Hydrodynamic modes in the turbulent mixing layer over a cavity can constructively interact with the acoustic modes of that cavity and lead to aeroacoustic instabilities. The resulting limit cycles can cause undesired structural vibrations or noise pollution in many industrial applications. To further the predictive understanding of this phenomenon, we propose two physics-based models which describe the nonlinear aeroacoustic response of a side branch aperture under harmonic forcing with variable acoustic pressure forcing amplitude $p_a$. One model is based on Howe's classic formulation that describes the shear layer as a thin vortex sheet, and the other is based on an assumed vertical velocity profile in the side branch aperture. These models are validated against experimental data. Particle image velocimetry (PIV) was performed to quantify the turbulent and coherent fluctuations of the shear layer under increasing $p_a$. The specific acoustic impedance $Z$ of the aperture was acquired over a range of frequencies for different bulk flow velocities $U$ and acoustic pressure forcing amplitudes $p_a$. In this work, we show that once the handful of parameters in the two models for $Z$ have been calibrated using experimental data at a given condition, it is possible to make robust analytical predictions of this impedance over a broad range of the frequency, bulk flow velocity, and forcing amplitude. In particular, the models allow prediction of a necessary condition for instability, implied by negative values of the acoustic resistance $\mathrm{Re}\left(Z\right)$, which corresponds to a reflection coefficient $R$ of the aperture with magnitude larger than 1. Furthermore, we demonstrate that the models are able to describe the nonlinear saturation of the aeroacoustic response caused by alteration of the mean flow at large forcing amplitudes, which was recently reported in literature. This effect stabilizes the coupling between the side branch opening and the acoustic field in the cavity, and its quantitative description may be of value for control of aeroacoustic instabilities. We visualize and compare the models' representations of the hydrodynamic response in the side branch aperture and of the saturation effect under increasing $p_a$.

中文翻译：

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湍流掠流作用下侧向受力侧支孔的非线性空气声响应建模

腔体上的湍流混合层中的流体动力模式可能会与该腔体的声学模式建设性地相互作用，并导致空气声学的不稳定性。在许多工业应用中，由此产生的极限循环会导致不希望的结构振动或噪声污染。为了进一步对此现象进行预测性理解，我们提出了两个基于物理学的模型，它们描述了在谐波强迫和可变声压强迫幅度下侧支孔的非线性空气声响应。$p_{\mathrm{一种}}$。一种模型基于Howe的经典公式，该公式将剪切层描述为薄旋涡片，另一种模型基于假设的侧分支孔中的垂直速度分布。这些模型已针对实验数据进行了验证。进行了粒子图像测速（PIV）以量化在增加下剪切层的湍流和相干波动$p_{\mathrm{一种}}$。比声阻抗$ž$ 在不同的整体流速下，在一定频率范围内获取了孔径的 $ü$ 和声压强迫振幅 $p_{\mathrm{一种}}$。在这项工作中，我们表明，一旦两个模型中的少数几个参数用于$ž$如果使用给定条件下的实验数据对这些阻抗进行校准，则可以在很宽的频率，整体流速和强迫幅度范围内对该阻抗进行可靠的分析预测。尤其是，这些模型允许预测不稳定性的必要条件，这是由声阻的负值暗示的$\mathrm{回覆}（ž）$，对应于反射系数 $\mathrm{[R}$孔径大于1的孔径。此外，我们证明了该模型能够描述由大强迫幅度下的平均流量变化引起的气动响应的非线性饱和，这在文献中已有报道。该效果稳定了侧分支开口与空腔中声场之间的耦合，并且其定量描述可能对控制空气声不稳定性具有价值。我们可视化并比较了模型在侧分支孔中的水动力响应以及在增加的情况下的饱和效应的表示。$p_{\mathrm{一种}}$。