BROADBAND TRANSMISSION LOSS PERFORMANCE OF A HEMISPHERICAL END-CHAMBER MUFFLER WITH SINGLE ENDINLET AND SINGLE/DOUBLE END-OUTLET

The axially short circular/elliptical cylindrical chamber is often used as a flow-reversing or straightflow
end-chamber in a multi-pass perforated duct muffler, a typical component of a modern-day
automotive exhaust system. However, due to its small expansion volume, such short end chambers
yield low acoustic attenuation (expressed in terms of Transmission Loss (TL)) in the low-frequency
range, induce a large back pressure and increasing the chamber length results in the occurrence of a
trough (due to the first axial mode) at a lower frequency that deteriorates the TL performance. In view
of these limitations, the use of a different geometry, namely, a rigid-wall hemispherical cavity as a
flow-reversal end-chamber muffler is investigated for potentially enhancing the TL performance over a
wider frequency range, especially at low frequencies. To this end, this paper analyses the TL
performance of a hemispherical end-chamber muffler having a single end-inlet and single/double endoutlet
by means of a 3-D semi-analytical formulation based on the modal expansion of the acoustic
field and the Green’s function approach. The 3-D acoustic field inside the rigid-wall hemispherical
end-chamber is expressed in terms of the orthogonal modal functions. The hemispherical end-chamber
muffler system is characterised using the uniform piston-driven model in terms of the impedance [Z]
matrix parameters obtained by computing the average of the 3-D Green’s function over the surface
area of the ports which are modelled as rigid pistons. The TL graphs computed by using the 3-D semianalytical
formulation are found to be in an excellent agreement with that obtained from the 3-D FEA,
thereby validating the technique used here. Furthermore, the 3-D modal expansion method enables one
to take into account, the relative polar angular location between the ports and also determine their
optimal radial offset distance (corresponding to appropriate pressure nodes on the end face) to obtain a
broadband TL performance. A comparison of the TL performance of the optimised hemispherical endchamber
muffler with that of an equivalent circular end-chamber having an equal volume demonstrates
a significantly higher frequency range over which a broadband attenuation is obtained by using the
hemispherical cavity. Similarly, a comparison with the TL graph of an equivalent axially short circular
end-chamber indicates that the former exhibits higher attenuation in the low-frequency range.