Analytical solutions of acoustic field in annular combustion chambers with non-uniform cross-sectional surface area and mean flow

Low-order acoustic network models, treating the complex combustor geometry as a net -work of simple geometry elements, are typically used to analyse circumferential combus-tion instabilities in annular combustion chambers. These elements are typically assumed to have uniform cross-sectional surface area and average radius so that the analytical so-lutions of the acoustic field within them can be directly obtained. However, this may lead to errors in the combustion instability analyses. The present work derives the analytical solutions of the acoustic field in annular combustion chambers with both varying cross-sectional surface area and average radius sustaining a mean flow. A wave equation for the pressure perturbation is firstly derived based on very few assumptions. Analytical solutions of the acoustic field are then derived based on a modified WKB approximation. These so-lutions are then validated by comparing them to results by numerically resolving the lin-earised Euler equations. Results show that accurate predictions can always be obtained for a smooth change of the cross-sectional surface area and small-to-moderate subsonic axial Mach numbers as long as the frequency is larger than a certain value. (c) 2021 Elsevier Ltd. All rights reserved.