Unbalanced Mirror-based Multimodal StraightForward Method for Impedance Eduction

This paper proposes the Unbalanced-version Mirror-based Multimodal StraightForward Method (abbreviated as Unbalanced MM-SFM or UMM-SFM), as an enhancement of the MM-SFM, for more precise impedance eduction of acoustic liners in complex broadband multimodal aeroacoustic environments. The unbalanced-mode-expansion algorithm is developed to adaptively expand each transverse mode into different numbers of vertical modes, according to the actual modal distributions of incident sound sources which may be non-uniform, for effectively decreasing the probes and improving the decomposition accuracy of dominant modes. A numerical experiment through Monte Carlo uncertainty analysis is conducted on two liner specimens under high-velocity flow conditions and high-frequency unbalanced multimodal fields. The impedance spectrum and its uncertainties educed by the UMM-SFM exhibit small average deviations from the references over a vast majority of tested frequencies, except for those near the anti-resonance. This verifies the effectiveness of the Unbalanced MM-SFM for accurate eduction using much fewer probes, and its robustness under the error to some degree from non-full resolving of actual modal components and the random perturbance induced from the flow.