A Resolution Independent Solution for Confined Axisymmetric Vortex Breakdown Flow

Abstract

Numerical simulation is performed for the vortex breakdown flows induced in a cylindrical container with rotating top disk. Solutions are obtained for the parameter ranges where steady axisymmetric flows are stable with respect to asymmetric disturbances. By varying the number of grid points and applying the Richardson extrapolation, resolution independent solutions are obtained and flow state diagram is numerically constructed on (h, Re)-plane (Re is the Reynolds number and h is the cylinder aspect ratio). The value of critical Reynolds number for the creation of breakdown bubbles agrees on the average within 1% discrepancy with the previous experiments. Solutions obtained in the present study are expected to be useful as a benchmark solution vis-a-vis newly developed numerical methods are compared.

Keywords

• b-type vortex breakdown
• confined swirling flows
• richardson extrapolation
• benchmark solution