Predictions of thermoacoustic instabilities in annular combustors are essential but difficult. Axial variations of flow and thermal parameters increase the cost of numerical simulations and restrict the application of analytical solutions. This work aims to find approximate analytical solutions for the acoustic field in annular ducts with linear gradients of axially non-uniform cross-sectional area and mean temperature. These solutions can be applied in low-order acoustic network models and enhance the ability of analytical methods to solve thermoacoustic instability problems in real annular chambers. A modified WKB method is used to solve the wave equation for the acoustic field, and an analytical solution with a wide range of applications is derived. The derivation of the equations requires assumptions such as low Mach number, high frequency and small non-uniformity. Cases with arbitrary distributions of cross-sectional surface area and mean temperature can be solved by the piecewise method as long as the assumptions are satisfied along the entire chamber.

环形燃烧器中热声不稳定性的预测是必不可少的，但也很困难。流动和热参数的轴向变化增加了数值模拟的成本并限制了解析解的应用。这项工作旨在为具有轴向非均匀横截面积和平均温度的线性梯度的环形管道中的声场找到近似解析解。这些解决方案可应用于低阶声学网络模型，并增强分析方法解决实际环形室中热声不稳定性问题的能力。采用改进的WKB方法求解声场波动方程，推导出具有广泛应用的解析解。方程的推导需要假设，例如低马赫数，高频和小的非均匀性。只要整个腔室的假设都得到满足，横截面积和平均温度可以任意分布的情况就可以用分段法求解。