Stability of conducting fluid flow between coaxial cylinders under thermal gradient and axial magnetic field

Abstract

Numerical simulations were performed to investigate the bifurcation in swirling flow between two coaxial vertical cylinders produced by the thermal gradient. The suppressed effects of an axial magnetic field on both vortex breakdown and fluid layers are analyzed. The governing Navier-Stokes, temperature, and potential equations are solved by using the finite-volume method. A conducting fluid is placed in the gap between two coaxial cylinders characterized by a small Prandtl number (Pr = 0.032). Three annular gaps were R = 0.7, 0.8, and 0.9 compared in terms of flow stability, and heat transfer rates. The combination of aspect ratio =1.5 and Reynolds number, Re=1500 is the detailed case in this study. In the hydrodynamic case, vortex breakdown takes place near the inner cylinder due to the increased pumping action of the Ekman boundary layer. In addition, the competition between buoyancy and viscous forces develops a fluid layered structure. It is shown that the onset of the oscillatory instability set in by increasing Reynolds number to the critical value. The results show that with an intensified magnetic field, the vortex breakdown disappears, the number of fluid layers will be reduced and the onset of the oscillatory instability will be retarded. Stability diagrams corresponding to the limits of transition from the multiple fluid layers to the one fluid layer are obtained.