SIDLAB References 2

The Modeling and Design of a Reactive Muffler to Reduce a Low Frequency Tone
Kato, D., Seybert, A., and Jones, D., “The Modeling and Design of a Reactive Muffler to Reduce a Low Frequency Tone,” SAE Technical Paper 2013-01-1885, 2013, doi:10.4271/2013-01-1885


Large reciprocating engines produce a tonal spectrum of sound radiating from their exhaust. Even after standard reactive mufflers and after-treatment devices are added, and the target A-weighted sound level has been achieved, very audible low frequency tones can remain, and their levels are sometimes even enhanced by the exhaust system, creating potential annoyance problems in neighboring communities. This paper describes a practical design approach to such a problem and demonstrates variation in critical system parameters that affect acoustical performance. These parameters include temperature, source impedance, end impedance, flow, and pipe lengths, which are explored through practical models. The results of field measurements before and after installation of a final design are included and demonstrate a significant reduction in the sound level at the frequencies of interest.


Increasing demand for energy in densely populated areas along with more awareness of environmental issues creates an engineering challenge to produce large machinery with minimal environmental impact. In particular, large diesel and natural gas engines used in generators and compressor stations require exhaust emission after-treatments for both chemicals and noise. Reduction of noise on these engines requires exhaust systems with sufficient attenuation to meet community regulations that not only require overall A-weighted sound levels below stated levels but that ensure that low frequency tones are also reduced. Even when the overall A-weighted sound levels are met, all aspects of the psychoacoustic annoyance problem are often not accounted for, particularly at low frequency tones. Such tones are often not judged “loud” by test panels using human subjects, but at the same time can be judged “annoying.” Low frequencies also propagate over distances with less attenuation than high frequencies and are obvious to listeners in communities even where there is otherwise traffic and other broadband background noise.In this paper, we discuss these issues in the context of a specific application of a 16-cylinder natural-gas-fired engine used to transport natural gas along a pipeline. Even though the engine was already muffled, it was found that the low frequency tones were still objectionable. These included tones at, nominally, 41 Hz and 8 Hz. The basic approach was to use transfer matrix theory coupled with SIDLAB, a muffler and exhaust system modeling program, to design an additional muffler that treated the objectionable tones. SIDLAB also has a flow analysis module that was used to predict the pressure drop of the final design. Data from the field were used to guide the design.

Simple Expansion Chamber

Expansion chambers are a basic element in reactive muffler designs where their performance is primarily a result of area change. Such a simple design would also be low in cost and fairly robust since their basic transmission loss curves consist of wide lobes rather than peaks. Figure 1 below shows the first design considered.

Figure 1 Simple expansion chamber and associated SIDLAB model.

Transmission loss, or TL, for this simple expansion chamber was calculated for different lengths of the expansion chamber. Figure 2 shows expected behavior as adjustments in the length parameter were made, with the width fixed at 1.85 m, in order to determine if the lobe peaks in the TL could be adjusted to line up with the target tones. Figure 2 shows that a length of about 3 meters was ideal for the 41 Hz tone but that making the lengths long enough to address the 8 Hz tone was not practical.

Figure 2 Expansion chamber length parameter change from 1 to 3 meters.

Figure 3 below shows that increasing the diameter increases the TL, as expected for an expansion chamber design. However, at a diameter of two meters, the TL was still only about 11 dB, not enough to satisfy the target TL of theproject. Diameters larger than two meters would help but would not be practical.

Figure 3 Expansion chamber diameter changed from 1 to 4 meters.

Expansion Chamber with Extended Pipes

The next design considered is shown in Figure 4. The graph in Figure 5 shows the effect of changing the length of the tube extending into the expansion chamber from 2 meters to 3.2 meters while the outlet tube length was held at zero. Figure 5 shows that this design had the effect of sharpening the transmission loss peaks and further showed that the optimum tube length for achieving attenuation at the target frequency of 41 Hz was 3 meters. Addressing the 8 Hz tone was still not in the practical range with this design.

Figure 4 Expansion chamber with extended pipe and associated SIDLAB model.

Figure 5 Expansion chamber with extended inlet pipe changed from 2 to 3.2 meters.

Expansion Chamber with Extended Pipe and Absorption

Figure 6 shows the next design considered. This design was explored next to quantify the effect of addinga large amount of absorbing material at one end of the expansion chamber. The material had a thickness of 0.25 meters and a flow resistivity of 10,000 mks rayls/meter. The material was retained with perforated metal consisting of 5 mm holes at 30 percent open area. Results in Figure 7 show the transmission loss of the expansion chamber with and without the absorbing material in place. The material had the effect of actually reducing the TL at the target frequency with some marginal increase in TL above the target tone demonstrating that absorbing material would not be of value. It is also well documented in other works that absorptive material has little effect at low frequencies where sound wavelengths are much larger than the absorptive material thickness.

Figure 6 Expansion chamber with extended inlet pipe, absorbing material retained at one end and associated SIDLAB model

Figure 7 Expansion chamber with extended inlet pipe; with and without absorbing material retained at one end.

Expansion Chamber with Extended Pipe, Absorption and a Quarter Wave Resonator

Figure 8 shows the design that was modeled to determine if adding a resonator could help the 8 Hz tone. In this design, a quarter-wave resonator was added just upstream of the expansion chamber. Figure 9 shows the effect of changing the length of the quarter-wave resonator from 12 to 15 meters in increments of 1 meter. Although a side branch of 15 meters appears to provide some attenuation at 8 Hz, it was much too long fit in the space allocated and was considered to be impractical. Helmholtz style resonators were also considered to help reduce the 8 Hz tone but initial calculations showed that the required resonator volumes were also not within the physical design constraints and the added complexity and cost of such a design was to be avoided.

Figure 8 Expansion chamber with extended inlet pipe, absorbing material retained at one end, quarter wave resonator and SIDLAB model.

Figure 9 Expansion chamber with extended inlet pipe and absorbing material and a quarter wave resonator with lengths from 12 to 15 meters.


For the final design, it was decided that an expansion chamber with extended pipes and no internal insulation was the best choice that was still within the constraints of the project. This design solves the main problem tone at 41 Hz. The 8 Hz tone was not addressed in the final design because of its large wavelength and therefore large components needed to treat it. Final small adjustments were made in the dimensions, and it was now time to calculate the insertion loss with possible variation in temperature and flow. Figure 10 shows the effect of varying temperature over the expected operating range of from 350 to 458 degrees Celsius. At the target frequency, there was adequate transmission loss over the range covered. Next the insertions loss was examined by modeling the length of pipes upstream and downstream of the expansion chamber, the pipe end condition, and using an assumed normalized source impedance of 0.7 and −0.7 for the real and imaginary parts respectively. Figure 11 compares the transmission loss to the insertion loss.

Figure 10 Final expansion chamber design with operating temperature varied from 350 to 458 degrees C.

Figure 11 Final expansion chamber design showing a comparison between transmission loss and insertion loss.

Although it appeared that the attenuation peak would not shift, there was concern over the dips below zero in the ILcurve, indicating possible amplification. Of particular concern was the dip at about 11 Hz that indicated a possibleenhancement of the 8 Hz tone. However, adding a typical system mass flow rate of 6 kg/s in the SIDLAB model demonstrated a reduction in amplification at the insertion loss low points. This effect is shown in Figure 12.

Figure 12 Final design transmission loss compared to insertion loss at no flow and with flow of 6 kg/sec

FIELD MEASUREMENTS FOR DESIGN CONFIRMATIONDetailed sound level measurements were repeated after the expansion chamber was added downstream of the existing exhaust muffler/catalyst systems on all three units at the compressor station. Sound level measurements were made close to the exhaust stack outlets of two of the three units and at the residential measurement location. Figure 13 shows a comparison of the sound levels before and after treatment while Figure 14, and its associated table, show the predicted and field-measured one-third octave insertion loss of the expansion chamber. The field-measured insertion loss is based on measurements at 12 feet from the stack outlet. Sound levels above about 125 Hz at the residence were influenced by noise sources other than the compressor station, and changes in those frequencies are not related to the addition of the expansion chamber. A small amount of amplification in the 63 Hz band was measured at the residence and was predicted by the model, but that band was still well below the limits in the vibration criteria curves. Figures 13 and 14 clearly demonstrate that the new design was quite effective at the problem frequency of 41 Hz with a measured insertion loss of approximately 26 dB. Generally, insertion loss values in other one-third octave bands were lower than predicted due to contamination of the field measurements from other noise sources at the compressor station. Even at 12 feet from the exhaust stack, the exhaust noise was not dominant at one-third octave bands other than 8, 16, 40, and 63 Hz. The insertion loss at the stack top and at the residence are somewhat different with a much larger decrease in the measured sound level at 16 Hz at the residence and with a slight increase in the measured levels at 8 Hz. The difference at 8 Hz is probably related to atmospheric differences between the two measurement periods, as the weather conditions were significantly different between the two. We do not have a theory to explain the large decrease at 16 Hz although a portion of this was predicted by the model.

Figure 13 Measured one-third octave sound pressure levels at the nearby residence, before and after the treatments described in this paper.

Figure 14 Predicted and field measured Insertion Loss of the expansion chamber, based on measurements at 12 feet from the exhaust stack outlet