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Mechanism of Disappearance of Vortex Breakdown in a Confined Flow

Abstract:

Abstract: This experimental and numerical work explains why a vortex breakdownbubble first emerges and then disappears as the fluid rotation speedsup. To this end, we explore a flow in a sealed cylindrical containerwith one end disk rotating and all other walls stationary. The rotationdrives the meridional circulation: the fluid filling the container movesaway from the rotating disk along the sidewall, converges to the axisnear the stationary disk, and goes back to the rotating disk near theaxis. As the rotation speed Re increases, a cell of countercirculation—a vortex breakdown bubble (VBB)—emerges, expands, contracts,and disappears. On the (h, Re) map, the boundary of the VBB regionconsists of two branches, which meet and terminate at a fold point as hdecreases (h= H/R,where His the height and Ris the radius of the cylinder). This study is the first to focus on theVB disappearance and explains the geometry of VBB region: why the VBBfirst emerges and then disappears as Re increases at a fixed h. In a fewwords, the mechanism is as follows. The convergence of the swirling flowto the axis reduces the pressure above the center of the stationarydisk. Suction because of the reduced pressure creates a VBB and attractsit closer to the disk. This VBB shift deteriorates the flow convergenceto the axis and concentrates the meridional circulation near thesidewall. The pressure grows above the still disk, the suction weakens,which kills the VBB, and the fluid stagnates near the axis. Thismechanism is even more pronounced in a two-fluid flow.