An In-duct Beamformer For The Estimation Of Far-field Directivity

Abstract

This paper presents a measurement technique for estimating the far-field directivity of the sound radiated from a duct using measurements of pressure made inside the duct. The technique is restricted to broadband, multi-mode sound fields whose directivity patterns are axi-symmetric, and whose modes are mutually uncorrelated. The technique uses a transfer function to relate the output from an in-duct axial beamformer to measurements of the far-field polar directivity. A transfer function for a hollow cylindrical duct with no flow is derived, and investigated in detail. The transfer function is shown to be insensitive to the mode-amplitude distribution inside the duct, and hence a predicted transfer function can be used to predict the directivity in practice where the noise source distribution is unknown. It is suggested that the proposed technique will be especially useful for fan rig experiements, where direct measurement of directivity, for example by use of an anechoic chamber, is impossible. The technique is validated using a no-flow experiment.