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首页> 外文期刊>European Journal of Mechanics, B. Fluids >Insight into the two-source structure of the jet noise spectrum using a generalized shell model of turbulence
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Insight into the two-source structure of the jet noise spectrum using a generalized shell model of turbulence

机译：使用广义湍流壳模型洞察射流噪声谱的两源结构

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摘要

There is a large body of experimental evidence which shows that the jet noise spectrum is composed of two sources. Our aim here is to prove, mathematically, that the two-source paradigm can be derived using a minimum number of self-consistent approximations based on our current knowledge of jet turbulence in cold flows. The starting point of the paper is Goldstein's (2003) [20] exact re-arrangement of the Navier-Stokes equations, which shows that turbulence enters the acoustic spectrum formula through the Reynolds stress auto-covariance tensor. We extend the shell model of turbulence using a more general symmetry approximation that amounts to assuming that the Reynolds stress auto-covariance is, firstly, axi-symmetric, and secondly is equivalent to the same tensor only after it has been averaged (point-wise) over the azimuthal separation. As a consequence of these two assumptions, the space-time Fourier transform of the Reynolds stress auto-covariance (which we refer to as the spectral tensor) depends on the transverse wave vector only through the square of its magnitude and, moreover, is also an axi-symmetric tensor. This defines the generalized shell model (or GSM) and we apply it to the jet noise problem. The final result shows that the acoustic spectrum can be written as the sum of two groups of terms, one of which corresponds to the peak jet noise in the weakly non-parallel flow limit.
机译：有大量的实验证据表明，射流噪声谱由两个来源组成。我们的目的是在数学上证明，根据我们目前对冷流中射流湍流的了解，可以使用最少数量的自洽近似来推导两源范式。本文的起点是Goldstein（2003）[20]对Navier-Stokes方程的精确重排，这表明湍流通过雷诺应力自协方差张量进入声谱公式。我们使用更通用的对称近似来扩展湍流的壳模型，该近似近似等于假设雷诺应力自协方差首先是轴对称的，其次才是在对等张量求平均后等效（点方向） ）在方位角上。由于这两个假设，雷诺应力自协方差的时空傅立叶变换（我们称为谱张量）仅取决于横波矢量的大小平方，而且还取决于横波矢量。轴对称张量。这定义了广义壳模型（或GSM），并将其应用于射流噪声问题。最终结果表明，声谱可以写为两组项之和，其中一组项对应于弱非平行流动极限中的峰值射流噪声。

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