2000 Fiscal Year Final Research Report Summary
TRANSITIONS AND INSTABILITIES OF FLOW IN A CHANNEL WITH A SUDDENLY EXPAN DED PART
| Project/Area Number |
09640494
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
物理学一般
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| Research Institution | DOSHISHA UNIVERSITY |
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Principal Investigator |
MIZUSHIMA Jiro DOSHISHA UNIVERSITY, DEPT.OF MECHANICAL ENGINEERING, PROFESSOR, 工学部, 教授 (70102027)
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| Project Period (FY) |
1997 – 2000
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| Keywords | CHANNEL FLOW / SUDDEN EXPANSION / STABILITY OF FLOW / BIFURCATION / TRANSITION TO TURBULENCE / PITCHFORK BIFURCATION / HOPF BIFURCATION |
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| Research Abstract |
Transitions and instabilities of flow in a symmetric channel with a suddenly expanded and contracted part are investigated theoretically by three different methods, i.e. the time marching method for dynamical equations, the SOR iterative method and the finite element method for steady-state equations. Linear and weakly nonlinear stability theories are applied to the flow. The transitions are confirmed experimentally by flow visualizations and velocity measurements. It is found that the flow is steady and symmetric at low Reynolds numbers, becomes asymmetric at a critical Reynolds number, gets the symmetry back at another critical Reynolds number and becomes oscillatory at very large Reynolds numbers. Multiple stable steady-state solutions are found in some cases, which lead to a hysteresis. The critical conditions for the existence of the multiple stable steady-state solutions are determined numerically and compared with the results of the linear and weakly nonlinear stability analyses. An exchange of modes for oscillatory instabilities is found to occur in the flow as the aspect ratio, the ratio of the length of the expanded part to its width, is varied, and its relation with the impinging free shear layer instability (IFLSI) is discussed. Transitions of flow in a channel with an inlet and two outlets are also investigated and the pressure distribution in the flow fields is obtained numerically.
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