for pipe-mounted model are compared to the experimental data obtained from an impedance tube setup. It is shown that the resonance frequency may be controlled by the length, shape, and perforation porosity of the extended neck without changing the cavity volume.

Helmholtz resonator with extended neck.

Helmholtz resonators are often used to reduce noise. They are particularly useful when noise has a narrow frequency band. In this study we aim to broaden its narrow band characteristics by combining many resonators. Serial and parallel arrangements of resonators have been tested to obtain broader impedance mismatch characteristics in the broader band. Theoretical and experimental results explain these characteristics in the absence of mean flow. The serial arrangement mainly increases the peak of TL at the resonance frequency. But the parallel arrangement logarithmically increases the peak of TL and expands the bandwidth. The change of acoustic characteristics is explained by introducing an “equivalent impedance analysis.” This shows that the transmission loss has a maximum value when the distance between resonators is λ∕4 of its wavelength. In this study we propose a novel design method that optimizes the arrangement of resonators while keeping the volume minimized. Various transmission loss characterist...

Silencer design by using array resonators for low-frequency band noise reduction

Aeroacoustic analysis of perforated muffler components

A numerical decoupling analysis of perforated pipe silencer elements

Experimental evaluation of impedance of perforates with grazing flow

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.

Analysis of concentric‐tube resonators having unpartitioned cavities

A simple method is presented for modeling perforated muffler components such as concentric resonators with perforated flow tube, and expansion chambers and reverse flow chambers with perforated inlet and outlet tubes. The theory includes mean flow, but is confined to those configurations having one acoustically long dimension. It is based on a segmentation procedure in which each segment is described by a transmission matrix. The four‐pole parameters of a component are then found from the product of the transmission matrices. The four‐pole parameters for configurations having through flow, cross flow, and reverse flow are presented. Because the product matrices are dimensionally small and because no inversion is needed, computational time is much lower than other methods such as finite element or finite difference. This allows rapid and economical modeling to be performed where iterative solutions are required because of dominating finite amplitude effects, for example.

A method for modeling perforated tube muffler components. I. Theory

This paper is the second of two papers describing a method for modeling muffler components having perforated flow tubes, as for example those found frequently in automotive applications. In the first paper the theoretical model was developed, whereas here the theory is applied to demostrate specifically the utility and potential of the model. The applications are idealized in the sense that effects which occur simultaneously in perforated‐tube mufflers are treated separately. These effects are (1) the nonlinear impedance of the perforation due to finite amplitude sound pressure, and (2) the change in impedance of the perforation with mean flow. The first effect is demonstrated with a straight through resonator, and the second with a cross‐flow chamber. Predicted results for transmission loss in both cases compared quite well with measurements. Crucial to the success of the modeling was a proper description of the perforate impedance. The confidence instilled by the results prompted an inquiry into the nat...

A method for modeling perforated tube muffler components. II. Applications

The one‐dimensional model of the concentric‐tube resonator [J. W. Sullivan and M. J. Crocker, J. Acoustic. Soc. Am. 64, 207–215 (1978)] assumes that (1) the impedance of the perforation is constant along the length of the flow tube and (2) spatial variations of acoustic pressure in the transverse direction of either tube or cavity are small. Some recent measurements on long resonators have indicated that when mean flow is present, net flow in the cavity, although small relative to that in the tube, affects the impedance in a bidirectional manner resulting in violation of assumption (1). Experiments using microphone probes have demonstrated the validity of assumption (2) provided the tube is perforated axisymmetrically. When asymmetric perforations are used, a circumferential cross mode is induced which invalidates the one‐dimensional model.

Some gas flow and acoustic pressure measurements inside a concentric‐tube resonator

General methods of identifying noise sources in vehicles are reviewed: subjective assessment, selective operation, selective wrapping, frequency analysis, change of excitation frequency or speed, acoustic mapping, surface velocity, acoustic intensity, and surface intensity. Two methods for studying truck noise sources are discussed in more detail: near-field measurement, and the coherence technique. Results of these two methods are compared with those of a third technique in which the same truck with different sources wrapped and then sequentially exposed was driven past a microphone using the SAE (Society of Automotive Engineers) J366b test. Also described are two stationary indoor standard tests for measuring vehicle noise: reduced drive-by simulation, and sound power. These tests could be used to supplement (or replace) the SAE J366b drive-by test in some cases. Data obtained using these three tests on the same truck are compared.

Joseph W. Sullivan

Papers

Analysis of concentric‐tube resonators having unpartitioned cavities

A method for modeling perforated tube muffler components. I. Theory

A method for modeling perforated tube muffler components. II. Applications

Some gas flow and acoustic pressure measurements inside a concentric‐tube resonator

Measurement of Truck and Vehicle Noise