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The effect of the convective momentum transfer on the acoustic boundary condition of perforated liners with grazing mean flow
International Journal of Aeroacoustics ( IF 1 ) Pub Date : 2021-07-07 , DOI: 10.1177/1475472x211023842
Anita Schulz 1 , Dirk Ronneberger 2 , Chenyang Weng 3 , Friedrich Bake 4
Affiliation  

The interaction of sound with sound-permeable hard walls subjected to grazing mean flow is investigated with a focus on the sound-induced exchange of streamwise momentum between the mean flow and the wall. Two generic wall types have to be distinguished, the homogeneously permeable wall and the wall with clearly separated openings, which is a more realistic model of technically feasible walls. To begin with, the focus is on the shear stress that drives the dynamics of the shearing mean flow over the homogeneous wall. This is analyzed by means of two simple mathematical models of shear stress diffusion, which come as two equivalent pairs of differential equations either for the acoustic shear stress and the wall-normal displacement, or for the streamwise and the wall-normal components of the acoustic velocity. The physical analysis is concentrated on the relation between shear stress and the wall-normal displacement of the fluid elements, which determines the effective admittance of the wall. The shear stress is represented by the momentum transfer impedance which is defined as the ratio between the acoustic wall shear stress and the in-wall velocity evaluated at the wall. It turns out that the strong increase of the acoustic wall shear stress due to transfer of mean flow momentum to the wall is the dominating mechanism which affects the effective admittance of the wall. Nevertheless, the suitability of the momentum transfer impedance as part of a complete boundary condition of the wall is questioned. The disagreement between the predicted momentum transfer impedance and some rare experimental data obtained with real inhomogeneous walls is considered as a strong indication that some further mechanisms are invoked by the inhomogeneity of real walls which are briefly discussed with regard to future studies.



中文翻译:

对流动量传递对掠平均流射孔衬管声学边界条件的影响

研究了声音与受平均流作用的透声硬壁的相互作用,重点是平均流和壁之间由声音引起的流向动量交换。必须区分两种通用墙类型,均质渗透墙和具有明显分开的开口的墙,这是技术上可行的墙的更现实模型。首先,重点是驱动均匀壁上剪切平均流动力学的剪切应力。这是通过两个简单的剪应力扩散数学模型进行分析的,它们是声学剪应力和壁法向位移的两个等效微分方程对,或者声学的流向和壁法向分量速度。物理分析集中在剪切应力与流体单元的壁法向位移之间的关系上,这决定了壁的有效导纳。剪切应力由动量传递阻抗表示,该阻抗定义为声壁剪切应力与壁内评估的壁内速度之间的比率。结果表明,由于平均流动动量向壁的转移而导致的声壁剪切应力的强烈增加是影响壁有效导纳的主要机制。然而,动量传递阻抗作为壁的完整边界条件的一部分的适用性受到质疑。

更新日期:2021-07-08
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