Quadrupole correlations governing the pattern of jet noise
Quadrupole correlations governing the pattern of jet noise
复制标题
控制喷射噪声模式的四极相关性
DOI：
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发表时间：
1967
影响因子：
3.7
通讯作者：
H. Ribner
中科院分区：
文献类型：
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作者：
H. Ribner
对流和折射的影响主导了喷流噪声的心形模式。这些都可以被修正，以产生涡流噪声发生器的小的“基本方向性”。Ribner(1963,1964)在假设各向同性湍流叠加在平均切变流动上的Lighthill理论的变体中预测了观测到的准椭球图案。这具有处理四极杆的联合效应而不单独展示它们的特点。本文对理论进行了重新表述，以计算不同的四极自相关和互相关对在给定方向上发出的声音的相对贡献。更正了一些小错误。在36个可能的四极关联中，只有9个对圆喷流的轴对称噪声模式产生了明显的非零贡献。这些关联贡献了COS4θ、COS2θSIN2θ或SIN4θ方向图，其中θ是与喷流轴的夹角。可以将其分离成称为“自噪声”(单独来自湍流)和“剪切噪声”(共同来自湍流和平均流)的部分。九种自噪声模式组合为$A；cos^4 heta(1)+A；cos^2sin^2 heta(frac{7}{8}+frac{7}{8}+frac{1}{8}+frac{1}{8})+A sin^2 heta(Frc{12}{32}&+&Frc{12}{32}+Frc{7}{32}+Frc{1}{32})\&=&A(cos^2 heta+sin^heta)^2=A；这在所有方向上都是一致的，因为它必须是各向同性湍流产生的。两个非零切变噪声相关图样合并为$B；cos^4 heta(1)+B；cos^2 heta sin^2 heta(frc{1}{2})=B(cos^2 heta+sin^2 heta)^2=A；因此，总体的“基本”图样(自噪声加剪切噪声)具有A+B(coS_2θ+coS_4θ)/2的形式；这与先前的结果略有不同。尺寸常数A和B具有相似的量级；因此，通过喷流轴的任何平面上的图案类似于适度偏心的椭圆。在前面工作的基础上，还讨论了频谱。由于自噪声与湍流速度分量成二次函数关系，而剪切噪声仅与剪切噪声成线性关系，因此自噪声相对向高频方向移动。这与折射图相结合，解释了在与轴线成小角度时辐射的喷流噪声的更深音调。最后，预测结果与最近的实验结果是一致的。
The effects of convection and refraction dominate the heart-shaped pattern of jet noise. These can be corrected out to yield the small ‘basic directivity’ of the eddy noise generators. The observed quasi-ellipsoidal pattern was predicted by Ribner (1963, 1964) in a variant of the Lighthill theory postulating isotropic turbulence superposed on a mean shear flow. This had the feature of dealing with the joint effects of the quadrupoles without displaying them individually. The present paper reformulates the theory so as to calculate the relative contributions of the different quadrupole self and cross-correlations to the sound emitted in a given direction. Some minor errors are corrected. Of the thirty-six possible quadrupole correlations only nine yield distinct non-vanishing contributions to the axisymmetric noise pattern of a round jet. The correlations contribute either cos4θ, cos2θ sin2θ or sin4θ directional patterns, where θ is the angle with the jet axis. A separation into parts called ‘self noise’ (from turbulence alone) and ‘shear noise’ (jointly from turbulence and mean flow) may be made. The nine self-noise patterns combine as $A; cos^4 heta(1)+A; cos^2sin^2 heta(frac{7}{8}+frac{7}{8}+frac{1}{8}+frac{1}{8})+A sin^2 heta (frac {12}{32} & + & frac{12}{32}+frac{7}{32}+frac{1}{32})\ & = & A(cos^2 heta+sin^ heta)^2 = A;$ this is uniform in all directions as it must be, arising from isotropic turbulence. The two non-vanishing shear-noise correlation patterns combine as $B;cos^4 heta (1) + B;cos^2 heta sin^2 heta(frac{1}{2})=B(cos^2 heta+sin^2 heta)^2 = A;$ The overall ‘basic’ pattern (self noise plus shear noise) thus has the form A + B(cos2θ + cos4θ)/2; this is a slight change from the previous result. The dimensional constants A and B are of comparable magnitude; the pattern in any plane through the jet axis thus resembles an ellipse of modest eccentricity. Frequency spectra are also discussed, following the earlier work. Since the self noise depends quadratically on turbulent velocity components and the shear noise only linearly, there is a relative shift of the self noise to higher frequencies. This in conjunction with refraction figures in the explanation of the deeper pitch of jet noise radiated at small angles to the axis. Finally, the predictions are shown to be compatible with recent experimental results.