A homotopy method for determining the eigenvalues of locally or non-locally reacting acoustic liners in flow ducts

This paper presents a unified algorithm for studying the eigenvalue problem of a lined duct using the homotopy method. Results from various validations show that the method developed in this work can provide accurate and reliable numerical solutions for sound-propagation computation. The investigation also indicates that homotopy methods not only overcome the computational difficulties of the existing methods for locally reacting liners, but also give a completely different way to calculate the eigenvalues of non-locally reacting liners, which have recently received considerable attention due to their potential application for future advanced liners. Finally, a model multi-segmented, non-locally reacting liner is employed to study the possibility of controlling sound attenuation through a bias flow. The simulation shows that by adjusting the bias flow of each segment, optimal sound attenuation can theoretically be achieved.