K.S. Peat

A numerical decoupling analysis of perforated pipe silencer elements

Coupled differential equations describing one-dimensional acoustic wave propagation in the perforated pipes and cavities of straight-through and cross-flow silencer elements are derived and then decoupled numerically. The deficiencies of previous analytical decoupling techniques are investigated and found to be of significant effect in terms of the transmission loss spectra as the Mach number increases toward the upper limit encountered in vehicle silencers, particularly for low porosity perforates. The numerical formulation presented here exhibits none of the numerical instabilities of a previous scheme. The numerical decoupling technique can accommodate in some measure axial variation of the flow and perforate impedance, such as occurs in cross-flow silencer elements, although the modelling in this case is not exact.

The transfer matrix of a uniform duct with a linear temperature gradient

Self-consistent expressions for the four-pole parameters of a uniform duct with a linear temperature gradient have been derived for the general case of a superimposed mean flow. These expressions, and their simplified derivatives for the case of no mean flow, differ from those in earlier literature in first order terms of the temperature gradient. Experimental measurements validate the approximations made and indicate little practical benefit in detailed modelling of temperature variations.

The acoustical impedance at discontinuities of ducts in the presence of a mean flow

Abstract At low frequencies only plane waves can continuously propagate along a uniform duct, but at a discontinuity in the duct cross-section higher order, evanescent acoustic waves are produced. The accuracy of a plane-wave analysis can be increased by the introduction of an equivalent impedance to account for these non-planar waves. In this paper, previous work in the field is extended to consider both the effects of a superimposed mean flow along the duct and the effects of high frequencies up to the plane-wave cut-off limit. It is shown that mean flow effects are negligible but that the variation of impedance with frequency is important.

Evaluation of Four-Pole Parameters for Ducts with Flow by the Finite Element Method

Abstract A finite element formulation of the equations of acoustic wave propagation in the presence of a mean flow of low Mach number has been obtained. The resulting equation system has been solved with two different sets of boundary conditions in order to obtain the four-pole parameters of a specified section of duct. The results have been compared with those of existing one-dimensional models of the flow. The finite element formulation has been developed as it enables one to determine accurately the wave propagation in a duct of any given geometry. The work is intended to aid in the prediction of the insertion loss of intake silencers on internal combustion engines.

The acoustic impedance of a circular orifice in grazing mean flow: Comparison with theory

It is well known that the presence of a grazing mean flow affects the acoustic impedance of an aperture, but the detailed nature and understanding of the influence is still unknown. In this paper, results from a recent theoretical analysis of the problem are compared with a new set of experimental results. The purpose is twofold. First, the experimental results are used to validate the theory. It is found that the theory predicts the resistance quite well, but not the reactance. Second, the theory is used to try and give some physical understanding to the experimental results. In particular, some scaling laws are confirmed, and it is also shown that measured negative resistance values are to be expected. They are not erroneous, as previously thought. Former sets of experimental data for this problem are notable for the amount of variation that they display. Thus, both the theory and the new experimental results are also compared with those earlier detailed results that most closely conform to the conditions assumed here, namely fully developed turbulent pipe flow of low Mach number past circular orifices. The main field of application is in flow ducts, in particular, flow through perforated tubes in exhaust mufflers.

The acoustical impedance at the junction of an extended inlet or outlet duct

Abstract At low frequencies only plane waves can continuously propagate along a uniform duct, but at a discontinuity in the duct cross-section higher order, evanescent acoustic waves are produced. The accuracy of a plane-wave analysis can be increased by the introduction of an equivalent impedance to account for these non-planar waves. Previous work has concentrated upon the equivalent impedance at sudden expansions or contractions of the duct cross-section. In this paper, equivalent impedance formulae are developed for the junctions of extended inlet and extended outlet duct systems. Such formulae are of practical importance in the accurate low-frequency analysis of reactive silencer systems.

ON THE CAUSES OF NEGATIVE SOURCE IMPEDANCE IN THE MEASUREMENT OF INTAKE AND EXHAUST NOISE SOURCES

Abstract In order to evaluate the acoustic field within a duct system some knowledge is required about the acoustic source, which is characterized by frequency-dependent values of both strength and impedance. However, in using various experimental techniques for various types of source to obtain these values, negative real parts of the source impedance have been measured. Negative source resistance is physically implausible. In some instances, one measurement method gives positive values of source resistance where another gives negative values. This paper reviews the possible causes of the problem, with reference to experimental and theoretical results, in an attempt to clarify the issue. Various possible origins of a negative source resistance have been investigated. It is noted that, for the time being, the violation of the assumption of a time-invariant source and the defect in the inherent algorithm of the load method are the most probable origins of the negative source resistance.

Approximations for the scattered field potential from higher mode transmission in rectangular apertures

This paper considers the wave fields that result when a plane wave impinges at an arbitrary angle on a rectangular aperture in a rigid, thick wall. A nondimensional form of a prior Fourier transform solution of this problem is derived, from which it is more easy to appreciate the relationship between the physical attributes of the aperture and incoming wave and the resultant acoustic fields. The scattered field from the aperture is examined in detail, in particular the modal contributions to the driving function for the amplitude of the velocity potential. Although the full scattered field contains both modal sum and modal coupling effects, it is shown that neglect of the modal coupling effects introduces minimal error to the solution in certain situations. An approximate analytical solution to the uncoupled analysis is then developed, which is accurate provided that the aperture is acoustically large, such that there are several cut-on modes within the aperture. The full nature of the scattered field can...

Higher mode sound transmission from a point source through a rectangular aperture

This paper considers the higher-order scattered and transmitted wave fields that result when an acoustic wave from a point source impinges at an arbitrary angle on a rectangular aperture in a rigid, thick wall. In this analysis, it is assumed that free field conditions exist on both sides of the aperture. Although the full scattered and transmitted pressure fields contain both modal sum and modal coupling effects, the modal coupling effects of the higher-order modes are ignored such that an approximate analytical solution to the uncoupled analysis can be utilized. Experiments have been undertaken to measure the sound pressure levels in the transmitted field that result when sound from a point source impinges on the opposite side of a rectangular aperture. Measurements were made with the source located at the required position to drive a particular in-aperture higher-order mode. The source was also located at positions that did not directly excite any in-aperture higher-order mode at a cut-on frequency. These results indicate that the approximate analysis developed here gives accurate solutions whether or not any mode of the aperture is driven at cut-on. Thus, the method can be used for any relative location of a source from a rectangular aperture of any dimensions.

Hausdorff Moments Method of Acoustical Imaging

The moments method has been shown to give accurate reconstructions in different types of model problems when exact but incomplete boundary spectral data is used. The majority of the error in reconstruction does not occur in the nonlinear step for the creation of the moments, but in the second step of the classical Hausdorff moments problem, which is linear and ill-posed. A Fourier technique for this problem is particularly prone to error when the function to be reconstructed is non-smooth. Knowledge of the value of the function on the boundary can be used to reduce these errors substantially. A Legendre technique is less susceptible to error due to non-smoothness of the function, such that it can be used to reconstruct a uniform field with isolated lumps in it, for which the Fourier technique is totally inappropriate. However the Legendre technique is more susceptible to error in the data than is the Fourier technique. The way forward would appear to be the development of some form of regularization procedure for error-prone data such that the Legendre technique remains accurate in such cases.