Acoustic propagation in ducts with axially varying parameters using the parabolized stability equations

Abstract

© 2019, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.The Parabolized Stability Equations (PSE) method has been extensively employed to compute the evolution of hydrodynamic instabilities in sheared flows. In its compressible-flow formulation, this method may also be used to compute sound propagation. Duct acoustics, in particular, may greatly benefit from its use, because complex boundary conditions and base-flows, including acoustic liners and developing boundary-layers, could be incorporated in the method. Furthermore, the PSE method is much less computationally demanding than standard numerical duct acoustics techniques. Aiming at unveiling this untapped potential, this work assessed the capabilities of PSE to predict sound propagation in cylindrical ducts. The acoustic field predicted with the PSE method for several simple duct models was compared with literature results. There was close agreement for ducts with uniform flow/constant wall impedance, sheared flow and axially varying base-flow temperature. The acoustic field predicted by the PSE for a duct with axially varying impedance displayed the expected trends and demonstrated that the method is able to account for such variation. Finally, prediction of acoustic propagation in a duct with turbulent boundary-layer showed that the PSE method can capture refraction and viscous dissipation of sound. These results showed that the method is able to accurately predict sound propagation through realistic duct models and is frugal with computational resources. We expect that the unveiled potentialities of the PSE method pave the way for faster acoustic liner design/optimization and deeper understanding on phenomena like liner instability.