Acoustic impedance of a cylindrical orifice
Acoustic impedance of a cylindrical orifice
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DOI：
10.1017/jfm.2020.187
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发表时间：
2020-06-10
影响因子：
3.7
通讯作者：
Schnitzer, Ory
中科院分区：
文献类型：
--
作者：
Brandao, Rodolfo;Schnitzer, Ory
我们使用匹配渐近推导出的解析公式的亚波长孔组成的圆柱形穿孔的刚性板的声阻抗。在无粘性的情况下，由于瑞利的孔的长度的端部校正示出构成一个指数精确的近似在限制的孔的纵横比是大的;在相反的限制，我们推导出一个代数精确的校正，取决于对数的纵横比，在零厚度屏幕的圆孔的阻抗。粘性效应被认为是在薄的斯托克斯边界层的限制，在那里的边界层分析结合互易参数提供了扰动的阻抗作为一个正交的基本无粘流。我们表明，对于大的纵横比，后者的扰动可以捕获指数精度通过引入第二端校正，其值计算在文献中常用的两个猜测之间，我们还推导出一个代数精确的近似在小纵横比的限制。粘性理论表明，阻力表现出最小值作为纵横比的函数，与孔半径保持固定。很明显，阻力在长的长宽比极限中增加;在相反的极限中，由于靠近孔口的尖锐边缘的大速度，阻力被放大。只有当板的厚度与斯托克斯边界层一样薄时，后一种放大作用才停止。本文导出的解析近似可用于改进谐振声学器件的电路建模。
We use matched asymptotics to derive analytical formulae for the acoustic impedance of a subwavelength orifice consisting of a cylindrical perforation in a rigid plate. In the inviscid case, an end correction to the length of the orifice due to Rayleigh is shown to constitute an exponentially accurate approximation in the limit where the aspect ratio of the orifice is large; in the opposite limit, we derive an algebraically accurate correction, depending upon the logarithm of the aspect ratio, to the impedance of a circular aperture in a zero-thickness screen. Viscous effects are considered in the limit of thin Stokes boundary layers, where a boundary-layer analysis in conjunction with a reciprocity argument provides the perturbation to the impedance as a quadrature of the basic inviscid flow. We show that for large aspect ratios the latter perturbation can be captured with exponential accuracy by introducing a second end correction whose value is calculated to be in between two guesses commonly used in the literature; we also derive an algebraically accurate approximation in the small-aspect-ratio limit. The viscous theory reveals that the resistance exhibits a minimum as a function of aspect ratio, with the orifice radius held fixed. It is evident that the resistance grows in the long-aspect-ratio limit; in the opposite limit, resistance is amplified owing to the large velocities close to the sharp edge of the orifice. The latter amplification arrests only when the plate is as thin as the Stokes boundary layer. The analytical approximations derived in this paper could be used to improve circuit modelling of resonating acoustic devices.