Abstract

Finite element solution for the classical problem of swirl flow in a cylinder with a rotating lid has been used to study the characteristic features of the stream-tube and identify the factors contributing to axial vortex breakdown. An increase of rotational Reynolds number has been found to result in (i) a decrease of total flow rate; (ii) an increase of flow rate through the boundary layer over the stationary walls; (iii) an increase of the throat area of the stream-tube, with the upstream axial vortex flow in some cases having a deficit in momentum flux needed to overcome the pressure and viscous forces; and (iv) an increase of distance for the axial flow to sustain deceleration in the diverging passage. Based on the analysis, it is hypothesized that “flow with particles in axial vortex motion having a deficit of momentum flux for axial flow when subjecting to a fluctuating radial force undergoes axial vortex breakdown.” This explanation has been able to justify the disappearance of vortex breakdown at larger Re of laminar regime and the absence of vortex breakdown in small aspect ratio cylinders. We report novel results pertaining to total flow rate and its distribution within the vessel. The momentum flux of axial vortex, a main determinant of bubble breakdown, is found to be governed by the total flow rate, distribution of flow through the boundary layers, and the Reynolds number. The proposed hypothesis has been verified by analyzing two cases, one involving a passive and the other involving an active mechanism for regulating the axial momentum.

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