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

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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.