Vortex Breakdown Flows in Cylindrical Geometry

摘要

This paper reports the numerical results of swirling flows driven in cylindrical container by constantly rotating the bottom disc while either no-slip or free-slip boundary condition is imposed on the top lid. For the closed cylinder case, axisymmetric steady state solutions exhibit good agreement with available experimental measurements on the parameter dependency of the flow pattern as well as the position of stagnation points on the axis of rotation when the values of parameters are within the range of axisymmetric flows. Based on the numerical solutions, the idea in [1] is pursued under an effort to predict the position of stagnation points by means of using simple criteria. A reduced equation is derived by post-processing the momentum equations which successfully approximates the Re dependency of the axial position of the stagnation points. For the cylinder with top free-slip case, extensive parametric study was performed over a wide parameter space which includes parameter regions not fully explored by the previous studies. Momentum balance, whose information is ignored in the previous studies is examined in detail and it is shown that the nature of the flow is different between the flows with small h and these with large h for this flow configuration. While simulated flow state diagram plotted on the (h, Re) plane for the top no-slip condition case exhibits good agreement with the previous simulation by Brons et al. [2], the counterpart for the top free-slip case does not coincide qualitatively with their numerical simulation [3] on some of the small parameter ranges. It is suggested furthermore that there is a possibility that many such small ranges exist which were not noticed in the previous numerical studies. These numerically predicted flow states are not yet confirmed by the experimental visualization nor by the full three-dimensional numerical computation and the results are open to the future studies.