Study of sound attenuation in elliptic ducts

The acoustic emission resulting from the reciprocating motion of machinery parts, such as the movement of pistons and the intake/exhaust of gases in an automotive engine, or the pressure pulsation generated in compressors cause noise pollution. Passive noise--attenuating devices such as mufflers are usually employed in the intake or the exhaust flow path of such systems. A typical muffler element consists of an expansion chamber with inlet and outlet ports for the passage of the exhaust fluid. The difference in the size of the ports from the chamber dimensions presents an impedance mismatch to the propagating acoustic wave, resulting in partial or complete reflection of the sound energy. Mufflers can broadly be classified as reactive type or dissipative type. Reactive mufflers employ the principle of impedance mismatch by incorporating area changes in the transmission path. Dissipative mufflers usually have some kind of absorptive lining that converts sound energy into heat. In comparison to reactive mufflers, dissipative mufflers usually have a sound attenuation over a wider frequency range. However, pressure drop and particle clogging limit their application. The sound attenuation characteristics of a muffler is dependent on various factors like shape and size of the muffler, orientations of inlet/ outlet ports, and number of inlet/outlet ports. Since the parameter space involved is potentially very large, only a few muffler geometries have been extensively studied in the past, viz. circular or rectangular chamber mufflers. More recently, mufflers having elliptical cross-sections have received some attention. These types of mufflers require smaller space across one of the dimensions, and are suitable for applications where space constraints are an important design consideration. The existing literature on elliptic reactive mufflers is not extensive; therefore, further attention to this geometry is required. The present work aims to study the sound attenuation in elliptic reactive mufflers using a perturbation-based approach. Although exact solutions for such geometries are available in terms of the elliptic eigenfunctions, the perturbation based approach may be implemented for more general asymmetric distortions (within moderate eccentricity). Using this approach, the effects of the ellipticity and port-extensions on the sound attenuation are analyzed in this work. The perturbation method is then extended to study the breakout noise from distorted ducts. It has been long established that distortions in ducts significantly alter the sound radiation when subjected to an internal acoustic field. However, most of the reported work had been confined to very small distortions, and plane-wave (acoustic) propagation within the duct. The present work aims to improve on these limitations and provide a solution method for studying the sound radiation from moderately distorted ducts when excited by a point acoustic source. Using an analytical approach suggested earlier, the radiated sound field of an elliptic duct (eccentricity e=0.6) is observed to be much higher (as much as 30 dB, Lw) than a cylindrical shell of comparable dimensions. The final part of this dissertation aims to determine the effect of a liquid phase on the sound attenuation in a muffler geometry. The liquid phase is expected to act like a compliant surface, thereby affecting the sound transmission. However, analytical study of a simple rectangular duct and experimental measurement of transmission loss indicate that the wall compliance effects are negligible and may be neglected