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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.

A process for predicting the transmission and insertion losses of multi-component exhaust systems is detailed in this paper. A two-tiered process incorporating boundary element analysis to evaluate multi-component systems is implemented. At the component level, the boundary element method is used to predict the transfer matrix for larger components where plane wave behavior is not expected within the component. The transfer matrix approach is then used to predict insertion loss for built-up systems with interconnecting duct or pipe work. This approach assumes plane wave behavior at the inlet and outlet of each component so it is limited to the low frequency regime. Results are compared with experimental results for HVAC systems.

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 cutoff 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.

A recently developed superposition approach for determining the insertion loss of a two-inlet muffler is reviewed. To validate the approach, calculated and measured insertion losses are compared for a small engine muffler with two inlets and one outlet. After which, the phasing between the two inputs is varied and the insertion loss is evaluated. Results show that the insertion loss is strongly affected by the phasing between sources at low frequencies while phasing between sources has a lesser impact at high frequencies. At the conclusion of the paper, the theory for applying the superposition approach to transmission loss is reviewed.

Over 30 years ago, A. H. Vincent of Westland Helicopters demonstrated that if a structure is excited harmonically, the response at another position (at a fixed frequency) will trace a circle in the complex plane as a result of a dynamic stiffness modification between two points. As either the real or imaginary part of an introduced dynamic stiffness is varied from minus infinity to plus infinity, the structural or acoustic response on any position will map a circle in the complex plane. This paper reviews the basis for this little known principle for vibro-acoustics problems and illustrates the viability for a cantilevered plate example. The applicability of the method is then considered for strictly acoustic systems like intake and exhaust systems. Specifically, it is shown that the response traces a circle in the complex plane if either the real or imaginary parts of the source or termination impedance are varied from minus to plus infinity.

Exhaust noise is a major contributor to the radiated noise level of a vehicle, especially at idle. The radiated noise level has to meet a certain criteria based on regulation and consumer demand. In many cases, the problem appears after the vehicle is manufactured and the tailpipe noise measurement is performed indicating a high noise level that needs to be reduced. This paper describes one of those cases where the radiated noise level of a certain passenger car at idle was required to be reduced by 6 dB(A). The exhaust system consists of one main muffler and one auxiliary muffler. A 1D two-port model of the exhaust system including the two mufflers was built using commercial software. This model was validated against the measurement of the two-port matrix of both mufflers. The model was then used together with tailpipe noise measurements to estimate the characteristics of the source strength and impedance.

The two-load method is commonly used to determine the transmission loss of a muffler or silencer. Several practical measurement considerations are examined in this paper. First of all, conical adapters are sometimes used to transition between impedance tubes and the muffler. It is demonstrated that the effect of adding the adapter can be quite significant at low frequencies especially if the adapter is short in length. The effect of changing the length of the adapter was examined via measurement and plane wave theory. Secondly, the effect of selecting the reference microphone was examined experimentally. It was found that measurements are improved by selecting a downstream reference. Finally, the effect of using different frequency response function estimation algorithms (H1, H2 and Hv) was compared sans flow. This had little effect on the measurement.

This paper documents a finite element approach to predict the attenuation of muffler and silencer systems that incorporate diesel particulate filters (DPF). Two finite element models were developed. The first is a micro FEM model, where a subset of channels is modeled and transmission matrices are determined in a manner consistent with prior published work by Allam and Åbom. Flow effects are considered at the inlet and outlet to the DPF as well as viscous effects in the channels themselves. The results are then used in a macro FEM model of the exhaust system where the transmission relationship from the micro-model is used to simulate the DPF. The modeling approach was validated experimentally on an example in which the plane wave cutoff frequency was exceeded in the chambers upstream and downstream to the DPF.

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.

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.

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.

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 two-load method is used to measure the transmission loss of thin panels in two different sized impedance tubes (3.49 cm and 10.16 cm). Samples were initially tested with a clamped boundary condition. This was followed by tests with an elastomer inserted between the tube and tested sample to adjust the boundary condition at the periphery. In all tests performed, the influence of the sample holding method could not be removed from the test. The measured transmission loss was compared to finite element simulation with good agreement for both impedance tubes. Additionally, the effect of a compliant boundary condition along the periphery of the sample was also validated via simulation.

Flow-generated noise has recently received a lot of attention within the process of designing exhaust and intake systems. Flow-generated noise can limit the amount of sound reduction a muffler can introduce inside ducts. This is more important in the modern system design where mufflers are compact and the flow speeds become higher in different sections inside the muffler. In this paper, three measurement techniques are used to measure the flow-generated noise from a duct element. The first is based on calculating the sound power levels inside a reverberation room according to ISO 3741. The radiated noise is measured from the muffler body as a source of noise, then from the tail pipe as an active one-port source. The second is based on sound power measurements inside the ducts using the active two-port theory. The third is measuring the sound pressure radiation inside an anechoic room.

In several applications, two-inlet single-outlet mufflers are possible to encounter in exhaust systems. They are usually used to merge two exhaust streams from two similar engines or from two sides of an engine. They have an advantage of reducing the back pressure on the engine(s). There is a lot of published research on the analysis of single-inlet single-outlet mufflers acting as a two-port. On the other hand, there are a few publications on the analysis of two-inlet single-outlet mufflers due to their complexity representing a three-port. A three-port is characterized by a 3×3 Scattering Matrix. The nine elements of this matrix represent the 3 reflection coefficients at each port, and the 6 transmission coefficients between the 3 ports in both directions. In this work, a two-inlet single-outlet muffler is studied. The elements of the scattering matrix were measured using the two-source two-microphone technique with and without flow.

The source in an intake/exhaust system is commonly modeled as a source strength and impedance combination. Both the strength and impedance are normally measured and measurement accuracy depends on selecting an appropriate acoustic load combination. An incident wave decomposition method is proposed which is based on acoustic wave decomposition concepts instead of an electric circuit analogy providing a more straightforward approach to investigating the effect of acoustic load selection. Based on studying wave reflections in the system, the uncertainty for determining source impedance is estimated.

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 measured. A measurement campaign was conducted to characterize the two-port transfer matrix of these devices. The simulation was performed using the two-port theory where the two-port models are limited to the plane wave range in the filter cavity.

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.

Additive manufacturing is slowly changing how components are developed and manufactured. As the technology develops over time, it is anticipated that industry will 3D print sound absorbers in production. Configurations may be considered that would be difficult to manufacture in another way. For exploratory purposes, several designs were 3D printed and positioned in an impedance tube for testing. Though the absorbers developed are based on well-established strategies, the absorbers considered are either difficult to manufacture by another means or take advantage of the unique features of 3D printed parts. The samples measured include long perforations, lightweight panels, and Helmholtz resonators with spiral wound necks. Selected results are compared with acoustic finite element analysis.

Bench tests are an important step to developing mufflers that perform adequately with acceptable pressure drop. Though the transmission loss of a muffler without flow is relatively simple to obtain using the two-load method, the presence of mean flow modifies the muffler behavior. The development of an insertion loss test rig is detailed. A blower produces the flow, and a silencer quiets the flow. Acoustic excitation is provided by a loudspeaker cluster right before the test muffler. The measurement platform allows for the measurement of flow-induced noise in the muffler. Also, the insertion loss of the muffler can be determined, and this capability was validated by comparison to a one-dimensional plane wave model.