Surface modes in sheared boundary layers over impedance linings
Surface modes in sheared boundary layers over impedance linings
复制标题
阻抗衬里上剪切边界层的表面模式
DOI：
10.1016/j.jsv.2013.02.028
复制
发表时间：
2013
影响因子：
4.7
通讯作者：
E. Brambley
中科院分区：
文献类型：
--
作者：
E. Brambley
表面模式，管道模式本地化接近管道壁，分析内衬圆柱形管道与均匀流除了薄边界层。以及完整的数值解的Pridmore-Brown方程，简化的数学模型给出管道衬里和边界层集中在一起，并使用一个单一的边界条件（修改的Myers边界条件以前提出的作者），从表面模式的色散关系。对于一个给定的频率，多达六个表面模式被证明存在，而不是最大的四个均匀滑移流。不仅是不同的数量和行为的表面模式的频域模式匹配技术，这取决于匹配过程中发现所有相关模式的重要性，但薄的边界层也示出导致不同的对流和绝对稳定性比均匀滑移流。数值例子给出比较的预测的表面模式色散关系的Pridmore-Brown方程的完整的解决方案，和表面模式预测的准确性被证明是显着增加相比，均匀的滑移流假设。不仅边界层厚度的重要性，但它的轮廓（双曲正切或线性）证明。在质量弹簧阻尼器或亥姆霍兹谐振器阻抗模型的假设下，还进行了Briggs-Bers稳定性分析。
Surface modes, being duct modes localized close to the duct wall, are analysed within a lined cylindrical duct with uniform flow apart from a thin boundary layer. As well as full numerical solutions of the Pridmore-Brown equation, simplified mathematical models are given where the duct lining and boundary layer are lumped together and modelled using a single boundary condition (a modification of the Myers boundary condition previously proposed by the author), from which a surface mode dispersion relation is derived. For a given frequency, up to six surface modes are shown to exist, rather than the maximum of four for uniform slipping flow. Not only is the different number and behaviour of surface modes important for frequency-domain mode-matching techniques, which depend on having found all relevant modes during matching, but the thin boundary layer is also shown to lead to different convective and absolute stability than for uniform slipping flow. Numerical examples are given comparing the predictions of the surface mode dispersion relation to full solutions of the Pridmore-Brown equation, and the accuracy with which surface modes are predicted is shown to be significantly increased compared with the uniform slipping flow assumption. The importance of not only the boundary layer thickness but also its profile (tanh or linear) is demonstrated. A Briggs–Bers stability analysis is also performed under the assumption of a mass–spring–damper or Helmholtz resonator impedance model.