Résumé:
We present a numerical study of swirling flows with heat transfer generated by two rotating end disks (co- and counterrotating)inside a cylindrical enclosure having an aspect ratio equals to 2, filled with a liquid metal, and submitted to a vertical temperature gradient and an axial magnetic field, is studied. The study is divided into two parts.
The first part of this study concerns the axisymmetric flow, 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 oscillatory regime, results are presented for various values of the Hartmann number, Ha=0,5, 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, Recr. Stability diagrams are established according to the numerical results of this investigation. These diagrams put in evidence the dependence of Recr with the increase of Ha for various values of Ri.
The second part, present the numerical results of the three-dimensional flow which were obtained by Fluent of the same configuration. The flow produced by co-rotating, when Re is increased, the axisymmetric basic state loses stability to circular patterns of axisymmetric vortices and spiral waves. In mixed convection we have found that, the first instabilities to nonaxisymmetric flow have azimuthal wavenumber m=1 .In counter-rotation case, when Re is increased, the axisymmetric basic state loses stability and different complex flows appear successively: steady states with an azimuthal wavenumber of 1 (called M), traveling waves (TW), near-heteroclinic cycles (Het), and steady states with an azimuthal wavenumber of 2 (P). With in particular the appearance of mode m=3 for Ha=20. The branch of steady states with m = 1 is the first to bifurcate from the basic state in mixed convection as Re increases .The flow between co-rotating end disks is very ifferent as the flow between counter-rotating end disks. Finally, a bifurcation diagrams are established and this study confirms the possibility of stabilization of a liquid metal flow by application of an axial magnetic field.
