| Summary: | 碩士 === 國立中興大學 === 應用數學系所 === 100 === This study investigated the flow bifurcations of the flows driving by pressure gradient in a rectangular curved tube. While the fluid flowing within a curved tube, due to the centrifugal effect, the secondary vortices can be induced in the cross section of the tube. The secondary flow states are dependent on the magnitude of the pressure gradient (q) and the aspect ratio (γ). In this study, the continuation method was applied to investigate the flow bifurcations in the curved tube with the increase in the pressure gradient and the aspect ratio.
The bifurcation diagrams are composed of a lot of solution branches and the solution branches are linked by limiting points or bifurcation points. The flow states in a solution branch belong to the same group. The existent regions of the flow states and the relationship between the states can also be distinguished from the bifurcation diagrams. In this study, two type of bifurcation diagrams were found, one is in the range of 0.9<γ<1.17, and another is in the range of 1.18<γ<1.25. The existent regions of the stable flows in the pressure gradient and the aspect ratio are determined from the bifurcation diagrams.
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