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

管道中突然膨胀的流动既有基础意义又有实际意义。它们出现在许多工程应用中，从热交换器到燃烧室，以及诸如通过狭窄通道的流动等生理问题。它们还提供了具有分离和再附着复杂性的开放流体流动的示例，并已用于测试计算流体动力学算法。在某些情况下，流动几何可以被看作是二维的，其中我们表明，随着雷诺数Re的增加，流动的中平面对称性在干草叉分叉处被打破。因此，在临界Re处，对称流动失去了对不对称状态的稳定性。分岔结构在数值和实验调查中被揭示出来，这也突出了实验中不完善的重要性，这刺激了大量关于该主题的其他研究，我们的论文迄今为止被引用了80多次。另一方面，层流在轴对称几何中的等效问题在很大程度上仍未得到研究，也未作为分岔问题得到检验。计划调查的主要目的是确定不稳定性的确切性质，并获得与平行数值分岔研究结果一致的定量结果。如果时间允许，我们还将寻求与管道流动有限振幅状态的现代研究的可能联系。

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.