Mechanism of Disappearance of Vortex Breakdown in a Confined Flow

This experimental and numerical work explains why a vortex breakdown bubble first emerges and then disappears as the fluid rotation speeds up. To this end, we explore a flow in a sealed cylindrical container with one end disk rotating and all other walls stationary. The rotation drives the meridional circulation: the fluid filling the container moves away from the rotating disk along the sidewall, converges to the axis near the stationary disk, and goes back to the rotating disk near the axis. As the rotation speed Re increases, a cell of counter circulation—a vortex breakdown bubble (VBB)—emerges, expands, contracts, and disappears. On the (h, Re) map, the boundary of the VBB region consists of two branches, which meet and terminate at a fold point as h decreases (h =H/R h=H/R, where H H is the height and R R is the radius of the cylinder). This study is the first to focus on the VB disappearance and explains the geometry of VBB region: why the VBB first emerges and then disappears as Re increases at a fixed h. In a few words, the mechanism is as follows. The convergence of the swirling flow to the axis reduces the pressure above the center of the stationary disk. Suction because of the reduced pressure creates a VBB and attracts it closer to the disk. This VBB shift deteriorates the flow convergence to the axis and concentrates the meridional circulation near the sidewall. The pressure grows above the still disk, the suction weakens, which kills the VBB, and the fluid stagnates near the axis. This mechanism is even more pronounced in a two-fluid flow.