Fluid Dynamic and Acoustic Modeling of Concentric-Tube Resonators/Silencers (1991)

<div class="htmlview paragraph">Two models used for the prediction of noise attenuation in silencers have been evaluated. One is a full non-linear one-dimensional fluid-dynamic model, representing the entire engine (from the air cleaner to the tail pipe). The other is a linear acoustic model, representing a silencer and the exhaust and tail pipes. The evaluation was made by comparing the models' predictions to transmission lose measurements obtained with a set of concentric-tube resonators under speaker excitation at room temperature. This represents a test of the models in the linear range (small pressure pulsation amplitudes). The comparisons showed that both of the models performed well under these conditions. For the non-linear model this comparison represents validation for only one special case, since the main application of the model is to prediction of engine performance, insertion loss in silencer, absolute level of noise radiated from tailpipe and engine backpressure.</div> <div class="htmlview paragraph">A COMMON APPROACH to the reduction of engine exhaust noise is the use of silencer systems with expansion chambers and resonators. These silencer elements operate on the reactive principle, reflecting the engine-generated pressure waves back to the source, transmitting (passing) only a part of the fluctuating energy towards the tail pipe.</div> <div class="htmlview paragraph">An extensive prior literature exists which shows that for certain specific geometric shapes the complex process (see e.g. review in Munjal [<span class="xref">1</span>]*) of wave reflections in a silencer-like geometry can be modeled with good accuracy by linear acoustic models. This has been shown by comparison to experiments carried out under speaker excitation (low pressure oscillation amplitude) and low mean flow velocities. The geometric shapes for which such acoustic models have been developed include constant area pipes, abrupt area changes and concentric tube resonators with perforated pipe elements. The majority of commonly used acoustic models are based on the assumption that only one-dimensional planar waves are present in the system, and are thus limited to the frequency range below the onset of transverse waves in the system, translating to an upper limit of about 3000 Hz in typical vehicular silencer applications. The acoustic models are based on linearized equations of motion, and are thus limited to the linear range of application, with sound wave levels on the order of 120-140 dB, i.e., pressure fluctuations on the order of 20-200 Pa = 0.0002-0.0020 bar.</div> <div class="htmlview paragraph">The actual engine exhaust systems deal with pressure waves that are much larger than that, in excess of 0.1 bar. Also, these waves are superposed on a high-speed flow, which can reach velocities of several hundred m/sec and even undergo shocks during each engine cycle. Under these conditions the acoustic models no longer apply. To deal with these high amplitude pressure waves and flows, a non-linear fluid-dynamic model must be used.</div> <div class="htmlview paragraph">It should be noted that any one-dimensional model, be it acoustic or non-linear, is limited by the above mentioned frequency limit. In addition, in practical exhaust systems the gas flow locally produces additional high frequency noise, which limits the usefulness of the one-dimensional approaches well below 3000 Hz, especially at higher engine speeds where gas velocities are high.</div> <div class="htmlview paragraph">The present paper describes two models and evaluates their performance by comparison to data. One is a full non-linear one-dimensional fluid-dynamic model, the other is an acoustic model. The two models have in common the assumption that the flow in the ducts of the system can be considered one-dimensional. The acoustic model uses linearized equations and thus is limited to small pressure amplitudes and small fluctuating velocities; it represents the silencer itself plus the pipes leading to it. This model operates in the spectral (frequency) domain.</div> <div class="htmlview paragraph">The non-linear model, on the other hand, represents the entire engine from the air cleaner to the tail pipe and has no limitation on the amplitude of pressure and velocity pulsations. The model is a time-domain calculation simulating the engine operation under steady-state or transient conditions.</div> <div class="htmlview paragraph">As part of the validation of the models, comparisons with data were carried out for the transmission loss produced by expansion chambers and concentric tube resonators using speaker excitation. This represents a test of the models in the linear range, where they should both apply and where simultaneous comparisons could be made to data.</div> <div class="htmlview paragraph">It should be stressed that the validation against the speaker data represents only one of the steps that has been taken to validate the non-linear model. That model is being used in many applications to engine exhaust noise evaluation and reduction. In that context it has been shown to produce accurate predictions of engine power, magnitude and frequency content of exhaust pressure pulsations, and reductions of these pulsations in silencers. The applications to engines will be the subject of a future publication.</div>