用于氢-空气火焰热声分析的模态瑞利方法

《Journal of Fluid Mechanics》：A modal Rayleigh method for thermoacoustic analysis of hydrogen–air flames

　　

摘要 本文提出了一种频率分辨的模态瑞利方法，该方法利用动态模态分解（DMD）重新表述了经典瑞利判据。该方法能够提供模式特异的、封闭形式的热声激发与吸收度量。该框架通过声学标度重建压力和热释放场，利用有限时内核分离自模态和交叉模态贡献，并用相位不变的正交效率对同相瑞利项进行增强，以量化耦合强度。该方法被应用于在220、437和800 Hz及多音调驱动下、四个当量比（$\phi = 0.4, 0.5, 0.6, 0.7$）的二维、声学驱动的、消音的氢-空气狭缝火焰。分析表明，火焰-声学耦合主要集中在火焰尖端附近，耦合强度和频率响应随当量比呈系统性变化，低频驱动促进了能量向高次谐波的非线性传递。贫燃火焰保持近线性且在高频率下解耦，而锁定在较高频率驱动下的富燃火焰在较低频率下表现出更强的非线性畸变。在模态瑞利指数为正的区域，远场声压级在对应频率上增加，证实了所提出的度量能够隔离反馈有效模式。总体而言，基于DMD的模态瑞利方法为火焰-声学相互作用提供了一种紧凑的、模式分辨的描述。

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