A study of wave propagation in a duct and mode radiation

In this paper we discuss two problems of classical duct acoustics: (1) wave propagation in infinite ducts with uniform flow based on a graphical approach, and (2) detection of mode radiation from a duct by an external circular microphone array. In (1) we show that the wave number vectors for a given flow Mach number form an ellipse whose center and shape depend on the Mach number only. We construct graphically the upstream and downstream wave number vectors of modes that propagate in the duct. We then show how one can infer from this graphical approach many known results in duct propagation such as the mode cut-off concept, the direction of energy propagation, the angle of the radiation lobe at peak directivity using Rice' s cutoff ratio concept, and other qualitative results. In (2) we give the mathematics behind the experimental detection of mode radiation from a duct by a circular array of microphones whose axis coincides with the engine axis. Since the external microphone array does not introduce additional noise sources inside the engine, as does a rotating rake of microphones positioned at the inlet, this measurement technique may be preferable to use of a rotating rake. The simplicity afforded by the lack of sophisticated rotating parts is an additional advantage over the rotating array.