Stability of Swirling Flows with Heat Transfer in a Cylindrical Enclosure with CO/Counter-Rotating End Disks Under an Axial Magnetic Field

Abstract

In this article, a numerical study of swirling flows with heat transfer generated by two rotating end disks (co- and counter-rotating) inside a cylindrical enclosure having an aspect ratio equal to 2, filled with a liquid metal, and submitted to a vertical temperature gradient and an axial magnetic field is studied. The governing Navier-Stokes, energy, and potential equations along with appropriate boundary conditions are solved by using the finite-volume method. The flow and temperature fields are presented by stream function and isotherms, respectively. This flow is very unstable and reveals a great richness of structures. In an oscillatory regime, results are presented for various values of the Hartmann number, Ha = 5, 10, 20 and 30, and Richardson numbers, Ri = 0, 0.5, 1, 2 and 4, in order to see their effects on the value of the critical Reynolds number, Re_cr. Stability diagrams are established according to the numerical results of this investigation. These diagrams show the dependence of Re_cr with the increase of Ha for various values of Ri. The flow between co-rotating end disks is very different from the flow between counter-rotating end disks. Finally, this study confirms the possibility of stabilization of a liquid metal flow by application of an axial magnetic field.