D. W. Herrin

A New Look at the High Frequency Boundary Element and Rayleigh Integral Approximations

This paper revisits the popular Rayleigh integral approximation, and also considers a second approximation, the high frequency boundary element method which is similar to the Rayleigh integral. Both methods are approximations to the boundary integral equation, and can solve problems in a fraction of the time required by the conventional boundary element method. The development of both methods from the Helmholtz integral equation is demonstrated and the differences between the two methods are delineated. Both methods were compared on practical examples including a running engine, gearbox, and construction cab. It was concluded that both methods can reliably predict the sound power for many problems but are inaccurate for sound pressure computations.

SELECTING MEASUREMENT LOCATIONS TO MINIMIZE RECONSTRUCTION ERROR USING THE INVERSE BOUNDARY ELEMENT METHOD

This paper details an approach to select measurement point locations for the inverse boundary element method. An accurate reconstruction of the vibration requires a well conditioned acoustic transfer matrix, which depends on measurement point selection. Matrix techniques can be used to regularize the solution though they often lead to poor reconstruction rank. A technique to determine the number of measurement points required, and their placement, prior to measurement has been developed using three criteria: uniqueness, completeness, and measurement point density. With this technique, the reconstruction error and the number of measurements can be minimized.

Prediction of sound pressure in the far field using the inverse boundary element method

The inverse boundary element method (BEM) is a numerical procedure whereby sound pressure measurements in the near field are used to predict the vibration on a vibrating surface. After the vibration on the surface (or particle velocity in the case of an opening) is determined, the sound pressure in the far field can be predicted using a forward BEM analysis. This paper will examine the applicability of the inverse BEM to predicting sound pressure in the far field on two examples; an engine cover and generator set. The results indicate that the inverse BEM can be used to accurately predict far field sound pressure. Additionally, it is demonstrated that a partial or patch BEM model of a surface can be utilized successfully in some instances as a means of reducing the computation time.

Practical Considerations in Reconstructing the Surface Vibration Using Inverse Numerical Acoustics

This paper explores the use of inverse numerical acoustics to reconstruct the surface vibration of a noise source. Inverse numerical acoustics is mainly used for source identification. This approach uses the measured sound pressure at a set of field points and the Helmholtz integral equation to reconstruct the normal surface velocity. The number of sound pressure measurements is considerably less than the number of surface vibration nodes. A brief guideline on choosing the number and location of the field points to provide an acceptable reproduction of the surface vibration is presented. The effect of adding a few measured velocities to improve the accuracy will also be discussed. Other practical considerations such as the shape of the field point mesh and effect of experimental errors on reconstruction accuracy will be presented. Examples will include a diesel engine and a transmission housing.

BEM Modeling of Mufflers with Diesel Particulate Filters and Catalytic Converters

The boundary element method (BEM) is used to evaluate the transmission loss (TL) of mufflers with a catalytic converter (CC) or diesel particulate filter (DPF). The CC or DPF may be modeled as a block of bulk-reacting material, or by the �element-to-element four-pole connection� in the BEM. The four-pole parameters of the block can be measured by the two-source method. To avoid cutting a small fragile sample from the brittle filter, we perform the measurement on the entire filter block connected to a pair of transition cones. A 1-D matrix inverse procedure is used to extract the four-pole parameters of the filter itself. However, the large diameter of the cross section may not justify the 1-D theory throughout the entire setup. To alleviate this restriction, we implement a 3-D BEM optimization to fine-tune the extracted four-pole parameters. This involves using the BEM to compute the impedance matrices of the substructures, and then adopting a MATLAB optimization routine to find the optimal parameters that produce the same TL as the measured TL. In our test cases with different configurations, this procedure gives better predictions than using the 1-D matrix inverse alone.

Measuring Bulk Properties of Sound-Absorbing Materials using the Two-Source Method

The two-source method was used to measure the bulk properties (complex characteristic impedance and complex wavenumber) of sound -absorbing materials, and results were compared to those obtained with the more commonly used two-cavity method. The results indicated that the two-source method is superior to the two-cavity method for materials having low absorption. Several applications using bulk properties are then presented. These include: (1) predicting the absorptive properties of an arbitrary thickness absorbing material or (2) layered material and (3) using bulk properties for a multi -domain boundary element analysis.

The Proper Use of Plane Wave Models for Muffler Design

In many industries, muffler and silencer design is primarily accomplished via trial and error . Prototypes are developed and tested, or numerical simulation (finite or boundary element analysis) is used to assess the performance. While these approaches reliably determine the transmission loss, designers often do not understand why their changes improve or degrade the muffler performance. Analyses are time consuming and models cannot be changed without some effort. The intent of the current work is to demonstrate how plane wave muffler models can be used in industry . It is first demonstrated that plane wave models can reliably determine the transmission loss for complicated mufflers below the cutof f frequency. Some tips for developing dependable plane wave models are summarized. Moreover, it is shown that plane wave models used correctly help designers develop intuition and a better understanding of the effect of their design changes.

Investigation of the Acoustic Performance of After Treatment Devices

There is a strong competition among automotive manufacturers to reduce the radiated noise levels. One important source is the engine exhaust where the main noise control strategy is by using efficient mufflers. Stricter vehicle noise regulations combined with various exhaust gas cleaning devices, removing space for traditional mufflers, are also creating new challenges. Thus, it is crucial to have efficient models and tools to design vehicle exhaust systems. In addition the need to reduce CO2 emissions puts requirements on the losses and pressure drop in exhaust systems. In this thesis a number of problems relevant for the design of modern exhaust systems for vehicles are addressed. First the modelling of perforated mufflers is investigated. Fifteen different configurations were modeled and compared to measurements using 1D models. The limitations of using 1D models due to 3D or non-plane wave effects are investigated. It is found that for all the cases investigated the 1D model is valid at least up to half the plane wave region. But with flow present, i.e., as in the real application the 3D effects are much less important and then normally a 1D model works well. Another interesting area that is investigated is the acoustic performance of after treatment devices. Diesel engines produce harmful exhaust emissions and high exhaust noise levels. One way of mitigating both exhaust emissions and noise is via the use of after treatment devices such as Catalytic Converters (CC), Selective Catalytic Reducers (SCR), Diesel Oxidation Catalysts (DOC), and Diesel Particulate Filters (DPF). The objective of this investigation is to characterize and simulate the acoustic performance of different types of filters so that maximum benefit can be achieved. A number of after treatment device configurations for trucks were selected and investigated.Finally, addressing the muffler design constraints, i.e., concerning space and pressure drop, a muffler optimization problem is formulated achieving the optimum muffler design through calculating the acoustic properties using an optimization technique. A shape optimization approach is presented for different muffler configurations, and the acoustic results are compared against optimum designs from the literature obtained using different optimization methods as well as design targets.

Accurate Measurement of Small Absorption Coefficients

In this paper procedures for estimating the sound absorption coefficient when the specimen has inherently low absorption are discussed. Examples of this include the measurement of the absorption coefficient of pavements, closed cell foams and other barrier materials whose absorption coefficient is nevertheless required, and the measurement of sound absorption of muffler components such as perforates. The focus of the paper is on (1) obtaining an accurate phase correction and (2) proper correction for tube attenuation when using impedance tube methods. For the latter it is shown that the equations for tube attenuation correction in the standards underestimate the actual tube attenuation, leading to an overestimate of the measured absorption coefficient. This error could be critical, for example, when one is attempting to qualify a facility for the measurement of pass-by noise. In this paper we propose a remedy – to measure the actual tube attenuation and to use this value, as opposed to the value recommended by the standards, to correct the measured sound absorption. We also recommend an alternative way to determine the microphone phase error.

Application of acoustic fabrics to improve the insertion loss of a partial enclosure

The sound absorption coefficient, transmission loss, and transfer impedance of different sound absorbing fabrics are measured. It is shown that the properties are similar to microperforated panels. Using microperforated panel equations, effective hole diameter and porosity are determined via a least squares curve fit. The effective parameters can then be used to predict the sound absorptive performance for different cavity depths. It is demonstrated that the fabrics have good sound absorptive performance over a wide range of frequencies. The fabric was then positioned in a partial enclosure. Single and double layers of the fabric were placed over an opening and the insertion loss as a result of fabric application was measured. The insertion loss is increased by approximately 5 dB if two layers of the fabric is used.