Analytical solutions for the acoustic field in a thin annular duct with temperature gradient and mean flow

The analytical solution for the one-dimensional acoustic field in a straight duct with arbitrary mean temperature gradient and mean flow has been recently derived based on an adapted WKB approximation (J. Li, A.S. Morgans, J. Sound Vib. 400 (2017) 248–269 [12]). These solutions reproduce the acoustic field very accurately across a wide range of flow conditions. These approaches are applied herein to a more complex configuration – a thin annular duct with arbitrary mean temperature gradient and mean flow; this is a common element (e.g., the annular combustion chamber) used in gas turbines and aero-engines. The derived analytical solutions are also validated on similar configurations and by using the same methods as our previous work.