带冷却偏置流的亥姆霍兹共振器消声机理研究

亥姆霍兹共振器（HRs）是在实践中用于抑制热声振荡的典型被动控制装置。为了保护亥姆霍兹共振器免受燃烧室高温气流的侵蚀，一般从 HR 空腔的背面注入冷却偏流，其温度远低于燃烧室。然而，这导致了燃烧室中冷流和热流的动态混合，从而在 HR 下游产生熵波，影响 HR 的吸声性能。本文推导了一个具有不同温度偏流的亥姆霍兹共振器与一维燃烧室管道耦合的声类比模型。该模型提供了关于 HR 的存在和熵波的产生如何影响声场的机制，阐释了背后的物理机理。它是由线性化的质量、动量和能量守恒方程与线性亥姆霍兹共振器模型结合而导出的。与已有的耦合理论模型的结果进行对比，通过 COMSOL 数值模拟验证了声类比模型的准确性。从目前的声学类比模型可以清楚地看出，HR 的冷却偏置流对燃烧室管一维声场的影响是既提供了与质量相关的声源项，又提供了熵相关的声源项。从声学上来说，该质量相关源项和熵源项都是单极子声源。同时推导了一个熵模型，它表明冷却偏置流和热切向流的动态掺混过程产生的熵声源与质量相关声源相比是一个负源。如果偏置流温度高于切向流温度，则熵相关源项成为正源。

因此，与质量相关的声源相比，熵扰动可能作为正/负声源，这取决于偏置流的温度是高于还是低于切向流温度。通过我们进一步推导表明，该熵相关声源可以和质量相关声源合并转化为一个体积声源，由此得出带冷却偏流亥姆霍兹共振所带来的总的声源效应：其本质是一个体积声源，该体积源取决于共振器处的平均声速和密度，而不是燃烧室处的平均声速和密度。当偏流质量流量与切向流流量之比大于约 5% 时，共振器两侧的平均流参数的差异就不再可以忽略。

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