This paper studies the acoustic behavior inside the deep annular and cylindrical cavity at low Mach number. The turbulent shear layer above the cavity acts as a broadband noise source and drives resonant standing waves inside the cavity for various modes. According to previous investigation, those resonant standing waves inside the cavity play an important role in the aeroacoustic resonance of cavity noise, which gives perfect prediction of tonal frequency from the solution of wave equation. From the perspective of engineering application, it is more important to predict the spatial distribution of tonal intensity. It is needed to point out that the solution of the linear wave equation also provides the relative spatial distribution tonal intensity and the absolute value of tonal intensity can be determined from the acoustic experiments that is measured only at some locations. Based on this idea, a scheme is setup and validated to predict the amplitude spatial distribution of tonal intensity of aeroacoustic resonance. For example, an analytical model is established to provide the relative mode shape of aeroacoustic resonance in a simple geometry of cavity, which is realized by solving the wave equation with boundary conditions in a semi-closed space. This model considers the freestream velocity scaling and the depth correction factor varying with the Helmholtz number. The experimental aeroacoustic result is acquired by measuring the pressure fluctuation at some locations of cavity internal wall with the use of surface microphones. The experimental results are used to supplement and validate this analytical model. The amplitude spatial distribution at any freestream velocity (low Mach number) can be acquired by measuring the pressure fluctuation once at the leading edge or trailing edge of cavity bottom at an arbitrary Mach number, as the amplitude of most modes reaches its maximum here.

中文翻译：

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环形腔内声共振空间分布研究：频率和强度

本文研究了低马赫数下深环形和圆柱形腔内的声学行为。腔上方的湍流剪切层充当宽带噪声源，并驱动腔内各种模式的谐振驻波。根据以往的研究，空腔内的共振驻波在空腔噪声的气动声学共振中起重要作用，可以从波动方程的解中完美地预测音调频率。从工程应用的角度来看，预测色调强度的空间分布更为重要。需要指出的是，线性波动方程的解还提供了相对空间分布的音调强度，音调强度的绝对值可以从声学实验中确定，仅在某些位置进行测量。基于这一思想，建立并验证了一种用于预测气动声学共振音调强度的幅度空间分布的方案。例如，建立解析模型以提供腔体简单几何结构中气动声学共振的相对模态形状，这是通过在半封闭空间中求解具有边界条件的波动方程来实现的。该模型考虑了随亥姆霍兹数变化的自由流速度缩放和深度校正因子。实验气动声学结果是通过使用表面传声器测量空腔内壁某些位置的压力波动而获得的。实验结果用于补充和验证该分析模型。任何自由流速度（低马赫数）下的振幅空间分布可以通过测量任意马赫数下腔底前缘或后缘的压力波动来获得，因为大多数模式的振幅在这里达到最大值。