Multiplicity Flow Solutions in a Four-Sided Lid-Driven Cavity

Abstract:

In this study, the continuation method was adopted to explore the flow field states and flow bifurcation of incompressible flow in a four-sided lid-driven square cavity. The four plates moved at the same velocity and the opposite plates moved in opposite directions to drive the fluid in the cavity to flow. The flow bifurcation of the cavity flow when changing the driving velocity of the four plates simultaneously was discussed. The Reynolds number ranges of stable and unstable multiple solutions were determined from linear stability analysis of the obtained state solution. When the aspect ratio was 1 and the four plates were driven under the same velocity simultaneously, there were two pitchfork bifurcation points and two turning points in the flow bifurcation. Between the bifurcation points and turning points, there were two stable asymmetric solutions and one unstable symmetric solution existing. The flow bifurcation of the four-sided lid-driven cavity flow was analyzed by changing the driving velocity of two side plates when the top and bottom plates moved at the same velocity in opposite directions. According to the numerical results, when the Reynolds number of the top and bottom plates was fixed at 250 and the driving velocity of two side plates was changed, there were two non-crossing solution branches in the flow bifurcation, and one solution branch had strongly asymmetric stable solution. The other solution branch existed in the whole range of Reynolds number, and had one asymmetric stable solution. According to the bifurcation diagram, there were two asymmetric stable solutions and one symmetric unstable solution in the region of Reynolds number greater than 144, and there was only one asymmetric stable solution in the region of Reynolds number less than or equal to 144.

• Periodical: Applied Mechanics and Materials (Volumes 368-370)
• Pages: 838-843
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.368-370.838
• Online since: August 2013
• Authors: Kuen Tsann Chen, Chih Ching Tsai, Win Jet Luo
• Keywords: Cavity Flow, Continuation Method, Flow Bifurcation, Reynolds Number

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