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.

本研究旨在研究在轴向磁场下充满导电粘性流体的垂直环带中的涡流击穿行为。考虑了三个环形间隙和环形高度与外筒半径的各种比率。底部圆盘旋转产生的 Ekman 边界层的泵送作用沿同轴圆柱的子午面建立了二次循环。对于雷诺数和纵横比的某些组合，涡流击穿气泡发生在内筒侧壁附近。使用有限体积法求解控制 Navier-Stokes 方程和势方程，其中存在稳定解。磁场、环形间隙的影响，再循环区的三维结构和涡流击穿位置的纵横比得到了发展。环形间隙的结果$\mathrm{电阻}=0.9$ 与那些 Escudier 的稳定性图进行比较，当 $\mathrm{电阻}=1.0$. 获得的结果表明，在磁场幅度超过临界值和电涡流被抑制之前，涡流击穿被抑制。稳定性图（Re – H/R${}_{○}$) 对应于在内筒侧壁附近发生的涡流击穿气泡。