1. Introduction

Exhaust noise of reciprocating internal combustion (IC) engines is certainly one of the biggest pollutants of the present-day urban environment. Fortunately, the use of a well-designed muffler (also known as a silencer) can significantly mitigate this problem by reducing the noise from IC engines [1]. Indeed, all automotive engines are invariably provided with exhaust mufflers, the theory and design practice of which is now over a hundred years! A primary design requirement of an automotive exhaust muffler is obtaining an adequate insertion loss so that the exhaust noise is reduced to the level of the noise from other components of the engine, or as required by the environmental noise pollution limits. Generally speaking, the amount of acoustic attenuation produced by a muffler is proportional to the expansion chamber volume in the low-frequency range which is particularly important because most of the engine noise is limited to the firing frequency and the first few harmonics. The necessity to have a sufficiently large volume is reinforced by the need to have a large expansion ratio, i.e., a sharp impedance mismatch. Table 5.​1 of [2] (reproduced from Bies and Hansen [3]) gives a good estimate of how important the muffler volume is in context with the attenuation produced at different octave band frequency bands; as a rule of thumb, small and large mufflers are approximately characterized by 5 and 15 times the piston displacement capacity of the engine, respectively. Unfortunately, however, the clearing space beneath the automobile body, where the muffler is typically located, is kept small because the stability of a vehicle requires a low center of gravity. Therefore, the space constraint along the vertically downward direction coupled with an additional essential requirement that the muffler shell should not touch the ground (especially on a rough terrain) often leads to the use of silencing chambers having a non-circular shape. Additionally, manufacturing defects or constraints might also force one to use non-axisymmetric chambers. In view of these design constraints, an elliptical and for that matter, a flat-oval chamber is popularly used in modern automobile exhaust systems, see, e.g., Figure 1.1a. Elliptical chamber with a straight-through flow configuration also finds use in the exhaust system of two-wheelers.