Weak shocks in open-ended ducts with complex geometry
The dynamics of weak shocks in ducts of complex geometry and the sound radiation produced by the reflection of a weak shock from the open end of a duct have been investigated. Duct geometries include expansion chambers with and without inlet or outlet tubes extended and enclosed perforated tubes....
| Summary: | The dynamics of weak shocks in ducts of complex geometry and the sound radiation produced by the reflection of a weak shock from the open end of a duct have been investigated. Duct geometries include expansion chambers with and without inlet or outlet tubes extended and enclosed perforated tubes. Internal and external pressure histories of the interaction of weak shocks with simple muffler elements have been recorded using a standard one-shot shock tube and a resonating shock tube. The excitation shock Mach number ranged from 1.05 to 1.55. Analytical investigations, including a synthesis of existing works on internal weak-shock interactions of an acoustic treatment of the sound radiation produced by weak shock waves, are presented. Combining the above analyses, models for the reduction in radiated sound per unit of incident shock amplitude, as a result of inserting a muffler between the source and the tailpipe exit, are developed.
For expansion chambers with and without extensions, the dependence of the transmitted and reflected waves and of the radiated sound on area ratio is compared with predictions. In particular, measured transmission coefficients for expansion chambers agree reasonably well with the predictions for all shock strengths; however, for large area ratios, the predicted sound attenuation is not observed, as waves diffracted at the upstream junction cause more sound to be radiated. For expansion chambers with internal extensions, sound attenuation is increased for low incident shock strengths; while for increasing incident shock strength, the internal transmission characteristics deteriorate, the reducing the sound attenuation.
For enclosed perforated tubes, the dependence of the transmitted and reflected waves and of the radiated sound on the perforated area ratio and incident shock strength is compared with predictions. For perforated tubes with infinite enclosure, the transmission and reflection coefficients depend on both incident shock strength and perforated area ratio, as predicted. However, agreement with data is obtained only after inserting a perforated discharge coefficient with the perforated area ratio in the theory. The reduction of sound radiation with perforated area ratio is measured for one incident shock strength and then compared with predictions. For small area ratios, there is agreement but for large area ratios the measurements show that less sound is radiated than predicted. For large area ratios, gradual compressions with smooth fronts (not shock fronts) are transmitted, resulting in less radiated sound. Enclosures have no effect on the sound attenuation for small perforate area ratios; however, as the perforate area ratio increases, the enclosure eventually inhibits further increase in sound attenuation.
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