Low-order acoustic network models, treating the complex combustor geometry as a network of simple geometry elements, are typically used to analyse circumferential combustion instabilities in annular combustion chambers. These elements are typically assumed to have uniform cross-sectional surface area and average radius so that the analytical solutions 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 solutions are then validated by comparing them to results by numerically resolving the linearised 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.

将复杂的燃烧器几何结构视为简单几何元素网络的低阶声网络模型通常用于分析环形燃烧室中的圆周燃烧不稳定性。通常假定这些元素具有均匀的横截面面积和平均半径，以便可以直接获得它们内部的声场的解析解。但是，这可能导致燃烧不稳定性分析中的错误。本工作得出具有变化的横截面面积和保持平均流量的平均半径的环形燃烧室中声场的解析解。首先基于非常少的假设来推导用于压力扰动的波动方程。然后基于修正的WKB近似推导声场的解析解。然后，通过数值求解线性化的Euler方程，将它们与结果进行比较，从而验证这些解决方案。结果表明，只要频率大于某个值，就始终可以获得准确的预测，以确保横截面表面积的平滑变化和小到中等的亚音速轴向马赫数。