Eigenvalue Analysis Method for Liner Noise Reduction Under Multiradial-Mode Incidence

Engine fan noise contains multiple radial modes, and the transmission loss (TL) of acoustic liners in such cases is influenced by both the power ratio among these radial modes and the phase difference between them. The objective of this paper is to develop a method for the rapid and accurate calculation of the attainable range of TL. Based on the transfer element method (TEM), a transmission matrix can be established, which directly relates the modal coefficient between the incident sound waves and the transmitted waves at the liner outlet. Following a mathematical processing of the transmission matrix, the Rayleigh quotient theorem is applied to analyze its eigenvalues, facilitating rapid and accurate calculation of the extreme values (maximum and minimum) of TL. TEM-based TL contour maps for two- and three-mode incidence, obtained from varying power ratios and phase differences, validate the predicted extreme values. For the scenario involving two radial modes, it is observed that the power ratios at the maximum and minimum TLs are reciprocals, which are characterized by a phase difference of 180 deg, and the underlying mechanisms are elucidated.