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Bifurcation phenomena in the flow through a sudden expansion in a pipe.

通过管道中突然膨胀的流动时出现分叉现象。

基本信息

批准号：
EP/E013724/1
负责人：
Kenneth Cliffe
金额：
$ 17.94万
依托单位：
University of Nottingham
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2007
资助国家：
英国
起止时间：
2007 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FE013724%2F1
关键词：
Bifurcation phenomena flow through sudden

项目摘要

Flows through a pipe with a sudden expansion are of both fundamentaland practical interest. They arise in many engineering applicationsranging from heat exchangers to combustion chambers and inphysiological problems such as the flow past stenoses. They alsoprovide examples of open fluid flows with the complexities ofseparation and reattachment and have been used to test computationalfluid dynamics algorithms. In some situations the flow geometry canusefully be considered as two-dimensional where we showed thatmid-plane symmetry of the flow is broken at pitchfork bifurcation as the Reynolds number, Re, is increased. Thus thesymmetric flow loses stability to a pair of asymmetric states at acritical Re. The bifurcation structure was revealed in a combinednumerical and experimental investigation which also highlighted theimportance of imperfections in the experiment andthis has stimulated a great deal of other research on the topic andour paper has more than eighty citations to date.The equivalent problem of laminar flows in the axisymmetric geometryon the other hand remains largely uninvestigated and is untested asa bifurcation problem. The primary objective of the planned investigation will be to establish the precise nature of the instability and obtain quantitativeagreement with the results of a parallel numerical bifurcationstudy.We will also seek possible connections with modern research on finite amplitude states in pipe flow, if time permits.

突然膨胀管道中的流动是一个既有基础又有实际意义的问题.它们出现在许多工程应用中，从热交换器到燃烧室，以及生理问题，如狭窄处的流动。它们也提供了开放的流体流动的例子与分离和再附着的复杂性，并已被用来测试计算流体动力学算法。在某些情况下，流动的几何形状可以有效地被认为是二维的，我们表明，随着雷诺数Re的增加，流动的中面对称性在分叉处被破坏。因此，对称流在临界Re处失去稳定性，变成一对非对称状态。分叉结构是在数值和实验相结合的研究中揭示的，这也突出了实验中缺陷的重要性，这激发了大量关于这个主题的其他研究，我们的论文迄今已有80多篇引文.另一方面，轴对称几何中层流的等效问题在很大程度上仍未被研究，也未被检验阿萨分叉问题.计划研究的主要目标是确定不稳定性的精确性质，并获得与并行数值分叉研究结果的定量一致性。如果时间允许，我们还将寻求与管流中有限振幅状态的现代研究的可能联系。