Attenuation and Regeneration of Sound in Ducts and Jet Diffusers

Abstract

The effect of noise regeneration by fluid flow on the performance of noise-attenuating structures is examined with special attention to muffler design. The insertion loss of a single element, as well as a continuous distribution of attenuating and noise-regenerating elements, is studied. For example, in a duct with an attenuation constant β per unit length and a regeneration r per unit length, the upper limit of the insertion loss is 10 log (2Eβ/r), where E is the source strength. It should be noted that the insertion loss of a noise-regenerating attenuator depends on the sound level to be reduced. An analysis of experimental data on jet noise indicates that the power spectrum of a circular jet depends on frequency, f, and Mach number, M, approximately as f2M5 at low frequencies, as f−2.5M9.5 at high frequencies, and as M7 at the peak frequency. In terms of the corresponding jet spectrum, for which an empirical analytical expression is given, the maximum attainable insertion loss of a jet muffler diffuser is presented as a function of frequency. The deviation of the characteristics of a “lossy” diffuser from this upper limit depends on the attenuation and regeneration characteristics of the acoustical elements in the muffler. These characteristics are investigated for the special element consisting of a perforated sheet, and the results are applied to an analysis of the insertion loss of a muffler diffuser of the perforated basket type.