Acoustic Characterization of an Engine Exhaust Source – a Review

For an engine running at a constant speed (RPM), the exhaust process and intake process are periodic. This enables use of the frequency-domain analysis of the essentially linear exhaust system consisting of the exhaust runners, manifold, exhaust pipe, the muffler proper and the tail pipe. Over the last forty years, transfer matrices have been derived for use with aeroacoustic state variables as well as the classical state variables of acoustic pressure and acoustic volume/mass velocity. This frequency-domain analysis, however, requires prior knowledge of the load-independent source characteristics ps and Zs, corresponding to the open-circuit voltage and internal impedance in an analogous electrical system (as per Thevenin theorem). Several methods have been suggested for prediction or measurement of the source characteristics over the years, but with little success. Alternatively, time-domain analysis of the exhaust system, making use of the method of characteristics, does not require prior knowledge of the source characteristics. On the other hand, it can, and indeed has been harnessed to evaluate the source characteristics for use with linear frequency-domain analysis. Unfortunately, the source characteristics so obtained are not load-independent because of the inherent non-linearity and time dependence of the piston motion, exhaust valve/port opening and high blow-down pressure in the cylinder. Besides, the time-domain analysis of complex muffler elements is very cumbersome and error-prone. Therefore, hybrid approach has been mooted where the time-domain analysis of the exhaust source is combined with the frequency-domain analysis of the exhaust muffler making use of the discrete Fourier transform pair. Here again, there are several difficulties and challenges. This paper reviews all these developments and presents the state of the art for estimating unmuffled exhaust noise and insertion loss of commercial mufflers.