Numerical Simulation of Unsteady Driven Cavity Flow

概要

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A numerical study is performed on the flow of an incompressible fluid driven in a square cavity. The behavior of unsteady flows beyond the first Hopf bifurcation is investigated. The first Hopf bifurcation is localized at \mathit{Re}_{\text{cr1}}=7987\pm 0.2% with the fundamental frequency f_{\text{B}}=0.4519, in good agreement with the previous studies. A secondary Hopf bifurcation occurs at \mathit{Re}_{\text{cr2}}=9575\pm 3%, which generates a quasi-periodic solution with two incommensurable frequencies f_{\text{B}} and f_{\text{H}}, up to the annihilation of f_{\text{B}} at \mathit{Re}_{\text{cr3}}=10975\pm 2%. While quasi-periodic flow is observed for \mathit{Re}_{\text{cr2}}\leq\mathit{Re}\leq\mathit{Re}_{\text{cr3}} on this solution branch, another branch of the periodic solution with fundamental frequency f_{\text{L}} (<f_{\text{H}}) appears for \mathit{Re}\geq\mathit{Re}_{\text{cr1\scale70%'}}=9310\pm 2% (<\mathit{Re}_{\text{cr2}}) via a subcritical Hopf bifurcation. Bistable periodic solutions with fundamental frequencies f_{\text{H}} and f_{\text{L}} coexist for \mathit{Re}_{\text{cr3}}\leq\mathit{Re} up to about 18400, which is the highest \mathit{Re} computed in the present study.
2011-09-15