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Helmholtz resonators are normally an afterthought in the design of mufflers to target a very specific low frequency, usually the fundamental firing frequency of the engine. Due to space limitations in a complex muffler design, a resonator may have to be built by punching a few small holes on a thin-walled tube to create a neck passage into a small, enclosed volume outside the tube. The short neck passage created by punching a few small holes on a thin-walled tube can pose a great challenge in numerical modeling, especially when the boundary element method (BEM) is used. In this paper, a few different BEM modeling approaches are compared to one another and to the finite element method (FEM). These include the multi-domain BEM implemented in a substructure BEM framework, modeling both sides of the thin-walled tube and the details of each small hole using the Helmholtz integral equation and the hypersingular integral equation, and modeling just the mid surface of the thin-walled tube.

Insertion loss in one-third or octave bands is widely used in industry to assess the performance of large silencers and mufflers. However, there is no standard procedure for determining the transmission loss in one-third or octave bands using measured data or simulation. In this paper, assuming that the source is broadband, three different approaches to convert the narrowband transmission loss data into one-third and octave bands are investigated. Each method is described in detail. To validate the three different approaches, narrowband transmission loss data of a simple expansion chamber and a large bar silencer is converted into one-third and octave bands, and results obtained from the three approaches are demonstrated to agree well with one another.

Prior research on assessing multiple inlet and outlet mufflers is limited, and only recently have researchers begun to consider suitable metrics for multiple inlet and outlet mufflers. In this paper, transmission loss and insertion loss are defined for multiple inlet and outlet mufflers using a superposition method that can be extended to any m-inlet n-outlet muffler. Transmission loss is determined assuming that the sources and terminations are anechoic. On the other hand, insertion loss considers reflections. For both metrics, the amplitude and phase relationship between the sources should be known a priori. This paper explains both metrics, and measurement of transmission and insertion loss are demonstrated for a 2-inlet 2-outlet muffler with good agreement.

A simplified method to model perforated tubes in mufflers is the equivalent transfer impedance approach. Various empirical formulas that consider the porosity, hole diameter, wall thickness, and flow type have been proposed to date. They normally work very well under the conditions that the formulas are intended for. However, there are situations that the empirical formulas may not be able to cover. In this paper, we propose a simple BEM-based numerical procedure to determine the transfer impedance from a small perforate sample, and then send the transfer impedance to the muffler BEM model for analysis purposes. Numerical results are verified in three test cases.

Partial enclosures are commonly utilized to reduce the radiated noise from equipment. Often, enclosure openings are fitted with silencers or louvers to further reduce the noise emitted. In the past, the boundary element method (BEM) has been applied to predict the insertion loss of the airborne path with good agreement with measurement. However, an alteration at the opening requires a new model and additional computational time. In this paper, a transfer function method is proposed to reduce the time required to assess the effect of modifications to an enclosure. The proposed method requires that the impedance at openings be known. Additionally, transfer functions relating the sound pressure at one opening to the volume velocity at other openings must be measured or determined using simulation. It is assumed that openings are much smaller than an acoustic wavelength. The sound power from each opening is determined from the specific acoustic impedance and sound pressure at the opening.

It was demonstrated that a bypass duct similar to a Herschel- Quincke tube could be used to increase the transmission loss of mufflers at selected frequencies. In many cases, the duct can be short and thought of as a leak. It was shown that the optimal length and cross-sectional area could be determined by using a simple optimization technique known as the Vincent Circle. Most importantly, it was demonstrated that the attenuation at low frequencies could be improved by as much as 15 dB. To prove the concept, a muffler was designed and optimized using transfer matrix theory. Then, the optimized muffler was constructed and the transmission loss measured using the two-load method. The measured results compared well with prediction from transfer matrix theory. Boundary element simulation was then used to further study the attenuation mechanism.

Transmission loss (TL) is a good performance measure of mufflers since it represents the muffler's inherent capability of sound attenuation. There are several existing numerical methods, which have been widely used to calculate the TL from numerical simulation results, such as the four-pole and three-point methods. In this paper, a new approach is proposed to evaluate the transmission loss based on the reciprocal work identity. The proposed method does not assume plane wave propagation in the inlet and outlet ducts, and more importantly, does not explicitly apply the anechoic termination impedance at the outlet. As a result, it has the potential of extending TL computation above the plane wave cut-off frequency.

Discontinuous boundary elements, such as constant elements, have been used in many engineering applications for years. In acoustics, the primary variables are sound pressure and normal particle velocity, and they can be defined at the center of each constant element. Since the acoustic variables do not need to be continuous across the element boundary, it is easy to write an algorithm to automatically refine the mesh by subdividing inside each element as frequency goes up. To take one step further, one may also choose to use a geometrically incompatible mesh, in which not only the primary variables but also the geometrical nodes do not need to be continuous across the element boundary. The main advantage is that a model can be quickly assembled from different sources without paying too much attention to the node-to-node continuity at junctions. As such, it is easy to add or remove a component at will to see its effect at the concept design stage.

In this paper, the transmission loss (TL) of mufflers with a built-in catalytic converter (CC) and/or a diesel particulate filter (DPF) is predicted using the boundary element method (BEM) by either modeling the CC or DPF as a block of bulk-reacting material or by using the “element-to-element four-pole connection” between two BEM substructures. The four-pole parameters of the CC or DPF can be obtained by a measurement procedure that involves using the two-source method on a test rig with a pair of transition cones followed by a few 1-D four-pole matrix inverse operations to extract the parameters. A 3-D BEM based optimization may be further applied to fine-tune the extracted four-pole parameters. To use the bulk-reacting material modeling in BEM, the four-pole parameters will have to be converted into an equivalent set of bulk-reacting material properties. Test cases including a muffler with a series connection of CC and DPF are presented in this paper.

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.

An energy source simulation method (ESSM) has been developed to determine sound energy density. Using this approach, a specified intensity boundary condition on the surface of a vibrating body is approximated by superimposing energy density sources placed inside the body. The unknown strengths for these sources are then found by minimizing the error on the boundary, using a least squares technique. The superposition of these energy density sources should then approximate the sound radiating from the body. The approach was evaluated in two-dimensions for a circle, square, and a more general geometry. The ESSM proved an excellent tool for predicting the energy density provided that power radiated uniformly in all directions. However, the ESSM could not accurately predict the directional characteristics of the energy density field if the power radiated significantly higher from one side of an object than other sides.

Typical automotive muffler designs contain complex internal components such as extended inlet/outlet tubes, thin baffles with eccentric holes, internal connecting tubes, perforated tubes, perforated baffles, flow plugs and sound-absorbing materials. An accurate performance prediction for highly complicated muffler designs would greatly reduce the effort in fabricating and testing of multiple design iterations for engineers. This paper discusses the use of a component-based computer simulation tool for design and analysis of exhaust mufflers. A comprehensive computer program based on the Direct Mixed-Body Boundary Element Method was developed to predict the transmission loss characteristics of muffler systems. The transmission loss is calculated by an improved four-pole method that does not require solving the boundary element matrix twice at each frequency, and hence, it is a significantly faster approach when compared to the conventional four-pole method.