Magnetohydrodynamic effect on vortex breakdown zones in coaxial cylinders

Abstract

Abstract This research aims to investigate the behavior of vortex breakdown in vertical annuli filled with a conducting viscous fluid under the axial magnetic field. Three annular gaps and various ratios of annular height to the radius of the outer cylinder are considered. The pumping action of the Ekman boundary layer produced by rotation of the bottom disk sets up a secondary circulation along the meridional plane of the coaxial cylinders. For certain combinations of Reynolds numbers and aspect ratios, the vortex breakdown bubble occurred near to sidewall of the inner cylinder. The governing Navier–Stokes and potential equations are solved by using the finite-volume method, where a steady solution exists. The effects of the magnetic field, annular gaps, and aspect ratios on the three-dimensional structure of the recirculation zones and the position of vortex breakdown are developed. The results of the annular gap R = 0 . 9 are compared with those Escudier’s stability diagram when R = 1 . 0 . The results obtained showed that the vortex breakdown is suppressed beyond the magnitude of the magnetic field exceeds a critical value and before the suppression of the electric vortex occurs. The stability diagrams (Re–H/R o ) corresponding to which a vortex breakdown bubble occurred near to the sidewall of the inner cylinder are obtained.