A method for quantifying the acoustic transfer function of a ducted rotor

This paper describes a method for analyzing the sound radiated by a low-speed axial flow ducted fan. The radiated sound depends on both the sound generated by the rotor and the geometry of the surfaces surrounding the source region. These surfaces act to modify the spectral content of the sound as perceived by an observer outside of the duct. The fan was considered as a compact region of axial dipole sources, so that the radiated sound could be described as the product of a frequency-dependent unsteady force and an effective transfer function. The primary goal of this study was to develop a method for quantifying the acoustic transfer function for this general class of system using radiated sound measurements. Microphone measurements were acquired of the radiated sound generated by a ten-bladed fan operating inside a finite length rigid duct. Two fundamental frequencies were found to be inherent in the system, one based on the parameters of the sound source, and the other based on the geometry of the duct. As previous studies have found, these two frequency scales allow for the separation of the radiated sound into source and transfer function spectra. A unique method for determining these separate functions is presented, with the primary assumption that the aeroacoustic sources follow a power law relationship with rotor tip relative speed. The resulting algorithm was shown to effectively quantify the acoustic transfer function. A set of mathematically defined input functions was used to evaluate the efficacy of the separation method. Additionally, the ducted rotor system was operated over a range of flow rates to produce different sound sources, and the transfer function calculated by the algorithm was found to be independent of this source mechanism.