Numerical and analytical study of rotating flow in an enclosed cylinder under an axial magnetic field

Rachid Bessaïh (1) , Mahfoud Kadja (2) , Kerstin Eckert (3) , Philippe Marty (4)

1 Faculté des Sciences de l'Ingénieur - Département de Génie Mécanique - Laboratoire d'Energétique appliquée et de Pollution
2 Laboratoire de thermo fluide
3 TU Dresden - Technische Universität Dresden = Dresden University of Technology
4 LEGI - Laboratoire des Écoulements Géophysiques et Industriels [Grenoble]

A numerical and analytical study of the steady laminar flow driven by a rotating disk at the top of an enclosed cylinder, having an aspect ratio H/R equal to 1, filled with a liquid metal, and submitted to an axial magnetic field B, is presented. The governing equations in cylindrical coordinates are solved by a finite volume method. In the absence of a magnetic field, the numerical method is validated via a comparison with experimental data; the latter was found to be in good agreement with the predictions. In the presence of a magnetic field, the analytical velocity profiles under the rotating disk and on the bottom wall obtained for a high value of the magnetic interaction parameter N are in excellent agreement with those obtained by numerical simulations. The effect of the top, bottom and vertical walls' conductivity on the flow is studied and found to be an important parameter in the control of the flow.

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Rachid Bessaïh, Mahfoud Kadja, Kerstin Eckert, Philippe Marty. Numerical and analytical study of rotating flow in an enclosed cylinder under an axial magnetic field. Acta Mechanica, 2003, 164, pp.175-188. ⟨10.1007/s00707-003-0021-x⟩. ⟨hal-00265324⟩