THE DEVELOPMENT OF A RAPID SINGLE SPECTRUM METHOD FOR DETERMINING THE BLOCKAGE CHARACTERISTICS OF A FINITE LENGTH DUCT

Abstract

A method for the determination of the blockage area function of a duct or pipe from a single measurement of its transfer function is presented. The technique extends a method developed by de Salis and Oldham (Journal of Sound and Vibration221, 180–186) [1] where the duct blockage area function reconstruction is achieved as a function of the resonance and anti-resonance frequencies of the unblocked and partially blocked duct. In each case the resonance and anti-resonance frequencies are determined from maximum length sequence measurements (MLS). The advantage of using MLS analysis is that it has inherently high noise immunity and as such gives a sufficiently large signal-to-noise ratio to reveal the positions of the anti-resonance frequencies in the duct transfer function. In the current paper the technique is further simplified as the resonance and anti-resonance frequencies of the unblocked and the partially blocked duct are determined from a single MLS measurement in the partially blocked duct using an approximation suggested by Wu 1994 (Applied Acoustics41, 229–236) [2]. However, Wu's approach utilized resonance frequency information alone and was thus limited to blockage area functions with no degree of symmetry in the longitudinal plane. In earlier work Wu and Fricke 1990 (Journal of the Acoustical Society of America87, 67–75) [3] have demonstrated that the method using resonance frequencies measured under two sets of boundary conditions could be applied to functions of all degrees of symmetry. In this paper it is shown that the additional determination of the duct anti-resonance frequencies enables Wu's limited reconstruction technique (Wu 1994 Applied Acoustics41, 229–236) [2] to achieve results equivalent to the two boundary condition technique (Wu and Fricke 1990 Journal of the Acoustical Society of America87, 67–75) [3]. Accuracy is enhanced as filtration of the measured transfer function is used to further reduce extraneous noise thus improving the resolution of the transfer function. The determination of the duct area function is achieved utilizing resonance and anti-resonance frequency information alone which renders the determination of the duct length unnecessary. The accuracy of the shift approximation method in achieving a reconstruction technique for the blockage area function of a finite length duct or pipe from a single measurement is demonstrated.