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A boundary element analysis on acoustic dissipation by wall visco-thermal boundary layer

壁面粘热边界层声耗散的边界元分析

基本信息

批准号：
10650596
负责人：
TERAO Michihito
金额：
$ 2.18万
依托单位：
Kanagawa university
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 1999
项目状态：
已结题

项目摘要

On acoustic energy dissipation at wall surfaces, especially at the solid surfaces of the apertures of resonators of Helmholtz type, the viscosity and thermal conductance there plays the leading role. By using the Stokes theory for the viscous mode and the Kirchhoff theory for the thermal mode, explicit expressions can been given for the acoustic resistance of the aperture of simple shape such as a long round tube. However for n neck of general shape with finite length, we have to solve implicit relationships between acoustic mode wave and the visco-thermal boundary layer.We employed a boundary element numerical approach along with the substructure techniques for the acoustic mode fields, and implemented a computer code to combine the acoustic mode and the visco-thermal mode through the effective acoustic mode admittance for the visco-thermal boundary layer. This admittance was derived from the Stokes and Kirchhoff theories, and includes the Laplacian of the acoustic pressure over the acoustic mode boundary. We took a finite difference approach for the Laplacian operation by employing the constant boundary element.To investigate the effectiveness of the numerical simulation, we conducted a series of numerical simulations and experiments for the dissipation factors of slit resonators, and compared the results. In the experiments, rigid specimens of highly precise dimensions are used. Consequently, the agreement between the dissipation factor by the numerical simulation and that by the experiment was excellent, as far as boundary element dimension was 0.1 mm or finer. To reduce the requirement of this fine element size, the use of a third order approximation element is under investigation.

在壁面，特别是亥姆霍兹型谐振器孔的固体表面上的声能耗散，那里的粘性和热导起着主导作用。对粘性模态采用Stokes理论，对热模态采用Kirchhoff理论，给出了长圆管等简单形状孔的声阻的显式表达式。本文采用边界元数值方法沿着子结构技术求解声学模态场，并通过计算粘热边界层的有效声学模态导纳，实现了声学模态和粘热模态的联合收割机耦合。该导纳从斯托克斯和基尔霍夫理论导出，并且包括声学模式边界上的声压的拉普拉斯算子。为了验证数值模拟的有效性，我们对狭缝谐振腔的损耗因子进行了一系列的数值模拟和实验，并对结果进行了比较。在实验中，使用了高精度尺寸的刚性试样。因此，数值模拟的耗散因子与实验的耗散因子之间的一致性非常好，只要边界元尺寸为0.1 mm或更小。为了减少这种精细元件尺寸的要求，正在研究使用三阶近似元件。