Numerical Study of Steady Axisymmetric Vortex Breakdown in a Cylindrical Container (lst Report, Limiting Reynolds Number of the Occurrence of Vortex Breakdown and the Location of Stagnation Point)

摘要

Numerical study is performed on the steady axsymmetric vortex breakdown within a cylindrical container with a rotating top lid. The cylindrical container is filled with incompressible viscous fluid and the swirling flow is driven in the container by the top lid rotating at a constant anguler velocity. This flow problem is governed by a combination of two non-dimensional physical parameters, i. e., the Reynolds number Re and the container aspect ratio h. In the past experimental studies, the occurrence of vortex breakdown is known to be confined in a narrow range of h and Re and the region diagram of vortex breakdown was constructed. In the present numerical investigation, the region diagram is reconstructed for the first time by the numerical computation. The axisymmetry of the flow is assumed and the resulting system of governing equations are solved by the Ψ-Ω method. The comparison of the present region diagram obtained for the steady solutions and that obtained experimentally by Escudier exhibited good agreement. This cross check of limiting Re values for the occurrence of vortex breakdown confirms the reliability of both computational method and the experimental methodology. Based on the present numerical solutions, the locations of stagnation points for various aspect ratio h are calculated as functions of Re and these values are also compared with available experimental data. The outcome of present comparison confirms the belief that the steady vortex breakdown within a cylindrical container is actually axisymmetric. Further argument will be discussed in the proceeding studies.