Calculation of duct acoustics with the parabolized stability equations

This study explores the use of parabolized stability equations (PSEs) for predicting sound propagation in ducts, a novel application in computational duct acoustics. The PSE, formulated in a general duct-fitted coordinate system, was validated against several test cases, including uniform flow, axial temperature gradients, and laminar/turbulent flows, demonstrating close agreement with existing literature. This paper highlights limitations of the PSE, particularly when the local Helmholtz number decreases, potentially causing mode cutoff, and suggests remedies for mitigating phase and amplitude errors. The efficiency of the PSE is further demonstrated through a comparison with linearized Euler equations for forward fan noise propagation in a turbofan inlet, showing 75.8% reduced computational time and 98.2% reduced memory usage. These computational advantages become more significant as problem size increases, with the PSE outperforming traditional finite element and parabolic approximation methods, especially in cases involving viscous shear flow effects. This makes the PSE particularly well-suited for applications such as boundary layer shielding and liner-boundary layer interactions. The study provides a promising avenue for future acoustic research and practical engineering applications, emphasizing the efficiency and accuracy of PSE in complex duct acoustics.