Mirror-based multimodal straightforward method for impedance eduction using a zigzag array

Abstract

The Mirror-based Multimodal StraightForward Method (MM-SFM) is proposed herein to realize accurate and reliable liner impedance eduction covering the wide frequency range of aeroengine fan noises. It adopts a novel zigzag array in the flow duct, and unfolds them by a coordinate transformation into a mapping diagonal array in an extended duct, which can increase the array transverse spacing Δz considerably. Then, it invokes the M-SFM incorporating the trust-region and extended Prony's algorithms, to decompose the three-dimensional multimodal aeroacoustic field and educe the impedance. A parametric study based on the Monte-Carlo uncertainty analysis is conducted through finite-element numerical experiments on a 51 × 51 mm2 flow duct, to survey the method performance under random perturbations. It indicates that, the educing accuracy and reliability are promoted by increasing Δz or the axial spacing Δx properly, and the decomposed-mode number M×N=10 is appropriate herein. In our studied cases, using the recommended array of Δz=25.5mm and Δx=22mm locating at the nodes of transverse mode m = 2, the MM-SFM generally produces accurate averaged educed impedances in a considerably extended frequency range from 100 Hz up to nearly 10 kHz, and has small educing uncertainties at most absorptive frequencies and thus a good reliability.