基于亥姆霍兹求解器预测和抑制燃气轮机环形燃烧室热声振荡

现代燃气轮机和航空发动机的燃烧室通常设计为沿周向均匀排布多个燃烧器
的环形结构。根据严苛低氮氧化物要求而采用的贫燃预混燃烧使得燃烧系统更易
发生声音与释热扰动的耦合，并最终导致热声振荡现象。这可能显著增加噪音和
氮氧化物的排放，导致燃烧室出现剧烈的压力振荡，甚至对结构造成不可逆转的
损坏。为了解决这个问题，在环形燃烧室中添加亥姆霍兹共振器、波长管等被动
控制方法被广泛使用。对于共振器的周向排布来说，根据其类型、数量以及安装
位置很容易产生数百万甚至数十亿种可能的排布方案。因此，快速找到最佳的共
振器排布方案是有效抑制热声振荡的关键。本文主要通过亥姆霍兹求解器预测燃
烧室热声模态，随后通过低阶网络模型从理论上求解共振器周向排布的最佳方案，
最终在燃烧室上进行数值结果验证。
首先，本文使用COMSOL 有限元软件对有热源的一维管路、引入BTM(燃烧
器传输矩阵) 的单燃烧器以及环形燃烧室模型进行热声模态预测，并与典型案例相
对比验证本文使用的亥姆霍兹求解器可以正确捕捉并预测热声模态。
然后，基于𝑘 − 𝜀 湍流模型和预混燃烧模型对重型燃气轮机进行RANS 数值计
算，得到燃烧系统的平均温度场、密度场等信息。并使用经典火焰传递函数(𝑛 − 𝜏
模型) 对火焰增益𝑛 和时间延迟𝜏 进行二维扫描，得到燃烧系统的热声模态衍化轨
迹图。由此预测了燃烧室的振荡频率区间，且该结果与实际机组运行中的振荡区
间吻合。
随后，通过建立周向一维共振器—燃烧室低阶网络模型研究了多类型多数量
共振器沿周向任意排布的不同方案。通过分析共振器在不同排布方案下的声学模
态得到了多个共振器的最佳周向排布—这种排布通常以较小或是零模态分裂强度
为标准，并且有着良好的不稳定性抑制效果。
最后，将最佳排布方案应用于真实环形燃烧系统中，通过在COMSOL 中求解
三维亥姆霍兹方程的数值方法捕获燃烧室的热声模式。通过在两个不同的周向排
布方案下进行火焰参数的扫描，捕捉到系统的热声模态的衍化轨迹并以此来验证
最佳排布方案的正确性。

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